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

[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.

 

[Mister T]

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

 

[Bartolomeo]

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

I thought it looks like that, An observer hires an infinitely large amount of assistants. He gives a clock to each of them. They stay at every feet from each other and fill the whole universe. Then observer flashes a lamp, let's say at 12. Rays of light go from clock to clock and every assistant adjusts his clock, since he knows distance and velocity of light. Then their clocks are synchronized by Einstein technique. They make judgement about time of event in certain point by readings of clocks in that place. Other clocks and rods move in this frame from clock to clock.
Any other observer does the same. He fills the whole space with clocks and synchronizes clocks by light. Since frames are in relative motions, clocks that belong to different observers show different times when they coincide. That leads to so called relativity of simultaneity. Different observers make different judgement about time of event. Am I wrong?

 

[Orodruin]

I thought it looks like that, An observer hires an infinitely large amount of assistants. He gives a clock to each of them. They stay at every feet from each other and fill the whole universe. Then observer flashes a lamp, let's say at 12. Rays of light go from clock to clock and every assistant adjusts his clock, since he knows distance and velocity of light. Then their clocks are synchronized by Einstein technique. They make judgement about time of event in certain point by readings of clocks in that place. Other clocks and rods move in this frame from clock to clock.
Any other observer does the same. He fills the whole space with clocks and synchronizes clocks by light. Since frames are in relative motions, clocks that belong to different observers show different times when they coincide. That leads to so called relativity of simultaneity. Different observers make different judgement about time of event. Am I wrong?

This is just a thought construct of a possible way of defining coordinates.

 

[Bartolomeo]

This is just a thought construct of a possible way of defining coordinates.

I thought that Special Relativity is based on this construct. Isn't it?

 

[Orodruin]

I thought that Special Relativity is based on this construct. Isn't it?

As I said:

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

 

[Bartolomeo]

HOWEVER :

If observer is always at rest, why then did you include:

"T1 moved to another spatial position X1"

I don’t know, how everyone can be at rest. I tried to assign a state of motion to an observer and to think what's going on then, but my reflections (they are not mine, to be frank) were met with cool.

Sometimes even scientific tycoons express ideas, that we have to introduce some kind of preferred 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.

I

 

[Mister T]

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

No! How could he? The burn marks from the two lightning strikes are there on the platform. The burn mark from where the flashes of light met is also there on the platform. That burn mark is not midway between the other two. The only way the strikes could be simultaneous is if the flashes moved at different speeds. Most physicists believed that the flashes do indeed travel at different speeds, but as the experimental evidence was collected it became apparent that the flashes do indeed travel at the same speed regardless of the speed of their source.

This leaves us with a couple of possibilities. Simultaneity is relative because the two inertial reference frames are equivalent, or there is something special about the frame of reference in which the strikes are simultaneous. Since we have no experimental evidence to support the latter conclusion, we assume the former is valid.

This is the nature of science. We accept the validity of things on a tentative basis. In this case what we're accepting is the equivalence of inertial reference frames. That acceptance is tentative. If it's demonstrated that there's a way to distinguish one inertial reference frame from another the acceptance goes away. Since that hasn't happened, despite a multitude of attempts to do it in a multitude of ways, we retain the acceptance. This is true of every so-called law of physics.

Note that this thought experiment can be arranged so the explosion burn mark on the platform is midway between the strike burn marks on the platform. When we do that we conclude that the flashes were simultaneous in the rest frame of the platform. But then the explosion burn mark on the train will not be midway, and we conclude that the flashes were not simultaneous in the rest frame of the train. The two frames are equivalent!

 

[Ibix]

No! How could he?

I think Grimble is correct here - his setup had simultaneity in the train frame.

 

[Ibix]

Yes, everything it is very simple. We don't need any world lines....Points A and B are at equal distances from E [the observer on the embankment] to the left and right.

...But the observer T1 [on the train] thinks ...Distance to A and B is the same.

My additions in square brackets.

If A and B are points (which is another name for the worldlines you say you don't need) then you are using each label to refer to two different things - the worldline through the lightning strike that is at rest in the embankment frame and the worldline through the same strike that is at rest in the train frame. As Orodruin says, this is a very similar mistake to the one Grimble is making.

You do seem to me to consistently have trouble separating things that are frame dependent and things that are not. At least, your writing is extremely confused about it.

 

[Ibix]

I thought that Special Relativity is based on this construct. Isn't it?

It's one way of doing it, and the oldest. Milne provided a different set of coordinates on flat spacetime, which turn out to be co-moving coordinates in FLRW spacetime in the zero mass limit (which is Minkowski spacetime). Rindler coordinates cover some of Minkowski spacetime. I've heard of the Edwards simultaneity criterion, although I know no more than the name. Dolby and Gull wrote a paper on "radar time" which is a generalisation of Einstein's simultaneity condition for observers who do not remain inertial, based on work by Bondi ("k-calculus").

Special relativity was developed with the Einstein simultaneity criterion. It's probably the simplest setup, unless you've a desperate need for anything else. But it is far from the only way to do things. You can even abandon coordinates and reference frames altogether and work in coordinate-free representations for many purposes, if you're confident enough.

 

[Mister T]

I think Grimble is correct here - his setup had simultaneity in the train frame.

And therefore not in the platform frame.