A spaceship traveling close to the speed of light sending some data....

[radres]

A spaceship traveling at speed of light close to speed of light (wrt inertial reference frame) sending some data every second on their clock to people who are stationary (wrt inertial reference frame). At what time these people would receive this data on their own clock?

Let's say for a second passed in the spaceship, 10 seconds passes for the stationary people.

Sorry if this makes no sense, I don't have a good understanding of relativity, I only know that at high speeds, the time is slower than the people at low speeds.

 

[Orodruin]

A spaceship traveling at speed of light (wrt inertial reference frame)

Assuming your spaceship has mass, it cannot do this.

If you exchange "at the speed of light" for "close to the speed of light", it will depend on whether the spaceship is moving towards or away from the people. The relation will be given by the relativistic Doppler formula.

 

[Ibix]

It's impossible to describe something with mass moving at the speed of light in relativity. However, you specified a tick rate ratio of 10:1, which implies a specific speed. If I see you traveling at speed $v$ then I will determine your clocks to be ticking once every $1/\sqrt {1-v^2/c^2}$ seconds.

As Orodruin says, when the people who are stationary in the inertial reference frame receive the pulses depends on where they are. The emitting ship is moving - so if it is coming towards you the second pulse does not have as far to travel as the first, so pulses come in squashed together. If it is moving away then the pulses come in spread apart. The relevant formula is that if the pulses are emitted with frequency $f$ (once per second, for example) then they are received with frequency $f'=f\sqrt {(c+v)/(c-v)}$. Note that $v$ can be positive ot negative and that I'm assuming that the ship is coming straight towards or straight away from the observer.

If the receiver corrects for the travel time of light then they will calculate that the pulses were emitted once every ten seconds.

Note that the situation is symmetric. The "moving" ship may regard itself as stationary and the "stationary" ship as moving, and will be able to carry out the same measurements and calculations.

 

[radres]

what if the ship is moving in circles around the receiver and keeping the radius with the receiver always constant, can we forget about doppler effect? would the constant velocity change of the ship affect the calculations?

 

[Ibix]

In that case, yes, the receiver would receive pulses every ten seconds. Note the $v^2$ in the time dilation formula - it's only the magnitude of the velocity that matters.

Note that this situation is no longer symmetric. The ship moving in circles would receive ten pulses per (its) second from the stationary ship was emitting once per second by its clock.

Note that the thrust or time requirements to do this experiment are likely to be absurd.

 

[BvU]

what if the ship is moving in circles around the receiver and keeping the radius with the receiver always constant, can we forget about doppler effect? would the constant velocity change of the ship affect the calculations?

Note that you have to follow an orbit e.g. around the solar system with a huge radius:
Orbiting the solar system (never mind the earth) at a sensible radius would also be impossible without crushing every bone of the space travellers: $v^2/r=10$ g at $10^{12}$ km ! That's 6000 astronomical units, less than an hour per round trip (pluto has 40 AU and 248 year) -- all calculated nonrelativistically, of course .

 

[radres]

Note that you have to follow an orbit e.g. around the solar system with a huge radius:
Orbiting the solar system (never mind the earth) at a sensible radius would also be impossible without crushing every bone of the space travellers: $v^2/r=10$ g at $10^{12}$ km ! That's 6000 astronomical units, less than an hour per round trip (pluto has 40 AU and 248 year) -- all calculated nonrelativistically, of course .

yes I see that but we are just doing some mental experiments and we happen to have all the tools and technology to achieve that :) also keep in mind that if you accelerate every atom of your body at the same rate no acceleration can crush your bones, it is the difference of acceleration throughout the body that crushes bones.

 

[Ibix]

also keep in mind that if you accelerate every atom of your body at the same rate no acceleration can crush your bones, it is the difference of acceleration throughout the body that crushes bones.

True as far as it goes. But we have no way to do that and you will be crushed. Also, accelerating all parts of your body at the same rate is a problematic statement in relativity. The different parts of your body don't agree on what "the same rate" means due to time dilation and the relativity of simultaneity. The end result is painful.

 

[BvU]

Care to hint at a way to accelerate every atom of an object in a practical manner ?

 

[radres]

Care to hint at a way to accelerate every atom of an object in a practical manner ?

I surely would care if I had any idea how. Again, we are not talking in terms of today's technology it's just mental experiments.

 

[Ibix]

Care to hint at a way to accelerate every atom of an object in a practical manner ?

As noted above, you can't do so at the same rate, since "at the same rate" is an incomplete sentence.

I surely would care if I had any idea how. Again, we are not talking in terms of today's technology it's just mental experiments.

It's fine to think about what happens in extreme circumstances and leave the details to the engineers, so to speak. It's important, though, to be aware that there can be complications that you can't handwave away.

 

[Jeronimus]

True as far as it goes. But we have no way to do that and you will be crushed. Also, accelerating all parts of your body at the same rate is a problematic statement in relativity. The different parts of your body don't agree on what "the same rate" means due to time dilation and the relativity of simultaneity. The end result is painful.

What about if we drilled a hole to the center of a planet, having the right size and mass, and then dropped an astronaut in there.

His legs would be subject to less acceleration than his head, seen from the perspective of an observer at rest to the planet. He would be shrinking as predicted by SR (length contraction).
If the size and mass of the planet was chosen properly, one might be able to calculate that the astronaut won't be able to register any acceleration at all, as in his body registering a change of structure due to pressure/forces he would be subject to - or "feeling" acceleration as some loosely describe it.

(Clocks that were formerly synced, located at the astronaut's legs and head, before he gets dropped into the hole, would go out of sync once he would be in free fall, but devices trying to measure acceleration by measuring a change in the (space) structure, like a mass connected to a spring, should fail, or so i believe)

Contrary to letting the astronaut drop from orbit onto the planet surface, where his legs would be subject to more acceleration than his head seen from the perspective of an observer on the planet surface, hence the astronaut's body would have counter a force trying to elongate him.

Just a few thoughts. I did not really think this out or tried to figure out how one would calculate this from the perspective of the astronaut and what kind of mass/size the planet would have to be.

 

[Ibix]

What about if we drilled a hole to the center of a planet, having the right size and mass, and then dropped an astronaut in there.

Well, this isn't special relativity any more.

His legs would be subject to less acceleration than his head, seen from the perspective of an observer at rest to the planet. He would be shrinking as predicted by SR (length contraction).

Given that you are relying on careully chosen tidal forces to do your work, I wouldn't bet on being able to use SR concepts like length contraction - certainly not without careful calculation beforehand.

I think what you are trying here is a variant on Bell's spaceship paradox. In the "vanilla" version of that, two ships initially at rest and joined by a string undergo equal constant proper accelerations. According to the original rest frame of the ships, the string ought to length contract and break. But in the frame of the ships, why would the string break? It isn't length contracting. The solution is to realize that there is no "frame of the ships" - due to the relativity of simultaneity the two ships aren't at relative rest from either of their perspectives. That was the kind of thing I (and Bell, I think) was warning that you can't handwave away.

But you could certainly set up a variant where the two ships' accelerations are carefully chosen so that the separation between them (as measured in their initial rest frame) decreases at the same rate as the string length contracts. But that isn't equal acceleration in the initial rest frame and I have my doubts that it amounts to equal acceleration in anything other than a very carefully picked non-inertial frame.

I'd also suggest that this is far enough off topic to be another thread if you want to continue the discussion.

 

[BvU]

also keep in mind that if you accelerate every atom of your body at the same rate no acceleration can crush your bones, it is the difference of acceleration throughout the body that crushes bones.

With an orbit radius of 6000 au the required centripetal force is pretty much the same for all your atoms.

 

[PAllen]

Well, this isn't special relativity any more.

Given that you are relying on careully chosen tidal forces to do your work, I wouldn't bet on being able to use SR concepts like length contraction - certainly not without careful calculation beforehand.

I think what you are trying here is a variant on Bell's spaceship paradox. In the "vanilla" version of that, two ships initially at rest and joined by a string undergo equal constant proper accelerations. According to the original rest frame of the ships, the string ought to length contract and break. But in the frame of the ships, why would the string break? It isn't length contracting. The solution is to realize that there is no "frame of the ships" - due to the relativity of simultaneity the two ships aren't at relative rest from either of their perspectives. That was the kind of thing I (and Bell, I think) was warning that you can't handwave away.

But you could certainly set up a variant where the two ships' accelerations are carefully chosen so that the separation between them (as measured in their initial rest frame) decreases at the same rate as the string length contracts. But that isn't equal acceleration in the initial rest frame and I have my doubts that it amounts to equal acceleration in anything other than a very carefully picked non-inertial frame.

I'd also suggest that this is far enough off topic to be another thread if you want to continue the discussion.

Born rigid acceleration achieves this. Indeed the proper acceleration varies continuously along the rockets and string such that all neighboring distances in MCIF frames remain constant. Obviously, in the initial inertial frame, the rockets get closer together.

Herglotz-Noether theorem puts severe constraints on Born rigid acceleration, but it is quite generally possible if you exclude rotation.

 

[Ibix]

Born rigid acceleration achieves this. Indeed the proper acceleration varies continuously along the rockets and string such that all neighboring distances in MCIF frames remain constant. Obviously, in the initial inertial frame, the rockets get closer together.

Herglotz-Noether theorem puts severe constraints on Born rigid acceleration, but it is quite generally possible if you exclude rotation.

Agreed. But OP was originally talking about the same acceleration being applied to the whole body. The proper acceleration clearly isn't the same along the length, and all I was noting was that I suspect that the only coordinate system where the coordinate acceleration is equal along the length is one constructed to achieve that.

 

[pervect]

what if the ship is moving in circles around the receiver and keeping the radius with the receiver always constant, can we forget about doppler effect? would the constant velocity change of the ship affect the calculations?

I believe you're asking about what physicists would call the transverse doppler effect. The short answer is yes, see the wiki_article for more details.

The transverse Doppler effect is the nominal redshift or blueshift predicted by special relativity that occurs when the emitter and receiver are at the point of closest approach. Light emitted at closest approach in the source frame will be blueshifted at the receiver. Light received at closest approach in the receiver frame will be redshifted relative to its source frequency.

If the space ship, considered to be small and pointlike (so we don't have to talk about what happens if it's not) is accelerating in a circular orbit and broadcasting a signal (via radio or laser, i.e. some known physical means that sends signals at the speed of light), said signal will be red-shifted when it's received by a stationary observer at the center of the space-ships circular orbit. This means that the received frequency will be lower, and if the space-ship was sending a video signal, the video will play out in slow motion.

If the receiver isn't at the center of the circular orbit, the velocity won't be transverse anymore, and you'll need a different more complicated calculation which basically involves a full doppler effect calculation. The distance from the receiver to the space-ship will only be constant if the receiver is at the center of the circular orbit.

Some experimental tests of this have been done (but with atoms, not spaceships), the results are in agreement with special relativity.

 

[timmdeeg]

If the space ship, considered to be small and pointlike (so we don't have to talk about what happens if it's not) is accelerating in a circular orbit and broadcasting a signal (via radio or laser, i.e. some known physical means that sends signals at the speed of light), said signal will be red-shifted when it's received by a stationary observer at the center of the space-ships circular orbit.

This situation appears analogous to the one in Schwarzschild spacetime, where the far away observer (who is in free-fall) sees the shell observer close to the black hole (who accelerates in his direction) redshifted. If true and assuming constant distance during the measurement of the redshift then an observer who hasn't any additional information couldn't distinguish between the two scenarios: If the source accelerates in a circular orbit with him at the center in flat spacetime or if it has constant r-coordinate in Schwarzschild spacetime,right?

 

[pervect]

This situation appears analogous to the one in Schwarzschild spacetime, where the far away observer (who is in free-fall) sees the shell observer close to the black hole (who accelerates in his direction) redshifted. If true and assuming constant distance during the measurement of the redshift then an observer who hasn't any additional information couldn't distinguish between the two scenarios: If the source accelerates in a circular orbit with him at the center in flat spacetime or if it has constant r-coordinate in Schwarzschild spacetime,right?

Given Ashby's analysis of the orbiting clocks in the GPS system, I'd say no. See for instance
Relativity[/PLAIN] in the Global Positioning System.

I'd say more, but I'm pressed for time.

 

[Peter Martin]

A spaceship traveling at speed of light close to speed of light (wrt inertial reference frame) sending some data every second on their clock to people who are stationary (wrt inertial reference frame). At what time these people would receive this data on their own clock?

Let's say for a second passed in the spaceship, 10 seconds passes for the stationary people.

Sorry if this makes no sense, I don't have a good understanding of relativity, I only know that at high speeds, the time is slower than the people at low speeds.

Although this "spaceship thought experiment" is included in most popular books on Special Relativity (SR) it does not demonstrate time dilation due to relative speed. If the spaceship were approaching Earth the data would arrive faster then once per second due to the decreasing distance the signal has to travel. SR never predicts "time contraction".

Time dilation is due to light's universal measured speed. (See "Einstein's light clock" for explanation.) If any thought experiment lacks the universal measured speed of light as a necessary condition -- as yours doesn't -- time dilation cannot be assumed. Many books written by "authorities" on SR contain similar thought experiments which are really unrelated to SR.

To test whether an example of time dilation is legitimate, reverse the situation. If time intervals get shorter it's not a demonstration of light's universal measured speed, but only of light's finite speed. The two are often conflated.

 

[PeterDonis]

If the spaceship were approaching Earth the data would arrive faster then once per second due to the decreasing distance the signal has to travel.

This is the Doppler effect, not time dilation. They are related but not the same. Time dilation is what you get when you take this direct observation and correct for the travel time of the light signals in order to calculate the rate at which they were emitted by the source. That rate will still be slower for an approaching source; the "slower" is time dilation.

SR never predicts "time contraction".

No, but it does predict exactly what you describe for the Doppler effect from an approaching source.

Many books written by "authorities" on SR contain similar thought experiments which are really unrelated to SR.

You will need to give specific references for this very strong claim.

 

[Peter Martin]

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine cited an example of time dilation using a moving railroad car and a flashlight. In the example, the conductor flashed a beam of light from the rear of the moving car toward the front. As the beam traveled forward with respect to the train’s direction, the front of the car receded from the oncoming light. Therefore, from the point of view of a trackside observer, the light took longer to traverse the moving car than it would have had the train been standing still on the tracks. Considering the time it took the light to make the journey as one unit of time on the train, the trackside observer would interpret the train’s “clock” as running “too slow”.

But again, this example was carefully chosen to illustrate the desired point. Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks. In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

 

[PeroK]

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine cited an example of time dilation using a moving railroad car and a flashlight. In the example, the conductor flashed a beam of light from the rear of the moving car toward the front. As the beam traveled forward with respect to the train’s direction, the front of the car receded from the oncoming light. Therefore, from the point of view of a trackside observer, the light took longer to traverse the moving car than it would have had the train been standing still on the tracks. Considering the time it took the light to make the journey as one unit of time on the train, the trackside observer would interpret the train’s “clock” as running “too slow”.

But again, this example was carefully chosen to illustrate the desired point. Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks. In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

Yes, but Discover magazine is hardly a reliable source for these matters. You won't find this sort of error in any serious textbook.

 

[PeterDonis]

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine

Fyi, this would probably not be an acceptable source here on PF; we want to see textbooks or peer-reviewed papers. The moderators would have to look at it to make a determination.

That said, your criticism of the article's argument is incorrect; the argument, at least as you present it here, is wrong, but not for the reason you give. See below.

Had the conductor flashed the light backward with respect to the train’s motion, the forward-moving rear of the car would have intercepted the oncoming light sooner than it would have were the train motionless on the tracks.

Yes; and what this demonstrates is relativity of simultaneity.

In this case, the trackside observer would see the light taking a shorter time for the experiment, and would interpret the train’s “clock” as running “too fast”

No, he would interpret it as relativity of simultaneity: light beams which would reach the ends of a motionless train simultaneously--or, equivalently, would reach the points on the track which would mark the ends of a motionless train simultaneously--do not reach the ends of a moving train simultaneously.

So a proper criticism of the argument, at least as you are presenting it here, is that the experiment is not about time dilation at all; it's about relativity of simultaneity. Neither the "forward" nor the "reverse" aspects of the scenario have anything to do with time dilation. To demonstrate time dilation, you would need a light pulse that goes out and comes back, as in a light clock, or some equivalent way of comparing clock rates.

To know whether the actual article is in fact making this mistake, I would have to see the article itself. It's quite possible that it is, since Discover magazine is not exactly a gold-plated source for relativity physics; but it's also possible that you are misinterpreting the argument given in the actual article.

 

[Mister T]

Although this "spaceship thought experiment" is included in most popular books on Special Relativity (SR) it does not demonstrate time dilation due to relative speed.

I'll repeat the request for a reference. Not because I'm challenging you, but rather because I really do want to understand the issue.

An article celebrating the centennial of SR in a 2005 issue of “Discover” Magazine cited an example of time dilation using a moving railroad car and a flashlight.

Okay, but popularizations of SR are almost always written by physicists with an expertise in SR, whereas Discover Magazine articles are usually written by people who are writers, not experts in SR.

Also, a reference includes enough information for us to find the article you're referring to.

 

[Peter Martin]

Yes, but Discover magazine is hardly a reliable source for these matters. You won't find this sort of error in any serious textbook.

How about "The Universe and Dr. Einstein" by Lincoln Barnett with a forward by Dr. Einstein himself? Serious enough for you? In Chapter 6, using the train-and-lightening thought experiment, he claims that the observer riding at the midpoint of the train will see the forward strike before seeing the rear strike. Not so. Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past. SR says that the measured speed of light is the same for all observers. This includes the observer on the train. It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

 

[Orodruin]

How about "The Universe and Dr. Einstein" by Lincoln Barnett with a forward by Dr. Einstein himself? Serious enough for you? In Chapter 6, using the train-and-lightening thought experiment, he claims that the observer riding at the midpoint of the train will see the forward strike before seeing the rear strike. Not so. Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past. SR says that the measured speed of light is the same for all observers. This includes the observer on the train. It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

No it isn't. It is you who are misinterpreting things. You need to be careful about specifying in what frame the lightning strikes are simultaneous. You cannot just say "simultaneous" without any qualifier that tells you what frame they are simultaneous in. If they are simultaneous in the ground's rest frame, the observer on the train will see the front strike first. This must be true in all reference frames and since the speed of light is the same in all directions, the strikes must therefore occur at different times in the train's rest frame.

If the strikes are simultaneous in the train's rest frame, then the ground observer will see the back strike first.

 

[jbriggs444]

It is the trackside observer who sees the front strike reaching the train observer first, not the train observer himself.

The sequence with which an observer sees (with his eyes) a set of flashes is an invariant physical fact. All observers agree on it. If two strikes are simultaneous in the trackside observer's frame then it will be a physical fact of the matter that the midpoint observer on the train will see the front flash first.

The two observers can and do account for that fact in different ways. The train observer will say that it is because the flashes were not simultaneous. The trackside observer will say that it is because the train observer moved toward one flash and away from the other.

 

[Mister T]

This isn't the example of the error I originally posed, but it is another false conclusion from a "serious" source.

But you've yet to establish your first claim that there was a false conclusion from a serious source.

It could very well be that the the writer of the Discover article made an error in his explanation of time dilation, as you originally claimed. But we don't know.

In your second claim about the relativity of simultaneity it is you who has made the error. It's possible for those two events be simultaneous in either frame, but not both. Because the two frames are equivalent.

 

[Peter Martin]

No it isn't. It is you who are misinterpreting things. You need to be careful about specifying in what frame the lightning strikes are simultaneous. You cannot just say "simultaneous" without any qualifier that tells you what frame they are simultaneous in. If they are simultaneous in the ground's rest frame, the observer on the train will see the front strike first. This must be true in all reference frames and since the speed of light is the same in all directions, the strikes must therefore occur at different times in the train's rest frame.

If the strikes are simultaneous in the train's rest frame, then the ground observer will see the back strike first.

This is my last response. Obviously, you are simply bent on being argumentative. If you read my description you will see than I never used the term "simultaneous'. I made quite clear the difference between what the train observer sees and what the trackside observer thinks the train observer sees. In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightning strike the track simultaneously at different points."

That's all I have to say. I think you just want to argue. I don't. Adios.

 

[Orodruin]

This is my last response. Obviously, you are simply bent on being argumentative. If you read my description you will see than I never used the term "simultaneous'. I made quite clear the difference between what the train observer sees and what the trackside observer thinks the train observer sees. In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightning strike the track simultaneously at different points."

That's all I have to say. I think you just want to argue. I don't. Adios.

I am sorry you feel this way. But consider that essentially everyone in this thread knows relativity much better than you do. From the perspective of those who actually know the subject, it is you who are being argumentative and hell-bent on not accepting conclusions that have been scrutinised by 100 years worth of physicists and that agree very well with experiments.

In fact, if you read the book you will see that the author made exactly the same mistake you falsely accuse me of making. "A thunderstorm breaks, and two bolts of lightning strike the track simultaneously at different points."

In popular literature, such assumptions will often be implicit. Since it is saying "strike the track simultaneously", the natural assumption would be to assume that this refers to the track's rest frame. You are making exactly the error of assuming that simultaneous in one frame means simultaneous in all frames. In fact, this is exactly what this thought experiment shows: Assuming that the light speed is the same in all directions in all inertial frames, the events cannot be simultaneous in the train's frame if they are simultaneous in the track's frame. This thought experiment by itself is not showing time dilation, it is showing relativity of simultaneity (although it is necessary to understand relative simultaneity if you want to understand why time dilation is symmetric).

 

[PeterDonis]

Since the train is an inertial reference frame it can be considered "at rest" while the countryside rushes past.

Yes, but in this frame the light rays are emitted at different times, which is why they are received at different times by the observer at the center of the train. Same speed, same distance, different emission times = different reception times.

If you read my description you will see than I never used the term "simultaneous'.

But you implicitly assumed that the light rays were emitted at the same time in the train frame. They're not. See above.

 

[Grimble]

Hmm; have you ever wondered why these age-old thought experiments, the light from two 'simultaneous' lightning strikes or alternatively light from a single source in the middle of the train, continue to cause so much discussion and dissension?

The basic premise is the simple one set out by Einstein in Chapter IX The Relativity of Simultaneity; observers at rest upon the embankment will observe the lights meeting at midpoint M proving that events A & B were simultaneous in their frame of reference. Observers at M' on the train '(considered with reference to the railway embankment)' are moving away from point M and therefore will not measure simultaneity.

All very simple and straightforward. So how do all the difficult questions arise?

​

Is there not something fundamental that is being overlooked here? - The change in perspective that Einstein introduced with his theories.
A fundamental change introduced with the theory of relativity was from the Objective 'God-like' view of what was being measured to the Subjective view of specific observers. Not surprisingly different observers make different measurements. Science suddenly changed from observing a single overall view to taking multiple different perspectives of different observers while still trying to present a single reality.

Nothing is fixed anymore it all depends on the relative movement of the observer and the observed.

So perhaps it would be better to examine what happens objectively and then calculate how this would be seen subjectively from different frames of reference.

Objectively: Light from two events A, B meet at event M. AM = BM so the light has traveled equal times at c from each source; therefore events A and B are simultaneous from an objective point of view. What do I mean by that? Well, they are simultaneous measured using the rods and clocks of the resting frame; i.e. measured by any observer at rest relative to events A, B and M.

But, subjectively, every observer is at rest relative to Spacetime - as mapped by their frame of reference in which they are by default at the origin or null point.
So for any observer present at M when events A and B occur will remain at M at the origin or null point of their frame of reference.

Taking any particular view such as the embankment and giving that the status of being the only truth is making it the privileged view. Einstein avoided that when he added

... and vice versa (relativity of simultaneity).

 

[Mister T]

Objectively: Light from two events A, B meet at event M. AM = BM so the light has traveled equal times at c from each source; therefore events A and B are simultaneous from an objective point of view. What do I mean by that? Well, they are simultaneous measured using the rods and clocks of the resting frame; i.e. measured by any observer at rest relative to events A, B and M.

Observers at rest on board the train can make the same claim. They can use rods and clocks of their resting frame to show that any observer at rest relative to events A, B, and M will see them as not being simultaneous. All you need to do is have the lightning strikes leave burn marks on both the train and the embankement. Likewise you can have an explosion occur at M that leaves the same type of burn marks.

Hmm; have you ever wondered why these age-old thought experiments, the light from two 'simultaneous' lightning strikes or alternatively light from a single source in the middle of the train, continue to cause so much discussion and dissension?

Lots of research has been done in an attempt to understand and improve student understanding of this and many other topics. But wondering why most people find it difficult to understand many of the topics of physics doesn't change the fact that they do.

Relativity of simultaneity is not demonstrated experimentally by this thought experiment. It is demonstrated every minute of every day at hundreds of places across the globe by scientists, engineers, and technicians who deal with precision timing, fast-moving particles, or both. It is not the human intellect that demonstrates the validity of this or any other physics concept, rather it is Nature's behavior.

 

[jbriggs444]

any observer at rest relative to events A, B and M

There is no such thing. Individual events do not define a state of motion.