Re: Twin paradox revisited ll

On Jul 19, 9:57 pm, stevendaryl3...@xxxxxxxxx (Daryl McCullough)
wrote:
bill says...

What *physical* information does the stay at home twin receive, other
than the frequency shift of the light or of radio messages from the
traveler's ship, that leads him to conclude that the traveler is aging
at the slower rate?

The stay-at-home twin has a *coordinate* system that assigns
a location and a time to every event. He uses that coordinate
system to answer such questions as: How old is the traveling
twin at time t? That's the only meaning to the statement
"The traveling twin ages slower"; it just means that using the
coordinate system of the stay-at-home twin

age of traveling twin at time t+1
- age of traveling twin at time t
< 1

So how does the stay-at-home twin set up a coordinate system?
Well, there are lots of different ways, that all turn out to
be equivalent according to Special Relativity. One approach
is to use what's called "slow clock transport". The stay-at-home
twin takes a bunch of identical clocks. He sets them all to
his local time. Then he moves the clocks *slowly* to other
locations. He puts one clock at 1 mile away, another clock
at 2 miles away, etc. Then the meaning of the phrase "The
traveling twin ages slower" is just this:

Let t_1 be the time shown on clock 1 when the traveling
twin reaches clock 1.

Let a_1 be the age of the traveling twin when he reaches
clock 1.

Let t_2 be the time shown on clock 2 when the traveling twin
reaches clock 2.

Let a_2 be the age of the traveling twin when he reaches
clock 2.

Then the statement "The traveling twin ages slower" is just
verified by checking that

a_2 - a_1 < t_2 - t_1

You don't need to use light signals or Doppler shifts
to measure this effect.

--
Daryl McCullough
Ithaca, NY

Alternatively the stay at home could say that the Hafele-Keating
experiment tends to ratify SR's concept that a moving clock runs slow
thus that the traveler's moving clock is ticking over at a slower rate
than his own clock but the original posting under discussion is that
the traveler insists that it is the earth clocks that are physically
ticking over at a *faster* rate than his own clock.


Bill

.

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