I don't think Hawking is talking about the 'walking' as being the thing which creates the effect.

I think he's talking about the fact that the person on top of the mountain experiences less gravity from the earth (equivalence)!

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Hawking:

”The theory of relativity gets rid of absolute time. Consider a pair of twins. Suppose that one twin goes to live on the top of a mountain while the other stays at sea level. The first twin would age faster than the second.

What Hawking is talking about here is the fact that a manufactured atomic clock will tick out time more rapidly on top of a mountain, because of less gravity at the top. A similar atomic clock will tick out time more slowly at sea level, because the gravitational potential is higher (stronger) at sea level. He suggests that the harmonic oscillation rates of our body’s atoms determine our aging rates. This is pure speculation. It isn’t even “physics” or “biology”. It’s guesswork.

We could just as easily speculate that the twin on top of the mountain will age more slowly if he has an outdoor swing and he swings a lot, since a pendulum clock will tick more slowly on top of a mountain.

You can not believe all these urban legends these guys tell you. Go to any biology book or website and see if any doctor or biologist ever mentions anything about this "mountain top" speculation. They don't do it. Only the physicists do, and Hawking is NOT a biologist

No it's not. It's physics, an application of relativity theory.

SeanF,

Here. See just what comes from this urban legend stuff that is taught by some physics teachers today:

“Einstein's Law of Relativity.

We look at the universe, and say, "How old is the universe? Looking back in time, the universe is about 15 billion years old." That's our view of time. But what is the Bible's view of time? How does it see time? Maybe it sees time differently. And that makes a big difference. Albert Einstein taught us that Big Bang cosmology brings not just space and matter into existence, but that time is part of the nitty gritty. Time is a dimension. Time is affected by your view of time. How you see time depends on where you're viewing it. A minute on the moon goes faster than a minute on the Earth. A minute on the sun goes slower. Time on the sun is actually stretched out so that if you could put a clock on the sun, it would tick more slowly. It's a small difference, but it's measurable and measured. If you could ripen oranges on the Sun, they would take longer to ripen. Why? Because time goes more slowly. Would you feel it going more slowly? No, because your biology would be part of the system. If you were living on the Sun, your heart would beat more slowly. Wherever you are, your biology is in synch with the local time.”

SOURCE

I see this type of stuff all over the internet now. I see it in books and magazine articles. I hear of “Eastern Mystics” talking about it. I see people talking about it on all sorts of internet message boards. These legends have become so much a part of our lives – and most people never remember them correctly – they cause a lot of young people today think we live in a mystical world of magic.

This is a shame.

OK. Here, at least is my final word on the subject. First, a couple of things I know we all agree on, but I just want to set out.

1) Special and General Relativity are both valid theories. I don't think I've come across as arguing that they aren't, but I just want to make sure.

2) We can consider the Earth as an inertial reference frame for the purposes of the experiment. As Sean pointed out in an earlier post, we can place the experiment in deep space and have the stationary (or inertial) twin sit in a non-moving spacecraft.

So, with that out of the way. I both agree with Sean's post, and to some extent disagree.

Start with the agreement. We have two travelers. One (A) stays in an inertial frame, the other (B) does not. Since A stays in an inertial frame, we can compute all of his observations, as Sean has done many times, using SR. He sees B's clock as running slowly throughout the trip, and is not surprised when his twin returns much younger than he is. Since A's frame remains inertial it is, to some extent, preferred compared to B's. The "paradox" only arises if we do not realize this point. Since we do realize that there is a difference between the two frames, the paradox vanishes. OK, so there's the agreement. We can resolve the twin paradox from A's point of view without reference to GR.

Now the disagreement. How does B describe the situation from his reference frame? We've all agreed that he's in a non-inertial reference frame due to his change in direction. I think we can also agree that we cannot use SR to describe events as observed from a non-inertial reference frame. That requires GR. If you don't believe me, try a textbook. Weidner &amp; Sells' Elementary Modern Physics puts it this way:

That puts it about as plainly as I think possible. The problem is that from B's point of view there has to be a time where he sees A's clock as running fast compared to his. That can't happen during the coasting periods. We've all agreed that during those periods he sees A's clock as running slow, as predicted by SR. The time when he sees A's clock running fast has to come during the non-inertial accelerations. To determine that, from B's non-inertial reference frame, requires GR.

So, Sean, to summarize, (although I know this won't be the last post anyone makes on this topic). I agree with you that we do not need general relativity to resolve the twin paradox from the point of view of the earth-bound inertial observer A. There is no paradox since we realize that B is in a non-inertial frame and therefore we cannot apply special relativity to his observations. However, to explain the events from the point of view of the traveller B requires general relativity since he is in a non-inertial frame.

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"If it was so, it might be, and if it were so, it would be, but as it isn't, it ain't. That's logic!" - Tweedledee

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Non moving relaive to what?

Einstein said in his 1905 paper, “...the view here to be developed will not require an “absolutely stationary space” provided with special properties...”

You can’t have an absolutely "stationary" spacecraft in space.

And both “twins” in his SR theory are “inertial”. Neither feels any acceleration at all.

In the SR theory, both “twins” (both clocks) are “inertial” because neither experiences any acceleration. They are both moving "relatively".

You might as well give up because the paradox of SR can not be resolved.

Which twins are those, and which theory--I assume you are talking about a specific work?

No we have not "all" agreed to that, and it is not true. In the 1905 theory, there is NO “change in direction”, and both clocks are moving “relatively”.

Einstein specifically said in the theory, “The length of the moving rod measured in the stationary system does not change, therefore, if v and -v are interchanged.”

This means that even if there is a change of direction, the change does not matter and causes no effect on either clock, because, as he said in the paper:



This means that a “change” in direction causes no effect. It is only the “relative motion” that causes an effect.

The reason that this is considered a paradox is that Special Relativity seems to imply that either one can be considered at rest, with the other moving. The confusion arises not because there are two equally valid inertial rest frames, but because there are three. A lot of explanations of the twin paradox have claimed that it is necessary to include a treatment of accelerations, involving GR. Not true.

The three inertial frames are 1) at-home twin 2) the going-away twin and 3) the coming-back twin. It doesn't make any difference that the last two are physically the same twin--they still define different inertial frames.

Hence you have the asymetry, and therefore there is no paradox.

O yes there is a change of direction in that 1905 paper, concerning the "twin paradox" (it's not called that in the paper, it's mentioned as a "peculiar consequence").
Ryback, I'm not sure where you got that, but it is lifted almost directly from this page.

Eta, thanks for the post. Very informative.

I guess I see it that we can define that the travelling twin instantaneously jumps from one inertial frame to another. Thus, while he does not spend the entire experiment in the same inertial frame, he does not spend any time at all in a non-inertial frame.

I do realize that instantaneous acceleration is not physically possible in reality, but I still think the "twin paradox" can be defined and explained in SR as such.

Basically - we could have two clocks (in different inertial frames) passing each other when they both show the exact same time. This should be indistinguishable from one clock instantaneously switching inertial frames at that point, which should be indistinguishable from one person switching inertial frames at that point.

Oh, well. At least my disagreement (such as it is) with you is a lot easier to deal with than my disagreement with Sam5!

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See my post above with the equation. In the first place, there is no “turning around” example in the theory itself. In the second place, Einstein said that didn’t matter, since:



So it is not the “turning around” that does it. The “turning around” does nothing. It is the “v” that does it, and it doesn’t matter what direction the clock or twin is moving.

We could have Jack and Jill both go out into space in opposite directions and “turn around”, and SR theory would say that they both see each other’s clocks as ticking slowly. So when they return to earth, they would both disagree as to which clock “lagged behind”.

This paradox has NO resolution, because the theory is incorrect.

That formula refers to the time dilation and length contraction. It does not refer to the simultaneity difference, which is both direction-dependent and distance-dependent.

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Right, and the observer with clock A will see the clock B as ticking slow, while the observer with clock B will see the A clock as ticking slow.

Show me where he says the clock rate slowdown is “direction dependent”.

Not true. Einstein explicitly described it in his 1905 paper on the subject.

That was the original analysis of the "twin paradox," and the result that Einstein obtained is the same we agree with today--and it wasn't a paradox then, nor now.

Do you see where I said, "That formula refers to the time dilation . . . "? "Time dilation" and "clock rate slowdown" are the same thing, and it is not direction-dependent.

Simultaneity is a different (though related) issue, and it is direction-dependent.

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This topic has hopelessly confused SR with GR. The Twin Paradox is an issue of GR and the example given at the beginning of the thread involves acceleration and the equivalence with gravity, both GR issues.

I thought we were talking about “time dilation” here and the “twins paradox”? Time dilation is NOT "direction dependent", so a "turnaround" causes no effect regarding observed time dilation.

If you want to write an essay about “simultaneity”, then go ahead, but tie it into the time dilation issue, and tell us why one “twin” sees something different from the other “twin”, during relative motion only and no “blasting off” of just one twin.

I say there is no paradox in GR, but there is in SR.

Do you see any way to resolve the “twins paradox” issue in SR, using SR only? I say there is no resolution in SR and that the SR theory is incorrect.

I also say that “relative motion” can not have any possible effect on any kind of clock, since the clock feels no kind of “force” applied to it through “relative motion” alone.

For example, the earth is moving “relative” to billions of other bodies, and we can’t possibly have any kind of real “time dilation” effect caused by our “relative motion” relative to those other bodies.

I do see a way. You can read it in the very first paper to discuss the issue, Einstein's 1905 paper on special relativity--ten years before his general relativity papers. He discusses the issue, derives the same result that one would derive from general relavity, and does not--even at the time--consider it a paradox. Neither do I.

The SR theory is not incorrect, as far as it goes, but a lot of people misunderstand it.

For pete's sake, Sam5, you keep quoting from Einstein's book - haven't you read it?

From Part I, Chapter 9, titled The Relativity of Simultaneity:

"We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity)."

Read the whole chapter, understand why the train observer concludes that lightning flash B took place earlier than lightning flash A. Once you do, it becomes clear that if the train were moving in the opposite direction, the observer would conclude that flash A occurred before flash B.

Ergo, the simultaneity is direction-dependent!

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We’ve already discussed this many times, and Einstein says in the chapter why the moving train observer sees the B light first:

“Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.”

That’s because the train observer is traveling toward the source B, and he will receive the beam from B at a velocity of c + v.

If he goes in the opposite direction, the effect would be the same and the numbers and shift would be the same, but the direction reversed, so he would see the A light first. Changing direction in SR does nothing to change the clock rates. The “v” is important but the direction is not.

Keep reading:

"Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A."

"Considered with reference to the railway embankment," yes. With reference to the railcar, no.
Bingo! You've almost got it!
Absolutely true! =D>
Oh. And you were so close.

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What false “conclusion” they might come to on the train, caused by the c + v and c – v phenomena, is not relevant to what actually takes place in both frames at the same time. We could just as easily use an example with two cannon firing at B and A. The train observers might “conclude” that cannon B fired first, but you and I know that it did not, and we will.... no, I will explain the whole situation to the train observers when they stop at the next station. I will explain the phenomena about the light and the sound.

Either you, or Einstein. Tough choice...

No. No. And No.

There is no such thing as "what happens in both frames at the same time" - that is covered in the chapter about the "relativity of simultaneity". Light waves do not travel as c+v or c-v but at c. There is no preferred frame of reference - each observer correctly describes the phenomena consistently with the same laws of physics.

This seems to be the nub of the problem. I for one do not agree that B sees A's clock as running slow during all the coasting periods, and fast during the accelerations. On his way out, B sees A's clock running slow and A sees B's clock running slow. Then B turns for home and immediately B sees A's clock running fast. A's clock continues to run fast from B's perspective all the way home. But A does not see B's clock running fast until some time after B's has turned for home. (Let's say B turns for home when he is 10 uncontracted light-years away: A won't see B's clock running fast until 10 years after B has turned around.)

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You obviously missed the whole point of my OP. Because both twins experience exactly the same accelerations, their age differences at the end of the experiment can have nothing to do with acceleration. They're entirely due to the fact that one twin is travelling at high velocities.

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