Re: Relativ-ism

MajorOz wrote:

We are all familiar with the twin phemenon: you go off at C and come
back later, having aged hardly at all, while I have.
My understanding is the one who does the ageing is the one who is
"afixed" to the larger mass -- like being on earth.
So........from some arbitrary point in space, you take off in a vehicle
of some mass, while I stay behind on a stationary vehicle or celestial
body of some other mass. Who ages, and how much? It seems that there
is some equation involving m1 and m2, etc.
I guess what I am asking is: does the ageing depend not only on the
mass of earth of the first example, but also on the "system" mass of
the stuff nearby?

The Earth and its mass is really a red herring in the classic twin paradox from special relativity; in fact, special relativity can't handle gravity (that's what general relativity is for). The idea of "staying behind" is usually intended to be colloquial, not to signify remaining near a large mass. In fact, there is an opposite effect (from general relativitY) that relates to being near large masses which I'll get to in a moment.

Special relativity says that relative motion affects time, but it does so symmetrically. If we're moving very fast relative to each other in empty space, then I perceive your clocks as being slowed down, but you perceive my clocks as being slowed down as well. That seems strange, but comparing clocks like that doesn't have much meaning unless we bring them together.

If I stay at rest and you speed away at high speed and then come back, when we compare our clocks yours will show less time. That applies to all physical clocks; it means that you will age less than I do during your trip. This is a detectable effect; fast-moving muons decay more slowly than stationary particles.

Note that I don't actually have to stay "at rest" (at rest with respect to what?). All I have to do is not accelerate. But to leave and come back, you obviously do. That's what breaks the symmetry mentioned above; you accelerated and I did not, and that's what makes you come back faster. Note that really what's relevant is a change in inertial frame; you can make the acceleration as gradual or as sudden as you like, but it will still have the same effect.

So the standard twin paradox from special relativity actually has nothing at all to do with mass. In general relativity, there is another effect called gravitational time dilation. This _is_ caused by being near a large gravitating mass. If two observers are in orbit (or hover, it doesn't matter what they're doing) near a gravitational mass, then the one in the weaker gravitational field (e.g., higher up) will perceive the other's (the one in th stronger gravitational field) clock as being slowed down.

So for a "real" twin paradox -- where I stay behind on the Earth's surface (in a gravitational field) and you leave at high speed and then return -- the two effects will compete. In practice, you need very strong gravitational fields for gravitational time dilation to be significant (just as you need very fast speeds for special relativistic time dilation to be significant), and the Earth's mass doesn't qualify. Furthermore, the gravitational field strength can only get so high before you fall into what must be a black hole, so there is a sort of "cap" to the degree of gravitational time dilation even in the most extreme case.

But to answer your primary question, no, the Earth's mass has nothing to do with the time dilation in the standard twin paradox.

--
Erik Max Francis && max@xxxxxxxxxxx && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM erikmaxfrancis
But the system has no wisdom / The Devil split us in pairs
-- Public Enemy
.

Relevant Pages

  • Re: Special Relativity is Dead! (Third Proof)
    ... concept of GR that a time dilation exists for acceleration. ... caused by acceleration but from gravity itself. ... corner his idiot theory of Special Relativity in less than twenty lines ...
    (sci.physics.relativity)
  • Re: Flatness & Newtonian Gravity
    ... special relativity has time dilation and length contraction. ... I was thinking of a scalar field theory for gravity, ...
    (sci.physics.research)
  • Re: What are the spatial dimensions of a *volumeless* object having
    ... But as far as gravity goes, if you follow the generally accepted ... The geodesic of a particle is the path of that particle along a ... mass is a function of time. ... time dilation. ...
    (sci.physics.relativity)
  • Re: Special (Relativity) for da pickle
    ... almost right critical word in TWO spots. ... Relativity, applicable to gravity, and Special Relativity, particularly ... applicable to energy and mass. ...
    (rec.gambling.poker)
  • Re: Is the mass of a free falling body increasing?
    ... > talking about gravity (or am I misinterpreting your ... > special relativity, you need a theory of gravity ... > that's compatible with special relativity. ... For several more decades the relativistic mass concept was ...
    (sci.physics.relativity)