Red/Blue Shift for measuring absolute velocity

[Ahkilleux]

Would it be possible to stand at a point, surrounded by sensors and fire beam of light of at specific frequency at every sensor and determine our absolute velocity without a reference based on the amount of red/blue shift detected in the frequency of each beam?

Wouldn't light observed by the detector in the direction you are moving fastest toward be red shifted by a greater magnitude than any of the other beams?

 

[Simon Bridge]

Would it be possible to stand at a point, surrounded by sensors and fire beam of light of at specific frequency at every sensor and determine our absolute velocity without a reference based on the amount of red/blue shift detected in the frequency of each beam?

No

Wouldn't light observed by the detector in the direction you are moving fastest toward be red shifted by a greater magnitude than any of the other beams?

No - the detector you are moving fastest towards would see the light blue-shifted.
The Doppler Shift would tell you your velocity with respect to the reference frame that the detectors are in. How do you know the detectors are absolutely stationary?

 

[Dale]

Would it be possible to stand at a point, surrounded by sensors and fire beam of light of at specific frequency at every sensor and determine our absolute velocity without a reference based on the amount of red/blue shift detected in the frequency of each beam?

Wouldn't light observed by the detector in the direction you are moving fastest toward be red shifted by a greater magnitude than any of the other beams?

The relativistic Doppler shift depends only on the relative velocity between detector and emitter. It does not depend on the absolute velocity of either.

 

[Ahkilleux]

"How do you know the detectors are absolutely stationary?" They wouldn't be. They would be moving at the same velocity as the emitter. But time would have passed between when the light was emitted and when it was received, so the true distance covered would be greater for some of the receivers and lesser for others.

My understanding is that it would take the same amount of measured time for the light to cover any of those distances, but does that also mean that the light would not be red or blue shifted?

One of the receivers would be moving away from the emitter's initial location ( though not away from the emitter ) and so one of those beams would cover more distance. I suppose the question is, even though it will take the same amount of perceived time for the beam to cover the longer distance, would the light be red shifted?

 

[Simon Bridge]

If emitter and detector are moving at the same speed there would be no doppler-shift.
An observer moving with the emitter would see the light hit the detectors simultaneously. As far as they are concerned the distance covered is the same in each case: the detectors are not moving.

An observer moving at a different relative speed would see different timings depending on the speed difference. The detectors are moving in their reference frame. This is what gives rise to time dilation: some beams travel a longer distance and they take longer to do this.

Remember: the speed of light is the same for all observers ... you cannot have the light travel a longer distance in the same perceived time without a broken clock.

 

[Ahkilleux]

Okay, I think I am starting to wrap my head around what you are saying. So relative to both the emitter and the receivers frames of reference the distance between them that the light travels is the same regardless of the fact that they may actually be moving at a high velocity and the point at which the beam actually hits the receiver may be no where near where the receiver was when the beam was fired.

However, if it were possible for an observer to be holding perfectly still in space and see this he would in fact see the beam travel the much greater distance over the course of a greater perceived time with the speed of light being the same constant. And perhaps assume that the receiver would be seeing red shifted light.

So the receiver would not be able to detect a red shift in the incoming beams frequency unless it was not only moving away from the incoming beam as seen by a motionless outside observer but also within its own frame of reference.

I guess what I was expecting would require the doppler shift of light be unaffected by velocity. But it would seem from your response that it, like time and distance is relative to the observers velocity.

 

[Dale]

I guess what I was expecting would require the doppler shift of light be unaffected by velocity. But it would seem from your response that it, like time and distance is relative to the observers velocity.

Again, the relativistic Doppler shift depends ONLY on the relative velocity between detector and emitter. It does not depend on some 3rd party observer's velocity.

 

[DrGreg]

...regardless of the fact that they may actually be moving at a high velocity and the point at which the beam actually hits the receiver may be no where near where the receiver was when the beam was fired.

However, if it were possible for an observer to be holding perfectly still in space...

...as seen by a motionless outside observer...

Within the theory of relativity, all of the expressions I have highlighted above have no meaning, unless you specify that you are measuring relative to some specific object or reference frame. It's meaningless to ask if A "actually is moving", but it's not meaningless to ask if A "is moving relative to B".

 

[Ahkilleux]

It's meaningless to ask if A "actually is moving", but it's not meaningless to ask if A "is moving relative to B".

Yeah I guess I was talking about velocity relative to space. So to clarify, you are stating that the theory of relativity does not allow for any possibility of any entities or even space it's self to be moving at a true and absolute 0 velocity? If nothing can have 0 velocity then how is it that light can have a constant velocity?

"Again, the relativistic Doppler shift depends ONLY on the relative velocity between detector and emitter. It does not depend on some 3rd party observer's velocity."

Dale - "Doppler shift depends ONLY on the relative velocity between detector and emitter."

Why not the velocity between the detector and the emitters original location? If A star emits light and then collides with another star forcing it in another direction, the light that we see which was emitted before the change in velocity of the star is unaffected by the stars new velocity so why would its doppler shift be altered?

If a planet is moving away from the origin of the light, wouldn't the light still be red shifted even if the star is as close to the planet when the light is finally received as it was when the light was emitted?

 

[Dale]

Why not the velocity between the detector and the emitters original location?

Because that is what the math says. The problem here is that you are assuming that the equations say something that they do not say. If you had bothered to actually work out the value of the Doppler shift for your device then you would have found it to be zero.

Why not the velocity between the detector and the emitters original location? If A star emits light and then collides with another star forcing it in another direction, the light that we see which was emitted before the change in velocity of the star is unaffected by the stars new velocity so why would its doppler shift be altered?

If a planet is moving away from the origin of the light, wouldn't the light still be red shifted even if the star is as close to the planet when the light is finally received as it was when the light was emitted?

I should have been explicit. The special relativistic Doppler is ONLY a function of the relative velocity of the emitter at the time of emission and the detector at the time of detection. In your OP the detectors and emitters were all inertial, so that distinction was unnecessary.

 

[Ahkilleux]

Because that is what the math says. The problem here is that you are assuming that the equations say something that they do not say. If you had bothered to actually work out the value of the Doppler shift for your device then you would have found it to be zero.

Okay, yeah I'm with you. Basically it was a fundamental misunderstanding of what causes the doppler shift. As I think you were trying to point out, the two bodies must have a non zero change in distance over time in order for there to be a shift, as it is the change in distance between each successive wave that causes the shift, so with no change in distance, there is no shift to measure.

My understanding was that simply moving to or from the source would cause a shift, but if both bodies are moving together, the waves are shifting in both directions equally and so the net shift is zero.

Thanks everyone for you answers, insights, and patience I think I have a much better grip on the concept. :-)

 

[Simon Bridge]

Yeah I guess I was talking about velocity relative to space.

You cannot have a velocity relative to space because you need some sort of distance from something to time your travel to get the speed and something for an origin to get the direction.

You are imagining space as having a "big grid" that Everything moves against and this seductive image is very misleading... as you are finding out. The "big grid" is always attached to an observer.

So to clarify, you are stating that the theory of relativity does not allow for any possibility of any entities or even space it's self to be moving at a true and absolute 0 velocity?

That is correct.

If nothing can have 0 velocity then how is it that light can have a constant velocity?

... the same way anything can have a constant velocity - that just means it is not accelerating in the reference frame of the observer.

But I guess you are asking how come light has this absolute velocity c right? The answer is that it doesn't. If it did then you'd be able to tell how fast you are "actually" going by comparing your speed to that of light.

What happens is that all observers measure the same speed for light. It is a consequence of this that there is no absolute reference frame.

Okay, yeah I'm with you. Basically it was a fundamental misunderstanding of what causes the doppler shift.

Yep - see below. Its an understandable confusion because the classical doppler shift for sound allows for an absolute reference frame - the medium the sound moves in. But these equations are also different for who does the moving. That is not the case for the relativistic doppler shift.

... the two bodies must have a non zero change in distance over time in order for there to be a shift,

They need to have a non-zero change in distance over time in order to be considered to have a non-zero speed! That's what speed is.

My understanding was that simply moving to or from the source would cause a shift,

That is correct - but if the source is always the same distance from you then you are not moving to or from it right? That's not what "moving to" and "moving from" means.

but if both bodies are moving together, the waves are shifting in both directions equally and so the net shift is zero.

Hopefully you understand better now - there was never any "shifting in both directions" to make the net **** zero.

If I go faster than you towards a light source, we both measure the same speed for the incoming photons but I count more waves per second than you so the light I see is bluer than the light you see. By comparing our measurements we can determine how much faster than you I am going.

That would be my speed in your reference frame. It will agree with other measurements like if you timed me over a fixed distance.

It all works out in reverse too: in my reference frame you are traveling away from the light ... so of course your light is red-shifted compared to mine. That makes total sense to me.

What's more, we are both blue-shifted according to the light source - by different amounts. Since we are usually interested in the light, we usually think of ourselves moving and the light stationary. But that's just a habit of thought and does not mean anything.

It takes a while to get used to this thinking.

 

[vociferous]

Okay, yeah I'm with you. Basically it was a fundamental misunderstanding of what causes the doppler shift. As I think you were trying to point out, the two bodies must have a non zero change in distance over time in order for there to be a shift, as it is the change in distance between each successive wave that causes the shift, so with no change in distance, there is no shift to measure.

My understanding was that simply moving to or from the source would cause a shift, but if both bodies are moving together, the waves are shifting in both directions equally and so the net shift is zero.

Thanks everyone for you answers, insights, and patience I think I have a much better grip on the concept. :-)

Until relatively recently (pardon the pun) in the history of physics, most physicists thought like you. They thought that there was some absolute medium of space called the aether that light propagated through. A couple of fellows named Michelson and Morley disproved the aether theory, showing that there is no such thing as "absolutely stationary". We can only measure the constant velocity of two things relative to each other.

Acceleration, on the other hand, is absolute and can be measured independent of other objects in space.

 

[Ahkilleux]

That is correct - but if the source is always the same distance from you then you are not moving to or from it right? That's not what "moving to" and "moving from" means.Hopefully you understand better now - there was never any "shifting in both directions" to make the net **** zero.

Yeah I guess what I meant by shifting in both directions for a net zero is that, at least in the case of sound, if both the emitter and detector are moving at the same velocity,then it would be like an ambulance chasing a car at the same velocity. Even though each sound wave is produced further in the direction of the car than the wave before it, the car on the listening end has moved away from the source by that same distance between each wave and so the effect is negated.

Basically what I meant by "simply moving to or from the source would cause a shift" is that I originally thought you only needed to move to the initial origin of the photon and that the wave form of the beam of light was instantly created. If so, the emitter and the detector didn't actually need to be moving toward each other. Rather, the detector only needed to be moving toward the location that the emitter was in when it emitted the photon. But in the case of a sound wave, the wave is not formed in a single instant, and so moving toward the origin of the sound means nothing if the sound emitter is also moving away from you at the same speed.

So really I suppose the misunderstanding was that the waveform of a beam of light was generated instantaneously rather than over time. Although I'm still not certain on that because my understanding of a light wave is that it is not a longitudinal compression wave as sound is.. so perhaps it IS instantly in wave form? If so then wouldn't the velocity of the source be irrelevant? Wouldn't only the velocity of the detector relative to the initial point of emission matter?

Regardless of whether or not that is the case, you made other points which invalidate my suggestion.

If I go faster than you towards a light source, we both measure the same speed for the incoming photons but I count more waves per second than you so the light I see is bluer than the light you see. By comparing our measurements we can determine how much faster than you I am going.

That would be my speed in your reference frame. It will agree with other measurements like if you timed me over a fixed distance.

Understood, but the root of the question then is, if the light source emits the beam while moving away from you at the same speed that you move toward it, does the fact that you are closing in on the initial point of emission cause a blue shift or, is it like sound where you need to be closing in on the actual emitter over time?

Since we are usually interested in the light, we usually think of ourselves moving and the light stationary. But that's just a habit of thought and does not mean anything.

Again, this hits at the root of my misunderstanding. Which again is the question of whether or not the wave form can be distinguished from the light emitted in a single instant in time or whether it requires you to sample a length of the beam over time.

If the latter is true, then as is the case with sound, moving toward the stationary point in space representing the initial emission point will not cause a blue shift unless you are also closing distance on the emitter it's self.

If the former is true then for the purposes of measuring blue shift, could we not assume the light is always stationary since its point of emission was a single instant in time where it was at a single point in space? Anyhow, my idea was based on the former being the case. Because if a wave length can be detected from a single photon of light emitted in a single instant, then the point at which that photon was emitted at that single instant in time represents a single absolute point. If you blue shift toward that point then you are moving faster in that direction than away from it.

So I thought I had a better grasp of things, but I think know I know less than I did before :). Perhaps for the best as I had some misconceptions and an unlearning was necessary.

 

[Ahkilleux]

Until relatively recently (pardon the pun) in the history of physics, most physicists thought like you. They thought that there was some absolute medium of space called the aether that light propagated through. A couple of fellows named Michelson and Morley disproved the aether theory, showing that there is no such thing as "absolutely stationary". We can only measure the constant velocity of two things relative to each other.

Acceleration, on the other hand, is absolute and can be measured independent of other objects in space.

I briefly noted those names and the term "aether" as i was looking up the idea of absolute velocity. I will have to do some more reading to get a grip on how the possibility of an absolute grid of space was disproved. It still just seems counter intuitive that nothingness would have a velocity. It seems like some sort of grid would exist even if nothing was attached to it. I mean I'm not arguing that if there is nothing attached to it, then the idea of knowing your velocity relative to it may be completely meaningless, but it seems like if such knowledge were possible to attain, that it could be used in some way to better understand everything else.

It just seems like if there is a maximum speed limit, then there should be a 0 speed. Meaning if everything is relative then shouldn't it be possible to reach the speed of light relative to an outside observers frame of reference? If not and our absolute speed regardless of any observer is truly limited to less then the speed of light, then we must have some absolute velocity right? In order to have an absolute velocity limit, you have to have an absolute velocity right? And if we don't have an absolute velocity limit, and the limit is only relative to our own frame of reference, then we could be moving at the speed of light or greater relative to some observer?

Anyhow, thanks! :-) i'll look into that "aether" some more.

 

[Simon Bridge]

It just seems like if there is a maximum speed limit, then there should be a 0 speed

In the same sense that c is a speed limit, there is also a zero speed ... just like every observer measures the same speed for light, every observer also measures the same speed for themselves: zero.

Understood, but the root of the question then is, if the light source emits the beam while moving away from you at the same speed that you move toward it, does the fact that you are closing in on the initial point of emission cause a blue shift or, is it like sound where you need to be closing in on the actual emitter over time?

For you to observe a blue shift, the source has to be moving towards you in your reference frame. You are always at the origin of your reference frame.

This is different to the classical case with sound - where you only need to be in motion with respect to the medium that is carrying the sound waves. With light, there is no medium to move against. Originally Aether was proposed as a theoretical medium for light but the theory fell over for lack of empirical support.

The most famous failed experiment of this kind, the Michealson Morely experiment, was quite similar to the kind of thing you were suggesting. Since the doppler shift was expected to be very small they used an interference method to measure it.

Have a look at: Empirical Evidence for special relativity for the shear weight of evidence concerning the different kinds of aetheric theories compared with special relativity. More added all the time - it's a very solid theory.

 

[vociferous]

I briefly noted those names and the term "aether" as i was looking up the idea of absolute velocity. I will have to do some more reading to get a grip on how the possibility of an absolute grid of space was disproved. It still just seems counter intuitive that nothingness would have a velocity. It seems like some sort of grid would exist even if nothing was attached to it. I mean I'm not arguing that if there is nothing attached to it, then the idea of knowing your velocity relative to it may be completely meaningless, but it seems like if such knowledge were possible to attain, that it could be used in some way to better understand everything else.

The aether was not quite the same as an absolute grid, just the closest physics has ever come to having a use for such a thing. The aether was supposed to be an otherwise undetectable substance that permeated the universe through which all light propagated, similar to how sound waves propagate through the atmosphere on earth. Just like you can tell when you are moving on Earth by feeling the breeze of the atmosphere against you as you run, Michelson and Morley built a device to detect the breeze of the aether as Earth moved through it.

It just seems like if there is a maximum speed limit, then there should be a 0 speed. Meaning if everything is relative then shouldn't it be possible to reach the speed of light relative to an outside observers frame of reference? If not and our absolute speed regardless of any observer is truly limited to less then the speed of light, then we must have some absolute velocity right? In order to have an absolute velocity limit, you have to have an absolute velocity right? And if we don't have an absolute velocity limit, and the limit is only relative to our own frame of reference, then we could be moving at the speed of light or greater relative to some observer?

Anyhow, thanks! :-) i'll look into that "aether" some more.

That would be true if space and time were absolute. But they are not. In Newtonian mechanics, if I am in a convertible traveling 100 mph and I get Roger Clemens to throw a baseball at 100 MPH, the baseball is traveling 200 mph relative to the ground. If I am in a convertible traveling ~ the speed of light and I shine a flashlight ahead, the person on the ground does not see the light traveling ~2c. They see the light traveling at 1c, just like I do. That means that our perceptions about the motion of the convertible must vary quite a bit.

So, the two important lessons here are:

1) From any given frame of reference, you are always moving at 0 speed with respect to the speed of light.

2) You can never travel quite as fast as the speed of light (unless your rest mass is zero) because E=mc^2 implies that as your speed approaches c, your relativistic mass approaches infinity. And because everything is relative, different frames of reference will see different things. For instance, if two vehicles were traveling away from each other, each almost at the speed of light, they would not see each other traveling away from each other at nearly 2c. They would see the other traveling away at nearly c. However, someone on the ground would see them moving apart from their position at nearly c, meaning that they were traveling apart from each other at nearly 2c.

 

[Ahkilleux]

In the same sense that c is a speed limit, there is also a zero speed ... just like every observer measures the same speed for light, every observer also measures the same speed for themselves: zero.

Yeah I suppose the answer then is infinity. What I mean by that is what I'm starting to understand is that you are always moving at near the speed of light relative to someone. And that someone is moving at near the speed of light relative to someone else and you can push that speed slider all the way back through the infinity of space and always find an observer that is looking at the previous observer as moving at near the speed of light. So in order for there to be an absolute zero velocity, there would have finite limit to existence.

Which leads to your next point..

For you to observe a blue shift, the source has to be moving towards you in your reference frame. You are always at the origin of your reference frame.

So then light it's self is only relative to our frame. By that I mean that all of the light we see would be very very shifted to some outside observer who sees us as moving at near the speed of light. If we are moving away from them at almost the speed of light and shine a light toward them they would see it red shifted.

For my suggestion to work, that would have to be a false statement. The light would have to only be shifted for them if the point from which or medium within which the light was emitted was moving toward them independent of the source.

My error then was in thinking that the speed of light in a vacuum was not only constant relative to our frame of reference but was in fact absolute. But if that were true, as was pointed out earlier, we could measure our absolute speed by measuring our speed relative to the speed of light. So that is finally sinking in :-).

Thanks again!

 

[Ahkilleux]

If I am in a convertible traveling ~ the speed of light and I shine a flashlight ahead, the person on the ground does not see the light traveling ~2c. They see the light traveling at 1c, just like I do. That means that our perceptions about the motion of the convertible must vary quite a bit.

Gotcha, and I understand that to be possible due to time dilation? Where my perception while moving at near the speed of light is slowed so greatly that to me a particle moving at a very slow velocity relative to me would in fact appear to be moving quite fast. So while to the person on the ground, the light I shine is moving at a velocity only slightly greater than me, to me it appears to be moving at... the speed of light.

2) You can never travel quite as fast as the speed of light (unless your rest mass is zero) because E=mc^2 implies that as your speed approaches c, your relativistic mass approaches infinity. And because everything is relative, different frames of reference will see different things. For instance, if two vehicles were traveling away from each other, each almost at the speed of light, they would not see each other traveling away from each other at nearly 2c. They would see the other traveling away at nearly c. However, someone on the ground would see them moving apart from their position at nearly c, meaning that they were traveling apart from each other at nearly 2c.

Now this point is a little more puzzling, since I would think that with time dilation the two vehicles would see each other as moving away from each other even faster than 2c rather than at almost 1c. But I suppose that is where space dilation kicks in? so the distance we are covering over time relative to each other appears to be greatly reduced and therefore our relative velocity is reduced?

Perhaps those are topics for another thread. I am now quite satisfied that my suggestion was heavily flawed :).

 

[Simon Bridge]

1) From any given frame of reference, you are always moving at 0 speed with respect to the speed of light.

No - you are always moving at zero speed with respect to yourself. What speed you are moving with respect to photons is more problematical.

2) You can never travel quite as fast as the speed of light (unless your rest mass is zero) because E=mc^2 implies that as your speed approaches c, your relativistic mass approaches infinity.

No it doesn't - you left off a gamma... though I suppose it's implied by the lack of subscript-0 in the m, most people wouldn't get that.

You will never observe yourself traveling at the speed of light because, being the observer, you are always stationary. You need general relativity to deal with accelerations properly. However, you will never be able to accelerate a mass in your reference frame to the speed of light because that would require an infinite amount of energy... this habit of thinking of yourself as doing the moving messes you up.

The relativistic mass increase idea is a bit of a fudge - it more kinetic energy than inertia.

And because everything is relative, different frames of reference will see different things. For instance, if two vehicles were traveling away from each other, each almost at the speed of light, they would not see each other traveling away from each other at nearly 2c. They would see the other traveling away at nearly c. However, someone on the ground would see them moving apart from their position at nearly c, meaning that they were traveling apart from each other at nearly 2c.

This works, though you have to be careful about who is measuring those speeds. The description of the problem implied some favored reference frame which was not specified. That's OK when you are used to it - the third observer is implicit - but it can confuse people who are still grappling with the concepts. Just saying.

If two objects are moving in opposite directions away from me at 0.9c then the distance between them is increasing at 1.8c ... the normal physics applies for me inside my own reference frame. It is only when I compare notes with the other two that things get funny.

Each of the objects sees me retreating at 0.9c ... fine so far, but they each see the other retreat at about 0.99448c

It takes people a while to get used to this stuff and most people don't bother.

 

[Dale]

You need general relativity to deal with accelerations properly.

One minor correction. You only need GR to deal with gravity. Non gravitational accelerations can be handled using just SR.

http://math.ucr.edu/home/baez/physics/Relativity/SR/acceleration.html

 

[Austin0]

My error then was in thinking that the speed of light in a vacuum was not only constant relative to our frame of reference but was in fact absolute. But if that were true, as was pointed out earlier, we could measure our absolute speed by measuring our speed relative to the speed of light. So that is finally sinking in :-).

Thanks again!

Hi I think it is generally accepted that the speed of light in a vacuum is absolute in the sense that all photons outside the influence of gravity travel at this speed. That this speed is a universal attribute of the spacetime geometry for EM propagation and also imposes a maximum limit on local travel of any kind.
(With the possible exception of velocities due to the expansion of the universe on global scales.)
But because we measure this speed at the same value in all possible frames it is not applicable as a basis for any determination of absolute motion which you have now realized..

 

[Simon Bridge]

Gotcha, and I understand that to be possible due to time dilation? Where my perception while moving at near the speed of light is slowed so greatly that to me a particle moving at a very slow velocity relative to me would in fact appear to be moving quite fast. So while to the person on the ground, the light I shine is moving at a velocity only slightly greater than me, to me it appears to be moving at... the speed of light.

Nope - the results of relativity are not about "perception" - it's not some sort of illusion. What each observer sees is really real. It's not "appears to be moving at..." it is moving like that. Time dilation doesn't make the moving clock appear to slow down time actually moves at different rates for different observers.

When we talk about a clock in this context we don't mean the thing that sits on a shelf going "tick-tock" - we are talking about an imaginary ideal clock that tells us how time is passing. When we conduct experiments in real life we have to use real clocks and make allowances for the differences. Similarly, when we say that one observer sees something we mean that they also take account of things like the time it takes light to travel from what they see to their eyes (or whatever they use to "see") and so on. What you'd actually physically see with your eyes may be quite different. This is all a way of being careful with language.

Try this one: Alice shoots a laser at Bob - Bob is on a train moving away from Alice at 0.9c (say). Alice and Bob both measure the speed of light from the beam. Classically youd expect Alice to measure c and Bob to measure 0.1c but what actually happens, and this has happened every time this experiment has been done in real life, Alice and Bob both measure c.

When Alice watches Bob do his measurement she notices that his stopwatches are all slow and his rulers are all short... "ahah!" she says, "he's making a mistake!" But hang on - when Bob looks back at Alice as she does her measurement - he sees that she has slow stopwatches and short rulers too! So which one is the true truth?

Bob does spectrographic analysis on the laser light and finds the characteristic lines in the lasers spectrum are shifted to the red... this tells him the laser is moving away from him, which he can see already.

Both Alice and Bob can see the ground - since Bob got on the train and started the engine etc both Alice and Bob will instinctively feel that it is Bob who is "really" doing the moving here.

Pull the camera back and we discover that Alice, Bob and the train are all inside a super-giant alien spacecraft being experimented on by alien behavioral psychologists. The "ground" turns out to be a giant conveyor belt and when Bob started the train it's wheels actually were pushing the ground backwards (i.e. the train remains stationary wrt the spacecraft ).

The whole spacecraft is traveling at 0.99c (along tracks direction), accelerating at 1g towards Andromeda in intergalactic space (same direction as Alice and Bob agree is "up"). Short of going outside, there is no experiment Alice and Bob can conduct to discover any of this. Of course, if the craft changed acceleration sharply they'd soon notice... but they may just decide that gravity is behaving strangely.

Now this point is a little more puzzling, since I would think that with time dilation the two vehicles would see each other as moving away from each other even faster than 2c rather than at almost 1c. But I suppose that is where space dilation kicks in? so the distance we are covering over time relative to each other appears to be greatly reduced and therefore our relative velocity is reduced?

Don't confuse the math with the reality. There are lots of different ways of doing the sums ... they don't see 2c because that would be physically impossible.

What's happening is that different observers will generally agree about events they both see but they disagree about how those events came to happen.

eg. I get on my supership and take a trip to Apha Centauri. It takes me a week. I park and find out that Mission Control has been waiting way waay longer than a week.

Everyone else explains the discrepancy by pointing out that time slowed down for me for the trip. But I can explain it too - time slowed down for everyone else during most of the trip but when I went to park, everyone elses time suddenly went really fast.

We'd instinctively feel that everyone else is right and I am wrong - but there is no special reason to assign a privileged status to Mission Control's reference frame (well, maybe if I get wages on Earth time...). None of these observations are illusory or mistaken and all the equipment is working.

Perhaps those are topics for another thread. I am now quite satisfied that my suggestion was heavily flawed :).

But in an interesting and subtle way ... there is a trick to thinking about this sort of thing and general relativity is another kettle of piranhas again.

We have evolved to think in terms of motion against some stationary background - which is why the idea that the Earth is in motion about the Sun was hard to accept (and still is for rather more people than you'd think.) We are used to the ground being stationary. We know intellectually that it can move but that does not sink in at the emotional/animal level even if you've been in an earthquake. "On uncertain ground" is a powerful image. It works because everybody is moving at close to the same speed pretty much all the time so we can find common ground in how things happen. It is only when we start to travel very fast that the fundamental lack of absolutes becomes obvious. What we are used to turns out to be an emergent behavior.

Deprived of that certainty, we grasp for something else. Perhaps the Sun is stationary? Nope. The fixed stars - they must be still right? Nope. Galactic center? Nope. The universe does not pivot about a fixed point and we just have to live with that.Anyway - I've found this FAQ to be quite accessible - you'll enjoy it because it sets out to talk about FTL. There are a lot of careful descriptions and you get to see geometric as well as equations methods. Common relativity puzzles are used to show the effects.

 

[Simon Bridge]

Oh, and thanks @DaleSpam
I was thinking about the acceleration looks like gravity thing but you are right. I was just getting concerned that the statements I was making make most sense at constant velocity... but our intuitive thinking includes experience of acceleration. eg.

If I am jogging and I pass you, it is as valid in SR to say that you are moving past me (in my reference frame) ... but if that's the case, how come I'm the one getting puffed out?

The situation is not symmetrical ... it's not really an inertial reference frame. When I say I'm jogging at a constant speed that's only an approximation. But we are so used to these approximations in everyday life that it becomes an act of discipline to exclude the assumptions from SR descriptions - which have to be more precise.

I've had quite a lot of practice explaining this stuff now but I'm still aware of holes in my descriptions.

@Austin0: there are different ways of being "absolute" ;) however:

Hi I think it is generally accepted that the speed of light in a vacuum is absolute in the sense that all photons outside the influence of gravity travel at this speed.

... surely - it is accepted that all observers will measure the speed of light to be this value (because of this it is a sign of a fundamental property of space-time). You do go on to say something like this but it sounds like you are making a separate observation there: light moves at c and all observers measure c. See?

Does gravity really change the speed that photos travel?
Is lightspeed not a constraint on non-local travel then?

I think you are quite correct to point to the fact that there are things that can go FTL without violating relativity though.