# Relative simultaneity

• Kiley

#### Kiley

Hello I'm having a lot of trouble understanding simultinaity and would appreciate any free book or article reccomendations.

## Answers and Replies

I haven't looked at the wikki article because I don't trust it and don't want to be given misinformation.
The main thing I'm having trouble with is it feels like the speed of light constant rule is being violated and I would like a bunch of examples of scenarios in order to prove to me it isn't being violated.
For example: imagine a ship going V to the right. Someone on Earth fires two lights that hit the edges of the ship simultaneously to the earth. There are three clocks on the edges and middle of the ship that are synchronized relative to the observer on the ship. What do they observe?

I prefer the train platform that einstein originally used.

Man standing on a platform has 2 lightning strikes equidistant from his eyes. He sees the lighting strikes occurring simultaneously.
A person is passing by on a train that is moving at close to speed of light at the exact moment the lighting strikes. In this instant, the person is located equidistant from the 2 lighting strikes on the train, but is accelerating towards one at almost the speed of light, and away from the other at almost the speed of light. In this instance, the person on the train observes the events to occur one after the other, with the light beam that they are traveling towards seen first, and the light beam they are traveling away form second. This is due to the fact that events occurring "simultaneously" is a matter of perspective, or it is relative the the observer. This is the basis of special relativity, that there is no absolute time anywhere.

When einstein then realized that gravity was an acceleration or a force, he was able to generalize this theory into the theory of general relativity.

Atleast that's my understanding. There is a great NOVA on einsteins general relativity and all of the thought experiments that led him to realize it. It was a lot more to do with the fact that gravity is a force than it does with simultaneity in my mind. But maybe that's just what I'm getting from it.
https://www.pbs.org/video/nova-inside-einsteins-mind/

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Look up Minkowski diagrams. They're basically displacement-time graphs, although time is conventionally drawn up the page. The key point to realize is that each choice of frame is simply a different choice of axes on the graph - axes slanted (it's a hyperbolic rotation, to be exact) with respect to the others. Because the axes aren't parallel, the idea of "at the same time" is different.

Then go and have a look at http://ibises.org.uk/Minkowski.html, which is a little Javascript I put together that let's you draw Minkowski diagrams and boost smoothly from frame to frame. Instructions are on the page. Down the bottom are some buttons that automatically draw a few standard scenarios. I'm afraid I wrote this before I had a touch-screen device, so it assumes you can right- and left-click. I should get round to adding a touch-screen friendly interface one of these days.

Dale
A person is passing by on a train that is moving at close to speed of light at the exact moment the lighting strikes.
This is confusing because the whole point is that "exact moment" is not a well-defined term - the two frames disagree on it. There are two resolutions to this. One is to specify which frame's simultaneity convention you are using. The other is to have the two observers pass at the instant they see the flashes, rather than when they occur. You seem to have used option one, but not specified the frame.
In this instant, the person is located equidistant from the 2 lighting strikes on the train, but is accelerating towards one at almost the speed of light, and away from the other at almost the speed of light.
There is no acceleration going on, and you can't measure acceleration in terms of speed anyway. It's like saying you are 2mph tall - it makes no sense.
In this instance, the person on the train observes the events to occur one after the other, with the light beam that they are traveling towards seen first, and the light beam they are traveling away form second.
This phrasing obscures a key point - the person on the train is not moving according to them. And the speed of light is constant and the strikes occurred at equal distances. And the speed of light is constant. So the strikes cannot be simultaneous in this frame, as you go on to say.
When einstein then realized that gravity was an acceleration or a force, he was able to generalize this theory into the theory of general relativity.
Gravity is neither an acceleration nor a force in general relativity.
Atleast that's my understanding. There is a great NOVA on einsteins general relativity and all of the thought experiments that led him to realize it. It was a lot more to do with the fact that gravity is a force than it does with simultaneity in my mind.
As noted, gravity is not a force in general relativity. Furthermore, the OP is asking about relative simultaneity, which is a special relativity phenomenon. General relativity is much more complex and, although the point that "simultaneous" is conventional remains true, concepts like "relative simultaneity" don't translate across very well since global inertial frames don't exist in curved spacetime.

jbriggs444
The main thing I'm having trouble with is it feels like the speed of light constant rule is being violated and I would like a bunch of examples of scenarios in order to prove to me it isn't being violated.
Usually this happens when you've confused yourself about which frame you're using, and are trying to reason about one frame using some observations from another.
For example: imagine a ship going V to the right. Someone on Earth fires two lights that hit the edges of the ship simultaneously to the earth. There are three clocks on the edges and middle of the ship that are synchronized relative to the observer on the ship. What do they observe?
We can straight up tell you the answer, but it might be more useful for you to tell us what you think happens and why it's problematic for you.

Far from contradicting the constant speed of light, it's exactly the relativity of simultaneity that allows different reference frames to measure the speed of light as identical (in a way that is understandable to all reference frames).

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I haven't looked at the wikki article because I don't trust it and don't want to be given misinformation.
Wikipedia articles on established science topics are generally of good quality and good places to start if you want to know more about a science topic, as long as it isn't too deep into a particular discipline.

m4r35n357
Wikipedia articles on established science topics are generally of good quality and good places to start if you want to know more about a science topic, as long as it isn't too deep into a particular discipline.
Is there any experimental verification for simultaneity

Is there any experimental verification for simultaneity
For relativistic simultaneity? Yes. The GPS system was designed with corrections for relativistic effects. If these effects didn't exist, with the exact numerical values that relativity predicts, then the GPS system wouldn't work.

Is there any experimental verification for simultaneity
Yes, but you can conclude it simply from the experimental results that show that time is relative. Can't have absolute simultaneity if you don't have absolute time.

FactChecker
Wikipedia articles on established science topics are generally of good quality and good places to start if you want to know more about a science topic, as long as it isn't too deep into a particular discipline.
That's true. Some of them have contributions by PF advisors, like @DrGreg.

Actually the train example is a bit flawed as the train motions is mostly irrelevant. The strikes come from outside the train frame of reference -- clouds not necessarily sharing the trains motion. A better example is that two explosions occur simultaneous aboard the train according to the train riding observer.

More importantly simultaneous can only be judged by an observer equidistant from the two events or calculated based on accurate distances and speed of light. Otherwise (perception-wise) first light from the most distant (from the observer's viewpoint) strike or explosion always arrives later regardless of the motion of the observed body. So there is always a perception that more distant events are not simultaneous with near ones even though an equidistant observer judges otherwise.

Worse if the train is passing the station, both observers opposite each other at its midpoint and then lightning strikes the equidistant ends of the train -- both will perceive simultaneous events. If both are twice as far from one end of the train than the other end, both will perceive the near event to be sooner by sound or theoretically by light. If the train is moving at relativistic speeds - the external observer will merely observe the forward explosion/strike (moving away) as red shifted or the rear strike/explosion (approaching) as blue shifted. Each due the movement of the light source as it emits light. If the duration of each light emitting event has equal fixed duration from the train-side frame of reference, then the receding (forward train source) length of emission time will be stretched and the approaching source in the rear of the train will appear to have a shortened time of emission.

Motion of the train is irrelevant to time of reception of initial light from an events (constant speed of light) though it can effect the perceived duration of an event. Only observer perceived distances from an event matter for receiving initial light. Do not confuse moving light sources for the actual light. The time and position of first event light emitted is NOT dragged forward in platform observers frame of reference by the train (until space is warped by gravitational effects at uber-relativistic speeds >99%). Once light is emitted it is frequency shifted due to differentials between observers frame of reference. Light effectively is not attached nor belong to any frame of reference because it has constant speed.

Light from events immediately crosses over into any observers frame of reference at a fixed position in that observer's frame and travels at constant light speed from there. First light will always arrive before later emitted light of a continuous observation (assuming Einstein's light speed limits remain true).Yes observation of CONTINUED series events by the platform observer could appear time warped (compressed) as events occur at closer and closer distances ( as a linear function of the speed of the relativistic train). Confusingly events onboard supposedly slow down in a very nonlinear way as train velocity approaches the speed of light

Thus to me it seems that although time passes at different rates between observers as time is slowed by relativity, simultaneity is not necessarily broken between the two observers as verified by an observer equidistant from the two events. A function (based on perceived relative velocity) does exist to synchronize clock rates and events.

Thus my argument that the example Einstein used is flawed even if the conclusion of his thesis may be correct.

Not sure but I think this paradox arises from the same flaw as Bell's spaceship paradox -- attributing and confusing more than one frame of reference to a single observer. (Not paradox: Two bodies joined by a string are one system and thus distance S does shrink - the paradox proving the postulate/assertion "S is constant" false by reduction to absurdity. Though internally to the system S appears constant to an "inside observer".)

But the fundamental assumption of Einstein's theories is that each observer has only one frame of reference - their own. Any two points or objects under observation must be assumed to be simultaneously in view despite narrow placement of human eyes and limits of human visual acuity. Either that can be satisfactorily simulated -- or one should be "ethically" forced to assume the observer is too close to one or both points and has become part of the "inside" observer frame of reference. Of course for large enough systems there maybe more than one "inside" observer viewpoint as boundaries overlap and become confused and blurred.

Actually the train example is a bit flawed as the train motions is mostly irrelevant.
A general rule of thumb: when one is describing a thought experiment that's been discussed by literally thousands of people over a century or more, it's far more likely to be your understanding of it that's flawed than the actual experiment.
The strikes come from outside the train frame of reference -- clouds not necessarily sharing the trains motion.
There is no such thing as "outside" a frame of reference in SR. All events are in all frames of reference.
A better example is that two explosions occur simultaneous aboard the train according to the train riding observer.
Makes absolutely no difference whether you use lightning strikes, fire crackers, or fire crackers ignited by lightning strikes.
More importantly simultaneous can only be judged by an observer equidistant from the two events or calculated based on accurate distances and speed of light.
This is not correct. Anyone can judge simultaneity by subtracting the travel time of light from the arrival time of the signals. The whole point of this thought experiment is that two observers following the same procedure for doing that can come to different conclusions.
Worse if the train is passing the station, both observers opposite each other at its midpoint and then lightning strikes the equidistant ends of the train -- both will perceive simultaneous events.
No they won't. In the train frame the flashes arrive at the train observer (who isn't moving) simultaneously from equidistant events, so the conclusion is that the events were simultaneous. In the platform frame the flashes arrive at the platform observer (who isn't moving) non-simultaneously from equidistant events, so the conclusion is that the events were non-simultaneous.
If both are twice as far from one end of the train than the other end, both will perceive the near event to be sooner by sound or theoretically by light.
No. Both will receive light from the nearer event sooner, true. But once they correct for the light travel times they will come to the same conclusions as their colleagues in the middle. The only reason for using observers in the middle of the train is that the maths for correcting for travel time (enough to determine simultaneity, anyway) is so trivial we don't bother to write it.
Motion of the train is irrelevant to time of reception of initial light from an events (constant speed of light) though it can effect the perceived duration of an event. Only observer perceived distances from an event matter for receiving initial light.
But the observer distances from the events do depend on the train (or platform) motion. One or other is in motion, so their distances from the flashes are different at reception time in the frame where they are in motion.
The time and position of first event light emitted is NOT dragged forward in platform observers frame of reference by the train
I don't think anyone has ever claimed they are.
until space is warped by gravitational effects at uber-relativistic speeds >99%
There are no gravitational effects here at any speed. You may wish to review John Baez's article on the subject: http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html
Once light is emitted it is frequency shifted due to differentials between observers frame of reference.
Not really. Redshift depends on the angle between the worldlines of the source and emitter at emission and reception respectively (at least in SR - GR is a bit more complicated). It isn't a property of light, so much as a property of the interaction between light and the receiver.
Light effectively is not attached nor belong to any frame of reference because it has constant speed.
Nothing is "attached" or "belongs to" any reference frame. A reference frame is just a way of representing events. "Attaching" something to it would be like claiming a river was attached to a map because it appeared on the map.
Light from events immediately crosses over into any observers frame of reference at a fixed position in that observer's frame and travels at constant light speed from there.
I'm afraid this is just word salad. You need to go and read up on what a reference frame actually is, since you apparently have a rather large collection of misconceptions about them.
First light will always arrive before later emitted light of a continuous observation (assuming Einstein's light speed limits remain true).Yes observation of CONTINUED series events by the platform observer could appear time warped (compressed) as events occur at closer and closer distances ( as a linear function of the speed of the relativistic train).
Here, you seem to be confusing the Doppler effect for the relativity of simultaneity and time dilation. Relativity of simultaneity and time dilation are what's left over after you correct for the Doppler effect due to varying light travel time.
Thus to me it seems that although time passes at different rates between observers as time is slowed by relativity, simultaneity is not necessarily broken between the two observers as verified by an observer equidistant from the two events.
This is clearly wrong. You can't have time dilation and the principle of relativity without having relativity of simultaneity. Otherwise you can't have the symmetric "we both agree that the other's clock runs slow" phenomenon without inconsistencies.
Not sure but I think this paradox arises from the same flaw as Bell's spaceship paradox
It arises because you seem to be very confused about frames and the behaviour of light.
But the fundamental assumption of Einstein's theories is that each observer has only one frame of reference - their own.
What? Where did you read that? It's utter nonsense. Freedom to choose any frame (or more general coordinates) is a gauge freedom in relativity. There may be a frame that it is natural to use (your own inertial rest frame, typically), but you are not required to use it.
Any two points or objects under observation must be assumed to be simultaneously in view despite narrow placement of human eyes and limits of human visual acuity. Either that can be satisfactorily simulated -- or one should be "ethically" forced to assume the observer is too close to one or both points and has become part of the "inside" observer frame of reference. Of course for large enough systems there maybe more than one "inside" observer viewpoint as boundaries overlap and become confused and blurred.
This is just silly. It's trivial to arrange mirrors and lenses to see both ends of a train from the middle. Or use cameras. Or any number of alternative experimental set ups.

To reiterate, Einstein's train is a really simple thought experiment. It says that the train observer receives flashes of light simultaneously from opposite ends of the train, while the platform observer does not (in the setup you specified). If you adopt the natural frame of reference for the train observer where the train is at rest, then this is because the events were simultaneous and equidistant - but during the time it took light to travel the platform observer moved a bit closer to where one flash happened so received the light from that one early and the other one late. If you adopt the natural frame for the platform observer where the platform is at rest, then this is because the front flash happened slightly after the back flash - but the train observer moved enough toward the forward event so that they happened to receive the flashes at the same time. Thus simultaneity is a relative thing if the speed of light is the same in all inertial frames of reference.

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FactChecker
Worse if the train is passing the station, both observers opposite each other at its midpoint and then lightning strikes the equidistant ends of the train -- both will perceive simultaneous events.
You have missed a fundamental point. Because of the Michelson-Morley experiment, Einstein was forced to hypothesize that the clocks in the moving frame are set to indicate a light speed of c. The consequence is that clocks in the forward direction of motion are set earlier than the clocks in the backward direction. So their indication of "simultaneous" is not the same as the clocks in the stationary reference frame. Observers in the two reference frames can not agree about simultaneity of two events that are separated in the direction of motion -- whether those events are lightning strikes or explosions. They may agree that light from lightning strikes reach a point simultaniously, but then they will not agree that the point was the midpoint of the two lightning strikes -- because if the point is the midpoint of one frame then it can not be the midpoint of the other.

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I haven't looked at the wikki article because I don't trust it and don't want to be given misinformation.
That makes me sad. A lot of us here use it, so perhaps beware any advice you might read here too. Part of learning any science is learning to verify and corroborate information for yourself once you have read it. This means even imperfect sources can teach you something!

I don't rely on trust, reputation or authority, and I don't think I'm in a minority here either.