Trying to understand how FTL would violate causality....

[Herman Trivilino]

As @Nugatory mentioned, this is not exactly the way to say it, but it is pretty close. The way to say what you want to say "If we were to discover that the photon has some extremely small but non zero mass"

Right. Or that if we were to discover that light has a speed relative to its source that's less than the maximum possible speed.

 

[Battlemage!]

As phrased, your question is inconsistent because if the speed of light is not exactly equal to the invariant maximum speed $c$, then its value is necessarily frame-dependent (as are all speeds less than $c$). Thus, there will exist frames in which light travels at speeds arbitrarily close to zero, and the hypothesis "the speed of light is really, really close to the maximum speed" is ill-formed.

What I mean in this make believe universe is that there is an invariant speed, but light isn't it. It's just much closer to it than anything else.

 

[PeterDonis]

It's just much closer to it than anything else.

And Nugatory's point is that, if light does not travel at the invariant speed, then how "close" the speed of light (meaning, the actual speed at which light is measured to travel) is to the invariant speed is frame-dependent; there will be frames in which the speed of light is not closer to the invariant speed than the speed of anything else. In fact, there will be frames in which the speed of light is zero--in which light is at rest.

 

[Battlemage!]

And Nugatory's point is that, if light does not travel at the invariant speed, then how "close" the speed of light (meaning, the actual speed at which light is measured to travel) is to the invariant speed is frame-dependent; there will be frames in which the speed of light is not closer to the invariant speed than the speed of anything else. In fact, there will be frames in which the speed of light is zero--in which light is at rest.

But shouldn't that only be a problem if the speed of light is the invariant speed?

 

[Nugatory]

But shouldn't that only be a problem if the speed of light is the invariant speed?

It is a problem for your description of that world: "The speed of light is really close to the invariant velocity". That's why Dale suggested that you think in terms of the photon rest mass instead.

 

[Battlemage!]

It is a problem for your description of that world: "The speed of light is really close to the invariant velocity". That's why Dale suggested that you think in terms of the photon rest mass instead.

Well let me ask another question, if you don't mind, so I can better grasp the situation:

Let's go back to actual special relativity. Say I am traveling parallel to the direction of a beam of light, and I try to look at a photon moving along the direction of the beam. Could I ever see that photon, as opposed to photons radiating perpendicularly to the beams which are (I'm assuming) the ones I normally see in such scenarios?

 

[Ibix]

You can only see a photon that hits a sensor such as your eye. If you see a laser beam, for example, what you are actually seeing is light scattered from the beam because it's passing through a scattering medium. This is why nightclubs pump in smoke before shining lasers through them. Also why it's always cloudy above Gotham. Batman wouldn't be able to see the bat signal on a clear starry night.

 

[Battlemage!]

You can only see a photon that hits a sensor such as your eye. If you see a laser beam, for example, what you are actually seeing is light scattered from the beam because it's passing through a scattering medium. This is why nightclubs pump in smoke before shining lasers through them. Also why it's always cloudy above Gotham. Batman wouldn't be able to see the bat signal on a clear starry night.

I thought as much.

So, if light isn't the maximum speed and I'm moving away from a photon at the same speed as the photon, I'd never see it, correct? I'm not seeing the logical inconsistency if the universe is Lorentz invariant but the speed of light isn't the maximum speed (aside from the fact that Maxwell's equations obviously suggest light as the speed limit). Since this isn't a homework thread, could someone spell it out for a dummy like myself? :)

 

[Ibix]

There isn't one. There is a logical inconsistency if there are two invariant speeds, which tells you that if light does not travel at the invariant speed then it does not have a single defined speed. There is no "speed of the neutron" and there would be no "speed of the photon". That's the point being made here - talking about "the speed of light not being the same as the invariant speed" is slightly wrong because in that case light doesn't have "a" speed, it has many. Better to talk about the photon having zero mass (and traveling at a well defined invariant speed) or non-zero masd (and acting like any other particle).

 

[Nugatory]

I'm not seeing the logical inconsistency if the universe is Lorentz invariant but the speed of light isn't the maximum speed (aside from the fact that Maxwell's equations obviously suggest light as the speed limit). Since this isn't a homework thread, could someone spell it out for a dummy like myself? :)

If the universe is Lorentz invariant, then it would be impossible for the speed of light to be "really, really close to the invariant speed", as you were trying to specify. Either it would be exactly the invariant speed or light would work like everything else from snails to bullets to cosmic muons and any number between zero and the invariant speed would be "the speed of light" depending on the frame we choose. The underlying problem is that the phrase "the speed of X" is undefined for all X not moving at the invariant speed; the invariant speed is unique in that you don't have to say what it is relative to.

If you want to describe a universe in which light does not travel at the invariant speed yet is close to the "speed of light is $c$" universe we think we live in, you would say "a universe in which photons have a very small rest mass".

 

[Battlemage!]

There isn't one. There is a logical inconsistency if there are two invariant speeds, which tells you that if light does not travel at the invariant speed then it does not have a single defined speed. There is no "speed of the neutron" and there would be no "speed of the photon". That's the point being made here - talking about "the speed of light not being the same as the invariant speed" is slightly wrong because in that case light doesn't have "a" speed, it has many. Better to talk about the photon having zero mass (and traveling at a well defined invariant speed) or non-zero masd (and acting like any other particle).

If the universe is Lorentz invariant, then it would be impossible for the speed of light to be "really, really close to the invariant speed", as you were trying to specify. Either it would be exactly the invariant speed or light would work like everything else from snails to bullets to cosmic muons and any number between zero and the invariant speed would be "the speed of light" depending on the frame we choose. The underlying problem is that the phrase "the speed of X" is undefined for all X not moving at the invariant speed; the invariant speed is unique in that you don't have to say what it is relative to.

If you want to describe a universe in which light does not travel at the invariant speed yet is close to the "speed of light is $c$" universe we think we live in, you would say "a universe in which photons have a very small rest mass".

Ah. When I said light might be really close to the maximum speed in this hypothetical universe, I meant just according to our current measuring devices sitting here at rest in our own frame.

Just like when we accerate particles "close to the speed of light" here in the real universe. Obviously in the frame of the hypervelocity particles, pulses of light still move away from them at c, but yet we can measure them to achieve near light speed.What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell? For example, in real life I imagine the first attempts to measure the speed of light might have ended with people believing it was infinite.

 

[Nugatory]

What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell

Sure. Google for "photon mass upper bound" and you'll find some discussion of different ways of calculating the maximum photon mass that would be consistent with current experiments.

For example, in real life I imagine the first attempts to measure the speed of light might have ended with people believing it was infinite.

The first recorded measurement of the speed of light was made by Galileo in 1638, and he carefully avoided going beyond what his experimental results (at least ten times the speed of sound) supported: "If not instantaneous, it is extraordinarily rapid".

 

[timmdeeg]

What I'm wondering is the following: IF light wasn't the speed limit, is there a logical scenario where our experiments might not be sensitive enough to tell?

In a practical sense this would mean that the speed of light emitted by a lamp which you measure in your frame depends on the relative motion between you and the lamp. If you adjust your speed closer and close to that of the lamp, then the speed of the light of this lamp will slower and slower measured in you frame.

 

[Battlemage!]

In a practical sense this would mean that the speed of light emitted by a lamp which you measure in your frame depends on the relative motion between you and the lamp. If you adjust your speed closer and close to that of the lamp, then the speed of the light of this lamp will slower and slower measured in you frame.

Yes but in practice we wouldn't be able to do that for a long while, which would mean in this hypothetical universe we might not be able to know that light wasn't the maximum speed.

After all, the speed transformstion equation is asymptotic (it can always approach bit never reach c), right?
On a slightly off topic note, here's an experiment verifying the Lorentz invariance of the kinetic energy of electrons, if I didn't miss read the anstract.

http://www.nature.com/nature/journal/v517/n7536/full/nature14091.html

 

[ArmChairPhysicist]

Now I could be wrong, but in the study I've done and thinking about the issue of "Time travel" and causality, neither exist. They are fantasy. If you went faster than light you will arrive at a destination faster, but not at a date that has not occurred. Due to dilation your physical system will have only experienced a short travel time, where as real time continued on. To paraphrase, a for every minute realtime, you and your area only experienced a few seconds. Everyone else observing experienced a minute and observed you experiencing a minute, but in your bubble that minute was only a few seconds. Note that these aren't real measurements, simply describing how I see this to work.
Logically and from what we have seen in science, time travel as we see in popular culture is impossible. That which has happened has already passed, that which has not happened doesn't exist, there is only now. You can adjust the relative "frame rate" of your time by attaining high speeds, but you aren't jumping forward or backward.

 

[PeterDonis]

for every minute realtime

There is no "realtime" in relativity; time is not absolute.

That which has happened has already passed, that which has not happened doesn't exist, there is only now.

There is no "now" in relativity; simultaneity is not absolute.

you aren't jumping forward or backward

If I rephrase this as "your path through spacetime must be continuous; it can't have jumps in it", then it is true. But it doesn't follow from the rest of the things you have said.

 

[timmdeeg]

Yes but in practice we wouldn't be able to do that for a long while, which would mean in this hypothetical universe we might not be able to know that light wasn't the maximum speed.

We would know that the speed of the light isn't invariant, because we have proofed that it depends on relative motion.

 

[Battlemage!]

We would know that the speed of the light isn't invariant, because we have proofed that it depends on relative motion.

What if, in this strange new universe, the difference is too small to detect? That is, what if the fringe shift in a newer Michaelson-Morley experiment is just too small to detect?

 

[Ibix]

It's still possible that photons do have a very very small mass. The upper bound consistent with experiment is absurdly low (because photons with mass have broader implications for electromagnetism than just slower speeds), but it is not and never will be zero.

In terms of relativity, we would just have to stop calling c the speed of light. And come up with a substitute for the light clock experiment.

 

[timmdeeg]

It's still possible that photons do have a very very small mass.

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

 

[Nugatory]

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

If you assume that these speeds are invariant, yes - there can be only one invariant speed, so they have to be the same. And there are fairly convincing theoretical reasons to expect both speeds to be invariant.

 

[timmdeeg]

If you assume that these speeds are invariant, yes- there can be only one invariant speed, so they have to be the same.

Yes, in this case.
The similarity is that in both cases oscillating charges and oscillating masses as well are emitting waves which propagate through empty space and can be detected elsewhere. So, naively one could suspect here a connection on a deeper level with the effect that both are either invariant (necessarily the same invariant speed then) or not. I'm not sure if this makes sense.

 

[Ibix]

If you assume that these speeds are invariant, yes - there can be only one invariant speed, so they have to be the same. And there are fairly convincing theoretical reasons to expect both speeds to be invariant.

I understand that the speed of gravitational waves drops out of the Einstein field equations, so more or less has to be the invariant speed unless we're chucking GR out of the window. But I thought it was possible to construct massive photons in a coherent way - Proca's work, further developed by Yukawa, I gather (e.g. https://galileospendulum.org/2013/07/26/what-if-photons-actually-have-mass/).

 

[Nugatory]

I understand that the speed of gravitational waves drops out of the Einstein field equations, so more or less has to be the invariant speed unless we're chucking GR out of the window. But I thought it was possible to construct massive photons in a coherent way - Proca's work, further developed by Yukawa, I gather (e.g. https://galileospendulum.org/2013/07/26/what-if-photons-actually-have-mass/).

That's what the hedge about "fairly convincing" was for.

 

[PAllen]

Is there a theoretical reason to assume the same propagation velocity of electromagnetic- and gravitational waves?

In classical GR there is a theoretical reason for GW to travel at the invariant speed. This is independent of whether you include EM in the matter energy sector of your GR model.

 

[timmdeeg]

In classical,GR there is a theoretical reason for GW to travel at the invariant speed. This is independent of whether you include EM in the matter energy sector of your GR model.

Okay, thanks.