Naive questions about SR: time and space dilation

[DaveC426913]

No matter how much I shed light on it, there's always some dark corners of relativity into which I have trouble seeing.

In a recent book I read, a starship with continuous acceleration approaches c to within many decimal places, creating a collosal time dilation - enough for the universe to age during a passenger's journey. Nevermind the implausibility, let's look at this as a thought experiment.

1] What does the passenger see when they look out the window? Specifically, they see time dilation of the universe (which is always reciprocal). They see time passing very slowly - the stars and galaxies will appear frozen. How is this reconciled with the fact that the universe is aging very fast?

Is it because the moment they decelerate, the universe will rapidly age until it matches their predictions?

I can't help but wonder if there is something in there about approaching versus receding - akin to a relativistic rocket receding from Earth, then turning around and approaching Earth. Is it possible they will see a rapidly aging universe looking ahead but a frozen one looking behind?2] Space will be highly compressed in the direction of their motion. Stars ahead will be flattened and close together. Is this also true looking behind? Will stars be flattened and close together in their rear view mirror? But not to the side. To the side, stars will be normally-shaped and normal distance.

 

[PAllen]

You need to think about Doppler and aberration. What the rocket would literally see is that (after a while) all of the stars positions have merged to a point in front of the ship, which will be extremely blueshifted and extremely intense (way beyond the aggregate brightness of the stars initially). To the extent you can 'conceptually' visualize rate of processes in this dot, they will appear very fast - Doppler wins over time dilation. The only star you could 'see' outside the forward dot is one exactly behind you, and it would look extremely redshifted, dim, and its processes would appear frozen.

If you factor out these effects, and compute positions as they would be in a momentarily comoving inertial frame, you would find that rate of processes on the stars was slower, and their current distance from you is reduced compared to when you started (but you don't 'see' their current distance because of light travel time). Distances behind and forward would be reduced identically when modeled this way (compared to when you started). Note, your whole field of view outside the bright dot in front corresponds to a tiny fraction of a degree around the direction directly behind you, as determined when you started.

 

[Nugatory]

I can't help but wonder if there is something in there about approaching versus receding - akin to a relativistic rocket receding from Earth, then turning around and approaching Earth. Is it possible they will see a rapidly aging universe looking ahead but a frozen one looking behind?

If by "see" you mean what your eyes and shipboard equipment are registering at any given moment, then the direction makes a big difference. Imagine that the universe is full of strobe lights, all at rest relative to one another and carefully designed to flash once per second according to an observer also at rest relative to them. As you speed along, you will literally see the strobes in front of you flashing more rapidly than once per second, and the ones behind you flashing less than once per second; this is the Doppler effect at work. Thus, what's in front will be seen to be running fast while what's behind will be seen to be running slow. Only when you correct for light travel time will you find that all the strobe lights in all directions are uniformly time-dilated relative to you. If you're accelerating you will find that a Rindler horizon has formed behind you; the strobes behind you will flash more slowly the farther away they are, and there's a distance beyond which you aren't seeing any flashes at all.

It's fair to describe this situation as "a rapidly aging universe looking ahead but a frozen one looking behind"... but of course the effect disappears if you then decelerate until your at rest relative to the ensemble of strobe lights.

 

[PAllen]

Note, in relation to the Rindler horizon, if (when you start accelerating) there was a star exactly in the direction you are accelerating away from, you will continue to see ever redder, dimmer, light from it forever, but you would consider it all to have been emitted long before you started accelerating (before it 'crossed' behind the Rindler horizon).

 

[Ibix]

Remember the time component of the Lorentz transforms. Anything a long way in front of your ship (large positive x) gets a healthy negative time after the transform. That means that, "now" in the frame of the stars is far in the past according to the spaceship. This is how clocks tick slowly but you see the end of the universe. Most of the history has already happened when you start...

This argument doesn't hold for stars behind your ship. But that doesn't matter - you are not surprised to see not a lot from stars behind you because they are racing away from you at near light speed. It'll take an extra age of the universe before you actually see what happens to them.

 

[PeroK]

@DaveC426913

An interesting exercise is to take the twin scenario and calculate what each twin actually sees. Assuming instantaneous acceleration and deceleration. You could use v = 0.8c and a travel distance of 4 light years in the rest frame. When does the stay-at-home see the light from each of the traveller's birthdays? And when does the traveling twin (I guess that's the one you'd be more interested in) see the light from the stay-at-home's birthdays?

Do it out and back.

The quick way is to use the Doppler formula, but you might want to do it by hand just to check.

 

[pervect]

I'd like to add a bit about the Rindler horizon. Suppose the point of origin is transmitting a signal to the space-ship, this transmitted signal has encoded a timestamp that gives the current time at the point of origin.. Let's say that the ship leaves right at the start of the year 3000 AD and the timestamped signal gives the time passed in Earth years. Ignoring GR effects of the geometry of the universe for just now, and assuming the ship is in the flat space-time of SR, the ship will continue to receive regular time updates for as long as its equipment can decode the increasingly weakened, increasingly redshifted signal. If the ship accelerates at a proper acceleration of 1 light year/year^2 (roughly 1 Earth gravity), even with ideal equipment it will never receive a signal timestamped later than 3001 AD. The received date will advance more and more slowly, and never get beyond the limiting value of 3001 AD.

This is rather similar to the way an object falling into a black hole appears to "freeze" from the viewpoint of a distant observer. Note however that it's rather basically wrong to conclude from the distant observers observations that the point of origin never gets older than 3001, that time ends for the point of origin on the year 3001. It's true that the spaceship never receives a signal from a later year (unless it stops accelerating), but an observer at the point of origin doesn't notice anything special happening at the year 3001, it's only special from the point of view of the accelerating spaceship. Other spaceships that start out at earlier or later dates likewise won't receive signals dated later than a year after their departure, there's nothing intrinsically special about the year 3001.

If this reminds you about discussions about falling into a black hole, that's good. Without going into a lot of detail (since it's not directly relevant to the thread anyway), one can regard the Rindler horizon as being the event horizon associated with the "gravity" that the accelerating elevator / spaceship sees, analogous but simpler mathematically than the event horizon of an actual black hole with mass.

 

[Erland]

Look up https://www.physicsforums.com/threads/what-relativity-really-looks-like.536936/

 

[A.T.]

You need to think about Doppler and aberration. What the rocket would literally see is that (after a while) all of the stars positions have merged to a point in front of the ship, which will be extremely blueshifted and extremely intense (way beyond the aggregate brightness of the stars initially). To the extent you can 'conceptually' visualize rate of processes in this dot, they will appear very fast - Doppler wins over time dilation.

You will also begin to see distant galaxies in front of you, which where previously extremely red.shifted due to expansion.

 

[PAllen]

You will also begin to see distant galaxies in front of you, which where previously extremely red.shifted due to expansion.

True, but I assumed this was an SR problem, without cosmological issues. I interpreted the OP as asking nothing about cosmological issues.