I Is Simultaneity Absolute or Relative in the Theory of Relativity?

[Nugatory]

@CClyde the issue with relativity of simultaneity is actually straightforward, although the various train/platform explanations are often confusing.
A) Two spatially separated events are simultaneous if they happened at the same time.
B) How do we determine what time some event not right under our nose happened? We take the time that light from the event reaches us, subtract the light travel time, and that's when it happened. This calculation is no more confusing than saying that if an aircraft lands at 4:00 after spending an hour in flight it must have taken off at 3:00.
C) If you and I are moving relative to one another applying the procedure in #B will lead us to different conclusions about when events not under noses actually happened.
D) All paradoxes, inconsistencies, and apparent violations of logic and physical laws go away when we use the Lorentz transformations to relate the time and position of the relevant events as reported by you and by me in #C.

 

[FactChecker]

We know as he said, the flashes arrived at the observer simultaneously, so what other simultaneity is John talking about?

John knows that the flashes reached the middle simultaneously. Reaching the middle simultaneously is not debatable because they are two things that happen at the same place and at the same time. All observers will agree on that.
But how does John know that the flashes started from the ends "simultaneously"? That is a different type of "simultaneous". John observes light as though he is stationary. Since the distances to the two ends are equal and the flashes reached the middle simultaneously, they must have started from the ends "simultaneously". That is a different "simultaneous" because it relies on the John being treated as stationary. If John synchronized two clocks at the ends, he could use that belief to set them at the same time when the flashes started. But a different observer, O2, who is moving with respect to John and believes that he, himself is the stationary one would disagree with John. O2 would say that the flashes started at different times. So the concept of "simultaneity" in separated locations is something that observers who are moving with respect to each other would not agree on. That is a different type of "simultaneity".

 

[Dale]

What does John/the observer mean when they say “the two events happened simultaneously”?

”The two events” means the “two momentary flashes of light”. And “happened simultaneously” means that those events have the same time coordinate.

We know as he said, the flashes arrived at the observer simultaneously, so what other simultaneity is John talking about?

The emission of the two flashes.

 

[Histspec]

What does John/the observer mean when they say “the two events happened simultaneously”?

We know as he said, the flashes arrived at the observer simultaneously, so what other simultaneity is John talking about?

Let's say you have two light emission (or arrival) events simultaneously at time t at positions $x_1$ and $x_2$ in inertial frame S, then the temporal Lorentz transformation gives: $$t_{1}'=\frac{t-vx_{1}/c^{2}}{\sqrt{1-v^{2}/c^{2}}},\ t_{2}'=\frac{t-vx_{2}/c^{2}}{\sqrt{1-v^{2}/c^{2}}}$$
Setting $\Delta t'=t'_2−t'_1$ and $\Delta x=x_2 −x_1$ we have $$(1)\ \Delta t'=\frac{-v\Delta x/c^{2}}{\sqrt{1-v^{2}/c^{2}}}$$ From that we read of: a) Two light emission (or arrival) events separated by spatial distance $Δx$ that happen simultaneously in S, don't happen simultaneously in S'.
In case we have $Δx=0$, formula (1) gives Δt'=0, thus: b) Two light emission (or arrival) events that happen at the same place and simultaneously in S, also happen simultaneously in S'.

 

[CClyde]

I think everyone has said essentially the same thing with differing amounts of explanation.
There are two simultaneities to consider, the emissions (two events as they have spatial separation) and the arrival of the light from those events at an observer (one event when simultaneous)

Assigning a time coordinate to the emission events is as Ibix said, a matter of convention. We cannot know our motion relative to the emission events, so we adopt a convention to set a time coordinate for the emissions. If they are the same, they are simultaneous.
But a convention such as the Einstein convention can only establish a time from observer to a source/reflector, not a time to a spacetime coordinate unless the two are the same which they would not be if the source frame is in motion relative to the event. This is why the moving frame (sources included) finds no simultaneity in the arrival times of light from two simultaneous emissions even thought the observer remains at equal distance from both sources as John Norton’s example shows.

This tells me there is a significance kinematic distinction between moving frames revealed in the simultaneity of light events.

Is there a flaw in this reasoning?

 

[Dale]

a convention such as the Einstein convention can only establish a time from observer to a source/reflector, not a time to a spacetime coordinate

This is wrong. Why on earth would you think this is correct?

This tells me there is a significance kinematic distinction between moving frames revealed in the simultaneity of light events.

There is no distinction in the kinematics. The kinematics of this situation are wholly contained in the second postulate which is exactly the same in both frames. We have already covered this.

Is there a flaw in this reasoning?

Yes, you make random unjustified assertions that are not at all correct.

 

[PeroK]

There are two simultaneities to consider

There is only one that is relevant. The time of an event.

, the emissions (two events as they have spatial separation) and the arrival of the light from those events at an observer (one event when simultaneous)

This is irrelevant, as not all events emit light and very few events can be "seen". A train timetable is based on where the train is and not when light from the train reaches you. For example, at train at Edinburgh train station cannot be seen from a London train station. There is no light signal from a departure event at Edinburgh to the destination station at London. And, yet, the event "train left Edinburgh on time at 13:45" is a well-defined event. Even if Edinburgh station was in pitch darkness.

Assigning a time coordinate to the emission events is as Ibix said, a matter of convention. We cannot know our motion relative to the emission events,

There is no such thing as "motion relative to an event". An event is a point in spacetime.

so we adopt a convention to set a time coordinate for the emissions. If they are the same, they are simultaneous.
But a convention such as the Einstein convention can only establish a time from observer to a source/reflector, not a time to a spacetime coordinate unless the two are the same which they would not be if the source frame is in motion relative to the event.

Again, there is no such thing as motion relative to an event. Note that your first fundamantal problem is that you do not properly understand the concept of spacetime.

This is why the moving frame (sources included) finds no simultaneity in the arrival times of light from two simultaneous emissions

Simultaneity of events has nothing to do with light signals from those events. You can do physics in a dark room. You do not need electromagnetic radiation to have a coordinate system.

Some of the texts on SR over-emphasise the role of light signals. But, even if there were no such thing as EM radiation, SR would still be a valid theory of spacetime.

This tells me there is a significance kinematic distinction between moving frames revealed in the simultaneity of light events.

Which is a fundamental misunderstanding on your part. Which, moreover, I doubt John Norton shares.

Is there a flaw in this reasoning?

Yes. As above, it's all wrong.

 

[FactChecker]

This tells me there is a significance kinematic distinction between moving frames revealed in the simultaneity of light events.

Any inertial reference frame (IRF) can assume that it is stationary and can assign times in all locations that make sense. All physics and physical behavior will be normal. The IRF can define "simultaneous" of two events, either at the same location or at separated locations. Everything would seem normal. That is not the problem. The problem is that any other IRF, moving relative to it, would define "simultaneous" differently for two spatially separated events.
When you say that there "is a significant kinematic difference", it is true that the two IRFs are different. But logical measures of time and distance in each take care of the difference and all physics is identical in the two.

 

[berkeman]

Mentor Note -- the OP is on a 10-day vacation from PF. Have a nice day.