From: Wade Cherrington (wade_c@uniserve.com)
Date: Thu Oct 29 1998 - 21:20:12 MST
>Question:
>
> If the general theory of relativity states that "the faster you go"
>[and approach the speed
>of light], the slower time will "be for you" "relative" to everything
>else...?
>
> Then if everything on the quantum level travels at near the speed of
>light, why would a
>complete object vs. single quantum particles change "time" as it
>increases speed ?... If the quantum
>particles that make everything up are already traveling at nearly the
>same speed, then why would time
>change if any of them take a general direction?
Suppose that atom A and atom B are chemically very similar atoms
far apart from each other such that no electromagnetic interactions
occur between them and that no external forces are acting on them.
While an electron in atom A might have the same average velocity relative
to nucleus A as electron B has relative to nucleus B, if
atom B is moving away from atom A then electron B will
have, in addition to its orbital velocity around
nucleus B, a translational velocity relative to nucleus A.
It is this relative translational velocity that is responsible for
time dilation between frames.
What special relativity shows is that if you have one point of reference
(the nucleus of an atom for example) and build a coordinate system
around it, then if another frame is moving away from the first
at a constant velocity, then systems evolving (clocks ticking,
electrons orbiting) in one frame will appear to run slower in
when measure from the other frame.
Time dilation only has any meaning relative to clocks that
are stationary in a reference system you are moving towards or away from.
In atoms, while electrons move AROUND the atom at nearly
light speed, they move AWAY from the nucleus, on average, with zero
velocity (on average, the electron in a hydrogen atom will
be found at the same Bohr radius). It is for this reason that
until one collection of matter starts moving away from another,
no time dilation effects between the two collections are present.
An aside:
While the above result between the two atom A/atom B systems is true,
and I think resolves the main point of your question, the situation in the
electron-nucleus system of a single atom is more complicated than I
might have implied.
Due to the speed of the electrons, there are relativistic effects to be
considered when setting up equations for the electronic wavefunction
(the function that will tell you the probability of finding an electron
at a certain location); this was first done successfully in the 30's by Dirac,
who replaced Shroedinger's Equation with one that took into account
relativistic effects of the electrons (Mathematically, this means he
made the Hamiltonian "Invariant under Lorentz transformations").
But this change only affected the final form of the wavefunctions
(it also leads to a natural meaning for the spin of an electron), which
had to now satisfy a different equation and use different coordinates.
The result is still true that in general, when you move an atom, the
electrons move along with it and in a time-averaged sense are "stationary"
relative to the nucleus, and hence you can treat matter as macroscopic
continua for the purposes of time dilation and other Lorentz transformation
effects such as length contraction.
I hope this helps answer your question.
Extropically,
Wade Cherrington
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