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

[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).

 

[Herman Trivilino]

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.

 

[PeterDonis]

Nothing is fixed anymore

This is not correct. SR still has things that are fixed; they just aren't the same things as in Newtonian mechanics.

Objectively: Light from two events A, B meet at event M.

This is correct; in fact it is the key objective fact about the entire scenario. And furthermore, this objective fact does pick out one particular inertial frame among all the possible ones. But you are not correctly describing how that frame is picked out, or what the implications are.

subjectively, every observer is at rest relative to Spacetime

Having a frame in which you are at rest does not make you "at rest relative to spacetime"; the latter concept doesn't even make sense.

 

[Grimble]

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

This is not correct. SR still has things that are fixed; they just aren't the same things as in Newtonian mechanics.

Having a frame in which you are at rest does not make you "at rest relative to spacetime"; the latter concept doesn't even make sense.

Apologies for the use of hyperbole; for of course events are points fixed in space and time; but what do we mean by 'at rest'?
Surely that can only be relative to a frame of reference - for when we refer to a point or body, or any Minkowski 'substantial point' it is has to be located within a frame of reference.
Any Frame of Reference gives a fixed map relative to the event at its origin, or null point; a map in which everything in Spacetime is moving relative to that frame of reference.
It is a somewhat tautological concept but every observer must be at rest relative to their frame of reference.

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.

Exactly! For then it is an observer from another frame for whom the train is moving. But the observer on the train, in his frame of reference is at rest and for him A, B and M' will be fixed points and AM' = M'B. For the train observer it is M and the embankment that is moving away.

The train observer will measure simultaneity but for them it is the embankment observer who is moving away and therefore won't.

 

[Orodruin]

Apologies for the use of hyperbole; for of course events are points fixed in space and time; but what do we mean by 'at rest'?
Surely that can only be relative to a frame of reference - for when we refer to a point or body, or any Minkowski 'substantial point' it is has to be located within a frame of reference.
Any Frame of Reference gives a fixed map relative to the event at its origin, or null point; a map in which everything in Spacetime is moving relative to that frame of reference.
It is a somewhat tautological concept but every observer must be at rest relative to their frame of reference.

You are missing the entire point. Events are single points in space-time and cannot be assigned a state of motion. In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

 

[Bartolomeo]

but what do we mean by 'at rest'?

In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

Maybe we can arrange these notions this way. I think that to be “at rest” means to introduce your own rest frame with Einstein synchronized clocks, as we do in Special Relativity. An observer cannot detect his absolute motion, but can subjectively assign himself this state. What actions he has to take, if he assigns himself state of motion? What his actions should be different from those, when observer assigns himself state of rest?

1) He shouldn’t introduce his own reference frame with synchronized clocks, but has to use other guy’s one. For example, there is a reference frame K with Einstein – synchronized clocks A and B. In this reference frame moves clock C. Observer "in motion" possesses clock C and compares readings of this clock with clock A first and clock B then (successively).

2) If an observer ascribes himself state of rest, he introduces his own reference frame and adds another clock D into another spatial position. He synchronizes clocks C and D by Einstein. Clock A (and then clock B) now moves in his reference frame. Then he compares readings of clock A with clock C first and clock B then. Obviously, clock A dilates. So, if we describe motion and use just one reference frame, we need 3 (three) clocks. If there are two reference frames and each is "at rest", we need 4 (four) clocks.

3) Let’s observer ascribes himself state of rest. Then another observer or observable object (source of light, for example) moves at parallel line to axis X in observer’s frame. In this case the observer, who assigns himself state of rest has to accept beams of light that were released, when this observer and source WERE at points of closest approach. If he has a telescope, he keeps his telescope along Y axis straight up.

4) If observer ascribes himself state of motion in other guy’s reference frame, he accepts beams of light, when he and observable object ARE at the points of closest approach. In this case he keeps his telescope at oblique angle to direction of his motion “into front”. The source appears to be in the front of him, though actually is straight “under” him at points of closest approach. He thinks that he keeps his telescope at oblique angle in order to take into account aberration of light, as astronomers do observing distant stars.

It should be noted, that if two observes move relatively to each other, they cannot ascribe themselves equal states simultaneously. Of one assigns himself state of rest, another has to assign himself state of motion. For example, if one observer releases beam of light straight up along y axis, another one, who moves in his frame, has to tilt his telescope at oblique angle to direction of his motion “into front”. They can calculate these angles using aberration of light formula.

Or vice versa.

Otherwise he will not see the beam of laser light.

 

[Grimble]

You are missing the entire point. Events are single points in space-time and cannot be assigned a state of motion. In order to assign a state of motion, you need to consider the world line of an observer, which is an extended one-dimensional curve in space-time.

I'm sorry I don't understand what you mean here. '... In order to assign a state of motion ...' - in order to assign a state of motion to what? An Event? But as you have just stated viz. ' Events are single points in space-time and cannot be assigned a state of motion. ' ...?

And I don't understand why do you say

You are missing the entire point. Events are single points in space-time and cannot be assigned a state of motion.

in response to me saying

for of course events are points fixed in space and time;

 

[Grimble]

Einstein was quite specific in chapter IX viz. As observed from the embankment:
- M is stationary mid way between A and B and therefore the lights will meet at point M.
- M' is moving toward light B and away from light A and will therefore see light B first.

I believe everyone accepts this, But do the observations from M' on the train lead to the same conclusion?

Let us take an allegory.
Let the Earth take the place of the train then a star will take the place of point B when the Earth is moving towards it and point A, 6 months later when the Earth is moving away from it.
Does the light from the star take less time to reach the Earth when the Earth is moving towards it and more time when the Earth is moving away from it?
i.e. does the speed of light vary according to the relative velocity of the Earth and the star?
For the observer on the Embankment the speed of light is constant it is the train's speed that affects the time of the lights arriving at M'.
For the observer on the train there is only the speed of light for they cannot be moving relative to the star for that would be the equivalent of the speed of the light from the star depending on the relative movement of the light source that is the star.

 

[Ibix]

Let the Earth take the place of the train then a star will take the place of point B when the Earth is moving towards it and point A, 6 months later when the Earth is moving away from it.
Does the light from the star take less time to reach the Earth when the Earth is moving towards it and more time when the Earth is moving away from it?
i.e. does the speed of light vary according to the relative velocity of the Earth and the star?
For the observer on the Embankment the speed of light is constant it is the train's speed that affects the time of the lights arriving at M'.
For the observer on the train there is only the speed of light for they cannot be moving relative to the star for that would be the equivalent of the speed of the light from the star depending on the relative movement of the light source that is the star.

Here, you are considering a non-inertial frame of reference, even leaving aside the complications of GR and pretending the solar system is actually an orrery. The coordinate speed of light is not constant or invariant in such frames, and there is not even necessarily a clear winner for a definition of spatial distance. Thus we can't generalise our SR-in-inertial-frames intuitions to such frames.

I expect the results to be consistent if the relevant calculations and definitions are handled carefully. All you are doing is changing from simple coordinates to complicated ones.

 

[Herman Trivilino]

Surely that can only be relative to a frame of reference - for when we refer to a point or body, or any Minkowski 'substantial point' it is has to be located within a frame of reference.

It has to be located in every frame of reference.

Exactly! For then it is an observer from another frame for whom the train is moving.

You miss the point. When the two light rays meet at M they trigger an explosion that leaves a burn mark on both the platform and the train. An observer on the platform will have a burn mark that's at rest relative to him. He can use rods at rest relative to him, and clocks at rest relative to him, to conclude that the two lightning strikes were not simultaneous.

It is a somewhat tautological concept but every observer must be at rest relative to their frame of reference.

It is entirely tautological because you are defining a person's frame as their rest frame. Note that there is no need to do such a thing, you just refer to it as their rest frame.

 

[Grimble]

An observer on the platform will have a burn mark that's at rest relative to him. He can use rods at rest relative to him, and clocks at rest relative to him, to conclude that the two lightning strikes were not simultaneous.

Really? But surely the observer on the platform concludes that they were simultaneous?

 

[Grimble]

Here, you are considering a non-inertial frame of reference, ...

OK then, lin simple terms.

Events A and B are fixed in space and time in each and every frame of reference.

The train is the rest frame of the observer at M'.

In the train frame A,B and M' are each fixed points.

For the lightning strikes to not be simultaneous M' must be moving relative to A and B.

The Observer at M' must be at rest in their rest frame! They can only be moving measured from another frame with which they have a relative velocity; or
the light sources at A and B would have to be moving in the train frame and we would have to abandon the 2nd postulate! viz.

The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

We can say the observer at M' is moving toward B and away from A in the embankment frame as the speed of light is c relative to M and M' is moving in that frame, but in the frame of M' that cannot be and M' cannot be moving relative to A and B.

What could Einstein mean in chapter IX, The Relativity of Simultaneity when he wrote:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).

[my highlighting]
by vice versa? Other than 'Events which are simultaneous with reference to the train are not simultaneous with respect to the embankment'?
i.e. that simultaneity is relative depending on the observer's frame of reference.

I am not trying to change anything here, all I am doing is applying the laws of relativity and reading exactly what Einstein himself wrote.

 

[Orodruin]

In the train frame A,B and M' are each fixed points.

No. If A and B are events they only exist at a particular time. You cannot say that an event is a fixed point in space - it is a point in space at a given point in time. There is no notion of an event "moving" because in order for something to move it must exist at different times. You keep repeating the same basic mistake - events cannot be assigned a state of motion and all your reasoning is built on the assumption that it can.

Edit: The following statements are therefore meaningless:

For the lightning strikes to not be simultaneous M' must be moving relative to A and B.

the light sources at A and B would have to be moving

in the frame of M' that cannot be and M' cannot be moving relative to A and B.

With regard to:

I am not trying to change anything here, all I am doing is applying the laws of relativity and reading exactly what Einstein himself wrote.

No, you are not doing what Einstein wrote. You have a fatal misunderstanding of what an event is. Note that the concept of an event is not particular to special relativity - the same assumptions that you do would be fallacies also in classical Newtonian mechanics. Regardless, despite what many laymen seem to think, Einstein's writing is not the definite authoritative go-to text on relativity and definitely not the most accessible. The understanding of relativity has developed significantly since 1905.

 

[Ibix]

In the train frame A,B and M' are each fixed points.

M' is not an event, I think. It seems to be the worldline of the observer on the train. A and B are events. To make fixed points from them you need to draw a worldline through them, and you have freedom to draw that worldline in any timelike direction. You've chosen to do that such that the worldlines are parallel to M'. Fine. But you need to be aware when you decide that "A and B are fixed points" then you have added structure that isn't inherent in the experiment.

The thing is that the observer on the embankment can also draw a pair of worldlines through A and B that are parallel to his worldline, M. So he can also consider the strikes to have occurred at fixed points by adding extra structure in the same way that the train observer did. Again, there's nothing wrong with this, but you need to be aware that you've done it.

We can say the observer at M' is moving toward B and away from A in the embankment frame

"M' is a worldline representing motion towards the worldline the embankment observer chose to draw through B" is the correct way to put that.

 

[_PJ_]

No. If A and B are events they only exist at a particular time. You cannot say that an event is a fixed point in space - it is a point in space at a given point in time. There is no notion of an event "moving" because in order for something to move it must exist at different times.

Events have a FIXED spacetime interval between them to ANY AND ALL observers.

 

[Bartolomeo]

It seems @Grimble understands

OK then, lin simple terms.
Events A and B are fixed in space and time in each and every frame of reference.

Yes, everything it is very simple. We don't need any world lines.

There is an Embankment. Observer E is in the center of the Embankment (in the origin). Points A and B are at equal distances from E to the left and right. Two flashes flash simultaneously in E reference frame. Two beams of light approach E at the same time. Distance from E to A and B is the same, he makes conclusion, that flashes flashed simultaneously.

A train moves relatively to the Embankment to the right (in positive X direction) . Observer T1 is in the center of the train. When flashes flashed, an observer T1 was just in the front of E. While light beams reached E, T1 moved to another spatial position X1 and light beams reached him not simultaneously, first the RIGHT (B) and then the LEFT (A).

But the observer T1 thinks like that. It is not I, who moved. I was at rest and moved nowhere. Distance to A and B is the same. It is the guy E moved to the left. But beams of light arrived not simultaneously, though distance was the same. I ACTUALLY saw flash B first and flash A then. Velocity of light is c thus flashes flashed at different moments.

The passenger T2 was going in another carriage of the train. HE IS a burn mark on the train. He appeared just in the front of E (in the origin), when light beams reached E. But T2 knows, that he is not in the center of the train, but he sees two light beams approaching him at the same time too since he is just in the front of E.

T2 thinks like that. I have always been at rest since my birthday. It is E approached me from the left. I moved nowhere, but light beams arrived simultaneously. I am not in the center and distances to A and B are different, thus B released flash earlier than A. Though light beams arrived simultaneously, they were released at different moments.

The same reflections (just opposite), if the flashes were released simultaneously in train’s frame.

 

[_PJ_]

Remember ALL frames are equivalently valid and correct.
A will "see" V occurring at W
B will "see" X occurring at Y

The only things that will be universally agreed upon are the speed of light and the spacetime interval between W and Y

 

[Orodruin]

It seems @Grimble understands
Yes, everything it is very simple. We don't need any world lines.
...
I ACTUALLY saw flash B first and flash A then. Velocity of light is c thus flashes flashed at different moments.

It seems to me that you are making the same mistake as Grimble, you are changing from referring to A and B as points in space in E to calling them events.

 

[_PJ_]

I tend to think of it like this:
An INSTANT is a coordinate position of time. (i.e. x,y,z)
A LOCATION is a coordinate position of space. (i.e. t)
An EVENT is a coordinate position of space and time. (i.e. x,y,z,t)

Suppressing spatial dimensions to just x
then locations can be described with f(x)
instants as f(t)
and events as f(x,t)

(Arguably -t or even -it for convention)

The spacetime interval is then considered as the square root of (x^2 - (ct)^2)
So you can see it necessarily involves position, time, and the arbiter of causality, c.

 

[Bartolomeo]

It seems to me that you are making the same mistake as Grimble, you are changing from referring to A and B as points in space in E to calling them events.

Very good article with very clear definitions
https://arxiv.org/ftp/physics/papers/0512/0512013.pdf

 

[Orodruin]

Very good article with very clear definitions
https://arxiv.org/ftp/physics/papers/0512/0512013.pdf

Why are you linking this? I do not have a problem with the train thought experiment and I am not sure how you consider linking an arxiv paper relates to your own understanding of the difference between an event and a position.

 

[Bartolomeo]

Why are you linking this? I do not have a problem with the train thought experiment and I am not sure how you consider linking an arxiv paper relates to your own understanding of the difference between an event and a position.

What kind of mistake Grimble ( and I) does?

 

[_PJ_]

I'm sorry I don't understand what you mean here. '... In order to assign a state of motion ...' - in order to assign a state of motion to what? An Event? But as you have just stated viz. ' Events are single points in space-time and cannot be assigned a state of motion. ' ...?

And I don't understand why do you say
in response to me saying

The state of motion is assigned to the observer.
If the observer is moving towards the event or way from the event (or worse, accelerating) then the measurement of WHEN the event occurred will be different.
The same as any two observers in different inertial frames from each other, will also measure the event differently.

I've said this like 3 times now.
EVENTS are not fixed. Only the spacetime interval (i.e. complete description of position AND time) between events along with the speed of light is constant.

 

[Orodruin]

What kind of mistake Grimble ( and I) does?

you are changing from referring to A and B as points in space in E to calling them events.

 

[Bartolomeo]

The state of motion is assigned to the observer.
If the observer is moving towards the event or way from the event (or worse, accelerating) then the measurement of WHEN the event occurred will be different.
The same as any two observers in different inertial frames from each other, will also measure the event differently.

Observer never moves in special relativity. Observer in special relativity is ALWAYS at rest and conducts measurements in his rest frame. He has two clocks in points A and B and makes judgments about time of events according to readings of these clocks.

 

[_PJ_]

Observer never moves in special relativity. Observer in special relativity is ALWAYS at rest and conducts measurements in his rest frame. He has two clocks in points A and B and makes judgments about time of events according to readings of these clocks.

Well that's essentially equivalent to realigning axes or suppressing dimensions solely to make calculations simpler.
Since there's no relative motion then yes, in this specific case, EVENTS can be considered by that particular observer to occur with fixed coordinates - since the observer's position in space is constant and both move through time at the same rate the constant spacetime interval between the observer and event is maintained.

____________________________HOWEVER :
If observer is always at rest, why then did you include:
"T1 moved to another spatial position X1"

 

[Orodruin]

Observer never moves in special relativity. Observer in special relativity is ALWAYS at rest and conducts measurements in his rest frame.

This is just plain wrong. You cannot claim an observer (or anything else) to be at rest without referring to what they are at rest relative to. A measurement is not something that is "conducted in a frame". Everything - including experiments - happens in all frames. However, the experiments may be set up to measure a particular quantity in a given frame.

He has two clocks in points A and B and makes judgments about time of events according to readings of these clocks.

There is nothing in relativity that requires an observer to have actual clocks. Just as an observation in quantum mechanics does not require a sentient being. The assignment of time coordinates in a Minkowski frame is independent of whether there are actual clocks or not. The observer can just as well draw conclusions based on the constant speed of light, the