Another Time Dilation Question

[PeterDonis]

He doesn't know anything about relativity or length contraction.

Please read post #24 again. It explicitly uses the term "length contraction", and claims that this explains the shorter travel time by the traveling twin's clock. I have already explained why that claim, while it is correct if we adopt a frame in which the traveling twin is at rest, is not and cannot be the whole explanation.

He simply empirically observes that his destination, seen through the window, is a mere few light months away

No, he doesn't. He can't make observations instantaneously, and distance isn't something that can be observed directly in a single instant anyway.

Once the star he's heading for passes him, he calculates that the Earth-star distance, in the frame in which he is at rest, was a few light-months--because it took only a few months for the star to reach him, at nearly the speed of light (he can measure the star's speed towards him using the Doppler effect). But that's not something he can observe when he's looking out his window just after Earth departs.

(and flattened)

This also makes no sense if he considers himself to be moving and his destination to be at rest. The flattening only makes sense if he is at rest and his destination is moving at nearly the speed of light.

It is just backing up what kochanskij said:

No, you are highlighting the very issue that I already pointed out with his post, that needs to be corrected--namely, that the traveling twin can say all the things kochanskij said, and consider himself to be moving at nearly the speed of light and the Earth and the star to be at rest. He can't, for the reasons I have already given. All of the effects being relied on--length contraction of the Earth-star distance, "flattening" of the star and the Earth, etc.--are frame-dependent; none of them are invariants. They are only true in a frame where the traveling twin is at rest and the Earth and the star are moving at nearly the speed of light.

 

[PeterDonis]

(and flattened)

Note, btw, that this is also not a direct observation; it's a calculation. For what gets directly observed, look up Penrose-Terrell rotation.

 

[PeterDonis]

He doesn't know anything about relativity or length contraction.

And for one more comment if we need it, you're contradicting what you yourself posted in post #7 of this thread--where you made the same point I've been making in the last few posts.

 

[kochanskij]

This is only part of the picture.

First, in order to apply length contraction to the Earth-star distance, as you are doing, we have to consider the traveling twin to be at rest, and the Earth and star as moving. That means that, on this view, it's not the twin, it's Earth and the star that are making a much shorter trip at almost $c$, so it takes less time.

But this still doesn't solve all of the problem, because on this view, the elapsed time for Earth and the star is also much smaller than the elapsed time for the twin! (That's because, on this view, it's Earth and the star that are time dilated, relative to the twin.) So if we just take what's said above into account, we will predict--wrongly--that clocks on Earth will show less elapsed time when the traveling twin returns! So there must be another missing piece involved to explain why Earth clocks actually show more time (a lot more, if the traveling twin's speed relative to Earth is almost $c$) when the traveling twin returns.

I strongly suggest reading the Insights article that's linked to in post #2 of this thread, and also the Usenet Physics FAQ article that is linked to in that article. In the latter article, the "Time Gap" section discusses the problem I described in the last paragraph.

Yes, there is another part to the scenario. I was just explaining why Twin A isn't going on a 10 lightyear trip, from his point of view. You are correct that he considers himself to be at rest (except during his turnaround) and the earth/star system is moving past him at almost C. Thank you for pointing out that I mis-spoke. Since the system is moving, its length contracts to be much less than 5 lightyears.
Yes, from the astronaut's point of view, earth's clock is indeed running slow. But what most people miss is the short period of acceleration at the turnaround. Relative to the astronaut, time on earth runs slow during the outbound leg and the inbound leg, and time on earth runs very fast during the short period of acceleration at turnaround. For example, relative to the astronaut, 2 years pass for him while 1 year passes on Earth during Earth's outbound leg. Then one hour passes for him while 8 years pass on earth during his turnaround acceleration period. Then 2 years pass for him while 1 year passes on Earth during Earth's inbound leg. All together, 4 years pass for the astronaut while 10 years pass on earth. The twin who experienced the acceleration is the younger one.

 

[kochanskij]

However, the first postulate of SR says that there is no concept of absolute (inertial) motion through space. Neither twin is moving through space any more fundamentally than the other.

When the astronaut is moving at a constant speed, he is in an inertial frame, so he can consider himself to be at rest. But during his turnaround, he is accelerating. He feels the force but the earth twin doesn't. He can not consider himself to be at rest during his acceleration.

 

[Sagittarius A-Star]

He feels the force but the earth twin doesn't. He can not consider himself to be at rest during his acceleration.

During his acceleration he can consider himself to be at rest in a pseudo-gravitational field, in which twin B ages more quickly than him because of gravitational time-dilation (equivalence principle).

Source:
https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html

 

[PeroK]

When the astronaut is moving at a constant speed, he is in an inertial frame, so he can consider himself to be at rest. But during his turnaround, he is accelerating. He feels the force but the earth twin doesn't. He can not consider himself to be at rest during his acceleration.

You can do the paradox without acceleration. Ultimately, therefore, it is about the difference in paths through spacetime. And not "something funny happens when you accelerate".

 

[Janus]

He doesn't know anything about relativity or length contraction. He simply knows he is in a moving spaceship (because he was there when it lifted off), and he does no calculations.

He simply empirically observes that his destination, seen through the window, is a mere few light months away (and flattened). That is how he can travel there (and back) without aging much from his naive, empirical point of view.

This POV is not intended to resolve every mystery for him (such as why the planet he's approaching is pancake-shaped), the point is simply that his trip - as experienced naively by him - from A to B, only last a few months because it is only a distance of a few light months.

It is just backing up what kochanskij said:

He would not physically "see" a pancaked planet, that is something inferred by applying Relativity. What he would physically see is blue-shifted light coming from the planet and the planet appearing to approach at a speed greater than c. Now, he will understand that the planet isn't physically approaching at that speed and that this apparent speed is simply an artifact of the propagation time between the planet and himself decreasing.

 

[DaveC426913]

OK. I've stepped in a pile of it and mucked up the thread for readers. Deferring to bigger brains.

 

[PeterDonis]

He can not consider himself to be at rest during his acceleration.

Sure he can, just not at rest in a single inertial frame. But he can consider himself to be at rest in a non-inertial frame.

 

[kochanskij]

During his acceleration he can consider himself to be at rest in a pseudo-gravitational field, in which twin B ages more quickly than him because of gravitational time-dilation (equivalence principle).

Source:
https://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_gr.html

Yes, absolutely right. Inertia force of acceleration can be regarded as a gravitational force. Just like fictitious centrifugal and Corriolis forces can allow us to consider a rotating frame to be inertial, the gravitational force allows us to consider an accelerated frame to be inertial. As you correctly pointed out, the time dilation effect could then be considered gravitational.

 

[kochanskij]

You can do the paradox without acceleration. Ultimately, therefore, it is about the difference in paths through spacetime. And not "something funny happens when you accelerate".

Thank you for pointing that out. You are correct. The fact that one twin changes from one inertial frame to another is the important event. (Outbound constant velocity frame to inbound constant velocity frame) This is usually done thru acceleration, but it doesn't have to involve acceleration.
If any readers want a better explanation, please ask. An example is the "3 twins paradox".

 

[PeterDonis]

Inertia force of acceleration can be regarded as a gravitational force.

No, neither of these are forces in relativity. They are effects of choosing a non-inertial frame. The key property that makes them not forces is that they are not felt--a body that is only moving in response to these "forces" feels no force at all and is weightless. In relativity, that makes them not forces.

Just like fictitious centrifugal and Corriolis forces can allow us to consider a rotating frame to be inertial, the gravitational force allows us to consider an accelerated frame to be inertial.

This is not correct. Frames in which such "fictitious forces" (the adjective is chosen for a good reason--see above) appear are not inertial frames.

the fact that one twin changes from one inertial frame to another is the important event.

In this particular scenario, yes, the turnaround is important.

However, this rule of thumb does not generalize.

Please read the Insights article that was linked to at the top of this thread, and the Usenet Physics FAQ article that it references. All of these rules of thumb are limited. The only fully general framework for dealing with such problems is the spacetime geometry/worldline framework, as described in those articles.

If any readers want a better explanation, please ask.

Unfortunately, you have shown that you are not a good person to ask. Please be more careful about posting in future threads.

An example is the "3 twins paradox".

If you have a reference for this, you can start a new thread if you want to discuss it or have a question about it.

This thread is now closed.