The Twin Paradox and the Equivalence Principle

[Dale]

Note that the CADO paper linked to above includes this paragraph:

"More than one reference frame for an accelerating observer have been defined, and there is no consensus about which one is most appropriate. This article describes one such reference frame: the CADO frame."​

That is fantastic news. It looks like Mike actually did learn the point from all of those arguments about CADO! I am very pleasantly surprised.

 

[Underwood]

Note that the CADO paper linked to above includes this paragraph:

"More than one reference frame for an accelerating observer have been defined, and there is no consensus about which one is most appropriate. This article describes one such reference frame: the CADO frame."​

Yeah, your right. Its further down the page. Sorry, I didn't see it.

The table of contents says they do compare the CADO frame to a couple of other frames in a section toward the bottom, but I haven't read that far yet.

 

[harrylin]

I found this link on a physics news group that gave me the answer I've been looking for, how to figure out how much older my home sister gets while I'm turning around. I haven't looked at very much of that web sight yet, its long, but I did find a formula on there that gives me the answer. I was surprised that its easy to do.

https://sites.google.com/site/cadoequation/cado-reference-frame

What you really asked, apparently, is how to calculate the difference in perceived distant age between different inertial frames - good for you that you found a detailed calculation example.

And I see that -happily- that calculation is consistent with our explanations here:
"It is possible for the traveler, by using only elementary observations and elementary calculations, to determine how much she has aged while that image was in transit, and thus to determine what her actual current age was at the instant that he received that image. If he does that correctly, he will get exactly the same result that the Lorentz equations would have given him (and the same result that the CADO equation would have given him)."*

But I wonder if you realize that you touched on a truly problematic issue of the equivalence principle solution with your phrasing "how much older my home sister gets while I'm turning around", and which surely played a role in it being downgraded. Did you consider such things as cause and effect, as well as when exactly this supposed far-away aging due to your turnaround must have happened? *ADDENDUM: If/when you switch between inertial frames then that corresponds to using the Lorentz transformations, and at first sight the web page that you found gives a shortcut to that. Here is the same directly with the Lorentz transformation for time, which looks to me just as simple:

t'=γ(t-vx/c²)

Using that website's example, in the outbound frame we can define that she is moving fast to the right;
x=vt and γ=2 so that v=+sqr(0.75)c=+0.866c and:
t'=2(t-0.75t)

For his age t=20 year at turn-around:
t'=2(20-15)=10 year = her age at turn-around according to the outbound frame.

If we switch to the return frame at turn-around, it's all the same except that now he reckons that she's moving to the left with v=-0.866c:

t'=2(t+0.75t)=2(20+15)=70 = her age at turn-around according to the inbound frame.
The difference is 70-10= 60 years.

And it's just as simple with the direct method: time delay between sending and receiving t2-t1 = (x2-x1)/(c-v)
Thus for this case:

For v=-0.866c: t2-t1 = sqr(0.75)* 20/(1+sqr(0.75)) = 129.28 yr. (inbound or return rocket frame)
For v=+0.866c: t2-t1 = sqr(0.75)* 20/(1-sqr(0.75)) = .. 9.28 yr. (outbound rocket frame)
Difference is.......... 120 yr.

So he now reckons that the signal left Earth 120 yr. earlier on his clock than originally estimated, which corresponds to her now being 60 yrs. older according to him than in his earlier estimation.