I think I solved the twin paradox

[Graystar]

How does the spacecraft accelerate instantaneously along its entire length?

 

The answer is: It can't. Doing so would require the compression or tension, depending on whether the thrust comes from the aft or forward end of the vehicle to propagate instantaneously.

 

I'm sure space-twin would reply, “why is my ship, at rest, compressing?”

 

There's this notion going around that if you feel acceleration you must be moving. I’ve read that about the twin paradox as well. There’s also the notion that the Earth really is moving because it has been flattened slightly due to spinning. That’s so ridiculous as to be laughable. If you’re standing on Earth, holding onto a rope connected to the Sun, and then the Earth moves away from you and the Sun, you’re going to feel acceleration even though you’re not moving! Don’t believe me? What do you think the tide is? It’s the moon’s gravity tugging at matter as it moves away. If the Earth were pliable enough it would be flattened along the orbit of the moon, in the same way that it’s flattened due to “spinning.” But we don’t say the Earth is moving relative to the moon, do we?

 

That’s the primary problem with the twin paradox...this idea that acceleration proves one is moving. What boggles my mind is how people who believe relativity can also believe that one twin is absolutely moving. Don’t they know everything is relative??

[swansont]

Janus’s response...

“The effects due to gravity are irrelevant to this observation.”

 

...was in response to my comment which started...

“Yes, but the muons, as well as the clocks flown around the world...”

 

So if Janus’s response was referring to muons only then that would have been clarified in the post. But it wasn’t. So my presumption is that Janus was referring to the airplanes as well. If that’s wrong, Janus is perfectly capable of clarifying that point for me.

 

The critical part of the Hafele-Keating experiment was the difference in the kinematic terms of the dilation. The gravitational terms don't cancel, because the flight times weren't equal, but they had the same sign. The kinematic terms, however, had opposite signs. Conceptually, the gravitational effects are indeed irrelevant.

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Consecutive posts merged

I'm sure space-twin would reply, “why is my ship, at rest, compressing?”

 

There's this notion going around that if you feel acceleration you must be moving. I’ve read that about the twin paradox as well. There’s also the notion that the Earth really is moving because it has been flattened slightly due to spinning. That’s so ridiculous as to be laughable. If you’re standing on Earth, holding onto a rope connected to the Sun, and then the Earth moves away from you and the Sun, you’re going to feel acceleration even though you’re not moving! Don’t believe me? What do you think the tide is? It’s the moon’s gravity tugging at matter as it moves away. If the Earth were pliable enough it would be flattened along the orbit of the moon, in the same way that it’s flattened due to “spinning.” But we don’t say the Earth is moving relative to the moon, do we?

 

That’s the primary problem with the twin paradox...this idea that acceleration proves one is moving. What boggles my mind is how people who believe relativity can also believe that one twin is absolutely moving. Don’t they know everything is relative??

 

The notion is that if you are accelerating then you know you are accelerating. And it is indeed the case. I'm not sure where you got the claim that the earth is moving because it's flattened — we know the earth is rotating, because it's rotating, and it is also flattened because it's rotating. Acceleration is not relative.

[Graystar]

Okay, lets do it this way. The twins are on a platform in space. There’s another platform one meter away. Space-twin instantly accelerates to 0.8666c towards the other platform. Space-twin’s body is facing the platform and, of course, has a depth to it. Lets call that depth 1 ST.

 

So lets try this again. If space-twin needs 1/2 a tick of his clock to move forward in time one tick of platform-twin’s clock, wouldn’t we also say that he has to travel two STs to move forward one PT?

[D H]

In whose frame?

 

You need to learn to construct space-time diagrams.

[Graystar]

In whose frame?

Neither. I'm asking about the transformation.

 

There's space-twin's frame on one side of the equal sign, and platform-twin's frame on the other. I gave one transformation that we all agree upon, 1/2 sec in space-twin's frame equals 1 sec in platform-twin's frame. So the question is what does 1 ST in space-twin's frame equal in platform-twin's frame?

[Janus]

Neither. I'm asking about the transformation.

 

There's space-twin's frame on one side of the equal sign, and platform-twin's frame on the other. I gave one transformation that we all agree upon, 1/2 sec in space-twin's frame equals 1 sec in platform-twin's frame. So the question is what does 1 ST in space-twin's frame equal in platform-twin's frame?

 

Without knowing which frame, we can't all agree on this. In the Platform-twin's frame 1 P-T sec = 1/2 S-T sec, but in the Space-twin's frame, 1 S-T sec = 1/2 P-T sec. In totally different frame, 1 P-T sec = 1 S-T sec and in yet another 1 S-T sec = 3.5 P-T sec.

 

In fact, there are an infinite number of frames that will all give different answers.

[Graystar]

Are you guys serious???

 

Twice I've written, "what does 1 ST in space-twin's frame equal in platform-twin's frame?"

 

...and you guys are still asking what frame???

 

Forget it.

[D H]

Suppose each person is holding a clock and a meter stick. Let's look at what each person sees:

• Space twin sees platform twin's clock ticking at half of the rate as his own clock and sees platform twin's meter stick as being 1/2 meter long.
   
   
  
• Platform twin sees space twin's clock ticking at half of the rate as his own clock and sees space twin's meter stick as being 1/2 meter long.

[Janus]

Are you guys serious???

 

Twice I've written, "what does 1 ST in space-twin's frame equal in platform-twin's frame?"

 

...and you guys are still asking what frame???

 

Forget it.

 

Because:

 

1. "what does 1 ST in space-twin's frame equal in platform-twin's frame?"

is a meaningless question.

 

You can ask "How does 1 S-T sec compare to 1 P-T sec in the P-T frame?" or "How does 1 S-T sec compare to 1 P-T sec in the S-T frame?" But when you use "in the S-T frame" and "in the P-Tframe" in the same question like you did, it is unclear as to what you are asking as you are mixing frames together.

 

2. When asked to clarify by DH, you answered "neither".

[stereologist]

It is amazing to me how many people claim that relativity does not work. Then again I see this even in peer reviewed journals. Well, not in relativity, but in biological journals posting ideas on sampling methodologies.

 

When I don't understand a well established issue like relativity or sampling I don't assume I am a genius who has seen in day 1 that the world is bonkers. I know, not assume, that the field is not going to be as simple to understand as I had hoped.

 

Good luck Graystar in figuring out where you are confused. It's worth the effort to understand these ideas.

[Sisyphus]

When I don't understand a well established issue like relativity or sampling I don't assume I am a genius who has seen in day 1 that the world is bonkers. I know, not assume, that the field is not going to be as simple to understand as I had hoped.

 

It's amazing how often people don't think that way, isn't it? When something doesn't immediately make sense, it must be wrong in some simple way that somehow everyone else missed.

[stereologist]

Here's a book written by Einstein himself. You could read this and see how things work.

 

Relativity: the special and general theory

By Albert Einstein, Robert W. Lawson

Translated by Robert W. Lawson

Edition: 3

Published by H. Holt and Company, 1921

[Janus]

Here's a book written by Einstein himself. You could read this and see how things work.

 

Relativity: the special and general theory

By Albert Einstein, Robert W. Lawson

Translated by Robert W. Lawson

Edition: 3

Published by H. Holt and Company, 1921

 

Ah yes, this book:

 

http://www.bartleby.com/173/

 

The problem I have with this book is that quite a bit is expected on the part of the reader to follow the arguments laid down. Things that are supposed to be obvious to the reader, aren't always so for all readers. As a result some readers can miss some of the vital points and come to wrong conclusions (or decide that the argument is faulty).

[swansont]

It is amazing to me how many people claim that relativity does not work. Then again I see this even in peer reviewed journals. Well, not in relativity, but in biological journals posting ideas on sampling methodologies.

 

When I don't understand a well established issue like relativity or sampling I don't assume I am a genius who has seen in day 1 that the world is bonkers. I know, not assume, that the field is not going to be as simple to understand as I had hoped.

 

Some people do challenge accepted science, but they only get a serious audience when they do it within the proper framework of science. I saw a poster at a recent conference discussing an experiment concerning the implications of photons having mass, and ways to test those implications, which was what they were doing. And that's perfectly good science to do.

 

But there's a huge difference between "if X is wrong, here's how we would know and here's our attempt to measure this effect" and simply going with "X is wrong, full stop."

[stereologist]

That's interesting swanson.

 

What I ran into was an author in a journal on neuroradiology demonstrating that a technique claimed to be unbiased was in fact severely biased. Apparently unaware of why the unbiased property applies goes on to demonstrate not that the method was wrong, but rather that they had no idea how to properly implement the method. When I asked the author of the paper on some of the details of their work they refused comment.

 

In another paper a person was proposing a correction to an unbiased method. The reason for this is that practical implementations are known to introduce small amounts of bias due to observational difficulties. The method is well known to over project, or to get a larger answer than is the true result. In the paper the author says his method corrects for overprojection, but provides a formula that always increases the value of the result.

 

Go figure!

[throng]

Not sure what you mean by "time dilation of the Earth".

The space twin accelerates out of Earth's frame and because of that his clock will run slower.

 

I was trying to flick your avatar.

[asprung]

The space twin carries some time dilation back to earth as he is said to return younger than his brother. What becomes of his length contraction?