On 12/25/2013 9:15 PM, LizR wrote:
On 26 December 2013 15:56, meekerdb <meeke...@verizon.net <mailto:meeke...@verizon.net>>
wrote:
On 12/25/2013 2:45 PM, LizR wrote:
On 26 December 2013 07:23, Jesse Mazer <laserma...@gmail.com
<mailto:laserma...@gmail.com>> wrote:
The notion that everything "travels through spacetime at the speed of
light"
was popularized by Brian Greene, but it only works if you choose a
rather odd
definition of "speed through spacetime", one which I haven't seen any
other
physicists make use of.
Mainly because it doesn't make sense. Speed is change of position with
time, hence
"speed in spacetime" equates to the angle a world-line makes relative to
some
world-line chosen as a basis, e.g. the rest frame of the Hubble flow.
Things don't
move through space-time, they move through space. They are 4 dimensional
objects
embedded in space-time.
But when you are "standing still" your time coordinate keeps increasing.
Your
4-velocity in your own inertial frame is always (1 0 0 0).
If you insist on using this "velocity through space-time view", yes.
Hey, it's not something I made up. Check Weinberg's "Gravitation and Cosmology". He uses
the 4-velocity frequently, e.g. in Ch9 eqn 9.8.1 thru 9.8.6 he writes the T^00 component
of the stress energy tensor as rho*U^0U^0, where U^0 is the time-like component of the
4-velocity of a perfect fluid. Robert Wald does much the same in "General Relativity". Or
look at page 50 of Misner, Thorne, and Wheeler where they write,"More fundamental than the
components of a vector is the vector itself. It is a geometric object with a meaning
independent of all coordinates. Thus a particle has a world line, P(tau), and a 4-velocity
U=dP/dtau, that have nothing to do with any coordinates."
But if you consider yourself to be a worldline then you have no 4-velocity, only a
3-velocity, which is measured as the angle your worldline makes to the vertical axis
(modulo the usual caveats about there being no preferred reference frames).
Here is a diagram of how time isn't...
Inline images 1
And here's a diagram of how it actually is...
Inline images 2
...both are from Chapter 11 of FOR.
First, I said nothing about a "present moment"; that's Edgar's concept. I referred to the
4-velocity. By treating the velocity as a 3-vector, instead of suppressing the
0-component, the above diagrams do not show how one's clock runs slower relative to the
coordinate frame. When you use some of your 4-velocity to move thru space, there is less
of it available to move you through time. So when you say it is the angle between the
"vertical axis" and the world line, that's a statement in a specific coordinate system.
But one's proper velocity is always 1, independent of coordinates.
Brent
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