Question about viewpoints in relativity

[georgiehutch]

Hi, I wonder if anyone can answer my question please.

I think I understand the basics of relativity and I know that if a person moves at a speed very close to the speed of light, time slows down in that spaceship and they could travel to the future of the stationary land around them whilst only having been gone a day in their time.

If it were possible a stationary person watching this spaceship would see them move slowly through time and stay younger than they would otherwise be and see their spaceship clock move slowly etc.

What I don't understand is what everything would look like to the person traveling near the speed of light (in terms of time not light spectrum or everything being a blur).

Because I have heard that time in the stationary area outside the spaceship would appear to move slower from the point of view of the traveller. I know this makes sense because the light they see travels greater distances so for that speed of light to stay constant things would have to look slow.

But isn't the reality that time is moving faster for the stationary person not slower?

So if the traveller were to get out his spaceship after a very fast trip but never took his eyes off his destination then time looked to be moving slow there and not fast so how could he suddenly be in the future? In the slow moving time he sees, when would he see all the events of the years passed while he was travelling?

 

[atyy]

Usually an observer's "viewpoint" in relativity means a rigid lattice of rods and clocks that are stationary with respect to that observer, and with the clocks synchronized in a certain way.

So when one says time slows down, it only means time with respect to another observer's lattice. It is a formal trick to make the laws of physics the "same" in all the lattices (the underlying idea is that the laws of physics have Lorentz symmetry).

With respect to viewpoint in the "ordinary" sense, moving faster at constant velocity is just as good as standing still (which is again the underlying Loremtz symmetry at work).

 

[georgiehutch]

So to use the twin paradox as an example, what does a traveling twin who comes back to find his brother on Earth 10 years older than him actually see on his journey if it was possible for him to never take his eyes off his brother on earth?

 

[atyy]

So to use the twin paradox as an example, what does a traveling twin who comes back to find his brother on Earth 10 years older than him actually see on his journey if it was possible for him to never take his eyes off his brother on earth?

In the twin paradox, the age difference is real. Most of the stuff you hear about time slowing down is about "coordinate time" and refers to the formal lattice of rods and clocks. However, the twin paradox is about "proper time" or "real time" that an observer sees elasped on an ideal clock (like an atomic clock) that he carries with him. The paradox really only comes about if one confuses "coordinate time" and "proper time".

The key idea to understanding the twin paradox is that the twins take different paths through spacetime. Each path has a different "spacetime length". This "spacetime length" is "proper time" or "real time". It's not any more paradoxical that one can start and end at the same location in space, yet have traveled different spatial distances. One just generalizes "3D length" in space to "4D length" in spacetime.

 

[atyy]

Oh yes, may I recommend the "Doppler shift analysis" http://www.desy.de/user/projects/Physics/Relativity/SR/TwinParadox/twin_doppler.html and the accompanying figure 2 of http://www.desy.de/user/projects/Physics/Relativity/SR/TwinParadox/twin_vase.html#doppler for what each twins sees if both of them send out light pulses regular intervals (regular according to each twin's own proper time).

 

[georgiehutch]

Thanks I am starting to grasp it now. Wikipedia says that if a ship in the twin paradox where v/c=0.866 and says

"The twin on the ship sees low frequency (red) images for 2.57 years. During that time, he would see the Earth twin in the image grow older by 2.57/3.73 = 0.69 years. He then sees high frequency (blue) images for the remaining 2.57 years of his trip. During that time, he would see the Earth twin in the image grow older by 2.57×3.73 = 9.59 years. When the journey is finished, the image of the Earth twin has aged by 0.69 + 9.59 = 10.28 years.

The Earth twin sees 9.59 years of slow (red) images of the ship twin, during which the ship twin ages (in the image) by 9.59/3.73 = 2.57 years. He then sees fast (blue) images for the remaining 0.69 years until the ship returns. In the fast images, the ship twin ages by 0.69×3.73 = 2.57 years. The total aging of the ship twin in the images received by Earth is 2.57+2.57 = 5.14 years, so the ship twin returns younger (5.14 years as opposed to 10.28 years on Earth)."

But in that case if at some points in their journey they watch their twin age quickly, wouldn't they also be able to see light by their twin moving faster than the speed of light? For instance how could you see a clock that runs by measuring light seconds with a light beam moving from one place to another moving faster than the speed of light.

 

[jtbell]

So to use the twin paradox as an example, what does a traveling twin who comes back to find his brother on Earth 10 years older than him actually see on his journey if it was possible for him to never take his eyes off his brother on earth?

See this post for a blow-by-blow account of a similar situation, as literally "seen" by both the stay-at-home twin and the traveling twin, using telescopes to watch each other:

https://www.physicsforums.com/showthread.php?p=510214#post510214