Re: High-level question about the relationship relativity and quantum mechanics
- From: "Juan R." González-Álvarez <juanREMOVE@xxxxxxxxxxxxxxxxxxxx>
- Date: Thu, 24 Sep 2009 11:51:56 +0000 (UTC)
Tom Roberts wrote on Tue, 22 Sep 2009 20:41:12 -0500:
Juan R. González-Álvarez wrote:
Tom Roberts wrote on Sun, 20 Sep 2009 19:05:14 -0500:
squarooticus wrote:
One thing that has always bugged me is the notion that the major goalThis is not true. All theories of high energy physics are Lorentz
of theoretical high-energy physics is to unify quantum mechanics and
relativity
invariant. That is, they conform to relativity. The need for Lorentz
invariance in theories was solidly established long before the advent
of high energy physics (aka elementary particle physics).
This is all plain wrong. There exists no unification of quantum
mechanics with relativity.
Read what I wrote. The type of quantum mechanics that is unified with
relativity is called quantum field theory. OF COURSE it is not the same
as the eponymous non-relativistic quantum mechanics.
And since it is *not* a relativistic quantum mechanics this is why is not
named "relativistic quantum mechanics" (RQM) but "relativistic quantum
field theory" (RQFT).
Moreover, being strict, there is not real unification even at RQFT level!
For instance in SR or in RQM the Lorentz transformations relate positions
and times measured in different intertial frames. The *formal* analog of the
transformations in RQFT has not relation to measurements of positions or
times.
As remarked by H. Bacry in 1989 Nucl. Phys. Proc. Suppl. 6, 222:
Every physicist would easily convince himself that all quantum cal-
culations are made in the energy-momentum space and that the
Minkowski xμ are just dummy variables without physical mean-
ing (although almost all textbooks insist on the fact that these
variables are not related with position, they use them to express
locality of interactions!)
As is well-known (read a textbook), any attempt to develop a
relativistic quantum mechanics failed and particle physicists abandoned
the problem and developed a relativistic quantum field theory.
Right. So what I wrote is not "all plain wrong" as you claimed above;
indeed, what I wrote and what you wrote say the same thing using
different words.
This is plain wrong, I did not say "the same thing".
(...)
Note that this is Special Relativity, not General Relativity. But
that's OK, as the processes studied in HEP are all so localized that
the curvature of spacetime is utterly negligible (factors of ~10^-42).
For HEP, all one needs in relativistic quantum field theory. Because
HEP are simple experiments.
<giggle> There's nothing "simple" about HEP experiments -- the LHC and
associated experiments are the largest and most complicated scientific
instrument in the world. And no knowledgeable theorist would consider
these experimental situations, or the standard model used to describe
them, "simple".
Deleting the links and sniping the extra information do not hide your
utter ignorance of modern state of research in physics Tom.
REINTRODUCING SNIPED PART:
A discussion of several approximations used in HEP are given in
http://www.canonicalscience.org/en/publicationzone/canonicalsciencereports/20083.html";
If you had followed the link, read, and understood it, you would know the
existence of the modern scientific field of complexity (Gell-Mann calls it
plectics).
If we draw a linear scale from simple scientific problems to complex problems
we find to HEP in the simplest side of the scale.
By being unable to accept this fact, you are showing the same "arrogance of
the particle physicists" denunciated by the nobel Prize for Physics P.W.
Anderson in his /Science/ paper about Complexity. See page 12 in above
canonical science report.
In the page 13, I quote the standard text from Goldberger and Watson,
explaining why the HEP theoretical analysis "can be done in a general and
straightforward manner". They add "The description of the interaction of the
system (i.e. during the collision) involves the most important and difficult
problems in physics".
I explain in the report some of the simplifications involved in HEP :-D
The standard model is *trivially simple* when compared with the advanced
formalism are being developed in other fields of science you unknow.
In my reference 32 you may find one of those advanced theoretical frameworks,
developed by Prigogine's group and recently published in Phys. Rev. A.
In the reference 13 you may find to one of the most cited particle-string
physicists in the world
http://en.wikipedia.org/wiki/Dimitri_Nanopoulos
adapting an *old* version of Prigogine theory to a generalization of
superstring theory, which (I at least wait you to know this) is more
complex and advanced than the standard model of HEP.
As explained in page 8 of the above canonical science report the excursion of
Nanopoulos and coworkers, in their own words, "beyond string theory or even
high-energy physics" is at best *outdated* now.
About the complexity of the experimental instruments used in HEP. I could say
much also. But I will merely add they are not sophisticated and complex enough
for resolving the time-dependent dynamics. Luckily this is why quantum field
theory is all that is needed to study the outcome of *those* HEP experiments.
But those simple formalisms are not enough in the rest of fields of science
where the HEP approximations do not hold.
The S-matrix used in HEP experiments is an approximation to the U_QFT, wich
is a local approximation to the propagator U=exp(Ht), which is an pure state
approximation to the exp(Lt) evolutor (see equation 4 in page 7 of the
canonical science report), which is an approximation to a more general
dynamical equation as eq. 3.
(...)
Hmmmm. Neither electric nor magnetic "fields" are really fields in the
modern sense (the names are archaic). The actual field is the Maxwell
2-form, which combines E and B in a way that is independent of frame.
No. Of course E and B are fields in the usual physical sense (this is
why we call them fields in modern literature).
No. Speaking loosely they can be considered "fields on space",
No, we do not mean "fields on space" when say that E and B are fields.
(...)
In fact your 'modern' Maxwell 2-form is an old covariant concept only
valid in the local limit.
It is valid wherever Maxwell's equations are valid. This is not "old"
(but it's not new, either), and is not any sort of approximation. Using
the language of differential forms, Maxwell's equations can be written
in terms of the Maxwell 2-form; they are IDENTICAL to the usual
Maxwell's equations when projected onto inertial coordinates of a flat
manifold, and have the advantage that they are also valid when projected
onto any coordinates, inertial or non-inertial, of a flat or curved
manifold.
As said before, the Maxwell 2-form is valid only in a local approximation
(again you show your ignorance of modern state of research).
Moreover, there adittional approximations involved in the description of
EM over curved spacetimes since the Riemanian metric g_ab is only valid
in the geometric limit of a physical theory of gravity.
One lesson of modern physics is to not attempt to describe things that
cannot be measured. That includes "fluxes of force-carrying
particles". Instead, describe things that can be measured like the
trajectories objects, etc. Modern quantum field theories have no
definite flux for their force carriers, but the trajectories of
objects are independent of frame.
As explained in virtually any textbook on quantum field theories,
position is not observable in those theories.
And yet all particle experiments are based on measuring particles'
TRAJECTORIES. You attempt to make a theoretical objection that has no
practical consequences, and you need to learn how theories are actually
used.
And as explained in any good treatise of RQFT those trajectories have no
physical correspondence to the (x,t) in RQFT, which is not a mechanics.
This is why the final S-matrix used in the laboratory does not depend on
time or position of any particle.
You show once again a complete ignorance of what is measured and what part of
measurements are compared (and how) to the predictions of RQFT.
--
http://www.canonicalscience.org/
BLOG:
http://www.canonicalscience.org/en/publicationzone/canonicalsciencetoday/canonicalsciencetoday.html
.
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