Re: Download a new book on quantum mechanics and relativity.

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 10/11/04 

Date: Mon, 11 Oct 2004 00:30:54 -0700

bernard.chaverondier wrote:
> "Eugene Stefanovich" <eugenev@synopsys.com> a écrit dans le message de
> news:41690D41.6040208@synopsys.com...
>
> Eugene
>
>>You postulate that events E and E' will be seen as
>>coinciding by all inertial observers [as soon as they are
>>seen as coinciding by a given inertial observer] Am I right?
>
>
> Chaverondier
> Yes, exactly
>
> Eugene
>
>>I do not make this assumption, and this
>>assumption is not compatible with my theory.
>
>
> Chaverondier
> I believe the reverse. You make the assumption that "two"
> events standing at the same space-time location in an ideal
> inertial system of coordinates may stand at different space-time
> locations in an other ideal inertial frame. This hypothesis leads
> to inconsistencies in your theory.

I am not sure I exactly understand what you are saying.
I think we first need to agree about definitions. Could you please
give me your definitions (with examples) of the following:

ideal inertial frame is.... for example...

non-ideal inertial frame is.... for example...

I never made an assumption that two events coinciding in one
reference frame also coincide in other reference frame. I actually
wrote the opposite: see 2nd paragraph in 1.2.2.

>
> Here is the problem. Actually, you consider as being
> indistiguishable two situations that can be distinguished
> in your theory because of the not Lorentz covariant
> dynamics of some phenomena.

Give me please your definitions:

Lorentz covariant dynamics is..., for example...

non-Lorentz covariant dynamics is..., for example...

>
> First situation : you change the state of motion of an ideal inertial
> observer (not that of the observed system where occurs the
> observed event). This boost gives rise to a Lorentz covariant
> transformation process modeling the change of state of motion
> of the ideal observer (ie the space-time coordinates of a given
> event transforms according to Lorentz transforms).
>
> Second situation : you change the state of motion of the
> observed system. This boost gives rise to a not Lorentz
> covariant transformation of the observed system.
> This boost has to be modelled by the appropriate
> unitary representation of the observed system in its
> state space. This second process is only approximatively
> Lorentz covariant and should not be confused with the
> Lorentz covariant change of ideal inertial observer.

I agree with you on one point: applying boost to an inertial
observer may be not the same as applying (opposite) boost to
the observed system. This difference is clearly seen on the example
of unstable particle. If observer O at rest sees a state of muon
which has a 100% chance of observing the muon, then moving observer O'
sees a small admixture of decay products in this state
(see 13.2.1). This "decay caused by boost" is required if we want to
preserve the group properties of the representation of the Poincare
group in the Hilbert space of the unstable system.
When I speak about relativistic invariance
I always speak about observations made by different observers on
THE SAME physical system. The state of muon seen by a moving
observer is obtained from the state of muon seen bu the observer at rest
is obtained by applying the interacting boost operator (see eq. (13.25))

On the other hand, we can define a state of (100%) muon moving
with nonzero velocity. In order to obtain such a state we can apply
the non-interacting boost operator (see eq. (13.26)).

>
> The symmetry of point of view characteristic of Minkowski
> space-time geometry cannot be preserved in the geometrical
> picture grounding your theory. If you try to preserve the
> symmetry of point of view in your geometrical grounding,
> you are lead to inconsitencies with the break of Lorentz
> covariance derived from your theory in chapter 11 and 12.

Please explain to me what is
"The symmetry of point of view characteristic of Minkowski
space-time geometry"

>
> Eugene.
>
>>If you advocate strict manifest covariance you
>>must admit that there should be a time operator.
>
>
> Chaverondier
> I suppose that you call strict manifest covariance the
> possibility to express all laws of physics in a covariant
> manner with regard to the Poincaré group action in 4D
> space-time, ie that all physically meaningful quantities
> should be framed as scalar, 4-vector, tensor...
> in the Minkowski space-time picture.
>
> This amounts to assume that the Lorentz
> covariance is satisfied by any phenomenon.
>
> This is not my point.

This is what I call "Lorentz" or "manifest" covariance.
My theory does not satisfy this requirement. I do not think
that this requirement has any physical basis. It is just an
arbitrary assumption made in Einstein's theory

However,
my theory satisfies the requirement of "relativistic
invariance":

"Descriptions of the system in different reference frames are
related by transformations which furnish a representation of
the Poincare group"

In my view this is the correct statement of the principle of
relativity, which must be satisfied in any relativistic theory.
My approach satisfies this requirement. Traditional Einstein's
relativity (with kinematical boosts) does not satisfy it.

The difference between "Lorentz" and "relativistic" invariance is
explained at the end of subsection 12.3.1.

>
> I don't advocate that all physical phenomena necessarily
> satisfy the Lorentz covariance. I believe rather in a
> deterministic, realistic, explictly non local interpretation
> of quantum measurements that conflicts with the principle
> of relativity of motion (hence with Lorentz covariance).

>
> In the framework of this quantum measurement interpretation,
> the Alain Aspect experiment is interpreted as an action
> at a distance in the framework of a space-time geometry
> (ie the Aristotle space-time SE(1)xSE(3)/SO(3) ) compatible
> with FTL interactions violating the principle of relativity
> of motion, hence the Lorentz covariance.

Please note that my approach exactly satisfies the principle of
relativity of motion. It does not obey the principle of "Lorentz"
or "manifest" covariance.

>
> Eugene
>
>>I hear a note of agreement with my views. That's good.
>>However, I still do not agree that the relativity principle
>>is violated in my approach.
>
>
> Chaverondier
> Presently, that's our only point of disagreement.
> All other discrepancies stem from there.
>
> Indeed, I have still no opinion about what Bilge advocates,
> ie that your theory (according to his views) wouldn't satisfy
> the requirement of charge conservation whilst you pretend
> the reverse because you assert to have a charge operator
> that commutes with the hamiltonian.

That's right. The proof that the commutator between H and Q
is zero is very simple. It can be seen for example from the fact
that in all mentioned interaction potentials (expressed in the general
form of eq. (9.47)) the sum of charges of created particles is
equal to the sum of charges of annihilated particles.

>
> Now, about the invariance of this Hamiltonian, I am inclined
> to think (presently, though I could change my mind later) that
> the lack of invariance of the Hamiltonian (which is pointed out
> by Bilge) may be (if exact) a correct feature (and not a flaw) that
> would simply express that Lorentz covariance is not compatible
> with the requirement of Poincaré Lie Algebra commutation
> relations connected to the representation of the Poincaré group
> in the state space of not Lorentz covariant physical systems.

Bilge just declared that the Hamiltonian is not invariant, without
any support of his claim. I have a detailed proof of the opposite
statement: All commutation relations of the Poincare group are
preserved in my approach. Therefore, the Hamiltonian IS invariant.
This proof is taken from Weinberg's paper. (There are few other papers
which contain different versions of the same proof.) I suggested
to analyze this proof in detail. No response from Bilge yet.

>
> Eugene
>
>>Let's take a 2-particle system.
>>Do you agree that operators P and Sigma
>>have a non-interacting form
>>P = p_1 + p_2
>>Sigma = sigma_1 + sigma_2
>
>
> They may have such a non-interacting form, yes.
>
>
>>where p_1 and p_2 are momenta of the two particles, and
>>sigma_1 and sigma_2 are angular momenta of the two particles?
>
>
> The same.
>
>
>>Do you agree that Hamiltonian H has interacting term:
>>H = h_1 + h_2 + V
>>where h_1 and h_2 are energies of the
>>two particles and V is interaction?
>
>
> Yes
>
>
>>Do you agree that boost operator has interaction term as well:
>>K = k_1 + k_2 + Z
>>where k_1 and k_2 are "boosts" of the
>>two particles and Z is interaction?
>
>
> You advocate this relation to be necessary to satisfy the
> commutation relations of the Lie algebra of the Poincaré
> group and I am inclined to believe that you might be right.

If you agree with the interacting form of boost

K = k_1 + k_2 + Z

you then should agree that when this boost operator is used in
the formula for transformation of particle's position to the
moving reference frame, the result is different from the case
of non-interacting particles. The boost transformations do depend
on interaction. That's my main point.

>
> Though I am unsure of these questions (because I have first
> to read your book with some scrutiny to be sure), I am pretty
> confident that you will not find the source of our present
> discrepancy of point of view here. What you will (maybe)
> prove with that (depending on the correctness of your
> Hamiltonian, even if you argue that it is not your one but
> Weinberg's one. As Bilge seems to disagree, I am unsure
> presently) is that the Lorentz covariance is broken by
> the required Poincaré Lie algebra commutation relations.

By "Lorentz covariance" you mean that observables of particles
transform by linear universal Lorentz formulas? Is it right?
If I understood you correctly, then you are exactly right.
Lorentz covariance contradicts the Poincare group properties.
I respect the Poincare group properties much more than the
artificial requirement of Lorentz covariance. So, I discard
the Lorentz covariance without hesitation.

Eugene.

>
> Though I am unsure, I am (presently) somewhat inclined
> to believe that you might perhaps be right about that issue.
>
> Bernard Chaverondier
> http://perso.wanadoo.fr/lebigbang/transformation.htm
> Derivation of Lorentz transforms and "canonical" inertial system
> of coordinates in the framework of Aristotle space-time.
> http://perso.wanadoo.fr/lebigbang/epr.htm
> Quantum determinism or Relativist locality ?
>
>

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