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STR, one-way speed of light and conventionality

  1. Oct 24, 2005 #1
    I've been reading about about the isotropic and homogeneous nature of the universe, and as far as I can tell, it's basically a convention -- i.e., space is the same in all directions and the same in all locations only on average, over a very large area; observational data could one day reveal that the universe is in fact not isotropic or homogeneos. It occurs to me that our knowledge of the speed of light is similar: we don't (or can't) really know the one-way speed of light; 300,000 km/s is just a convention we adopt (based on our measurement of the round-trip speed of light). Does this have anything to do with symmetry and conservation laws? Does anyone have any thoughts on possible connections between the things I've just mentioned here?
    (I'm coming at physics from a philosophy background, so my technical knowledge is very limited, but it feels like there must be something interesting going on when STR and theories about the nature of space seem to depend in some important way on convention). Any ideas would be much appreciated! Thanks.
     
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  3. Oct 24, 2005 #2
    Sure we can. All you need is some kind of synchronization at different places.

    Radio telescope arrays and Very-Long-Baseline-Interferometry relies directly on the one-way speed of light.

    For that matter, the standard two-slit interference pattern relies directly on the one-way speed of light, I think.
     
  4. Oct 24, 2005 #3

    JesseM

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    The one-way speed of light depends on your choice of coordinate systems, and any physical situation can be analyzed from the point of view of any coordinate system you choose, it's just a matter of finding the correct expression for the laws of physics in that coordinate system. But as n8trix guessed, the reason for preferring the coordinate systems given by the Lorentz transformation has to do with symmetry--all the known fundamental laws of physics are Lorentz-invariant, which means that they will look the same in every inertial coordinate system given by the Lorentz transform. If you chose to synchronize clocks in a different way, then the one-way speed of light might no longer be constant, but this would mean that each inertial observer would have to use different equations to express the laws of physics in their own rest frame.

    Another way of thinking about this is that the synchronization convention assumed in the Lorentz transformation is the only one that each observer can physically implement without knowing their velocity relative to any other object in a universe, so they could synchronize their clocks in the required way even if they were stuck in a windowless box. Other synchronization conventions wouldn't be purely intrinsic in this way, they'd require each observer to measure his velocity relative to some preferred reference frame and take that velocity into account when synchronizing their own clocks.
     
  5. Oct 24, 2005 #4

    pervect

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    My $.02 - available evidence shows that the clock synchronization that makes the speed of light isotropic is also the same clock synchronization that makes the measurement of the velocity of an object with specified mass and momentum the same in all spatial directions.

    Other clock synchronization methods would make the speed of light anisotropic, but would also make the velocity of an object of a specified mass and momentum anisotropic - there would be some "preferred direction" in space with such an anisotropic synchronization method.

    Let's make it specific - if the velocity of light going east is different than the velocity of light going west, then the velocity of a material object of mass 1kg with a momentum of 200,000,000 kg-m /s will also be different when it goes east than when it goes west.

    For definiteness, one knows that the momentum going east is the same as the momentum going west when two objects of the same mass collide inelastically and come to a dead stop.
     
  6. Oct 25, 2005 #5

    SpaceTiger

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    The way you state this is a bit deceptive. Homogeneity and isotropy are, at the moment, observational facts, not just a convention. That is, the universe is homogeneous and isotropic on large scales as best as we've been able to observe. However, what you then say is true -- we may one day make an observation that contradict homogeneity and isotropy. This is the same with any physical theory, however.

    "Convention" usually refers to the selection of a particular means of expression amongst a degenerate set of them. For example, it's "conventional" to solve particular orbital dynamics problems in spherical coordinates, but this is not the only way of solving the problem. We could just as well work in cartesian or cylindrical coordinates and get the same physical result. The primary reason we don't is that the problem becomes more mathematically challenging. There do exist such conventions for the description of the universe, but the fact that there is a frame in which the universe is homogeneous and isotropic is a physically meaningful statement. In other words, we could easily imagine universes in which no such frame existed.
     
  7. Oct 26, 2005 #6
    Thanks for replying, everyone.

    I think what you're saying may be slowly sinking in. Bear in mind I just started reading about the Lorentz transformation and I have the mathematical prowess of a sixth-grader.

    1) What is the synchronization convention assumed in the Lorentz transformation?

    2)

    Can you (or somebody) elaborate on this?

    BTW, for anyone interested in enlightening me, the original question was: How is the conventionality of the one-way speed of light related to the isotropy of space, especially in connection with symmetry and conservation laws? Are these connections surprising or interesting? Can anyone help me here? Thanks!
     
  8. Oct 26, 2005 #7
    Thanks for replying, everyone.
    I think what you're saying may be slowly sinking in. Bear in mind I just started reading about the Lorentz transformation and I have the mathematical prowess of a sixth-grader.
    1) What is the synchronization convention assumed in the Lorentz transformation?
    2)
    Can you (or somebody) elaborate on this?
    BTW, for anyone interested in enlightening me, the original question was: How is the conventionality of the one-way speed of light related to the isotropy of space, especially in connection with symmetry and conservation laws? Are these connections surprising or interesting? Can anyone help me here? Thanks!
     
  9. Oct 26, 2005 #8

    Aether

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    Einstein's synchronization convention.
    The conventionality of the one-way speed of light has to do with how clocks at different points in space are synchronized with each other, and is not directly related to the isotropy of space.

    Isotropic Universe
    If you think of the universe as being made up of an expanding cosmological fluid (as an expanding gas cloud after an explosion for example...BANG!), and you are located somewhere within the expanding fluid, then there is one frame/velocity at which you are comoving with the local fluid (like a balloon drifting with the wind), and that is the only frame/velocity where the universe would look isotropic to you. Relative to the Sun, there is a frame moving at about 368km/sec in the direction of the constellation of Leo in which the Cosmic Microwave Background Radiation (CMBR) looks isotropic, and that is the best candidate (as far as I know) for our local comoving frame (e.g., the universe looks more isotropic in that frame than in any other).

    Conventionality of the One-Way Speed of Light
    Einstein's clock synchronization convention assumes that the one-way speed of light is isotropic (the same in every direction), and that is easy to implement in the real world because light/radio signals are easy to engineer. The main (theoretical) alternative convention maintains "absolute simultaneity", but that can't be implemented (yet) because it requires an instantaneous signal to pass between clocks in order to synchronize them in this way. "Quantum entanglement" provides a hint that instantaneous signals may exist in nature, but they haven't proved useful (as far as I know) for synchronizing clocks yet.

    Symmetry and conservation laws
    Local Lorentz symmetry is what is currently known to exist in nature, and it doesn't allow for instantaneous signals. Detection of an instantaneous signal by which clocks could be synchronized to maintain absolute simultaneity would mean that a new higher symmetry exists, and a new conservation law would take effect.

    The connections are not only interesting, they are fascinating. The "locally preferred frame" and the "locally comoving frame" are two different frames/velocities that would be interesting to measure. With those two pieces of information in hand, we would finally know our absolute coordinates in space and time. "Relativity" forbids this unless/until we find an "instantaneous signal" that is useful for synchronizing clocks. Also, even if we were to discover a higher symmetry, a new form of relativity would probably also take effect with respect to that higher symmetry; for example, we might discover our absolute coordinates within our universe, but the coordinates of our universe among the universes would still be relative. This is the physicist's version of the "universal doubt caster" that is so beloved among philosophers (e.g., "...we demand rigidly defined areas of doubt and uncertainty..."), and gives license to solve big puzzles without fear of being left without an even bigger puzzle to solve as a result.

    In general, the variation (or constancy) of any dimensionful constant (such as the speed of light) in time and space is a matter of convention and lacks any real physical meaning in and of itself. It is the variation of dimensionless constants, such as the fine structure constant, in time and space which might have some real physical meaning (see J.P. Uzan, The fundamental constants and their variation: observational and theoretical status, Rev. Mod. Phys. 75, 403 (2003)).
     
    Last edited: Oct 26, 2005
  10. Oct 26, 2005 #9

    JesseM

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    The physical basis for the coordinate systems used in SR is the idea that each observer has a set of rulers at rest relative to himself with a bunch of clocks attached at different locations along the rulers, and that to assign space and time coordinates to an event, he looks at local readings on the ruler and clock that were right next to the event when it happened. This leaves the problem of how to synchronize clocks at different locations, though--you can't just bring them together, synchronize them in a common location, and then move them apart, since the clocks will slow down when you move them. So Einstein suggested in his 1905 paper that a natural way to synchronize clocks would be using light-signals, with each observer making the assumption that light travels at the same speed in all directions in his frame. For example, you could set off a flash at the midpoint of two clocks, and then set them both to read the same time at the moment the light from the flash reached them. But if you think about this a little, you'll see that if each observer synchronizes his own clocks in this way, it will necessarily lead to each observer seeing every other observer's clocks as being out-of-sync. For example, imagine I'm in a rocket travelling by you at high velocity, and I synchronize two onboard clocks at the front and back of the rocket by setting off a flash in the middle of the rocket and setting them to read the same time when the light hits them. In your frame, though, the back of the rocket is moving towards the point where the flash was set off while the front of the rocket is moving away from that point, so if you assume those two light beams move at the same speed in your frame, then in your frame the light will catch up with the back clock before it catches up with the front clock, so if both clocks read the same time when the light hits them this means the back clock must be ahead of the front clock in your frame.
    Sure, an alternate synchronization convention would be for one special observer to synchronize his clocks using Einstein's procedure, but then for every other observer to set his clocks in such a way that they will still be seen as synchronized in this special observer's coordinate system (this will require them to know their velocity relative to the special observer). If the special observer uses coordinates x,t and some other observer moving at velocity v in his frame uses coordinates x',t', then this synchronization convention will result in the following coordinate transformation:
    [tex]t' = t / \gamma[/tex]
    [tex]x' = \gamma (x - vt)[/tex]
    where [tex]\gamma = 1/\sqrt{1 - v^2/c^2}[/tex]
    Compare with the Lorentz transformation used when you use Einstein's synchronization convention:
    [tex]t' = \gamma (t - vx/c^2)[/tex]
    [tex]x' = \gamma (x - vt)[/tex]
    That factor of [tex]vx / c^2[/tex] in the parentheses of the time transformation insures that clocks at different locations along the x-axis which are in sync in the first frame will not be in sync in the second.
    I think pervect addressed this above, if you use an alternate synchronization convention the speed of light will be different in different directions, but also two objects with the same mass and equal and opposite momentums will not have equal and opposite velocities, so the relation between the momentum of the speed of an object with a given mass will depend on its direction, introducing an anisotropy in space.
     
    Last edited: Oct 26, 2005
  11. Oct 26, 2005 #10

    JesseM

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    It can't be implemented in an intrinsic way, with each observer setting up his coordinate system in a windowless box, but an alternate synchronization convention that maintains absolute simultaneity can certainly be implemented physically if you just pick an arbitrary observer to be the "preferred" one and have all other observers measure their velocities relative to him and set their clocks in such a way that they'll appear synchronized in his frame.
    Why would you call it a "higher" symmetry? Normally that means a larger symmetry that incorporates the original one, but if there were physical effects that picked out a preferred definition of simultaneity, this would simply invalidate Lorentz-symmetry, at least for whatever laws govern these new effects.
    It's not very clear what you mean by "the coordinates of our universe among the universes" here.
    But as we've discussed before, the idea that certain quantities such as the one-way speed of light are coordinate-dependent is really conceptually distinct from the idea that such quantities are dimensionful. It is possible to have dimensionful quantities which do not depend on your choice of coordinate system (the mass of an electron expressed in grams, say), and likewise it is possible to have dimensionless quantities that do depend on your choice of coordinate system (the ratio between the one-way speed of two different objects, for example).
     
  12. Oct 27, 2005 #11

    Aether

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    Yes, the alternative clock synchronization convention can be physically implemented in this way. However, if any instantaneous signal is ever shown to be useful for synchronizing clocks at different locations, then clock synchronization using such an instantaneous signal would no longer be a matter of convention, and the one-way speed of light would be proved by experiment to be generally anisotropic.

    Is there any reason why quantum entanglement hasn't been used to synchronize two distant clocks in a perfectly straight forward manner so that they maintain absolute simultaneity? Or has it?

    There are at least two types (conceivably) of instantaneous signals which could be useful for clock synchronization: peer-to-peer signals which might simply invalidate Lorentz symmetry as you say, or time-varying dimensionless constants which might indicate a larger symmetry that incorporates Lorentz symmetry.

    Our absolute coordinates within infinite Euclidean space and time could not be determined by establishing an instantaneous peer-to-peer connection between events within our own universe.

    Let's take the two-way speed of light [itex]c_0[/itex] as an example of "dimensionful quantities which do not depend on your choice of coordinate system", and the ratio of two one-way speeds of light (in opposing directions) within a coordinate system maintaining absolute simultaneity [itex](1-v/c_0)/(1+v/c_0)[/itex] as an example of "dimensionless quantities that do depend on your choice of coordinate system". It is true that the constancy of the one-way speed of light depends on your (conventional) choice of coordinate system, but it also depends on the constancy of the two-way speed of light which does not depend on your choice of coordinate system. My original statement applies to the two-way speed of light as well as the one-way speed of light (e.g., the variation of the speed of light in "time and space"). A larger symmetry, or an invalidation of Lorentz symmetry, would have to involve more than conventional choices. Although [itex](1-v/c_0)/(1+v/c_0)[/itex] is an example of "dimensionless quantities that do depend on your choice of coordinate system", that does not necessarily mean that such a choice has to be conventional.

    These statements are not wrong, but they are coordinate-dependent and seem likely to be misinterpreted as having some deep physical meaning which they do not. At worst, each observer (who chooses "to synchronize clocks in a different way") would have to transform their "equations to express the laws of physics in their own rest frame" to a preferred frame and then from there to any other arbitrary frame. Sure, this could be annoying if motivated by nothing more than some arbitrary convention. However, if the one-way speed of light is ever proved by experiment to be anisotropic, then this "two-step transform" would not be a significant obstacle to anyone.
     
    Last edited: Oct 27, 2005
  13. Oct 27, 2005 #12

    JesseM

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    That doesn't really make sense to me. The one-way speed of light is always going to be a coordinate-dependent quantity, and no matter what the laws of physics are, nothing is stopping you from using any coordinate system you want. The laws of physics may pick out some coordinate system as more "natural" for some reason, but if that's the criterion you're using, you should agree that according to the current known laws of physics, the most natural set of coordinates are the ones given by the Lorentz transformation and therefore that experiments currently support the statement that the one-way speed of light is isotropic.
    How would you do that, exactly? Quantum entanglement can't be used to communicate information faster than light. The results of local measurements on a particle will be the same regardless of whether the particle has an entangled partner or not, it's only when you are able to compare measurements made on more than one entangled particle that you see interesting statistical correlations between them that show "entanglement", and of course you can't compare the measurements until a signal travelling at the speed of light has had time to pass from both of them to you.
    Why would time-varying dimensionless constants indicate a larger symmetry that incorporates Lorentz symmetry? And if you think time-varying dimensionless constants can somehow pick out a preferred reference frame (I don't see how), then again, this would simply violate Lorentz symmetry rather than incorporate it into a larger symmetry.
    And if a preferred definition of simultaneity was found, this would pick out a preferred frame and violate Lorentz-symmetry for whatever laws are governing these phenomena.
    Again, to the extent coordinate-dependent statements are more than just conventional, it's because some coordinate systems are more "natural" to use given the known laws of physics than others. For instance, Lorentz-symmetric laws have the property that they will look the same expressed in any coordinate system given by the Lorentz transformation. So do you agree that, given all current known fundamental laws are Lorentz-symmetric, it is more than just a matter of convention to say that the one-way speed of light is isotropic?
    If it makes sense to talk about a coordinate-dependent quantity like the one-way speed of light being proven to be one way or another "by experiment", then you have to acknowledge that people who currently say the one-way speed of light is isotropic are making a statement that is firmly supported "by experiment" as well. You seemed unwilling to do this on the other thread, was I misunderstanding, have you changed your mind, or would you deny that this statement is in fact supported by all experiments to date?
     
  14. Oct 27, 2005 #13

    Aether

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    I agree that Einstein's clock synchronization convention is not completely arbitrary, but it falls very far short of being "proven by experiment". See next paragraph.

    We didn't talk in any detail about instantaneous signals in the other thread. If we could actually pass instantaneous signals between the emitter and the receiver of a light signal, then we could directly measure the one-way speed of light (in either direction) using a single clock. There is no clock synchronization convention involved, and the measurement is not coordinate dependent. The dimensionless ratio of light speeds (in opposite directions) between the emitter and detector would not be coordinate-dependent if measured in this way.

    I am not sure about that at this time, so I am asking. It does not seem necessary to communicate information faster than light in order to synchronize two clocks using an instantaneous signal. It is only necessary to identify a specific event (or pattern) occurring at both clocks as having been simultaneous, and this can be done retroactively with no problem.

    Let's come back to this after we have agreed on what a hypothetical instantaneous peer-to-peer signal would mean.
     
    Last edited: Oct 27, 2005
  15. Oct 27, 2005 #14

    JesseM

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    Then you are guilty of a double standard. If experiments did pick out a preferred reference frame and a preferred definition of simultaneity, this would only "prove by experiment" that the one-way speed of light is not isotropic in precisely the same sense that the lack of a preferred frame can be said to "prove by experiment" that the one-way speed of light is isotropic--namely, in the sense that these experimental results make one choice of coordinate system more "natural" than others, even though it is still perfectly possible to use other coordinate systems. Do you agree that even if we found a preferred frame, there'd still be nothing stopping us from continuing to use the Lorentz transform with its multiple definitions of simultaneity, it's just that the new laws of physics would not look as nice & elegant in such coordinate systems? Do you agree that given what is currently known about physics, there is nothing stopping us from using something like the Mansouri/Sexl coordinate transformation, it's just that the current laws of physics do not look as nice & elegant in such coordinate systems? If so, then please explain in more detail why you think the situation is not totally symmetrical, and why you feel it is justified to say that new experimental results could "prove" the one-way speed of light is not isotropic yet current experimental results cannot be said to support the statement that the one-way speed of light is isotropic.
    No you couldn't, it would still depend on your choice of coordinate system. Signals that were "instantaneous" in a single preferred frame would make it seem more "natural" to use only coordinate systems whose definition of simultaneity agrees with that preferred frame, but we would still have no obligation to use such a coordinate system, just as we currently have no obligation to use only coordinate systems where the speed of light is the same in all directions, even though it is more "natural" to do so.
    Of course there is! It's a convention that all observers synchronize their clocks using this new effect which you label "instantaneous". No matter what the effect is, we have no obligation to label it "instantaneous", we'd be free to pick a coordinate system where the signal is FTL but non-instantaneous in one direction, and where the signal actually moves backwards in time in another direction, ie the signal is received at an earlier time-coordinate than it was sent (just as with light, the one-way speed of your new type of signal would be coordinate-dependent).
    But what events would that be? Either experimenter can measure their own particle whenever he wants, there's no physical effect that causes them to pick a particular moment to make the measurement.
     
  16. Oct 27, 2005 #15

    Aether

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    This hinges on the next two paragraphs, so let's come back to this after resolving the issue(s) of what it would mean to be able to pass instantaneous signals between the emitter and the detector of a light signal.

    Let's come back to this after resolving the issue(s) in the next paragraph.

    When I said "If we could actually pass instantaneous signals between the emitter and the receiver of a light signal, then we could directly measure the one-way speed of light (in either direction) with a single clock", I meant "If we could actually pass instantaneous signals between the emitter and the receiver of a light signal (in either direction), then we could directly measure the one-way speed of light (in either direction) with a single clock".

    I'm talking about a case where we can send a signal and receive an echo without any delay.

    I don't know. I have not studied this, at least not recently, and am just asking.
     
  17. Oct 27, 2005 #16

    JesseM

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    "Instantaneously" depends on your choice of coordinate system, and "without delay" is only coordinate-independent if you are talking about sending a signal and receiving a reply, in which case you can only say that the average two-way speed of the signals is infinitely fast, but not their one-way speed. Even if you found a physical effect which would allow you to send signals instantaneously in one choice of coordinate system, you could pick other coordinate systems where the signal was moving FTL but non-instantaneously in some directions, and backwards in time in other directions. Assuming the signals are instantaneous in one frame, in other frames the FTL vs. back in time effect would be symmetrical, so if a signal travels at 2c in one direction in my frame, it travels backwards in time at 2c in the opposite direction, insuring that if I send a signal to you 10 light years away and it takes 5 years to reach you in my frame, then when you send an echo back to me it will reach me 5 years before it was sent in my frame, so that I receive your echo the same time I sent the original signal.
    OK, then my answer is that there's nothing about entanglement that could be used to experimentally pick out a preferred frame or a preferred definition of simultaneity, the most fundamental laws of QM known today are all Lorentz-symmetric.
     
    Last edited: Oct 27, 2005
  18. Oct 27, 2005 #17

    Aether

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    OK. I agree that we are free to use coordinates like that so that (if we wanted to) we could explore the possibility that "if a signal travels at 2c in one direction in my frame, it travels backwards in time at 2c in the opposite direction" for example. I have actually heard a serious explanation of the origin of inertia that used a coordinate system like that.

    OK.

    Previously tabled issues:
    OK.

    I agree that "there'd still be nothing stopping us from continuing to use the Lorentz transform with its multiple definitions of simultaneity", but it seems that there would be more of a physical significance to any such discovery than "just that the new laws of physics would not look as nice & elegant in such coordinate systems"...unless this a fundamental limit to physics (or perhaps to human knowledge of physics) in general.

    Yes, but "given what is currently known about physics" I would (and do) qualify the use of any coordinate system whatsoever which makes an assumption about the one-way speed of light by using the word "conventional".

    Current experimental results cannot be said to "prove" that the one-way speed of light is isotropic because they don't include one single measurement of a coordinate independent dimensionless ratio of the one-way speed of light traveling in two different directions. If new experimental results don't include such a measurement, then they can't prove anything about the one-way speed of light either. I assumed that a signal having zero round-trip travel time would be useful for making such a measurement.

    They may or they may not. However, if the time-variation was predictable in such a way as to allow us to define a new invariant quantity, then that would be the signature of a new symmetry component. If the time-variation was smooth...

    "Indeed, it is difficult to imagine a change in the form of physical laws (e.g., a Newtonian gravitation force behaving on Earth as the inverse of the square of the distance and, somewhere else as another power). A smooth change in the physical constants is much easier to conceive." -- p. 403 (Uzan, 2003).

    ...then it seems most natural to model this as an infinite sequence (e.g., foliation) of hypersurfaces (of constant [tex]\alpha[/itex], or whatever dimensionless time-varying fundamental constant you want to use) in which local Lorentz symmetry holds on each hypersurface, but each hypersurface is connected to the previous one by some form of infinitesimal exotic boost that is characteristic of the new symmetry component.
     
    Last edited: Oct 28, 2005
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