On 26 December 2013 19:11, meekerdb <meeke...@verizon.net> wrote:
> On 12/25/2013 9:15 PM, LizR wrote:
> On 26 December 2013 15:56, meekerdb <meeke...@verizon.net> wrote:
>> On 12/25/2013 2:45 PM, LizR wrote:
>> On 26 December 2013 07:23, Jesse Mazer <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."
OK, Brent, my apologies if I have misread you. But you are supporting a
view that doesn't make sense in terms of SR - nothing is actually moving
through spacetime, and giving (apparent) support to the notion that it is
isn't going to help.
I don't have most of those books you mention, but I do have "Gravitation"
(which my other half got for his 18th birthday in 1973) open to page 51,
box 2.1 - "Farewell to "ict" - and have just had my mind suitably boggled
by reading about 4-velocities. Please note, everyone (I'm sure Brent knows
this already) that these are NOT velocities *through* space-time, they are
handy vectors for working out what is going on at a point along an object's
world-line. The object doesn't move through space-time, it exists at
various points in space-time which joined together make a 4 dimensional
object known as a world line. One can draw vectors at points along this
world line and use them to work out its "4-velocity", which I assume is a
quantity useful for working out how its clock goes in relation to other
objects, and/or how the various Lorentz transformations work - or something
along these (world) lines - but this does *not* mean that things are moving
through space-time or that there is a common present moment, or that the
past doesn't exist, or any of the other things Mr Owen has claimed. I think
Brent, who knows all this stuff backwards and sideways, is just toying with
us .... naughty Mr Meeker.
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