From: Party of Citizens (citizens@vcn.bc.ca)
Date: Sun Jun 08 2003 - 16:35:16 MDT
> From: Anders Sandberg <asa@nada.kth.se>
> To: <extropians@extropy.org>
> Sent: Sunday, June 08, 2003 12:48 AM
> Subject: Re: [Para-Discuss] faster than light?
>
>
> > On Sat, Jun 07, 2003 at 05:05:34PM -0700, Party of Citizens wrote:
> > > If C is defined as the fastest speed in the universe, does that change
> the
> > > result of E=MC2 calculations? Or could it be that they are invalid and
> > > have never been empirically validated?
> >
> > 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?
Doesn't light move at significantly different speeds in certain mediums?
If so, why choose 186,000 m/sec as the invariant speed?
and then the attempts to explain this
> > observation led to the relativity postulates (roughly, that there exists
> > this kind of invariant velocity and that physics looks the same in all
> > inertial frames). From this one can then derive testable (and indeed
> > tested) predictions like length contraction, time dilation and
> > mass-energy equivalence. E=mc^2 is a consequence of the postulates.
> >
> > Now, if one tries to use a c in the calculations that is not the
> > invariant speed then there will be a systematic discrepancy from the
> > momentum and time dilation effects observed in every particle
> > accelerator. It could of course be that physical light moves slightly
> > slower than the invariant velocity (light moves slower than c in many
> > media, and it is a common textbook exercise to show how the relativity
> > equations would look if everything was filled with a refractive ether
> > that made it slower), but in this case the difference has to be
> > extremely small and cosmological constraints (see below) limit it.
> >
> > If something moves faster than the invariant speed there will be
> > reference frames where it moves at arbitrary speeds, including backwards
> > in time. So FTL gravity waves would likely end up having the same bad
> > effects on cosmology as finite speed photons, even when ignoring the
> > causality issue.
> >
> > To sum up, special relativity has a very simple and elegant mathematical
> > form. The invariant velocity c is a bit like the invariant number 1 in
> > multiplication; it has to exist in the group structure of Lorenz
> > transformations. It does not say anything about whether there are things
> > that move at that speed or not in physics, or even whether physics obeys
> > the Lorenz group. That is just experimental observations, which seem to
> > fit extremely well.
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?
> > [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?
> > Given the relativity equations (still valid even if light is slow) and
> > the observable energy E of a photon at speed v we get:
> >
> > m_0 = E^2/[v^2 c^2/(c^2-v^2) + c^4]
> >
> > If v is close to c and E close to the observed pc value, then m_0 will
> > be extremely small. Putting E=h nu (Planck's relation) into it we get a
> > rest mass for photons of frequency nu:
> >
> > m_0 = h^2 nu^2/[v^2 c^2/(c^2-v^2) + c^4]
> >
> > Note that for small nu m_0 becomes even smaller.
> >
> > Particles with a finite rest mass m_0 will be generated in processes
> > above energy 2 m_0 c^2 (another experimentally observed fact). This
> > means that during the big bang a certain fraction of the energy ought to
> > have ended up as photons just as it did with neutrinos and
> > electron/positron pairs. But adding a rest mass completely messes up the
> > amount of photons at different frequencies - the spectrum would not end
> > up as the blackbody spectrum we all know and love, but rather look like
> > the other particle spectra that are predicted in cosmology. In addition,
> > a lot of slow photons would have been able to manifest at lower
> > energies, cooling down the universe and objects in it much faster than
> > otherwise. In fact, it would change all blackbody spectra, so I guess
> > the constraint isn't really cosmological but experimental - if photons
> > could move slower than the invariant speed we would see a very different
> > world. ]
> >
> >
> > --
> > -----------------------------------------------------------------------
> > 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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