Date: Wed, 1 Jan 2003 00:28:46 -0600 (CST)
Jim Choate wrote:
> Tim May wrote...
>
>> "I don't believe, necessarily, in certain forms of the Copenhagen
>> Interpretation, especially anything about signals propagating
>> instantaneously,
>'instantaneously' from -whose- perspective?
From anyone's perspective. A signal carries information. You can't
use quantum mechanics to propagate a signal faster than light. If
you think otherwise, allow me to refer you to the last chapter in
"Quantum Mechanics", L. Schiff, where you will find the commutation
relations for electromagnetic fields.
>> Yes, this has been a fashionable set of statements, very smiliar to
>> "quantum mechanics is merely a useful tool for calclating the outcome
>> of experiments".
> Only so long as there are -not- relativistic effects, which -do- happen
> -any- time a photon is involved.
Don't be ridiculous. Relativistic quantum mechanics is not even a new
discipline. See Bjorken & Drell, Vols. I and II, written circa 1963. The
dirac equation has been around for almost 3/4 of a century and the
klein-gordon equation has been around about 80 years. Had the physicists
of the 1920's been able to interpret the klein-gordon equation at the
time, we would have probably had a relativistic theory before the
non-relativistic theory. The schroedinger equation is a result of needing
an equation that's linear in the time variable, due to not knowing at the
time, how to interpret the quadratic which appears if one substitutes the
quantum operators for the dynamical variables in E^2 = p^2 + m^2 (c==1).
Your comment about photons is equally ridiculous. I can derive the qed
lagrangian from the dirac equation in about 1 page of arithmetic, just by
requiring the lagrangian to be locally gauge invariant and applying
noether's theorem to obtain the conserved current. What do you think the
A^{u} in the covariant derivative is? Nevermind, I'll tell you. It's the
field of the electron. Sure, relativity is involved. And it's involved in
a very well understood way. Just start with the dirac lagrangian,
L = \Psibar(p/ - m)\Psi and make the substitution \Psi->\Psi\exp(iS),
where S is ann arbitrary function of the spacetime variable, to obtain
the new lagrangian, L'. For the lagrangian to be locally gauge invariant,
the variation, \delta L = L' - L, must vanish to first order.
General relativity is irrelevant, since (1) we aren't in a strong
gravitational field and the gravitational interaction is about 10^{-32} of
the strength of the E&M field, anyway, (2) spacetime is locally flat and
the minimal coupling model in general relativity assumes there is no
curvature coupling, (3) The main difference would end up being that the
photons would propagate along null geodesics that are curved rather than
along null geodesics that are flat. (4) You can replace the ordinary
gauge covariant derivatives with the general relativistically covariant
derivatives. [See for example, "Problem Book for General Relativity",
Lighthman, et al, where there is a worked example which includes a
mention of curvature coupling (I think that's the name of the book, but
I don't have it handy, to check it)].
For relativistic quantum field theory to even work, one must appeal
to the same unobservability of the wavefunction, if one is to obtain
a conserved current.
>***Reality is -observer- dependent***
>The major hole in -all- current QM systems is they do not take into
>account relativistic effects. Which are required -any time- a photon is
>involved.
There is no "major hole". Not even a minor pinprick. You should take a
look at any relativistic quantum mechanics text or any text on quantum
field theory [Gauge Theories of the Strong, Weak and Electromagnetic
Interactions", C. Quigg, is straightforward and physically illuminating].
QED is the most precise theory ever proposed in the entire
history of science. It's a purely relativistic field theory which served
as the prototype for the standard model, which currently explains all
known phenomena except gravity. Incorporating gravity and the standard
model into a single theory is a _technical_ issue not an issue of either
quanum mechanics or general relativity being wrong. Quite the contrary,
both are bviously correct for any purpose that doesn't include black holes
or possibly neutron stars, and even in those cases, one can do quantum
field theory. See "Aspects of Quantum Field Theory in Curved Spacetime",
S. Fulling, for an example of quantum field theory in curved spacetime.
>> I used to chant this too, but the recent (well, over the last 10 years)
>> experimental work in EPR has convinced me that there's really something
>> odd going on here.
>> "Many worlds" (first proposed in the 50s and recently revived) is one
>> possible explanation for why, for instance, photons in the double slit
>> experiment "know" about the slit they didn't go through. And while I am
>> not particularly convinced that this is the explanation (there are other
>> basic things about the QM world it doesn't explain, such as why I
>> measure THIS outcome rather than THAT outcome), I'm personally at the
>> point where I think some form of answer is needed, and that the above
>> intellectual dodge is no longer valid. So at least many worlds is one
>> possible attempt to answer why photons are able to "know"
>> instantaneously about correlated photons far removed (and for me, and
>> the late John Bell it is inescapable that they do indeed find out
>> instantaneously).
> The error in this approach is not into taking account the relativity of
> the experiment. From the traditional approach we are testing the photon
> with the instrument, -but- the photon is also testing the instrument.
That is ridiculous.
> How big is the slit -from the perspective of the photon-? In other words;
> how big is the cosmos to a signle photon?
If you understood special relativity, you would know that the photon
has _no_ restframe. There exists no spacetime point to which one can
perform a lorentz transform to a photon. What do you think it means for
light to have only transverse polarizations?
"How big is the slit to -from the perspective of the photon-" is
equally meaningless.
> The answer is it has no dimension. Now since there is no time or distance
> scale from the perspective of the photon exactly -what- is happening
> instantaneously? Answer, nothing.
I have no idea what this is supposed to mean. Elementary particles
cannot be anthropomorphised in such terms. The photon is a 4-dimensional
object.
