From: Anders Sandberg (asa@nada.kth.se)
Date: Mon Jun 09 2003 - 02:11:12 MDT
On Sun, Jun 08, 2003 at 03:35:16PM -0700, Party of Citizens wrote:
> > > No. The c of importance is the velocity that is left invariant by all
> > > Lorenz transformations. It just happens historically that it was first
> > > empirically observed that light moves at the same velocity regardless of
> > > the speed of the observer,
>
> Does gravity move at the same velocity regardless of the speed of the
> observer?
>
> Is the speed of gravity invariant?
I think these questions were nicely answered in Hal's post.
As The Straight Dope puts it: "To put it in technical terms, general
relativity is only self-consistent if the speed of gravity is Lorentz
invariant (that is, the same for all observers), and the only speed for
which that works is c".
Beside the theoretical observations based on neutron-star orbit
stability people also have done some direct experimental speed tests,
although the accuracy leaves a lot to be desired:
http://www.nature.com/nsu/030106/030106-8.html
> Doesn't light move at significantly different speeds in certain mediums?
> If so, why choose 186,000 m/sec as the invariant speed?
The invariant speed was not choosen by human physicists, it was set by
physics. We can only do experiments to see what value it has.
Even if there were no light the invariant speed would exist.
> I think this "just" is very important. Could you please give the citation
> for an experimental-empirical verification of E=mc2? For example, has a
> nuclear reactor ever published empirical reports on the reduction of mass
> as it burns fuel?
The most common verification is found in nuclear and particle physics,
where the masses and velocities of atoms and particles can be measured
before and after an interaction or decay. Binding energy can be shown to
produce mass.
From http://www.seop.leeds.ac.uk/entries/equivME/#4 :
Cockcroft and Walton (1932) are routinely credited with the first
experimental verification of mass-energy equivalence. Einstein (1905b)
had conjectured that the equivalence of mass and energy could be tested
by "weighing" an atom before and after it undergoes radioactive decay.
But there was no way of performing this experiment or another experiment
that would directly confirm mass-energy equivalence at the time.
Technological developments allowed Cockcroft and Walton to take a
different approach. They studied the bombardment of a lithium atom (Li)
by a proton (p), which produces two alpha particles (alpha). This
reaction is symbolized by the following equation:
p + Li = 2alpha
In this reaction, there is a decrease in the total rest-mass as the
reaction proceeds from left to right: the total rest-mass of proton and
the Lithium atom is greater than the total rest-mass of the two alpha
particles. Furthermore, there is also an increase in the total kinetic
energy: the kinetic energy of the proton is less than the total kinetic
energy of the two alpha particles. (One only considers the kinetic
energy of the proton because the Lithium atom is considered at rest, and
hence has zero kinetic energy.) Cockcroft and Walton were able to
measure the kinetic energies of the incident proton and the out-going
alpha particles very precisely. They found that the decrease in
rest-mass corresponds to the increase in kinetic energy according to
Einstein's famous equation E = mc2 (to an accuracy of better than 1%).
Hence, the total mass and energy of the entire system is conserved.
(literature references on the site)
> > > [Cosmological constraints: Because if photons can move at other
> > > velocities than the invariant velocity (if they move slowly we can
> > > always set up a fast moving lab moving alongside to examine photons at
> > > rest - this is actually a good Gedankenexperiment to see why
> > > electromagnetic waves have to move at the invariant speed; you can't
> > > have a stationary wave packet in vacuum) they would have a rest mass.
>
> Don't the experiments by Alain Aspect and others show that a photon can be
> move in two different directions and can be measured in two different
> places at the same time? "They" arrive at the final, measured locations
> faster than 186,000 m/sec do they not?
No. You are thinking of the EPR setup, where entangled photon *pairs*
are created.
Photons can move in an indeterminate way due to quantum uncertainty, so
that their position is undefined before it hits a detector. But after
that point it cannot interact with another detector, regardless of
distance. If photons did, the law of energy conservation would go out of
the window.
-- ----------------------------------------------------------------------- Anders Sandberg Towards Ascension! asa@nada.kth.se http://www.nada.kth.se/~asa/ GCS/M/S/O d++ -p+ c++++ !l u+ e++ m++ s+/+ n--- h+/* f+ g+ w++ t+ r+ !y
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