James and the Twin Paradox

[Ed3]

James wrote,

They discuss the Twins Paradox and a couple of others, because those can be resolved,

This is the second claim that he has made that the paradox has been resolved. Each time these claims get made they add to the google count.

Despite the fact that numerous claims (737,000) to the contrary have been made, the statement is false. If he or any other person wishes to debate the point I will oblige.

Ed

[phyllo]

Is that a sequel to ‘James and the Giant Peach’?

[James_S_Saint]

Well, did you want to discuss the Twins Paradox or your Triplets Paradox?

Your analysis involved three parties;

Two Twins, Kirk I and Kirk II, board the identical spaceships Enterprise I and Enterprise II respectively. Since Vulcans live longer than Humans, the overwhelming majority of Physicists have voted that Spock should stay on the (inertial) space station.

Your analysis involved the time dilation between each of the three parties K1-S, K2-S, and K1-K2.

In that analysis, you found that the math didn’t work out. Congrats. But that wasn’t the Twins Paradox.

The Twins Paradox involved only your Kirk1 and Kirk2. There is no Spock. Or alternatively, Spock and Kirk1. And that is the one that I believe is logically resolvable because it is only concerned with K1-K2 or S-K1.

[Ed3]

Hi Phyllo,

This is definitely a very odd fantasy ride.

I generally agree with conventional (relativistic) physics and James does his RM. This time the roles are reversed.

Not sure what rabbit hole we have gone down.

Ed

PS I like your input in either case.

[Ed3]

James,

Either S K1 or S K2 is the conventional paradox.

Ed

[James_S_Saint]

@Ed3

James,

Either S K1 or S K2 is the conventional paradox.

Ed

Fine. That conventional paradox is resolved by merely attending to the “Frame of Origin”, unless you can show otherwise.

In every proposed twins paradox, there is a Frame of Origin. The frame of origin is where the twins were at rest with respect to each other and to where they return. In the original scenario, that was “the Earth” and is referred to as “the inertial frame”.

It is called “the inertial frame” because it is the one frame declared “inertial; not movable”. But the issue comes to mind as to how either frame can be considered the one that isn’t moving. SR declares that such a notion is irrelevant. But if it is ignored, an apparent paradox arises.

So as to clear up the picture a bit, let’s presume that neither twin stands perfectly still, but rather one twin (Twin A) just very minutely drifts away from the Frame of Origin while the other twin (Twin B) takes off in his ultra fast rocket. This is merely to provide distinction and reveal that there are always 3 frames involved.

And further, so as to get away from the complexities of gravitation issues, lets put them out in space originally standing on a small floating space station far away from any gravity field.

The time dilation factor is always applied to whichever one leaves the Frame of Origin.

Twin B gets in his rocket and rockets away. Twin A gets into his rocket and sticks ores out his windows and begins to row hoping to catch a few gas particles drifting by from Twin B’s exhaust.

If we apply the time dilation to the one doing all of the serious moving, Twin B’s clock will run slower and he will age less. We cannot simply reverse the reasoning and say that it is all relative because Twin A is not moving away from the Frame of Origin.

That is pretty much the end of the story, but…

Some scenarios remove any sign of the Frame of Origin so as to make their point clear. The problem is that in every case, there must always be a Frame of Origin where their clocks were staying in sync whether anything is standing as a sign of it or not. If two items are moving away from each other, there must be a frame indicating a synchronized clock situation. The issue becomes how to find out where that frame would be.

If the ships merely see nothing but each other separating, they might not know which is accelerating from the Frame of Origin, but that is only a matter of their awareness. If they later find that one has greater time dilation than the other, it can be deduced as to which was accelerating more from the Frame of Origin.

If they see no difference in their clocks, then they can deduce that they were both leaving the Frame of Origin merely in different directions.

Without determining the Frame of Origin, the Twins cannot know which of them will age more until they meet again.

[Ed3]

James

So which frame of origin?

Ed

You can not believe that simply being in a rest frame your reality is more real than the reality of the accelerated frame.

P.S.

If you do believe that nonsense then why do you think that Wiki and Nova bother to show an analysis of the accelerated periods?

[James_S_Saint]

@Ed3

James

So which frame of origin?

Ed

Pay attention;

@James S Saint

The frame of origin is where the twins were at rest with respect to each other and to where they return.

So as to clear up the picture a bit, let’s presume that neither twin stands perfectly still, but rather one twin (Twin A) just very minutely drifts away from the Frame of Origin while the other twin (Twin B) takes off in his ultra fast rocket. This is merely to provide distinction and reveal that there are always 3 frames involved.

[Ed3]

James,

My initial reaction was too quick. See the rest of my edited post.

Why did you involve yet another accelerated reference frame (Drifted away)?

Ed

[James_S_Saint]

This is really just a question of simultaneous equations and having to have more frames of reference than variables (parties). That is something one would think that any mathematician 100 years ago would know instinctively.

What they didn’t seem to realize is that where ever the clocks were synchronized constitutes a frame or reference. They could hang a buoy out in space to mark that spot if necessary.

I had the Twin A “drift a little” so that;

@James S Saint

So as to clear up the picture a bit, let’s presume that neither twin stands perfectly still, but rather one twin (Twin A) just very minutely drifts away from the Frame of Origin

So Twin A is “effectively still”, moving extremely slowly, merely to reveal that there is an otherwise hidden frame of reference to the paradox. With the required three frames, the math becomes trivial for a mathematician.

But none of this has to do with any absolute universal frame of reference (RM:AO deals with that notion).

[Ed3]

James,

All I really ask is that you not repeat the phrase “the twin paradox has been resolved” unless you feel that you can prove it.

Ed

[James_S_Saint]

@Ed3

James,

All I really ask is that you not repeat the phrase “the twin paradox has been resolved” unless you feel that you can prove it.

Ed

Well, in logic terms it is obviously resolved but if you want the math, your the mathematician.

Do you have some question about it? Did you want it in German too?

And the same is true concerning RM:AO. The logic is resolved, but the math gets really strange and needs someone like yourself to put it in standard math terms.

[Ed3]

Hi James,

I am sorry, you still seem to believe that the paradox has been debunked.

Could you explain why one more time?

Thanks Ed

Sorry not necessary - I will read your post.

Ed

[James_S_Saint]

@Ed3

Could you explain why one more time.

Okay, a little at a time.

We begin with 3 frames of reference; Spock’s, Kirk’s, and the “Frame of Origin”.

The frame of origin, “fO”, is where it all begins. Spock’s clock and Kirk’s clock are synchronized. As long as they stay at that location with respect to each other, the clocks stay synchronized. I think that part everyone can agree to.

The question is usually asked, “who ages more if one begins to move, since neither party can be used for an inertial frame?”

If either party accelerates from f0, his clock will decelerate and thus display less time passage. If Kirk zips away at near the speed of light, he will not age nearly as much as Spock. Their clocks will be out of sync. The Lorentz equations will foretell exactly how much. His variations in acceleration might make the math more difficult to track, but the results should be consistent with relativity concerns.

Any questions so far?

[phyllo]

You’re saying that the process of acceleration slows down the clock for the rest of the journey?

How does the rate of acceleration relate to the passage of time for the twins?

[James_S_Saint]

@phyllo

You’re saying that the process of acceleration slows down the clock for the rest of the journey?

How does the rate of acceleration relate to the passage of time for the twins?

The process of acceleration is a process of varying speed. At each differential speed, there is a Lorentz transformation for the time dilation (from Ed’s thread);

Or from Wiki;

,

If that is integrated over the duration of the acceleration, a total time dilation should be evident. If no deceleration occurs, the dilation caused by the acceleration will remain constant. The clock that is still moving relative to f0 will still be turning slower than before the acceleration.

There are other formulae for the concern of Lorentzian acceleration, but they must resolve to the integral of the speed variation, else relativity has yet another issue.

[The_Golden_Turd]

So if they continue on traveling, one faster than the other, who will reach the end of the universe, be it the spatial or temporal sense, first?

[phyllo]

The universe is a doughnut. There is no end to reach.
[attachment=0]homer contemplates universe.jpg[/attachment]

[James_S_Saint]

@Contra-Nietzsche

So if they continue on traveling, one faster than the other, who will reach the end of the universe, be it the spatial or temporal sense, first?

Since there is no end to it, I suspect they will never experimentally know the answer to that.

But it wouldn’t surprise me to find that they have spent $10 billion of government money trying to find out. They did something equally as insane with the Higgs boson search and even rewarded themselves with a Nobel prize for fooling the population (which seems to be the whole point in Nobel prizes. Even Obama got one for the same reason).

[The_Golden_Turd]

So wait, your understanding of Time, Direction, and Relativity presumes no limit to the universe. Your presumption of gravity, for example, rests on the premise of a infinite universe, as so for the weak and strong forces?

Like, are they operating at a equal tangent towards the center of a galaxy? Who is closer to the intersteller winds, and galactic winds, on any given trajectory? Someone is always going to be a winner and loser in those variables.