Calculating Observer C's Speed from Point A as Observed by Observer B

[Harmony]

Let says there's a starting point A. Two observer, B and C travel from point A in opposite direction with 90%c. How can we calculate the speed of observer C as observed by observer B?

 

[JesseM]

See How do you add velocities in special relativity? If an Earth observer sees B's ship moving at velocity v to his right, and C sees the Earth moving at velocity u to his right (which means the Earth observer sees C moving at u to his left), then C will see B moving at $$(u + v)/(1 + uv/c^2)$$. In this case, both u and v are 0.9c, so C will see B moving at 1.8c/(1 + 0.81) = 0.994475c in his own rest frame.

 

[Harmony]

Is it true, that to both observer, time is dilated at the same rate?

 

[Doc Al]

Yes. Each observer measures the other's clocks to run slow by the same factor.

 

[Harmony]

Let say both of them stop at the same time after some distance? What will happen?

 

[Doc Al]

Let say both of them stop at the same time after some distance?

At the same time according to who? Realize that observers in relative motion will disagree as to whether two events happen at the same time or not.

What will happen?

What do you mean?

 

[Harmony]

I apologize for not making my question clearer.
1.Stop at the same time according to an observer at the starting point A, which doesn't move from the point.
2. Observer A notice that observer B remain young while he himself becomes old. I believe that observer B will thinks the same way as observer B. If they both stop, will both observer be young?

 

[fargoth]

they will both look younger to an observer at rest in point A...
but what does B and C see? interesting... I am not sure.

 

[Janus]

I apologize for not making my question clearer.
1.Stop at the same time according to an observer at the starting point A, which doesn't move from the point.
2. Observer A notice that observer B remain young while he himself becomes old. I believe that observer B will thinks the same way as observer B. If they both stop, will both observer be young?

B and C will determine that they are both the same age and that A is older. This because when C and B 'stop' they undergo acceleration and there are additional relativistic factors to consider during acceleration. In addition, B and C will not determine that they stopped at the same time.

The end result will be that each will note a period (while they themselves are coming to a "stop".) where the other ages more rapidly then they do and that just cancels out the period where the other aged more slowly.

 

[Wizardsblade]

Just a curious question, if B and C where in identical ships and where each told to stop after 30 seconds would they both stop at the same time to A?

The end result will be that each will note a period (while they themselves are coming to a "stop".) where the other ages more rapidly then they do and that just cancels out the period where the other aged more slowly.

Is this because of the loss of simultaneity or the propagation time of the light?

 

[selfAdjoint]

Just a curious question, if B and C where in identical ships and where each told to stop after 30 seconds would they both stop at the same time to A?
Is this because of the loss of simultaneity or the propagation time of the light?

It is possible for A to see them stop simultaneously in his time, but any other A', moving at a speed relative to A, would not see them simultaneous. Simultaneity is just not an invariant concept, it is tied to particular observation frames, so physicsts, who look for invariant and covariant things to build a physics independent of observers, ignore simultaneity.

And the loss of simulaneity is due to the finite speed of light.

 

[Harmony]

Is it correct to say,that every observer in different velocity and position observes events differently?

 

[Garth]

Is it correct to say,that every observer in different velocity and position observes events differently?

Yes - observations of space - length, time - duration, inertial (relativistic) mass and simultaneity are relative to the observer's world-line through space-time. (Her 4-velocity). That is why it is called the Theory of Special or General Relativity.

The velocity of light, the space-time interval $\tau$ between events and the rest mass of an object are invariant to any observer.

The space-time interval is given by the metric, which in SR is given by:

$$d\tau^2 = dt^2 - (\frac{1}{c^2})(dx^2 + dy^2 + dz^2)$$ in Cartesian coordinates.

To get the interval $\tau$ between two events (x₁, y₁, z₁) and (x₂, y₂, z₂) you have to integrate along the geodesic between them.

Garth

 

[tbc]

Hi, new to the forum, how is everybody?

Anyway, I am also a relative n00b to relativity, but i was struck by a thought
a while ago that i couldn't figure out:

I was thinking, if the closer you get to the speed of light relative to other objects, the slower time passes for those obects. I also think i read that at the speed of light there is no passing of time.

Light passes every other object at the speed of light (obviously enough) so, would every other object appear to be stationary in time?

If this IS the case then one would expect no (time related) change in a passing photon, from creation to destruction. In simple terms, the photon does not 'age' from 'birth' to crashing into a surface. So, if you were the photon (use your imagination) you would experience nothing between being created and being destroyed.

(i know I am dragging on but please bear with me)

Because the speed is relative, no time would pass for an observer of the photon. This would lead to the idea of the observer seeing the photon being created AND being destroyed at the same time!

This does not happen, so i know I've gone wrong somewhere...I just don't know where!
This has been bothering me for a while so any response will be very welcome.

Thanks,
TBC

 

[JesseM]

Because the speed is relative, no time would pass for an observer of the photon. This would lead to the idea of the observer seeing the photon being created AND being destroyed at the same time!
This does not happen, so i know I've gone wrong somewhere...I just don't know where!

Why do you think the observer would see no time pass, as opposed to the photon? Are you saying that since the relative speed between the observer and the photon is c, we can look at a frame where the observer is moving at c and the photon is at rest? The problem is that photons don't actually have their own rest frame in relativity--it would violate the rule that the laws of physics must work the same way in all inertial reference frames. When people talk about what things would look like from a photon's point of view, they're either misusing the concept of different reference frames or they're talking about the limit of what you would see as your speed approached c (relative to some outside landmarks like the Earth and the galaxy).

 

[tbc]

ah, i think my mistake was (as you say) trying to imagine the photon at rest, with everything else traveling past at c - an idea i was uncomfortable with at the best of times, but its only now that see how impossible that is.

I guess i meant the limit of what someone traveling close to c would be... but the idea only worked when the speed was c itself.

The reason i thought the observer would experience no passing of time is (as you seem to have guessed) because i assumed that the observer could be said to be moving at c relative to the photon.

Thanks a lot for the reply JesseM!

If anyone else has any comments or something to add i'd still be grateful, cheers