| Topic: |
Science > Physics |
| User: |
"TefJlives" |
| Date: |
17 Apr 2007 05:31:27 PM |
| Object: |
Relativity question |
Hi all,
I'm wondering something. Suppose, all engineering questions aside, we
decided that we want to send a probe to Alpha Centauri and then return
it here. When it comes back we compare the clock on the rocket with
the clock that has remained on earth. Let us say that Alpha Centauri
is 4 light years away. What is the least amount that the clocks could
differ by? What is the most?(Assuming accelerating directly towards
AC, decelerating to 0 when we get there, then accelerating directly
back towards earth) It seems that at least one of the answers should
be 8 years, because that would be kind of the limiting case if we
could travel the speed of light. A sneaky suspicion actually tells me
that maybe both answers are 8 years, but my brother thinks the lower
limit should be 0, if we go really, really slow. I don't know how to
calculate this. Let's pretend we have no gravity fields, or maybe not,
whichever is more elegant.
Greg
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| User: "Dirk Van de moortel" |
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| Title: Re: Relativity question |
18 Apr 2007 03:31:20 AM |
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"TefJlives" <gmarkowsky@gmail.com> wrote in message news:1176849087.444957.121730@y5g2000hsa.googlegroups.com...
Hi all,
I'm wondering something. Suppose, all engineering questions aside, we
decided that we want to send a probe to Alpha Centauri and then return
it here. When it comes back we compare the clock on the rocket with
the clock that has remained on earth. Let us say that Alpha Centauri
is 4 light years away. What is the least amount that the clocks could
differ by? What is the most?(Assuming accelerating directly towards
AC, decelerating to 0 when we get there, then accelerating directly
back towards earth) It seems that at least one of the answers should
be 8 years, because that would be kind of the limiting case if we
could travel the speed of light. A sneaky suspicion actually tells me
that maybe both answers are 8 years, but my brother thinks the lower
limit should be 0, if we go really, really slow. I don't know how to
calculate this. Let's pretend we have no gravity fields, or maybe not,
whichever is more elegant.
To avoid losing information by using numbers, replace your 4
years with D, and use units where light speed c = 1.
Total time according to stay-at-home: 2T = 2D/v
Total time according to traveller: 2T sqrt(1-v^2)
Difference: 2T ( 1 - sqrt(1-v^2) ) = 2D ( 1 - sqrt(1-v^2) ) / v
The curve
y = 1 - sqrt(1-x^2)
is a circle with centre (x,y) = (0,1) and radius 1, so
when x varies between 0 and 1, y varies between 0 and 1.
Alternatively, you can calculate the limits for v to 0 and 1 of
( 1 - sqrt(1-v^2) ) / v
and you'll find
v -> 0 gives 0
v -> 1 gives 1
So the time difference varies between 0 and 2D.
Dirk Vdm
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| User: "Uncle Al" |
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| Title: Re: Relativity question |
17 Apr 2007 06:16:54 PM |
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TefJlives wrote:
Hi all,
I'm wondering something. Suppose, all engineering questions aside, we
decided that we want to send a probe to Alpha Centauri and then return
it here.
Kinda silly to return the hardware. Broadcast collected data multiple
times.
When it comes back we compare the clock on the rocket with
the clock that has remained on earth.
The Twins Paradox. You'll need at least three clocks on each side
(think about it). The clocks that move through the most space will
record passage of the least time,
Annalen der Physik 4 XVII 891 (1905)
http://www.fourmilab.ch/etexts/einstein/specrel/www/
Let us say that Alpha Centauri
is 4 light years away. What is the least amount that the clocks could
differ by?
Does gravitational well potential count?
Annalen der Physik 4 XLIX pp. 769 (1916)
Otherwise, minimal clock mismatch is only a matter of patience. Zero
is acheivable, below. Lots of patience and hope the sun doesn't bloat
in the interim.
What is the most?(Assuming accelerating directly towards
AC, decelerating to 0 when we get there, then accelerating directly
back towards earth)
Magically burp it to within an epsilon of lightspeed and back. Choose
your reference frames and run the maths.
It seems that at least one of the answers should
be 8 years, because that would be kind of the limiting case if we
could travel the speed of light.
Traveling clocks at 99.999% of lightspeed still skew considering only
Special Relativity. 4 lightyears each way give an 8-year mismatch
close enough. 1/beta = 223.61 factor of time dilation. 8 Earth years
(2921.9 days including leap years) are then 13.1 ship days.
A sneaky suspicion actually tells me
that maybe both answers are 8 years, but my brother thinks the lower
limit should be 0, if we go really, really slow. I don't know how to
calculate this. Let's pretend we have no gravity fields, or maybe not,
whichever is more elegant.
If you go really slow then both sets of clocks can remain exactly
sychronized. Clocks deep in the Earth's gravitational well run more
slowly than clocks at its periphery (confirmed by GPS). Time effects
from Special and General Relativity can cancel. It's gonna be an
impossibly long duration trip.
<http://en.wikipedia.org/wiki/Hafele-Keating_experiment>
<http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html>
<http://metrologyforum.tm.agilent.com/pdf/flying_clock_math.pdf>
http://metrologyforum.tm.agilent.com/cesium.shtml
http://arxiv.org/abs/physics/0008012
Hafele-Keating Experiment
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "Androcles" |
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| Title: Re: Relativity question |
18 Apr 2007 12:46:55 AM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message =
news:46255566.E93E0C9E@hate.spam.net...
[snip river of *****]
1) GPS works
2) Sub-idiot
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| User: "Dirk Van de moortel" |
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| Title: Re: Relativity question |
18 Apr 2007 03:32:12 AM |
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"Androcles" <Engineer@hogwarts.physics.co.uk> wrote in message news:jhiVh.38477$Zb2.11377@fe2.news.blueyonder.co.uk...
"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:46255566.E93E0C9E@hate.spam.net...
[snip river of *****]
1) GPS works
2) Sub-idiot
It's strange how someone who pretends to killfile me, constantly
takes over my expressions :-)
Is there a name for this kind of phenomenon?
Dirk Vdm
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| User: "Uncle Al" |
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| Title: Re: Relativity question |
18 Apr 2007 08:59:08 AM |
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Dirk Van de moortel wrote:
"Androcles" <Engineer@hogwarts.physics.co.uk> wrote in message news:jhiVh.38477$Zb2.11377@fe2.news.blueyonder.co.uk...
"Uncle Al" <UncleAl0@hate.spam.net> wrote in message
news:46255566.E93E0C9E@hate.spam.net...
[snip river of *****]
1) GPS works
2) Sub-idiot
It's strange how someone who pretends to killfile me, constantly
takes over my expressions :-)
Is there a name for this kind of phenomenon?
Sure! Androclitty is stoooopid. Androclitty is a capon in a
henhouse. Androclitty is clueless as to why all the roosters are
getting lots but Androclitty isn't getting any.
Androclitty suspects it is the roosters' fault since he looks at his
own crotch and cannot see any reason for malfunction - clean as a
whistle.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "TefJlives" |
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| Title: Re: Relativity question |
18 Apr 2007 01:53:20 PM |
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Thanks for all the replies, physics related and not. I think I get it
now.
Greg
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| User: "H. Wabnig .... .-- .- -... -. .. --. @ .- --- -. DOT .- -" |
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| Title: Re: Relativity question |
18 Apr 2007 02:23:43 AM |
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On Wed, 18 Apr 2007 05:46:55 GMT, "Androcles"
<Engineer@hogwarts.physics.co.uk> wrote:
"Uncle Al" <UncleAl0@hate.spam.net> wrote in message news:46255566.E93E0C9E@hate.spam.net...
[snip river of *****]
1) GPS works
2) Sub-idiot
Never mind.
In Androcles math a train leaves London, straight up to Birmingham,
returns to London, and then Androcles calculates the travel distance:
London - London = zero.
And the train did it in no time,
traveltime (L to B) - traveltime (B to L ) = zero.
And Androcles average speed was 0 / 0
w.
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