# Relativity of simultaneity

• I
• CClyde

#### CClyde

TL;DR Summary
Is the relativity of simultaneity an operational distinction between inertial frames in motion.
When two remote events are observed/measured to be simultaneous in one inertial frame, the same events will not be simultaneous when observed from a second frame in uniform motion relative to the first.

Why is this distinction in the kinematics of light not considered an operational distinction between inertial frames?

Why is this distinction in the kinematics of light not considered an operational distinction between inertial frames?
What exactly do you mean by that? The kinematics of light is the same in all inertial reference frames. That's very much the point where classical physics and SR diverge.

FactChecker and Dale
Why is this distinction in the kinematics of light not considered an operational distinction between inertial frames?
What does it mean for something to be "an operational distinction between inertial frames"?

I agree with @PeroK that the kinematics are the same in all inertial frames, so I am also not sure what you mean by "distinction in the kinematics of light".

I think of operational distinction as a different result from the same operation that distinguishes one from the other.

How can the kinematics be the same in all inertial frames if one observer finds the events are simultaneous and the other finds they are not simultaneous?
When two events occur simultaneously, kinematics that are not simultaneous result from the motion of the observer frame, not the events.

I think of operational distinction as a different result from the same operation that distinguishes one from the other.
Then it is not an operational distinction. The operation is "identify two events that are simultaneous in one frame and determine if they are simultaneous in the other". This does not distinguish one from the other. That operation, performed in either frame, yields the same result.

How can the kinematics be the same in all inertial frames if one observer finds the events are simultaneous and the other finds they are not simultaneous?
For me the kinematics is simply the second postulate: light moves at ##c##. Maybe you simply mean "kinematics" in a different sense than I do.

Suppose we were dealing with purely non-relativistic Newtonian physics and we had two different coordinate systems, say two observers watching a race car from opposite sides of the track. One observer says the cars are going at 100 mph to the right and the other says the cars are going at 100 mph to the left. Would you consider the distinction between left and right to be part of the "kinematics"?

How can the kinematics be the same in all inertial frames if one observer finds the events are simultaneous and the other finds they are not simultaneous?
Because "simultaneous" is just a convention; it's not part of kinematics.

Then it is not an operational distinction. The operation is "identify two events that are simultaneous in one frame and determine if they are simultaneous in the other". This does not distinguish one from the other. That operation, performed in either frame, yields the same result.
The operation is “measure the time of arrival of light from two simultaneous events at equal distance” The same operation in each frame yields a different result and the results are not a reciprocal symmetry we expect to find from the Newtonian equivalence in your example of race cars.

Because "simultaneous" is just a convention; it's not part of kinematics.
A train approaches a platform of identical length. As it reaches the platform, the alignment of the back of the train with the back of the platform is simultaneous with the alignment of the front of the train with the front of the platform. Is this simultaneity a convention, or the kinematics?

not the events.
Events don't have kinematics.

The point is simply that "simultaneous" is not an absolute thing, unlike in Newtonian physics. It's part of your definition of a frame, explicitly or implicitly. I still don't really understand your question, so I don't know if that answers it.

The operation is “measure the time of arrival of light from two simultaneous events at equal distance” The same operation in each frame yields a different result
This operation yields the same result in each frame. I am not sure why you think it yields a different result.

The different frames will disagree whether a given pair of events are simultaneous, but they agree on the result of the operation you specified. Specifically, in both frames if you measure the time of arrival of light from two simultaneous events at equal distance you will get that the times of arrival are equal. That follows immediately from the 2nd postulate.

not a reciprocal symmetry we expect to find from the Newtonian equivalence in your example of race cars.
You didn't answer the question that I asked of you though. I was trying to ascertain if you and I have a different meaning of the term "kinematics". Would you consider the difference between 100 mph to the right and 100 mph to the left to be a difference in "kinematics"?

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A train approaches a platform of identical length. As it reaches the platform, the alignment of the back of the train with the back of the platform is simultaneous with the alignment of the front of the train with the front of the platform.
Simultaneous in what frame? Simultaneity is frame dependent. That's why it's a convention.

A train approaches a platform of identical length. As it reaches the platform, the alignment of the back of the train with the back of the platform is simultaneous with the alignment of the front of the train with the front of the platform. Is this simultaneity a convention, or the kinematics?
If the train is moving at sufficient speed relative to the platform, then:

a) In the platform frame, the train will be measured as shorter than the platform. Hence, the rear of the train will pass the rear of the platform before the front of the train passes the front of the platform. The two events are not simultaneous in that frame.

b) In the train frame, the platform is measured as shorter than the train. Hence, the rear of the train will pass the rear of the platform after the front of the train passes the front of the platform. The two events are not simultaneous in that frame.

c) In a frame where both the train and platform are moving with equal speeds in opposite directions, the train and the platform will be measured to have the same length. The two events in question will be simultaneous in that frame.

phinds
@ Dale
Yes, they are the same speed, different direction.
But that is not what you asked originally. Two observers at opposite sides of the track will see the same kinematics because they are facing each other.

@PeterDonis, Ibix and PeroK
There is a difference between the simultaneity of two events and the simultaneity of the light of those two events arriving at an observer. The former is not frame dependent thus cannot be transformed away by motion. The latter can and is transformed away by motion which is the basis for the relativity of simultaneity.

The frame of an observer has no effect on the simultaneity of events. The frame of an observer determines the simultaneity of observables, not the events that emit the light observed.

So if my original question is taken as it was intended, it is the events not the arrival of the light from such events that are simultaneous. Any change from simultaneous observed in inertial frames is then a reflection of the motion of the frames, not the events. Thus when two events occur simultaneously and two inertial observers disagree on the simultaneity of the events, either one is wrong, or both are wrong, but they can’t both be right because the events did occur simultaneously.
Yet according to the principle of relativity, they are both right because the laws will not distinguish the motion of one frame from the other. When in fact the simultaneity, or lack thereof is exactly what does distinguish the motion of one frame from the other, one accurately reflects the events, the other does not.

weirdoguy, Motore and berkeman
There is a difference between the simultaneity of two events and the simultaneity of the light of those two events arriving at an observer. The former is not frame dependent thus cannot be transformed away by motion. The latter can and is transformed away by motion which is the basis for the relativity of simultaneity.
No, you have it backwards. The simultaneity of two different events is frame dependent. The "simultaneity" of light from two different events arriving at an observer at the same event (i.e., at the same instant on the observer's worldline) is not.

The frame of an observer has no effect on the simultaneity of events. The frame of an observer determines the simultaneity of observables, not the events that emit the light observed.
I have no idea where you are getting this from. In standard special relativity, simultaneity depends on an observer's choice of frame.

Do you have a reference for the claims you are making?

bhobba and Dale
Yes, they are the same speed, different direction.
But that is not what you asked originally. Two observers at opposite sides of the track will see the same kinematics because they are facing each other.
Ok, then we are using the word “kinematics” the same. So indeed, the relativity of simultaneity is the same kinematics also.

There is a difference between the simultaneity of two events and the simultaneity of the light of those two events arriving at an observer. The former is not frame dependent thus cannot be transformed away by motion. The latter can and is transformed away by motion which is the basis for the relativity of simultaneity.
You have this exactly backwards

The frame of an observer has no effect on the simultaneity of events.
This is flat out wrong. This has been well understood for 118 years now, since Einstein’s 1905 paper on SR.

Simultaneity is like “left”. What is simultaneous in one frame is not simultaneous in another, just like what is left in one frame is right in another.

There is a difference between the simultaneity of two events and the simultaneity of the light of those two events arriving at an observer. The former is not frame dependent thus cannot be transformed away by motion. The latter can and is transformed away by motion which is the basis for the relativity of simultaneity.
You have this exactly backwards. Whether or not the light pulses arrive at a specified observer simultaneously is an invariant. Whether they were emitted simultaneously must therefore be frame dependant.

The usual way to see this is to equip an observer with a bomb triggered by a photosensor, set so that one pulse illuminating it is not enough to trigger but two is. So the bomb only goes off if the pulses arrive at the observer simultaneously. Frames cannot disagree on whether the bomb went off or not, so they must agree on whether or not the pulses arrived simultaneously.

bhobba and Dale
Consider this analogy.

In this diagram, the two points A and B are at the same ##y## coordinate in the blue coordinate system, but are at different ##y## coordinates in the red coordinate system.

In relativity, something similar happens with the ##t## coordinate (time). Two events can be at the same ##t## coordinate in one coordinate system, but at different ##t## coordinates in another coordinate system. And "simultaneous" means "at the same ##t## coordinate".

PhDeezNutz, phinds, Vanadium 50 and 4 others
There is a difference between the simultaneity of two events and the simultaneity of the light of those two events arriving at an observer.
The measured time of an event is not when light from the event reaches a particular observer. If the Rover lands on Mars, then the images take at least 20 minutes to reach Earth. But, the time of the event is measured to be 20 minutes before the images arrive.

Note that technically we should be talking about reference frames, rather than isolated observers (although a lot of sources are sloppy about the distinction). In the rest frame of the solar system, events on Mars are seen on Earth at least 20 minutes after they occur (as measured in that reference frame).

A more extreme case is that of distant galaxies where we are now receiving the light from billions of years in the past and see those galaxies as they were billions of years ago (as measured in the comoving reference frame - or comoving coodinates).

PS the finite travel time of light from an event to an observation of the event is not what SR is based on. This is part of all physics (Newtonian and SR). For example, an early measurement of the speed of light was made using observations of the orbit of Jupiter's moons, which appeared to get out of sync as Jupiter moved relative to Earth. The conclusion was that the speed of light is finite:

https://en.wikipedia.org/wiki/Rømer's_determination_of_the_speed_of_light

The key postulate of SR is not that the speed of light is finite, but that it is invariant. In any case, the finite travel time of light from an event to an observer is not what the relativity of simultaneity is all about.

bhobba, vanhees71 and Ibix
If the Rover lands on Mars, then the images take at least 20 minutes to reach Earth. But, the time of the event is measured to be 20 minutes before the images arrive.
An important point, @CClyde. The experiment you are talking about uses the fact that both frames know that both light pulses travelled for the same length of time before reaching that frame's stationary observer to deduce something about the pulse emission times. It is not saying that the emissions happened when the pulses arrive, just that (given this specific experimental setup) the time between the emission events in that frame must be equal to the time between that frame's stationary observer's reception events.

bhobba and PeroK
The measured time of an event is not when light from the event reaches a particular observer.
Is this a case of this common confusion again?:
I think this is due to the common use of "observer" as a synonym for "reference frame".

bhobba and Dale
Why do you think that's a confusion? An observer in the sense of physics always refers to a frame of reference. Of course an "observer" doesn't need to be a human but can be an arbitrary measurement device, which stores somehow the results it measures like the big detectors at the LHC. They themselves also determine the frame of reference!

The "relativity of simultaneity" is something on the t-axis.

A similar, more intuitive, effect exists on the x-axis, the "relativity of same location":
Two distinct events have the same x-coordinate in one frame and different x'-coordinates in the other frame.

bhobba, vanhees71 and Dale
The latter is only easier to comprehend, because this we have in everyday life. If I'm sitting in a train, I don't move relative to the train and from this point of view I'm "always at the same place", while somebody on the platform sees me moving (relative to the platform).

Of course, the relativity of simultaneity is not intuitive for us, because we don't move close to the speed of light relative to objects in our surroundings (our "reference frames"), and thus with good approximation we can use our clocks as Newtonian clocks showing "absolute time".

Why do you think that's a confusion? An observer in the sense of physics always refers to a frame of reference.
With the word "observer" there's potential for confusion between what one actually sees directly and what one calculates to have happened. This particular thought experiment really hinges on a clear distinction between the two because it uses the former to infer the latter, rather than just assuming you've got the latter somehow.

And because an observer is a tetrad, while a global inertial frame is a tetrad field.

vanhees71 and Dale
I am with @Ibix and @A.T. here. It is clearly confusing terminology as evidenced by the fact that it confuses so many students.

One of the worst things that comes from it is the idea that a person must use the reference frame in which they are at rest. It is directly antithetical to the principle of relativity, but the standard relativity pedagogy, obsessed with observers, leads to that impression.

vanhees71
Hm, may be. But consider the example of the Doppler effect of light in a vacuum. Then, clearly which frequency of the em. wave is measured is given as the time-component of ##k^{\mu}## in the rest frame of the detector ("the observer"). Of course you can calculate it in any frame by using ##\omega_{\text{obs}}=k_{\mu} u^{\mu}##, where ##u^{\mu}## is the four-velocity of the detector in the arbitrary "computational frame".

Dale

After a Mentor discussion, the thread is reopened provisionally.

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I am quoting John D. Norton; Department of History and Philosophy of Science University of Pittsburgh from his web page - https://sites.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/Special_relativity_rel_sim/index.html

This same explanation can be found with minor variations in almost every text book on the planet.

“… a long platform with an observer located at its midpoint. At either end, at the places marked A and B, there are two momentary flashes of light.”
“Noticing that they arrive at the same moment and that they come from places equal distances away, the observer will decide that the two events happened simultaneous.”

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?

Thank you.

What does John/the observer mean when they say “the two events happened simultaneously”?
That the emission events were simultaneous using the Einstein simultaneity convention associated with the chosen observer. Everyone will agree that the chosen observer's reception events were simultaneous because they are actually one event, but may have different simultaneity conventions that say that the emission events were not simultaneous.

vanhees71
We know as he said, the flashes arrived at the observer simultaneously, so what other simultaneity is John talking about?
You are up against a weakness of the English language here. In formal physics "simultaneity" is a relationship between two events: Two events are simultaneous if they have the same time coordinate.

In this train/platform example, there are three events: Flash of light leaves left-hand source, flash of light leaves right-hand source, two flashes of light reach the person in the center, we subtract the light travel time from the arrival time to assign time coordinates to the two emission events, we see that we've calculated the same time coordinate for both emissions so they are simultaneous.
(If you analyze the event in a moving frame there will be additional relevant events involving light flashes reaching an observer at rest in the moving frame).

The English language, in natural usage, also applies the word "simultaneous" to the single event "two flashes of light reach person in center". This gives us the indisputable but also unhelpful tautology that every event has the same time coordinate as itself.

vanhees71 and jbriggs444
@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.

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vanhees71, Dale and Ibix
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".

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Histspec
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.

vanhees71 and 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'.

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Dale and vanhees71
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?