I was listening to Feynman on space-time and he challenged the audience to find a paradox in simultaneity over large distances, or a paradox resulting from knowing what was happening in a region of space outside your light cone...is there one i can't think of? it seems like there shouldn't be an obvious one because non-simultaneity is so counterintuitive to our local experience anyways...

## Answers and Replies

turin
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Did he mean a pseudo-paradox or an actual current problem that needs to be worked out. I can think of an example that would seem like a paradox to those who want to disprove SR: phase velocity.

turin - can you elaborate on phase velocity?

i think Feynman meant a paradox (of any kind) that results from information being ferried about instantaneously (or even in excess of c)...for instance, if we had an instantaneous radio hookup (of whatever hypothetical technology you like) with Alpha Centauri, what paradoxes would arise? we would, in a sense, be speaking with someone who is 4 years in the past...yet, there is nothing he could tell us that we could use to effect our past because we have simply shifted simultaneity, bringing our sense of time in Alpha Centauri forward four years...is this insistent of a paradox? hypothetically, we could hear about their stars terrible supernova four years ahead of time, we could shield our eyes...is that a paradox? not really...but maybe it leads to one...i can't think of it... :zzz:

turin
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phase velocity is the "speed" at which the point of contact for a wave front moves along the surface it hits. Take the example of us and then some planet orbiting alpha centari. Imagine an electromagnetic pulse sent from far away that first hits alpha centari and then a minute or two later hits Earth. The phase velocity was:
4 lyrs pr minute (or two).
This seems trivially inconsequential, but in QM, the em pulse may be a photon (I think) and so it would collapse if it hits alpha centari. That would mean that it has affected what would happen to Earth just a minute or two later, but, that's just the law of probability, and it really isn't a direct cause from alpha centari to Earth.

What about wormholes? I don't think anyone has yet demonstrated the operation of a wormhole, but that would give you a short-cut through space time. This could possibly cause a paradox. You can think of a wormhole that connects alpha centari to Earth. Then, if you walk through it, at the very moment that you have "disappeared" from Earth, you have appeared on (a planet near) alpha centari. At first glance, this doesn't seem to violate conservation of mass or energy, right? But, what if you consider a frame of reference that moves along a line that goes from Earth to alpha centari at a relativistic speed. Then, the relativity of simultaneity would cause conservation of mass to be violated, because there would either be some period of time in which you had simply vanished from Earth without a trace, or (more profoundly) there would be some period of time in which you were both on Earth and on alpha centari simultaneously. I don't know if you have to adjust the relativity of simultaneity for the tremendous curvature of a wormhole or something else like that, but a wormhole is just a (rather) fancy idea to begin with, anyway, so this is (very much) like saying that time travel causes a paradox. Yes, it may cause a paradox, but that's OK (unless someone actually does build a wormhole or time machine).

When an object moves fast, its lightcone tilt. This is a result of the four-vector always being the same length. Now imagine having an event started by a stationary "person" and observed by two fast moving observers, moving in opposite directions. No problem so far, using relativity theory, they can account for everything.

Now make the event an entanglement of two photons and send them of in opposite directions. A and B measures the photons the same time (relativistically speaking). Is there a chance that the two observers do not measure the same value?

The experiment has actually been done ... :-)

turin
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techwonder,
That's very interesting. Do you have a reference? I want to read more about that.

NateTG
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turin said:
techwonder,
That's very interesting. Do you have a reference? I want to read more about that.

Look for Einstein Rosen Podonsky (not sure about that spelling) or EPR paradox, and Bell's theorem.

Regarding the question about pardoxes:

One fundemental notion of physics is the notion of cause and effect. In SR and GR, super-relative communication breaks causality, so that the notion of causality becomes ambiguous. In other words, which direction the communication went depends on the observer.

As long as you assume that everything is reversible, this isn't a big deal, but there are Quantum Mechanical and Theromodynamic considerations that are affected by the direction of time. An experiment could, for example, be set up, so that in order to reverse the communication an inverse explosion would have to occur.

The EPR paradox, combined with Bell's theorem, and experimenal results indicates that any explanation of physical phenomena will either have to allow for non-local interactions of some type, or for unexpected mathematical models of the electron.

turin
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NateTG said:
Look for Einstein Rosen Podonsky (not sure about that spelling) or EPR paradox, and Bell's theorem.
I suspected as much.

NateTG said:
In SR and GR, super-relative communication breaks causality, so that the notion of causality becomes ambiguous.
...

As long as you assume that everything is reversible, this isn't a big deal, ...
I'm quite skeptical about this. I have always understood a strict adherence to causality within SR alone without appealing to the second law of thermo, for instance. My basis has been that the parameter for any physical process is related to the proper time. If the velocity is >c, then the proper time parametrization is ambiguous (or imaginary, or has some kind of fatality). Is it that the parametrization according to &lambda; = a&tau; + b constitutes an appeal to thermo or some such discipline with a second law type requirement?

NateTG said:
An experiment could, for example, be set up, so that in order to reverse the communication an inverse explosion would have to occur.
Well, I am not sure I understand the problem in this example. From my interpretation, this is either an implosion or an inelastic collision, both of which I have seen with my own eyes.

http://www.timephysics.com/sitebuilder/images/SIMULATENITY-520x420.jpg [Broken]

Is simultaneity preserved or not. Lack of simultaneity leads of Andromeda Paradox. However this simple thought throws light on this subject and argues that simultaneity must be preserved:

The thought experiment deals with simultaneity. A space ship is moving at a high velocity from left to right. According to relativity speed of light should be constant for the observer within the ship as well as the stationary observer on the ground.

Light rays sent simultaneously from the front and back of the ship will meet in the center of the ship for the observer within the ship. While for the non moving observer on the ground the light pulses should meet more towards the back of the ship.

This information could be used to set up an experiment so that a cat is shot by a gun if the rays of light do not meet in the center. (lucky for the cat).

So for the observer in the ship the light rays meet in the center so the cat should be alive while for the observer on the ground the cat should be dead as the light rays do not meet in the center.

Which point of view is correct. Is the cat alive or dead? One way of solving this problem would be to say that the firing mechanism will obey the laws within the moving ship so the cat will be alive. This means that point of view of the non moving observer on the ground is superfluous. This point is clearly shown to be
correct by photon acceleration caused by moving plasmas showing that simultaneity is preserved so there is no need for the block universe.

http://www.timephysics.com/nature-of-time.html [Broken]

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phase velocity is the "speed" at which the point of contact for a wave front moves along the surface it hits.

Hmmm, I hadn't heard that interpretation before. It's extremely interesting if it is true but I have doubts about that. Mathematically phase velocity is simply the wave or wave packet's angular frequency divided by the wave number. For a plane wave it's really the velocity of the plane in which the phase stays constant. It's direction is not necessarily parallel (or perpendicular) to the wave propagation vector.

If the wave front hits a surface that it cannot penetrate, the refracted or rebounding wave along the surface should propagate at the velocity in which energy flows along the surface. Normally that would be less than c for any type of dielectric. Maybe you mean only the wave front's passing through a mathematical "surface" or plane in empty space?

Maybe your source had assumed the Coloumb Gauge applied in which the potential propagates at infinite velocity? I suppose it must be true that between any points in the plane of constant phase there is an implicit instantaneous propagation of potential. But a plane of constant phase might only occur in specific types of waves. In other words most EM waves are more properly spherical and the abstraction to a planar wave creates the unrealistic situation of a plane of constant phase with implicit instantaneous propagation of potential.

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Doc Al
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This thread is way old.