The Twin Paradox and Cosmic Inflation

Factual Questions
1

Einstein had a famous thought experiment:
One twin hopped on a space ship that can go at nearly the speed of light, and the other stays behind on earth.
For twenty days or so the first twin is flying at near lightspeed for, say, twenty hours.
He comes back to earth to find his brother has aged twenty YEARS.

The paradox arises from a concept in relativity; from each twin’s point of view, the OTHER twin has…relatively…sped away and moved at near lightspeed, so each would conclude the other should age while time passes slowly for himself.

The paradox is resolved when one takes into account that only the twin that got on the space ship was subject to acceleration.

Now…

Suppose we take this idea and apply to twins in galaxies which are expanding away from each other, as per Hubble.

As I understand it, separate galaxies are NOT rushing away from each other through space: space itself is expanding.

Is this expansion an acceleration which…theoretically…produces a twin paradox?

2

That is correct; light from distant galaxies is red-shifted.

Like the “twin paradox”, however, it is not really anything to do with acceleration.

3

The twin paradox is all about changing reference frames. The attendant acceleration is just a feature/symptom, not a cause. If you lived long enough, and you had an equally long lived twin you could each start on one of two nearby galaxies, then wait for the universe to expand, and then travel to your twin’s galaxy to meet your twin again. The reference frame change when you travel to your twin should provide a twin paradox. Just over insane time periods.

The two galaxies are each in different reference frames and your travel is in a third, which gets you the paradox.

4

How do the two twins get back together at the end? If they don’t do that, then no meaningful comparison of their ages is possible.

5

I’m not following how the twin paradox is resolved. Everything in the universe is in motion, correct? Why does space ship guy age more slowly than earthbound guy? Relative to each other, they’re just moving apart…?

6

It gets resolved when they come back together and it turns out that they disagree on how far the travel distance (relative to each other) was, or, equivalently, how many ticks passed on their clocks. This apparent paradox goes away when you consider 4-dimensional velocity, which they do agree on (it is the speed of light, which is a geometrical constant).

7

If nothing else, their experience was much different – one sat restfully on earth while the other experienced many Gs on the way out, got slammed against the other side of the ship as it stopped and reversed, many Gs on the way in, got slammed again as the ship stopped.

The acceleration is what moves you from special relativity to general relativity in my simple understanding, and GR is where the twin paradox pops up.

If they were just moving at different speeds, they would perceive each other’s clocks moving more slowly or whatever, but both reference frames would be “correct”.

Anyway, that’s my simple, mostly incorrect, understanding.

I don’t know about the Cosmic Inflation question.

8

No, the twin paradox can be described on ordinary, flat space-time and therefore does not use any General Relativity per se. You can consider accelerated (non-inertial) frames of reference, but there is no actual gravitational field involved.

If you analyse things correctly, you should discover that cosmological redshift and the Doppler effect are the same effect, in some sense. I suppose the expansion of the universe is described by General relativity because now you are describing the universe by putting a metric, involving a scale factor, on it, and the space might not be flat in general (cf. all the other threads about attempts to discover the shape of the universe).

9

Let me provide how I finally came to understand time dilation. I understand no one here needs this explanation, but it will give you the background for how my confusion continues.

I don’t remember what article or online piece provided this, but here’s how it clicked for me. I’m sure I’m butchering this and using terms poorly, but please indulge me.

Picture a stationary boxcar. In the boxcar sits a man, let’s call him Fred, who has the ability to measure with precision what occurs outside his car.

On a parallel track a train passes traveling at near light speed. It pulls a boxcar with a glass side (so Fred can see into it). In that moving boxcar there’s a fellow (Steve!) who has a device that emits a photon from the floor straight up to the ceiling where it hits a mirror and returns. Ten feet up and ten feet down. That up and down takes a nanosecond (or whatever the right time would be for c).

Steve fires away as he passes Fred’s stationary boxcar. From Steve’s perspective, the photon traveled 20 feet in a nanosecond. From Fred’s perspective, it was NOT straight up and down because the train was moving. Let’s say he witnesses 15 feet up (on a slant) and 15 feet down (also on a slant).

Well, since c is constant in every frame of reference, the photon’s trip up and down must have taken longer than a nanosecond for Fred. Hence, time moved more slowly for Fred than for Steve.

Eureka, I shouted (well, not really). This is how it clicked for me…until it didn’t. Because suppose we switched roles and Fred in the stationary boxcar was the photon shooter-upper and Steve measured it as he sped on by. Would the same effect, only reversed, occur? It would take a nanosecond for Fred, but Steve would measure a greater distance and consequently a longer time occurring for the photons round trip, even though he was traveling at near light speed.

Again, thanks for indulging me, but what am I getting wrong? Obviously they can’t both be experiencing a slower passage of time.

10

Nothing; they indeed both see each other’s photons red-shifted/time passing slower. As @Chronos says, there is not going to be any difference unless one of them turns around and comes back (and subsequently they will look blue-shifted), in which case they are not going to agree on when that happens, that is, on the duration of the inbound/outbound legs.

In the case of the Milky Way and some cosmologically distant galaxy, same thing, we see them red-shifted and they see us redshifted.

11

So would their clocks be in sync so long as Steve’s train never made a return trip?

And thanks for your response.

12

Yes, it is symmetric, but not in “sync”, each one sees the other’s clock ticking slower, by the same factor.

13

I think it’s sinking in now. Thanks for providing some “time dilation for dummies.”

14

I don’t understand this. Without the acceleration, both twins see the other aging more slowly and there’s no paradox. I thought that once you get into non-inertial reference frames, you leave SR.

Is the OPs question, “is cosmic inflation the same as other forms of acceleration”? I don’t know the answer, but I’m interested in it. I would say that there seems to be something different with cosmic inflation because I understand that objects can move apart faster than c (in a sense?) since space itself is expanding.

15

From Star Trek as I understand it, when a ship was in warp drive, there was no twin paradox because space itself was being affected. It was not a situation where one entity was accelerating through space and the other entity was not accelerating through the same space. So it would seem that the answer to your question would be no if that theory is correct.

16

My understanding, at least how I think about it, isn’t that space is stretching out like the ever popular analogy of a rubber sheet being stretched. It’s more like more space is constantly being created, pushing existing space further apart as new space is created. I think of it as a bunch of grains of sand, with new grains of sand constantly popping up into existence between the existing grains of sand..