Re: Time dilation

From: Androcles (androc1es_at_nospamblueyonder.co.uk)
Date: 09/02/04 

Date: Thu, 02 Sep 2004 13:49:19 GMT

"Jon Bell" <jtbellj3p@presby.edu> wrote in message
news:ch72n9$2s3$2@jtbell.presby.edu...
| In article <MoyZc.24196$7i2.879367@news20.bellglobal.com>,
| Robert Finch <robfinch@sympatico.ca> wrote:
| >
| >If time dilation is based on relative velocity, couldn't the people on
| >Earth also be younger than the astronaut when he returns ? Meaning there
| >would be two alternate realities ?
|
| Sam has posted links to general explanations of the "twin paradox". Here
| are worked-out numerical examples, analyzing the same situation using two
| different approaches. The result of both is that both twins agree that
| the "traveling" one ages more.
|
| http://www.google.com/groups?as_umsgid=cdscn6%24cej%241@jtbell.presby.edu
|
| http://www.google.com/groups?as_umsgid=bnq8m5%24i2i%241@jtbell.presby.edu
|
| By the way, there's a newsgroup specifically about relativity, namely
| sci.physics.relativity. I've crossposted this message there, and set
| followups to go there only, by default.
|
| --
| Jon Bell <jtbellm4h@presby.edu> Presbyterian College
| Dept. of Physics and Computer Science Clinton, South Carolina USA
There is another link given by Koks:
http://www.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/TwinParadox/twin_doppler.html

The Twin Paradox: The Doppler Shift Explanation
===================================
Let us focus on what Stella and Terence actually see with their own eyes.
(Just to emphasize that we're talking about direct observation here, I'll
put the verb "see" and its brothers in the HTML strong font throughout this
section.)

[Androcles: I'll use capital where Koks uses bold]

To make things interesting, we'll equip them with unbelievably
powerful telescopes, so each twin can WATCH the other's clock throughout the
trip. If each twin SAW the other clock run slow throughout the trip, then
we would have a contradiction. But this is not what they SEE.
{Androcles: Oh yes it is what they SEE.]

Just in case it's too hard to read the clock hands through the telescope,
we'll add a flash unit to each clock, set to flash once a second. You might
guess at first that Terence SEES Stella's clock flashing once every 7
seconds (with the time dilation factor we've chosen) and vice versa. Not
so!

[Androcles: Koks seems to think we are not aware of doppler shift as it
would normally apply to sound for some reason, the equation for which is
f' = f (c+/-v)/c+/-u). Koks doesn't like to use equations much. ]

On the Outbound Leg, Terence SEES a flash rate of approximately one flash
per 14 seconds; on the Inbound Leg, he SEES her clock going at about 14
flashes per second. That is, he SEES it running fast! Stella SEES the same
behavior in Terence's clock.

[Androcles: Koks has just denied his earlier assertion "this is not what
they SEE."]

What gives?

[Androcles: Bull*** gives. Koks offers no proof whatsoever. No equations,
just assertion.]

Well, the section title gave it away: just replace the words "flashes per
second" with "cycles per second", and you'll recognize the familiar Doppler
shift at work.

[ Androcles: I prefer flashes per year, then I don't have to worry about
large numbers. As with any clock, we can have a minute flash that occurs
 every 60 seconds, an hour flash every 60 minutes,a day flash every 24 hours
and a yearly flash every 365.25 days.]

The regular pulses are redshifted to lower frequencies during the Outbound
Leg, and blueshifted to higher frequencies during the Inbound Leg. (I
invite you to consider laser-based clocks instead of flash units, for added
techno-jazz.)

[Androcles: Here Koks is correct. He is supplying techno-jazz and wants to
 beef it up. ]

The Doppler shift factors I gave (1/14 and 14/1) come from the relativistic
Doppler formula.

[ Androcles:

f' = f.sqrt([1-v/c] / [1+v/c] ) and
f' = f.sqrt([1+v/c] / [1-v/c] ) as we know. Let's resolve Koks' velocity
from them.
v = 0.9898c, f' = 0.0715c.
v = -0.9898c, f' = 14.
Yep, looks like he's got the right relativistic equation.]

The relativistic formula takes into account both the "delay through
distance" effect of the non-relativistic formula, and the relativistic time
dilation. In other words, Terence computes that Stella's clock is really
running slow by a factor of about 7 the whole time, but he SEES it running
fast during the Inbound Leg because each flash has a shorter distance to
travel. And Stella computes the same for Terence.

All well and good, but this discussion at first just seems to sharpen the
paradox!

[Androcles: It most certainly does ]

 Stella SEES what Terence SEES: a slow clock on the Outbound Leg, a fast
clock on the Inbound Leg. Whence comes the asymmetry between Stella and
Terence?

[Androcles: There is none, of course.]

Answer: in the length of the Inbound and Outbound Legs, as SEEN.

[Androcles: This is a HUGE joke. Nobody has EVER SEEN a length contraction.
It is ALWAYS a calculation, never an observation. ]

For Stella, each Leg takes about a year.

[ Androcles: Got that? One year each way for Stella. The excrement of the
male bovine. If the destination is 7 light years away and it takes 1 year to
get there, then Stella is travelling at 7c. Now, we could take Koks' flash
rate of one a second emitted, but let's make it one flash a year instead.
That way we have the same principle but don't have to bother with large
numbers. Playing it Koks' way, only one flash maximum is sent on the
outbound journey that takes 7 years, and 13 are sent on the return, (the
last arriving with Stella and not counted), total 14 flashes. You can
multiply that by 60*60*25*365.25 for flashes per second if you like, but why
bother? ]

Terence maintains that Stella's Turnaround takes place at year 7 at a
distance of nearly 7 light-years, so he won't SEE it until nearly year 14.

[Androcles: That's right, he won't. What he'll SEE is a total of 14 flashes,
but these are emitted at one a year which proves Stella took 14 years for
the round trip. Of course he won't see the first until Stella gets to
Turn-Around,
comes back chasing its heels, but then, She WAS moving at damned near c,
 so he wouldn't expect to and nor would I. And on the return trip, each
yearly
 flash is going to have Stella hot on its heels too, so the whole shebang
wont
 be SEEN until nearly year 14. Hence the frequency is 14 as required.]

Terence SEES a long Outbound Leg and a very short Inbound Leg.

[Androcles: Bull***. Total and absolute bull***. Nobody has ever SEEN
length contraction, and certainly not stay-at-home Terence. Last time I
looked up at the sky, the stars were no nearer or further away than they are
tonight. Koks is clearly a headcase destined for the lunatic asylum if he
wants anyone to believe that.]

So there's the fundamental asymmetry: the switch from redshift to blueshift
occurs at Stella's Turnaround.

[Androcles: What an amazing observation! Perhaps Koks thought we would not
realize that! Nor is there any assymetry. ]

 Stella SEES Terence's telescopic image age slowly on her Outbound Leg, but
the image more than makes up for its dawdling on the Inbound Leg. Terence
SEES Stella's image off to a slow start too, but here the image's final
burst of rapid aging comes too late to win the race.

[Androcles: What race? Koks can't count to 14, and this guy is supposed to
be a Ph.D.! He sure didn't get it from my Alma Mater. Terence SEES 14
flashes from Stella, Stella SEES 14 flashes from Terence, all of which
observations are made in year 14 and there is no assymetry.]

 Androcles.

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