Bob: “The observers must AGREE with each other about what they know each other saw; what they disagree about is whether that means the events were simultaneous.”

Which implies that we need to examine what simultaneity means.

Simultaneity requires two events that are equidistant in time from an observer.

This must depend upon the way that Time is measured for that observer.

The time axis of a frame of reference as described by Minkowski is drawn vertically and is seen as a fourth Cartesian axis. In such a diagram two events will be simultaneous if they lie on the same time coordinate, parallel to the x and y axes.

While we know that for a moving frame time is dilated and length contracted and that this will effect such determination of simultaneity.

There are two ways we measure/consider time:

As ongoing background time e.g. the time of day or as an interval between two events.

Background time is measured as proper time; time measured along the worldline of a clock such as the clock at the origin of a reference frame. This is the Cartesian time axis of the time dimension we are familiar with.

The time interval from an event can be measured by the distance light would have travelled from that event – a sphere of light, if you will. This would best be measured using a Spherical Coordinate System.

That is a cast iron guarantee; they are simultaneous. Scientifically tested!

There is nothing relative about that! It is an absolute truth!”

Yes, it’s true – for M.

If the flashes happen to be simultaneous for M, then M (given this setup) will see the flashes simultaneously. And M’ will not (can’t) disagree! As I tried to help you see with the bomb in my first reply … M and M’ cannot disagree about what occurs at M or M’. In this case, M’ is agreeing with M, that the flashes reach M at the same time. (If M has the bomb, it will blow up. M’ will see the explosion!)

But what you are doing here (with “cast iron” etc) is – assuming – that simultaneity is absolute; that events are either simultaneous or not. You are missing the point – that Einstein showed that simultaneity is in fact relative. It makes a difference who is looking.

TyroJack: “Then why did he label it the Relativity of Simultaneity?”

Because M’ will not agree that the events were simultaneous.

As shown, from the point of view of M, the flashes reach M’ at different times. And as above, M and M’ can’t disagree about that! (e.g. If M’ is holding that bomb, neither M nor M’ will see it explode).

In short:

The observers must AGREE with each other about what they know each other saw; what they disagree about is whether that means the events were simultaneous.

M says: “I am in the middle of the events and saw them at the same time, so they were simultaneous. But I know M’ is moving towards one event and away from the other, so M’ won’t see the events at the same time.”

M’ says: “I am in the middle of the events and saw them at different times, so they were not simultaneous. But I know M is moving towards the later event and away from the earlier event, so have calculated that M will in fact see the events at the same time.”

…

TyroJack: “The one thing I am not saying is that simultaneity is absolute; it is relative to the motion of each frame. It can only satisfy Einstein’s test for an observer at rest, for that is part of his test for simultaneity – the observer has to remain at the midpoint between A and B.”

No, you ARE saying simultaneity is absolute. You started that reply with the insistence that if the events were simultaneous according to M, then the events ARE simultaneous, “cast iron guarantee”, “absolute truth”, etc. You think if M says the events are simultaneous, that that means every other observer (e.g. M’) must agree that the events are simultaneous. That’s absolute, not relative. If “relative” here simply amounts to an illusion about what each observer thinks the other sees, it could all have been written much more simply.

Remember; M’ won’t disagree that the flashes reached M at the same time. But likewise, M’ won’t disagree that the flashes reach M’ at different times. This is consistent. You are creating an inconsistency – effectively claiming that M can see the flashes reach M’ at different times, but that M’ will somehow see the events at the same time. (The bomb goes off or it doesn’t!)

(I’d add that you are taking the test for simultaenity much too literally; but don’t want to distract from the main point right now.)

]]>Consider Einstein’s test for simultaneity: the observer at the centre between two flashes of light that reach him simultaneously. This thought experiment uses exactly that scenario. So M is proving the simultaneity of the lightning strikes, because he is at rest equidistant from them.

That is a cast iron guarantee; they are simultaneous. Scientifically tested!

There is nothing relative about that! It is an absolute truth!

Then why did he label it the Relativity of Simultaneity?

In my original post I point out nine places in Einstein’s description where he insists that what he is describing is from the viewpoint of the embankment Observer.

He is stationary and measures simultaneity while the moving observer does not. This has nothing to do with who is on the Embankment but everything to do with who is stationary and who is moving.

The train observer can only be moving measured from another frame, because measured from his frame the roles are reversed and it is he who is at rest and the embankment that is moving.

This is the Relativity of Simultaneity, it is relative to one who is at rest (that is from whose frame it is measured) but cannot be for a moving observer. It is this view as Einstein was at pains to explain that demonstrates relativity.

The accepted interpretation, has nothing relative about it. The embankment observer measures simultaneity. Full stop.

The biggest problem with the traditional accepted interpretation is in using what the embankment observer sees as the only reality. It is the view from one frame and is relative to that observer. It is not an absolute version of what is happening.

M and M’ are not points fixed in Spacetime; they are points in frames of reference, which are relative to those individual maps of Spacetime.

The point where the lights meet is the event. Events are fixed in Spacetime. Their coordinates are particular to the individual frames.

In the Embankment Frame the train observer moves away from the lights meeting event; while from the Train Frame it is the embankment observer who is moving away – that is relativity – it is the essence of what relativity is about.

The one thing I am not saying is that simultaneity is absolute; it is relative to the motion of each frame. It can only satisfy Einstein’s test for an observer at rest, for that is part of his test for simultaneity – the observer has to remain at the midpoint between A and B.

It is like time dilation and length contraction: how fast is the clock really running? it reads different times from within its frame where it is at rest from the time measured in any frame where it is moving, as a function of its speed. How does a clock read two different times at the same moment?

Yet we know both times are correct and real! It is all relative.

It’s perfectly valid for one observer to figure what the other observer might observe. The point in the thought experiment by Einstein is that these observations can’t contradict; the flashes will either reach M’ at the same time or they won’t. M’ is a single location, so events occurring at M’ will be simultaneous or not, according to all observers. (e.g. the bomb held by M’ in my previous reply will either explode or it won’t). Since the flashes are stipulated (pre-defined for the experiment) to be simultaneous for M, it’s clear they can’t be simultaneous for M’. This isn’t an illusion for M, it’s the reality for both M and M’. This isn’t making the frame of M preferred, it just happens to be that A and B were simultaneous for M. Two – other – flashes might happen to be simultaneous for M’, and not for M.

There’s nothing “special” about events being simultaneous. In the standard scenario, where we stipulate simultaneous flashes for M on the embankment; M’ will see the flashes at different times. But M’ will be able to figure that M would see the flashes at the same time – M’ does not disagree with M! M’ says “the flashes were not simultaneous, but M’ saw them at the same time because they were moving towards the later flash”. That’s not making the M’ frame any more “preferred” than the M frame is “preferred” for saying those particular flashes were simultaneous. All observers can observe events; that the events happen to be simultaneous in one frame is nothing to do with having a “preferred” frame.

You really are 90% of the way there. It’s true M’ can consider themselves as at rest and M to be moving. And all the rest. But … any two events that M’ considers simultaneous can’t be simultaneous for M (and vice versa). Not just as some kind of illusion, but as the reality of their view on the Universe.

What you are arguing for is the exact opposite of the Relativity of Simultaneity. You are arguing for the Absoluteness of Simultaneity.

]]>BUT one cannot deduce from that one Frame of Reference what an observer in another Frame will perceive or measure!

Doing so is automatically giving that first Frame, preference. It is making the view from that initial frame ‘reality’.

We have three Spacetime Events. A and B where the lightning strikes and A and B on the train are colocated with A and B on the track and let us call it point C, dead centre between A and B where M and M’ are colocated.

In any frame of reference Events are fixed, they cannot move as movement is a change of location over time and an Event only exist for a moment in time.

Therefore the only location in Spacetime where those rays of light will meet is at point C.

In any Frame Spacetime is fixed because that is how it is mapped by that frame of Reference; In the Embankment frame M is permanently located at point C and will measure simultaneity when the reflected lights meet there, while M’ is moving away – in the Embankment frame.

In the train frame, the train is at rest in Spacetime and the train observer will remain at C, in that frame, and see the lights meet while M is moving away.

It is all about how the events are measured within each frame. No preferences. Each measures Simultaneity in their frame, and that simultaneity can not be measured from the other frame.

That is why it is the Relativity of Simultaneity.

When M determines that the flashes don’t arrive together at M’, that’s not something that can be contradicted by M’.

Imagine M’ is holding a bomb that explodes if the flashes reach him or her at the same time from front and back. As M can determine (when the events happen to be simultaneous for M), the flashes don’t reach the bomb (M’) at the same time, and the bomb held by M’ won’t explode. You can’t then say “oh but from M’ perspective the flashes do arrive at the same time and the bomb does explode”. That’s a contradiction; the bomb either explodes or it doesn’t and both observers can say why: e.g. M says M’ was moving toward one flash and away from the other; M’ says the flashes were not simultaneous, both know the M’ bomb didn’t explode.

You are correct that the roles can be reversed (vice versa). The train observer could consider two events to be simultaneous; but they’d be different events than any that the embankment observer considers simultaneous.

They can’t both consider the same two events as simultaneous … which your summary seems to imply.

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