Relativistic Twins

[davar55]

Originally Posted by chalsall

May I respectfully suggest that you might not be the right person to be asking trick questions?

A good friend of mine once advised: "Be aware of the listening into which you are speaking.

Wasn't me, it was the authors of my physics text.

Not merely pedagogical, but necessary to the
understanding of particle kinematics.

Now don't you start denigrating my intelligence or knowledge
without a shred of justification.

[chalsall]

Originally Posted by davar55

Wasn't me, it was the authors of my physics text.

Here's some respectful advise...

Don't repeat trick questions if you don't understand them deeply.

[LaurV]

[offtopic_private_opinion]
This is a typical example of a situation when your past is haunting you... There is a discussion about some elementary physics, where, you know... the guy is right! (about the displacement story, definitions, etc, he may not understand them, or he does, who knows, but the definitions and related stuff is right). But he is just struggling to get out from a big sh!thole where he entered in the past, because he played with stuff over his head (and over my head too!), and because of that, nobody pays attention to what he is saying anymore. Everybody assumes that he is continuing to talk stuff over his head, getting deeper and deeper, over his head, in that hole...
[/offtopic_private_opinion]

[chalsall]

Originally Posted by LaurV

But he is just struggling to get out from a big sh!thole where he entered in the past, because he played with stuff over his head

But please keep in mind one of the Scientific Methodology's touch stones...

Anyone is free to say at any time: "Sorry, I made a mistake.

I have heard of standing ovations at conferences for such statements.

[davar55]

Originally Posted by chalsall

But please keep in mind one of the Scientific Methodology's touch stones...

Anyone is free to say at any time: "Sorry, I made a mistake.

I have heard of standing ovations at conferences for such statements.

Yes and so far I've heard no such admissions from anyone here.

I stand by my discussion of this thread's topic.
And by my cosmology monograph.
No one has legitimately challenged any of it.

[davar55]

Originally Posted by LaurV

[offtopic_private_opinion]
This is a typical example of a situation when your past is haunting you... There is a discussion about some elementary physics, where, you know... the guy is right! (about the displacement story, definitions, etc, he may not understand them, or he does, who knows, but the definitions and related stuff is right). But he is just struggling to get out from a big sh!thole where he entered in the past, because he played with stuff over his head (and over my head too!), and because of that, nobody pays attention to what he is saying anymore. Everybody assumes that he is continuing to talk stuff over his head, getting deeper and deeper, over his head, in that hole...
[/offtopic_private_opinion]

Hey, I like you too. But that's a lot of poppyc*ck.

[ewmayer]

@Dave:

Admittedly, "displacement" is a problematic term because it is used in so many physics and engineering contexts, sometimes as a vector, sometimes as a scalar. Displacement of your car's engine = scalar (volume), displacement along a strike-slip fault = scalar (distance) but could also mean vector if one is mapping larger-scale ground movements around the fault, etc.

Anyhoo, in the context of the classically posed Twin paradox, all that matters is distance and speed-relative-to-light.

----------------------

Originally Posted by Mr. P-1

The traditional twin paradox is easily resolved by noting that there is no single inertial frame of reference with respect to which which the travelling twin is stationary throughout his journey. In fact, with respect to any IFoR, the travelling twin will be travelling faster than the stay-at-home twin for at least one of the legs of his journey. Moreover this leg will dominate the calculation.

However, consider the following variation: In a closed universe, the travelling twin circumnavigates it without ever accelerating. Of course, from his inertial point of view it is the stay-at-home twin who has circumnavigated the universe. So what do their respective clocks show when ultimately they meet again?

While your 2nd scenario may be topologically possible, I wonder if it violates the basic tenets of ralativity w.r.to inertial frames, such as

In an inertial frame, Newton's first law (the law of inertia) is satisfied: Any free motion has a constant magnitude and direction.

Now, speaking in terms of GR, when I think "free motion" I think "0g motion (as measured by an internal accelerometer) along a geodesic" - e.g. an astronaut orbiting the earth is falling freely, feels no acceleration, but because the path he takes is curved, is in a non-inertial FoR. Question is: Must this be true of any closed path, even in the "closed universe" topology you describe? I believe so, but need to do some further reading.

[cheesehead]

Originally Posted by davar55

Isn't acceleration more important than simply the high (near c) velocity?

Although there is a bit of time-dilation due to gravity acceleration, in the version of the twin-paradox to which you refer, it's far smaller than the dilation due to relative velocity. In order for the gravity acceleration term to be significant next to the velocity contribution, the acceleration would have to be well into the human-body-squashing range, and the returning twin would be dead.

Originally Posted by davar55

But isn't the traveled round-trip of fly guy just a zero-total-force incident, since f=ma and a is a vector too?

But total force is not relevant to time dilation here.

time dilation, which is a function of velocity

You keep making the same simple oversight about that function, typical of the shallowness of your challenges to mainstream physics.

Originally Posted by davar55

total velocity = total displacement / time

in a round trip, total velocity is zero

But "total velocity" has nothing to do with time-dilation.

Originally Posted by davar55

(0) I can certainly understand the desire to cling to one's preconceived notions, even in the face of overwhelming evidence/argumentation. :)

You certainly do cling!

Originally Posted by davar55

My point is that ignoring acceleration going or coming back invalidates the analysis totally.

No, that's just one more illustration of the shallowness of your understanding of time dilation.

You keep making the same mistake.

Originally Posted by davar55

No, total displacement is independent of the path, and only depends on the starting point and ending point. Any other answer is simply missing the point of the trick question.

Your insistence on the importance of "total displacement" in the twins paradox is basically the same oversight as before.

One more time: suppose a trip goes from origin O = (0,0,0) to another point A = (a,b,c), then to point B = (d,e,f) then back to O= (0,0,0). The total displacement for the whole trip is a vector of magnitude zero.

... but this is irrelevant to the twin paradox.

If you integrate differential distance (scalar) over a path, you get total distance (scalar) NOT total displacement (vector, which in a round trip equals zero).

... but this is irrelevant to the twin paradox.

And repeatedly claiming my cluelessness is beneath you and this forum we both enjoy.

You've been exhibiting the Dunning-Kruger Effect for quite a while.

Here's an itty-bitty clue that's been "hiding" in plain sight:

v²/c²

[cheesehead]

Originally Posted by davar55

I stand by my discussion of this thread's topic.

Let's see where you stand after you realize your repeated oversight, and the irrelevancy of your arguments here dawns upon you.

And by my cosmology monograph.
No one has legitimately challenged any of it.

That _you_ categorize a challenge as "illegitimate" certainly doesn't make it so.

[davar55]

Originally Posted by cheesehead

Here's an itty-bitty clue that's been "hiding" in plain sight:
v²/c²

If by this you are implying I don't understand Lorentz factors,
please check my answer to your question re: relativistic Doppler
effect (in the thread you asked it, I believe the same one
containing cosmo3.txt, the monograph), which you haven't
re-responded to. (I hope you're feeling better, btw).

[cheesehead]

It's still in plain sight.