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

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

Date: Mon, 04 Oct 2004 21:39:01 -0700

bernard.chaverondier wrote:
> "Eugene Stefanovich" <eugenev@synopsys.com> a écrit dans le message de
> news:4161C9E8.1060604@synopsys.com...
>
> 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 proven false) if we had a
> common basis. For that aim to be reached, the geometrical
> tools and concepts you agree to use in your theory have to be
> carefully defined without depending on theories that are shaken
> by your new hypotheses. Presently, in my opinion, this is not
> the case. Your chapter 1 assumes space, time, durations, lengthes
> rotations, translations, inertial frames and doesn't provide the
> mathematical structure that fasten them together and provide their
> physics justification in terms of symmetries (more specifically
> energy, momentum and angular momentum conservation)
>
> So, before demonstrating anything, tell me the geometrical
> basics you would agree to be that of your theory
> (I sketch the questions below in a very coarse and
> hand wavy manner so as to keep this post short)
>
> 1 What mathematical structure do you accept for the set of all events ?
> Would you agree to start immediately with a 4D affine space-time
> (because you don't bother with RG presently) so as to provide an
> immediate definition of space-time translation ?

First I choose one inertial observer. A assume that this
observer can erect three mutually perpendicular axes, that he has
all necessary measuring rods, protractors, and everything needed
to perform measurements, including Geiger counters, Stern-Gerlach
apparatuses, etc. He also has a clock which assigns to each measurement
a real number - the time of the measurement.
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).

>
> 2 What do you define as being time ? Would you agree with the
> possibility to provide your affine space-time with a time metrics,
> ie a rank 1 metrics (providing your set of events with a characteristic
> foliation into 3D slices of simultaneity allowing you later to define
> in a rigorous manner what is a space translation) ?

Time is a real number which observer assigns to the observed events
according
to the reading of the clock. Two events are simultaneous (from the
  point of view of this observer) if they have
the same time labels.

>
> If not, 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) ?

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. You have your inertial
  frame, I have mine. Astronauts on the space station have theirs.
(I presume also that we completely disregard all effects of gravity.
We do our physics exercises far from gravitating bodies). Space
translation is a transformation from one reference frame to another
  frame
shifted at some distance. I think it is sufficiently obvious and
does not require more justification.

>
> 3 What is your mathematical definition of space ? Would you agree
> with the possibility to provide your affine space-time with a space
> metrics, ie a rank 3 metrics (providing your set of events with a
> characteristic foliation into 1D motionless lines allowing you
> later to define in a rigorous manner what is a time translation) ?

As I said, each observer assigns to all events 3 coordinates x, y, and
z. He may notice, that under rotations (see later) the combination
(x1-x2)^2 + (y1-y2)^2 + z1-z2)^2 for any two events or points in space
remains unchanged. So, he may say that space is a 3D continuum with
Euclidean metric.

>
> If not, how do you define time translations ?

Simple. It is easier to imagine reference frame or observer as
an instantaneous thing which lives just a short instance. So, I
am one observer at time 8:17 pm. I am another observer (shifted in time
by 1 minute) at time 8:18 pm. In order to perform 1 min time translation
(of your own reference frame) just wait 1 minute.

>
> 4 What do you define as being rotations ? Would you agree
> to define them as affine transformations that preserve globally
> slices of simultaneity, preserve your space metrics and time metrics
> (hence your space-time foliation) and have a motionless worldline
> as a fix point ?

I probably agree with you, but I woudn't describe rotation in so many
fancy words. Rotation is simply when I turn my body and all my measuring
apparatuses.

>
> 5 What do you define as an inertial frame ?
> Here I could provide my answer which needs
> to define what is a boost (on the basis of physical
> requirements), then derive the Lorentz transforms and
> then define what type of coordinate systems can be
> called inertial frames ? But I prefer to know
> your answer first.
> (see http://perso.wanadoo.fr/lebigbang/epr.htm
> and http://perso.wanadoo.fr/lebigbang/transformation.htm )

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.) and moves uniformly
without rotation (with respect to distant stars).

Two observers (reference frames) may have different velocities.
The transformation which changes from an observer to another
observer with different velocity is called boost. So, we have
10 basic transformations between observers: time translations,
space translations, rotations and boosts. This is simple and
obvious.

There is no need to know anything about spacetime foliation
to imagine all this.

All inertial observers are fully equivalent. They see the
world around them differently, but there is no way to say
whose view of the world is better. There is no preferred
direction in space, there is no prefered location in space.
There is no reference frame at absolute rest.
All time instants are indistinguishable.

>
> As far as the geometrical basics of your theory are
> not defined in a careful manner it is not possible
> to state the proof you require.

I am glad you raised this issue, because we really need to start
our discussion from such basics as meaning of inertial observers.

>
> Eugene Stefanovich
>
>>Are you talking about your approach or about my approach.
>>I don't have "motionless frames", because there is no
>>absolute motion in my approach. All reference frames
>>are equivalent and you cannot say objectively which
>>one moving and which one is at rest.
>
>
> Chaverondier
> Why not ? Then define precisely what are your inertial
> frames mathematically grounded on. Then we can discuss
> this topic. As I don't know what are your inertial frames,
> I can't.

An astronaut in a space craft with all engines turned off and
without spinning motion at a fixed time instant is a good
example of inertial observer.

>
> Eugene Stefanovich
>
>>You are trying to prove that instantaneous signaling contradict
>>causality. This would be correct if you use universal linear
>>Lorentz transformations for space and time coordinates of events.
>
>
> Chaverondier
> What are your inertial frames grounded on ? Are your inertial frames
> accounting in some manner for the interactions of some particles ?

We haven't started to talk about interacting particles yet.

> If not, your inertial frames are space-time systems of coordinates
> which transform into each other thanks to Lorentz transforms

When you start to talk about Lorentz transforms you need to ask
"Lorentz transforms of what?". 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. 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). 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 (all
observers are equivalent), but we also know the mathematical structure
  of this symmetry group.

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.

Different observers do not agree about position, velocity,
etc of the meteorite. But if they want to translate the results of
measurements from one observer to another,
they can do a trick: they attach
an inertial observer R to the meteorite, so that the observer R
and the rock
move together (this is possible, because both observer R and the
rock move freely without external forces). Now they can use
Poincare group properties to figure out parameters (trajectory)
of the observer R and therefore parameters (trajectory) of the
meteorite. They can find that these parameters transform exactly
by Lorentz formulas. 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.

This is all easy. Now comes the difficult part. Suppose that all
meteorites in the system bear a non-zero charge. The charge is
substantial, so that trajectories of meteorites are not straight lines
anymore. The rocks interact, and their trajectories are curved. How
our observers are going to find the transformations of these
trajectories? We cannot attach an inertial observer to the meteorite
and use Poincare group properties, as we did before.
The meteorite is not moving along
straight line with constant velocity, so there is no such observer
which is always adjacent to the meteorite. We cannot guarantee that
boost transformations of trajectories of meteorites will be the
same Lorentz transformations as for non-interacting meteorites.

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.

> (and
> into which free particle propagate along straight lines at constant
> speed).
>
> In such a case, the use of Lorentz transforms when only
> space and time localisation of events is involved (and not
> the dynamics of interacting particles) are perfectly legitimate.
>
> If the principle of relativity is stated as (coarsely)
>
> * the observation of the "same events" at the "same
> locations" and at the "same moment" in two inertial
> frames when a change of inertial frame is involved
>
> then it gives rise to the Lorentz covariance.
>
> On the contrary, if the principle of relativity is stated as
>
> * the evolution of observables when an inertial frame
> change is involved is modeled by a projective unitary
> representation of the Poincaré group in the Hilbert
> space of states of the observed system, (in agreement
> with the appropriate commutators of the Lie algebra
> of this group).
>
> then, according to your claim, it gives rise to your theory.
>
> If the second formulation is adopted and needs to reject
> the first one, then you can't avoid the possibility to detect
> absolute motion.

I do not agree with your definition of the principle of relativity.
The logic of my derivation of interaction-dependence of boost
transformations is this:

The principle of relativity is:

1) all inertial observers are physically equivalent.

   Then you need another postulate:

2) the group of transformations between inertial observers is the
Poincare group.

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.

>
> Perhaps I am wrong, but if you want to prove me that
> I am wrong, you have (in my opinion) to define more precisely
> the geometrical structure from where all the geometrical
> tools you use spring out.
>
> Eugene Stefanovich
>
>>My point is that such transformations are not applicable when
>>you consider events connected to each other by interaction
>>(e.g. change of trajectory of particle A and induced change of
>>trajectory of particle B interacting with A via Coulomb force).
>>If you take into account interaction dependence of boost
>>transformations you'll obtain that instantaneous interactions
>>do not contradict causality (see subsection 12.3.3).
>
>
> Chaverondier
> Presently, I think that even in your theory I can prove
> that instantaneous interactions can preserve the principle
> of causality, provided the principle of relativity of
> motion be violated (so that the detection of absolute
> motion is allowed).

Nope. Instantaneous interactions and causality and the
principle of relativity can peasefully coexist together.

>
> I cannot prove that now because you reject some basics
> of relativity without replacing them by the appropriate
> geometrical construction that is needed to derive this
> proof (or prove that you are right though I doubt it).

I hope the above explanations clarified the picture a little bit.

>
> Eugene Stefanovich
>
>>I am sorry, I lose focus when you mention "space-time" and
>>"geometry". I don't think I understand what it means. Can we speak
>>in terms of observable positions of events and their measured times?
>
>
> No, because these observables need to be observed in an
> inertial frame, which need to know what is an inertial frame,
> because positions needs to refer to the definition of lengthes,
> because moments needs to refer to the definition of durations
> and so on. The inertial frames, lengthes, durations have to be
> defined in a consistent manner grounded on invariance with regard
> to translations and rotations. All that needs a geometry because
> your work adresses these issues in a drastic manner.

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 spacetime, which I don't like
at all.

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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