"Eugene Stefanovich" wrote in message
...


Eugene Stefanovich wrote:


Bill Hobba wrote:

"Eugene Stefanovich" wrote in message
...

Hello everybody,

I am pleased to announce that a new book
is available for download on my web-site www.meopemuk.com.
The title of the book is "Relativistic quantum dynamics"
It describes a successful attempt to unite relativity
and quantum mechanics, avoiding paradoxes and divergences.
Some of these topics were already discussed on this
newsgroup. Many thanks to those who participated.
Especially to Bill Hobba and Bilge.



Had a quick peek. You claim Einstein did not justify the assertion
that the
Lorentz transformation is valid for all space-time events. Now I am
not a
historian, I am better versed in modern treatments of relativity. And
in
those treatments no assumption is made about the nature of the
space-time
events. Thus, as a possible hidden assumption, such a statement is,
well to
put it bluntly, without any foundation.

I know I have given the following ancient post by Tom Roberts many
times,
but I will give it again to ensue people can see no such hidden
assumption
is made:


http://groups.google.com/groups?q=to...t.com&rnum= 7.


Bill




I am not pretending to be historically correct. You can substitute word
"Einstein" with the phrase "most modern treatments of special
relativity" there.
In three paragraphs after that, I briefly discuss why existing attempts
(including Tom Robert's paper; by the way, thanks for sending this
paper to me) to justify universality and linearity of Lorentz
transformations for interacting systems are not sufficient.
We discussed this point with you quite extensively. You do not agree
with me, I know that.

Let us agree about our disagreement: we have two competing theories:
One (commonly accepted) theory is based on the assumption of
universality of Lorentz transformations. This theory has serious
troubles in description of dynamics of interacting particles
(I mentioned Currie-Jordan-Sudarshan theorem many times).
Another theory (described in the book) does not assume the
universality of Lorentz
transformations, or you can say it assumes dynamical character of
boosts. In this approach, the unification of relativity with quantum
mechanics is seemless, and dynamics of interacting systems
is consistently described.

So, if we look not just at foundations of the theories
(they may be interpreted subjectively) but also at the results
delivered by the two theories, we should give preference to
my approach.

Eugene.

On a second thought I think I was too generous to your approach.
I cannot agree that space looks homogeneous and isotropic for particle A
if there is particle B nearby. Different directions in space definitely
do not look equivalent for A. So, I reject Robert's "proof" of
Lorentz transformations.

The point however is it is assumed that the interaction occurs in a flat
space-time background to which the above assumptions apply. If you are
attacking that assumption then I agree SR may have a case to answer (and
answered in GR). I may be mistaken in your views but my reading of them is
the above is not the assumption your are attacking. For example look at
classical mechanics (eg Landau - Mechanics). In analyzing particles in a
classical gravitational field it is assumed such a field is superimposed on
an inertial frame even though its existence breaks isotropy.

Thanks
Bill


In my book you can find a proof of inverse statement (Statement G in
subsection 1.2.2): "boosts are dynamical". I would be glad to know
about any holes in my postulates and the logic I use to derive
this statement.

Eugene.

Bill Hobba wrote:
"Eugene Stefanovich" wrote in message
...


Eugene Stefanovich wrote:


Bill Hobba wrote:


"Eugene Stefanovich" wrote in message
...


Hello everybody,

I am pleased to announce that a new book
is available for download on my web-site www.meopemuk.com.
The title of the book is "Relativistic quantum dynamics"
It describes a successful attempt to unite relativity
and quantum mechanics, avoiding paradoxes and divergences.
Some of these topics were already discussed on this
newsgroup. Many thanks to those who participated.
Especially to Bill Hobba and Bilge.



Had a quick peek. You claim Einstein did not justify the assertion
that the
Lorentz transformation is valid for all space-time events. Now I am
not a
historian, I am better versed in modern treatments of relativity. And

in

those treatments no assumption is made about the nature of the

space-time

events. Thus, as a possible hidden assumption, such a statement is,
well to
put it bluntly, without any foundation.

I know I have given the following ancient post by Tom Roberts many

times,

but I will give it again to ensue people can see no such hidden
assumption
is made:



http://groups.google.com/groups?q=to...t.com&rnum= 7.


Bill




I am not pretending to be historically correct. You can substitute word
"Einstein" with the phrase "most modern treatments of special
relativity" there.
In three paragraphs after that, I briefly discuss why existing attempts
(including Tom Robert's paper; by the way, thanks for sending this
paper to me) to justify universality and linearity of Lorentz
transformations for interacting systems are not sufficient.
We discussed this point with you quite extensively. You do not agree
with me, I know that.

Let us agree about our disagreement: we have two competing theories:
One (commonly accepted) theory is based on the assumption of
universality of Lorentz transformations. This theory has serious
troubles in description of dynamics of interacting particles
(I mentioned Currie-Jordan-Sudarshan theorem many times).
Another theory (described in the book) does not assume the
universality of Lorentz
transformations, or you can say it assumes dynamical character of
boosts. In this approach, the unification of relativity with quantum
mechanics is seemless, and dynamics of interacting systems
is consistently described.

So, if we look not just at foundations of the theories
(they may be interpreted subjectively) but also at the results
delivered by the two theories, we should give preference to
my approach.

Eugene.


On a second thought I think I was too generous to your approach.
I cannot agree that space looks homogeneous and isotropic for particle A
if there is particle B nearby. Different directions in space definitely
do not look equivalent for A. So, I reject Robert's "proof" of
Lorentz transformations.


The point however is it is assumed that the interaction occurs in a flat
space-time background to which the above assumptions apply. If you are
attacking that assumption then I agree SR may have a case to answer (and
answered in GR).

Let us forget about "space-time background". I do not know what this
means exactly. Let us speak about observable things - positions of
particles which are expectation values of their position operators.
We have observer O which observes that particle A has position x_A
and particle B has position x_B. Now, the question is about position
measurements by moving observer O'. Your line of reasoning is this:
For particle A all directions in space are equivalent. From this
you derive Lorentz transformations. I.e., you obtain that for observer
O' the measured value of position of particle A can be obtained
from x_A by using some universal formula independent on where
the particle B is.

I say, that all directions in space are not equivalent for A, because
there is particle B sticking around, and you cannot disregard that.
I don't know what this particle is doing there. Maybe it is "curving the
space-time" or whatever. But this particle is there, and certainly
destroys the symmetry of the neighborhood. My point is that you
cannot pretend that all directions in space ate equivalent for particle
A. Therefore your derivation of Lorentz transformations for the position
of A fails. Correct transformation must take into account the presence
of B and depend on the stregth of inrteraction between A and B
(if A and B interact, of course).


In my book, I do not derive boost transformations in this way.
I do my derivation in subsections 7.3.6 and 7.3.7 for one
free particle. The transformations for many-particle
systems are discussed in 12.3.1 and 12.3.3.

GR has nothing to do with it, because GR uses the same SR idea of
universal space-time, only curved. Please understand me, I am not
trying to say that EM interactions curve space-time. I do not want
to talk in terms of space-time at all. I want to talk in terms
of particle observables (positions, momenta, spins). I do not care what
kind of space-time is behind these observables, or if there is any
space-time at all.



I may be mistaken in your views but my reading of them is
the above is not the assumption your are attacking. For example look at
classical mechanics (eg Landau - Mechanics).

I don't have this book with me now. But I remember they used
homogeneity-isotropy argument to derive action for one free particle.
(is it what you are talking about?) I have no objections to that.
And indeed, in my approach, boost transformations of position for
one free particle are consistent with Lorentz transformations
(see 7.3.6 and 7.3.7)

Eugene.

In analyzing particles in a
classical gravitational field it is assumed such a field is superimposed on
an inertial frame even though its existence breaks isotropy.

Thanks
Bill


In my book you can find a proof of inverse statement (Statement G in
subsection 1.2.2): "boosts are dynamical". I would be glad to know
about any holes in my postulates and the logic I use to derive
this statement.

Eugene.

Bill Hobba wrote:


The point however is it is assumed that the interaction occurs in a flat
space-time background to which the above assumptions apply. If you are
attacking that assumption then I agree SR may have a case to answer (and
answered in GR). I may be mistaken in your views but my reading of them is
the above is not the assumption your are attacking. For example look at
classical mechanics (eg Landau - Mechanics). In analyzing particles in a
classical gravitational field it is assumed such a field is superimposed on
an inertial frame even though its existence breaks isotropy.

Thanks
Bill



Bill:

After some thought I think I got it why we cannot understand each other.
You assume existence of some background space-time, which is somewhat
similar to old ether. Physical events are "embedded" in this space-time
like flies in jelly. When observer changes, the "jelly" gets deformed
and flies just follow this deformation. Lorentz transformations are
universal. If a fly and a bee happen to be close to each other for
one observer, they will be close to each other for all other observers.
The 4D jelly does not allow them to go apart.

I do not accept this jelly-type background. I do not want to talk
about any "background" or "space-time" or even "space" for that matter.
I am interested only in values of physical observables registered by
measuring apparatuses. When I talk about position of a particle
I want to talk about three real numbers x, y, and z, which have
been recorded by bubble chamber, or Geiger counter, of photograhic
plate, or whatever measuring apparatus for position you have.
In this approach, it is not clear a priori whether boost
transformations of coordinates of different events are described by
the same Lorentz formula. In order to find the boost transformations
of x, y, and z, I need first to represent x, y, and z as quantum
Hermitian opetators (the classical approach in which x, y, and z
are functions on the phase space also works), then build the
"total boost operator" K of the physical system, and then use
normal quantum mechanical formula

x(\theta) = exp(-iK \theta) x exp(iK \theta)

where \theta is the rapidity of the boost.
Operator K depends on the interaction in physical system.
Therefore boost transformations of x depend on the interaction as well.

Two events (the fly and the bee) related to different
physical systems may coincide for one observer and be at different
"space-time points" for other observers.

I think my approach is more general than yours, because it does
not assume
existence of any background, space-time or space. It only uses
commutation relations between operators of observables.

I think I made my position more clear, or did I?

Eugene.

"Eugene Stefanovich" wrote in message
...


Bill Hobba wrote:


The point however is it is assumed that the interaction occurs in a flat
space-time background to which the above assumptions apply. If you are
attacking that assumption then I agree SR may have a case to answer (and
answered in GR). I may be mistaken in your views but my reading of them
is
the above is not the assumption your are attacking. For example look at
classical mechanics (eg Landau - Mechanics). In analyzing particles in
a
classical gravitational field it is assumed such a field is superimposed
on
an inertial frame even though its existence breaks isotropy.

Thanks
Bill



Bill:

After some thought I think I got it why we cannot understand each other.
You assume existence of some background space-time, which is somewhat
similar to old ether. Physical events are "embedded" in this space-time
like flies in jelly. When observer changes, the "jelly" gets deformed
and flies just follow this deformation. Lorentz transformations are
universal. If a fly and a bee happen to be close to each other for
one observer, they will be close to each other for all other observers.
The 4D jelly does not allow them to go apart.

I do not accept this jelly-type background. I do not want to talk
about any "background" or "space-time" or even "space" for that matter.
I am interested only in values of physical observables registered by
measuring apparatuses. When I talk about position of a particle
I want to talk about three real numbers x, y, and z, which have
been recorded by bubble chamber, or Geiger counter, of photograhic
plate, or whatever measuring apparatus for position you have.
In this approach, it is not clear a priori whether boost
transformations of coordinates of different events are described by
the same Lorentz formula. In order to find the boost transformations
of x, y, and z, I need first to represent x, y, and z as quantum
Hermitian opetators (the classical approach in which x, y, and z
are functions on the phase space also works), then build the
"total boost operator" K of the physical system, and then use
normal quantum mechanical formula

x(\theta) = exp(-iK \theta) x exp(iK \theta)

where \theta is the rapidity of the boost.
Operator K depends on the interaction in physical system.
Therefore boost transformations of x depend on the interaction as well.

Two events (the fly and the bee) related to different
physical systems may coincide for one observer and be at different
"space-time points" for other observers.

I think my approach is more general than yours, because it does
not assume
existence of any background, space-time or space. It only uses
commutation relations between operators of observables.

I think I made my position more clear, or did I?

Eugene.

Sorry for not responding sooner - some private matters have kept me
occupied. Promise to give a more detailed reply soon - probably anyway.

Thanks
Bill