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Do high/low pass lenses exist? For an experiment I will hopefully be soon conducting at Johns Hopkins I need two different lenses.
The first needs to allow all wavelengths above 500 nm to pass (thus a high pass filter) and cut off everything else.
The second needs to allow all wavelengths below 370 nm to pass (thus a low pass filter) and cut off everything else.
My knowledge of optics is middling. I know that good old glass cuts of UV light, but I was hoping for something more specific. Does anyone know of the theory necessary to "tune" materials to make such filters?
Truth be told, I'm an experimentalist, so simply giving me a retail source that has such lenses would get me to where I need to go! But learning the theory would be nice as well.
Thanks,
Sam
| What you're looking for isn't a lens so much as a filter. There are filters for whatever purpose you might want out there in the world, and they are relatively inexpensive. Doing a google search on Optics Filters, I came across a couple of sites that might help you.
*
*Edmond's Optics
*Optical Filters USA
| {
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Would you be weightless at the center of the Earth? If you could travel to the center of the Earth (or any planet), would you be weightless there?
| The simplest way to think about it is that there is mass all around you in the center of the Earth so you get an equal gravitational "pull" from all directions. The pulls cancel out so you get no acceleration.
If one assumes constant density for the Earth (which isn't strictly speaking true but it is close enough for this illustration) the gravitational acceleration drops linearly from 1g at the surface to 0 at the center of the Earth. So you'd get a zero if you stepped on a scale at the center of the Earth.
The more complicated explanation is that acceleration due to gravity is the derivative of the gravitational potential. This potential is a minimum at the center of the Earth and grows quadratically up to the surface. It then continues to increase at a lower rate. Since at the exact center is flat (like the bottom of a valley), the derivative which is a measure of the rate of change is zero, and there is no acceleration.
Interestingly, even though you would be weightless there, the effects of gravity are highest at the center of the Earth. You get more gravitational time dilation, for example, than you do at the surface.
| {
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Is there a limit to loudness? Is there any reason to believe that any measure of loudness (e.g. sound pressure) might have an upper boundary, similar to upper limit (c) of the speed of mass?
| Let's talk about the sound waves in the air first. Physically they are longitudinal waves of pressure. The bunch of air in one place will get compressed (in comparison with equilibrium state) and after that will expand, compressing the adjacent air and so on the wave propagates. These (single frequency) waves are essentially described by three numbers: the speed of propagation (called speed of sound; it depends on the type of the material and the temperature), the frequency of oscillation (determining the pitch), and the amplitude of oscillation.
It is the amplitude of oscillations which determines the loudness. So you are essentially asking whether there is any limit on amplitude of compression. Well, of course. At high enough pressures, the air would freeze even at normal temperatures. So this is the limit for air. Similar thing would happen with liquids: at certain pressures they would condense into solids. You could continue with phases of matter in this way and applying higher and higher pressures you would eventually end up with a black hole. That would be an ultimate limit.
But of course, in reality the limit is set by our engineering capabilities and I doubt it's possible to create sound waves that would be able to freeze air.
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The final death of a black hole What are the different death scenarios for a black hole? I know they can evaporate through Hawking radiation - but is there any other way? What if you just kept shoveling more and more mass and energy into the black hole?
| If you shovel lots of mass and energy into a black hole, you will most likely get a bigger black hole. It will not get indigestion, and it will not explode due to being full. You may get accretion and jets if your shoveling is suitably generic.
Any list of possible "final death" scenarios will depend on your threshold for improbable events, and possibly which theory of quantum gravity you choose to accept. Hawking radiation appears to be a fairly random process, and there is a very small but nontrivial probability for a black hole to destroy itself with a spontaneous eruption of big chunks of matter and energy. The far more likely scenario seems to be that the temperature (and hence the flux from the radiation) increases steadily as the mass of the black hole decreases, until there is a very small hot black hole whose behavior can't be described well with semi-classical methods.
(This paragraph is very speculative, and may not reflect expert opinion.) It seems possible to me that a collapsing body can form an apparent horizon (with respect to distant observers), and not collapse to form a singularity. The final death may just be that it emits Hawking radiation until the radius crosses some threshold and the horizon disappears to reveal a dense macroscopic object made of matter.
| {
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Why GPS is at LEO? Why GPS/GLONASS/Galileo satellites are on low earth orbit?
Why geostationary orbit is so bad? Sattelites might be placed there 'statically' and more precise...
The only problem I can see is navigation close to poles, but they have this problem anyway.
| This question always interested me.
I found this recently -
"Another issue we wrestled with is which satellite orbits to use. We did not want to be in geostationary or geosynchronous orbits. The reason was these alternatives would force us to deploy ground stations on the other side of the globe, whereas, by putting them in some orbit that periodically passed across the United States, you could update the knowledge of where they were and what time it was on the satellite, then store that information in the satellite and continue to broadcast as it went around the Earth. That is the fundamental way we ended up with twelve-hour orbits. We also wanted to be reasonably high because we didn’t want the orbits significantly disturbed by the atmospheric drag. At the same time, by going high you had more visibility, more coverage on the Earth. So with an Earth coverage antenna and suitable power densities on the Earth, you ended up with the ability of twenty-four satellites to provide very solid, total Earth coverage."
Brad Parkinson
See:
http://www.ieeeghn.org/wiki/index.php/Oral-History:Brad_Parkinson#Parkinson.27s_educational_background_and_the_origins_of_GPS.5D
| {
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Accuracy of the Boltzmann equation I have had this question for some time now. Hopefully someone can answer it.
I know that the Boltzmann equation is widely regarded as a cornerstone of statistical mechanics and many applications have been explored with a linearized version.
I also know that it's extremely hard to obtain exact solutions, which has started a considerable amount of investigation looking for an equally good (or acceptable) formalism to analyse systems that otherwise would be impossible or would take a great deal of computational resources to obtain a solution using the Boltzmann equation.
In spite of this, I never heard a precise description about the degree of accuracy (in comparison with experiments) that can be drawn from the Boltzmann equation. Obviously, I expect that accuracy depends on the system at hand, however, it would be great to hear about some specific examples.
Recommended readings would also be appreciated.
Thanks in advance.
| @Robert Smith
Well you're asking a question about the accuracy of an equation. The equation is created under certain assumptions about small objects sometimes called "particles" or "atoms". So if the equation accurately describes the system in question, then the behavior of the sytem should be described by solutions to the governing equations. So questions as to accuracy of the equations, is really revealed by whether the systems behavior follows the solutions to the equations.
Since the boltzmann's distribution is a solution to boltzmann's transport equation under certain conditions, it is the question of whether the system deviates from a boltzmann distribution under situations where it should hold that would indicate a situation where the boltzmann equation may no longer be valid.
So if you are still confused as how my answer relates to the question, it might be that you are not asking the right questions.
http://arxiv.org/PS_cache/astro-ph/pdf/9807/9807078v1.pdf
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Derivation of Maxwell's equations from field tensor lagrangian I've started reading Peskin and Schroeder on my own time, and I'm a bit confused about how to obtain Maxwell's equations from the (source-free) lagrangian density $L = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu}$ (where $F^{\mu\nu} = \partial^\mu A^\nu - \partial^\nu A^\mu$ is the field tensor).
Substituting in for the definition of the field tensor yields $L = -\frac{1}{2}[(\partial_\mu A_\nu)(\partial^\mu A^\nu) - (\partial_\mu A_\nu)(\partial^\nu A^\mu)]$. I know I should be using $A^\mu$ as the dynamical variable in the Euler-Lagrange equations, which become $\frac{\partial L}{\partial A_\mu} - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)} = - \partial_\mu\frac{\partial L}{\partial(\partial_\mu A_\nu)}$, but I'm confused about how to proceed from here.
I know I should end up with $\partial_\mu F^{\mu\nu} = 0$, but I don't quite see why. Since $\mu$ and $\nu$ are dummy indices, I should be able to change them: how do the indices in the lagrangian relate to the indices in the derivatives in the Euler-Lagrange equations?
| Well, you are almost there. Use the fact that
$$ {\partial (\partial_{\mu} A_{\nu}) \over \partial(\partial_{\rho} A_{\sigma})} = \delta_{\mu}^{\rho} \delta_{\nu}^{\sigma}$$
which is valid because $\partial_{\mu} A_{\nu}$ are $d^2$ independent components.
| {
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movement of photons In a typical photon experiment the photon is depicted as moving across the page, say from right to left.
Suppose we were actually able to witness such an experiment, from the side (to position of reader to a page).
If the photon is actually moving from left to right can I, standing at 90 degrees to the motion, see the photon?
| Dear Peter, the pictures are drawn to indicate that the photons are there. They are there even if you don't see them. There are many things that we can't see - or we can't see directly or at a given moment - but they still exist. And of course, you don't see the photons (with a wrong direction) by normal methods - you would have to collide them against something else that you could observe but that would change the propagation of the photons on the page.
However, if you want to be fancy, the answer is that you can actually see photons by other photons. Because of quantum effects (with a virtual box-like loop of an electron, and four attached photons), the electromagnetic waves are slightly non-linear. So light can collide with other light so you could actually "shine" a very powerful beam of light to see another beam.
You can't do it in your kitchen but this phenomenon has actually been tested experimentally at SLAC, California. It works: see this thread:
Scattering of light by light: experimental status
| {
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When one thinks of a field of operators in QFT, is it reasonable to think of a matrix being associated with each point in space time? Is it correct to visualize operators existing as matrices parameterized by spacetime coordinates in the context of QFT?
| Given that a quantum field is a field of operators and given that you can think of operators as (possibly infinite) matrices acting on a Hilbert (or, better, Fock) space, your assumption is correct. However, I wouldn't call it "visualizing" as I find operators more tangible than Matrices.
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Why is quantum entanglement considered to be an active link between particles? From everything I've read about quantum mechanics and quantum entanglement phenomena, it's not obvious to me why quantum entanglement is considered to be an active link. That is, it's stated every time that measurement of one particle affects the other.
In my head, there is a less magic explanation: the entangling measurement affects both particles in a way which makes their states identical, though unknown. In this case measuring one particle will reveal information about state of the other, but without a magical instant modification of remote entangled particle.
Obviously, I'm not the only one who had this idea. What are the problems associated with this view, and why is the magic view preferred?
| I think that the best picture to understand this correlation is given by many-worlds interpretation:
A singlet decomposes in a coupled pair of particles superposition $|+⟩_A|-⟩_B + |-⟩_A|+⟩_B$, so observer A sees a simple superposition of $|+⟩ + |-⟩$ (which is a partial trace of the global density matrix) and so does B.
In the many worlds interpretation, observer A will be split in a $+$ and a $-$ observer (and so will observer B). Now, where will the correlation effect manifest itself?
The 'coupling' effect is brought when observer A and observer B join together at subluminal speeds to compare notes of their measurements: (remember that according to many-worlds, we have two observers A and two observers B) .
Observer A+ is disallowed by angular momentum conservation to interact with observer B+, (otherwise they will both agree that angular momentum was not conserved). Likewise, observer A- is disallowed to interact with observer B- by the same reason.
So the remaining interactions between observers are:
*
*A+ interacts with B-
*A- interacts with B+
so the final state is a superposition of $|+⟩_A|-⟩_B$ and $|-⟩_A|+⟩_B$, which is interpreted as a 'correlation between remote observations'.
| {
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Vortex in liquid collects particles in center At xmas, I had a cup of tea with some debris at the bottom from the leaves. With less than an inch of tea left, I'd shake the cup to get a little vortex going, then stop shaking and watch it spin. At first, the particles were dispersed fairly evenly throughout the liquid, but as time went on (and the vortex slowed, although I don't know if it's relevant) the particles would collect in the middle, until, by the time the liquid appeared to almost no longer be turning, all the little bits were collected in this nice neat pile in the center.
What's the physical explanation of the accumulation of particles in the middle?
My guess is that it's something to do with a larger radius costing the particles more work through friction...
| My simple non-mathematical theory to explain this counter-intuitive behaviour is based on hydrostatic pressure.
The rotating liquid develops a vortex shaped surface that makes the centre of rotation the shallowest and the periphery the deepest region. The hydrostatic pressure at the periphery is therefore higher than at the centre, so there is a pressure gradient. A particle suspended in the rotating liquid, or resting on the bottom, has a greater force on the side facing the periphery than the force on the side facing the centre. This causes the particle to move towards the centre of rotation. The force on a particle at the centre is uniform in all directions, so it remains stationary.
If this theory is true we should expect that particles floating at the surface would not display this behaviour, because there would be no such hydrostatic pressure gradient as the liquid surface is uniformly at atmospheric pressure.
Also, preventing the rotating liquid surface to adopt a vortex shape (e.g. by enclosing the liquid surface by a transparent sheet?) should suppress this behaviour.
As yet I have not tested my theory in these ways!
| {
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Is there a maximum possible acceleration? I'm thinking equivalence principle, possibilities of unbounded space-time curvature, quantum gravity.
| For QED there is a critical acceleration, which is the acceleration felt by an electron subject to the Schwinger field (http://en.wikipedia.org/wiki/Schwinger_limit).
This is at the critical acceleration
$$
a_S = \frac{m_ec^3}{\hbar} = 2.33 \cdot 10^{29} \frac{m}{s^2}
$$
Beyond this field, nonlinear effects if the QED vacuum and pair creation occur which will influence the dynamics of an electron accelerated by this field.
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What would happen if you put your hand in front of the 7 TeV beam at LHC? Some speculation here:
http://www.youtube.com/watch?v=_NMqPT6oKJ8
Is there a possibility it would pass 'undetected' through your hand, or is it certain death?
Can you conclude it to be vital, or only loose your hand?
Would it simply make a small cylindrical hole through your hand, or is there some sort of explosion-effect?
Assume your hand has a cross section of 50cm², and a thickness of 2cm, how much of the beam's energy would be transferred to your hand?
| Back in the 1970s there were some researchers who put seeds in a beam path to see what would happen. The plants which grew from the seeds were deformed. One would have to look this up to get the details.
If you put your hand in the LHC beam one question is what would hurt the most; the damage due to high energy particle slamming into nuclei in your hand, or the high velocity shoe mark you would get on your butt. A reasonable amount of the beam energy would be deposited in your hand, where primary damage would be from nuclei blasted to bits from the protons and secondary radiation from that. You would have radiation damage. However, I suspect it would be comparable to getting a radiation does from a synchrotron source. Most damaged cells would die, those which are mildly damaged might have genome changes which could lead to transformed cells, maybe even runaway cell growth. Runaway cell growth in somatic cell lines is what we call cancer.
| {
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Free electrons and energy states Ok, background - studying for the physics part of my radiology exams, and came across a question that went something like this
An electron fired through a tungsten target loses energy by:
a) Bremsstrauhlung
b) collisions with bound target electrons
c) giving off characteristic radiation
d) all of the above
Now, by the process of elimination d must be right, because both a and b are
My question regards c - characteristic radiation
My understanding of this process is the excitation of the electron to a higher energy state, usually a more peripheral valence shell, which then releases that extra energy when it drops back (or another drops in to fill the hole)
So, what I don't get is how a free electron (like one fired from the filament to the target) has energy states. By definition, it is unbound, and therefore there are no binding energies to create quantised energy states.
Is there a property I am overlooking, is the question wrong, or is it a fudge?
I apologise if this has been asked. I looked at the suggested answers, and did a google search of stack exchange, but my phone can't use the search bar here directly, so I could have missed something
| The (c) option is badly worded, in my opinion. The characteristic radiation is emitted by the atom and this indirectly contributes to the original electron (say, A) losing energy.
This is how it happens, roughly: An electron A fired into the target can ionize one of the atoms which ejects an electron B. In doing so, the electron A loses energy. But the effect is seen when the ionized atom emits characteristic radiation when one of the higher shell electrons falls into the shell from which the atom ejected electron B.
So there's no question of free particles in bound states. Free particles by definition are not in bound states.
| {
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Why does a ballerina speed up when she pulls in her arms? My friend thinks it's because she has less air resistance but I'm not sure.
| Joe's answer is of course right and I gave it +1. However, let me say some slightly complementary things.
Whenever the laws of physics don't depend on the orientation in space, a number known as the angular momentum is conserved. For a rotating body - including the body of a lady - the angular momentum $J$ may be written as the product of the moment of inertia $I$ and the angular frequency $\omega$ (the number of revolutions per second, multiplied by $2\pi=6.28$):
$$ J = I \omega $$
The moment of inertia $I$ is approximately equal to
$$ I = MR^2 $$
where $M$ is the mass and $R$ is equal to the weighted average distance of the atoms (weighted by the mass) from the axis. (More precisely, I need to compute the average $R^2$.)
It's up to you whether she is spinning clockwise or counter-clockwise.
So if the ballerina pulls in her arms, she becomes closer to the axis, and $R$ decreases. Her mass $M$ doesn't change but the moment of inertia $I$ decreases, too. Because $J=I\omega$ has to be conserved and $I$ decreased, $\omega$ inevitably increases.
You may also explain the increased angular frequency of the rotation in terms of forces and torques. If the arms move closer to the axis, they exert a torque on the ballerina that speeds her up. I would need some cross products here but I am afraid that wouldn't be fully appreciated.
These issues were also discussed here:
Why do galaxies and water going down a plug hole spin?
Why do galaxies and bathtub whirlpools spin?
Cheers
LM
| {
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Two slit experiment: Where does the energy go? In Physics class we were doing the two slit experiment with a helium-neon red laser. We used this to work out the wavelength of the laser light to a high degree of accuracy. On the piece of paper the light shined on there were patterns of interference, both constructive and destructive. My question is, when the part of the paper appeared dark, where did the energy in the light go?
| It goes where the photons go. Best explanation I've seen is in Feynman "QED: the strange theory of light and matter". One does not have to unlearn anything. It is even more interesting after reading his more technical works.
| {
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Why are snowflakes symmetrical? The title says it all. Why are snowflakes symmetrical in shape and not a mush of ice?
Is it a property of water freezing or what? Does anyone care to explain it to me? I'm intrigued by this and couldn't find an explanation.
| Not all snowflakes are symmetrical. One can disrupt the symmetry quite easily by introducing impurities or some mechanical artifact. In nature, snowflakes have plenty of time to form and it is more natural for them to form symmetric shapes because of the molecular structure of water.
That is, when there is more time for the molecules to move about and position themselves they will do so in a way that is in accordance with some crystalline structure that the molecule can exhibit.(you can use other things besides water to get "crystals")
The nature of the shape depends on many many factors but to see that such diversity can come from something simple you just have to look at IFS's. Basically you take some very simple rules and generate a huge number of variations by making small changes in the rules.
http://en.wikipedia.org/wiki/Iterated_function_system
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Stopping Distance (frictionless) Assuming I have a body travelling in space at a rate of $1000~\text{m/s}$. Let's also assume my maximum deceleration speed is $10~\text{m/s}^2$. How can I calculate the minimum stopping distance of the body?
All the formulas I can find seem to require either time or distance, but not one or the other.
| If the speed is $1000 m/s$ and the deceleration is $10 m/s^2$, it will take $100 s$ to stop. The average speed in that time is $500 m/s$, so the distance traveled is
$$500m/s*100s = 5*10^4m$$
Working through the same logic with an initial speed $v$ and a deceleration $a$, the final distance $d$ traveled before stopping is
$$d = v_{avg}*t = (v/2)*(v/a) = \frac{v^2}{2a}$$
This formula becomes more interesting when you learn a bit more physics because it's simple example of the work-energy theorem.
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Is causality a formalised concept in physics? I have never seen a “causality operator” in physics. When people invoke the informal concept of causality aren’t they really talking about consistency (perhaps in a temporal context)?
For example, if you allow material object velocities > c in SR you will be able to prove that at a definite space-time location the physical state of an object is undefined (for example, a light might be shown to be both on and off). This merely shows that SR is formally inconsistent if the v <= c boundary condition is violated, doesn’t it; despite there being a narrative saying FTL travel violates causality?
Note: this is a spinoff from the question: The transactional interpretation of quantum mechanics.
| In the axiomatic approach to quantum field theory, sometimes also called local or algebraic quantum field theory, pioneered by Araki, Haag, Kastler, Bogoljiobov et. alt., causality is formalized as an axiom, most often called the "locality" axiom.
The idea is this: To every bounded open subset of Minkowski spacetime we associate an operator algebra, all selfadjoint elements of this algebra represent all observables of this region, that is everything that is measurable in this region. Then algebras associated to two spacelike separated regions are assumed to commute, this is the locality or causality axiom.
When two observables aka selfadjoint operators commute, this means of course that measuring aka observing the first will have no effect on measuring aka observing the second and vice versa, therefore there cannot be any causal relationship of the events of measuring them.
BTW: The Reeh-Schlieder theorem seems - intuitively - to violate causality/locality, so it is interesting to note that it is possible to prove this theorem without invoking the locality axiom. The reason for this is that the Reeh-Schlieder theorem is about entanglement effects which don't violate locality in the sense of SR.
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Will tensile strength keep a cable from snapping indefinitely? Trying to secure a wall hanging using magnets; me and a coworker came up with an interesting question:
When the hanging is hung using 1 magnet, the weight of it causes it to quickly drag the magnet down and the hanging drops. Using n magnets retards this process; causing it to fall more slowly, but does there exist a number of magnets m such that their combined strength will prevent the hanging from slipping, entirely and permanently?
Because this doesn't make for a very good question; we worked at it and arrived at a similar one; but slightly more idealized:
A weight is suspended, perfectly still, from a wire in a frictionless vacuum. If the mass of the weight is too great; it will gradually distend the cable, causing it to snap and release the weight; but will a light enough weight hang there indefinitely, or will the mass of the weight (and indeed the cable) cause the cable to snap sooner or later?
| Metals normally have crystalline, ordered structure. An atom moving from one appropriate site of the crystal lattice to the next one has to overcome a high energy barrier. If the tension is too small to distort the crystal structure, atoms will stay in their places and your weight will hang forever*.
* By forever I mean long time for any practical purpose, like thousands of years. Sometimes atoms do randomly jump inside the crystal. By putting a tension we slightly favor one direction for these jumps so eventually the cable will stretch but it will rust much faster.
| {
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Can Loop Quantum Gravity connect in any way with string theory? The one difficulty I see with LQG is that it requires an enormous number of degrees of freedom, e.g. these spin variables in the net. This is in contrast to stringy holographic theory where the fields in a space are equivalent to fields on a boundary or a horizon of one dimension lower. In this setting entropy of a black hole is the entanglement entropy of states interior and exterior to the black hole. This reduces the amount of data, and thus entropy, required.
Are there suggestions, conjectures or maybe serious theory which attempts to describe the spin variables of LQG according to such entanglements in string-brane theory?
| I'm not sure anyone has tried (except possibly Smolin in some of his older papers). But it wouldn't be that hard: take a simple loop-quantum-gravity spin-foam-analog model in 25+1 dimensions (which is going to be rather more complex than the usual 3+1 dimensional spin foam), pick a ground-state-like solution for it that looks something like an extended space-time (preferable one that is flat and large along at least some dimensions, so mostly made up of large graphs that embed well in 25+1-dimensional space), try using that instead of flat 25+1 dimensional space as the background space-time in which a bosonic string world-sheet is embedded, and see what happens. For a start, see if the string still considers 26 to be the critical dimension.
In theory, you should see phenomena suggesting that the string world-sheet is in some sense a quantum of diffeomorphism, and that from the spin-foam viewpoint it can be "gauged away" by moving to a slightly different spin foam solution. At a wild guess, since the string worldsheet propagates along the 2-d spacetime elements in the 25+1-dimensional spin foam, it should have the same the effect as changing the spins on these elements by one unit.
| {
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Renormalization and Infinites Measuring a qubit and ending up with a bit feels a little like tossing out infinities in renormalization. Does neglecting the part of the wave function with a vanishing Hilbert space norm amount to renormalizing of Hilbert space?
| No, those are two very different processes (as far as I understand).
*
*Renormalization: When you are calculating vacuum expectation values, for instance $\langle \Omega\mid T(\phi(\mathbf{p})\phi(0))\mid \Omega\rangle$, you discover that these values are infinite. However, you can interpret this infinity, in a consistent manner, as the value of this correlation function at other momentum $\mathbf{p}^{\prime}$ and a finite part that relates the correlation function at the two different momenta. Nothing is really lost in the renormalization procedure, it is just a matter of how to introduce a measured quantity (the correlation function at this other momentum) into the theory.
*Measurement: The measurement concerns a certain state $\mid \psi\rangle$ coupled to the a measurement device. Originally, before being coupled, the pure state has entropy equal to zero. Later, by the time evolution of the coupled system, the system being measured has, after tracing over the measurement device states, entropy larger than zero. The difference is the information lost by the system in the process. So, something is lost in the measurement process, contrary to renormalization.
| {
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Why are there only derivatives to the first order in the Lagrangian? Why is the Lagrangian a function of the position and velocity (possibly also of time) and why are dependences on higher order derivatives (acceleration, jerk,...) excluded?
Is there a good reason for this or is it simply "because it works".
| There are implications for causality when a equation of motion contains higher than second derivatives of the fields, EM radiation from charged bodies goes over the derivative of the acceleration
i don't know the details of WHY but this book should give more details:
(Causality and Dispersion Relations)
http://books.google.com/books?id=QDzHqxE4anEC&lpg=PP1&dq=causality%20dispersion%20relations&pg=PP1#v=onepage&q&f=false
| {
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Why beauty is a good guide in physics? Dirac once said that he was mainly guided by mathematical beauty more than anything else in his discovery of the famous Dirac equation. Most of the deepest equations of physics are also the most beautiful ones e.g. Maxwell's equations of classical electrodynamics, Einstein's equations of general relativity. Beauty is always considered as an important guide in physics. My question is, can/should anyone trust mathematical aesthetics so much that even without experimental verification, one can be fairly confident of its validity? (Like Einstein once believed to have said - when asked what could have been his reaction if experiments showed GR was wrong - Then I would have felt sorry for the dear Lord)
| BEAUTY =SYMMMETRY you only have to look the 'patterns' in nature (nautilus shell, flowers) etc.. also SYMMETRY means SIMPLICITY since you can generate beautiful figures from simple patterns
| {
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How to avoid getting shocked by static electricity? sometimes I get "charged" and the next thing I touch something that conducts electricity such as a person, a car, a motal door, etc I get shocked by static electricity.
I'm trying to avoid this so if I suspect being "charged" I try to touch something that does not conduct electricity (such as a wooden table) as soon as possible, in the belief that this will "uncharge me".
*
*Is it true that touching wood will uncharge you?
*How and when do I get charged? I noticed that it happens only in parts of the years, and after I get out of the car...
| This happens to me all the time; I collect an electrostatic charge just sitting at the computer; earlier Sir Dumpty often was the medium for discharge - an audible zzzt as my accumulated charge discharged through his snout when he came to snuffle against my arm/hand/palm.
A simple solution would probably be to touch the floor/earth; do not touch metal if you can avoid it.
| {
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Why is the relationship between atomic number and density not linear? What are the factors that affect the density of an atom?
| Examine the densities of di-atomic gaseous elements ($\text{H}_2$, $\text{N}_2$, $\text{O}_2$) at STP. Compare to their respective atomic weights. Also look at the densities of the noble gasses at STP. Again, note how they scale roughly with the atomic weight.
By choosing materials that are more or less ideal gases I've isolated the system from the effects of almost all the messy chemistry that cause other states of matter to not scale (the exception is the question of how many atoms go into each molecule which is why I separated my examples into two groups).
For the condensed states of mater (liquid and solids) the chemistry involves itself more strongly in terms of inter-molecular forces. This is most evident in crystalline solids as the geometry of the crystal sets the number density of atoms in terms of both the length of inter-atomic bonds and the symmetries of the crystalline structure.
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Determining Maximum Velocity of an object traveling horizontally I'm in the process of working on a physics related game. I'm looking to find the maximum velocity of an object given it's mass and the force acting on it when it is traveling horizontally. I believe there must be a method of calculating this but I'm unaware of it. Is there a formula for this scenario? I'm unaware if this is the same calculation as terminal velocity but I don't believe it is. Thanks for any help!
| Assume the object is moving on a frictionless surface in the absence of a gravitational field with a certain velocity or it is at rest. Calculate the kinetic energy of this object as a result of its uniform motion or rest. The formula for kinetic energy is:$K.E \ =\ \Large \frac{1}{2} \large mv^2$
Applying a force for a certain distance on thsi object imparts energy to the body, which immediately manifests as a change in velocity and a resultant change in its total kinetic energy.
Then the energy imparted to the object will be:$E\ =\ \large F\times d$Here 'F' is the force applied, and 'd' is the displacement over which the force has been applied. After the effect of the force wears out, a uniform velocity is attained by the object which can be calculated by combining the above two equations:
$\Large v\ = \ \sqrt{\frac {2(K.E\ +\ E)}{m}}$
I must tell you that I am 15 years old and this is simply an idea I've provided for your perusal. This idea is given in the context of classical mechanics.
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How to explain the weak force to a layman? I'm trying to explain in simple terms what the weak interaction does, but I'm having trouble since it doesn't resemble other forces he's familiar with and I haven't been able to come up (or find on the web) with a good, simple visualization for it.
| I like the history oriented approach, when explaining something to a layman. In this case you could start by briefly explaining the fundamental forces and how we needed a new force to model beta decay.
| {
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What would happen if $F=m\dot{a}$? What would happen if instead of $F=m \frac{d^2x}{dt^2}$, we had $F=m \frac{d^3x}{dt^3}$ or higher?
Intuitively, I have always seen a justification for $\sim 1/r^2$ forces as the "forces being divided equally over the area of a sphere of radius $r$".
But why $n=2$ in $F=m\frac{d^nx}{dt^n}$ ?
| In statics, you can still have a force without acceleration so $F$ is independent of $a$. $F$ is the cause of the change in the position of an object initially at rest in some frame. To give it physical meaning, you have to define how it's to be measured and one way would be to define 1 unit of F causing one unit of compression in some standard spring.
Now if $F$ causes a body at rest to change its position, then over a time dt the postion has changed by dx. Your job as a physicist is to construct an equation relating F to the change in velocity of the body.
So with all this in mind, what would happen if $F=m*d^3x/dt^3$ ?
It would mean that even though $F$ is the cause behind the change in velocity of a body, there are some changes in the velocity possible where $F = 0$ such as for $a = const$. You would end up with particles accelerating in arbitary directions for $F = 0$.
| {
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Electromagnetic fields vs electromagnetic radiation As I understand, light is what is more generally called "electromagnetic radiation", right?
The energy radiated by a star, by an antenna, by a light bulb, by your cell phone, etc.. are all the same kind of energy: electromagnetic energy, i.e. photons traveling through space.
So far, so good? (if not please clarify)
On the other hand, there are these things called "electromagnetic fields", for example earth's magnetic field, or the magnetic field around magnets, the electric field around a charge or those fields that coils and capacitors produce.
Now here is my question:
*
*Are these two things (electromagnetic fields and electromagnetic radiation) two forms of the same thing? or they are two completely different phenomena?
*If they are different things, What does light (radiation) have to do with electromagtetism?
I'm not asking for a complex theoretical answer, just an intuitive explanation.
| Electromagnetic radiations are electromagnetic waves in the electromagnetic field. It is disturbance of the electromagnetic field propagated with the velocity of light. Electromagnetic field itself is a seat of energy. $u = 1/2 (\epsilon_0E^2 + B^2/\mu_0)$
Where $u$ is the energy density of the em field. Other symbols carry their usual meanings.
During propagation of electromagnetic waves, energy is carried from one place to another in accordance with Poynting's theorem.
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What is the usefulness of the Wigner-Eckart theorem? I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why it is useful and perhaps just help me understand a bit more about it. I have had two years of undergrad mechanics and I think I have a reasonably firm grasp of the earlier material out of Sakurai, so don't be afraid to get a little technical.
| And if you are interested in "where" it might come useful: Some of the selection rules for optical transitions can be obtained from it, and I faintly recall that it helps rewriting the Hamiltonian for Spin-Orbit coupling into a much more convenient form.
| {
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Black holes in a head-on collision Assume two uncharged non-rotating black holes traveling straight at each other with no outside forces acting on the system. What is thought to happen to the kinetic energy of these two masses when they collide? Is the excess energy lost through gravitational radiation? What would the effect of these gravity waves be on matter or energy that they encounter?
| When two black hole collide the horizon area of the resulting black hole must exceed the sum of the areas of the two initial black holes. This places an upper limit on the amount of gravitational radiation which is produced. If the two initial black holes have equal masses $M$ then the finial black hole must obey
$$
4\pi(2M_f)^2~=~16\pi(M_f)^2\ge~4\pi (2M) ^2~+~4\pi (2M)^2~=~32\pi M^2
$$
and so $M_f~\ge~\sqrt{2}M$. The amount of gravitational radiation emitted is then $E~\le~(2~-~\sqrt{2})M$ which is $.585M$
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Bose-Einstein condensate in 1D I've read that for a Bose-Einstein gas in 1D there's no condensation. Why this happenes? How can I prove that?
| The claim is often that there is no condensation in $d<3$. The other answers are correct, but let's be clear, there are actually two assumptions present in the claim:
*
*Assume you have $N$ noninteracting bosons in $d$-dimensions in a hypervolume $L^d$
*Assume that these bosons have an energy-momentum relationship of $E(p) = Ap^s$.
Now, the way we calculate the critical temperature ($1/\beta_c$) for BEC requires satisfying the equation
$$\int_0^\infty \frac{\rho(E)dE}{e^{\beta_c E}-1}=N$$
where $\rho(E)$ is the density of states. Whether this integral is convergent or not depends on the values of both $s$ and $d$. The details of the proof are up to you though. :)
| {
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Mathematical background for Quantum Mechanics What are some good sources to learn the mathematical background of Quantum Mechanics?
I am talking functional analysis, operator theory etc etc...
| A good place to look for book recommendations for mathematical physicists is this page of John Baez:
*
*books, how to learn math and physics
I have to agree with the others that the best way to learn the mathematical background of QM is to learn QM, you'll see yourself what kind of mathematical tools you'll have to study further.
Anyway, here are a few tips: If you decide to attend a math course on functional analysis, see that it is about linear operators on Hilbert space leading to the spectral theorem. That's the part of functional analysis you'll need first in QM. "Functional Analysis" is a broad topic, and many math faculties start with more abstract stuff you'll need only later (like Banach algebras or topological vector spaces).
Here is an example of a book that is taylored for the special needs of physicists learning QM:
*
*Nino Boccara: "Functional Analysis. And Introduction for Phycisists".
It is short, it explains everything in detail and covers the essential topics for QM:
*
*Measure and Integration
*Lebesgue Spaces
*Hilbert Spaces
*Distributions, Fourier and Laplace Transforms
*Linear Operators, Bounded and Unbounded, Spectral Theory
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Noether's theorem vs. Heisenberg uncertainty principle In continuation of another question about Noether's theorem I wonder whether there exists some kind of relationship between this theorem and the Heisenberg uncertainty principle.
Because both the principle and the theorem relate energy with time, momentum with space, direction with angular momentum. When this is a general fact then e.g. electrical charge and electrostatic potential(*) should be partners in an uncertainty relationship too. Are they?
I feel that these results look so basic and general that I hope that a pure physical reasoning (without math or only with a minimal amout of math) exists.
Also compare this question where again momentum and space are connected, this time through a Fourier transform.
(*) i.e. electric potential and magnetic vector potential combined.
| Noether theorem is as valid in CM(*) as in QM(**). It deals with conservation laws and symmetries. In CM the variables are certain, in QM they may be uncertain.
HUP belongs to QM and gives a limitation on canonically conjugated variable uncertainties in a given state.
If some variable in QM is uncertain, it does not mean its expectation value is not conserved. A superposition of free motions states $e^{ipr}$ is also a free motion state although the momentum, for example, may be uncertain. The dynamics of the momentum expectation value is determined with an external force, like in CM (see the Ehrenfest's equations). No external force, no variation of the expectation value <p(t)>.
So I do not see any relationship between HUP and Noether.
(*) Classical mechanics
(**) Quantum mechanics
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Gravitational and gauge-gravitational anomalies in ${\cal N}=1$ $D=4$ supergravity coupled to a SUSY gauge theory with chiral matter When people talk about the first superstring revolution they often mention the miraculous cancellation of anomalies via the Green-Schwarz mechanism. My question is whether such a string-theoretic mechanism is also at work when the 4D gravitational and gauge-gravitational anomalies are tackled? In this context, would it be fair to say that a possible discovery of superpartners at the LHC, which automatically implies some version of ${\cal N}=1$ $D=4$ supergravity, imply that stringy couplings (higher order in $\alpha'$) must be present in the corresponding Lagrangian to cancel the anomalies? What type of coupling are those?
| There are no purely gravitational anomalies in $D=4$. The one source of gauge-gravitational anomalies is a triangle diagram with one gauge vertex and two graviton vertices. This vanishes provided that ${\rm Tr}_L Q=0$ where the trace runs over all left-handed fermions and $Q$ is the gauge generator with the potential anomaly. In the SM the only potential nonzero contribution arises from taking $Q=Y$, where $Y$ is the generator of the
$U(1)$ part of $SU(3) \times SU(2) \times U(1)$. In the SM with standard fermion assignments this trace vanishes. In string compactifications one often gets additional $U(1)$ symmetries, and sometimes one finds these are anomalous by the above criterion. In such situations one finds a version of the Green-Schwarz mechanism involving a coupling of an axion-like mode
to the gauge field which ends up giving a mass to the $U(1)$ gauge field. The axion-like field arises in string theory as a two-form field $B$, but in $D=4$ one can dualize to a scalar via $H=dB=*da$.
| {
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Did spacetime start with the Big bang? Did spacetime start with the Big Bang? I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang?
| I seriously doubt that.
There are quite a few theories trying to discuss "the beginning of the universe", and not all of them agree with having a "beginning" to the universe.
I don't have concrete facts to support what I'm about to say so consider it as "just another idea."
"Our whole universe was in a hot dense place, then fourteen billion years ago expansion started."
So there was a big explosion, and everything tried to get away from every other thing. This process has been going on for about fourteen billion years, and it will eventually stop. Because a big portion of the attracting/repelling forces (electromagnetic force which can attract and repel) will have been neutralized (like a stone which does have electrons and protons but doesn't attract or repel), and the attracting forces (gravity) will take over. The universe starts to get smaller and denser, and collapse into a small hot dense place, and in "hot places", the repelling forces will eventually take over, and so another bang happens, and it will create a universe much like of our own.
| {
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Resistance between two points on a conducting surface Suppose we have a cylindrical resistor, with resistance given by $R=\rho\cdot l/(\pi r^2)$
Let $d$ be the distance between two points in the interior of the resistor and let $r\gg d\gg l$.
Ie. it is approximately a 2D-surface (a rather thin disk).
What is the resistance between these two points?
Let $r,l\gg d$, (ie a 3D volume), is the resistance $0$ ?
Clarification:
A voltage difference is applied between two points a distance $d$ apart, inside a material with resistivity $\rho$, and the current is measured, the proportionality constant $V/I$ is called $R$. The material is a cylinder of height $l$ and radius $r$, and the two points are situated close to the center, we can write $R$ as a function of $l$, $r$ and $d$, $R(l,r,d)$, for small $d$.
The questions are then:
What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow \infty} R(l,r,d) $$
What is $$ \lim_{r \rightarrow \infty} \lim_{l \rightarrow 0} R(l,r,d) $$
| "Resistance between two points" is not a well-defined concept. If c is a curve connnecting point A to point B, the electromotive force V along c is a well-defined thing (it's the circulation of the electric vector field along c), and resistance would be the factor R such that V = RI when I is the intensity flowing through a thin tube borne by c. But it's clear that intensity depends on the cross section of this virtual tube, a non-defined entity here. So we have no proper definition of "resistance R between A and B" that would allow us to compute it.
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Should you really lean into a punch? There's a conventional wisdom that the best way to minimize the force impact of a punch to the head is to lean into it, rather than away from it.
Is it true? If so, why?
EDIT: Hard to search for where I got this CW, but heres one, and another. The reason it seems counter-intuitive is that I'd think if you move in the direction that a force is going to collide into you with, the collision would theoretically be softer. You see that when you catch a baseball barehanded; it hurts much more when you move towards the ball, rather than away from the ball, as it hits your hand.
| My guess would be that the objective is to reduce the amount of energy dissipated into a localised area, rather than reducing the force of the strike itself.
Consider that if you lean into a strike, your muscles will flex and become more rigid. The shockwave from the impact will then travel through the rigid muscle instead of being dissipated. The energy will then be spread out over a larger area (and if your stance is good enough, maybe into the ground).
The get an idea of what I mean, compare a newton's cradle made out of steel and one made from flesh like substance. Also similar to boxers wrapping their hands and wrists.
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Cooling a cup of coffee with help of a spoon During breakfast with my colleagues, a question popped into my head:
What is the fastest method to cool a cup of coffee, if your only available instrument is a spoon?
A qualitative answer would be nice, but if we could find a mathematical model or even better make the experiment (we don't have the means here:-s) for this it would be great! :-D
So far, the options that we have considered are (any other creative methods are also welcome):
Stir the coffee with the spoon:
Pros:
*
*The whirlpool has a greater surface than the flat coffee, so it is better for heat exchange with the air.
*Due to the difference in speed between the liquid and the surrounding air, the Bernoulli effect should lower the pressure and that would cool it too to keep the atmospheric pressure constant.
Cons:
*
*Joule effect should heat the coffee.
Leave the spoon inside the cup:
As the metal is a good heat conductor (and we are not talking about a wooden spoon!), and there is some part inside the liquid and another outside, it should help with the heat transfer, right?
A side question about this is what is better, to put it like normal or reversed, with the handle inside the cup? (I think it is better reversed, as there is more surface in contact with the air, as in the CPU heat sinks).
Insert and remove the spoon repeatedly:
The reasoning for this is that the spoon cools off faster when it's outside.
(I personally think it doesn't pay off the difference between keeping it always inside, as as it gets cooler, the lesser the temperature gradient and the worse for the heat transfer).
| How about this:
Before putting the coffee into the cup, pour the hot coffee directly onto the spoon, allowing the excess to drizzle into the coffee cup. The goal here is to make the coffee flow downstream onto the spoon and then into the cup, with as much distance as possible.
The more distance there is between the spoon, cup, and source of coffee, the more it can cool down from the air.
You can feel this effect when taking a shower. If you adjust the heat of the water, and lift the showerhead closer and farther from your body, you can feel the temperature change the more it travels through the air.
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If Betelgeuse were to go supernova If Betelgeuse were to go supernova would the sky be twice as bright, or day time extended, depending on what time of year it happened in.
Basically when it does supernova how bright and large will it appear in the sky, and how do you work out the apparent brightness and size for something that hasn't happened yet?
| Most models of type II supernovae expect that the explosion has a peak luminosity of around $10^8$ to $10^9$ solar luminosities. This gives it a peak absolute magnitude of -15.16 to -17.16. At a distance of 200 parsecs, this is an apparent magnitude of -8.652 to -11.15.
Okay, so how bright is that? Well, the full moon has an apparent magnitude usually around -12.75. This means the total luminosity from the explosion of Betelgeuse would be something like $1/1000$ times the luminosity of the full moon. But the human eye sees things logarithmically, so we might expect that it looks like its about a third as bright as the full moon.
This matches up roughly to descriptions of SN 1006 which was a supernova 1,000 years ago. Observers at the time described a slowly growing ball in the sky about a quarter the brightness of the moon.
As for your second question, how we predict the brightness: We have our estimates about the brightness of the supernova mostly from computer simulations. Supernovas occur when large stars run out of fuel and their core collapses, causing all the mass to suddenly fall inward. A series of complicated nuclear reactions take place as the matter rebounds in a huge shockwave. The parameters of this whole process are quite nasty to work out in detail and the results depend somewhat (but less than you might think) upon the size and composition of the star. We've figured out those parameters mostly by running lots and lots of computer simulations with different parameters and figuring out which sets of parameters match up best with observations of actual supernovae.
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How fast does gravity propagate? A thought experiment: Imagine the Sun is suddenly removed. We wouldn't notice a difference for 8 minutes, because that's how long light takes to get from the Sun's surface to Earth.
However, what about the Sun's gravitational effect? If gravity propagates at the speed of light, for 8 minutes the Earth will continue to follow an orbit around nothing. If however, gravity is due to a distortion of spacetime, this distortion will cease to exist as soon as the mass is removed, thus the Earth will leave through the orbit tangent, so we could observe the Sun's disappearance more quickly.
What is the state of the research around such a thought experiment? Can this be inferred from observation?
| Since general relativity is a local theory just like any good classical field theory, the Earth will respond to the local curvature which can change only once the information about the disappearance of the Sun has been communicated to the Earth's position (through the propagation of gravitational waves).
So yes, the Earth would continue to orbit what should've been the position of the Sun for 8 minutes before flying off tangentially. But I should add that such a disappearance of mass is unphysical anyway since you can't have mass-energy just poofing away or even disappearing and instantaneously appearing somewhere else. (In the second case, mass-energy would be conserved only in the frame of reference in which the disappearance and appearance are simultaneous - this is all a consequence of GR being a classical field theory).
A more realistic situation would be some mass configuration shifting its shape non-spherically in which case the orbits of satellites would be perturbed but only once there has been enough time for gravitational waves to reach the satellite.
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What does it take to become a top physicist? What does it take to become a top physicist?
Why do so many extremely talented young upstarts totally flop as they move to more advanced physics?
| A great brain and hard work are required to be a top physicist. To be an average or below physicist is possible through a deficiency in one and a surplus in the other (I would consider myself to be moderate intelligence but a very hard worker which makes up for it to some degree). As you can see, one of these traits is naturally obtained and the other can be acquired.
There is the common perception amongst non-physicist laymen that all physicists are pretty much equally intelligent. Nothing could be further from the truth. We live on the upper end of the bell curve which is hardly constant.
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Do extra-dimensional theories like ADD or Randall-Sundrum require string theory to be true? What I mean is could it turn out that the world is not described by string theory / M-Theory, but that nevertheless some version of one of these extra-dimensional theories is true?
I have no real background in this area. I just read Randall and Sundrum's 1999 paper "A Large Mass Hierarchy from a Small Extra Dimension" (http://arxiv.org/PS_cache/hep-ph/pdf/9905/9905221v1.pdf). Other than the use of the term "brane" and a couple of references to string excitations at TeV scale, I don't see much about string theory, and I notice their theory only requires 1 extra dimension, not 6 or 7.
| Well, we have to answer another question first: "Is there any complete or consistent theory of quantum gravity which doesn't arise from string theory?"
Constructing RS models and ADD models is "phenomenological model-building".
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Electricity takes the path of least resistance?
Electricity takes the path of least resistance!
Is this statement correct?
If so, why is it the case? If there are two paths available, and one, for example, has a resistor, why would the current run through the other path only, and not both?
|
Electricity takes the path of least resistance. Is this statement correct?
YES
People often don't understand what the shortest path means. If I have a lightning rod connected to a wire which has a slight bend in it people still believe that the current will follow the wire to Earth and are astonished when the voltage jumps to a tree 15 feet away. We are talking here about millions of volts and hundreds of thousands of amperes. At these frequencies the slight bend will present an enormous impedance to the current and the tree is far more attractive in spite of the distance.
BTW: when a lightning rod gets struck it is not doing its job. It has a point and it is known that electrons will gather around this point and since the lightning is negative like will repulse like. That is the principle of the workings of a lightning rod.
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What is Fermi surface and why is this concept so useful in metals research? What is Fermi surface and why is this concept so useful in metals research?
Particularly, I can somewhat appreciate the Fermi energy idea - the radius of Fermi surface which is a sphere. But is there any quantitative use of more complicated Fermi surfaces?
| I think what you might be interested in are Van Hove singularities or the critical points of the Fermi surface, where the density of states as given by $dN/dK_{|k=k_f|}$ diverges. Now $dN/dk$ is proportional to the inverse of the gradient of the energy $ dN/dk \propto 1/\nabla E $. The locations with the greatest d.o.s. on the Fermi surface will exhibit singularities in various absorption and emission spectra. These are precisely those locations where the Fermi surface fails to be a smooth, differentiable surface.
Critical surfaces can be 0D (Fermi point), 1D (line), 2D (Fermi surface). Complicated substances (such as the High $T_c$ superconductors for e.g. which are composed of layers of cuprates) will in general have complicated Fermi surfaces. Because critical surfaces are topological entities they are robust with respect to small perturbations of the microscopic Hamiltonian of the system. In other words the critical surfaces determine the universality class to which the given surface belongs. The universality class determines whether a given material is a superconductor, ferromagnet, Mott insulator etc. Clearly to take a material from one universality class to another requires that one cross a phase boundary. Such a change also requires that the Fermi surface topology undergo a change. Consequently changes in Fermi surface topology can be understood as signs of phase transitions.
A Fermi surface is also important for reasons other than its topology, which describes the global characteristics of the material. Others will likely mention some of the complementary local aspects of the Fermi surface.
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Observation of cosmological topological defects Are there any projects/experiments running for the observation of topological defects (domain walls, monopoles, etc)?
Are there any past/canceled or future such projects?
| See e.g.
http://arxiv.org/abs/hep-ex/0302011
MoEDAL at CERN has survived since that time. This is about the magnetic monopoles. Domain walls may be too much stuff too wish for so I don't think that someone is looking for them and nothing else. Cosmic strings are being constantly looked for in the telescopes but so far, the bounds are tightening - they don't seem to be abundant (or they're totally absent).
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Is it really possible for water to be held in a "cone shape" for a brief period of time? I just saw this "trick" where a cup of water is turned over onto a table without spilling (using a piece of cardboard. After removing the cardboard from underneath the cup, the person then removes the cup in a particular way (lifts straight up and twists) and lo and behold, the water stays in it's position as if the cup were still there!? (watch the video to fully understand) Is this really possible? If so, and the real question I'm looking to have answered is, how?
After further research it appears that deionized water is needed as well.
| Its a trick.
There are 2 vessels:
the outer that we saw, and an inner one, transparent and soft.
Stopt it at 1:48 you will see the water move out from the bottom. Under atmospheric pression the vessel merge down. The image after this moment is truncated and we can not see the remnants in the table.
The water was previously set in rotational motion (before the image restarts after those words).
added:
It is not needed to explore the inner characteristics of the inner vessel but I will try.
My first tough : It can be a soft plastic bag.
My second try: It can be made of ice. But I suspect it is not so. Rinse the interoir of the vessel, then fridge until ice coated. Rinse again, and repeat,...or two equal vessels one inside the other separated by water and fridge.
Now, with the tiny ice coating prepared. Rinse the exterior of the vessel with warm water. Wait a little and the exterior will be decoupled from the interior vessel. Start the show
added again, my final conclusion
It is a soft bag. The rotational effect is really need to keep the vertical wall under more tension and will prevent the object from immediate collapse. The centrifugal force will add strength to the vertical wall and the vertical component of force will be lower.
If it was the icy vessel the rotational effect was not needed.
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How to build a laser in the garage? So I wonder if it is any how possible to build laser at home. A powerful one to melt brick.
| Yes. 100W CO2 laser is doable at home, and some in fact did that.
100W one will BURN really well.
No other types of power lasers are doable at home. (well, probably there is also killing 200 DVD-RW drives and collimating them all - I am actually doing that, I have 45 RW drives ;-) )
The only problems is that you still need few rare things like IR mirrors & transparent window which are very hard to find in garage (there is not much materials transparent at 10um).
Probably the optimal solution would be just buy finished CO2 tube from China (100-200$) and build cooling & power supply system by yourself. This is way way more realistic.
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meaning of an integral in the continuity equation This is about continuity equation. What does the last integral mean?
$$\frac{\mathrm{d}Q_V}{\mathrm{d}t}=\iiint_V \mathrm{d}^3x \,\frac{\partial\rho}{\partial t}=-\iiint_V\! \mathrm{d}^3x\,\operatorname{div}\,\mathbf{j}=-\iint\limits_{\partial V}\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\;\;\;\subset\!\supset \mathbf j\;\cdot\mathbf n\,{d}S\,,$$
EDIT:
And what does $\partial V$ mean? Why not S like surface?
| Note that the range of integration has changed from $V$ meaning over the volume to $\partial{V}$ and that the variable of integration has changed from $\text{d}^3x$ to $\text{d}S$.
It means an integral over the surface that bounds the volume.
The closed curve over the integration signs implies that the surface must be closed.
This expression is an application of what physicist tend to call Gauss's Law, and mathematicians tend to know as the divergence theorem.
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Are elementary particles ultimate fate of black holes? From the "no hair theorem" we know that black holes have only 3 characteristic external observables, mass, electric charge and angular momentum (except the possible exceptions in the higher dimensional theories). These make them very similar to elementary particles. One question naively comes to mind. Is it possible that elementary particles are ultimate nuggets of the final stages of black holes after emitting all the Hawking radiation it could?
| This is indeed a tempting suggestion (see also this paper). However, there is a crucial difference between elementary particles and macroscopic black holes: the latter are described, to a good approximation, by non-quantum (aka classical) physics, while elementary particles are described by quantum physics. The reason for this is simple.
If the classical radius of an object is larger than its Compton wavelength, then a classical description is sufficient. For black holes whose Schwarzschild radius is bigger than the Planck length this is fulfilled. However, for elementary particles this is not fulfilled (e.g. for an electron the "radius" would refer to the classical electron radius, which is about $10^{-13}$cm, whereas its Compton wavelength is about three orders of magnitude larger).
Near the Planck scale your intuition is probably correct, and there is no fundamental difference between black holes and elementary particles - both could be described by certain string excitations.
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Special Relativistic Time Dilation -- A computer in a very fast centrifuge Ok, I've stumbled onto what I think is a bit of a paradox.
First off, say you had some computer in a very fast(near light speed) centrifuge. You provide power to this computer via a metal plate on the "wall" of the centrifuge's container, so it works similar to how subways and streetcars are powered.
If the computer normally would consume 200 watts, how much power would it consume at say 1/2 of light speed? Would it consume 400 watts from our still viewpoint?
Also, what if you were to be capable of communicating with this computer? Would the centrifuge-computer receive AND transmit messages faster from our still viewpoint? I'm a bit lost in even thinking about it.
| One thing to be aware of is that the principle of relativity would not apply to this computer--rotating reference frames are not inertial, and therefore, will not be related to 'stationary' reference frames by simple Lorentz transformations. Also note that if there are any capacitors or anything along those lines in the computer, then they would be accelerating with respect to a rest frame, and this acceleration would produce electromagnetic waves (and even failing this, accelerating current-carrying wires would have a similar effect), which would create a potentially measurable difference between the frame of the computer and the rest frame.
My instinct for this problem, though, is that the power consumption of the computer would go down, not up--the computer uses energy in its rest frame, which has a slower clock than the lab frame. So, it would go on using 200 J every second of ITS proper time, which would correspond to more time in the lab frame.
| {
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List of freely available physics books I'm trying to amass a list of physics books with open-source licenses, like Creative Commons, GPL, etc. The books can be about a particular field in physics or about physics in general.
What are some freely available great physics books on the Internet?
edit: I'm aware that there are tons of freely available lecture notes online. Still, it'd be nice to be able to know the best available free resources around.
As a starter:
http://www.phys.uu.nl/~thooft/theorist.html
jump to list sorted by medium / type
Table of contents sorted by field (in alphabetical order):
*
*Chaos Theory
*Earth System Physics
*Mathematical Physics
*Quantum Field Theory
| Structure and Interpretation of Classical Mechanics Sussman, Wisdom, Mayer
A No-Nonsense Introduction to General Relativity, Sean Carroll
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Paradoxical interaction between a massive charged sphere and a point charge Suppose we have a sphere of radius $r$ and mass m and a negatively charged
test particle at distance d from its center, $d\gg r$. If the sphere is electrically neutral, the particle will fall toward the sphere because of gravity. As we deposit electrons on the surface of the sphere, the Coulomb force will overcome gravity and the test particle will start to accelerate away. Now suppose we keep adding even more electrons to the sphere. If we have n electrons, the distribution of their pairwise distances has a mean proportional to $r$, and there are $n(n-1)/2$ such pairs, so the binding energy is about $n^2/r$. If this term is included in the total mass-energy of the sphere, the gravitational force on the test particle would seem to be increasing quadratically with $n$, and therefore eventually overcomes the linearly-increasing Coulomb force. The particle slows down, turns around, and starts falling again. This seems absurd; what is wrong with this analysis?
| The statement that the gravitational attraction will eventually dominate the coulomb repulsion as n increases is correct.
You probably think the restmass of the electrons will invoke gravitational attraction, but that part is neglible for high electrondensities on the sphere. The gravitational attraction by (the curvature of spacetime caused by) bindingenergy is far greater for high densities.
I don't know where the breakpoint is, but suppose I look way past that limit, i.e. an incredible dense sphere(or shell) of electrons. If I make it dense enough, that could very well become a black hole. Note that this would be a strange black hole, since the 'mass' of such a black hole consists almost entirely of the bindingenergy, and not the restmasses of the electrons. From this point of view it might be more easily imaginable that the gravitional attraction will dominate eventually.
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Why are all-Sky images drawn as a filled ellipse? There is some convention? how is this 3d to 2d mapping done?
here an example
| The ellipse is a particular way to draw the surface of a sphere - like the sphere of the skies around us, or the surface of the Earth - on a flat piece of paper or screen (because of the curvature of the sphere, it cannot be "flattened" without distortions). This one is called the Mollweide projection and it preserves the areas (and completely sacrifices correct representation of the angles):
http://en.wikipedia.org/wiki/Mollweide_projection
http://en.wikipedia.org/wiki/Map_projection
The second link enumerates many other ways how to draw the spherical surface.
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Does hot air really rise? "Heat rises" or "warm air rises" is a widely used phrase (and widely accepted phenomenon).
Does hot air really rise? Or is it simply displaced by colder (denser) air pulled down by gravity?
| "Hot air" is just air molecules (M) moving faster (F); "cold air" is M moving more slowly (S). The collisions between the FMs and SMs force both Ms in all directions (SM faster than before, FMs slower than before, but still faster than most SMs). The space below them, however, is crowded with SMs, so those FMs knocked upward keep going fast -- until they hit the (albeit fewer) SMs above them, continuing the process. Shake a half-full bag of popcorn: the big kernels work their way up, leaving the smaller and denser corn below.
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I need help with finding distance traveled How do I find the distance traveled of an object if the speed is not constant?
| You can use a simple way it does include calculus.First find the maximum value of s(distance/displacement).By using the differentiation formula :ds/dt.Then add the time (t) value to the s equation.
EXAMPLE:Lets say t=2 then apply the vale to the s equation say : s=20t-5t^2
=20(2)-5(2)^2
=40-20=20
So the max value of s=20 then multiply with 2 and voila
you got your total distance(s=40m).
Hope this helps.
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Snell's law starting from QED? Can one "interpret" Snell's law in terms of QED and the photon picture? How would one justifiy this interpretation with some degree of mathematical rigour? At the end I would like to have a direct path from QED to Snell's law as an approximation which is mathematically exact to some degree and gives a deeper physical insight (i.e. from a microscopic = qft perspective) to Snell's law.
| In regard to the single photon aspect of the question, I speculate that the explanation is similar to the Mossbauer effect, ie the photon is absorbed and re-emitted by the entire mirror/crystal rather than a single atom. If you insist on thinking of a single photon being absorbed and re-emitted by a single atom, you are going to have to invoke the regularity of the mirror or crystal and use constructive and destructive interference, as mentioned in other answers.
You can see the necessity of a coherent many body solution from the fact that a single atom does not refract or reflect, it scatters, and similarly for a rough mirror.
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Fresnel transform How is it possible to encrypt multiple images using fresnel transform and inverse the operation to de-multiplex those images?
| The particular application the OP is asking about might be better on Theoretical Computer Science or Math, but the long and the short of it comes down to three properties of the transform
*
*The Fresnel transform is a special case of the Linear Canonical Transform (and also of the Generalized Fresnel Transform (here as free PDF) to make an explicit physics connection).
*The LCT can be represented by 2x2 matrix (exhibited in the wikipedia article and discussed at greater length in the paper by James et. al) and may be composed.
*The representation of the Fresnel transform as a non-zero determinant, which means that ti is invertible, and the inverted matrix also represents an instance of the LCD, which means that the original data may be recovered.
To this we add two facts concerning holograms...
*
*Holograms represent a Fresnel transform of the a three dimensional data set into a two dimensional representation.
*If we voxelize a 3D space we get a stack of pixelized 2D images (though I imagine this necessitates finding a discrete version of the transform, but that is old hat in numeric analysis).
...and it's obvious, right?
::phew!::
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Are water waves (i.e. on the surface of the ocean) longitudinal or transverse? I'm convinced that water waves for example:
are a combination of longitudinal and transverse. Any references or proofs of this or otherwise?
| I will just say what I think I know:
In the open ocean or great lakes the waves are transverse: the water goes up and down. They are originated by the winds in the surface.
Near the shore the waves become also longitudinal: the small distance from the the surface to the bottom of ocean make the difference.
added:
I described the net transport of energy along the direction of propagation of the waves.
In deep waters it is the vertical motion of the surface that is able to do work (on devices that extend more than a wavelength) against the gravitational field.
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Why are Saturn's rings so thin? Take a look at this picture (from APOD https://apod.nasa.gov/apod/ap110308.html):
I presume that rocks within rings smash each other. Below the picture there is a note which says that Saturn's rings are about 1 km thick.
Is it an explained phenomenon?
| If one could assume that the ring is a continuous distribution of mass, we could try minimizing the total energy of the system (self energy + energy of interaction with Saturn). These two conditions along with the condition that total mass of the disc is a constant, would (I think) leave us with a unique geometry (inner and outer radius, thickness).
EDIT: Some Googling gave this paper: http://dx.doi.org/10.1016/0019-1035(79)90084-8
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Why is the decibel scale logarithmic? Could someone explain in simple terms (let's say, limited to a high school calculus vocabulary) why decibels are measured on a logarithmic scale?
(This isn't homework, just good old fashioned curiousity.)
| It's a historical accident which has left us a lasting pain in the ass. There's no reason to express sound as decibels: writing the pressure level in Pascals in scientific notation is just as convenient as writing a level in decibels relative to some reference pressure level. And it's often MORE convenient for calculating certain things (i.e. a noise floor expressed in pascals-per-root-Hz makes sense; dB-per-root-Hz or dB-per-Hz makes no sense)
That being said, there are a few possible reasons for using dB:
1) For folks that don't know scientific notation.
2) To match human physiology/psychology, since human perception of sound has a roughly logarithmic response to the pressure level.
3) For attenuators or amplifiers, you can just add things (this is more common when dealing with RF). If I put a 10 dB attenuator in series with a 5 dB attenuator I get a 15 dB attenuator. And if I put a +2 dB power level of RF into a 15 dB attenuators, I get a -13 dB power out. And even though I don't like dB, I do have to admit that's pretty convenient.
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dynamic casimir effect A few years ago, when i studied the casimir effect interpretation as the filtering out of vacuum modes with appropiate boundary conditions, i had the following dilemma; supposedly the derivation of the force between the walls was entirely equivalent to just calculating Van der Waals forces. This, as it was argued, compelled us to not take too seriously the idea of a negative energy density of the space between the walls.
However, i was left wondering what would happen if one would take the interpretation based on vacuum modes a bit further, and we could somehow switch on and off the permitivity $\epsilon$ of the conductor; what sort of long range radiation we would expect to see?
A possible experimental implementation would be if the layers where superconductive, and then a magnetic field would be switched on just to break the superconductive phase.
We probably need to use the Dirac-Heisenberg-Wigner formalism for these sort of dynamic quantum systems, but what would be intuitively expected to be detected?
| A friend recently brought to my attention that this experiment was actually performed 6 months after i posted the question in this site:
http://blogs.nature.com/news/2011/11/light_coaxed_from_nothingness.html
http://www.chalmers.se/en/news/pages/chalmers-scientists-create-light-from-vacuum.aspx
Christopher Wilson from Chalmers (and his team) used the same mechanism that i've proposed in here: using a superconducting magnet to oscillate the mirror surface.
I'm glad to see that the idea really works!
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Coriolis effect on Tsunami The Japanese tsunami, moving at about 700 km/h, affected areas as distant as Chile's coast, 20 hours after the earthquake. How does the Coriolis force affect tsunami? Also, I saw an image of a boat caught within a large whirlpool. Is the whirlpool's rotation due to Coriolis force?
| The Coriolis effect is proportional to velocity:
$\boldsymbol{ F}_C = -2 \, m \, \boldsymbol{\Omega \times v}$,
where $\boldsymbol{\Omega}$ is the angular velocity (of the earth).
As waves, tsunamis have very high velocities, you would think it would be enough to see the Coriolis effect, but in fact there is little effect.
When in deep water, tsunamis move very quickly, but the water of which they are composed move very slowly. A typical example, is a wavelength of 200km, amplitude of 1 meter, and a period of around 30 minutes. Therefore, the water only has a speed of on the order of 1 meter per hour. This is a tiny fraction of the speed of clouds in the atmosphere which are effected by the Coriolis effect.
When a tsunami nears land, its height increases dramatically and so the distance the water moves increases as well. Suppose the tsunami moves a distance of 10km with a period of 30 minutes. This implies an average speed of 40km/hour which is fast enough to bring the Coriolis effect into play.
Putting the numbers ($\boldsymbol{v} = 40\; \textrm{km}/\textrm{hour}$ and $\boldsymbol{\Omega} = 2\pi/24\;\textrm{hours}\;\;$ ), into the equation, we find a maximum acceleration of about:
$\boldsymbol{ F}_C/m = 0.0016\;\textrm{m}/\textrm{s}^2$.
Since this is small compared to the gravitational acceleration (9.8 m/s$^2$ ) that is governing the last stages of a tsunami, the effect will be completely negligible. Local terrain completely determines the tsunami's behavior.
By the way, the Coriolis effect is able to effect clouds because they move for very long times. Over a time of 2 hours, an acceleration of $0.0016 \textrm{m}/\textrm{s}^2$ causes a change in velocity of about $12 \textrm{m}/\textrm{s}$.
| {
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Why does Fukushima pressure rise?
Possible Duplicate:
Why didn't the control rods in Fukushima shut down the reactor?
They say that pressure rises and that this can be dangerous. But why does this happen if the reactor is shutdown ?
| Because even if reactor is not-critical, there are lots of radioactive materials in the fuel which decays and produce some heat. You cannot stop that process. Although it gives much less heat than nuclear fission, it is still significant and can cause meltdown.
The same reason is why spent nuclear fuel is stored under water for few years - it just selfheat and can melt.
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Uses of the 'Golden Ratio' in Physics What are some physics applications of the golden ratio?
$$\varphi~=~ \frac{1+\sqrt{5}}{2}~\approx~ 1.6180339887\ldots$$
Does it ever function specifically as a constant in any formulas or theorems?
EDIT: Original title said Golden Radio... facepalm. I originally asked this question at math.stackexchange but the answers there were all too abstract or useless for me.
| In general, no, the golden ratio is not used often in physics. As a graduate student in experimental physics, I have never encountered the golden ratio in my work, except in toy problems.
| {
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Can a nuclear reactor meltdown be contained with molten lead? If lead can absorb or block radiation, would it be possible to pump molten lead into a reactor core which is melting, so that it would eventually cool and contain the radiation?
Is there something that can be dumped into the core that will both stop the reaction (extremely rapidly) AND will not combine with radioactive material and evaporate into the atmosphere, thus causing a radioactive cloud?
| A problem that seems to have been overlooked is the atomic mass of lead.
Lead, although heavier than all non radioactive elements, is lighter than all
radioactive elements. The result of injecting molten lead into a molten core
would be a layer of molten lead floating on top of the molten fuel.
Further, depending on the structural integrity of the pressure vessel and the
amount of lead to be added, the additional weight could rupture the vessel.
| {
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What are the reasons to expect that gravity should be quantized? What I am interested to see are specific examples/reasons why gravity should be quantized. Something more than "well, everything else is, so why not gravity too". For example, isn't it possible that a quantum field theory on curved space-time would be the way treat QFT and gravity in questions where the effects of neither can be ignored?
| For the sake of argument, I might offer up a plausible alternative. We might have some quantum underpinning to gravitation, but we might in fact not really have quantum gravity. It is possible that gravitation is an emergent phenomenon from a quantum field theoretic substratum, where the continuity of spacetime might be similar to the large scale observation of superconductivity or superfluidity. The AdS/CFT is a matter of classical geometry and its relationship to a quantum field theory. So the $AdS_4/QFT$ suggests a continuity of spacetime which has a correspondence with the quark-gluon plasma, which has a Bjorken hydrodynamic scaling. The fluid dynamics of QCD, currently apparent in some LHC and RHIC heavy ion physics, might hint at this sort of connection.
So we might not really have a quantum gravity as such. or if there are quantum spacetime effects it might be more in the way of quantum corrections to fluctuations with some underlying quantum field. Currently there are models which give quantum gravity up to 7 loop corrections, or 8 orders of quantization. Of course the tree level of quantum gravity is formally the same as classical gravity.
This is suggested not as some theory I am offering up, but as a possible way to think about things.
| {
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For an accelerated charge to radiate, is an electromagnetic field as the source necessary? For an accelerated charge to radiate, must an electromagnetic field be the source of the force?
Would it radiate if accelerated by a gravitational field?
| Your question is somewhat abstruse, but here's what I think you're asking:
Put a charged particle in a uniform external magnetic field. The particle will move in a circular orbit, but since it's accelerating, it will radiate and its orbit will decay.
Now remove the magnetic field. Grab the charge and forcibly swing it around in the same circle as before by some other, unknown means. Does it still radiate in the same way as before?
The answer is yes because Maxwell's equations are linear. Therefore we can analyze any situation in classical electromagnetism by superposition.
| {
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CPT violation and how could quark masses differ from anti-quark masses? A recent experimental paper measures a difference between the top quark and anti-top quark masses:
Fermilab-Pub-11-062-E, CDF Collaboration, Measurement of the mass difference between $t$ and $\bar{t}$ quarks
We present a direct measurement of the
mass difference between $t$ and
$\bar{t}$ quarks using $t\bar{t}$
candidate events in the lepton+jets
channel, collected with the CDF II
detector at Fermilab's 1.96 TeV
Tevatron $p\bar{p}$ Collider. We make an
event by event estimate of the mass
difference to construct templates for
top quark pair signal events and
background events. The resulting mass
difference distribution of data is
compared to templates of signals and
background using a maximum likelihood
fit. From a sample corresponding to an
integrated luminosity of 1/5.6 fb, we
measure a mass difference,
$\mathrm{M}_{t} -
> \mathrm{M}_{\bar{t}}$ $= -3.3 \pm
> 1.4(\textrm{stat}) \pm 1.0(\textrm{syst})$, approximately two standard deviations away from the CPT
hypothesis of zero mass difference.
This is the most precise measurement
of a mass difference between $t$ and
its $\bar{t}$ partner to date.
http://arxiv.org/abs/1103.2782
This seems to pile on to the recent evidence showing differences between the masses of the neutrinos and anti-neutrinos. But unlike neutrinos, quarks can't be Majorana spinors. So what theoretical explanations for this are possible?
| I suppose it will be a painful wait for the 5 sigma. Well, quarks are confined, so maybe it's OK for them to exhibit genuine CPT violation, whereas the neutral particles need renaming according to the mirror picture. But on the other hand, the quark braids have neutral strands, and if we mix (say for the proton) the uud, udu and duu sets, then there are enough neutral strands for component Majorana states.
| {
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What is the most energy efficient way to boil an egg? Starting with a pot of cold tap water, I want to cook a hard-boiled egg using the minimum amount of energy. Is it more energy efficient to bring a pot to boil first and then put the egg in it, or to put the egg in the pot of cold water first and let it heat up with the water?
| "Energy efficient" usually means "with minimal production of entropy". For that you need, 1) a well insulated (on the sides) pot, 2) minimal loss from heating element, 3) the smallest possible (and practical) amount of water amount that can boil an egg (i.e. conver its whole surface) and 4) put the egg at the beginning of the process (not drop it once the water boils because that generates extra entropy because of the temperature gradient).
Pressure cooking can be more efficient because it needs less time of the heating element. But since the temperature reaches more that ~100°C that can give a different cooking process, and not qualify as a "boiled egg" because of changes in taste and consistency. http://www.hippressurecooking.com/2011/04/hip-modernist-soft-medium-and-hard.html
| {
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Quaternions and 4-vectors I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity:
$$(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$$
Is it useful? Is it used? Does it bring anything? Or is it just funny?
| There is a book:
"Quaternions, Clifford Algebras and Relativistic Physics." by Patrik R. Girard. Find this if you want to learn more -- very good reading, not very complex and not very long. I'll just cite the first paragraph of chapter 3.
From the very beginning of special relativity, complex quaternions have been used
to formulate that theory [45]. This chapter establishes the expression of the Lorentz
group using complex quaternions and gives a few applications. Complex quaternions
constitute a natural transition towards the Clifford algebra H ⊗ H.
Well and the reference:
[45] L. Silberstein, The Theory of Relativity, Macmillan, London, 1914.
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Can electricity transfer radioactivity? If a cable used to power something is exposed to a radioactive source will it over time make the entire cable radioactive?
| Are you worried that the cables that go to the Fukushima reactors will carry radioactivity out?
The answer is No. You should read up a bit on radioactivity and educate yourself, since it is one of the facts of life. In the article you will see that it is atoms that are responsible for radioactivity whereas the current in the cables is due to electrons. The parts of the cables that are in a radiation environment will become radioactive, but that activity will remain in the locality, and the length of cable that was exposed. It in no way can be transmitted away from the region the way the current is transmitted.
| {
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What properties do you need for building a tower? When I was a boy I used to daydream about building a tower so tall that the top of it would project into near space.
There would perhaps be a zero gravity area in the penthouse where my friends and I could bounce around and play space versions of various earth-based games and sports in most excellent zero-g conditions.
Much to my continued disappointment and despite all the technological advances of the last thirty or so years, no one has built such a structure.
Can anyone explain the physical limitations/constraints that are preventing someone from realising my fantasy of a 'Space Tower'?
UPDATE: This Kickstarter Project seems to be pretty confident ...
| Rather than using material, perhaps magnetic fields configured in stages. Imagine a stack of plates separated at a distance on the order of a meter. Magnetic fields, from superconducting magnetics repeal the plates above or below. Sensors and an electronic system dynamically adjust the fields. I wonder if the fields would need to become attractive at some point due to centifigual forces from the earths rotation.
| {
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Do cosmological and Doppler redshift produce different patterns? For a given black body radiation curve, would the changes to the spectrum resulting from cosmological expansion and those from Doppler effects be distinguishable on the basis of the shapes of the resulting curves alone? Or, put another way, starting from the same spectrum, can both processes produce the same observation (for suitably chosen magnitudes of expansion or velocity)?
| This addresses the comment to Professor Bunn's answer more than the original question:
Any spacetime described by the FLRW metric, where objects are static in comoving coordinates and redshift is due to expansion of space, can in principle be also described, via an appropriate change of coordinates, by a spherically-symmetric (SS) metric, where objects move along radial timelike geodesics and redshift is due to positional (gtt) and Doppler factors. Since both metrics describe the same physical system, they are observationally equivalent in all respects.
To note, the equivalent SS metric is static, meaning that gtt and grr do not depend on time, only in the empty (Milne) and lambda-vacuum (de Sitter) cases. Moreover, even in the next simplest case, the flat matter-only FLRW model known as Einstein-de Sitter model, gtt and grr cannot be expressed algebraically in terms of non-comoving time, as I mentioned in my answer to this question. I take it as a strong hint that the FLRW model with expansion of space is the real thing, but even if you take a purely utilitarian position, you can at least say that expansion of space is the only conceptual framework with which it is possible to work.
| {
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Will Earth Hour do damage to power supply system? There is always a debate around Earth Hour every year, and the opposite side of Earth Hour usually claims that
The (sudden) decrease and increase of the power usage in the start and end of Earth Hour will cause much more power loss (than the save of power), and even do damage to the power supply system.
Is this statement true? To what extent?
Thank you very much.
| As the vast majority of people aren't stupid enough to fall for the scam/hoax, the effects will be miniscule.
And of those who do, as said, their electric lights are only a small percentage of their total power consumption (and most likely they'll compensate by turning to other electrical appliances that consume more electricity than those lights).
| {
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What future technologies does particle physics and string theory promise? What practical application can we expect from particle physics a century or two from now? What use can we make of quark-gluon plasmas or strange quarks? How can we harness W- and Z-bosons or the Higgs boson? Nuclear physics has given us nuclear plants and the promise of fusion power in the near future. What about particle physics? If we extend our timeframe, what promise does string theory give us? Can we make use of black holes?
| Cultural enrichment.
Let me explain. String theory is a work of art. Art has no practical application, you say? No! It is practical in enriching culture and uplifting the emotions of mankind. So is string theory. The emotional satisfaction that you get out of it. Shout it out to the whole world!
We fund art, so why not string theory! Oh, yeah!
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Definitions and usage of Covariant, Form-invariant & Invariant? Just wondering about the definitions and usage of these three terms.
To my understanding so far, "covariant" and "form-invariant" are used when referring to physical laws, and these words are synonyms?
"Invariant" on the other hand refers to physical quantities?
Would you ever use "invariant" when talking about a law? I ask as I'm slightly confused over a sentence in my undergrad modern physics textbook:
"In general, Newton's laws must be replaced by Einstein's relativistic laws...which hold for all speeds and are invariant, as are all physical laws, under the Lorentz transformations." [emphasis added]
~ Serway, Moses & Moyer. Modern Physics, 3rd ed.
Did they just use the wrong word?
| These words do have different meanings, this is a general guide to their differences. In different fields they may have slightly varying definitions. I would recommend looking them up to be certain.
Invariant means does not change at all. Everything is the same (whether physical law, quantity or anything). In terms of vectors, invariant is a scalar which does not transform.
Form-invariant means the form does not change, for example the inverse square law, will always be inverse square but the constants may differ.
Covariant, has a specific meaning when relating it to vectors, as it specifies the transformation rules. (This is as opposed to contravariant which is the other one).
For more information see wikipedia, towards the end of the Mathematics of four vectors section.
To specifically answer your question on the phrase, Einsten's relativistic laws are invariant under Lorentz transformations, the laws don't change at all. The constants don't change, neither does the form.
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Why there's a whirl when you drain the bathtub? At first I thought it's because of Coriolis, but then someone told me that at the bathtub scale that's not the predominant force in this phenomenon.
| Since you want to explain it to your daughter, take a plastic bottle, cut the bottom open, turn it upside town, hold the top closed and fill it with water. Give her that bottle and have her release the top (which is on the bottom now, sorry for the bad phrasing). The water will whirl in different orientations whenever you repeat this (if it whirls at all) and she can influence it by accelerating the bottle in a circular motion to understand that an initial disturbance is responsible for the whirl orientation.
| {
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Why does Venus spin in the opposite direction? Given: Law of Conservation of Angular Momentum.
*
*Reverse spinning with dense atmosphere (92 times > Earth & CO2 dominant sulphur based).
*Surface same degree of aging all over.
*Hypothetical large impact is not a sufficient answer.
Assuming any object large enough to alter a planets rotation or even orbit would likely destroy most of its shape, yet Venus has retained a spherical property with a seemingly flat, even terrain indicating no volcanoes,and few if any visible meteor impacts. It would be fragmented and dispersed for billions of years. Even the question of what meteor, comet, asteroid composition could survive traveling that close to the sun's temperature, radiation, electromagnetic energy, solar flares, or gravity to equal a mass reactionary change as to alter it's spin.
| There seems a lot of conjecture in any event. Venus could have been a meteor, with an innate spin, that swung by the Sun and have been captured into our Solar systems anticlockwise orbital arrangement. Retaining her original spin momentum, clockwise relative to the others.
| {
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How might a resonant antenna and black body radiation interact? How does an antenna behave when it is cooled so that its black-body radiation is emitting energy at its resonant frequency?
Edit: To clarify, its not how they're related in general, but how might thermal radiation and resonance interact with each other when their spectra are aligned well?
Edit: Also, I'm sure that the thermal radiation spectra that have a significant peaks are associated with incredibly high temperatures, and peak at incredibly small wavelengths, rendering such an antenna completely impractical to build. Still, I'm still interested in the theoretical concept.
| OK, the simple answer:
When there is a resonance in the antenna you have a coherent phenomenon. All the bands of electrons of the antenna are marching in tune.
The black body radiation is an incoherent phenomenon coming from the individual atoms of the antenna. Even if the peak of the black body radiation were sitting on the resonance of the antenna it is still an incoherent phenomenon that cannot couple to the coherent behavior of the electrons in the current that resonate.
Think of a single violin tune and a crowd of people talking. The noise of the people does not cover the clarity of the violin even in high volumes.
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Dangerous dose of I-131? I was searching a lot and could only find dosages for curing cancer and allowed emission, but no Iodine-131 dose that could be connected with increased thyroid cancer risk (like, 10mSv is the radiation dose resulting with measurable increase of cancer).
The Central Laboratory of Radiological Protection publishes Iodine-131 content in air measured in $\mu$Bq/m$^3$.
The number has grown by 3 orders of magnitude since the Fukushima accident, and while I strongly believe it's still good 6 orders of magnitude below dangerous levels, there's no convincing of some people without solid numbers - and finding these has proven quite hard.
So how can I then get either the safe levels of I-131 in air in ($\mu$Bq/m$^3$) , or a way to (indirectly - this gonna be convoluted) convert the content in air ($\mu$Bq/m$^3$) to dose equivalent radiation ($\mu$Sv) from absorbed Iodine?
| It's difficult to get hard figures without exposing people and seeing how many die! Then the problem is that for low levels of exposure you have to workout how many extra people have died
The Nation Cancer Institute has some calculators and papers based on US nuclear testign exposure
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Measuring the spin of a single electron Is it possible to measure the spin of a single electron? What papers have been published on answering this question? Would the measurement require a super sensitive SQUID, Superconductive Quantum Interference Device?
| I was browsing old questions and noticed this one. I think I ought to take issue with the idea you can measure the spin of a single electron. Suppose I prepare an electron in a definite spin state and send it into another room; I don't think there is any way someone else can tell what state I prepared the electron in. Putting it through a Stern Gerlach apparatus certainly won't do. Isn't saying that you can measure the spin of an electron the same as saying you can measure its position and momentum simultaneously?
EDIT: I notice DarenW referes to a paper by Stenson, and it turns out I stumbled on a related paper on my own and it made a big impression on me. The paper I found is actually Stenson's master's thesis, which I will find a link to once I finish this post, and I will post it in the comment field of Daren's answer. As for my own analysis of Stenson's paper, it spans a number of blogposts beginning here. The conclusion is fascinating: if you put a beam of silver atoms through a Stern Gerlach apparatus, it doesn't split into two paths: it spreads out into a donut! I've sketched the deposition pattern for a polarized beam here, and you can read the analysis on my blog.
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What are the conditions to be satisfied by a theory in order to be a quantum theory? This is in continuation to my previous question. It is not a duplicate of the previous one. This question arises because of the answers and discussions in that question.
Can we call a theory, quantum theory, if it is consistent with HUP? For example, suppose there is a finite and self consistent theory of gravity which incorporates the uncertainty principle. Can we at once call this theory a quantum theory of gravity or does it have to satisfy other conditions too?
This question may be too basic but it is intriguing my mind.
| *
*.NET is a framework
*Software that is built using languages supported by .NET is called .NET software.
*That software may or may not break if some part of .NET breaks.
*It is necessary to have .NET in place for the software to work.
Now replace .NET with QM and software with theory. :-D
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What reflective media do laser shows use? I am having a hard time in finding out what exact light media laser shows use. I am trying to build a laser show myself. I know that the laser light is reflected off these particles in such a way that that it makes the laser line "viewable" in all directions
Can somebody explain to me how exactly do the collection of particles make it viewable in all directions and what exact conditions are necessary? Does the angle of the incoming laser light matter? Does the size of the particles matter? Does the uniformity of how the particles are dispersed matter? Would water vapor work?
I have tried using a fog machine, but the red laser that I am using only reflects off of the fog particles in a way that makes it viewable only from a certain perspective. This would not be a good show to the people standing in one side of the room vs. another.
| http://en.wikipedia.org/wiki/Theatrical_smoke_and_fog describes the methods used to create smoke. Also I think, in a room filled with people (like at evening parties), the humidity gets high enough to make light beams visible.
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How to measure the spin of a neutral particle? If a charged particle with charge $q$ and mass $m$ has spin $s \neq 0$ we can measure an intrinsic magnetic moment $\mu = g \frac{q}{2m}\hbar \sqrt{s(s+1)}$. This is how spin was discovered in the first place in the Stern-Gerlach Experiment.
But for a neutral particle $\mu = 0$, so we cannot measure the spin of the particle in the same manner. But it is said, that e.g. the Neutron or the Neutrino both have a spin $s=1/2$. How was or can this be measured?
| Also the neutron has a magnetic moment. Check this out. The reason is that the neutron is not an elementary particle but built up from quarks which have charge...
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What is the difference between $|0\rangle $ and $0$? What is the difference between $|0\rangle $ and $0$ in the context of $$a_- |0\rangle =0~?$$
| You may consider 0 as an eigenvalue and write $a|0\rangle = 0|0\rangle$.
Any eigenvector $a|\alpha \rangle = \alpha |\alpha \rangle$ is of different "length" than the corresponding normalized vector $|\alpha \rangle$. In your particular case the vector $0|0\rangle$ is of zeroth length.
| {
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Can a disk like object (like UFO's) really fly? UFOs as shown in movies are shown as disk like objects with raised centers that emit some sort of light from bottom. Can such a thing fly?
My very limited knowledge in physics tell me that a disk like object may not be able to maneuver unless it has thrusters on sides and simple light can not be enough to make any object go up in the air.
Is it possible?
| In mid 2010, Japan Aerospace Exploration Agency launched IKAROS, a spacecraft that is pushed by the radiation of the Sun.
Explanation: If you consider relativistic effects, light (photons) have no mass, but they can carry momentum $p=h/\lambda$ per photon particle, where $h$ is Planck's constant and $\lambda$ is light's wavelength. So, if UFOs can generate very bright light (very high intensity), theoretically they can push themselves against the gravity.
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Making a "heavier-than-air" craft float How big would a hollow rigid object need to be to float, (not in water but in air) if all of the air was vacuumed out and the container sealed?
| Just to flesh out Jim's answer.
Assume you made a cube (makes the math easier!) 1m x 1m x 1m
Aluminium has a density of 2700kg/m^3
And you need the cubeto have a mass of less than 1.2Kg
- so can use (1.2/2700) m^3 of material
The surface area is 6m^2 then you can have a thickness of (1.2/2700)m^3 / 6m^2 = 70um
Or about half the thickness of a hair!
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Have CMB photons "cooled" or been "stretched"? Introductory texts and popular accounts of why we see the "once hot" CMB as microwaves nearly always say something about the photons "cooling" since the Big Bang. But isn't that misleading? Don't those photons have long ("cool") wavelengths because space expanded since they were emitted. There's no separate "cooling" process, is there?
| I will use most of @Ted answer to describe 'hot' but I will ask a more basic question:
I think the best way to think about it is that the sentence "the
photons have cooled" is simply describing a fact, not explaining that
fact. At early times, the photons at any given location had a thermal
(blackbody) distribution corresponding to a high temperature (as
measured by observers at rest in the natural, comoving reference
frame). At later times, the photons at any given location had a
thermal distribution corresponding to a lower temperature. That's what
we mean when we say that they "cooled.
Of course, it's then very natural to ask
Q : What would happen if CMB photons in the past were really hot?
A : It is an impossibility!
as seen here: Remaining Problems in Interpretation of the Cosmic Microwave Background :
the expected CMB temperature increases would be prohibitive to star
formation in galaxies at redshifts higher than $z=2$ where nevertheless the
cosmologically most relevant supernovae have been observed
The official interpretation of the CMB, in a hot past universe, is in trouble. One good reason to consider that larger atoms in the past radiated at larger wavelengths, explaining the cosmological red-shift as is demonstrated here: A self-similar model of the Universe unveils the nature of dark energy
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Alcubierre Drive - Clarification on relativistic effects On the Wikipedia article on the Alcubierre drive, it says:
Since the ship is not moving within this bubble, but carried along as the region itself moves, conventional relativistic effects such as time dilation do not apply in the way they would in the case of a ship moving at high velocity through flat spacetime relative to other objects.
And...
Also, this method of travel does not actually involve moving faster than light in a local sense, since a light beam within the bubble would still always move faster than the ship; it is only "faster than light" in the sense that, thanks to the contraction of the space in front of it, the ship could reach its destination faster than a light beam restricted to travelling outside the warp bubble.
I'm confused about the statement "conventional relativistic effects such as time dilation do not apply".
Say Bob lives on Earth, and Jill lives on a planet in Andromeda, and we'll say for the sake of argument that they're stationary. If I were to travel from Bob to Jill using an Alcubierre drive such that the journey would take me, say, 1 week from my reference frame... how long would Jill have to wait from her reference frame? Do the time dilation effects cancel out altogether? Would she only wait 1 week?
| Spacetime is constructed in such a way that the travellers own proper time is equal to the coordinate time of the external, distant observers. Thus, there is no time dilation. This is clear from Alcubierre's original article:
Of course, other kinds of warp drive spacetimes also need to be checked individually, i.e. whether they have time dilation.
| {
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Supergravity calculation using computer algebra system in early days I was having a look at the original paper on supergravity by Ferrara, Freedman and van Nieuwenhuizen available here. The abstract has an interesting line saying that
Added note: This term has now been shown to vanish by a computer calculation, so that the action presented here does possess full local supersymmetry.
But the paper was written in 1976! Do you have any info what kind of computer and computer algebra system did they use? Is it documented anywhere?
| I don't know about this particular paper, but I do know that several early supergravity computations were checked using a computer algebra program 'Abra' written in Pascal by Mees de Roo. You could do gamma matrix algebra and Fierz transformations with it (among others), and it had a quite clever method to interactively work on parts of long expressions. This system was part of the inspiration for my own 'Cadabra' system.
I don't think Abra is publically available.
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Why does a rotating tire use the static, rather than the dynamic coefficient of friction? The explanation I have heard of the difference between static and dynamic friction is that static friction is stronger because bonds form when one object is put on top of another object and these have to be overcome to get the movement started.
For a rotating tire, although the point on the ground will be stationary for an instant, it would seem that bonds wouldn't have time to form. So, why isn't the dynamic coefficient of friction used?
| A car drives at 20 m/s. The circumference of the wheel is 2m, so the rotation rate is 10 Hz. A reasonable percentage of the tire is in contact with the ground - maybe around $5\%$. That would give a contact time of $5\times 10^{-3}$ s.
This is a pretty long time in molecular terms. The distance between molecules divided by the speed of light is around $10^{-18}$ s, so that's the fastest we can imagine some sort of bonding occurring. That 16 orders of magnitude faster than the contact time.
Real chemical reactions must be slower, but with $10^{16}$ "clicks" of time for the chemistry to sort itself out, there should be plenty of time for the tire to stick.
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Why do they store gold bars with the narrow side down? I watched on TV as they where showing gold bars stored in bank vaults and I noticed that they always stack them with the narrow side down and the wide side up. Like this:
So there has to be a mechanical reason why is that. Any ideas?
| They do not always seem to be that shape. For some cuboids which are not designed to be moved regularly, see this picture from Fort Knox.
But for bullion bars in the world market (about 10.9-13.4 kg of gold) which have the standard sort of trapezium cross-section, the top when casting is the wider area to get them out of the mould, so the wider area is defined as the "top" in the international specification) and the fineness, hallmarks and serial numbers usually stamped on top (as illustrated here). Stacking them top face up makes these easier to read for the bars on top, as well as easier to move. Pure gold bars may dent if dropped because of gold's softness, requiring recasting, so some care is needed.
| {
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Relativistic space-time geometry What subject (suggest book titles, etc.) should I study to get a clear grasping of hypersurfaces, 2-surfaces, and integration on them, mostly in special relativity (I'm not messing with general relativity yet).
| As others mentioned, special relativity (by definition really) doesn't have anything to do with curved surfaces! Special relativity has a particular metric (minkowski metric) which has no curvature. If your interested in manifolds (particularly integration on them, since integration in minkowski space is pretty trivial) and things like that, you really getting into general relativity.
Although I am sure many people will have pedagogical arguments against the following approach, I will say it anyway... You don't really need to do an in depth study of mathematical SR to do GR. Really once you understand the basic properties of minkowski space, know what a lorenz transformation is, understand things like length contraction, etc, you really should just jump right into GR. One sorta friendly way to go about it is apply SR to E&M (covariant formalization) as a way to play around with tensors a little.
As far as recommendations of what books to get, take a look at Sean Carroll's notes (http://preposterousuniverse.com/grnotes/) and if you like them get his book too! Perhaps also looking at the first two sections will give you a better idea of what you are looking for.
EDIT: After commenting, I thought I would also just post a link to O'Neills Amazon Page. His books are probably more mathematical than what you are looking for, but they could be very useful to someone else.
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What is meant by positive and negative gravity/energy/spacetime-curvature? I have recently come across some cosmological assertions (based on empirical data) about the universe being self contained in the sense that it is entirely capable of coming into existence from a zero-energy initial state. This is based on the observation that at grand scale the positive and negative gravity/energy etc. cancel out each other.
What do the terms positive and negative actually mean in this context?
| This is a very misleading claim which keeps being touted in popular science books and the media.
I asked about this earlier over here.
Total energy of the Universe
From what I can see, there is a lot of controversy over what total energy even means in the context of general relativity, so claims about "negative energy of gravity" balancing the positive energy of matter are basically vacuous.
| {
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Laplacian of $1/r^2$ (context: electromagnetism and Poisson equation) We know that a point charge $q$ located at the origin $r=0$ produces a potential $\sim \frac{q}{r}$, and this is consistent with the fact that the Laplacian of $\frac{q}{r}$ is
$$\nabla^2\frac{q}{r}~=~-4\pi q~ \delta^3(\vec{r}).$$
My question is, what is the Laplacian of $\frac{1}{r^2}$ (at the origin!)? Is there a charge distribution that would cause this potential?
| The electric field from your potential is:
$$E(r) = {2\over r^3}$$
Using Gauss's law, the total charge in a sphere of radius R is:
$$Q(r) = \oint E \cdot dS = 4\pi r^2 {2\over r^3} = {8\pi\over r}$$
The total charge is decreasing with r, so there is a negative charge cloud of density
$$ \rho(r) = {1\over 4\pi r^2} {dQ\over dr} = - {4\over r^4}$$
But the total charge at infinity is zero, so there is a positive charge at the origin, cancelling the negative charge cloud, of a divergent magnitude. If you assume this charge is a sphere of infinitesimal radius $\epsilon$, the positive charge at the origin is
$$Q_0 = \int_\epsilon^\infty 4\pi r^2 {4\over r^4} = {16\pi \over \epsilon}$$
This is not a distribution in the mathematical sense, but it is certainly ok to work with, so long as you keep the $\epsilon$ around and take the limit $\epsilon$ goes to zero at the end of the day. Mathematicians have not had the last word on the class of appropriate generalized solutions yet.
| {
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Is dark matter repulsive to dark matter? Why? I think I saw in a video that if dark matter wasn't repulsive to dark matter, it would have formed dense massive objects or even black holes which we should have detected.
So, could dark matter be repulsive to dark matter? If so, what are the reasons? Could it be like the opposite pole of gravity that attracts ordinary matter and repulses dark matter?
| Lubos Motl's answer is exactly right. Dark matter has "ordinary" gravitational properties: it attracts other matter, and it attracts itself (i.e., each dark matter particle attracts each other one, as you'd expect).
But it's true that dark matter doesn't seem to have collapsed into very dense structures -- that is, things like stars and planets. Dark matter does cluster, collapsing gravitationally into clumps, but those clumps are much larger and more diffuse than the clumps of ordinary matter we're so familiar with. Why not?
The answer seems to be that dark matter has few ways to dissipate energy. Imagine that you have a diffuse cloud of stuff that starts to collapse under its own weight. If there's no way for it to dissipate its energy, it can't form a stable, dense structure. All the particles will fall in towards the center, but then they'll have so much kinetic energy that they'll pop right back out again. In order to collapse to a dense structure, things need the ability to "cool."
Ordinary atomic matter has various ways of dissipating energy and cooling, such as emitting radiation, which allow it to collapse and not rebound. As far as we can tell, dark matter is weakly interacting: it doesn't emit or absorb radiation, and collisions between dark matter particles are rare. Since it's hard for it to cool, it doesn't form these structures.
| {
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What is the smoking gun signature of string theory? What is the smoking gun signature of string theory? Suppose we have a complete and consistent model of quantum gravity with a zero or negative cosmological constant, but all we are given is its complete S-matrix. Using only this information, how do we figure out whether or not this model corresponds to a string theory compactification?
If the cosmological constant is positive, what can we use in place of the S-matrix?
| I ( an experimentalist) will wade in where angels ( theorists) fear to tread :).
There exists this great in length report by CMS where you will see in the introduction part of the motivation for the experiment as :
Various alternatives to the Standard Model invoke new symmetries,
new forces or constituents. Furthermore, there are high hopes for discoveries that could pave the way toward a unified theory. These discoveries could take the form of supersymmetry or extra dimensions, the latter often requiring modification of gravity at the TeV scale.
So experimentalist have been lured to look for extra dimensions, one of the possible marks of string theory, as "predicted" by various phenomenological models.
If nothing new/unexpected like this is found, it will not preclude that string theories are waiting for us as the theory of everything in the future.
If a signal of extra dimensions is found in the data, then string theorists will be singing a different, not so cautious song.
| {
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Anti-matter repelled by gravity - is it a serious hypothesis?
Possible Duplicate:
Why would Antimatter behave differently via Gravity?
Regarding the following statement in this article:
Most important of these is whether ordinary gravity attracts or repels antimatter. In other words, does antihydrogen fall up or down?
Is this a seriously considered hypothesis? What would be the consequences on general relativity?
If this is seriously studied, can you point to some not-too-cryptic studies on the (anti ;-)matter?
| The only problem with this is that antimatter has the same mass as its matter counterpart. So this means that is effected the same way by gravity as normal matter.
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