FTL train + FTL communication thought experiment

[girts]

Please move this if it belongs to other subforums.

So i thought about some other stuff and then somehow this idea appeared to me, now according to physics it is impossible to communicate information faster than the speed of light through vacuum which is "c".
So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.
So please look at this thought experiment, what happens if we have say a train but instead of traveling in a straight line it would travel in a circle, as it travels around the circle there are 4 stations set 90 degrees apart, say the train somehow manages to travel faster than c with respect to an observer located at either of those stations as the train passes them by, the observer wants to send a direct radio message to the train (assuming there is vacuum) but since the train ravels faster than c the radio signal can't reach the train, so the observer sends the radio signal to the center point of the circle which has a certain radius to the observer and has a radio station located in it. from center the signal gets redirected to the train, and the train can respond back via the same path through the center,since the train is always a fixed distance (radius) away from the center point and so is the observer then given those distance are not very long they will be easily traveled by the radio signal traveling at c, so even though the observer can't reach the train for those 180 degrees from the point where it passes the observer to the point where the train crosses the midpoint, redirecting through the middle can solve this problem.
Please see the attached image,
my question is this does this is a violation of the FTL rule or does this not count because the two observers are not traveling on a straight line in opposite directions ?

 

[jbriggs444]

So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.

Do you know how velocities add in special relativity?

 

[sophiecentaur]

Do you know how velocities add in special relativity?

There's another problem here. The train is moving in a circle so acceleration is involved. SR doesn't cover that situation.

 

[tnich]

Please move this if it belongs to other subforums.

So i thought about some other stuff and then somehow this idea appeared to me, now according to physics it is impossible to communicate information faster than the speed of light through vacuum which is "c".
So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.
So please look at this thought experiment, what happens if we have say a train but instead of traveling in a straight line it would travel in a circle, as it travels around the circle there are 4 stations set 90 degrees apart, say the train somehow manages to travel faster than c with respect to an observer located at either of those stations as the train passes them by, the observer wants to send a direct radio message to the train (assuming there is vacuum) but since the train ravels faster than c the radio signal can't reach the train, so the observer sends the radio signal to the center point of the circle which has a certain radius to the observer and has a radio station located in it. from center the signal gets redirected to the train, and the train can respond back via the same path through the center,since the train is always a fixed distance (radius) away from the center point and so is the observer then given those distance are not very long they will be easily traveled by the radio signal traveling at c, so even though the observer can't reach the train for those 180 degrees from the point where it passes the observer to the point where the train crosses the midpoint, redirecting through the middle can solve this problem.
Please see the attached image,
my question is this does this is a violation of the FTL rule or does this not count because the two observers are not traveling on a straight line in opposite directions ?View attachment 224248

In my reference frame - the reference frame in which I am at rest - nothing can move faster than the speed of light. The same is true in your reference frame. So even if some observer sees you and I traveling away from each other at more than the speed of light, then in my reference frame, you are still moving away from me at less than the speed of light.
The speed of light c is the same in all reference frames. If you send me a message at the speed of light, then even in the frame of the observer, it will travel at the speed of light, not at c - v_you. A message you send me by radio or laser will reach me, and if you appear to me to be a distance $d$ away when you send it, then it will take time $t=\frac d c$ to reach me.
This is very counter-intuitive, I know.

 

[jbriggs444]

There's another problem here. The train is moving in a circle so acceleration is involved. SR doesn't cover that situation.

Two problems with that assessment.

1. SR handles acceleration just fine.
2. The scenario does not involve any attempt to make use of an accelerated frame. One could replace the train by a moving dot projected by a laser pointer.

It is no problem to send a signal on a short path between two endpoints while a projected dot traverses a longer and FTL path.

[That's how the Big Bad Wolf got to grandma's house before Little Red Riding Hood]

 

[sophiecentaur]

1. SR handles acceleration just fine.

So where does the Inertial Frame requirement come in? There seem to be statements in my Google hits that seem to imply that SR only works in an inertial frame and others that consider acceleration. Which step am I missing?

 

[Mister T]

So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.

To understand why this can't be true just imagine that you are co-moving with one of those two objects. That object is at rest relative to you. The other object has a speed less than $c$ relative to you. You can therefore send a light signal to the other object.

 

[Nugatory]

There seem to be statements in my Google hits that seem to imply that SR only works in an inertial frame and others that consider acceleration. Which step am I missing?

The statements that you're finding in Google are just plain wrong.

It's a common misconception. Most intro treatments assume that the student is not familiar with the mathematical tools needed to work with acceleration - so their examples all use inertial frames, leading to the impression that that's the only kind that work.

 

[Mister T]

So where does the Inertial Frame requirement come in? There seem to be statements in my Google hits that seem to imply that SR only works in an inertial frame and others that consider acceleration. Which step am I missing?

I think it's just a matter of how one defines SR and GR. One can take Einstein's 1905 theory and use it to describe the behavior of an object that has a nonzero acceleration in some inertial reference frame.

 

[Nugatory]

So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.

This is not correct. If A is moving to the left at .9c relative to me and B is moving to the right relative to me at .9c, A and B will not be moving at 1.8c relative to one another - their relative speed will be something less than c. Thus, I will find that a light signal from A and moving at c relative to me will eventually catch up with B; and A and B will agree. For more on how this works and why the relative speed is not 1.8c you should google for "relativistic velocity addition".

ow according to physics it is impossible to communicate information faster than the speed of light through vacuum which is "c".
... So please look at this thought experiment,

In your thought experiment no information is moving faster than c. There's a point where the message is sent and a point where the message is received, there's a time when the message is sent and a time when the message is received. We calculate the ditance between those two points, we calculate the travel time, we divide one into the other to get the speed, and we come up with something less than c.

A more precise way of stating the "cannot communicate faster than light rule" would be to say that event at which a message is transmitted and the event at which it is received cannot be "spacelike-separated" - that's another good Google search.

If you can get hold of a copy of Taylor and Wheeler's book "Spacetime Physics" give it a try - accessible to a motivated high-school student, and incomparably better than random googling if you're serious about understanding this stuff.

 

[Ibix]

it is impossible to communicate information faster than the speed of light through vacuum which is "c".

Correct.

So for any two bodies moving in opposite directions with great speed so that the total sum of the speeds exceeds c it would be impossible to send EM radio signals between the bodies as he signals could not reach the other traveling body.

Their speeds in some reference frame added together may be anything up to almost 2c, true, but this does not have the implication you seem to think. The most obvious way to see this is to imagine each ship emitting a pulse of light, which will slowly pull ahead of each ship. It's true that practical communication is difficult because the ship will arrive very shortly after the radio signal, so it's seldom worth replying - the ship will have reached me before I finish spell-checking. But it's possible.

Additionally, if we switch to the rest frame of one of the ships then that ship is at rest (by definition) and it's obvious that light gets ahead of it. Obviously the other ship is moving even nearer c (although never above c - speeds don't add linearly) so the time available to reply is still really short. But it's still possible in principle.

say the train somehow manages to travel faster than c with respect to an observer located at either of those stations

That's impossible.

my question is this does this is a violation of the FTL rule or does this not count because the two observers are not traveling on a straight line in opposite directions ?

I don't understand why you think this involves faster than light communication. You're using light to do it...

 

[PeroK]

So where does the Inertial Frame requirement come in? There seem to be statements in my Google hits that seem to imply that SR only works in an inertial frame and others that consider acceleration. Which step am I missing?

Try these:

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

https://en.wikipedia.org/wiki/Acceleration_(special_relativity)

 

[Ibix]

So where does the Inertial Frame requirement come in? There seem to be statements in my Google hits that seem to imply that SR only works in an inertial frame and others that consider acceleration. Which step am I missing?

SR as originally formulated worked in inertial frames of reference. It could always handle accelerating objects.

However, the development of relativity in non-inertial frames of reference led to the development of general relativity. There was some ambiguity around whether accelerated frames of reference (in the absence of gravity) should be considered part of SR or GR. The modern view, I think, is that frames are a human convenience, so to divide physics into "flat spacetime and inertial reference frames" and "curved spacetime and flat spacetime (non-inertial reference frames only)" would reflect history not physics.

Not all sources seem to be clear on the distinction between an accelerating object and an accelerating frame. And not all sources agree on the distinction I made between physics and history.

 

[girts]

Ok i see your main concern with this, the fact that I mistakenly said that two bodies traveling in opposite directions each having a speed near c cannot communicate with one another, well true normally they can because as you said light travels at c in every frame, but the reason i made this incorrect statement was because I was thinking in cosmic scale, and it is true that for objects separated by a distance long enough and adding the space expansion fact after certain distances oppositely moving observers cannot communicate anymore because the distance between them is expanding faster than c, correct?Now let's apply this to my diagram I am not trying to say I am correct rather I am trying to make sure that either I am correct or wrong.
Now let's say our circular train track is not small but rather large, say as large as the outer diameter of our solar system or larger, everything else is kept the same.
Now surely I could say the train is traveling at 1.5c along the tracks and so from the point of an observer standing in one of the stations the train would pass away faster than c right? And you would say that this is impossible and you would be correct, but as we know our space expands and so the bodies contained within it travel apart faster then c because they sort of "ride" the expanding space much like a surfer rides a wave and the surfers total speed is his own plus that of the wave right?
so what if we have several train tracks on top of one another in our circular loop, and let's say that each of our tracks is moving at 0.5c speed , simply like ball bearing rims travelings around, and let's say that our train located on the top tracks is also traveling at some 0.5c so that means that the total speed of the train with respect to an observer at one of the stations is the sum of all the individual track speeds + the speed of the train itself which would then account over c, so what happens now? the observer sends a radio signal directly to the passing train does the signal catch the train or have we achieved the "expanding spacetime" situation? but he can always send the signal through the center which always has a fixed length and so the signal would get through in that way but not in a direct way?

I hope you follow my analogy of the several co-moving train tracks and expanding spacetime.
oh and by the way if so far things are correct, than is it theoretically possible to achieve a speed greater than c with respect to two observers one being on the train and one at rest with respect to the train if the train is built the way I proposed , with multiple tracks where each track has a separate speed not greater than c but adding the track and train speeds the total speed exceeds c in those reference frames?

 

[Ibix]

Now let's say our circular train track is not small but rather large, say as large as the outer diameter of our solar system or larger

That's invisibly small on the kind of scale you need for cosmological expansion to come into play.

Now surely I could say the train is traveling at 1.5c

No. Nothing can exceed the speed of light.

but as we know our space expands and so the bodies contained within it travel apart faster then c because they sort of "ride" the expanding space much like a surfer rides a wave and the surfers total speed is his own plus that of the wave right?

That's not a very accurate picture. Also, two nearby objects will never exceed c relative to one another. Very very distant objects don't have that restriction because comparing their velocities isn't a well-defined concept. It's more accurate to think of the definition of the distance between them changing than to think of them moving apart.

so that means that the total speed of the train with respect to an observer at one of the stations is the sum of all the individual track speeds + the speed of the train itself which would then account over c,

Velocities do not add linearly. The correction is minuscule at every day speeds, but extremely significant at relativistic speeds. Your topmost train does not exceed c relative to anything local, such as the track.

the observer sends a radio signal directly to the passing train does the signal catch the train or have we achieved the "expanding spacetime" situation?

There is no expanding space (not spacetime in this case - that never expands) here and no problem communicating.

than is it theoretically possible to achieve a speed greater than c with respect to two observers one being on the train and one at rest with respect to the train if the train is built the way I proposed , with multiple tracks where each track has a separate speed not greater than c but adding the track and train speeds the total speed exceeds c in those reference frames?

No. Look up "relativistic velocity addition".

 

[Mister T]

Ok i see your main concern with this, the fact that I mistakenly said that two bodies traveling in opposite directions each having a speed near c cannot communicate with one another, well true normally they can because as you said light travels at c in every frame, but the reason i made this incorrect statement was because I was thinking in cosmic scale, and it is true that for objects separated by a distance long enough and adding the space expansion fact after certain distances oppositely moving observers cannot communicate anymore because the distance between them is expanding faster than c, correct?

No. What I said in Post #7 still applies.

 

[girts]

ok, let's get "back to basics" here with what I said. pardon if I don't mention individual user nicknames while replying , their just so many its hard to follow.

first of all, when you say that "nothing exceeds the speed of light" right sure I agree but we should specify that this nothing relates to a physical object traveling through space with respect to an observer which is at rest with respect to the object. The same for example would not be true for the case of spacetime expansion, yes I understand it is true for the individual objects getting separated but looking from a "third person's" viewpoint we see that light cannot reach the "other side"When I was talking about my example I implied in my second post that we should look upon it from relativistic viewpoint, so for example a train traveling on a track can't reach c physically but a train traveling on a track which itself is say traveling on another track which then is moving around on yet another track, so what happens now? sure comparing simply each train with its corresponding track will give us less than c but for an observer standing at one of the stations and watching only the train as his reference point not the many moving tracks now what does he conclude, isn't this exactly as the "doppler effect" where one can either add or subtract the pitch (frequency) of sound based on the speed of sound through the medium and then either + or - the speed of the carrier platform on which the sound originates like an ambulance car, but we know that the total speed of the sound is made up of two parts one of which is the speed of sound itself and the other is the platform from which it originates.
much like in far far galaxies expanding we know that the reason why they move apart faster than c is because their own speed and the rate of expansion between them. doesn't the same apply to my example where each individual train track is moving with less than c but adding the multiple values results in a speed higher than c if looked from a specific viewpoint

in other words isn't there in thsi situation at least one reference frame where the train exceeds c with respect to the observer at rest standing in one of the stations?

 

[Ibix]

in other words isn't there in thsi situation at least one reference frame where the train exceeds c with respect to the observer at rest standing in one of the stations?

You don't appear to be reading the answers you are getting. No, there is no such frame. Look up "relativistic velocity addition", as I suggested in my last post.

 

[PeterDonis]

adding the space expansion fact

I would strongly advise not adding this complication until you are clear about the simpler case of flat spacetime. "Space expansion" means curved spacetime, which opens a whole other can of worms. (Note, though, that @Ibix is still correct on the main point: no observer that is next to the train, i.e., at a station watching the train pass through the same station, ever sees the train moving past him faster than c, even in an expanding universe.)

 

[Mister T]

sure comparing simply each train with its corresponding track will give us less than c but for an observer standing at one of the stations and watching only the train as his reference point not the many moving tracks now what does he conclude,

That the train has a speed less than $c$.

in other words isn't there in this situation at least one reference frame where the train exceeds c with respect to the observer at rest standing in one of the stations?

No.

 

[sweet springs]

From wiki Velocity-addition formula https://en.wikipedia.org/wiki/Velocity-addition_formula

$$u=\frac{v+u'}{1+\frac{uu'}{c^2}}$$

Say v=0.9c and u'=0.9c, u=1.8/1.81 c = 0.99 c < c.

 

[Ibix]

Note that there's a typo in @sweet springs formula - it should read $$ u=\frac{v+u'}{1+vu'/c^2}$$It's fairly easy to show that requiring $u>c$ leads to the implication that either $u'>c$ or $v>c$. Also, it's easy to see that if both $u'$ and $v$ are much smaller than $c$ then the denominator is very close to 1 and the formula reduces to the familiar Newtonian form.

 

[girts]

Ok I get it, velocities add up to a certain speed but after that time dilation and relativistic factors come into play the higher the speed the more so up until the point where no matter how hard you try you never exceed light speed no matter from which observers point you look.

It's actually quite interesting that nature alters the sum of two velocities itself if the velocities are high enough, for example for ordinary speeds like say a man being ejected from a traveling rocket or a man running down a train moving at speed x the speeds simply add up but here they don't even though the scenario and means of achieving it stay the same.
But I assume we could at least theoretically construct a device which could maybe achieve something close to c with respect to an observer at rest, by simply putting the train or whatever is moving along the tracks on multiple platforms so that the speed of each platform is only a fraction of the total speed.

 

[girts]

https://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_adding/index.html

just in case anyone reading this thread with the same question , this link was very helpful and it explained the stuff in an easy way.so essentially the reason why the two oppositely traveling bodies could still communicate and their speeds added would not result in higher than c is because if as you said a co-moving object with one of the bodies saw a light beam emitted towards the other body the light beam would still travel at c and not c-(the speed of the moving body) so for all observers light travels at c no matter the reference frame? so what happens here is that one can take one of the moving bodies and treat it as being at rest with respect to the other moving body in the opposite direction regarding emitted light? and since no object can move in a single direction faster than light then it doesn't matter that the light beam is emitted from an escaping body it still only considers the speed of the body the beam is trying to reach?

 

[Mister T]

Ok I get it, velocities add up to a certain speed [...]

The velocities combine in some way, but addition is not the right way to combine them. What you can do is define a parameter $\theta$ such that $$\tanh \theta=\frac{v}{c}.$$ The correct way to combine $\theta$'s is to add them. But addition is not the correct way to combine $v$'s.

It's actually quite interesting that nature alters the sum of two velocities itself if the velocities are high enough, for example for ordinary speeds like say a man being ejected from a traveling rocket or a man running down a train moving at speed x the speeds simply add up but here they don't even though the scenario and means of achieving it stay the same.

Nature alters nothing! It's the Newtonian notion that velocities add, a notion that exists in your mind not in Nature, that needs to be altered.

If you had two wedges, each forming an angle $\theta$, and you stacked them to form a new wedge, the angle of the new wedge would be $2\theta$. But if you instead looked at the slope of the wedges, $\tan \theta$, you will find that the slope of the new wedge would not be $2 \tan \theta$. If the angle $\theta$ is small enough then the slope of the new wedge is approximately $2 \tan \theta$, but Nature doesn't somehow alter things for larger angles, it's just that it appears to humans who are familiar only with small slopes that slopes add.

But I assume we could at least theoretically construct a device which could maybe achieve something close to c with respect to an observer at rest, by simply putting the train or whatever is moving along the tracks on multiple platforms so that the speed of each platform is only a fraction of the total speed.

No engineer would do it that way when there are ways that are faster, better, and cheaper. Do a search for particle accelerators. Some are straight, like the Stanford Linear Accelerator (SLAC) and some are round, like the Large Hadron Collider (LHC) or Fermi Lab. They accelerate particles to speeds close to $c$ using all kinds of clever schemes, but none of them involve accelerating the accelerator itself so that the speed of particles can be added to the speed of the accelerator. That would be folly!

 

[girts]

yes Mister T , I am well aware that we use particle accelerators for relativistic particle velocities and all associated experiments, it;s just that a human sized object traveling at or near such velocities could maybe have some other already known but still interesting aspects of experimentation.
I have read long ago that due to time dilation a human traveling near c would age much less than an average person on a rest frame here on earth, I assume that by accelerating protons in the LHC we can't observe their "aging" properties, in order to do that we would need a more complex object like a molecule or maybe a body?as for the other stuff pardon I did not really get the wedge analogy , couldn't "picture it" in my mind.
But i can agree that the Newtonian idea is a very simplified model of reality and so works for "ordinary"everyday things like summing the impact speed of a frontal car crash which indeed is very precise if simply added i assume the minor imprecision simply gets larger with increasing speed and so once in relativistic speed teritory becomes very large and important

 

[Ibix]

I have read long ago that due to time dilation a human traveling near c would age much less than an average person on a rest frame here on earth, I assume that by accelerating protons in the LHC we can't observe their "aging" properties, in order to do that we would need a more complex object like a molecule or maybe a body?

One of the earliest tests of relativity was the lengthening of the decay times of relativistic muons due to time dilation.

 

[Mister T]

I assume that by accelerating protons in the LHC we can't observe their "aging" properties, in order to do that we would need a more complex object like a molecule or maybe a body?

You need something that ages, and protons don't age, as far as we know. But muons do, and as @Ibix points out, experiments done with them show that Einstein got it right. But the story doesn't end there. It's just the beginning. Lots of stuff has been done that further shows that Einstein got it right. Lots. In fact, it's an overwhelming amount of stuff.

Atomic clocks aboard orbiting satellites are "human-sized" objects, and these clocks are so precise that high speeds are not necessary to show time dilation. If the engineers ignored time dilation the clocks would be so far out of sync that the global positioning system (GPS) would at best be able to tell you what city you're in, but as it is they can tell you what street corner you're on in that city!

 

[Sorcerer]

You need something that ages, and protons don't age, as far as we know. But muons do, and as @Ibix points out, experiments done with them show that Einstein got it right. But the story doesn't end there. It's just the beginning. Lots of stuff has been done that further shows that Einstein got it right. Lots. In fact, it's an overwhelming amount of stuff.

Atomic clocks aboard orbiting satellites are "human-sized" objects, and these clocks are so precise that high speeds are not necessary to show time dilation. If the engineers ignored time dilation the clocks would be so far out of sync that the global positioning system (GPS) would at best be able to tell you what city you're in, but as it is they can tell you what street corner you're on in that city!

Yes there are so many. But what I don’t get is, why is there any logical need for any but he Michelson-Morley experiment? Once you establish that light speed is indepent of the speed of its source, only two possibilities remain as far as I can tell: the speed of light is infinite and the Galilean transformation holds, or the speed of light is finite and the Lorentz transformation holds.

As light appears to have a finite speed, the Lorentz transformation holds.
Edit- Wait. I suppose you could have an infinite “out going” speed and a (1/2)c return speed, netting a total two way speed of c, but I’m pretty sure the net result would still be the Lorentz transformation.

 

[Vanadium 50]

But what I don’t get is, why is there any logical need for any but he Michelson-Morley experiment? Once you establish that light speed is indepent of the speed of its source

And was this established by 1887?

 

[Nugatory]

But what I don’t get is, why is there any logical need for any but he Michelson-Morley experiment? Once you establish that light speed is indepent of the speed of its source...

M-M was one negative experimental result. It's a very big step to get from there to the positive conclusion about the speed of light and acceptance of the more counterintuitive (counter to Galilean intuition, that is) implications of the Lorentz transformations.

 

[Ibix]

But what I don’t get is, why is there any logical need for any but he Michelson-Morley experiment?

Well Michelson and Morley can be criticised for having their receiver and emitter co-moving and in a closed room. Some kind of ether dragging hypothesis isn't implausible on this basis alone. Other experiments were needed and were done - e.g. stellar aberration measurements make ether dragging highly implausible.

 

[Sorcerer]

And was this established by 1887?

No. In this case I'm just referring to the fact that "skeptical" people (these days) always ask for experiment after experiment, not any historical incidents, when as far as I can tell, you only need two (determining that light speed is finite and the Michelson-Morley experiment).

 

[Sorcerer]

M-M was one negative experimental result. It's a very big step to get from there to the positive conclusion about the speed of light and acceptance of the more counterintuitive (counter to Galilean intuition, that is) implications of the Lorentz transformations.

I wasn't very clear. I didn't mean that single experiment. I was referring to TODAY about what people ask for. And today that experiment has been redone over and over and over again, so it is more or less without doubt.I suppose I should have been more clear, as my other post was about the history of SR.

 

[Sorcerer]

Well Michelson and Morley can be criticised for having their receiver and emitter co-moving and in a closed room. Some kind of ether dragging hypothesis isn't implausible on this basis alone. Other experiments were needed and were done - e.g. stellar aberration measurements make ether dragging highly implausible.

So what about speaking of TODAY, rather than back then?

Would knowing that the speed of light is finite, and then finding all the repeated negative results of the Michelson-Morley experiment be enough to deduce the Lorentz transformation?