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

From: Eugene Stefanovich (eugenev_at_synopsys.com)
Date: 10/05/04 

Date: Tue, 05 Oct 2004 13:26:28 -0700

bernard.chaverondier wrote:
> "Eugene Stefanovich" <eugenev@synopsys.com> a écrit dans le message de
> news:41622565.7080302@synopsys.com...
>
> bernard.chaverondier
>
>>>>>If all symmetries of relativity are satisfied, then, there can be
>>>>>only one speed c at which interactions propagate at a speed
>>>>>independent on the motion of their source. If this speed
>>>>>of propagation is infinite you get the Galilean Relativity
>>>>
>
> Eugene Stefanovich
>
>>>>Why? Prove it!
>>>
>
> Chaverondier
>
>>>Presently, in the framework of _your_ theory, I can't.
>>>My assertion could be proven (or disproved ) if we had a
>>>common basis. So, tell me the geometrical basics you would
>>>agree with. 1 What mathematical structure do you accept
>>>for the set of all events ?
>>
>
> Eugene Stefanovich
>
>>First I choose one inertial observer.
>
>
> Chaverondier
> You can't. It's too soon. Your theory tosses in some way
> Special Relativity because right from the beginning, you claim
> that equivalence of physics laws in all inertial frames is not the same
> than Lorentz covariance and claim this assertion to be an additional
> axiom. You cannot support such claims without providing a precise
> mathematical model of what is an inertial frame in your theory.
>
> If you disagree that inertial frames are an inertial system
> of coordinates (I will tell what it is below) you have
> to define _mathematically_ what is an inertial frame.
>
> It is not to harass you with tiny details. This inertial frame
> mathematical definition is a central concept in your theory
> because, if our discussion progresses how I think that it
> may, I will probably be up to prove you that you have
> * either to suppress Faster Than Light
> interactions in your theory
> * or to discard the principle of relativity of motion
> (the impossibility to detect absolute motion) as
> suggests the CJS theorem proving the incompatibility
> of interaction of particles with the principle of relativity
> in a non quantum context.

I disagree with both of your proposals. FTL interactions do not
contradict the relativity postulate and Poincare group properties.
Interactions between particles are perfectly compatible with relativity,
but they are not compatible with universal Lorentz transformations.

>
> Eugene Stefanovich
>
>>Assume that this observer can erect
>>three mutually perpendicular axes, that
>>he has all necessary measuring rods,
>
>
> Chaverondier
> From a mathematical point of view, you have first to
> introduce the for real numbers that are needed to locate all
> events, that's to say a 4D manifold. Indeed, you can't define the
> measuring rods and perpendicularity conditions (that's to say a
> rank 3 spatial metric) and the measuring clocks (that's to say
> a rank 1 time metric) as far as you have not a 4D manifold
> where these geometrical tools can take place.
>
> * So as to get a picture deprived of space-time curvature,
> because you don't bother to account for gravity presently
> so as to satisfy the Keep It SImple point of view, you have
> to assume the constancy of these two metrics in any of the
> cards mapping your 4D manifold (your set of events).
>
> Now, for the sake of convenience, let us call it a space-time.
> Up to now we have introduced only geometrical tools you
> agree to pour in, so that they don't conflict with your views
> of physics.
>
> * these two metrics provide your space-time
> (your set of events) with a foliated manifold structure.
> * the foliation of your space-time into motionless
> 1D world lines which form the characteristic foliation of your
> rank 3 space metrics (indeed, we haven't so far introduced
> the tools that are necessary to define inertial observers
> foliating the space-time into moving 1D worldlines)
> * the foliation of your space-time into 3D slices
> of simultaneity which form the characteristic foliation
> of your rank 1 time metric.
>
> * then you can introduce Orthonormalized systems of coordinates
> (t0,x0,0,z0) (Aristotle frames R0) which are such that
> * the space metrics dL0^2 writes as
> dL0^2 = dx0^2+dy0^2+dz0^2
> * the time metrics dT0^2 writes as
> dT0^2 = dt0^2
>
> * Then you can introduce canonical transformations of
> this metric space-time as transformations preserving these
> two metrics (hence their characteristic foliation, ie
> any leaf transforms into an other leaf)
> * the time translations are transformations
> that let our time leaves unchanged (a 1D motionless world
> line transforms into the same 1D motionless world line)
> * the space translations let our space leaves
> unchanged (a 3D simultaneity slice transforms into the
> same 3D simultaneity slice)
> * the space rotations let your 3D space slices
> of simultaneity unchanged (a 3D simultaneity slice
> transforms into the same 3D simultaneity slice) and
> at least one motionless world line is unchanged.
>
> Hence our space-time is now equipped with the Aristotle
> group structure encompassing the space-time translations
> and the space rotations. The Aristotle frames transform into
> each other in accordance with actions of the Aristotle group
> SE(1)xSE(3) (group product of the time Euclidean group
> of time translations by the space Euclidean group of space
> isometries)
>
> Of course, we may pretend that all that is a geometrical
> model of what takes place in a given inertial frame, but, as
> this concept of inertial frame has not be given an appropriate
> mathematical model up to here, it is an assertion which would
> be deprived of any mathematical content (even if some
> heuristic meaning can be attached to such an idea, this isn't
> a relevant feature in the verification process of mathematical
> consistency of your theory you are engaged now)
>
> Eugene Stefanovich
>
>>He also has a clock which assigns to each measurement
>>a real number - the time of the measurement.
>
>
> Chaverondier
> I have introduced above the time metrics that provides you
> with the minimal mathematical content you require to be up
> to use it.
>
> Eugene Stefanovich
>
>>Then I assume that this observer can register events and
>>measure their positions in space. So, he can assign three
>>real numbers (x, y, and z) to each event. So, events are
>>characterized by at least 4 real numbers (position and time).
>
>
> Chaverondier
> From a mathematical point of view, these 4 numbers picture
> of space-time location of events has to be set right form the
> beginning. It is so in my above proposal thanks to the introduction
> of a 4D manifold. Indeed you can't define durations and lengths
> without a 4D manifold where the time and space metrics that
> model such things can take place.
>
> Chaverondier
>
>>>how do you define space translations (as we have not
>>>defined what is an inertial frame and can't as far as space
>>>and time themselves have not been defined first) ?
>>
>
> Eugene Stefanovich
>
>>I think that you don't need to know anything about space and
>>time in order to define inertial frame. Inertial frame (or observer)
>>is self-evident and does not require definition.
>
>
> Chaverondier
> I strongly disagree about this point. Your theory drastically
> requires a precise mathematical model of what you name
> an inertial frame. This is a pivotal concept in your theory.
> You cannot prove anything if you don't define what it is
> mathematically.
>
> Eugene Stefanovich
>
>> You have your inertial frame, I have mine.
>
>
> Chaverondier
> Up to here, you have no inertial frame. You
> haven't defined what it is mathematically.
>
> As far as I can see, the best mathematical definition of an
> inertial frame is to consider it as a system of space and time
> coordinates endowed with appropriate properties about the
> way they transform into each other. Indeed, each observer
> in its inertial frame will ascribe a time and a space coordinate
> to any event, so that any inertial frame will necessarily be
> ascribed a system of space-time coordinates locating events.
>
> Now, as we have now introduced space, time as well as time
> and space metrics, we can now ascribe a time measurement
> and a position measurement to any event in a given Aristotle
> frame. We are now up to define inertial frames as systems
> of coordinates stemming from appropriate space-time
> transformations (called boosts) of Aristotle frames.
>
> Theses boosts will be derived on the basis of the
> mathematical hypotheses expressing the physics properties
> we consider to be required (noteworthy an appropriate
> expression of the principle of relativity of motion).
>
> In these inertial frames, you can define mathematically,
> a time metric and a space metric stemming from these
> boosts. You need these metrics so as to be able to speak
> of durations and distances measurements in a given frame.
> Hence you have to define them in such a manner that
> they satisfy the principle of relativity. Consequently,
>
> If R0 is an Aristotle frame and R an inertial one,
> (ie a boosted one)
> * the "same" rod in R or in R0 have to be seen as
> having the same length in R as in R0
> * the "same" clock in R or in R0 has to be seen as
> ticking at same rate in R as in R0
>
> Hence, if coordinates (t0, x0, y0, z0) in an Aristotle
> frame R0 transforms to coordinates (t,x,y,z) thanks to
> a boost, you must have a covariant definition of the
> time and space metrics in the inertial frame R.
> * if in R0 you have
> dL0^2 = dx0^2+dy0^2+dz0^2
> dT0^2 = dt0^2
> * then, in R you must have
> dL^2 = dx^2 + dy^2 + dz^2
> dT^2 = dt^2
>
> Notice that this is not a complete expression of the
> principle of relativity. The symmetry of point of view
> between an observer standing in R and an observer
> standing in R0 has also to be accounted for (as well
> as some other physics requirements that are needed
> to define what is a boost in an unique manner).
>
> Then, given these physics assumptions we can derive
> the expression of boosts. I don't go further into these
> details so as to try to keep this post a decent length.
> That's what I did in
> http://perso.wanadoo.fr/lebigbang/epr.htm and
> http://perso.wanadoo.fr/lebigbang/transformation.htm
>
> Chaverondier
>
>>>5 What do you define as an inertial frame ?
>>
>
> Eugene Stefanovich
>
>>Easy. This is observer (it could be a person or a Pioneer
>>spacecraft, doesn't matter) which has necessary measuring
>>equipment (like measuring rods, clocks, etc.)
>
>
> Chaverondier
> So that an inertial frame can be associated with the possibility
> to ascribe any event with 1 time and 3 space coordinates because
> the observer has the measuring tools that allow him for such
> a space-time parameterization associated with his inertial frame.
>
> Hence, form a mathematical point of view, we can define
> an inertial frame as a system of space and time coordinates
> and these systems have to transform in an appropriate
> manner thanks to the restricted Poincaré group actions
> (which appear to be spanned by boosts together
> with the restricted Aristotle group actions)
>
> Indeed inertial systems of space-time coordinates
> form the space time parameterization that enter all
> your models, measurement results, equations and
> so on, so that they have to be defined in a rigorous
> mathematical manner.
>
> Notice that I don't require you to assume that all laws
> of physics satisfy the covariance with regard to the
> transformations of your inertial frames
> (ie inertial systems of coordinates)
>
> I only need that you define the way these systems
> of inertial frames of coordinates transforms into
> each other when an inertial frame change is involved.
>
> After that, you can decide if only free particles
> or all laws of physics satisfies the covariance
> with regard to these transformations.
>
> That's an other matter and you are free of your choice
> provided that your theory is self consistent (and of
> course doesn't contradict known experimental results)
> Your chapter 1 has to be enough mathematically detailed
> so as to ensure that your theory doesn't discard at some
> place an hypothesis that is taken for granted and used
> implicitly or explicitly at some other place.
>
> Eugene Stefanovich
>
>>I am glad you raised this issue, because we
>>really need to start our discussion from such
>>basics as meaning of inertial observers.
>
>
> Chaverondier
> Fine, so that I think that our discussion should be
> fruitful, even if it is a difficult one (don't imagine
> that I underestimate its difficulty or the value of
> your work whatever our present discrepancy of
> point of view).
>
> Eugene Stefanovich
>
>>When you start to talk about Lorentz transforms
>>you need to ask "Lorentz transforms of what?".
>
>
> Chaverondier
> Absolutely. As soon as you have defined your space-time
> parameterization (and restricted your choice to inertial frames
> of coordinates) you can define what are Lorentz transforms.
> These are precisely the transformations of inertial system of
> coordinates into each others.

That's not how I understand Lorentz transformations. In my language
Lorentz transformations (or, generally, boost transformations -
Lorentz transformations are just linear versions of the latter)
are transformations between values of observables of physical systems
measured by different inertial observers.

>
> Eugene Stefanovich
>
>>So far we described our inertial observers (e.g., astronauts
>>moving in free space along all possible directions).
>>We haven't introduced any physical system yet.
>
>
> Chaverondier
> Yes we have. We have the measuring rods and clocks
> (modeled as space and time metrics on a manifold) and
> the inertial systems of coordinates without which you are
> deprived of space-time parameterization up to characterize
> the location and the moment when physics events occur
> as well as lengths and durations.
>
> Space-time parameterization and numerization of measurement
> outcomes can't exist independently of measuring tools
> satisfying symmetries requirements which are precisely
> at the root of the geometry embedded in space-time and
> implicitly used in your work. This has to be done explicitly
> so as to prove that there is no inconsistency between an
> implicit geometrical assumption and an explicit one.
>
> Eugene Stefanovich
>
>>When astronauts (observers) look out of their windows they
>>see nothing, just black cosmos, and probably other observers.
>>Each observer can measure properties of other observers
>>(position, angle, velocity, time).
>
>
> Chaverondier
> These measurements are coded in accordance with a manner to
> ascribe space and time coordinates to events as well as a length
> to a given rod and a period to the ticking rate of a given clock.
>
> Eugene Stefanovich
>
>>When these measurements are compared, observers may figure
>>out that the set of transformations between them is a 10-parameter
>>group called Poincare group. That's a big step forward. Now
>>we not only know that there is some symmetry in nature...
>
>
> Chaverondier
> We have to know of this symmetries and use them right from
> the beginning of our mathematical construction. They are needed
> to build the time metrics, space metrics and inertial frames concepts.
> It's the basis to define the way you ascribe numerical values
> to measurement outcomes and their location in the space-time
> parameterization provided by an inertial frame of coordinates.
>
> Eugene Stefanovich
>
>>Now suppose, there appears some object (physical system),
>>let's say a meteorite. All observers start to measure its properties
>>and conclude that the meteorite moves along straight line with
>>constant velocity.
>
>
> Chaverondier
> This is precisely one of the properties you need in order to define
> what is an inertial system of coordinates. As far as no other properties
> than its space-time trajectory is considered, a free particle is a straight
> worldline. An inertial frame of coordinates has to satisfy to the
> requirement that a free particle in an Aristotle frame is again
> a free particle (a straight worldline) when observed in an
> inertial frame (ie a boosted Aristotle frame). This contrives
> boosts to be 4D diffeomorphisms transforming straight lines into
> straight lines. This requires them to be affine transformations
> of Aristotle space-time (which proves the linearity of inertial
> system of coordinates transforms, ie Lorentz transforms).
>
> Eugene Stefanovich
>
>>The same Lorentz formulas will be applicable
>>for events related to systems of such non-interacting rocks
>>(e.g. to collisions of such rocks). See my derivation of
>>Lorentz transformations in subsection 2.3.3.
>
>
> Chaverondier
> Hence, you agree that an inertial frames can be
> defined as systems of coordinates transforming
> into each other thanks to the Lorentz transforms.

No. I understand that there are many inertial frames.
They are connected to each other by inertial transformations
(rotations, translations, ...). This transformations form
the Poincare group.

When we consider a physical system viewed from different inertial
frames we can discuss boost transformations of its observables
between different frames (observers). I demonstrated (in section 2.3)
that when there is a non-interacting system of particles, we can
"attach" an inertial reference frame to each particle, use formulas
resulting from Poincare group properties, and derive linear Lorentz
transformations of positions and times of events with such particles.
When particles (or meteorites) interact with each other, we
cannot do this exercise. Boost transformations must be derived from
dynamical properties of the system (interaction).

>
> Eugene Stefanovich
>
>>Now comes the difficult part. Suppose that all meteorites
>>in the system bear a non-zero charge. It is easy to find out
>>how positions and velocities of interacting meteorites will
>>change with respect to translations and rotations. These
>>transformations are kinematical.
>
>
>>To find out how time translations affect positions and
>>velocities is difficult : these transformations are dynamical.
>>For each meteorite, the change of its position in time depends
>>on positions and velocities of other meteorites in the system
>>and forces acting between them. To figure out the result of
>>boost transformation is as difficult as for time translation.
>>Boosts are dynamical as well.
>
>
> Chaverondier
> Agreed
>
> Eugene Stefanovich
>
>>The principle of relativity is:
>>1) all inertial observers are physically equivalent.
>
>
> Chaverondier
> 1/ provided that an inertial observer be defined as an inertial
> system of coordinates. If not, you have to define what is an inertial
> observer and not misrepresent the inertial frame with a dynamical
> system, encompassing interacting particles, space-time parameterized
> in that inertial frame.
>
> Eugene Stefanovich
>
>> Then you need another postulate:
>>2) the group of transformations between
>>inertial observers is the Poincare group.
>
>
> Chaverondier
> In my proposal, this postulate was not stated a priori.
> I gathered any requirements and any required symmetries
> from physics considerations and derived as a consequence
> the restrited Poincaré group as the symmetry group
> transforming inertial systems of coordinates into each
> others. System of coordinates, whatever they are, don't
> exist independently of physics phenomena ruling the
> symmetries satisfied by the measuring apparatuses
> of the observer (noteworthy rods ans clocks).
>
> Eugene Stefanovich
>
>>The third important postulate defines the space of states
>>of the physical system. This can be a Hilbert space for
>>quantum system or phase space for classical system. It then
>>follows from postulates 1) and 2) that inertial transformations
>>of observers are represented in the state space by unitary
>>operators (in the quantum case) or canonical transformations
>>(in the classical case). Let's take quantum case for definiteness.
>>The generators of the representation of the Poincare group are
>>denoted by P (space translations), J (rotations), H (time
>>translations), and K (boosts). The dynamical character of time
>>translations is expressed by the form H = H_0 +V of the Hamiltonian.
>>V is interaction, H_0 is free-particle Hamiltonian. The dynamical
>>character of boosts is expressed by the form K = K_0 + Z.
>>Z is boost interaction and K_0 is boost operator for the system of
>>non-interacting particles. When you consider the Poincare group,
>>it is impossible to have non-zero V and zero Z. This would
>>contradict Poincare commutation relations. Therefore, each interaction
>>in the Hamiltonian V is accompanied by interaction in the boost
>>operator Z. Boosts are dynamical, and boost transformations of
>>trajectories of interacting particles are different from Lorentz
>>transformations.
>
>
> Chaverondier
> Agreed. I know you doubt it, but I consider your above
> statement as an extension of the CJS theorem proving
> that the principle of relativity of motion doesn't apply to
> interacting particles.

Disagreed. The principle of relativity is valid everywhere.
This is my postulate A. I do not see any disagreement with this
  principle so far.

>
> I don't know exactly what should be thought of the required
> gauge transformation that Bilge is strongly arguing about but
> I think you should investigate that matter with some scrutiny.
> If gauge transformations requirement provide you with a wrong
> Hamiltonian, you have to know exactly what goes wrong in this
> picture.

Why you think the Hamiltonian is wrong? This is the same Hamiltonian as
used by Weinberg, Bjorken & Drell, and everybody else in QED.

> It wouldn't be to much a surprise to me if that were
> connected to the fact that quantum diffusion begins with free
> particles and ends with free particles so that some conditions
> that are physically correct at the beginning and at the end of
> the dynamical phenomenon are not anymore so during the
> quantum interaction.
>
> I don't believe the quantum dynamics to be a Lorentz covariant
> process. That's one of the strong reasons why I am interested
> in your theory which sems to fill a gap, as it seems provides a
> dynamical model of quantum diffusion and solve ultraviolet
> Quantum Field Theory divergences. All that is really appealing
> whatever our present discrepancy of point of view.
>
> Eugene Stefanovich
>
>>Instantaneous interactions and causality and the
>>principle of relativity can peacefully coexist together.
>
>
> Chaverondier
> I think that this discrepancy should be cleared up when we will
> agree on the geometrical basics grounding your mathematical
> model of space, time, rod lengths, clock ticking rates, inertial
> frames and boosts.
>
> Eugene Stefanovich
>
>>OK, I probably do have what you call geometry, but I prefer
>>to use terms "measuring rods", "clocks", "distances" etc,
>>instead of "geometry". That's because I am afraid that you'll
>>drag me into the 4D Minkowski space-time, which I don't
>>like at all.
>
>
> Chaverondier
> You are right to be afraid. If you define the geometrical tools you
> need in a rigorous manner, I don't believe that you may find a way
> out to preserve the principle of relativity of motion. In such a case,
> your work should be considered as encompassing, at his heart, a quantum
> extension of the no-interaction CJS theorem proving the incompatibility
> of the dynamics of interacting particles with the principle of relativity.

I disagree again. All frames of reference are equivalent, and the
principle of relativity is not violated.
I have a difficulty in following your logic.
I don't understand how we can
"define" measuring rods and clocks from anything more basic.
I don't understand why do we need to "define" them at all.. These
  notions
seem rather self-evident to me to require any "mathematical definition".

Eugene.

>
> Bernard Chaverondier
> http://perso.wanadoo.fr/lebigbang/transformation.htm
> Derivation of Lorentz transforms and "canonical" inertial
> frames in the framework of Aristotle space-time.
> http://perso.wanadoo.fr/lebigbang/epr.htm
> Quantum determinism or Relativist locality ?
>
>
>

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