Can the Twin Paradox be simplified?

Could you tell me what you mean by "synchronized to each other"?

 

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Assuming the ability to synchronize their watches initially.., Absolutely!

But only once both groups come together will they know which group was actually in motion relative to the other, by comparing whose watches then are observed to be fast or slow.

 

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A light signal is sent from the first blue army guy to the second blue army guy who is holding up a mirror. The light is reflected back to the first blue army guy who times how long light takes to make a round-trip journey between the two blue army guys. Once the first blue army guy has this information, he is able to tell the second blue army guy how to set his watch.

For example, if the light takes 2 seconds to make the round trip, the second blue army guy is instructed to set his watch so that it appears to be exactly one second ahead of the first army guy's watch. This compensates for the time required for the image to reach his eyes. After that, the third blue army guy can sync his watch to the second blue army guy in the same way, and so on...

 

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Can you expand on this part? I'm not being difficult but talking this out will help me think it through, and these details are important.

 

Sure, my pleasure. Let's say that all the blue army guys are equally spaced. Since they are lined up along the x axis, all they have to do is make sure they stand on x=0, x=1, x=2, and so on. Also, lets say that their wristwatches have digital displays which do not display any time until the watch has been set to a certain time, and the display has been turned on.

The first blue army guy has higher rank than the rest of the guys, so it is his job to give them orders on how to synchronize their watches. So he sends a test signal to the second blue army guy, who uses a mirror to reflect it back to the first blue army guy. That is, the test signal travels from x=0 to x=1 and then back to x=0. The length of that path is known to be two units of length.

The first army guy uses his watch to time how long the test signal takes to travel those two units. In the example I gave above, the test signal requires two seconds to complete the path. So the first blue army guy gets on his radio and gives his orders to the troops. He says, "You will set your own watch to appear to your own eyes to be exactly one second ahead of the man before you." Then he waits as long as required for that message to reach the farthest army guy.

Next, the first blue army guy sets his watch to 0.000 seconds, and turns on its display at the same time. The second blue army guy is watching him do this through his telescope. As soon as he sees the first guy's watch display 0.000 seconds, he sets his own watch to 1.000 second, and turns on its display at the same time. This procedure continues down the line until all the blue army guys have synchronized watches.

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Notes:

1. If you are worried about human errors, imagine this procedure done by machines instead of humans

2. If you are wondering why the first army guy instructed them to set their watches ahead by one second, it is to take into account the amount of time required for the light to travel from one guy's digital display to the next guy's eyes.

3. The red army guys have the same kind of watches, and they synchronize them in the same way.

4. There is no need for the red army to try to synchronize their watches to the blue army, or vice-versa.

 

"quicky concepts" by keith

 

Ahh, the old "I don't care what mainstream physicists have agreed on, I don't understand it, therefore it must be wrong".

Well, well, so you don't understand the paper, you don't understand what mainstream physics agreed on this subject (because it disproves your claims) so, you decided to declare the experimental evidence invalid.

Actually, experiment proves your claim as being false.

 

Are you retorting with the ole "I read it on a webpage so it must be right" defense? What happened to logical discussion? BTW, we've already established that you do not speak for the mainstream physics community.

 

No, I am just pointing out (and this is the second time in two different threads), that you are contracting the mainstream view on the subject.

 

I have this comedic scene in my mind of you taking a debate class, where your turn at the podium consists of rigorous, silent pointing at textbooks.

Anyway, I've given a couple of issues I have with the clock hypothesis. Perhaps you would care to discuss them?

They're basing the conclusion of "verification" on the muon experiment which is exactly what I was analyzing. I'm working under the presumption that we're all capable of logical discussion without an appeal to authority.

 

I am pointing at the mainstream view, the one that contradicts your beliefs. I have given you several explanations why your view is fringe, now it is up to you to try to understand them.

 

Got it. So you're incapable of discussions beyond appeals to authority. If I were you I would probably be hesitant to rely on my own logic and intuition, as well.

 

Not really, at some point you need to realize that your "logic and intuition" comes at odds with mainstream physics. So, instead of arguing, you need to start studying, I have given you quite a few references.

 

Yes, Tach, and before you emerged from your banishment we were having a fine DISCUSSION, full of mutual respect and logic and ponderables. If you care to DISCUSS the issues that I've raised with the clock hypothesis, please do so. If your contribution is to simply reaffirm the existence of the clock hypothesis, in the absence of any other logical defense, I'll consider it trolling.

 

No, the point is to show how the mainstream clock hypothesis falsifies your fringe views on the issue. This was always the point.

 

I'm discussing the merits of the clock hypothesis, not the existence of it. I've warned you more than once now, if you fire back another empty post I'll report you for trolling the thread.

 

Its "merits" are already established by mainstream science. As such, it is standard practice to use it in order to refute fringe claims, like yours. For example, this page does a very good job in explaining to you the same exact thing I explained earlier.

 

I accept that the clock hypothesis is mainstream; I would like to discuss the merits of the hypothesis, regardless. If you would care to discuss the merits of the clock hypothesis, specifically those issues that I addressed earlier, please continue posting in this thread; otherwise, please move on. This is your last warning before I ask for a mod intervention.

The issues that I raised are:

1. The muons in the acceleration experiment were both already accelerated to an equivalent energy. If the energies added to a body through acceleration are what cause time dilation, then this experiment would not account for it.
   
2. The orbital nature of the acceleration on the "captive" muon is suspect to me. The analogy I gave was that an interest rate's affect upon an account's balance can be cancelled out if we fluctuate it appropriately. I then pointed out that constant linear acceleration would obviously yield a different result.
   
3. Acceleration would account for both SR and GR time dilation, while relative velocity does not, therefore it is more appealing to me.

 

This is kind of a lame link when pointing toward a "mainstream" view.

But there is this from the USNET link just below the article,

Does a clock's acceleration affect its timing rate?
The clock postulate is not meant to be obvious, and it can't be proved.... But we don't know if it's true; it's just a postulate....​

There is also the point to be remembered that the clock paradox is an SR hypothetical. Things change once you move into a GR world.

I think the biggest source of confussion comes from attempts to project the hypothetical into real world conditions. To explore the issue as a function of SR, requires that we set aside both gravitation and the equivalence principle. Once the hypothetical involves either, it is no longer "just" an issue of SR and things get real complicated.

 

Indeed, postulates cannot be proven, they can only be falsified. By experiment. They can also be confirmed by experiment. As such, the cited experiments falsify your and RJBeery's misconceptions on the issue that was already discussed in two different threads.