Special relativity and the flow of time?

[PeterDonis]

When things happen compared to your clock depends on the relative motion and the difference in gravitational potential.

No, it depends on your choice of coordinates/simultaneity convention.

Whatever your frame of reference, the speed of light relative to you is always c.

This is not correct either since we are talking about events distant from the observer's worldline. The "speed of light relative to you" at events not on your worldline is also a matter of your choice of coordinates. It does not always have to be $c$. What will always be $c$ is the speed you measure for light rays passing you--but that means you are measuring their speed at events on your worldline, not at distant locations.

 

[Nugatory]

What would occur in such situation?

Both astronauts will reach their respective stars at the same time using a frame in which the two stars are at rest. They will spend the same amount of time in flight, cover the same distance,and be moving at the same speed (but in different directions).

Using other frames, they will arrive at different times, travel at different speeds, and cover different distances. However: in no frame will their speeds reach or exceed $c$ (unless you do the experiment with flashes of light, in which case both will be moving at speed $c$ in opposite directions in all frames); and in all frames the distance traveled by each will be equal to the speed times the time in flight.

The best way to understand this problem is to write down the coordinates of the three events using coordinates in which both stars are at rest:
Event 1: the astronauts start their respective journeys at the event $x=0$, $t=0$
Event 2: left-moving astronaut reaches his star at the event $x=-D$, $t=D/v$
Event 3: right-moving astronaut reaches his star at the event $x=D$, $t=D/v$.
Here $v$ is the speed of the astronauts in this frame and $D$ is the distance from the starting point to each star.

Then use the Lorentz transformations to find when and where these events happen in some other frame, such as one in one or the astronauts is at rest (you can't do this with light flashes because there is no frame on which a light flash is at rest)... and that will tell you what happens.

It would be a good exercise to verify that the results you get this way are consistent with the formulas for time dilation, length contraction, and velocity addition: that is, speed times time in flight is equal to the distance traveled for both astronauts.

 

[vanhees71]

Pardon me if this has been asked before, but I'm confused with the implication that SR makes, that there is no objective moment of present. Do the science still believe that the time flows (i don't mean the arrow of time, but the phenomena of flowing/passing, eq. flowing of a river)? I mean, how can it flow if the spacetime itself is not bound to any present moment? In comparison, a river only flows if you observe it from a present moment.

In SR to the contrary of you believe time doesn't flow, but spacetime just is a four-dimensional pseudo-Euclidean affine 4D manifold with a fundamental form of signature (1,3) (or if you use the east-coast convention (3,1)). As soon as you forget to think of time and space in the Newtonian way, SR becomes much simpler!

 

[Janus]

Is this lack of unique way of saying what happens in distant places related to the distance or to the difference in the volume of mass/gravity between me and the distant location?

about the train car and platform-thought experiement mentioned on wikipedia-article about the RoS: if the action of light actually changes by changing the point of observation, then isn't this actually an issue in nature of light rather than in nature of time?

No, What is happening is that the way light behaves discloses something about the nature of time.
You can change the train car and platform experiment so that the train and platform observers are at the same point when they see the flashes.
In this scenario, the the light from the two flashes meet at the platform observer's position at the same moment that the train observer is passing him. Thus both observers detect both flashes simultaneously. They also both measure the speed of light for the two flashes to have the same speed relative to themselves.
The platform observer, knowing that he was exactly halfway between the points from which the flashes were emitted both when he sees the light from them and when the flashes were emitted concludes that the flashes were emitted simultaneously.
The train observer knows that he is halfway between the sources of the flashes when he detects the light from them, But not when they were emitted. Prior to seeing the flashes, he was nearer to one source than he was to the other. If he measures the speed of the light from both flashes as being the same relative to himself, the only way he could detect the two flashes reaching him a the same time is if they left the sources at different times. Thus he concludes that the flashes were not emitted simultaneously.
Thus we have two observers at the exact same point, seeing the exact same light flashes but coming to different conclusions as to whether those flashes originated simultaneously or not.

Another thing to avoid is to attach to much importance to light itself. What is really important is the speed at which light travels, 'c'. It is the fact that this invariant speed exists that leads to Relativistic effects. Light is just convenient to use in these examples because it is something that we can measure that moves at that speed, and it makes the problem easy to visualize. These Relativistic effects would still take place even if we didn't use light, But showing this to be the case would be more involved.

 

[Akriel]

No, What is happening is that the way light behaves discloses something about the nature of time.
You can change the train car and platform experiment so that the train and platform observers are at the same point when they see the flashes.
In this scenario, the the light from the two flashes meet at the platform observer's position at the same moment that the train observer is passing him. Thus both observers detect both flashes simultaneously. They also both measure the speed of light for the two flashes to have the same speed relative to themselves.
The platform observer, knowing that he was exactly halfway between the points from which the flashes were emitted both when he sees the light from them and when the flashes were emitted concludes that the flashes were emitted simultaneously.
The train observer knows that he is halfway between the sources of the flashes when he detects the light from them, But not when they were emitted. Prior to seeing the flashes, he was nearer to one source than he was to the other. If he measures the speed of the light from both flashes as being the same relative to himself, the only way he could detect the two flashes reaching him a the same time is if they left the sources at different times. Thus he concludes that the flashes were not emitted simultaneously.
Thus we have two observers at the exact same point, seeing the exact same light flashes but coming to different conclusions as to whether those flashes originated simultaneously or not.

Another thing to avoid is to attach to much importance to light itself. What is really important is the speed at which light travels, 'c'. It is the fact that this invariant speed exists that leads to Relativistic effects. Light is just convenient to use in these examples because it is something that we can measure that moves at that speed, and it makes the problem easy to visualize. These Relativistic effects would still take place even if we didn't use light, But showing this to be the case would be more involved.

I still see the issue in the nature of the light (or to be more exact, in the nature of the c), rather than in the nature of time. The moments when each observer detects the flashes are different, but it seems to occur due to the nature of the c, rather than that the dimension of time is somehow altered trough the relative speed of the observer.

It seems so that when you make the calculation you get a different values for t in each of the observers with each flash, but i don't see why i should conclude that it is due to the nature of time itself, rather than it just being a result of the constant of c. we already now that the c is a constant, so wouldn't it be more complex to assume that in besides of that, also the spacetime is somehow reacting to the experiement, rather than just being the scene where the experiement takes place?

 

[Dale]

i don't see why i should conclude that it is due to the nature of time itself, rather than it just being a result of the constant of c.

You seem to think that these are independent. If c is invariant* then time dilates. One is logically implied by the other.

*and the principle of relativity holds

 

[Herman Trivilino]

It seems so that when you make the calculation you get a different values for t in each of the observers with each flash, but i don't see why i should conclude that it is due to the nature of time itself, rather than it just being a result of the constant of c.

It can't be one without the other, that's the point of the exercise. And if you don't think it has anything to do with the nature of time itself, you had a lot of company. Many if not most physicists didn't buy into it when it was first presented to them. But that was over 110 years ago, now we know for sure that time dilates and simultaneity is relative. It's demonstrated every time an engineer has to calibrate GPS clocks, or when technicians send particle beams through tunnels. It's done every minute of every day at hundreds of places worldwide. It's a fact of modern life!

 

[Akriel]

It can't be one without the other, that's the point of the exercise. And if you don't think it has anything to do with the nature of time itself, you had a lot of company. Many if not most physicists didn't buy into it when it was first presented to them. But that was over 110 years ago, now we know for sure that time dilates and simultaneity is relative. It's demonstrated every time an engineer has to calibrate GPS clocks, or when technicians send particle beams through tunnels. It's done every minute of every day at hundreds of places worldwide. It's a fact of modern life!

for sure I'm not starting to argue against experiementally confirmed facts. Do we have confirmed the time dilation in sub speed of light experiements as well?

 

[Ibix]

The twin paradox was carried out by Hafele and Keating in an aircraft - Google their names.

 

[Dale]

for sure I'm not starting to argue against experiementally confirmed facts. Do we have confirmed the time dilation in sub speed of light experiements as well?

Yes, we have many. See sections 4 and 5 here:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[Akriel]

Yes, we have many. See sections 4 and 5 here:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

Thank you for your time, going to read the article.

 

[Dale]

Thank you for your time, going to read the article.

FYI, my favorites are the particle lifetime experiments. Those show that it is not just EM (light) but also the strong and weak nuclear forces.