I read somewhere long ago that relativistic quantum mechanics has
limitations of applicability and i try to find the reference.
1- Grab this excerpt before someone realises it
might be more than an excerpt and removes it from
the server.
http://lesswrong.com/lw/pk/feynman_paths/
2- Buy or borrow a copy of the book it came from.
http://en.wikipedia.org/wiki/QED_(book)
3-Read these at least once:
http://en.wikipedia.org/wiki/Path_integral_formulation
http://nobelprize.org/nobel_prizes/physics/articles/ekspong/index.html
http://nobelprize.org/nobel_prizes/physics/laureates/1965/feynman-lecture.html
4- Rephrase your question. :-)
Kind regards,
Sue...
There is not consistent relativistic quantum mechanics and probably
cannot have any.
Currently there is a relativistic quantum field theory, which is not
compatible with non-relativistic quantum mechanics and that only can
study certain simple relativistic phenomena as free particle scattering.
I can only wonder at the opinions you got from my colleagues.
(Relativistic) Quantum Electrodynamics, for which three people
received the Nobel prize, is the most precise predictor of certain
physical constants in the history of physics. It is applicable to the
interaction of electrons and photons, principally, but it a miracle of
modern physics.
Fortunately, it is beyond the reach of the cranks who post in
sci.physics.rellativity.
Uncle Ben
I will try to rephrase after you tty (please) to explain what all
these have to do with my question and your answer. Are you afraid or
you do not know?
>
> Kind regards,
>
> Sue...
I think Relativistic) Quantum Electrodynamics makes no predictions of
values but of probabilities of values.
If I say that the probability of you being 6' or taller is 0.6, do I
say anything about the specific value of your height?
Maybe it is a stupid question, I don't know. I keep hearing
conflicting views and aphorisms thrown from one side to the other.
Once I read if I recall correctly that Relativistic) Quantum
Electrodynamics is not compatible with orthodox QM.
Your response to Uncle_Ben is erroneous.
That will be clearer if you actually work
through the Snell's law derivation offered
in the first link.
That purpose of the exercise is so you
can see how real quantities represented
as a probability, loose none of their
~realness~.
Fortunately, the inverse does not apply.
Imaginary quantities *can* gain some
~realness~ (Gaussian distribution)
The gaming house and Lloyd's of London
~really~ wins every bet in the long haul.
So QED is not quite playing with a two
headed coin, but it might be 1.99 heads
on select applications.
Sue...
>
>
>
> > Kind regards,
>
> > Sue...
>
>
QED is compatible with SR. Ordinary QM is not, but it is very useful
in the laboratory frame of reference if your laboratory is not the
famous Large Hadron Collider.
:-)
QED predicts the value of the atomic "fine structure constant" to a
very high precision -- probably higher precision than that we know of
the speed of light. Where probability comes in is in the behavior of
very small systems, such as the hydrogen. In the hydrogen atom, the
electron is not orbiting the nucleus lika a planet orbits the sun. It
is a diffuse cloud of possible positions.
QM is a strange and wonderful thing: An electron can go through two
slits at once and interfere with itself on the other side! Nobody
knows why QM works, but it does.
Are you a physics student? Are you here because you are studying
relativity? If so, read my post titled "Correction: Orientation for
beginners".
It is under the nickname "Uncle Ben'" I was "greenba" for a day
because of Google foulups.
Uncle Ben
Yes - it called Quantum Field Theory and is the most exactly verified
physical theory in existence.
>
> I read somewhere long ago that relativistic quantum mechanics has
> limitations of applicability and i try to find the reference.
>
Yes it does have limitations. It can only be used as a theory of gravity if
you have a cut-off about the plank scale. Beyond that no one knows. See
for example:
http://arxiv.org/abs/gr-qc/9512024
Thanks
Bill
Yes and no. QM is a weird and wonderful thing, and the appearance of
probabilities at its foundation is part of that weirdness. However whether
it is an essential part of QM or simply a by product of other axioms is open
to debate (look up Quantum Decoherence).
>If I say that the probability of you being 6' or taller is 0.6, do I
> say anything about the specific value of your height?
No. But then again exact values are unverifiable since every method of
measurement has uncertainties.
> Maybe it is a stupid question, I don't know.
It's not a stupid question. However understanding the answer will require
you, like many things in science, to abandon common sense views. One of
those common sense views is that things can be known with exactitude. This
is something we bandy about using everyday language. However it falls to
pieces when analysed exactly. Another example is the surface of water. We
think of water as having a surface where air ends and water begins. But on
close examination we find that is not true. As we get closer to what we
call a waters surface we find the water vapour in the air increases and as
we move below the water surface we find air dissolved in the water. There
is no actual identifiable surface where water begins and air ends. You will
find an excellent explanation of this sort of stuff in the first few
chapters of Feynmans classic Lectures on Physics. Read it, devour it, and
learn how a physicist thinks about the world.
> I keep hearing
> conflicting views and aphorisms thrown from one side to the other.
Different views exist as to what QM means. That's because a number of views
of what the axioms of QM are saying are consistent with those axioms. Most
theories are not like that - QM is a bit unique in that regard. It not that
other theories don't have different views of its axioms - its just that
there is no commonly agreed one in QM. For example it is not well known
(but in fact true) that electromagnetism can be formulated without the need
of fields (Fenyman and Wheeler did that in a classic paper). So in a
certain sense fields are redundant. Yet most physicists would not view it
that way and treat fields as quite real.
> Once I read if I recall correctly that Relativistic) Quantum
> Electrodynamics is not compatible with orthodox QM.
It is totally compatible.
>
>> Fortunately, it is beyond the reach of the cranks who post in
> > sci.physics.rellativity.
Fortunately however not everyone who posts here is a crank. Uncle Ben, PD,
and Tom Roberts for example most definitely are not. And they are not the
only ones.
Thanks
Bill
Hmmmm... Perhaps I should reconsider all
the arguments they have presented against
relativity.
Sue...
>
> Thanks
> Bill
Reading Feynman emphasizing the difference between science and math or
philosophy is always a delight.
>> I keep hearing
>> conflicting views and aphorisms thrown from one side to the other.
>
> Different views exist as to what QM means. That's because a number of
> views of what the axioms of QM are saying are consistent with those
> axioms. Most theories are not like that - QM is a bit unique in that
> regard. It not that other theories don't have different views of its
> axioms - its just that there is no commonly agreed one in QM. For
> example it is not well known (but in fact true) that electromagnetism
> can be formulated without the need of fields (Fenyman and Wheeler did
> that in a classic paper). So in a certain sense fields are redundant.
> Yet most physicists would not view it that way and treat fields as quite
> real.
Yes, fields are redundant, and valid only in some limit, but neither
Wheeler nor Feynman proved that.
First they only worked classical theory.
Second, their theory is not so consistent as it seems in a first look,
troubles with self-action and time-symmetry remain in their approach.
Third it lacks a useful Hamiltonian formulation. I know no statistical
mechanics build over their electrodynamics for instance.
Four, it does not really work in quantum theory. For instance, Feynman
original QED formulation used the Dirac equation like a wavefunction
equation. However, the Dirac equation is an identity for the Dirac field,
by reasons of consistency, in modern quantum field theory .
>> Once I read if I recall correctly that Relativistic) Quantum
>> Electrodynamics is not compatible with orthodox QM.
>
> It is totally compatible.
As was remarked before they are not. Some differences between QM and QFT
are reported in QFT textbooks. For instance Mandl and Shaw textbook
reports that one of main differences is that x is an observable in QM but
an parameter in QFT.
http://www.amazon.com/Quantum-Field-Theory-F-Mandl/dp/0471105090
I have given some details about position operators and other limitations
of relativistic quantum field theory in
http://groups.google.com/group/sci.physics.research/msg/2d122982d6771c1d
http://groups.google.com/group/sci.physics.research/msg/a13703cc6e13729b
There is many more differences. It is safe to say both are different, but
related, theories. Just after formulation of QED Dirac remarked this
disjoint character of QED when wrote, in his "Mathematical Foundations of
Quantum Theory", that:
"Most physicists are very satisfied with this situation. They
argue that if one has rules for doing calculations and the results
agree with observation, that is all that one requires. But it is not
all that one requires. One requires a single comprehensive theory
applying to all physical phenomena. Not one theory for dealing with
non-relativistic effects and a separate disjoint theory for dealing
with certain relativistic effects. [...] For these reasons I find the
present quantum electrodynamics quite unsatisfactory. One ought not to
be complacent about its faults [...] One must seek a new relativistic
quantum mechanics and one's prime concern must be to base it on
sound mathematics.»
Many people has searched a new relativistic quantum mechanics, but as was
said in an early message cannot possible have a "consistent relativistic
quantum mechanics".
> "Joe Avery" <joe_ave...@yahoo.com> wrote in message
>
news:ff551c18-90d5-4c5b...@d38g2000prn.googlegroups.com...
>> Are STR and QM already merged in a single theory that produces the sum
>> of the predictions of the two theories and more?
>
> Yes - it called Quantum Field Theory and is the most exactly verified
> physical theory in existence.
Bill, you are repeating the same mistakes forever.
Quantum field theory is not a relativistic quantum theory. Relativistic
quantum field theory is a "separate disjoint theory" that cannot explain
"non-relativistic observations" as Dirac remarked (see Dirac quote in my
other message).
There exists one known attempt to unify STR and QM named the Stuckelberg,
Horwitz, & Piron theory:
http://en.wikipedia.org/wiki/Relativistic_dynamics
I gave an introduction to the classical version of this theory in my blog
http://canonicalscience.blogspot.com/2007/08/relativistic-lagrangian-and-
limitations_20.html
The quantum version follows from using the usual correspondence rule
classical function --> operator
and the resulting wave equation is
i hbar (& Psi / & tau) = K Psi
Here Psi is a wavefunction in a generalized 4N space. Tau is a new
concept of time not available in SR, GR, or in relativistic quantum field
theory. Tau is *not* proper time but a many body time. And K is the
quantum operator corresponds to the classical Hamiltonian K writen above
in my blog.
>> I read somewhere long ago that relativistic quantum mechanics has
>> limitations of applicability and i try to find the reference.
>>
>>
> Yes it does have limitations. It can only be used as a theory of gravity
> if you have a cut-off about the plank scale. Beyond that no one knows.
> See for example:
> http://arxiv.org/abs/gr-qc/9512024
How the author recognizes at the start of the preprint, GR is
incompatible with QM. Unfortunately, the author seems to forget this in
subsequent development.
If one expands GR as a perturbation over flat background, the resulting
theory is *not* a field theory (effective or not). Essentially because
the flat background is not the real spacetime but as Strauman calls "a
kind of unobservable aether".
As a consequence, causality constrainst of field theory (effective or
not) cannot be applied to (30). There is a beatiful but short comment
about the limitation of this perturbative quantization method of GR in
Wald textbook.
Moreover, the h_ab 'field' in (30) has not physical meaning in GR, and
there is not associated graviton concept was physically admisible. In
fact, there is not valid GR concept of energy associated to those
'gravitons'.
There is many other difficulties that the author is ignoring in that
preprint.
He writes:
"When a field theorist describes the ingredients of general
relativity, it is interesting to see how much the description differs
from that of conventional relativists."
This is a clear statement of the usual confusion between field theory
(over flat background) and general relativity, which has propagated to
quantum gravity research (e.g. string versus loops war).
There is many invalid treatments in literature, including invalid
'proofs' by Deser, Thirring, and others that general relativity is
equivalent to a spin-2 field theory. Feynman well-known statement (done
in his Caltech lecture in gravity) that general relativity has "both a
geometrical and a non-geometrical formulation" is wrong. Just as are MTW
claims about the subject.
A general discussion of why General relativity is incompatible with field
theory, and the usual proofs are incorrect, is given in my last work
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/20090416.html
http://www.canonicalscience.org/en/publicationzone/drafts.html
In this work I also give objections to the Stuckelberg theory.
An interesting work discussing the confusion among general relativists
and field theoreticians is "From Gravitons to Gravity: Myths and Reality"
http://arxiv.org/abs/gr-qc/0409089
Regards
> Bill Hobba wrote on Wed, 17 Jun 2009 05:03:36 +0000:
>
>> "Joe Avery" <joe_ave...@yahoo.com> wrote in message
>>
>
news:ff551c18-90d5-4c5b...@d38g2000prn.googlegroups.com...
>>> Are STR and QM already merged in a single theory that produces the
>>> sum of the predictions of the two theories and more?
>>
>> Yes - it called Quantum Field Theory and is the most exactly verified
>> physical theory in existence.
>
> Bill, you are repeating the same mistakes forever.
>
> Quantum field theory is not a relativistic quantum theory.
Typo: "Quantum field theory is not a relativistic quantum mechanics."
Hmmm. While correct in technical detail, this misses the main point:
there is indeed a single theory that combines SR and QM (speaking a bit
loosely, as I explain below).
>>> Once I read if I recall correctly that Relativistic) Quantum
>>> Electrodynamics is not compatible with orthodox QM.
>> It is totally compatible.
>
> As was remarked before they are not. Some differences between QM and QFT
> are reported in QFT textbooks. For instance Mandl and Shaw textbook
> reports that one of main differences is that x is an observable in QM but
> an parameter in QFT.
You missed a PUN there; perhaps Mandl and Shaw did also.
In QM, the observable "x" means the POSITION OF A
PARTICLE, whereas in QFT "x" is a COORDINATE ON THE
MANIFOLD. There is no reason to expect any sort of
"correspondence" between quantities of such different
character. The appropriate correspondence is to the
coordinate in QM, and that is not an operator. The
historical conventions that make it usual to use the
same symbol for such different quantities are DIFFERENT.
But don't be fooled -- the symbol used is IRRELEVANT.
That said, it is indeed difficult to construct the
position operator of QM from the fields of QFT, and I
know of no rigorous treatment.
QED is indeed "compatible" with QM, in that for observations within
their common domain they predict outcomes identical to within
measurement resolutions. That is, they are EXPERIMENTALLY compatible.
As I have remarked before, it is subtle to compare different theories of
physics, with different domains of applicability. In general, they will
describe a given phenomenon or measurement in completely different
terms, and there may well be no rigorous mathematical limit that takes
one into the other. This is not a problem -- what is required is that
the experiments that support and confirm the (older) theory with the
smaller domain (here QM) not refute the (newer) theory with the larger
domain (here QED).
It would be ludicrous to require the first attempt at
a theory to restrict the form of all following theories
by requiring earlier theories to be rigorous limits of
later ones. No PHYSICIST does so.
Sometimes there is such a limit. For example, there is a clear and
obvious limit, v->0, in which relativistic mechanics goes rigorously
into Newtonian mechanics (to first order in v/c, but for typical
applications v/c < 10^-6 so first order is sufficient to be better than
experimental resolutions).
As you have said before, there is no RIGOROUS limit from GR to Newtonian
gravitation, because you insist on an EXACTLY flat spatial submanifold.
No matter, because there is an appropriate limit with an approximately
flat spatial submanifold which is flat to far better than measurement
accuracy (the deviation from flatness of the spatial metric components
is the same order in \phi as g_tt, but the effects of spatial
non-flatness enter in higher order into the dynamics and remain below
measurement accuracy).
The relationship between QED and QM is similar -- AFAIK there is no
RIGOROUS limit that takes QED into QM. But no matter, because for
measurements within their common domain they make predictions that are
experimentally indistinguishable.
Don't miss the forest for the trees. The modern theories of physics (GR,
QED) include the domains of the older corresponding theories (NM, QM).
Necessarily so.
Tom Roberts
Hmmmm. Strictly speaking you may be correct. QFT is the framework that
contains relativistic quantum theories. The full detail can be found in
chapter 3 of Zee - QFT in a Nutshell. As he makes clear 'note that a (0+1)
dimensional quantum field theory is just quantum mechanics.' - page 18
Chapter 3. The thing is when spatial dimensions are added one gets a
relativistic theory. In fact as Zee puts it (Chapter 3 - page 17) 'It is
interesting that Lornetz invariance with c playing the role of the speed of
light emerges naturally'. But that changes nothing essential about my
statement. We have a theory where they are merged and it is the most
exactly verified physical theory in existence. The fact it also contains
within it bog standard QM is not really germane.
Thanks
Bill
> "Juan R. González-Álvarez" <juanR...@canonicalscience.com> wrote in
> message news:pan.2009.06...@canonicalscience.com...
>> Bill Hobba wrote on Wed, 17 Jun 2009 05:03:36 +0000:
>>
>>> "Joe Avery" <joe_ave...@yahoo.com> wrote in message
>>>
>>
news:ff551c18-90d5-4c5b...@d38g2000prn.googlegroups.com...
>>>> Are STR and QM already merged in a single theory that produces the
>>>> sum of the predictions of the two theories and more?
>>>
>>> Yes - it called Quantum Field Theory and is the most exactly verified
>>> physical theory in existence.
>>
>> Bill, you are repeating the same mistakes forever.
>>
>> Quantum field theory is not a relativistic quantum theory.
>
> Hmmmm. Strictly speaking you may be correct. QFT is the framework that
> contains relativistic quantum theories.
Hmmm. As said in a subsequent message (before your reply) that was a typo.
I want to say: "Quantum field theory is not a relativistic quantum
mechanics."
It is well-known now that QFT is not the framework that contains
relativistic quantum theories, but QFT is a subset of relativistic
quantum theories, which are not mechanical.
> The full detail can be found in
> chapter 3 of Zee - QFT in a Nutshell. As he makes clear 'note that a
> (0+1) dimensional quantum field theory is just quantum mechanics.' -
> page 18 Chapter 3. The thing is when spatial dimensions are added one
> gets a relativistic theory. In fact as Zee puts it (Chapter 3 - page
> 17) 'It is interesting that Lornetz invariance with c playing the role
> of the speed of light emerges naturally'. But that changes nothing
> essential about my statement. We have a theory where they are merged
> and it is the most exactly verified physical theory in existence. The
> fact it also contains within it bog standard QM is not really germane.
Of course, Zee, in his superfitial account of QFT is ignoring the details
given in the references and messages I submited and are archived in
sci.physics.research, just as you now sniped part of my message,
including the links :-D
Regards.
> Juan R. González-Álvarez wrote:
>> Bill Hobba wrote on Wed, 17 Jun 2009 05:03:36 +0000:
>>> "Joe Avery" <joe_ave...@yahoo.com> wrote
>>>> Are STR and QM already merged in a single theory that produces the
>>>> sum of the predictions of the two theories and more?
>>> Yes - it called Quantum Field Theory and is the most exactly verified
>>> physical theory in existence.
>>
>> Quantum field theory is not a relativistic quantum [mechanics].
>> Relativistic quantum field theory is a "separate disjoint theory" that
>> cannot explain "non-relativistic observations" as Dirac remarked (see
>> Dirac quote in my other message).
>
> Hmmm. While correct in technical detail, this misses the main point:
> there is indeed a single theory that combines SR and QM (speaking a bit
> loosely, as I explain below).
Unfortunately this misses the main point: there is not consistent
unification of SR with QM. People who developed R-QFT knew that when
*abandoned* the posibility to build a RQM.
Unfortunately, you sniped all references, links to Wikipedia containing
more references (including two recent books)...
Evidently if you close the eyes you may not see your home in fire, but
this may be a stupid thing to do :-D
>>>> Once I read if I recall correctly that Relativistic) Quantum
>>>> Electrodynamics is not compatible with orthodox QM.
>>> It is totally compatible.
>>
>> As was remarked before they are not. Some differences between QM and
>> QFT are reported in QFT textbooks. For instance Mandl and Shaw textbook
>> reports that one of main differences is that x is an observable in QM
>> but an parameter in QFT.
>
> You missed a PUN there; perhaps Mandl and Shaw did also. In QM,
the
> observable "x" means the POSITION OF A PARTICLE, whereas in QFT
"x" is
> a COORDINATE ON THE MANIFOLD.
Thanks by the laugh.
(...)
> QED is indeed "compatible" with QM, in that for observations within
> their common domain they predict outcomes identical to within
> measurement resolutions. That is, they are EXPERIMENTALLY compatible.
This is another complete misinterpretation of the whole issue.
(...)
> As you have said before, there is no RIGOROUS limit from GR to Newtonian
> gravitation, because you insist on an EXACTLY flat spatial submanifold.
> No matter, because there is an appropriate limit with an approximately
> flat spatial submanifold which is flat to far better than measurement
> accuracy (the deviation from flatness of the spatial metric components
> is the same order in \phi as g_tt, but the effects of spatial
> non-flatness enter in higher order into the dynamics and remain below
> measurement accuracy).
You are right that GR cannot give a nonzero gravitational acceleration
plus flat spatial metrics gamma_ij in any limit... and that is all you
are right here.
I want just to emphasize that I have showed that the field theory of
gravity wirked by Feynman and others, the recent relational theory of
gravity, and Stefanovich 'dressed' approach *give* a nonzero acceleration
*plus* the correct spatial geometry all at once. Still those three
theories also fail to reproduce the Newtonian limit:
http://www.canonicalscience.org/en/publicationzone/
canonicalsciencetoday/20090416.html
http://www.canonicalscience.org/en/publicationzone/drafts.html
Tom you are being again exposed in public, but this is what happen when
you pretend to review theories/works you *never* read [#].
(...)
[#] You can continue to ignore my good advice to not comment on theories/
works you never studied before, but then you will be puting you in
the company of many crackpots in this forum, including those that
refusing to read a textbook in relativity pretended to show us that
the Hamiltonian of SR was *their* nonsense H = -mc(1 - v^2/c^2).
Philosophy of Quantum Physics No BS | pt 2 EPR
http://fr.youtube.com/watch?v=F8PjWddmM2s&feature=related
--
Ahmed Ouahi, Architect
Best Regards!
"Juan R. Gonz�lez-�lvarez" <juanR...@canonicalscience.com> kirjoitti
viestiss�:pan.2009.06...@canonicalscience.com...
I appreciate you responding here but it is clear you have a very
superficial connection with the subject as it is evident from your
statements. I am a psychologist by formal training but I have studied
a little of physics (you can never study enough) in my spare time. You
seem to miss the deeper issues involved in a unification of Relativity
with Quantum Mechanics. The issues with unification do not arise from
the unclear axiomatic foundation of QM as you claim but from the
results of experiments. For example, relativity of entanglement cannot
be formally established in such a unification. Take a foliation where
spacelike hypersurfaces define orthogonal timelike vectors with
different time parameters assigned to different hyperplanes of
simultaneity. A wave collapse in one foliation is not necessarily a
wave collapse in another foliation. This is a serious issue.
Non abelian gauge theories involve strongly delocalized field
variables and their quantization requires either a non-regular
representation of canonical commutation relation or a violation of
positivity of their vacuum correlation functions. In either case,
there is no quantum mechanical interpretation of such variables and
these theories have a disjoint character, as Alvarez kindly pointed
out.
This is my take, based on my readings. It appears that a unification
of relativity and quantum mechanics does not exist at all and it is
even impossible but there are all sorts of cranks around pushing their
own agenda or misconceptions. A crank is not necessarily a non-
physicist. There are many cranks that reached high recognition in
physics for strange reasons. There are cranks who teach in high
positions. I say there are cranks all over the place. I suspect out of
10 physicists, 9 are cranks. This is what psychology tells me. the
strongest indication of a crank physicists is one who appears to be
extremely confident of what he know. {Pessimistic meta-induction is
the strongest argument ever against confidence in physical theories.
They are all destined to evaporate at some point in time. Remember
that.
Joe