What has the speed of light got to do with time travel?

[sammy8761]

Just wondering what the connection is between them, I understand that it relative to what we see but time in general? why not the speed of sound as its only another sense right? Just interested to know why light is so special?

thanks guys,

Sorry messed up title should be speed of light! doh!

 

[Dale]

Just interested to know why light is so special?

Light is special because it does not require a medium in which to propagate.

 

[sammy8761]

Light is special because it does not require a medium in which to propagate.

I apologise but I am afraid i don't understand.

 

[Janus]

The speed of light is the only speed that everyone measures as having the same value relative to themselves.

So what does this have to do with time?

Consider this scenerio:

You have a two people, one riding a train and one standing on the embankment. Lightning strikes at two points along the track at equal distances from the second observer. The light from these strikes arives at this person at the same moment the person riding the train passes him. Thus both people see the lightning strikes at the same time.

Each person is also able to measure the speed of that light relative to himself. when the embankment observer does this he determines that the strikes occurred at the same instant, as the strikes were at equal distances from him and the light from each strike traveled at the same speed relative to him.

The person on the train will also measure that the both flashes of light traveled at the same speed relative to himself. But he also knows that he is in motion relative to the points at which the strikes took place. Thus for him to be at a point an equal distance from the strikes when he sees them, he had to be closer to one strike than other when they took place, abd thus for him to be able to see the light from both strikes at the same time, the strikes themselves would have to have taken place at different times (one strike would have had to take place before the other.)

Thus we have two observers seeing the same lightning flashes but obe concluding tthat the strikes took place simultaneously, and the other concluding that they did not. All because both measure the same speed for the speed of light.

 

[epkid08]

Just wondering what the connection is between them, I understand that it relative to what we see but time in general? why not the speed of sound as its only another sense right? Just interested to know why light is so special?

thanks guys,

Sorry messed up title should be speed of light! doh!

Define time travel

 

[peter0302]

The speed of light has nothing to do with time travel except in science fiction stories.

There is no reason to believe that "exceeding the speed of light" would result in backwards-in-time travel. Any such idea is mere speculation. The equations say that your clock would be mvoing in imaginary units - multiples of 'i' - which has no meaningful physical interpretation.

The only even remotely credible possibility of traveling backwards in time involves certain paths in general relativity involving extremely high mass-energies and gravitational fields. It has nothing to do with the speed of light (except to the extent that the GR equations have c as a parameter).

 

[JesseM]

Janus gave an explanation of why, if the speed of light is the same in each observer's frame of reference, that means different observers must disagree on whether events at different locations, like the two lightning strikes, happened simultaneously or at different moments. You can also watch a youtube video here which gives a nice illustration of the train thought-experiment. But I want to add a little to this to make the connection to "time travel" more clear. One of the basic principles of relativity is that each inertial (non-accelerating) observer measures the same value for the speed of light in a vacuum, but another principle is that all the laws of physics appear the same in each observer's own rest frame. This means that if I am in a sealed windowless spaceship moving inertially, and you are in a different sealed windowless spaceship which is in motion relative to my ship (and also moving inertially), then if I do some experiment on board my ship and you perform an identical experiment on yours, we should always get the same result. Now, imagine we both had some device which could transmit information faster than light--"instantaneously", let's say.

Now let's repeat the idea of the train thought-experiment, and suppose the observer on the side of the tracks has an FTL transmitter at the location of the strike at the back of the train, and at the moment the strike happens this transmitter sends a signal to a receiver at the location of the strike at the front of the train. Since both strikes happen simultaneously in the frame of the observer on the side of the tracks, and since the transmitter transmits information instantaneously in the frame of the observer on the side of the tracks, that means the receiver will get the message about the strike at the back of the train at the same moment that the lightning is striking right next to its own location at the front of the train (of course the train is moving relative to the receiver, so its location only coincides with the front of the train for a moment). But now remember that in the frame of the observer on board the train, the lightning actually hit the back of the train after it hit the front of the train. So in this frame, the receiver is actually receiving information about an event that "hasn't happened yet"!

This wouldn't be so bad if we just imagined that one frame's definition of simultaneity was the "correct" one and the other wasn't. But if the laws of physics work exactly the same in every frame, that must apply to whatever laws of physics govern the FTL transmitter too...so, if it's possible to build a transmitter which sends information back in time according to the train-observer's definition of simultaneity, it must also be possible to build a transmitter which sends information back in time according to the track-observer's definition of simultaneity. It works out so that if you are moving away from me at some significant fraction of light speed, and we each had FTL transmitters of this kind, then I'd be able to send a message to you which traveled "instantaneously" in my frame but "backwards in time" in your frame, and then you could immediately send a reply which traveled "instantaneously" in your frame but "backwards in time" in my frame, and the result would be that I'd actually receive your reply before I sent the original message! In this case every frame would agree that causality had been violated and that information had traveled back in time. Of course, this is a pretty good argument for suspecting that FTL communication is forbidden by the laws of physics...

 

[JesseM]

The speed of light has nothing to do with time travel except in science fiction stories.

There is no reason to believe that "exceeding the speed of light" would result in backwards-in-time travel. Any such idea is mere speculation. The equations say that your clock would be mvoing in imaginary units - multiples of 'i' - which has no meaningful physical interpretation.

Incorrect, see my post above. The issue is not what a faster-than-light clock would experience--trying to use the Lorentz transformation in this case gives nonsense answers as you point out, but then it also gives nonsense answers to what a clock moving at exactly the speed of light would experience, yet this doesn't mean we can't transmit signals which move at the speed of light in our frame, and similarly your point about the nonsensicality of FTL clocks also doesn't rule out the possibility of sending signals which move at FTL speeds in our frame (see this article on the hypothetical 'tachyons'). But because of the relativity of simultaneity, any signal which moves FTL in one frame would seem to move backwards in time in another, and if FTL signals obey the principle of relativity which says all laws of physics work the same way in every inertial frame, this means that two slower-than-light observers can bounce FTL signals between them in such a way that one of them will receive the other's reply before she even sent her original message. There's a helpful explanation of this using spacetime diagrams on this page.

 

[peter0302]

I don't, and didn't, equate "time travel" with backwards-in-time signaling.

 

[JesseM]

I don't, and didn't, equate "time travel" with backwards-in-time signaling.

Well, normally I think physicists would interpret time travel as causality violation, and certainly sending information backwards in time would be a violation of causality. And if you can send information back in time I think you should be able to do quantum teleportation backwards in time too.

 

[peter0302]

If you define quantum teleportation as "travel" ok... since the source object is destroyed I don't think that's what the OP has in mind.

To me time travel is the idea of moving a person either backwards in time or forwards in time faster than normal. And the common myth in sci-fi and I think in the general public is that traveling faster than light would allow you to do this, just like in Superman reversing the rotation of the Earth sends you back in time. There isn't even a theoretical basis to believe that you would be traveling backwards in time if you exceeded the speed of light. Your lorentz factor would be imaginary, not negative, implying it's a nonsensical scenario.

I do agree with you that the only thing standing in the way of FTL or B-I-T signaling is causality problems, which itself is a dubious concept. We all know in QM traditional causality gets thrown out the window. Maybe there will be a way to learn information about the future via a signal from it; but that doesn't mean anyone suddenly found themselves hundreds of years in the past. That will never happen.

 

[JesseM]

If you define quantum teleportation as "travel" ok... since the source object is destroyed I don't think that's what the OP has in mind.

According to quantum indistinguishability I think it's basically meaningless to ask whether the teleported system is really the "same" as the original system or whether it's really a "copy", for the same sort of reasons that it's meaningless to ask which slit a photon in the double-slit experiment "really" went through in cases where you see an interference pattern (under certain interpretations of QM these questions might have a true answer, but an answer that would be impossible in principle to determine experimentally).

To me time travel is the idea of moving a person either backwards in time or forwards in time faster than normal. And the common myth in sci-fi and I think in the general public is that traveling faster than light would allow you to do this, just like in Superman reversing the rotation of the Earth sends you back in time. There isn't even a theoretical basis to believe that you would be traveling backwards in time if you exceeded the speed of light. Your lorentz factor would be imaginary, not negative, implying it's a nonsensical scenario.

There's no theoretical basis for saying that the Lorentz transformation would allow you to figure out how things look in the "frame" of an FTL object, no--the principle of relativity would be violated by such a frame. But if tachyons existed, and if they could interact, one might be able to design some type of "clock" out of tachyonic matter even if its rate of ticking at various speeds could not be inferred from the Lorentz transform. And it is true that if such a tachyonic clock could exist, then if it was ticking forward in some frames it would necessarily be ticking backwards in others.

I do agree with you that the only thing standing in the way of FTL or B-I-T signaling is causality problems, which itself is a dubious concept. We all know in QM traditional causality gets thrown out the window.

"Causality" in physics is not really the same as vague philosophical notions of "cause and effect" (which are dubious even in classical physics because classical laws are time-symmetric and thus there's no basis for saying the present state of the universe is determined by its past state but not by its future state). In quantum field theory it is still provably impossible to use measurements at one location to gain information about any events outside the light cone of that point, so quantum theory is still said to obey causality.

Maybe there will be a way to learn information about the future via a signal from it; but that doesn't mean anyone suddenly found themselves hundreds of years in the past. That will never happen.

In terms of causal paradoxes, being able to send information into the past is every bit as problematic as sending matter into the past (you could send a message to your younger self trying to get them to change history, or even upload your mind into a computer simulation and send your mind back in time), so I don't see why you'd be so confident that the latter will never happen if you think the first is possible. General relativity does open up the possibility of material objects going back in time and interacting with earlier points on their own worldline, though many physicists would probably bet on quantum gravity eliminating this possibility.

 

[peter0302]

According to quantum indistinguishability I think it's basically meaningless to ask whether the teleported system is really the "same" as the original system or whether it's really a "copy", for the same sort of reasons that it's meaningless to ask which slit a photon in the double-slit experiment "really" went through in cases where you see an interference pattern (under certain interpretations of QM these questions might have a true answer, but an answer that would be impossible in principle to determine experimentally).

Ok, I take it you'll be first in line to volunteer for the quantum transporter?

In terms of causal paradoxes, being able to send information into the past is every bit as problematic as sending matter into the past (you could send a message to your younger self trying to get them to change history, or even upload your mind into a computer simulation and send your mind back in time), so I don't see why you'd be so confident that the latter will never happen if you think the first is possible.

Two reasons: 1) signaling is not travel; 2) MWI avoids causality paradoxes.

 

[cristo]

1) signaling is not travel;

As stated above, "signalling" is sending information into the past. How do you propose this information is sent?

 

[Antenna Guy]

"Causality" in physics is not really the same as vague philosophical notions of "cause and effect"

You don't seem to realize that logic falls with the domain of philosophy.

Regards,

Bill

 

[JesseM]

Ok, I take it you'll be first in line to volunteer for the quantum transporter?

Quantum transportation of macroscopic objects is pretty ridiculously futuristic, but if some form of transporter had been invented (even a non-quantum one that was able to measure the position and momentum of every atom in an object up to the limits of the uncertainty principle) and had been tested on other brainy organisms with no evidence of long-term problems...well, I still probably wouldn't volunteer to be the first human to try it (their might be some kind of subtle errors in reproducing the brain that just weren't apparent in animals), but my objections wouldn't be on the philosophical grounds that it'd just be a "copy" and not really "me" (after all, the matter which makes up my brain is almost completely replaced by new matter every two months or so according to http://www.dichotomistic.com/mind_readings_molecular_turnover.html, but I'm not worried that I'm going to be replaced by a 'copy' in two months just because my brain won't be made of the same atoms).

Two reasons: 1) signaling is not travel; 2) MWI avoids causality paradoxes.

You can't have it both ways! If the MWI avoids the dangers of paradoxes for sending information back in time, then it would obviously do the same for sending physical objects back in time (which as I said might be possible according to general relativity). The point is that there is absolutely no good reason to think that sending objects back in time is any more physically problematic than sending information back in time.

 

[JesseM]

You don't seem to realize that logic falls with the domain of philosophy.

What's your point? Just because logic is a part of philosophy and is also used in science, that doesn't mean all philosophy (including notions of 'cause and effect' which are not part of logic) is part of science too. Just think of it as a Venn diagram with "logic" in the overlap between the circle marked "philosophy" and the circle marked "concepts essential to science".

 

[peter0302]

Quantum transportation of macroscopic objects is pretty ridiculously futuristic, but if some form of transporter had been invented (even a non-quantum one that was able to measure the position and momentum of every atom in an object up to the limits of the uncertainty principle) and had been tested on other brainy organisms with no evidence of long-term problems...well, I still probably wouldn't volunteer to be the first human to try it (their might be some kind of subtle errors in reproducing the brain that just weren't apparent in animals), but my objections wouldn't be on the philosophical grounds that it'd just be a "copy" and not really "me" (after all, the matter which makes up my brain is almost completely replaced by new matter every two months or so according to http://www.dichotomistic.com/mind_readings_molecular_turnover.html, but I'm not worried that I'm going to be replaced by a 'copy' in two months just because my brain won't be made of the same atoms).

Wow, ok, a very interesting (and consistent) viewpoint.

You can't have it both ways! If the MWI avoids the dangers of paradoxes for sending information back in time, then it would obviously do the same for sending physical objects back in time (which as I said might be possible according to general relativity). The point is that there is absolutely no good reason to think that sending objects back in time is any more physically problematic than sending information back in time.

Well you didn't my earlier post where I mentioned GR opens up possibilities for time travel. But if you do go into the past - or send a signal into the past - it will be a different past than yours and won't affect yours. You can't do the Back to the Future thing where you change the past and come back to a different future. I think mainstream physicists are unanimous that that is not possible under any theoretical model. Anyway, that's "time travel" to me. If the OP meant something different, he should clarify.

Oh and Cristo, I don't know what your point is. Signaling and travel are two different things because, if for no other reason, one can happen at the speed of light, and the other cannot.

 

[Antenna Guy]

What's your point?

That you don't seem to understand philosophy.

Just because logic is a part of philosophy and is also used in science, that doesn't mean all philosophy (including notions of 'cause and effect' which are not part of logic) is part of science too.

"cause and effect" and "if this then that" are different ways of saying the same thing. Consider: "if these are your initial conditions (cause), then this is what results (effect)". Causality is not the ambiguous concept you make it out to be.

Regards,

Bill

 

[JesseM]

That you don't seem to understand philosophy.

Perhaps you could point out what specific aspect I don't understand.

"cause and effect" and "if this then that" are different ways of saying the same thing.

Not according to any philosopher I've ever read. For example, we could say that "if X is a human, then X must have a mother", but you wouldn't say the person "caused" their mother. You can read the article The Metaphysics of Causation from the Stanford Encyclopedia of Philosophy to see a discussion of causation in philosophy (along with related articles like Causal Processes and Counterfactual Theories of Causation and Probabilistic Causation and Backward Causation), it's a lot more complicated then just logical implications of the form "if X, then Y" (if you think there are any professional philosophers who say causation is nothing more than logical implication, please name them).

 

[Antenna Guy]

Perhaps you could point out what specific aspect I don't understand.

How much you rely upon it.

If you wish to discuss this further, I'd suggest either PM, or another forum.

Regards,

Bill

 

[JesseM]

How much you rely upon it.

If you wish to discuss this further, I'd suggest either PM, or another forum.

OK, please start a thread in the appropriate forum (philosophy, I assume) that discusses why you think I was incorrect to say that "vague philosophical notions of cause and effect" (like the ones discussed in the articles I linked to) don't have much relevance to physics.

 

[peter0302]

Hey Bill, if you can provide a mathematically rigorous definition of "causation" I'd love to see it.

 

[atyy]

Would this answer work? - Light has to do with time travel, because anything that travels at the speed of light doesn't experience time.

 

[JesseM]

Would this answer work? - Light has to do with time travel, because anything that travels at the speed of light doesn't experience time.

No, in relativity anything moving at the speed of light won't have its own inertial rest frame, so you can't really talk about what it "experiences".

 

[atyy]

No, in relativity anything moving at the speed of light won't have its own inertial rest frame, so you can't really talk about what it "experiences".

That seems consistent with what I suggested. However, to consider your objection, the proper time of a trajectory of light is not undefined. It is well defined to be zero.

 

[peter0302]

Huh?

If you mean the time dilation equation yields zero as v->c, that is true. But when v=c, the answer is most certainly not well defined. It is 1 / sqrt(0). Last time I checked, 1 / 0 was still undefined.

 

[JesseM]

That seems consistent with what I suggested. However, to consider your objection, the proper time of a trajectory of light is not undefined. It is well defined to be zero.

It's true that along a photon worldline the proper time is zero. I don't really see what this has to do with time travel, though.

 

[atyy]

It's true that along a photon worldline the proper time is zero. I don't really see what this has to do with time travel, though.

Just time travel in the normal sense, where it is said that we do travel through time - at the rate of 1 second per second

Actually, there is an interesting heuristic I've heard. From the "missing" solar neutrinos, it was hypothesized that neutrinos "oscillate". If null-particles don't "experience" time, then they cannot "oscillate". So if neutrinos "oscillate", they cannot be null-particles. I don't know if this language can be turned into something well-defined, since photons obviously oscillate too in some sense.

 

[eNathan]

Just wondering what the connection is between them, I understand that it relative to what we see but time in general? why not the speed of sound as its only another sense right? Just interested to know why light is so special?

thanks guys,

Sorry messed up title should be speed of light! doh!

Wow, this thread is certiantly turning into a train wreak.. always nice to see that happen without someone wanting to stop it

Short answer: Let's define "time travel," according to Special Relativity, to be observers experiencing different amounts of elapsed time due to your velocity relative to each other. Light itself has virtually nothing to do with this definition of "time travel," however, the speed that light naturally travels at has much to do with it! The faster an object's velocity, the slower time will run when compared to another frame of reference. Let's say a stationary frame of reference, to keep things easy.

What happends if you reach the speed of light? Time stops. Of course, this is just silly hypothetical non-reality physics, but everybody loves to think it would. Consequently, ftl travel would logically mean reverse time travel. These concepts are what give birth to science fiction works for the most part. However, SR itself is definatly not fiction.

But agian, why is it the speed of light that's so special? Anything that has 0 mass, such as light, will indefinatly travel at the speed of light for reasons I won't go into here. It is theorized that gravity -- if it travels -- does so at light speed (c). So again, it's not that light is special, but the speed of light definatly is.

Light is special because it does not require a medium in which to propagate.

Isn't the medium of space required for light to propagate?

 

[JesseM]

What happends if you reach the speed of light? Time stops. Of course, this is just silly hypothetical non-reality physics, but everybody loves to think it would. Consequently, ftl travel would logically mean reverse time travel.

If you mean that a clock moving at light speed would be stopped, and therefore that a clock moving faster than light would be running backwards, you're wrong, the Lorentz transformation simply doesn't give a meaningful answer about the rate of ticking of an FTL clock (if you try to apply the Lorentz transformation to an FTL clock, you get the nonsensical answer that the time between its ticks would be an imaginary number). As I've said before, the reason FTL is associated with time travel has nothing to do with FTL clocks or what would be seen by an FTL observer, and everything to do with how FTL signals would look from the perspective of slower-than-light observers; because different slower-than-light frames define simultaneity differently, if you have a signal that moves FTL, it will always be possible to find a frame where the time that a message is received is actually earlier than the time it was sent.

 

[atyy]

Actually, there is an interesting heuristic I've heard. From the "missing" solar neutrinos, it was hypothesized that neutrinos "oscillate". If null-particles don't "experience" time, then they cannot "oscillate". So if neutrinos "oscillate", they cannot be null-particles. I don't know if this language can be turned into something well-defined, since photons obviously oscillate too in some sense.

So it turns out this can actually make some sense.

The absence of neutrino oscillations does not mean that neutrinos have zero mass. However, the existence of neutrino oscillations imply that at least one neutrino has mass. Each neutrino is itself a wave, and the mass difference is the change in relative phase between neutrino waves. What has this got to do with light not "experiencing" time?

The idea that light does not "experience" time can be made sensible in a limited way. For example, light moves relative to us, so we can use the successive peaks and troughs of a light wave moving past us to measure time. In this sense, we "experience" time. However, the speed of light is the same for light of all frequencies, so light does not move relative to light. If two light waves of different frequencies set out in the same direction, any particular peak in one of the waves will not move relative to the nearest peak or trough in the other wave. It will never experience the peaks and troughs of the other wave moving past it. In this sense, a light wave does not "experience" time.

So basically, light not "experiencing" time means that light waves of different frequencies maintain constant relative phase. Furthermore, by analogy to neutrino oscillations, a "photon oscillation" would be a change in relative phase between two light waves of different frequencies. For this to happen, there must be a slight difference in their velocities, and at least one wave cannot travel at the speed of light. Since things that do not travel at the speed of light must have mass, "photon oscillations" would imply that at least one frequency of light is massive.

http://en.wikipedia.org/wiki/Neutrino_oscillation
http://arxiv.org/abs/hep-ph/9905257

 

[WillBlake]

What's your point? Just because logic is a part of philosophy and is also used in science, that doesn't mean all philosophy (including notions of 'cause and effect' which are not part of logic) is part of science too. Just think of it as a Venn diagram with "logic" in the overlap between the circle marked "philosophy" and the circle marked "concepts essential to science".

Without getting too philosophical, science and philosophy are based on the same method of thinking which is an "if, then" system, there is no difference. Science boasts of having "facts" but these are simply agreed upon conjectures and labels which help us deal with reality as we sense it, just like philosophy does. Mysticism is outside these realms.

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light. This makes sense to me because time is also zero at the speed of light. So to travel back in time, we would have to go less than zero, by this reference point. More interesting, is the question as to why we can't go slower than zero as we conventionally define it? These two limits of speed are the same thing. If we can go slower, we can experience time at a faster rate. I would like to see some math which tackles the question of going slower than zero as we currently define it. This may answer your dilemma. My math is rusty, and I only have a doctorate of philosophy in biotechnology.

 

[JesseM]

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light. This makes sense to me because time is also zero at the speed of light.

The notion that time dilation approaches infinity as you approach the speed of light only applies to inertial coordinate systems in SR. You can invent a coordinate system where light is at rest and we are moving at c or close to it, but this is not a valid inertial coordinate system in SR, so you can't assume that time dilation in this system works anything like the way it works in inertial frames.

I would like to see some math which tackles the question of going slower than zero as we currently define it.

If you're asking about a speed slower than zero, then I've told you before that this is nonsense because of the very definition of speed. You might as well ask about a number whose absolute value is less than zero, or a square with five corners.

 

[atyy]

To provide my viewpoint on the speed of light and time, may I suggest the following: It is easier for me to understand these concepts, if I use the speed of light as the reference point, that is: it is zero and we are currently moving close to the speed of light.

I am going to speculate a bit here, so I don't know if this is right. I am using "!=" to mean "not equal".

Yes, it is interesting why we cannot set the speed of light to be zero, whereas we can set say 32^oF o be 0^oC. Anyway, it seems that as long as we only add or subtract temperatures, that is not a problem, because 0+5!=0+1 [Eqn 1]. If we do multiply temperatures, as in thermodynamics, then it does matter that we use absolute zero as a reference, not 0^oC, because 0X1=0X5.

Now, we can set the speed of light to be 1, because 1X5!=1X1 [Eqn 2]. Comparing Eqn 1 and Eqn 2, we see that 0 with respect to addition is like 1 with respect to multiplication. So if you want to define the speed of light as zero, it may work if you, for starters, define addition to be multiplication and multiplication to be addition. The mathematicians have thought long and hard about this and they call this "abstract algebra":
http://en.wikipedia.org/wiki/Group_(mathematics )
http://en.wikipedia.org/wiki/Field_(mathematics )
Note particularly in the definition of a field, that "For technical reasons, 1 is required not to equal 0."

You can certainly take the speed of light to be negative, as long as you interchange all positives and negatives in your equations.

The basic idea in the renaming game is that you can rename things anyway you like. One major rule is: you can give two different names to the same thing, but you cannot give two different things the same name. How to play the renaming game in physics is called "gauge theory". Now this game is obviously very confusing, so instead of reading Wikipedia on gauge theory, I recommend:
V Parameswaran Nair, Quantum Field Theory: A Modern Perspective (Springer, 2005)
Xiao-Gang Wen, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons (OUP 2004)
Peter Olver, Equivalence, Invariants and Symmetry (CUP 1995).
These books don't talk about renaming zero and one, but they talk about renaming 1 to be 3 and 8 to be 9, and zillions of other sorts of renaming.

 

[JesseM]

Yes, it is interesting why we cannot set the speed of light to be zero

You can, but just not if you use an inertial coordinate system.

You can certainly take the speed of light to be negative, as long as you interchange all positives and negatives in your equations.

Not without changing the definition of speed, which is normally defined as the norm of the velocity vector (and the norm of a vector is positive)

 

[atyy]

You can, but just not if you use an inertial coordinate system.

Oooh interesting! How does that work in a non-inertial frame?

Not without changing the definition of speed, which is normally defined as the norm of the velocity vector (and the norm of a vector is positive)

Yes, I should have said velocity. Perhaps we can also reverse the signature convention?

 

[JesseM]

Oooh interesting! How does that work in a non-inertial frame?

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

 

[atyy]

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

That seems to be somewhat different from setting c=0. It seems to be more about where we set x or t to be 0?

 

[atyy]

You can define a non-inertial coordinate system in pretty much any arbitrary way you dream up. For instance, if we define the coordinates of some inertial frame as x and t, here's a simple coordinate transformation that gives a non-inertial frame where the speed of photons moving in the +x direction will be zero:

x' = x - ct
t' = t

OK, that seems to work.

 

[JesseM]

That seems to be somewhat different from setting c=0.

What do you mean by "setting c=0"? When people talk about setting c=1 they really must mean picking a system of units where c has a value of 1 in those units, but they're still assuming the same kind of inertial coordinate systems where c is the maximum speed. I'm talking about picking a coordinate system where the speed of photons in one direction is zero, regardless of your choice of units.

It seems to be more about where we set x or t to be 0?

Well, it's about the whole coordinate system, not the placement of the origin. In the example I gave, the non-inertial coordinate system's origin coincided with that of the inertial one, but you could also come up with a transformation where the origin x=0,t=0 of the inertial frame corresponded to some other position x'=X,t'=T in the non-inertial one:

x' = x - ct + X
t' = t + T

You can see that the placement of the origin doesn't matter here, it's still true that a photon moving in the +x direction of the inertial frame has a speed of 0 in the non-inertial one.

 

[atyy]

What do you mean by "setting c=0"? When people talk about setting c=1 they really must mean picking a system of units where c has a value of 1 in those units, but they're still assuming the same kind of inertial coordinate systems where c is the maximum speed. I'm talking about picking a coordinate system where the speed of photons in one direction is zero, regardless of your choice of units.

Yes, that's why I didn't understand your proposal right away.

Well, it's about the whole coordinate system, not the placement of the origin. In the example I gave, the non-inertial coordinate system's origin coincided with that of the inertial one, but you could also come up with a transformation where the origin x=0,t=0 of the inertial frame corresponded to some other position x'=X,t'=T in the non-inertial one:

x' = x - ct + X
t' = t + T

You can see that the placement of the origin doesn't matter here, it's still true that a photon moving in the +x direction of the inertial frame has a speed of 0 in the non-inertial one.

Does this have anything to do with black holes?

 

[JesseM]

Does this have anything to do with black holes?

Not that I know of, it's just a different coordinate system to use in flat spacetime, whereas black holes necessarily involve curved spacetime...what made you think of them? I guess the only relationship I can think of is that in GR only local coordinate systems can be inertial ('local' meaning coordinate systems in an arbitrarily small neighborhood of an event, small enough that curvature is negligible), so any coordinate system you use to describe an entire black hole spacetime will be non-inertial, and therefore you can't guarantee that light will still move at c in this system (for example, in Schwarzschild coordinates light rays can actually be frozen at the event horizon, although in the locally inertial coordinate system of a freefalling observer passing right next to the ray as he crosses the horizon, the ray would still be moving at c).

 

[atyy]

Not that I know of, it's just a different coordinate system to use in flat spacetime, whereas black holes necessarily involve curved spacetime...what made you think of them?

for example, in Schwarzschild coordinates light rays can actually be frozen at the event horizon, although in the locally inertial coordinate system of a freefalling observer passing right next to the ray as he crosses the horizon, the ray would still be moving at c

Yes, I was wondering about that. The difference there is between coordinate time and proper time. So similarly for velocities, there is coordinate velocity c_x, and "proper velocity" c (not a standard term). The former can be set any way we want, as long as the transformation preserves the rank of the Jacobian, I think. The latter is a conversion factor between space and time, and I suspect cannot be set to zero because of our choice of notation to describe the field structure of the real numbers. Physically, I'm guessing that we cannot set the conversion factor between space and time, nor the conversion factor between spatial x and spatial y, to be zero because that would be equivalent to reducing spacetime from 4 to 3 dimensional. A second reason must be somehow related to idea that we cannot set the proper time of light to anything except zero.

 

[JesseM]

Yes, I was wondering about that. The difference there is between coordinate time and proper time.

Is it only that, or is there also an issue with coordinate position vs. position as measured in a local inertial coordinate system? I don't know enough about Schwarzschild coordinates to say.

So similarly for velocities, there is coordinate velocity c_x, and "proper velocity" c (not a standard term).

What do you mean by "proper velocity"? Something to do with velocity as measured in local inertial frames? Of course for any object moving slower than light, different local freefalling observers will measure its velocity differently in their own local inertial frame.

The latter is essentially the conversion factor between space and time, and I suspect cannot be set to zero because of our choice of notation to describe the field structure of the real numbers. Physically, I'm guessing that we cannot set the conversion factor between space and time, nor the conversion factor between spatial x and spatial y, to be zero because that would be equivalent to reducing spacetime from 4 to 3 dimensional.

I can't really evaluate what you're saying without knowing how you are defining "proper velocity". As for the conversion factor between space and time, it's the metric which gives you a line element at every point, and that line element tells you how to integrate dt, dx, dy, and dz in your chosen coordinate system in order to get the physical value for the integral of ds along a given path through spacetime (if you're integrating along a timelike worldline, the integral of ds is usually just the proper time converted into a distance). If your coordinate system is an inertial one in flat spacetime, the line element is the familiar ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, where you're multiplying dt by the "conversion factor" of c before adding it to the spatial increments, but for non-inertial coordinate systems the line element might look completely different. For example, p. 116 of this book mentions that in Schwarzschild coordinates the line element would be:

ds^2 = (1 - \frac{2m}{r}) c^2 dt^2 - \frac{1}{(1 - \frac{2m}{r})} dr^2 - r^2 ( d\theta^2 + r^2 sin^2 \theta d\phi^2 )

So you still have the c^2 factor included in the function you're multiplying dt^2 by (which makes sense since everything is supposed to be in units of distance rather than time), but you're also multiplying by a more complicated function as well.

 

[atyy]

I can't really evaluate what you're saying without knowing how you are defining "proper velocity". As for the conversion factor between space and time, it's the metric which gives you a line element at every point, and that line element tells you how to integrate dt, dx, dy, and dz in your chosen coordinate system in order to get the physical value for the integral of ds along a given path through spacetime (if you're integrating along a timelike worldline, the integral of ds is usually just the proper time converted into a distance). If your coordinate system is an inertial one in flat spacetime, the line element is the familiar ds^2 = c^2 dt^2 - dx^2 - dy^2 - dz^2, where you're multiplying dt by the "conversion factor" of c before adding it to the spatial increments, but for non-inertial coordinate systems the line element might look completely different. For example, p. 116 of this book mentions that in Schwarzschild coordinates the line element would be:

ds^2 = (1 - \frac{2m}{r}) c^2 dt^2 - \frac{1}{(1 - \frac{2m}{r})} dr^2 - r^2 ( d\theta^2 + r^2 sin^2 \theta d\phi^2 )

So you still have the c^2 factor included in the function you're multiplying dt^2 by (which makes sense since everything is supposed to be in units of distance rather than time), but you're also multiplying by a more complicated function as well.

By "proper velocity" I just meant "c" everywhere in your equations. For example, the non-inertial transformation you first suggested "x'=x-ct, t'=t" doesn't set c=0, it makes the coordinate velocity zero, which is why I was initially confused by your suggestion. I just needed a term to distinguish "c" from the coordinate velocity c_x, and made up "proper velocity" by analogy to "proper time" as an invariant quantity. The line element is some complicated function in general, but I think of "c" as the conversion factor between space and time because it always goes with cdt, no matter how complicated the expression is.

Anyway, to summarize:

1) c_x can be set in any way consistent with a smooth coordinate transfomation, including the nice example you gave

2) c can be set arbitarily to anything except 0, because (this is the speculative part):

-our notation of the field structure of the real numbers defines 0 as the identity under addition, and 1 as the identity under multiplication, so setting c to 0 is not a problem if we only did addition, but it is a problem if we do multiplication because multiplying by 0 gives different things the same name.

-c is the conversion factor between space and time, if you set it to zero, you will be reducing spacetime form 4 to 3 dimensions. However, this cannot be the complete reason, because we can always use some other velocity to do the conversion.

-the proper time of light must be zero, and this corresponds to c being non-zero.

 

[JesseM]

I think you're making this over-complicated...if we're just talking about unit conversions rather than coordinate transformations, no sensible unit conversion will make any quantity which is nonzero in one system of units be zero in the other (unless we're measuring something where by convention we allow the value to be negative or positive, like temperature in degrees celsius). For example, if I used a crazy system of distance units called "kookoos" with the conversion 1 meter = 0 kookoos, that would mean that any finite number of meters would be 0 kookoos, and any finite number of kookoos would be an infinite number of meters--not a very useful set of units for measuring distances in the real world! And this point about unit conversions applies regardless of whether what I'm measuring is the speed of light, or the speed of a car in some particular frame, or the distance from New York to Los Angeles, or my own weight.

 

[atyy]

I think you're making this over-complicated...if we're just talking about unit conversions rather than coordinate transformations, no sensible unit conversion will make any quantity which is nonzero in one system of units be zero in the other (unless we're measuring something where by convention we allow the value to be negative or positive, like temperature in degrees celsius). For example, if I used a crazy system of distance units called "kookoos" with the conversion 1 meter = 0 kookoos, that would mean that any finite number of meters would be 0 kookoos, and any finite number of kookoos would be an infinite number of meters--not a very useful set of units for measuring distances in the real world! And this point about unit conversions applies regardless of whether what I'm measuring is the speed of light, or the speed of a car in some particular frame, or the distance from New York to Los Angeles, or my own weight.

I'd quite happily set my weight to 0.

 

[WillBlake]

The notion that time dilation approaches infinity as you approach the speed of light only applies to inertial coordinate systems in SR. You can invent a coordinate system where light is at rest and we are moving at c or close to it, but this is not a valid inertial coordinate system in SR, so you can't assume that time dilation in this system works anything like the way it works in inertial frames.

If you're asking about a speed slower than zero, then I've told you before that this is nonsense because of the very definition of speed. You might as well ask about a number whose absolute value is less than zero, or a square with five corners.

If I understand this statement correctly, we do not have an appropriate system to set the speed of light to zero. Is this an insurmountable problem? If so, it is too bad, because I feel it would serve as a better method for measuring reality. Moment to moment, time is zero, its passage is just an illusion due to our speed (or is it velocity? :-)).

 

[sanman]

Hi guys, I am responding to comments on the train thought experiment from the first page of this thread. Hope I'm not derailing the conversation. (inadvertent pun)

Anyway, just because one were to propagate information about an event FTL, that doesn't mean one is violating causality, because the propagation of that event would still be happening after the fact of that event. I think Hawking himself made comments to this effect, a few years back. As long as you accept that what you are seeing has already happened before you observed it, then "time travel" is really reduced to "time dilation/contraction".

But one thing that's always bothered me is the question of why the speed of light is always the same to every observer, regardless of reference frame velocity.
How is it possible for light to exhibit this characteristic?
What is the underlying reason for it?

And of course, why does the speed of light have the particular value it has? (ie. 3x10^8 m/s)
What were to happen if it were twice that speed, or two-thirds that speed?
What would be the consequences? How would our universe change?