# Struggling with the Special Relativity and simultaneity

## Main Question or Discussion Point

As I understand, one of the Special Relativity roots is the statement that two events SIMULTANEOUS in one inertial frame are NOT necessarily simultaneous in another inertial frame that is moving against the first one. To illustrate and PROVE this statement Einstein gave his well known example with two lightning strikes and the observers on a station and in the passing by train.

But the FACT (proven by the Michelson-Morley experiments) is that BOTH observers DO see the strikes simultaneously, and it is only a deduction from his "way of thinking" that the station observer concludes that the train observer sees the front lightning before the rear one (and vice versa for the train observer about the station one).

STRUGGLING TO UNDERSTAND this example I do NOT see that it illustrates the absence of simultaneity. On the contrary it seems to raise the question about possible simultaneity of events for all inertial frames, moving against one another.

I hope you understand my plea for help and will show me how to get out of my conundrum.

Many thanks for attention.

Related Special and General Relativity News on Phys.org
bcrowell
Staff Emeritus
Gold Member
But the FACT [...] is that BOTH observers DO see the strikes simultaneously, and it is only a deduction from his "way of thinking" that the station observer concludes that the train observer sees the front lightning before the rear one (and vice versa for the train observer about the station one).
Yes, this is exactly right (except for the part about the MM experiment that I snipped out, which is not that closely related).

Simultaneity in general is never anything but a "deduction from a certain way of thinking." This is true in Newtonian mechanics just as much as in SR.

It seems as though you think of the absolute nature of simultaneity as something that is intuitively reasonable and should be the default, while the relativity of simultaneity is something that requires proof. I would say that the burden of proof is the other way around. Since simultaneity is never anything but a "deduction from a certain way of thinking," there is no reason to assume that it is absolute. To say that it is absolute would be a very strong assertion, which would require proof.

bcrowell:

The M-M experiment proved that the speed of light is the same for all inertial frames and that is why the train observer sees the simultaneity like the station one.
Do you agree?

Janus
Staff Emeritus
Gold Member
bcrowell:

The M-M experiment proved that the speed of light is the same for all inertial frames and that is why the train observer sees the simultaneity like the station one.
Do you agree?
It is because the speed of light is the same for all inertial frames that the train observer doesn't see the same simultaneity as the station observer.

First we establish that the lightning strikes occur at the same time according to the station observer and at the moment that the train observer is adjacent to him. He also, being halfway between the lightning strikes, sees the light from both flashes simultaneously. But because the train is moving towards one flash and away from the other, He runs into the light coming from one direction before it reaches the station observer, and the light from the other flash passes the station observer before it reaches the train observer. This means that one flash reaches the train observer after the other. It also means that the train observer is adjacent to different points of the tracks when each flash reaches him.

If you now consider what happens according to the train observer, he must agree with the station observer as to where he is with relation to the tracks when each light reaches him. Anything else will result in a physical contradiction. For example, if the station observer sees one light hit when the train observer is next to mile post 10 and the second one hits when he is next to mile post 30, The train observer must see the same thing. he can't say that both lights reached him when he was next to mile post 20. (If we put a bomb at mile post 20, that is set to explode if both lights reach it at the same time as the train observer does, we can't have the train observer saying the bomb went off and the station observer saying it didn't. )

The train observer is also halfway between the two points of the train where the lightning strikes, and since, according to him, it takes an equal amount of time for the light to travel from these two points to him ( the speed of light relative to him is the same in both directions), and he must see the light from the strikes at different times to prevent actual physical contradictions between frames, he must conclude that the strikes did not occur at the same time.

Mister T
Gold Member
But the FACT (proven by the Michelson-Morley experiments) is that BOTH observers DO see the strikes simultaneously, and it is only a deduction from his "way of thinking" that the station observer concludes that the train observer sees the front lightning before the rear one (and vice versa for the train observer about the station one).
Not that he SEES them arrive at different times, but rather that they must have STARTED their journeys at different times in order for them to have arrived at the same time. After all, one had a further journey than the other. If the speed of those light beams could be added to or subtracted from the train's speed then he could conclude that they had started their journeys at the same time. But since the speed of light is independent of the train's speed, the notion of absolute simultaneity must be abandoned.

Einstein said this was the last piece of the special relativity puzzle for him, and that its realization caused him to sit upright from his sleeping position in the middle of the night. After that came publication of the theory.

Last edited:
DAC
" Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train." Einstein.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
Not that he SEES them arrive at different times, but rather that they must have STARTED their journeys at different times in order for them to have arrived at the same time.
The events are also equidistant from the train observer. If they occured at different times he also sees them at different times. The train observer will see the strikes at different times and this is perfectly compatible with the description from the ground frame which will also conclude that the train observer will see the strikes at different times.

bcrowell
Staff Emeritus
Gold Member
bcrowell:

The M-M experiment proved that the speed of light is the same for all inertial frames and that is why the train observer sees the simultaneity like the station one.
Do you agree?
Not really. The MM experiment is neither logically nor historically very important. Historically, it played little or no role in Einstein's initial development of SR. Logically, it's just an experiment involving light, and light plays no fundamental role in relativity. Simultaneity does not need to be defined operationally by a method involving light.

Mister T
Gold Member
Not really. The MM experiment is neither logically nor historically very important. Historically, it played little or no role in Einstein's initial development of SR. Logically, it's just an experiment involving light, and light plays no fundamental role in relativity. Simultaneity does not need to be defined operationally by a method involving light.
The historical significance of the MM experiment is the role it played in the acceptance by other scientists of the significance of Einstein's 1905 theory of relativity. Other scientists were publishing theoretical explanations of the outcome of MM and Einstein's theory, even if it didn't mention MM specifically, addressed the same issues as those competing explanations. Without MM Einstein's 1905 relativity publication might not have been noticed so much and so soon, significantly altering the course of Einstein's professional life and of the development of theoretical physics.

The train observer will see the strikes at different times
The FACT is that the train observer actually DOES see the strikes at the SAME time, while the station observer only CALCULATES/THINKS that the train observer does not, as IMPLIED by Einstein in his example (experimental measurements - in the train frame, calculations - in the station frame) in the one of two equal points of view.

Nugatory
Mentor
The FACT is that the train observer actually DOES see the strikes at the SAME time, while the station observer only CALCULATES/THINKS that the train observer does not, as IMPLIED by Einstein in his example (experimental measurements - in the train frame, calculations - in the station frame) in the one of two equal points of view.
No, that is not right. The facts are statements of the form "A flash of light reached an observer at the moment that that observer's wristwatch read time ##T##". All observers, regardless of their state of motion, agree about the truth of these facts (which implies that if two flashes of light arrive at any observer at the same time, then all observers will agree that the arrival was simultaneous).

Any statement made by any observer, regardless of their state of motion, about the the simultaneity or not of the emission events has to be based on calculation.

15characters
PeterDonis
Mentor
2019 Award
The FACT is that the train observer actually DOES see the strikes at the SAME time
No, he doesn't. He sees the front strike first, then the rear one. That is, the light flash emitted by the front strike reaches the train observer at one event on the train observer's worldline, and the light flash emitted by the rear strike reaches the train observer at a different, later event on his worldline. Since any observer sees something when the light emitted by it reaches his worldline, the train observer sees the front strike before he sees the rear one.

By contrast, both light flashes reach the station observer at the same event on the station observer's worldline. So the station observer sees both flashes at the same time.

As for what the two observers calculate, the train observer also calculates, after allowing for light travel time, that the front flash happened before the rear flash, according to his definition of simultaneity. Whereas the station observer calculates, after allowing for light travel time, that the front flash and the rear flash happened at the same time, according to his definition of simultaneity.

15characters
Mister T
Gold Member
The FACT is that the train observer actually DOES see the strikes at the SAME time, while the station observer only CALCULATES/THINKS that the train observer does not,
Nope. The station observer knows that the train observer sees them arrive at the same time.

Where are you reading or seeing the account of this thought experiment? Perhaps if we knew that, and you could tell us just what it is you're looking at that leads you to your conclusion, we could make some progress. There are at least two versions of this thought experiment out there.

In the versions I've seen these two events happen at the same time, in all frames of reference:

1. Front flash of light arrives at center of train.
2. Rear flash arrives at center of train.

Both the train observer and the station observer are present at the center of the train when both events occur.

Perhaps we should agree on this before proceeding.

Last edited:
bcrowell
Staff Emeritus
Gold Member
It sounds like different people may be talking about different versions of the scenario. It can probably be posed in different ways. I have a version of it in this book http://www.lightandmatter.com/lm/ in discussion question A at the end of section 24.3.

Mister T
Gold Member
It sounds like different people may be talking about different versions of the scenario.
It appears I may be the offender here. My apologies to the OP for the obfuscations.

It can probably be posed in different ways. I have a version of it in this book http://www.lightandmatter.com/lm/ in discussion question A at the end of section 24.3.
In that particular scenario it's the emission of the flashes, not the reception of the flashes, that occur at the instant when train observer and the station observer occupy the same position. That's different from the one I've been talking about where the reception of the flashes occurs when the two observers occupy the same position.

Each of these two scenarios can then be described in two different ways, with either observer being the one who experiences the events simultaneously.

Last edited:
Where are you reading or seeing the account of this thought experiment? Perhaps if we knew that
Albert Einstein "Relativity. The Special and General Theory"

Mister T
Gold Member
Albert Einstein "Relativity. The Special and General Theory"
In that case, please allow me to start over ...

But the FACT (proven by the Michelson-Morley experiments) is that BOTH observers DO see the strikes simultaneously, and it is only a deduction from his "way of thinking" that the station observer concludes that the train observer sees the front lightning before the rear one (and vice versa for the train observer about the station one).
The train observer will actually see the flashes arrive at different times. It is not merely that the station observer calculates this to be true, it is also the fact that the train observer will actually see it happen. And since, in the train's frame of reference, they traveled equal distances they must have been emitted at different times.

If the MM experiment had a different outcome then it would be true that the train observer would see the flashes at the same time. This can be verified by using pitched baseballs rather than light beams to conduct the thought experiment, provided the baseballs and the train move at the lower speeds that we see baseballs and trains move. In this case both observers would see the baseballs arrive at the same time, and would calculate that they were thrown at the same time. Any differences (due to relativistic effects) would be too small to measure.

If you don't mind please consider my version of this famous thought experiment.

Near each of the observers there is a beer bottle dispenser activated only if two lights strike it at the same, most exactly, time. You are on a cruise ship (a third independently moving inertial frame). With a beer bottle in hand each observer will send a joyous tweet. Would you see two or only one tweet?

Mister T
Gold Member
IIRC, I based the version in my book (linked to from #14) closely on the version in that book. BTW, that book is also available online: https://www.marxists.org/reference/archive/einstein/works/1910s/relative/
I'm not sure what I was recalling when I wrote my first responses. I've since read the passage in your book and reviewed the passage in the OpenStax College Physics textbook. That review caused me to send the following note to the editors:

The chapter on relativity contains an error that needs to be fixed. It's in this passage on simultaneity:

"Now suppose we use this method to measure the time interval between two flashes of light produced by flash lamps. (See Figure 28.5.) Two flash lamps with observer A midway between them are on a rail car that moves to the right relative to observer B. The light flashes are emitted just as A passes B, so that both A and B are equidistant from the lamps when the light is emitted."

The light flashes can be emitted just as A passes B in only one frame of reference. This statement is stated as being valid without referring to the frame of reference in which it is valid. I suggest stating that things are arranged by B in such way that the flashes are emitted just as A passes B.

The way it's currently stated leads students to believe that the events really are simultaneous in A's frame, but only appear to B to be not simultaneous in A's frame. This misconception is reinforced because nowhere is it stated that A observes the flashes arriving at different times. Only that B reaches this conclusion by calculation.

PeterDonis
Mentor
2019 Award
Near each of the observers there is a beer bottle dispenser activated only if two lights strike it at the same, most exactly, time. You are on a cruise ship (a third independently moving inertial frame). With a beer bottle in hand each observer will send a joyous tweet. Would you see two or only one tweet?
One, from the station observer (at least, for the version of the thought experiment I'm thinking of).

Last edited:
Mister T
Gold Member
Near each of the observers there is a beer bottle dispenser activated only if two lights strike it at the same, most exactly, time. You are on a cruise ship (a third independently moving inertial frame). With a beer bottle in hand each observer will send a joyous tweet. Would you see two or only one tweet?
One. The other won't tweet because the flashes of light arrive at different times.

bcrowell
Staff Emeritus
Gold Member
I'm not sure what I was recalling when I wrote my first responses. I've since read the passage in your book and reviewed the passage in the OpenStax College Physics textbook. That review caused me to send the following note to the editors:
This is on p. 1107 of the book (p. 1117 of the pdf). The download page is https://openstaxcollege.org/textbooks/college-physics/pdf .

I don't see anything wrong. They've simply interchanged the roles of the train and earth compared to Einstein's description. They've chosen a different formulation than Einstein's, but different doesn't mean wrong.

Mister T