# I Shining a light beam back -- relativity

1. Feb 23, 2017

### Invutil

According to the textbook, "In this case, you (A) and Jackie (B) no longer agree about her speed _relative_ to the speed of the light beam. She'll see the light beam pass by her at the speed of light, c, but you'll see it going only 0.1c faster than she is going."

Illustration here, under "The Speed of Light" heading: http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/lec11.html

My question is, does her rate of time slow down or her length increase, so that to her it appears that the light travelled a full 1c instead of 0.1c in a second?

And what if she shines a light back?

2. Feb 23, 2017

### phinds

Exactly as the quote says: "She'll see the light beam pass by her at the speed of light, c ...". All observers see light traveling at c.

3. Feb 23, 2017

### Invutil

I get that works from the general idea of interferometer experiments, which by 1947 showed to an error of +-4 km (within the bounds of Earth's rotation speed around the sun at 30 km/s) that light speed is unaffected by direction or motion, and from the airplane cesium clock experiments. But if each filmed the other person, each would see the other's time slowed down right? So it is like there is a time warp between them? My other question: we can't assume the airplane has a single rest frame throughout the flight, so we know it is absolutely moving and is the time dilated side? It seems like quantum theory to say that each side is correct in having a rest frame and all the possibilities happen at the same time.

4. Feb 24, 2017

### Orodruin

Staff Emeritus
There is no such thing as absolute motion. Not in relativity nor in classical mechanics.

It is not a matter of time slowing or lengths increasing, it is a matter of the geometry of space-time as a whole.

Beware here. When you say "filmed" you would also need to take into account that light does not arrive instantly and that the distance between them changes. Relativistic effects such as time dilation and length contraction are what remains after you account for this.

5. Feb 24, 2017

### Ibix

If you film someone the Doppler effect will mean that their clocks will appear faster as they approach and slower as they recede. If you subtract out the light travel time, you will calculate that their clocks tick slowly, yes.

There's no time warping going on. It's easiest if you think of spacetime as a four-dimensional entity. The path you follow through spacetime is called a worldline, and different paths have different lengths - but the "length" of a worldline turns out to be the elapsed time on that route. Then the Hafele-Keating experiment to which you refer is not very different from noting that not all routes from London to Edinburgh are the same length.

There's an Insight on this forum by Orodruin on the geometric view of the twin paradox - I'd take a look at that.

6. Feb 24, 2017

### Mister T

That's very observant. You noticed something of importance. An observer who remains at the airport is fundamentally different from an observer who flies around the world inside the airplane. The observers' roles are not symmetrical. Situations where both observers move relative to each other in a straight line at a steady speed are fundamentally different because there the observers' roles are symmetrical.

A situation like the one with the airplane comes up so often that it's famous. It's called the twin paradox. It's a comparison of two proper times, as opposed to the other situation mentioned above, which is always a comparison of a proper time to a dilated time.

7. Feb 24, 2017

### Staff: Mentor

8. Feb 24, 2017

### phinds

Of course we can because it does. In YOUR rest frame, you are never moving. What you are getting at, I think, is that the airplane in not in uniform inertial motion throughout the flight because it undergoes acceleration at the takeoff and landing. Another way of saying that would be that the airplane does not have an inertial rest frame throughout the flight, but note the adjective "inertial" in front of rest frame.

9. Feb 24, 2017

### Staff: Mentor

Or to be precise, the frame in which the airplane is at rest throughout the flight is not an inertial frame.

10. Feb 24, 2017

### phinds

Yes, better. Thanks.

11. Feb 25, 2017

### Invutil

Does the direction/vector of velocity matter?

If the other side is moving closer, into the shining light, it would seem they are travelling by 1c + 0.9c or (1c + 0.9c)/(1 + 0.9c * 1c / c^2) = 1c, so their perceived time rate looking at the outside world would have to increase so the light seems to go slower in their seconds.

And if we use the train example, which calculates time dilation, it would seem they have to be slower on the train in all cases.

We can draw a slightly complicated triangle if the direction of light is not perpindicular to velocity.

Does absolute space and velocity work then?

Also, the equation (ct')2 + (vt)2 = (ct)2 seems to say "Lose some time by gaining some position offset". Is it right then that, if you gain time, it is everything else moving relative to you?

And, in the train example, velocity is inward to B, but A's time goes slower, while its effect according to Doppler should be an increased frequency.

12. Feb 25, 2017

### Mister T

They will always observe their own time passing just as it would if they weren't travelling.

However, when the time that passes for the traveler is compared to the time that passes for a non-traveler there's a discrepancy.

13. Feb 26, 2017

### Invutil

Couldn't all of the interferometer experiments results be explained if we assumed the emitter inertia passed on to the lightwave/photons and so we would not see any sideways fringe or forward change in the speed of light? And is Doppler shift from the stars not exactly the speed of light affected by inertia of emitter? Assuming the time for the first crest to cross the distance and the speed of the crests is the same thing. Sound has an aether (air) but light doesn't, so there shouldn't be any speed limit / barrier.

If at any time our absolute acceleration at any point through space is >0.0000001c, this would seem to matter though.

Last edited: Feb 26, 2017
14. Feb 26, 2017

### Ibix

You can see that the speed of light is source independent because you would expect binary stars to appear to have uneven orbits otherwise. Light from the bit of the orbit coming towards us would get here early while light from the bit going away would be late. We don't see this.

The state of motion of the source affects the energy and direction of the light. Just not its speed.

15. Feb 26, 2017

### phinds

c is a measure of speed, not acceleration

16. Feb 26, 2017

### Invutil

If light is emitted with its own speed, like sound waves, it seems like light is then in an aether that is at rest with relation to the local universe. Now I think I have to dig around in the Michelson-Morley and de Sitter experiments.

I was considering measuring the speed of light as it travels along a path length of 1 km, which should cause a 3x10^-8 m offset as the Earth is accelerated 3 mm/s^2 off by the Sun.

17. Feb 26, 2017

### Staff: Mentor

Except that the speed of light is the same regardless of the velocity of the observer. This is unlike a sound wave, where the measured wave velocity does depend on the velocity of the observer relative to the medium. Measuring the speed of light is a trivial exercise nowadays and experiments have consistently shown the velocity to be c regardless of the motion of the emitter or observer.

Also, there is no rest frame for the local universe. Any arbitrary frame is perfectly acceptable (though we commonly use a frame at rest with respect to the CMB simply for convenience).

18. Feb 26, 2017

### Invutil

I've shown the contradictions in that kind of reasoning above. And it seems there is some uncertainty about the de Sitter binary star experiment.

19. Feb 26, 2017

### Staff: Mentor

I'm sorry I don't see where you've shown any contradictions.

Well, there is. Sorry.

20. Feb 26, 2017

### Mister T

Yes. But then you'd have light traveling at different speeds in a vacuum. Other measurements show that light doesn't do that!

Tell that to the scientists, technicians, and engineers who accelerate particles for a living. Why would it take ten times as much energy to go from rest to a speed of $0.9999 c$ as it does to go from rest to a speed $0.99c$? You've got 90% of the energy being expended to raise the speed that last 1%. And if you try to go faster that problem gets worse. You expend 100 times more energy and you get a further speed increase of one-millionth of 1%.

The way anyone (not just you) thinks things "should" be has no bearing on how they actually are.

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