Quantum Ph. Vs. Relativity
Siddhartha
There has always been some fuss about Quantum Physics and Relativity being
incompatible somehow. I was wondering if someone could shed some light on
this for me. Is this still the case? I know that Entanglement was something
that Relativists (if I might call them that) found rather displeasing. Is
this the incompatibility that people refer to? And has some manner of
reconciliation been achieved, or are the two theories still at odds with
each other?
I would very much appreciate some insight on this.
Thanks
Sam Wormley
> There has always been some fuss about Quantum Physics and Relativity being
> incompatible somehow. I was wondering if someone could shed some light on
> this for me. Is this still the case? I know that Entanglement was something
> that Relativists (if I might call them that) found rather displeasing. Is
> this the incompatibility that people refer to? And has some manner of
> reconciliation been achieved, or are the two theories still at odds with
> each other?
>
Early universe--which theory do you use.
Black holes, collapsing stars--which theory do you use.
FrediFizzx
news:dbf7jj$9q9$1...@news-int.gatech.edu...
IMHO, relativity and quantum physics is a marriage made in heaven. ;-)
I do believe that relativistic concepts can help to explain fundamental
quantum principles.
Now, no one has really come up with a successful quantum gravity theory
(QFT of GR) yet but I expect that to be solved in the not too far
future. Maybe that is what you are thinking of?
FrediFizzx
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
bskaruna
...it is the concept of "understanding" how things are working...
relativistically or with respect to another...
Anything that has something to be seen or hasn't been
seen are explained to have properties for their existence....
i'm a too confusing...?
....
or we go back to the mechanical way of thinking to understand
relativity and quantum physics..?
Siddhartha
news:3k0o2cF...@individual.net...
Thank you all for your helpful comments. If I might impose on your
generosity with one more question: Has the difficulty with Quantum
Entanglement (which was discussed in the EPR paper) been resolved? That is,
Relativists were averse to the "instantaneous communication" that could
apparently take place between entangled electrons even when separated by
large distances. Since this is now accepted as a very real phenomenon, I was
wondering whether the Relativists have found some way of reconciling this
idea with the principles of Relativity.
Again, I would be very grateful for any input on this.
Thanks
Sam Wormley
There is no "instantaneous communication" of arbitrary information.
That is still constrained by the speed of light.
You might enjoy:
Entanglement: The Greatest Mystery in Physics
Amir D Aczel
2002 John Wiley & Sons/Four Walls Eight
Windows 302pp 16.99/$28.00 hb
Zigoteau
Hi, Sid,
[original post]
> There has always been some fuss about Quantum Physics and Relativity being
> incompatible somehow. I was wondering if someone could shed some light on
> this for me. Is this still the case?
Yes, as long as you are talking about General Relativity (GR). Quantum
physics and special relativity have been reconciled for decades.
> I know that Entanglement was something
> that Relativists (if I might call them that) found rather displeasing.
Entanglement is not a concept in pure relativity theory, special or
general. It is a quantum concept. Quantum physics and GR have not yet
been satisfactorily combined. It is not clear how they mesh together.
> Is
> this the incompatibility that people refer to?
It's part of it.
> And has some manner of
> reconciliation been achieved,
No.
> or are the two theories still at odds with
> each other?
Not so much at odds, more at cross-purposes. Their domains of
applicability are so vastly different from one another that neither has
anything to say about problems where the other gives good predictions
(good = very closely in line with experiment).
> If I might impose on your
> generosity with one more question: Has the difficulty with Quantum
> Entanglement (which was discussed in the EPR paper) been resolved?
Which difficulty?
Quantum entanglement has been experimentally confirmed. This is not a
problem. We know how to analyze experiments and come up with a
prediction that corresponds to the observed result.
The confirmation of QE clashes with the intuition of many people. This
has not been resolved.
> That is,
> Relativists were averse to the "instantaneous communication" that could
> apparently take place between entangled electrons even when separated by
> large distances. Since this is now accepted as a very real phenomenon, I was
> wondering whether the Relativists have found some way of reconciling this
> idea with the principles of Relativity.
No, although when you say "communication", I hope you realize that it
is a funny sort of communication conveying no useful information. There
are lots of proposals for reconciliation, but nothing that everyone can
agree on.
Cheers,
Zigoteau.
Gregory L. Hansen
Schroedinger's equation:
H |psi> = E |psi>
In the Newtonian sense,
H = p^2 / 2m + V(x)
In the relativistic sense,
H = sqrt(m^2 c^4 + p^2 c^2) + V(x)
In either case, promote variables to operators and get your equation of
motion. There are some issues with doing that in the relativistic version
because of the square root, but Dirac figured it out about seventy years
ago, and that resulted in quantum electrodynamics which has been famously
successful.
In undergrad quantum mechanics the students are actually taught a
semi-classical theory. That is, the particles are treated quantum
mechanically, but the fields they interact with are not quantized. And
that's a good approximation for a lot of stuff. In a vaguely similar way,
gravity can be included semi-classically by doing quantum field theory on
a curved manifold, which is enough, e.g., to do some problems in black
hole thermodynamics, like Hawking radiation.
Quantized gravity is where everything goes splat-boofa. I don't know much
about that.
--
"Voice or no voice, the people can always be brought to the bidding of
the leaders. This is easy. All you have to do is to tell them they
are being attacked, and denounce the pacifists for lack of patriotism
and exposing the country to danger." -- Hermann Goering
Gregory L. Hansen
Siddhartha <gtg...@mail.gatech.edu> wrote:
>Thank you all for your helpful comments. If I might impose on your
>generosity with one more question: Has the difficulty with Quantum
>Entanglement (which was discussed in the EPR paper) been resolved? That is,
>Relativists were averse to the "instantaneous communication" that could
>apparently take place between entangled electrons even when separated by
>large distances. Since this is now accepted as a very real phenomenon, I was
>wondering whether the Relativists have found some way of reconciling this
>idea with the principles of Relativity.
>Again, I would be very grateful for any input on this.
Here's how I think of quantum entanglement.
Suppose a red ball and a blue ball are placed in an urn. One drawn at
random, sealed in a small box, and sent by express delivery to Stan in New
York, the other packed and sent to Vladimir in Moscow. When Vladimir
opens his package and sees the color of the ball, he immediately knows
which color ball Stan got. And vice versa when Stan opens his package.
There is no need to communicate, except knowing what the possible results
are.
When you turn that into a quantum mechanical problem, the wavefunction
will be something like
|psi> = (|Stan has red and Vladimir has blue>
+ |Stan has blue and Validimir has red>)/sqrt(2)
The quantum mechanical problem is no different from the classical problem
in the sense that when Vladimir knows which color he got, he immediately
knows which color Stan got because Stan will get whatever color Vladimir
doesn't. No communication required.
Selecting which possible result actually occurs is the million dollar
question (how much is the Nobel worth these days?), and there are about a
dozen interpretations of quantum mechanics with no real agreement. But
it's the same million dollar question that applies to a single observer.
--
"You're not as dumb as you look. Or sound. Or our best testing
indicates." -- Monty Burns to Homer Simpson
Uncle Al
>
> Hello.
> There has always been some fuss about Quantum Physics and Relativity being
> incompatible somehow.
GR has c=c, G=G, h=0
QFT has c=c, G=0, h=h
The two are utterly incompatible starting at founding hypotheses.
thermodynamics + Bekenstein bound = metric gravitation.
Go quantize sound in air.
> I was wondering if someone could shed some light on
> this for me. Is this still the case? I know that Entanglement was something
> that Relativists (if I might call them that) found rather displeasing. Is
> this the incompatibility that people refer to? And has some manner of
> reconciliation been achieved, or are the two theories still at odds with
> each other?
> I would very much appreciate some insight on this.
Entanglement and instantaneous wavefunction collapse into an
observable are irrelevant to relativity because neither can convey
information superluminally. Ditto phase velocity vs. group velocity.
Lots of classes of stuff can exceed lightspeed propagation, but none
of them can convey information at faster than lightspeed.
Google
"Einstein-Podolsky-Rosen" 35,800 hits
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Jan Panteltje
glha...@steel.ucs.indiana.edu (Gregory L. Hansen) wrote in
<dbgg93$mll$4...@rainier.uits.indiana.edu>:
>When you turn that into a quantum mechanical problem, the wavefunction
>will be something like
>
> |psi> = (|Stan has red and Vladimir has blue>
> + |Stan has blue and Validimir has red>)/sqrt(2)
>
>The quantum mechanical problem is no different from the classical problem
>in the sense that when Vladimir knows which color he got, he immediately
>knows which color Stan got because Stan will get whatever color Vladimir
>doesn't. No communication required.
>
>Selecting which possible result actually occurs is the million dollar
>question (how much is the Nobel worth these days?), and there are about a
>dozen interpretations of quantum mechanics with no real agreement. But
>it's the same million dollar question that applies to a single observer.
not arriving ;-)
Greysky
Resolved? There was never any ambiguity about how information is transferred
in a quantum system. The problems were located mainly in the brains of the
scientists observing quantum phenomena.
>That is,
> Relativists were averse to the "instantaneous communication" that could
> apparently take place between entangled electrons even when separated by
> large distances.
They still are 'averse' to non-local communications. But, the universe
doesn't give a whit about the personal hangups of humanity. With the final
admission of EPR phenomena into the main body of knowledge, we are now able
to come to two conclusions concerning both relativity and quantum physics.
First, is that QM takes precedence over Relativity. In any domain where the
two ideas directly butt heads, such as quantum gravity, quantum physics will
always give the most correct description of reality. And second, our
knowledge of QM is presently incomplete - as witnesed by such silly-assed
statements like, 'No meaningful information can transfer faster than light."
Such a statement presupposes concepts valid in general relativity will also
be meaningful when applied to purely quantum phenomena without a full
understanding of either theory as it applies to reality ( like quantum
gravity)
> Since this is now accepted as a very real phenomenon, I was
> wondering whether the Relativists have found some way of reconciling this
> idea with the principles of Relativity.
They ignore it. Which, from the point of view of einsteinian realtivity is
exactly what they should do.
> Again, I would be very grateful for any input on this.
You need to peruse my website to get a fresh take on old problems.
>
> Thanks
>
>
Greysky
www.allocations.cc
Learn how to build a FTL radio.
Eugene Stefanovich
More precisely, you should be talking about incompatibility between
Quantum physics and Einstein's special theory of relativity (STR).
Note that STR does not follow logically from
Relativity (= the principle of relativity stating that
all inertial frames of reference are equivalent) and the postulate
of the invariance of the speed of light. There is no
problem to reconcile quantum mechanics with the principle of
relativity and with the invariance of the speed of light.
This has been done by Wigner in 1939. However, there is a big
problem in reconciling QM with STR.
The main point of STR is that the time and position of an
event form components
of a 4-vector and transform according to Lorentz formulas
between different inertial observers. In STR, these transformations are
assumed to be universal and independent on the interactions in the
physical systems where the event occurs (note that this is an arbitrary
assumption which does not follow
from two major postulates of STR). This can be also formulated
in the language of 4D Minkowski space-time in which time and position
are coordinates with equal rights.
In QM, time and position do not have equal right. Position is an
observable
described by a triple of Hermitian operators. Time is a classical
parameter whose value does not depend on the state of observed physical
system. Thus time is not an observable, and there is no Hermitian
operator associated with time. This means that in QM there is no
symmetry between space and time characteristic to STR.
This is the fundamental contradiction between QM and STR.
This contradiction remains alive and well between QM and
the general theory of relativity (GTR). Sometimes it is called
"the problem of time".
I think the only way to avoid this contradiction
is to abandon the assuption of universality of Lorentz transformations.
This means we need to abandon the Minkowski space-time, the "manifest
covariance", and other attributes of STR. We should return back to
the basic principle of relativity and its combination with QM
a'la Wigner. Such a combination is free of contradictions and
is well-known for many years. It involves, basically, construction
of an unitary representation of the Poincare group in the Hilbert
space of considered physical system. The details can be found in
physics/0504062.
Eugene.
Eugene Stefanovich
Great explanation!
I totally agree. The only mystery is quantum indeterminism,
i.e., why Stan sometimes gets a red ball and sometimes the blue one.
However, in more than 100 years of quantum physics nobody has given
even a shred of explanation for quantum probabilities.
I doubt that such an explanation exists: quantum events are just
unpredictible. There is no point to seek the explanation.
That's the beauty of QM.
Eugene.
jollyro...@yahoo.com
The General Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial
dimensions.
The Specific Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial
dimensions at the rate of c in quantized units of the Planck length.
Relativistic, classical, and quantum mechanical phenomena, as well as
time itself, are emergent properties of this fundamental principle.
Newton's laws, the principle of Inertia, Einstein's postulates, and
the inherent wave-particle duality of QM may be explained with this
model.
A few years back, while surfing a towering wave on the Outer Banks of
North Carolina, a beautiful thought occurred to me. Suppose the wave I
was riding represented a coordinate in a dimension. Then although I
was approaching shore, I was not moving in this dimension.
The dimension itself was moving with me-I was surfing the dimension.
In a flash I saw that that is why photons never age-they are moving
along with the fourth dimension, and thus stationary relative to it.
In another flash I saw that that is why a photon's space-time
interval is represented by a null vector, or a 0, no matter how far it
travels. Indeed Einstein stated that an object's velocity through
space-time was always c-even stationary objects are traveling at the
velocity c through time! How could this be, were it not for a fourth
expanding dimension, which matter could surf as photons, giving rise to
our notion of time? And so it is that Moving Dimensions Theory was
born as the wave crested and crashed about me, thundering on down, as I
fought to remain surfing amidst the foam, facing the setting sun
silhouetting the Hatteras light.
And the waves kept on crashing that night. The nonlocal EPR
paradox/effect could be explained by the underlying nonlocality of an
expanding fourth dimension. The equivalence of mass and energy, the
wave-particle duality of all light and matter, the constant speed of
light-it could all be understood via a single principle of Moving
Dimensions Theory: the fourth dimension is expanding relative to the
three spatial dimensions. MDT reached back thousands of years to
resolve Zeno's paradox, then voyaged forth to ease Godel's,
Einstein's, Hawking's, and Penrose's concerns with the
paradoxical nature of a block universe, and arrived in the present,
quelling the oft exaggerated conflicts between relativity and quantum
mechanics, and pointing the way to the future by accounting for
time's arrow and entropy herself. At long last GR and QM could be
married in theory as harmoniously as they are in nature with Moving
Dimensions Theory's simple postulate:
The General Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial
dimensions.
The Specific Postulate of Moving Dimensions Theory:
The fourth dimension is expanding relative to the three spatial
dimensions at the rate of c in quantized units of the Planck length.
Classical physics, quantum mechanics, and relativity descend from this
simple postulate. Light, and thus all energy, is quantized as the
dimension which transports it expands in a quantized manner. Light
travels at a constant velocity in all frames because velocity is
measured relative to time which is measured relative to the light that
is transported by the fourth expanding dimension. Thus both
fundamental constants h and c emerge from the fundamental nature of the
expansion of the fourth dimension relative to the three spatial
dimensions. And thus MDT provides a simple, unifying postulate
accounting for the classical, relativistic, and quantum mechanical
properties of this universe.
Moving Dimensions Theory states: THE FOURTH DIMENSION IS EXPANDING AT A
RATE OF C RELATIVE TO THE THREE SPATIAL DIMENSIONS IN QUANTIZED UNITS
OF THE PLANCK LENGTH, GIVING RISE TO TIME AND ALL QUANTUM MECHANICAL
AND RELATIVISTIC PHENOMENA.
This explains the EPR effect, double slit experiment, and more.
Nonlocality in Quantum Mechanics: The Distribution of Localization
The nonlocal interactions and "spooky" action-at-a-distance
observed in quantum mechanics are simply explained by the nonlocality
of the fourth expanding dimension as accounted for in Moving Dimensions
Theory. Think about what it means for a dimension to expand. A point in
the dimension expands equally in all directions. That point is now
distributed throughout the other stationary dimensions, yet defines the
exact same place in that expanding dimension. In the case of an
expanding fourth dimension in the context of three stationary
dimensions, that point will appear as a spherical wavefront expanding
at the rate of c relative to the three stationary dimensions, in units
of the Planck length.
And so it is that photons do not age, as they stay at the exact same
place in the expanding fourth dimension. And so it is that two distant
particles can influence one-another instantaneously, as until they are
measured, aspects of their wave functions can exist in the exact same
place in time, though distributed throughout space.
This explains wave-particle duality and phenomona such as interference
patterns and action-at-a-distance. The component of the matter in the
expanding time dimension exhibits wave properties as it expands through
the three dimensions. The component of the matter in the spatial
dimensions exhibits particle-like behavior.
When a photon is measured (when it interacts with localized lab
equipment) it leaves the expanding fourth dimension and appears in one
single point in the spatial dimensions. This has been referred to as
the collapse of the wave function or an irreversible process.
Moving dimensions theory explains many other phenomena and will play a
key role in string theory and LQG.
More on the history of Moving Dimensions Theory:
Zigoteau
Hi, Eugene,
> More precisely, you should be talking about incompatibility between
> Quantum physics and Einstein's special theory of relativity (STR).
> Note that STR does not follow logically from
> Relativity (= the principle of relativity stating that
> all inertial frames of reference are equivalent) and the postulate
> of the invariance of the speed of light. There is no
> problem to reconcile quantum mechanics with the principle of
> relativity and with the invariance of the speed of light.
> This has been done by Wigner in 1939. However, there is a big
> problem in reconciling QM with STR.
I can't go along with you there.
> The main point of STR is that the time and position of an
> event form components
> of a 4-vector and transform according to Lorentz formulas
> between different inertial observers. In STR, these transformations are
> assumed to be universal and independent on the interactions in the
> physical systems where the event occurs (note that this is an arbitrary
> assumption which does not follow
> from two major postulates of STR). This can be also formulated
> in the language of 4D Minkowski space-time in which time and position
> are coordinates with equal rights.
> In QM, time and position do not have equal right.
Yes, they do.
> Position is an observable
> described by a triple of Hermitian operators.
Position of what, exactly? Modern relativistic quantum theories are
field theories. Are you still perhaps thinking in terms of the
Schroedinger wave equation, which is (a) not relativistic (b) cannot
handle reactions of particles, which are observed experimentally and
(c) normally quantizes only electrons, not photons.
> Time is a classical
> parameter whose value does not depend on the state of observed physical
> system. Thus time is not an observable, and there is no Hermitian
> operator associated with time. This means that in QM there is no
> symmetry between space and time characteristic to STR.
>
> This is the fundamental contradiction between QM and STR.
> This contradiction remains alive and well between QM and
> the general theory of relativity (GTR). Sometimes it is called
> "the problem of time".
>
> I think the only way to avoid this contradiction
> is to abandon the assuption of universality of Lorentz transformations.
> This means we need to abandon the Minkowski space-time, the "manifest
> covariance", and other attributes of STR. We should return back to
> the basic principle of relativity and its combination with QM
> a'la Wigner. Such a combination is free of contradictions and
> is well-known for many years. It involves, basically, construction
> of an unitary representation of the Poincare group in the Hilbert
> space of considered physical system. The details can be found in
> physics/0504062.
Cheers,
Zigoteau.
Eugene Stefanovich
Zigoteau wrote:
>>Position is an observable
>>described by a triple of Hermitian operators.
>
>
>
> Position of what, exactly?
Position of a particle or a hydrogen atom, or other system.
> Modern relativistic quantum theories are
> field theories. Are you still perhaps thinking in terms of the
> Schroedinger wave equation, which is (a) not relativistic (b) cannot
> handle reactions of particles, which are observed experimentally and
> (c) normally quantizes only electrons, not photons.
I have explained my approach in the book "Relativistic quantum
dynamics" physics/0504062. In RQD, dynamics and interaction of
particle systems is described by the Schroedinger equation with the
Hamiltonian that satisfies all relativistic requirements (commutation
relations of the Poincare group). The S-matrix predicted by this
Hamiltonian is exactly the same as the S-matrix of renormalized QED.
It describes all reactions, including those with particle creation
and annihilation. Both electrons and photons are treated as particles
(i.e., "quantized"). In contrast to QED, this approach also can
describe the time evolution of interacting particle systems.
Quantum fields are used there as formal mathematical constructs
(linear combinations of particle creation and annihilation operators)
that simplify the derivation of the Hamiltonian and the proof of its
relativistic properties.
Eugene.
Zigoteau
Hi, Eugene,
> > Modern relativistic quantum theories are
> > field theories. Are you still perhaps thinking in terms of the
> > Schroedinger wave equation, which is (a) not relativistic (b) cannot
> > handle reactions of particles, which are observed experimentally and
> > (c) normally quantizes only electrons, not photons.
>
> I have explained my approach in the book "Relativistic quantum
> dynamics" physics/0504062. In RQD, dynamics and interaction of
> particle systems is described by the Schroedinger equation with the
> Hamiltonian that satisfies all relativistic requirements (commutation
> relations of the Poincare group).
I had the feeling that when you were talking about QM, it had to be
something like this, and not the current mainstream version of QM. Why
should I bother reading your non-refereed paper if it is not as good as
existing alternatives?
> The S-matrix predicted by this
> Hamiltonian is exactly the same as the S-matrix of renormalized QED.
I am not sure what you are saying here. If that is the case, then your
theory is Lorentz-invariant, and it reconciles QM and SR, in which case
I do not understand why you told Sid that they could not be.
> It describes all reactions, including those with particle creation
> and annihilation. Both electrons and photons are treated as particles
> (i.e., "quantized"). In contrast to QED, this approach also can
> describe the time evolution of interacting particle systems.
> Quantum fields are used there as formal mathematical constructs
> (linear combinations of particle creation and annihilation operators)
> that simplify the derivation of the Hamiltonian and the proof of its
> relativistic properties.
I think you are saying that the only difficulties encountered in
combining QM and SR are with your particular flavor of QM. Mainstream
QM is totally compatible with SR.
Cheers,
Zigoteau.
Eugene Stefanovich
Hi, Zigoteau:
>>I have explained my approach in the book "Relativistic quantum
>>dynamics" physics/0504062. In RQD, dynamics and interaction of
>>particle systems is described by the Schroedinger equation with the
>>Hamiltonian that satisfies all relativistic requirements (commutation
>>relations of the Poincare group).
>
>
>
> I had the feeling that when you were talking about QM, it had to be
> something like this, and not the current mainstream version of QM.
On the contrary, I use the orthodox version of quantum mechanics in my
studies (the one with Hilbert space, wave functions, Hermitian operators
of observables, the Hamiltonian, etc.).
> Why
> should I bother reading your non-refereed paper if it is not as good as
> existing alternatives?
If you think that modern theoretical physics is a brilliant theory that
is logically consistent and explains every bit of experimental
observations, then, probably, you should not bother, unless you are
interested in a second opinion.
I have a number of questions/complaints to currently accepted theories
(such as special relativity, general relativity, Maxwell
electrodynamics, QED). I think, my approach has a better chance to
address these problems. I'll list here just a few of them.
Special relativity:
1. Universality (interaction-independence) of Lorentz transformations
does not follow from 2 postulates of special relativity. This is an
additional postulate. Currie-Jordan-Sudarshan theorem demonstrates
that this postulate (i.e., the manifest covariance of particles'
world-lines) is incompatible with the presence of interactions
between particles.
2. Alleged symmetry between space and time coordinates is not
compatible with the logical structure of quantum mechanics in which
time is a classical parameter and position is an observable
expressed by an Hermitian operator.
3. There are numerous experiments (Nimtz, Ranfagni, Chiao,..) that
demonstrate that in certain conditions (e.g., FTIR) light signals
can propagate faster than c.
General relativity:
4. A uniformly accelerated charge radiates. However, a charge placed
in a constant gravitational field does not radiate. Therefore, the
Einstein's equivalence principle (gravity = uniform acceleration)
doesn't hold for charged objects (see, e.g. gr-qc/9303025)
5. Point 2. above is valid also in general relativity. It is also
known as "the problem of time" which is (in my view) the main obstacle
for "quantizing gravity"
Classical (Maxwell) electrodynamics:
6. unresolved controversy about "radiation reaction" force,
pre-acceleration, etc.
7. violation of the 3rd Newton's law in magnetic interactions
between moving charges
8. unphysical "hidden momentum"
(see, e.g. E. Comay, Am. J. Phys. 64 (1996), 1028).
9. Interesting example of energy non-conservation due to
retarded propagation of interactions (physics/0201042).
QED:
10. Current theory is formulated in terms of non-observable
bare and virtual particles. RQD formulation in terms of physical
particles removes a number of contradictions (like non-trivial
vacuum, ultraviolet divergences) and allows to calculate the
time evolution of interacting systems
>>The S-matrix predicted by this
>>Hamiltonian is exactly the same as the S-matrix of renormalized QED.
>
>
>
> I am not sure what you are saying here. If that is the case, then your
> theory is Lorentz-invariant, and it reconciles QM and SR, in which case
> I do not understand why you told Sid that they could not be.
It is true that RQD is exactly equivalent to the renormalized QED at
the level of
S-matrix, and the S-matrix is invariant with respect to Lorentz
transformations. However, QED cannot describe the time evolution
of interacting systems (there is just no acceptable Hamiltonian in
QED). RQD can do that. Time-dependent observables in interacting
systems of particles do not transform (between moving frames of
reference) according to universal Lorentz
formulas of SR. RQD provides the correct transformation laws
dependent on interaction.
>>It describes all reactions, including those with particle creation
>>and annihilation. Both electrons and photons are treated as particles
>>(i.e., "quantized"). In contrast to QED, this approach also can
>>describe the time evolution of interacting particle systems.
>>Quantum fields are used there as formal mathematical constructs
>>(linear combinations of particle creation and annihilation operators)
>>that simplify the derivation of the Hamiltonian and the proof of its
>>relativistic properties.
>
>
>
> I think you are saying that the only difficulties encountered in
> combining QM and SR are with your particular flavor of QM. Mainstream
> QM is totally compatible with SR.
I can repeat that I am using the traditional mainstream version of QM,
and I am applying this version to relativistic systems in which
creation/annihilation of particles is allowed. In this way I obtain
a much improved variant of "quantum field theory" that is free of
numerous contradictions characteristic for QED. Check it
for yourself in physics/0504062.
Cheers.
Eugene.
mark...@yahoo.com
> Hello.
> There has always been some fuss about Quantum Physics and Relativity being
> incompatible somehow. I was wondering if someone could shed some light on
> this for me.
The former says time changes and is a process, the latter says it
nothing changes because it (actually, not *it* but *each*) is a
direction in spacetime. The discrepancy really comes to a head in the
"problem of time" of quantum gravity, the basic feature of "the problem
of time" being that the states all have frozen time and, literally,
nothing happens or changes.
The other major problem is that the boundary between past vs. not-past;
future vs. not-future has to be blurred in a quantum theory of gravity.
This is better explained by explaining what this boundary actually is.
In Newtonian physics, the past of an event is independent of its
position. It consists of all those events, everywhere, which lie at an
earlier snapshot of space; the future of the event consists of all
those events which lie on a later snapshot. The spacetime of Newton is
layered into a series of snapshots. The one remaining snapshot -- the
one the event lies on -- consists of all those events "simultaneous"
with it. It is 3-dimensional and is simultaneously the boundary of the
event's past and future.
In relativity there is no such layering of snapshots. Instead, the
past and future of an event depends on its location. The past of the
event is a solid sphere which contracts at light speed to the place and
time of the event. The future of the event is a solid sphere which
expands at light speed from the place and time of the event. There are
2 boundaries, and an entire region outside the two boundaries (the
absolute elsewhere) comprising the events which are neither before nor
after the event. The surface of the shrinking sphere is called the
past light cone of the event, the surface of the expanding sphere is
the future light cone of the event.
In quantum theory (of gravity) the actual definitions of the spheres is
blurred. So, since it's possible, in quantum theory, for two states to
be superposed on each other; it's possible here to have a state where
event A lies to the future of event B, a second state where it does
not, and to actually be in a 3rd state which is a superposition of
these other two states -- in which event B is NEITHER in the future of
A nor NOT in the future of A.
The punchline is that every known formulation of quantum theory
requires a clear-cut definition of what's the past and future of what
because ... quantum theory treats time as a process.
Check mate.
Eugene Stefanovich
A minor correction: everywhere you say "relativity" you should say
"Einstein's special (or general) theory of relativity".
There is another theory in which the principle of relativity
(= equivalence of all inertial observers) is respected and the speed
of light is observer-independent, however,
the transformations of observables are given by universal Lorentz
formulas only approximately and the space-time "unification"
does not play any role.
In this theory (RQD, physics/0504062), interactions propagate
instantaneously. So, if events A and B are related to each other
by interaction, then they occur simultaneously even if they are
far apart.
Interestingly, the interaction-dependence of boost transformations
implies that A and B remain simultaneous even in the moving reference
frame. So, the principle of causality is not violated: B never occurs
before A. This offers a solution to the "problem of time" you mentioned
above.
Eugene.
Zigoteau
Hi, Eugene,
> On the contrary, I use the orthodox version of quantum mechanics in my
> studies (the one with Hilbert space, wave functions, Hermitian operators
> of observables, the Hamiltonian, etc.).
> If you think that modern theoretical physics is a brilliant theory that
> is logically consistent and explains every bit of experimental
> observations, then, probably, you should not bother, unless you are
> interested in a second opinion.
You've pushed some of my buttons. I've downloaded your Arxiv paper but
am a bit daunted by its size.
> I have a number of questions/complaints to currently accepted theories
> (such as special relativity, general relativity, Maxwell
> electrodynamics, QED). I think, my approach has a better chance to
> address these problems. I'll list here just a few of them.
>
> Special relativity:
> 1. Universality (interaction-independence) of Lorentz transformations
> does not follow from 2 postulates of special relativity. This is an
> additional postulate. Currie-Jordan-Sudarshan theorem demonstrates
> that this postulate (i.e., the manifest covariance of particles'
> world-lines) is incompatible with the presence of interactions
> between particles.
Surely QM particles do not have world-lines in the same way as
Newtonian or Einsteinian dynamics? I must get up to speed with this
theorem. I take it that the reference is D. G. Currie, T. F. Jordan,
and E. C. G. Sudarshan, Rev. Mod. Phys. 35 (1963) 350. ?
> 2. Alleged symmetry between space and time coordinates is not
> compatible with the logical structure of quantum mechanics in which
> time is a classical parameter and position is an observable
> expressed by an Hermitian operator.
This is not something that has ever bothered me. I grant you that the
Fock-space formulation of QM does not treat time and space on the same
basis. However, this is the notation you are retaining. AFAICS the
criticism of the inequivalence of space and time does not apply to the
second-quantization notation of QFT. I do admit that
second-quantization notation lacks transparency. There are aspects
whose validity does not jump out of the page at me, and which I have
taken on trust.
> 3. There are numerous experiments (Nimtz, Ranfagni, Chiao,..) that
> demonstrate that in certain conditions (e.g., FTIR) light signals
> can propagate faster than c.
I have grave reservations about these experimental findings, and
believe that they have been misinterpreted.
> General relativity:
> 4. A uniformly accelerated charge radiates. However, a charge placed
> in a constant gravitational field does not radiate. Therefore, the
> Einstein's equivalence principle (gravity = uniform acceleration)
> doesn't hold for charged objects (see, e.g. gr-qc/9303025)
I think that you are being on the one hand to restrictive and on the
other too permissive about Einstein's equivalence principle. The
observations are consistent with the idea that the electromagnetic
vector potential due to a point charge is the solution to a certain
covariant wave equation. What more do you want?
> 5. Point 2. above is valid also in general relativity. It is also
> known as "the problem of time" which is (in my view) the main obstacle
> for "quantizing gravity"
>
> Classical (Maxwell) electrodynamics:
> 6. unresolved controversy about "radiation reaction" force,
> pre-acceleration, etc.
Surely this is a problem of the mathematical ill-conditioning of the
covariant wave equation with certain choices of boundary condition, and
not a criticism of the physics involved?
> 7. violation of the 3rd Newton's law in magnetic interactions
> between moving charges
Do you have a reference?
> 8. unphysical "hidden momentum"
> (see, e.g. E. Comay, Am. J. Phys. 64 (1996), 1028).
>
> 9. Interesting example of energy non-conservation due to
> retarded propagation of interactions (physics/0201042).
>
> QED:
> 10. Current theory is formulated in terms of non-observable
> bare and virtual particles. RQD formulation in terms of physical
> particles removes a number of contradictions (like non-trivial
> vacuum, ultraviolet divergences) and allows to calculate the
> time evolution of interacting systems
Divergences are of course problematic, but AFAICS that is a problem of
mathematical analysis. Divergences also occur in classical
electromagnetism. Show me how to pour out the bathwater without losing
the baby.
> It is true that RQD is exactly equivalent to the renormalized QED at
> the level of
> S-matrix, and the S-matrix is invariant with respect to Lorentz
> transformations. However, QED cannot describe the time evolution
> of interacting systems (there is just no acceptable Hamiltonian in
> QED).
I have seen any number of textbooks on QED that claim that something
like gamma.psi.A.psi is perfectly acceptable as an interaction
Hamiltonian. Admittedly I get lost in the details, and I know that
there are a lot of self-proclaimed experts on the subject who are
outright liars. I am uncomfortable with perturbation methods, but have
heard on many occasions that there is no aceptable alternative. I would
appreciate references to your claim.
> RQD can do that. Time-dependent observables in interacting
> systems of particles do not transform (between moving frames of
> reference) according to universal Lorentz
> formulas of SR. RQD provides the correct transformation laws
> dependent on interaction.
> I can repeat that I am using the traditional mainstream version of QM,
> and I am applying this version to relativistic systems in which
> creation/annihilation of particles is allowed. In this way I obtain
> a much improved variant of "quantum field theory" that is free of
> numerous contradictions characteristic for QED. Check it
> for yourself in physics/0504062.
469 pages!!! I will take it in little bits. Currie-Jordan-Sudarshan
sounds like a good place to start.
Cheers,
Zigoteau.
Zigoteau
I haven't gotten myself a copy of the Currie-Jordan-Sudarshan paper
yet, but there's plenty on the web that describes it in detail.
Interesting.
I would say that Einstein's relativity principle rates fairly highly on
the list of things that a satisfactory theory of physics must comply
with. The CJS result means that a valid equation of motion does not
have to be derivable from a Hamiltonian or Lagrangian. I must say that
I have never seen the cogency of the idea, although I am aware that
everyone does it on page 1. Thanks for making me aware of it.
Now on to the other 468 pages (groan).
Cheers,
Zigoteau
Eugene Stefanovich
Zigoteau wrote:
>
> Hi, Eugene,
>
> You've pushed some of my buttons. I've downloaded your Arxiv paper but
> am a bit daunted by its size.
There is a compressed version of the book published in
E.V. Stefanovich, "Is Minkowski Space-Time Compatible with Quantum
Mechanics?" Found. Phys. 32, 673-703 (2002). You can start from
there. You can get the PDF file from my web-site
www.geocities.com/meopemuk
>> 1. Universality (interaction-independence) of Lorentz transformations
>> does not follow from 2 postulates of special relativity. This is an
>> additional postulate. Currie-Jordan-Sudarshan theorem demonstrates
>> that this postulate (i.e., the manifest covariance of particles'
>> world-lines) is incompatible with the presence of interactions
>> between particles.
>
>
>
> Surely QM particles do not have world-lines in the same way as
> Newtonian or Einsteinian dynamics? I must get up to speed with this
> theorem. I take it that the reference is D. G. Currie, T. F. Jordan,
> and E. C. G. Sudarshan, Rev. Mod. Phys. 35 (1963) 350. ?
Yes, this is the reference. You can also find a (somewhat simplified)
proof of the CJS theorem in subsection 12.3.2 of my book.
You are right, this theorem refers to classical particles, so it
is not directly relevant to QM. However, classical trajectories
(wordlines) appear in the classical limit of QM, and if special
relativity and the manifest covariance have universal applicability
(as textbooks teach us), then they could be applied also in this
limit. CJS theorem tells us that this is impossible.
>> 2. Alleged symmetry between space and time coordinates is not
>> compatible with the logical structure of quantum mechanics in which
>> time is a classical parameter and position is an observable
>> expressed by an Hermitian operator.
>
>
>
> This is not something that has ever bothered me. I grant you that the
> Fock-space formulation of QM does not treat time and space on the same
> basis. However, this is the notation you are retaining. AFAICS the
> criticism of the inequivalence of space and time does not apply to the
> second-quantization notation of QFT. I do admit that
> second-quantization notation lacks transparency. There are aspects
> whose validity does not jump out of the page at me, and which I have
> taken on trust.
You are right that modern QFT adopts a description in terms of
quantum fields psi(x,t), where parameters x and t are formally
equivalent. However, this description has a number of problems, like
infinite renormalization, the inability to describe the time evolution
of interacting systems, etc. (see point 10. below). RQD provides an
alternative formulation of QED which is based on good old quantum
mechanical notions: Hilbert space, wave function, Hamiltonian, etc.
In this formulation, there is no space-time "unification", but the
principle of relativity remains valid.
>> 3. There are numerous experiments (Nimtz, Ranfagni, Chiao,..) that
>> demonstrate that in certain conditions (e.g., FTIR) light signals
>> can propagate faster than c.
>
>
>
> I have grave reservations about these experimental findings, and
> believe that they have been misinterpreted.
I respect your belief, but I think that these experiments found
true superluminal effects that cannot be reconciled with STR.
I believe that this will become more and more clear as more
similar experiments with greater resolution will be performed.
>>General relativity:
>> 4. A uniformly accelerated charge radiates. However, a charge placed
>> in a constant gravitational field does not radiate. Therefore, the
>> Einstein's equivalence principle (gravity = uniform acceleration)
>> doesn't hold for charged objects (see, e.g. gr-qc/9303025)
>
>
>
> I think that you are being on the one hand to restrictive and on the
> other too permissive about Einstein's equivalence principle. The
> observations are consistent with the idea that the electromagnetic
> vector potential due to a point charge is the solution to a certain
> covariant wave equation. What more do you want?
I am not talking about theory and equations here. I am just saying
that three fundamental statements (that can be independently verified
in experiments) contradict each other:
1. accelerated charge radiates.
2. a charge in a static gravity field does not radiate.
3. Einstein's equivalence principle (gravity = uniform acceleration)
Moreover, I don't buy the idea that Maxwell's electrodynamics has
been exhaustively confirmed by experiments. There are quite a few
holes. Some of them are listed below. I can also add a series
of experiments performed over the years by Peter Graneau and others.
They
seem to disprove the Biot-Savart force law between moving charges.
You can start from P. Graneau, N. Graneau "Electrodynamic force
law controversy", Phys. Rev. E 63 (2001), 058601 and
P. Graneau "Ampere tension in electric conductors" IEEE Trans.
on Magnetics, 20 (1984), 444 and retrieve further
references from there.
>>Classical (Maxwell) electrodynamics:
>> 6. unresolved controversy about "radiation reaction" force,
>> pre-acceleration, etc.
>
> Surely this is a problem of the mathematical ill-conditioning of the
> covariant wave equation with certain choices of boundary condition, and
> not a criticism of the physics involved?
This IS a criticism of the physics involved. The main point of my book
is that a lot of controversies in physics (including the "radiation
reaction" paradoxes) can be successfully solved if we abandon the idea
of fields. This includes both quantum fields in QED and Faraday-Maxwell
fields in classical electrodynamics. I propose to build a quantum
relativistic theory
of particles (electrons, protons, photons) that interact via
instantaneous action-at-a-distance. There are no fields in my approach.
This surely sounds like a radical proposal, and many people would say
that this has long be proven impossible, and that this contradicts
an enormous amount of knowledge accumulated in the last 150 years,
etc. Please hold your judgement until you read the book.
>
>
>
>> 7. violation of the 3rd Newton's law in magnetic interactions
>> between moving charges
>
>
>
> Do you have a reference?
E. Breitenberger "Magnetic interactions between charged particles",
Am. J. Phys. 36 (1968), 505.
>>QED:
>> 10. Current theory is formulated in terms of non-observable
>> bare and virtual particles. RQD formulation in terms of physical
>> particles removes a number of contradictions (like non-trivial
>> vacuum, ultraviolet divergences) and allows to calculate the
>> time evolution of interacting systems
>
>
>
> Divergences are of course problematic, but AFAICS that is a problem of
> mathematical analysis. Divergences also occur in classical
> electromagnetism. Show me how to pour out the bathwater without losing
> the baby.
QED without divergences is formulated in chapter 12 of my book.
>>It is true that RQD is exactly equivalent to the renormalized QED at
>>the level of
>>S-matrix, and the S-matrix is invariant with respect to Lorentz
>>transformations. However, QED cannot describe the time evolution
>>of interacting systems (there is just no acceptable Hamiltonian in
>>QED).
>
>
>
> I have seen any number of textbooks on QED that claim that something
> like gamma.psi.A.psi is perfectly acceptable as an interaction
> Hamiltonian. Admittedly I get lost in the details, and I know that
> there are a lot of self-proclaimed experts on the subject who are
> outright liars.
The main point of my approach to QED is that gamma.psi.A.psi is not
an acceptable interaction operator. Please read chapter 12 of the
book to see how the correct interaction in QED should be constructed.
If you are lost in the details, I am here to help you.
> I am uncomfortable with perturbation methods, but have
> heard on many occasions that there is no aceptable alternative. I would
> appreciate references to your claim.
I don't know any working alternative to the perturbation theory in QED.
Eugene.
Eugene Stefanovich
Zigoteau wrote:
> I would say that Einstein's relativity principle rates fairly highly on
> the list of things that a satisfactory theory of physics must comply
> with.
Please note that I am not questioning the validity of the Einstein's
relativity principle (all inertial frames of reference are equivalent).
This principle has been formulated centuries ago by Galileo, and proved
experimentally.
I am not questioning the invariance of the speed of light, which
is the second Einstein's postulate. This property of light simply
results from the masslessness of the photon in RQD.
I am questioning, though, the logic by which Einstein combined
these two postulates and arrived to the idea of exact, universal,
interaction-independent Lorentz transformations and to the idea
of space-time unification. In chapter 1 of my book I show that
there is a big hole in Einstein's logic. More careful analysis
shows that Lorentz transformations must contain interaction-dependent
corrections and that 4D Minkowski space-time is just an approximation.
People often place the equality sign between the principle of relativity
and the special theory of relativity. Please don't do this mistake.
Eugene.
Zigoteau
Hi Eugene,
Thanks for the detailed response, references, and the papers on your
website.
Of all the sci.physics contributors proposing "solutions" to the
difficulties and paradoxes of modern quantum field theory over the last
few years, I must say that you are the only one who has been able to
answer all my questions satisfactorily (Advocatus Diaboli: "So far, at
least").
I am particularly impressed by your approach via the CJS theorem, of
which I was previously unaware. I appreciate your argument about the
need for detailed correspondence between quantum and classical dynamics
in the macroscopic limit. All the textbooks I have on my shelf that
start on page 1 with a derivation of quantum equations of motion from a
Lagrangian variational principle. CJS means that they belong in my
garbage tin. I am not quite sure how you manage to square Lorentz
invariance with instantaneous interaction, but I look forward to
enlightenment.
Since I work 9-5 on problems considerably downstream of this, it is
going to take some time to digest your various papers, but I shall
persevere. I have fond memories of Schrödinger wave mechanics.
In your comments about Maxwellian electrodynamics, you say nothing
about the Wheeler and Feynman papers. I don't like the description
'retrocausal'. My take on the first one, Rev. Mod. Phys. 17 (1945) 157,
is that they set out a real-space solution to the standard equations
which for point particles is mathematically much better conditioned
than the usual one. Essentially, the Fourier transform is only
self-inverse for discontinuous functions if the value at the
discontinuity is the average of the two limits from above and below,
and only the Wheeler-Feynman form of the Greens function has this
property. Have you compared the CJS theorem to the classical trajectory
of a pair of charged point particles in a Minkowski space? If there is
a paradox, does it have to do with self-interaction?
The longest journey begins with the first step. Some quite short ones,
too. Here goes.
Cheers,
Zigoteau.
Eugene Stefanovich
thank you for your kind words.
Zigoteau wrote:
> I am not quite sure how you manage to square Lorentz
> invariance with instantaneous interaction, but I look forward to
> enlightenment.
The solution suggested by RQD is that boost (or Lorentz)
transformations depend on interactions. It should be no surprise
that time translations are generated by the Hamiltonian dependent on
interactions in the system. Then why everybody insist that Lorentz
transformations should be universal and interaction-independent?
In fact, if somebody assumes that time translations depend on
interactions and boost transformations don't, then he is in conflict
with Poincare commutation relations. Then his theory is not
relativistically invariant.
If the interaction dependence of boosts is properly taken into
account, then it appears that instantaneous interactions do not
violate causality.
> In your comments about Maxwellian electrodynamics, you say nothing
> about the Wheeler and Feynman papers. I don't like the description
> 'retrocausal'. My take on the first one, Rev. Mod. Phys. 17 (1945) 157,
> is that they set out a real-space solution to the standard equations
> which for point particles is mathematically much better conditioned
> than the usual one. Essentially, the Fourier transform is only
> self-inverse for discontinuous functions if the value at the
> discontinuity is the average of the two limits from above and below,
> and only the Wheeler-Feynman form of the Greens function has this
> property.
I have only superficial knowledge of the Wheeler-Feynman work.
I don't find their idea especially attractive. In my view,
the causality principle is a must, and future should not determine
the present under any circumstances.
> Have you compared the CJS theorem to the classical trajectory
> of a pair of charged point particles in a Minkowski space? If there is
> a paradox, does it have to do with self-interaction?
There is a qualitative discussion of the trajectories of two interacting
charges in subsection 12.3.5 of my book. A quantitative description is
much more difficult. In Maxwell's electrodynamics taking into account
the retardation of interactions become tricky, and the "radiation
reaction" problem remains unsolved. In the classical limit of RQD,
the part of interaction not involving the radiation of photons can be
solved relatively easily. The radiation part is non-trivial.
The RQD Hamiltonian provides "bremstrahlung" terms that describe
the emission of one or two photons in collisions of charged particles,
but in classical collisions the number of emitted "soft photons" is
huge. It is not yet clear how to describe them in classical terms.
Eugene.
Ben Rudiak-Gould
> Here's how I think of quantum entanglement.
>
> Suppose a red ball and a blue ball are placed in an urn. One drawn at
> random, sealed in a small box, and sent by express delivery to Stan in New
> York, the other packed and sent to Vladimir in Moscow. When Vladimir
> opens his package and sees the color of the ball, he immediately knows
> which color ball Stan got. And vice versa when Stan opens his package.
> There is no need to communicate, except knowing what the possible results
> are.
That's Bertlmann's socks.
The case of Bertlmann's socks is often cited. Dr. Bertlmann likes to wear
two socks of different colours. Which colour he will have on a given foot
on a given day is quite unpredictable. But when you see that the first
sock is pink you can already be sure that the second sock will not be
pink. Observation of the first, and experience of Bertlmann, gives
immediate information about the second. There is no accounting for the
tastes, but apart from that there is no mystery here. And is not the EPR
business just the same?
-- John Bell, _Bertlmann's Socks and Nature of Reality_
The EPR business is not the same, as he goes on to explain.
-- Ben
(who never wears socks of the same color, except on formal occasions)
Gregory L. Hansen
But the EPR business does reduce to the standard single-observer
measurement problem, such as "Which slit does the photon go through?"
Adding a second observer changes nothing. It's as though two observers
instead of just one were measuring which slit the photon goes through.
>
>
>-- Ben
>
>(who never wears socks of the same color, except on formal occasions)
I once went grocery shopping in an absent state of mind, and people seemed
to be looking at my funny. I realized later that I had a black shoe on
one foot and a white shoe on the other. My shoes were jumbled together
and I didn't pay much attention when I put them on.
--
"Let us learn to dream, gentlemen, then perhaps we shall find the
truth... But let us beware of publishing our dreams before they have been
put to the proof by the waking understanding." -- Friedrich August Kekulé
Eugene Stefanovich
Whether or not there is a mystery depends on your preferred
interpretation of quantum mechanics. More specifically, it depends on
whether you believe the wave function describes individual system or
an ensemble of systems. Let me explain this.
The standard Copenhagen interpretation claims that the wave function
describes each individual copy of the physical system. For example,
the couple of balls sent in packages is described by a wave function.
Thus before the packages were opened, the balls were in an undetermined
state. With 1/2 probability there was a blue ball in Moscow and a red
ball in New York. With 1/2 probability there was a red ball in Moscow
and a blue ball in New York. As soon as Vladimir (or Stan) opens his box
(measurement is made), the wave function collapses to one of the two
possible outcomes.
This creates an impression of instantaneous signalling: the ball in
Moscow decides to turn blue and sends a mysterious spooky signal to
its counterpart in New York: "turn red immediately!"
The result of the collapse is unpredictable. The Copenhagen
interpretation says that the reason of quantum uncertainties is
in uncotrollable interaction of the measuring apparatus with the
physical system. Before the measurement was done, the balls didn't
have certain properties. They acquired certain properties (color)
only after the measurement.
However, we can accept another interpretation of quantum mechanics
in which the paradox disappears. In this interpretation, the wave
function describes an ensemble of similarly prepared physical systems,
not individual system. Each individual system has well-defined
properties both before the measurement and after the measurement.
There is no wave function collapse initiated by the measurement
process. The randomness of measurement results is related to
the randomness in system preparation (not to the randomness of
the measurement collapse).
According to this interpretation, in the above example,
the balls in boxes have well-defined colors,
and opening the box does not produce any collapse. By opening the
box Vladimir just confirms that the ball there was red, and logically
concludes that Stan's ball is blue. Each particular copy of the
system (two balls) is in a well-defined state, no uncertainties.
Then when quantum uncertainties come into play? They are revealed
when you decide to repeat the experiment many times. If you send
packages many times, you'll notice that sometimes Vladimir gets
blue balls and sometimes he gets red balls. Why it is so?
Because the preparation of the system (which ball goes to which box)
is random. Somebody who sends the balls just doesn't care when
he writes addresses on the packages. And we cannot do anything about
it. It is a law of nature that when a quantum system is prepared,
its properties come out at random. There is no mystery in measurement.
There is a mystery in the system preparation.
You can repeat exactly the same arguments in the case of
Bertlmann's Socks.
If you accept the point of view that the wave function description
applies to the ensemble, and that the preparation of physical
systems contains a random element, then EPR paradox is not a
paradox at all. There is no collapse of the wave function,
there is no "spooky" action-at-a-distance. The only "mystery"
is why Nature behaves unpredictably when system states are prepared.
But this is the fundamental mystery of quantum mechanics.
It hasn't been solved in 100 years of quantum mechanics, and,
my guess is, it won't be solved ever.
Eugene.
mark...@yahoo.com
> A minor correction: everywhere you say "relativity" you should say
> "Einstein's special (or general) theory of relativity".
You mean: "Einstein, Hilbert, Poincare', Weyl, [insert about 100 other
names here]" theory of relativity.
> There is another theory in which the principle of relativity
> (= equivalence of all inertial observers) is respected and the speed
> of light is observer-independent
Then it's not "another".
>From the invariance of the light cone ALONE, Minkowski geometry can be
rigorously derived. In fact, the only solution to the functional
equations
R(r,e|r|/c)^2 - c^2 T(r,e|r|/c)^2
e = +/- 1; r in R^3; R: R^3 -> R^3; T: R -> R
is linear and expressible as a combination of
(a) a rescaling R(r,t) = kr; T(r,t) = kt
(b) a translation R(r,t) = r + a; T(r,t) = t + b
(c) 3-dimensional rotations
(d) Lorentz transformations.
A.A. Robb, in 1914, provided an axiomatization of Minkowski geometry
that required ONLY the temporal logic generated by the light cone and
defined everything from it (lengths, congruence, angles, orthogonality,
etc). In the 1960's this was extended to a formalization that required
as its sole primitives (a) the concept of a space-time point, and (b)
the light-cone relation, itself ((r1,t1) ~~ (r2,t2) <--> |r1-r2|^2 =
c^2 (t1-t2)^2). From this, and this alone, the entire structure of
Minkowski geometry can be defined ... including congruence, angles,
lengths, parallelism, etc.
> In this theory (RQD, physics/0504062), interactions propagate
> [sic] instantaneously.
Minor correction: there is no "instantaneously" if the above-mentioned
principle (invariance of light cone) holds. They'd be propagation of
actions along spacelike intervals.
In any case, that's not contravened by relativity. Tachyons come out
of the Wigner classification of the Poincare' group, too.
Eugene Stefanovich
mark...@yahoo.com wrote:
> Eugene Stefanovich wrote:
>
>>A minor correction: everywhere you say "relativity" you should say
>>"Einstein's special (or general) theory of relativity".
>
>
> You mean: "Einstein, Hilbert, Poincare', Weyl, [insert about 100 other
> names here]" theory of relativity.
That's right.
>>There is another theory in which the principle of relativity
>>(= equivalence of all inertial observers) is respected and the speed
>>of light is observer-independent
>
>
> Then it's not "another".
Yes it is "another" theory. Just use pure logic. Einstein's [+100 other
names] two postulates explicitly call by name just one type of physical
system - light (in his second postulates). Thus, formally, we are not
allowed
to extend automatically the conclusions drawn from his two postulates
(time dilation, length contraction, the ban on superluminal processes,
etc.) to other types of physical systems, e.g., systems of particles
interacting with each other. If you do make such an extension, you must
introduce at least one more postulate. For example, you can say that
space-time coordinates of all events transform in exactly the same
manner as events associated with light rays, i.e., they transform by
Lorentz formulas. This (or similar) assumption is always made in
discussions of special relativity. Without this assumption you cannot
claim that Lorentz transformations have universal applicability, and
you cannot introduce the Minkowski space-time unification.
In my approach, I do not introduce this third postulate. So, in spite
of respecting two Einstein's postulates, I get a different theory.
Predictions of this theory are exactly the same as predictions of STR
for light rays and events with non-interacting particles. However,
for interacting particles the predictions are different: boost
transformations in the presence of interactions are slightly different
from Lorentz formulas.
>
>>From the invariance of the light cone ALONE, Minkowski geometry can be
> rigorously derived. In fact, the only solution to the functional
> equations
> R(r,e|r|/c)^2 - c^2 T(r,e|r|/c)^2
> e = +/- 1; r in R^3; R: R^3 -> R^3; T: R -> R
> is linear and expressible as a combination of
> (a) a rescaling R(r,t) = kr; T(r,t) = kt
> (b) a translation R(r,t) = r + a; T(r,t) = t + b
> (c) 3-dimensional rotations
> (d) Lorentz transformations.
>
> A.A. Robb, in 1914, provided an axiomatization of Minkowski geometry
> that required ONLY the temporal logic generated by the light cone and
> defined everything from it (lengths, congruence, angles, orthogonality,
> etc). In the 1960's this was extended to a formalization that required
> as its sole primitives (a) the concept of a space-time point, and (b)
> the light-cone relation, itself ((r1,t1) ~~ (r2,t2) <--> |r1-r2|^2 =
> c^2 (t1-t2)^2). From this, and this alone, the entire structure of
> Minkowski geometry can be defined ... including congruence, angles,
> lengths, parallelism, etc.
I know a dosen or so papers in which similar "proofs" are presented.
All of them have one or two assumptions which limit their applicability
to non-interacting particles only. If you like, you can pick any such
proof and I'll show you where the logical mistake was made.
On the other hand, there is a powerful theorem
D. G. Currie, T. F. Jordan, and E. C. G. Sudarshan,
"Relativistic invariance and Hamiltonian theories of interacting
particles", Rev. Mod. Phys. 35 (1963), 350
which basically says that wordlines of interacting particles
cannot transform by Lorentz formulas.
>>In this theory (RQD, physics/0504062), interactions propagate
>>[sic] instantaneously.
>
>
> Minor correction: there is no "instantaneously" if the above-mentioned
> principle (invariance of light cone) holds. They'd be propagation of
> actions along spacelike intervals.
This is not true in RQD.
>
> In any case, that's not contravened by relativity. Tachyons come out
> of the Wigner classification of the Poincare' group, too.
Tachyons are indeed consistent with the Wigner classification, but
their existence contradicts the principle of causality. By a well-known
argument, if a signal is transmitted by faster-than-light particles,
then in a moving frame of reference the signal may be received before
it was sent. I think it is not acceptable.
In my approach, there are
no tachyons. Free particles do not move faster than light.
However, interactions between particles can (and do) propagate
faster than light (in fact, they propagate infinitely fast).
This does not contradict the above causality argument, because of
interaction-dependence of the boost transformations mentioned above.
I could write here more detailed arguments in support of my views,
but due to obvious space limitations I refer you to my book and
to the article
E. V. Stefanovich, "Is Minkowski space-time compatible with
quantum mechanics?" Found. Phys. 32 (2002), 673.
Eugene.