locality, causality and Bell's theorem
Oh No
sacrifice at least one of qm, locality, causality and realism. In
practice, qm is overwhelming supported by experiment. Physics makes no
sense if we sacrifice realism, so it seems we have a problem with either
locality or causality.
In fact I do not think we have to sacrifice either, but we do have to be
careful about how we state locality and causality, and we certainly have
to dismiss naive statements based on an assumption of background
spacetime. Bell's theorem should not lead us to reject locality or, but
we should reject the notion of a fundamental spacetime.
Locality (proposed definition)
-----------------------------------------
A particle is in contact with another when it interacts with it. A
particle can be considered to be in a neighbourhood of another if, in
principle, a photons may pass from one to the other and one may return
within a small proper time period.
This Cartesian definition reflects the locality condition in qed. The
entangled particles in Bell's theorem are separated, in accordance with
our intuitive ideas.
Causality (proposed definition)
-------------------------------------------
There is a causal relation between two measurements if the outcome of
one measurement alters the probability of the outcome the other.
By this definition there is no causal relationship between the
measurements of the entangled particles in Bell's theorem. The
measurement of one particle does not alter the probabilities for the
results of measurement of the other. Only when the two experimenters get
together and compare results do they find a correlation. This can only
be done at a later time, showing that the correlation is causally
related to the measurements, but not that the measurements are causally
related to each other.
Conclusion
----------------
In my view the resolution of Bell's theorem is not that we must reject
realism, locality or causality, but rather we must recognise that space-
time is an emergent concept. The notion of spacetime separation can only
be said to exist when spacetime exists, that is to say *after* the
required physical processes have taken place for its emergence. This has
not happened at the time of the measurements, but it has happened when
the experimenters get together and establish the correlation. We cannot
say that the outcome of one measurement has effected the other, because
this presupposes the existence of spacetime, and puts the logical cart
before the horse. The measurement results can only be correlated in
terms of a spacetime structure which does not exist at the time of the
measurements. The structure of spacetime emerges from the measurement
results, not the other way about.
Regards
--
Charles Francis
moderator sci.physics.foundations.
charles (dot) e (dot) h (dot) francis (at) googlemail.com (remove spaces and
braces)
N:dlzc D:aol T:com (dlzc)
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
....
> Locality (proposed definition)
> -----------------------------------------
> A particle is in contact with another when it
> interacts with it. A particle can be considered
> to be in a neighbourhood of another if, in
> principle, a photons may pass from one to the
> other and one may return within a small proper
> time period.
This invokes spacetime. Comes with "time and c".
....
> Conclusion
> ----------------
> In my view the resolution of Bell's theorem is
> not that we must reject realism, locality or
> causality, but rather we must recognise that
> space-time is an emergent concept.
.... rather than "concept", how about "property". A property of
all systems in which conservation laws hold, and a non-orthogonal
property shared by multiple systems that still derive mass /
length / time from the superset of all systems.
> The notion of spacetime separation can only
> be said to exist when spacetime exists, that
> is to say *after* the required physical
> processes have taken place for its emergence.
Can't separation itself be described without invoking space or
time? Is a nucleus separate from its electron cloud, without
describing "orbital" parameters? Or an atom from similar atoms
in different molecules? Pauli exclusion within a molecule seems
to say there is no separation...
> This has not happened at the time of the
> measurements, but it has happened when
> the experimenters get together and establish
> the correlation. We cannot say that the
> outcome of one measurement has effected the
> other, because this presupposes the existence
> of spacetime, and puts the logical cart before
> the horse. The measurement results can only
> be correlated in terms of a spacetime structure
> which does not exist at the time of the
> measurements. The structure of spacetime
> emerges from the measurement results, not
> the other way about.
I submit the "binding energy" issued to the Universe at large:
1) defines a new entangled system (if not always in the "spooky
action at a distance" meaning), and
2) separates the sub-system from the Universe at large, in that
interactions can only be with the system... not any "constituent"
of the system.
What follows is that any bound system exists at all points in
spacetime, with finite probability.
David A. Smith
Oh No
>Dear Oh No:
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
> ....
>> Locality (proposed definition)
>> -----------------------------------------
>> A particle is in contact with another when it
>> interacts with it. A particle can be considered
>> to be in a neighbourhood of another if, in
>> principle, a photons may pass from one to the
>> other and one may return within a small proper
>> time period.
>
>This invokes spacetime. Comes with "time and c".
It invokes only proper time, which is just an ordering for a particle.
Spacetime is far more complicated. Technically qed allows a photon to be
emitted anywhere and absorbed anywhere. Spacetime only appears in the
expectation of many such emission/absorption processes. c appears in
this expectation, and defines the scale of space, rather than the other
way about.
>
> ....
>> Conclusion
>> ----------------
>> In my view the resolution of Bell's theorem is
>> not that we must reject realism, locality or
>> causality, but rather we must recognise that
>> space-time is an emergent concept.
>
> .... rather than "concept", how about "property". A property of
>all systems in which conservation laws hold, and a non-orthogonal
>property shared by multiple systems that still derive mass /
>length / time from the superset of all systems.
>
>> The notion of spacetime separation can only
>> be said to exist when spacetime exists, that
>> is to say *after* the required physical
>> processes have taken place for its emergence.
>
>Can't separation itself be described without invoking space or
>time?
It can in the sense of "not-contact", but to quantify separation we need
to be able to talk of the proper time for two way processes to take
place.
>Is a nucleus separate from its electron cloud, without
>describing "orbital" parameters? Or an atom from similar atoms
>in different molecules? Pauli exclusion within a molecule seems
>to say there is no separation...
Pauli exclusion does not apply between nucleus and electron. Or is that
not what you meant. I do not see how we can talk of separation for two
electrons in the same shell, but already in an atom there are many
photon interchange events, and we have at least a partially emergent
spacetime structure.
N:dlzc D:aol T:com (dlzc)
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
news:n6uDZZEz...@charlesfrancis.wanadoo.co.uk...
> Thus spake "N:dlzc D:aol T:com (dlzc)" <dl...@cox.net>
>>Dear Oh No:
>>
>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>>news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
>> ....
>>> Locality (proposed definition)
>>> -----------------------------------------
>>> A particle is in contact with another when it
>>> interacts with it. A particle can be considered
>>> to be in a neighbourhood of another if, in
>>> principle, a photons may pass from one to the
>>> other and one may return within a small proper
>>> time period.
>>
>>This invokes spacetime. Comes with "time and c".
>
> It invokes only proper time, which is just an
> ordering for a particle.
"photons may pass"... completes spacetime, in company with three
bodies (separated pair and the Universe et al) and the various
laws of conservation.
> Spacetime is far more complicated.
Perhaps.
> Technically qed allows a photon to be emitted
> anywhere and absorbed anywhere. Spacetime
> only appears in the expectation of many such
> emission/absorption processes. c appears in
> this expectation, and defines the scale of space,
> rather than the other way about.
I disagree (which I am sure you hold to be no surprise). If
objects have uniform "size", they are ultimately bound by
photons, I believe. If a spatial interval is measured, it is
done so using photons (even ones binding the substance of a
ruler). Spacetime is issue from multiple bodies, most of which
are light.
>> ....
>>> Conclusion
>>> ----------------
>>> In my view the resolution of Bell's theorem is
>>> not that we must reject realism, locality or
>>> causality, but rather we must recognise that
>>> space-time is an emergent concept.
>>
>> .... rather than "concept", how about "property".
>>A property of all systems in which conservation
>>laws hold, and a non-orthogonal property shared
>>by multiple systems that still derive mass /
>>length / time from the superset of all systems.
>>
>>> The notion of spacetime separation can only
>>> be said to exist when spacetime exists, that
>>> is to say *after* the required physical
>>> processes have taken place for its emergence.
>>
>>Can't separation itself be described without
>>invoking space or time?
>
> It can in the sense of "not-contact", but to
> quantify separation we need to be able to talk
> of the proper time for two way processes to take
> place.
Do we? Can we define it in terms of probabilities of
interaction, without invoking rulers?
>>Is a nucleus separate from its electron cloud,
>>without describing "orbital" parameters? Or an
>>atom from similar atoms in different molecules?
>>Pauli exclusion within a molecule seems
>>to say there is no separation...
>
> Pauli exclusion does not apply between nucleus
> and electron.
But it does between electrons. It applies between "like" members
of a bound system, but has yet to be extended beyond the
molecular level (that I know of). Is Pauli exclusion responsible
for the resultant states of the two entwined particles?
> Or is that not what you meant. I do not see how
> we can talk of separation for two electrons in the
> same shell, but already in an atom there are
> many photon interchange events, and we have at
> least a partially emergent spacetime structure.
I agree. I don't believe we'd get "fully emergent" until we had
a large but finite population of such atoms. But I am unsure why
I feel an infinite number of atoms could not yield a spacetime
such as we have.
David A. Smith
neur...@yahoo.com.au
After seeing where my earlier "position" thread was going,
the Masked Quantum Damsel fell asleep in the dungeon library
for a while (and none of the knights were either smart
enough or brave enough to kiss her awake - so on she
slumbered).
Inexplicably, you seem to be in my thoughts as I awake...
Prince Charles the Wise wrote:
> Locality (proposed definition)
> -----------------------------------------
> A particle is in contact with another when it interacts with
> it. A particle can be considered to be in a neighbourhood of
> another if, in principle, a photons may pass from one to the
> other and one may return within a small proper time period.
Similarly to Dear David, I don't think this is sufficiently
fundamental. You seem to implicitly define "particle" as
"Poincare irrep", but then I don't know how you attribute a
"proper time" property to it, since there's no such thing in
an arbitrary Poincare irrep (characterized only by mass,
total spin, and spin orientation) unless you make additional
assumptions about the details of the representation (ie
Minkowski spacetime).
Also, what about neutrinos? If they don't interact with
photons, then do they not have a locality feature in their
interactions with other types of particles? Defining
locality purely in terms of photons thus seems too
narrow.
You speak of "when" two particles "interact", but you
haven't defined these terms in a fundamentally rigorous way.
Presumably, two Poincare irreps are considered to have
"interacted" if they no longer have the same 4-momentum,
total-spin, or spin-orientation "after" the "interaction"?
As you see, I've been forced to use scare-quotes liberally
to indicate terms that are not well-defined in this context.
Classically, one calls such an interaction an "event",
and names an idealized manifold of such events "spacetime".
So we really only need to define "interaction", presumably
via a souped-up modification of the concept of "scattering".
Oh dear, watch out! I've just woken up, and I feel a
strangely-urgent need of a brain-fart, so anyone with a
sensitive nose should stop reading now!
Attempting something a little more rigorous, perhaps we
should say something along the following lines...
Consider a tensor product of Poincare irreps (each
decomposed into +ve and -ve energy sectors, or
particle/antiparticle if you want to bring charges into it).
So far this is non-interacting, with superselected +ve/-ve
energy sectors (they don't superpose). Now consider a class
of mappings (which I'll call "interaction operators")
between the tensor product space which *can* mix the
individual +ve/-ve sectors. (This corresponds to
annihilating a given set of particles and creating another.)
Also require that successive application of interaction
operators forms a group (actually maybe only semigroup is
necessary here, but I'll stick with group for now).
Now impose the constraint that the total momenta, spin, etc,
of initial and final *sets* of particles are conserved. (We
should probably also demand conservation of the sign of
total energy - which is why I mentioned semigroup above. It
kinda covers the "causality" stuff) This restricts the
allowed set of interaction operators. Find the infinitesimal
generators of this group and demand that, when direct-summed
with the free Poincare generators, we still get the Poincare
algebra.
Astute readers may have already realized that this looks
suspiciously like the construction of interacting Poincare
representations a little like Weinberg vol-1, but also
contains hints of the obscure work of Kita. Even more astute
readers may have also noticed that the crucial new step lies
in using group actions which mix annihiliation and creation
operators to construct a meaning for "interaction", out of
the building blocks from a *free* Poincare representation,
and therefore a meaning for "event".
Did anyone shout "Bogoliubov"?
> Conclusion
> ----------
>
> In my view the resolution of Bell's theorem is not that we
> must reject realism, locality or causality, but rather we
> must recognise that space-time is an emergent concept. The
> notion of spacetime separation can only be said to exist
> when spacetime exists, that is to say *after* the required
> physical processes have taken place for its emergence. [...]
> has not happened at the time of the measurements, but it has
> happened when the experimenters get together and establish
> the correlation. [...] The measurement results can only be
> correlated in terms of a spacetime structure which does not
> exist at the time of the measurements. The structure of
> spacetime emerges from the measurement results, not the
> other way about.
While asleep in the dungeon I also had a dream that I was
once again *carefully* studying Mermin's scroll:
N.D.Mermin: "What Is Quantum Mechanics Trying to Tell Us?"
Available as: quant-ph/9801057v2
What you (Prince Charles) have described above in your
conclusion is pretty much *exactly* aligned with his
interpretation of quantum mechanics.
Mermin expresses it like this:
----quote from Mermin quant-ph/9801057v2 ----
My complete answer to the late 19th century question "what is
electrodynamics trying to tell us?" would simply be this:
Fields in empty space have physical reality; the
medium that supports them does not.
Having thus removed the mystery from electrodynamics, let me
immediately do the same for quantum mechanics:
Correlations have physical reality; that which they
correlate does not.
--- end quote ----
Having now re-studied Mermin's paper carefully, it's pretty
obvious I didn't entirely get it the first time (a few years
ago). It really does deserve closer meditation.
My translation of the above into different language is:
"Numbers we get from an experiment have physical reality;
mappings do not."
States are just abstract mappings between an observable
property and a number. Observable property sets are just
a means for organizing the numbers. :-)
So maybe what needs to be abandoned is "mapping realism".
---
LOL from a yawning MQD!
Oh No
>(Yawn) Good morning Prince Charles!
>
>After seeing where my earlier "position" thread was going,
>the Masked Quantum Damsel fell asleep in the dungeon library
>for a while (and none of the knights were either smart
>enough or brave enough to kiss her awake - so on she
>slumbered).
>
>Inexplicably, you seem to be in my thoughts as I awake...
>
>Prince Charles the Wise wrote:
>
> > Locality (proposed definition)
> > -----------------------------------------
> > A particle is in contact with another when it interacts with
> > it. A particle can be considered to be in a neighbourhood of
> > another if, in principle, a photons may pass from one to the
> > other and one may return within a small proper time period.
>
>Similarly to Dear David, I don't think this is sufficiently
>fundamental. You seem to implicitly define "particle" as
>"Poincare irrep", but then I don't know how you attribute a
>"proper time" property to it, since there's no such thing in
>an arbitrary Poincare irrep (characterized only by mass,
>total spin, and spin orientation) unless you make additional
>assumptions about the details of the representation (ie
>Minkowski spacetime).
I dislike the definitions of a physical object in terms of mathematical
structure. In particular, I cannot use Minkowski spacetime, because it
should be emergent from particles. On my site, in the first instance I
use the definition
Definition: A particle is any physical entity whose position can be
measured at given time, such that the result of such measurement is a
position coordinate, (or a neighbourhood of negligible size).
(here I refer to a mathematical neighbourhood in the set of position
coordinates)
Definition: An elementary particle is one which cannot, even in
principle, be subdivided into particles for which separate positions can
be measured.
But later this has to be extended for photons because we cannot talk of
the measurements of the position of a photon, but only of measurement of
the position at which it was annihilated, or the position at which it
was created.
>Also, what about neutrinos? If they don't interact with
>photons, then do they not have a locality feature in their
>interactions with other types of particles? Defining
>locality purely in terms of photons thus seems too
>narrow.
I don't get as far as developing the theory of neutrinos, but similar
considerations apply. Since photons do not interact with neutrinos, we
cannot measure their position.
>You speak of "when" two particles "interact", but you
>haven't defined these terms in a fundamentally rigorous way.
>Presumably, two Poincare irreps are considered to have
>"interacted" if they no longer have the same 4-momentum,
>total-spin, or spin-orientation "after" the "interaction"?
The fundamental must be physical behaviour. It is not clear to me that
we can formalise the definition of fundamental physical objects. They
are their own definition, and we require intuition to understand them.
Physical behaviour is most accurately portrayed in Feynman diagrams (I
trust such audacity does not cause the damsel to swoon). An interaction
is a node. Atm we only have nodes in which electrons emit/absorb
photons.
>
>As you see, I've been forced to use scare-quotes liberally
>to indicate terms that are not well-defined in this context.
>
>Classically, one calls such an interaction an "event",
>and names an idealized manifold of such events "spacetime".
At this level we do not have a manifold. Feynman diagrams are graphs,
meaning that only the configuration of lines and vertices is relevant.
>So we really only need to define "interaction", presumably
>via a souped-up modification of the concept of "scattering".
Scattering does give us the simplest Feynman diagrams. We need something
more complicated to describe a position measurement. We will also have
to label the lines with proper time. The conjecture is that Feynman
rules are equivalent to summing topologically equivalent diagrams over
all proper time labellings.
>
>Oh dear, watch out! I've just woken up,
That is more than I can say. I spend the first couple of hours each day
trying to wake up. After that, I am exhausted by the effort.
>and I feel a
>strangely-urgent need of a brain-fart, so anyone with a
>sensitive nose should stop reading now!
>
>Attempting something a little more rigorous, perhaps we
>should say something along the following lines...
>
>Consider a tensor product of Poincare irreps (each
>decomposed into +ve and -ve energy sectors, or
>particle/antiparticle if you want to bring charges into it).
>So far this is non-interacting, with superselected +ve/-ve
>energy sectors (they don't superpose). Now consider a class
>of mappings (which I'll call "interaction operators")
>between the tensor product space which *can* mix the
>individual +ve/-ve sectors. (This corresponds to
>annihilating a given set of particles and creating another.)
>Also require that successive application of interaction
>operators forms a group (actually maybe only semigroup is
>necessary here, but I'll stick with group for now).
So far, so good, though a bit of work must be done in order to bring in
Poincare..
>Now impose the constraint that the total momenta, spin, etc,
>of initial and final *sets* of particles are conserved. (We
>should probably also demand conservation of the sign of
>total energy - which is why I mentioned semigroup above. It
>kinda covers the "causality" stuff)
We can demonstrate conservation laws.
>This restricts the
>allowed set of interaction operators. Find the infinitesimal
>generators of this group and demand that, when direct-summed
>with the free Poincare generators, we still get the Poincare
>algebra.
>
>Astute readers may have already realized that this looks
>suspiciously like the construction of interacting Poincare
>representations a little like Weinberg vol-1, but also
>contains hints of the obscure work of Kita. Even more astute
>readers may have also noticed that the crucial new step lies
>in using group actions which mix annihiliation and creation
>operators to construct a meaning for "interaction", out of
>the building blocks from a *free* Poincare representation,
>and therefore a meaning for "event".
>Did anyone shout "Bogoliubov"?
Too early in the morning for shouting.
It is a mystery to me how a physical field can be supported on a non-
physical medium
>let me
>immediately do the same for quantum mechanics:
>
> Correlations have physical reality; that which they
> correlate does not.
>
>--- end quote ----
Is this not, in essence, what Everett really said (as distinct from that
which he is famed as having said, when de Witt unfairly took the pee)
>Having now re-studied Mermin's paper carefully, it's pretty
>obvious I didn't entirely get it the first time (a few years
>ago). It really does deserve closer meditation.
>
>My translation of the above into different language is:
>
>
> "Numbers we get from an experiment have physical reality;
> mappings do not."
>
>States are just abstract mappings between an observable
>property and a number. Observable property sets are just
>a means for organizing the numbers. :-)
>
>So maybe what needs to be abandoned is "mapping realism".
>
It is quite a while since I read Mermin. My recollection is that his is
one of a class of what I call "information theoretic" interpretations,
all of which say, in different words, pretty much the same thing, and
which add very little, if anything, to each other. "Quantum mechanics
does not give a direct description of nature, but rather describes what
we can know of nature". Imv this is correct but tells us no more than
Von Neumann. I might tend to class these interpretations as what you
call "brain fart". A fart is, of course, an essential bodily function
for the perpetrator. Those too inhibited to enjoy one risk severe
discomfort and ill health. My own small contribution to the atmosphere
is at http://www.teleconnection.info/rqg/FoundationsOfQuantumTheory. I
seek to move things along a bit by translating the formal language of
quantum theory into common language, and thereby to show that the
apparently bizarre truth values of quantum logic are actually intuitive
truth values for the sentence structures under consideration.
Oh No
>Dear Oh No:
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>news:n6uDZZEz...@charlesfrancis.wanadoo.co.uk...
>> Thus spake "N:dlzc D:aol T:com (dlzc)" <dl...@cox.net>
>>>Dear Oh No:
>>>
>>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> wrote in message
>>>news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
>>> ....
>>>> Locality (proposed definition)
>>>> -----------------------------------------
>>>> A particle is in contact with another when it
>>>> interacts with it. A particle can be considered
>>>> to be in a neighbourhood of another if, in
>>>> principle, a photons may pass from one to the
>>>> other and one may return within a small proper
>>>> time period.
>>>
>>>This invokes spacetime. Comes with "time and c".
>>
>> It invokes only proper time, which is just an
>> ordering for a particle.
>
>"photons may pass"... completes spacetime, in company with three
>bodies (separated pair and the Universe et al) and the various
>laws of conservation.
Hmmm. OK, "pass" was not intended to invoke the connotation of passage
through something. One may only say that a photon can be emitted by one
particle and absorbed by another, and then that a photon is emitted by
the second and obsorbed by the first.
>
>> Spacetime is far more complicated.
>
>Perhaps.
>
>> Technically qed allows a photon to be emitted
>> anywhere and absorbed anywhere. Spacetime
>> only appears in the expectation of many such
>> emission/absorption processes. c appears in
>> this expectation, and defines the scale of space,
>> rather than the other way about.
>
>I disagree (which I am sure you hold to be no surprise). If
>objects have uniform "size", they are ultimately bound by
>photons, I believe. If a spatial interval is measured, it is
>done so using photons (even ones binding the substance of a
>ruler). Spacetime is issue from multiple bodies, most of which
>are light.
I am not sure what you disagree with. This defines spacial interval as a
measure of the binding between the particles constituting a body. That
seems sound to me.
>>>> Conclusion
>>>> ----------------
>>>> In my view the resolution of Bell's theorem is
>>>> not that we must reject realism, locality or
>>>> causality, but rather we must recognise that
>>>> space-time is an emergent concept.
>>>
>>> .... rather than "concept", how about "property".
>>>A property of all systems in which conservation
>>>laws hold, and a non-orthogonal property shared
>>>by multiple systems that still derive mass /
>>>length / time from the superset of all systems.
>>>
>>>> The notion of spacetime separation can only
>>>> be said to exist when spacetime exists, that
>>>> is to say *after* the required physical
>>>> processes have taken place for its emergence.
>>>
>>>Can't separation itself be described without
>>>invoking space or time?
>>
>> It can in the sense of "not-contact", but to
>> quantify separation we need to be able to talk
>> of the proper time for two way processes to take
>> place.
>
>Do we? Can we define it in terms of probabilities of
>interaction, without invoking rulers?
I find this far from clear. The probability of interaction is governed
by the fine structure constant, and leads to the numerical value of
charge, but this does not seem directly related to distance scale.
>>>Is a nucleus separate from its electron cloud,
>>>without describing "orbital" parameters? Or an
>>>atom from similar atoms in different molecules?
>>>Pauli exclusion within a molecule seems
>>>to say there is no separation...
>>
>> Pauli exclusion does not apply between nucleus
>> and electron.
>
>But it does between electrons. It applies between "like" members
>of a bound system, but has yet to be extended beyond the
>molecular level (that I know of). Is Pauli exclusion responsible
>for the resultant states of the two entwined particles?
We get entanglement with bosons also.
>
>> Or is that not what you meant. I do not see how
>> we can talk of separation for two electrons in the
>> same shell, but already in an atom there are
>> many photon interchange events, and we have at
>> least a partially emergent spacetime structure.
>
>I agree. I don't believe we'd get "fully emergent" until we had
>a large but finite population of such atoms. But I am unsure why
>I feel an infinite number of atoms could not yield a spacetime
>such as we have.
>
It is all very well for mathematicians to develop consistent infinite
structures, but those structures have properties which, imv, renders
them unsuitable for the description of physics.
harry
<neur...@yahoo.com.au> wrote in message
news:90302011-6df0-4a6d...@k30g2000hse.googlegroups.com...
> (Yawn) Good morning Prince Charles!
> While asleep in the dungeon I also had a dream that I was
> once again *carefully* studying Mermin's scroll:
>
> N.D.Mermin: "What Is Quantum Mechanics Trying to Tell Us?"
> Available as: quant-ph/9801057v2
>
> What you (Prince Charles) have described above in your
> conclusion is pretty much *exactly* aligned with his
> interpretation of quantum mechanics.
>
> Mermin expresses it like this:
>
> ----quote from Mermin quant-ph/9801057v2 ----
>
> My complete answer to the late 19th century question "what is
> electrodynamics trying to tell us?" would simply be this:
>
> Fields in empty space have physical reality; the
> medium that supports them does not.
To me that is obviously erroneous although perhaps popular. However, my
disagreement might be partly apparent or simply due to a different
definition of "physical reality" - see below!
> Having thus removed the mystery from electrodynamics, let me
> immediately do the same for quantum mechanics:
>
> Correlations have physical reality; that which they
> correlate does not.
Again, I don't swallow that.
> --- end quote ----
>
> Having now re-studied Mermin's paper carefully, it's pretty
> obvious I didn't entirely get it the first time (a few years
> ago). It really does deserve closer meditation.
>
> My translation of the above into different language is:
>
> "Numbers we get from an experiment have physical reality;
> mappings do not."
Well that is to me obviously correct. :-)
I mean with "physical reality" descriptions that refer to truly existing
("really") entities in nature ("physical"), no matter if they are directly
observable or possibly inferable from observations (physical reality does
not depend on my ability to observe it). Mermin means something else: "That
whereof physics can speak". However, modern physics does not speak of
physical reality; that is left to natural philosophy! Modern physics only
speaks of observation of physical phenomena (with as exception the use of
models; but such models don't necesarily mean to represent physical reality
itself). Which just goes to show how different formulations convey different
meanings...
> States are just abstract mappings between an observable
> property and a number. Observable property sets are just
> a means for organizing the numbers. :-)
>
> So maybe what needs to be abandoned is "mapping realism".
Who proposes a "mapping realism"??
Regards,
Harald
neur...@yahoo.com.au
(Yawn again - this time 'cause I'm headed for beddy-byes.)
> I dislike the definitions of a physical object in terms
> of mathematical structure.
Your brain is doing it automatically all the time as it
processes sensory input, although your subconscious doesn't
call it "maths". :-)
> Definition: A particle is any physical entity whose position
> can be measured at given time, such that the result of such
> measurement is a position coordinate, (or a neighbourhood of
> negligible size).
> (here I refer to a mathematical neighbourhood in the set of
> position coordinates)
>
> Definition: An elementary particle is one which cannot, even
> in principle, be subdivided into particles for which
> separate positions can be measured.
OK, so... in your particle definition you implicitly assume
a trivial Lie algebra of 4-position entities. I'll call that
Lie algebra "P". The set of your "elementary particles" is
then the dual space P* (the set of all linear functionals
over P). A particular particle is a particular element of
P*. Presumably, composite particles live in tensor products
of P*, or maybe (PxPx...)*, depending on the details.
>> Also, what about neutrinos? ....
> I don't get as far as developing the theory of neutrinos,
> but similar considerations apply. Since photons do not
> interact with neutrinos, we cannot measure their position.
Sounds a bit restrictive.
>> You speak of "when" two particles "interact", but you
>> haven't defined these terms in a fundamentally rigorous way.
>> Presumably, two Poincare irreps are considered to have
>> "interacted" if they no longer have the same 4-momentum,
>> total-spin, or spin-orientation "after" the "interaction"?
> The fundamental must be physical behaviour. It is not clear
> to me that we can formalise the definition of fundamental
> physical objects. They are their own definition, and we
> require intuition to understand them.
Lie algebras and their dual spaces seem to go a long way
towards a formal definition. (Naturally any such definition
must align with our physical intuition to be useful.)
> Physical behaviour is most accurately portrayed in Feynman
> diagrams (I trust such audacity does not cause the damsel to
> swoon). An interaction is a node. Atm we only have nodes in
> which electrons emit/absorb photons.
No, I won't faint at that, but here you have implicitly
introduced a Poincare algebra (I presume) in order to
describe fully the external legs. And you seem to be
implicitly presuming a vertex algebra defining the possible
nodes, allowing one to build up a physically sensible
diagram. That's all well and good, though it begs the
question of where the vertex algebra came from. (Actually,
that's kinda what I was driving towards in my previous
post.)
>> Classically, one calls such an interaction an "event", and
>> names an idealized manifold of such events "spacetime".
> At this level we do not have a manifold. Feynman diagrams
> are graphs, meaning that only the configuration of lines and
> vertices is relevant.
That's fine.
> Scattering does give us the simplest Feynman diagrams. We
> need something more complicated to describe a position
> measurement. We will also have to label the lines with
> proper time. The conjecture is that Feynman rules are
> equivalent to summing topologically equivalent diagrams over
> all proper time labellings.
Don't the Feynman rules merely derive from whatever vertex
algebra you chose at the start?
>> Oh dear, watch out! I've just woken up,
> That is more than I can say. I spend the first couple of
> hours each day trying to wake up. After that, I am exhausted
> by the effort.
Oh my poor dear Prince Charles! You really do need a young
princess nearby, don't you? To elevate the heart rate, I mean. :-)
>> Now impose the constraint that the total momenta, spin, etc,
>> of initial and final *sets* of particles are conserved. (We
>> should probably also demand conservation of the sign of
>> total energy - which is why I mentioned semigroup above. It
>> kinda covers the "causality" stuff)
> We can demonstrate conservation laws.
Only if you choose the vertex algebra correctly. That's
what I meant when I said:
>> This restricts the allowed set of interaction operators.
. . . . . .
>> Correlations have physical reality;
>> that which they correlate does not.
> Is this not, in essence, what Everett really said (as
> distinct from that which he is famed as having said, when de
> Witt unfairly took the pee)
I know what you mean. The first time I looked at Everett's
paper, I thought his "relational" ideas sounded entirely
more reasonable than all the many-worlds nonsense that
spouted up around it.
Mermin spends quite a bit of time explaining why his ideas
do not lead to the many-worlds fairy land.
>> So maybe what needs to be abandoned is "mapping realism".
> It is quite a while since I read Mermin. My recollection is
> that his is one of a class of what I call "information
> theoretic" interpretations, all of which say, in different
> words, pretty much the same thing, and which add very
> little, if anything, to each other. "Quantum mechanics does
> not give a direct description of nature, but rather
> describes what we can know of nature". Imv this is correct
> but tells us no more than Von Neumann. I might tend to class
> these interpretations as what you call "brain fart".
Secretly, I think _all_ "interpretations" are probably in
this class, (with the possible exception of
"shut-up-and-calculate" - which is what other people yell
when they've had enough).
> My own small contribution to the atmosphere is at
> http://www.teleconnection.info/rqg/FoundationsOfQuantumTheory.
I think the more important bit lies obscured underneath your
quantum covariance ideas. IIUC, you solve the old problem of
having both momenta and position in a single separable
Hilbert space by discretizing position. (It is known that
for them to place nice and continuously together one needs a
non-separable space, but those are a bitch to work with.)
You kinda dodge around the core problem of finding a
physically-sensible Lie algebra that includes position as a
1st-class citizen and only then proceeding to construct
unitary reps.
----
LOL from the MQD as she retires to her bower!
Oh No
>> I dislike the definitions of a physical object in terms
>> of mathematical structure.
>
>Your brain is doing it automatically all the time as it
>processes sensory input, although your subconscious doesn't
>call it "maths". :-)
>
> > Definition: A particle is any physical entity whose position
> > can be measured at given time, such that the result of such
> > measurement is a position coordinate, (or a neighbourhood of
> > negligible size).
> > (here I refer to a mathematical neighbourhood in the set of
> > position coordinates)
> >
> > Definition: An elementary particle is one which cannot, even
> > in principle, be subdivided into particles for which
> > separate positions can be measured.
>
>OK, so... in your particle definition you implicitly assume
>a trivial Lie algebra of 4-position entities. I'll call that
>Lie algebra "P". The set of your "elementary particles" is
>then the dual space P* (the set of all linear functionals
>over P). A particular particle is a particular element of
>P*.
I'm not so convinced about that. Neglecting, for one moment, that since
I make things discrete it would be a lie to call them a Lie, this dual
space is simply the space of wave functions (at least, I guess this is
to which you refer). But the wave functions are not particles. They are
representations of kets, and kets are not particles but are rather
formal statements I can make about what would happen in measurement of a
particle.
Doesn't calling this Lie algebra merely introduce an unwanted level of
abstraction, one which will make the problem harder, rather than easier,
to think about?
>Presumably, composite particles live in tensor products
>of P*, or maybe (PxPx...)*, depending on the details.
yeah. the former
>>> Also, what about neutrinos? ....
>
>> I don't get as far as developing the theory of neutrinos,
>> but similar considerations apply. Since photons do not
>> interact with neutrinos, we cannot measure their position.
>
>Sounds a bit restrictive.
I am not unhappy if the restrictions are imposed by nature, or if we
must introduce layers into the model imposed by nature. Qed seems like a
good model in which to start. Since I can only directly measure position
of charged particles, that is fine. I don't see issues with introducing
neutrinos, but the location of a neutrino can only be defined
indirectly, from the location of an electron it interacts with.
>>> You speak of "when" two particles "interact", but you
>>> haven't defined these terms in a fundamentally rigorous way.
>>> Presumably, two Poincare irreps are considered to have
>>> "interacted" if they no longer have the same 4-momentum,
>>> total-spin, or spin-orientation "after" the "interaction"?
>
>> The fundamental must be physical behaviour. It is not clear
>> to me that we can formalise the definition of fundamental
>> physical objects. They are their own definition, and we
>> require intuition to understand them.
>
>Lie algebras and their dual spaces seem to go a long way
>towards a formal definition. (Naturally any such definition
>must align with our physical intuition to be useful.)
My intuition is that a particle is a sizeless entity, a point, having
neither length nor breadth. I see no need to embed a point into a
geometry if some other structure (Feynman graphs) better portrays
physics.
>> Physical behaviour is most accurately portrayed in Feynman
>> diagrams (I trust such audacity does not cause the damsel to
>> swoon). An interaction is a node. Atm we only have nodes in
>> which electrons emit/absorb photons.
>
>No, I won't faint at that, but here you have implicitly
>introduced a Poincare algebra (I presume) in order to
>describe fully the external legs. And you seem to be
>implicitly presuming a vertex algebra defining the possible
>nodes, allowing one to build up a physically sensible
>diagram. That's all well and good, though it begs the
>question of where the vertex algebra came from. (Actually,
>that's kinda what I was driving towards in my previous
>post.)
External legs represent measured states. The algebra comes from the
statements we can make about where a particle would be found if we were
to do measurement. This applies also to the vertices, because "if we
were to do a measurement" is just a counterfactual conditional clause -
we do not have to actually do the measurement to have a sensible
linguistic construct.
>
>>> Classically, one calls such an interaction an "event", and
>>> names an idealized manifold of such events "spacetime".
>
>> At this level we do not have a manifold. Feynman diagrams
>> are graphs, meaning that only the configuration of lines and
>> vertices is relevant.
>
>That's fine.
Good. We want to do something to extend the classical notion of "event"
to include the nodes. Actually, I think I was trying to avoid the word
event for that reason, but don't quote me. My memory isn't that long.
>
>> Scattering does give us the simplest Feynman diagrams. We
>> need something more complicated to describe a position
>> measurement. We will also have to label the lines with
>> proper time. The conjecture is that Feynman rules are
>> equivalent to summing topologically equivalent diagrams over
>> all proper time labellings.
>
>Don't the Feynman rules merely derive from whatever vertex
>algebra you chose at the start?
I think they should, but this is approaching the diagrams from a
different angle. I did hear there are some guys at the Perimeter
Institute trying to find qft by starting with spin networks, but I
haven't seen anything published. In any case, I think to get anywhere
the lines must be labelled with proper times, not with spins (does that
make a mathematical difference, I wonder) and I don't hold out much hope
if one doesn't start with electron and photon lines (which I have not
seen in the context of spin networks).
>>> Oh dear, watch out! I've just woken up,
>
>> That is more than I can say. I spend the first couple of
>> hours each day trying to wake up. After that, I am exhausted
>> by the effort.
>
>Oh my poor dear Prince Charles! You really do need a young
>princess nearby, don't you? To elevate the heart rate, I mean. :-)
That would be the cure for all ills. I went to see my doctor about it.
There was some confusion about the distinction between a princess with
an interest in physics and one with an interesting physique, but either
way the answer was the same. You can't get one on the NHS. (The DHSS do
a line in wicked witches, but I don't wish to try that again).
>>> Now impose the constraint that the total momenta, spin, etc,
>>> of initial and final *sets* of particles are conserved. (We
>>> should probably also demand conservation of the sign of
>>> total energy - which is why I mentioned semigroup above. It
>>> kinda covers the "causality" stuff)
>
>> We can demonstrate conservation laws.
>
>Only if you choose the vertex algebra correctly. That's
>what I meant when I said:
>
>>> This restricts the allowed set of interaction operators.
Indeed it is severely restricted. The ordering of the logic as per my
site is that we should be able to do measurements on any synchronous
slice (for different observers), so commutation of the interaction
operators outside the lightcone must vanish. Ergo the locality condition
and that pretty effectively ties us down.
>
>>> So maybe what needs to be abandoned is "mapping realism".
>
>> It is quite a while since I read Mermin. My recollection is
>> that his is one of a class of what I call "information
>> theoretic" interpretations, all of which say, in different
>> words, pretty much the same thing, and which add very
>> little, if anything, to each other. "Quantum mechanics does
>> not give a direct description of nature, but rather
>> describes what we can know of nature". Imv this is correct
>> but tells us no more than Von Neumann. I might tend to class
>> these interpretations as what you call "brain fart".
>
>Secretly, I think _all_ "interpretations" are probably in
>this class, (with the possible exception of
>"shut-up-and-calculate" - which is what other people yell
>when they've had enough).
As I say, "shut-up-and-calculate" is bad for physical health. Or should
that be the health of Physics.
>> My own small contribution to the atmosphere is at
>> http://www.teleconnection.info/rqg/FoundationsOfQuantumTheory.
>
>I think the more important bit lies obscured underneath your
>quantum covariance ideas.
Quantum covariance is actually necessitated by the original brain fart,
that kets refer to discrete measurement results, but it is also required
to properly justify lattice regularisation (or causal perturbation
theory if one prefers).
>IIUC, you solve the old problem of
>having both momenta and position in a single separable
>Hilbert space by discretizing position. (It is known that
>for them to place nice and continuously together one needs a
>non-separable space, but those are a bitch to work with.)
>
>You kinda dodge around the core problem of finding a
>physically-sensible Lie algebra that includes position as a
>1st-class citizen and only then proceeding to construct
>unitary reps.
That's the idea. Instead of tackling the dragon head on, one does a
dance to amuse it. After that it becomes quite tame and loses its
appetite for Princesses, becoming quite content with fish and chips, or
whatever you are having for supper.
Salviati
news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
> As stated by Bell, the implication of his theorem is that we must
> sacrifice at least one of qm, locality, causality and realism. In
> practice, qm is overwhelming supported by experiment. Physics makes no
> sense if we sacrifice realism, so it seems we have a problem with either
> locality or causality.
While I appreciate these and the following sentences, I would like to
express my doubt. Do experiments actually support all aspects of qm?
I am sure that the fathers of qm did not see the possibility that complex
representation exp(i wt) is redundant if one excludes negative elapsed time
from reality.
Also, Hilbert space is based on Cantor's naive belief in more than
infinitely many numbers. He himself admitted that the combination of naked
axioms, in particular the axiom of extensionality in combination with the
axiom of infinity manage to maintain this belief without obvious
contradictions.
> In fact I do not think we have to sacrifice either,
So do I.
> but we do have to be
> careful about how we state locality and causality, and we certainly have
> to dismiss naive statements based on an assumption of background
> spacetime. Bell's theorem should not lead us to reject locality or, but
> we should reject the notion of a fundamental spacetime.
Why not reject the reality of future spacetime?
> Locality (proposed definition)
> -----------------------------------------
> A particle is in contact with another when it interacts with it. A
> particle can be considered to be in a neighbourhood of another if, in
> principle, a photons may pass from one to the other and one may return
> within a small proper time period.
Small is a relative property.
> Causality (proposed definition)
> -------------------------------------------
> There is a causal relation between two measurements if the outcome of
> one measurement alters the probability of the outcome the other.
Relations like cause-effect or father-son are arrow-like.
> Conclusion
> ----------------
> In my view the resolution of Bell's theorem is not that we must reject
> realism, locality or causality, but rather we must recognise that space-
> time is an emergent concept.
Yes, future emerges.
> The measurement results can only be correlated in
> terms of a spacetime structure which does not exist at the time of the
> measurements. The structure of spacetime emerges from the measurement
> results, not the other way about.
Regards,
Salviati
dlzc
> Thus spake "N:dlzcD:aol T:com (dlzc)" <dl...@cox.net>
> >Dear Oh No:
>
> >"Oh No" <N...@charlesfrancis.wanadoo.co.uk> wrote in message
> >news:n6uDZZEz...@charlesfrancis.wanadoo.co.uk...
> >> Thus spake "N:dlzcD:aol T:com (dlzc)" <dl...@cox.net>
> >>>Dear Oh No:
>
> >>>"Oh No" <N...@charlesfrancis.wanadoo.co.uk> wrote in message
> >>>news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
> >>> ....
> >>>> Locality (proposed definition)
> >>>> -----------------------------------------
> >>>> A particle is in contact with another when it
> >>>> interacts with it. A particle can be considered
> >>>> to be in a neighbourhood of another if, in
> >>>> principle, a photons may pass from one to the
> >>>> other and one may return within a small proper
> >>>> time period.
>
> >>>This invokes spacetime. Comes with "time and c".
>
> >> It invokes only proper time, which is just an
> >> ordering for a particle.
>
> >"photons may pass"... completes spacetime, in
> >company with three bodies (separated pair and
> >the Universe et al) and the various laws of
> > conservation.
>
> Hmmm. OK, "pass" was not intended to invoke
> the connotation of passage through something.
> One may only say that a photon can be emitted
> by one particle and absorbed by another, and
> then that a photon is emitted by the second and
> obsorbed by the first.
What separates the two particles of the system, that the emission by
"first" and receipt of "acknowledgement" by "first" is not
simultaneous? Spacetime (not the artificial construct, but that wich
underlies it) is a property of "system", not particle. Like
"population mean".
> >> Technically qed allows a photon to be emitted
> >> anywhere and absorbed anywhere. Spacetime
> >> only appears in the expectation of many such
> >> emission/absorption processes. c appears in
> >> this expectation, and defines the scale of space,
> >> rather than the other way about.
>
> >I disagree (which I am sure you hold to be no
> >surprise). If objects have uniform "size", they
> >are ultimately bound by photons, I believe. If a
> >spatial interval is measured, it is done so using
> >photons (even ones binding the substance of a
> >ruler). Spacetime is issue from multiple bodies,
> >most of which are light.
>
> I am not sure what you disagree with. This
> defines spacial interval as a measure of the
> binding between the particles constituting a body.
> That seems sound to me.
I must have been tired when I wrote that "disagree" part. ;>)
> >>>> Conclusion
> >>>> ----------------
> >>>> In my view the resolution of Bell's theorem is
> >>>> not that we must reject realism, locality or
> >>>> causality, but rather we must recognise that
> >>>> space-time is an emergent concept.
...
Is there any rule that says bosons can't be part of a system? What if
the only requirement for "sub system hood" is that the members yield
"binding energy" to the system at large?
> >> Or is that not what you meant. I do not see how
> >> we can talk of separation for two electrons in the
> >> same shell, but already in an atom there are
> >> many photon interchange events, and we have at
> >> least a partially emergent spacetime structure.
>
> >I agree. I don't believe we'd get "fully emergent"
> >until we had a large but finite population of such
> >atoms. But I am unsure why I feel an infinite
> >number of atoms could not yield a spacetime
> >such as we have.
>
> It is all very well for mathematicians to develop
> consistent infinite structures, but those structures
> have properties which, imv, renders them
> unsuitable for the description of physics.
Nice chatting with you!
David A. Smith
Oh No
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>news:KD3YHfBU...@charlesfrancis.wanadoo.co.uk...
>> As stated by Bell, the implication of his theorem is that we must
>> sacrifice at least one of qm, locality, causality and realism. In
>> practice, qm is overwhelming supported by experiment. Physics makes no
>> sense if we sacrifice realism, so it seems we have a problem with either
>> locality or causality.
>
>While I appreciate these and the following sentences, I would like to
>express my doubt. Do experiments actually support all aspects of qm?
Yes. There never has been an experiment which contradicts it.
>
>I am sure that the fathers of qm did not see the possibility that complex
>representation exp(i wt) is redundant if one excludes negative elapsed time
>from reality.
The founding fathers of quantum mechanics were neither stupid nor
uneducated. It is time you stopped making this accusation, since, as has
been explained to you many times, it only indicates that you do not
understand what you are talking about. I must apologise for not having
read this post accurately, or I would not have passed it.
>
>Also, Hilbert space is based on Cantor's naive belief in more than
>infinitely many numbers.
It is not. Infinite dimensional Hilbert space can be perfectly well
based on the concept of a limit, and, these days, Hilbert space can be
finite dimensional.
>Why not reject the reality of future spacetime?
Because it makes absolutely no difference to the laws of physics.
>> Locality (proposed definition)
>> -----------------------------------------
>> A particle is in contact with another when it interacts with it. A
>> particle can be considered to be in a neighbourhood of another if, in
>> principle, a photons may pass from one to the other and one may return
>> within a small proper time period.
>
>Small is a relative property.
It is made precise in mathematics. It means that fro all sufficiently
small values, a proposition is true. It does not quantify small - that
would be a matter for the problem in hand and is here unspecified.
neur...@yahoo.com.au
> Who is this sorceress who peers inside my head?
(Departing at a gallop to be measured elsewhere, the Masked
Quantum Damsel calls back to Prince Charles...)
I bet you'll think about me as you (try to) drift off to
sleep tonight!
>>> Definition: A particle is any physical entity whose position
>>> can be measured at given time, such that the result of such
>>> measurement is a position coordinate, (or a neighbourhood of
>>> negligible size). (here I refer to a mathematical
>>> neighbourhood in the set of position coordinates)
>> OK, so... in your particle definition you implicitly assume
>> a trivial Lie algebra of 4-position entities. I'll call that
>> Lie algebra "P". The set of your "elementary particles" is
>> then the dual space P* (the set of all linear functionals
>> over P). A particular particle is a particular element of
>> P*.
> I'm not so convinced about that. Neglecting, for one moment,
> that since I make things discrete it would be a lie to call
> them a Lie, ...
Oh dear, you really need to work on your puns. That was
truly dreadful!
BTW, I said "Lie algebra", not "Lie group". (Not all Lie
algebras can be integrated to a full Lie group.)
> this dual space is simply the space of wave functions (at
> least, I guess this is to which you refer).
I was trying to keep it abstract. Ie, encapsulate your
definition in the smallest mathematical notion I could
think of.
But thinking about it a bit more... you used the notions of
"point" and "neighbourhood of negligible size"
interchangeably in your definition. These are very different
animals mathematically. The former is easy to express as the
dual space I mentioned, but for the latter you've got to set
up a generalization of the dual space, ie a space of
mappings from the algebra to pinned volumes, and then
discuss limits. I think you need to pick one or the other as
a starting point, not both.
> Doesn't calling this Lie algebra merely introduce an
> unwanted level of abstraction, one which will make the
> problem harder, rather than easier, to think about?
I was just trying to establish clearly what you're talking
about. To do that non-fuzzily needs math. It doesn't *have*
to be a Lie algebra, but that just seemed like the obvious
choice.
And yes, thinking fuzzily is much easier than thinking
clearly. (Ha!)
> My intuition is that a particle is a sizeless entity, a
> point, having neither length nor breadth. I see no need to
> embed a point into a geometry if some other structure
> (Feynman graphs) better portrays physics.
This is another reason to choose more rigorously between
"points" or "volumes of infinitesimal size" in your
foundations.
>> You kinda dodge around the core problem of finding a
>> physically-sensible Lie algebra that includes position as a
>> 1st-class citizen and only then proceeding to construct
>> unitary reps.
> That's the idea. Instead of tackling the dragon head on, one
> does a dance to amuse it. After that it becomes quite tame
> and loses its appetite for Princesses, ...
I've encountered a few fire-breathing dragons in my time.
The boy dragons invariably turn out to be pussy cats in
disguise!
----
LOL from the fast-galloping Princess!
Igor
Additional timelike dimensions should be able to solve this problem
quite well.
Oh No
>Prince Charles wondered:
>
>> Who is this sorceress who peers inside my head?
>
>(Departing at a gallop to be measured elsewhere, the Masked
>Quantum Damsel calls back to Prince Charles...)
>
>I bet you'll think about me as you (try to) drift off to
>sleep tonight!
What is the face behind the mask?
>>>> Definition: A particle is any physical entity whose position
>>>> can be measured at given time, such that the result of such
>>>> measurement is a position coordinate, (or a neighbourhood of
>>>> negligible size). (here I refer to a mathematical
>>>> neighbourhood in the set of position coordinates)
>
>>> OK, so... in your particle definition you implicitly assume
>>> a trivial Lie algebra of 4-position entities. I'll call that
>>> Lie algebra "P". The set of your "elementary particles" is
>>> then the dual space P* (the set of all linear functionals
>>> over P). A particular particle is a particular element of
>>> P*.
>
>> I'm not so convinced about that. Neglecting, for one moment,
>> that since I make things discrete it would be a lie to call
>> them a Lie, ...
>
>Oh dear, you really need to work on your puns. That was
>truly dreadful!
I know. It doesn't even rhyme. At least it doesn't if one can remember
to pronounce uncle Sophus' name correctly. I can't think of anyone who
does that. Are you sure you want me to work on puns? Could be really
painful.
>
>> this dual space is simply the space of wave functions (at
>> least, I guess this is to which you refer).
>
>I was trying to keep it abstract. Ie, encapsulate your
>definition in the smallest mathematical notion I could
>think of.
>
>But thinking about it a bit more... you used the notions of
>"point" and "neighbourhood of negligible size"
>interchangeably in your definition.
Did I? That was naughty. I shall take it as a slapped wrist.
> These are very different
>animals mathematically. The former is easy to express as the
>dual space I mentioned, but for the latter you've got to set
>up a generalization of the dual space, ie a space of
>mappings from the algebra to pinned volumes, and then
>discuss limits. I think you need to pick one or the other as
>a starting point, not both.
Point (in the context of particle) should be taken as an abstraction of
physical reality. It needs to be used as a primary concept for the
mathematical structure referring to physics (much as with Euclid, but
not using Euclid's axioms). One could take it as "element" in a set
theoretic presentation.
I used "neighbourhood" in the conventional mathematical sense as a
subset of R^n. I cannot justify using this as an abstraction of physical
reality, but merely as a part of a mathematical description of the set
of possible values resulting from measurement.
>
>> Doesn't calling this Lie algebra merely introduce an
>> unwanted level of abstraction, one which will make the
>> problem harder, rather than easier, to think about?
>
>I was just trying to establish clearly what you're talking
>about. To do that non-fuzzily needs math. It doesn't *have*
>to be a Lie algebra, but that just seemed like the obvious
>choice.
Oh, I agree that you were doing what all the good mathemagical
physicists do. I am the one out of step. It's just that by being out of
step, I think I can try to focus on something a little different from
usual, and I think it is advantageous.
>And yes, thinking fuzzily is much easier than thinking
>clearly. (Ha!)
Oh I don't think so. Once one has a mathemagical structure, everything
about that structure becomes clear (with a little work). It is much
harder to think about how that structure applies to nature. Because we
do not start off by knowing, a priore, what nature is, this is
necessarily fuzzy and one has to think very long and hard to make it
clear. My problem with heading straight for an abstract structure, like
Lie algebra, is that I think one can then focus clearly on the structure
and sweep the difficult bit under the carpet. I want to focus on the
fuzzy bit, and make that clear, rather than focus on something which is
already clear.
>> My intuition is that a particle is a sizeless entity, a
>> point, having neither length nor breadth. I see no need to
>> embed a point into a geometry if some other structure
>> (Feynman graphs) better portrays physics.
>
>This is another reason to choose more rigorously between
>"points" or "volumes of infinitesimal size" in your
>foundations.
I feel sadly misunderstood. Doubtless I was ambiguous. It is difficult
not to be. I cannot talk of a volume of infinitesimal size without
imposing a whole lot of mathematical structure which I think plays no
role in modelling the fundamental structures of physical reality. More
literally a point is sizeless in the sense that it has no structure by
means of which size can be conferred (as distinct from having zero size,
which would mean that the concept of size makes sense and has value
zero).
>>> You kinda dodge around the core problem of finding a
>>> physically-sensible Lie algebra that includes position as a
>>> 1st-class citizen and only then proceeding to construct
>>> unitary reps.
>
>> That's the idea. Instead of tackling the dragon head on, one
>> does a dance to amuse it. After that it becomes quite tame
>> and loses its appetite for Princesses, ...
>
>I've encountered a few fire-breathing dragons in my time.
>The boy dragons invariably turn out to be pussy cats in
>disguise!
I have a friend who claims that delightful young princesses are really
dragons in disguise...
Salviati
> Thus spake Salviati <eckard.b...@arcor.de>
>>I am sure that the fathers of qm did not see the possibility that complex
>>representation exp(i wt) is redundant if one excludes negative elapsed
>>time
>>from reality.
>
> The founding fathers of quantum mechanics were neither stupid nor
> uneducated. It is time you stopped making this accusation, since, as has
> been explained to you many times, it only indicates that you do not
> understand what you are talking about. I must apologise for not having
> read this post accurately, or I would not have passed it.
I never wrote that the fathers of quantum mechanics were stupid or
uneducated. Nobody asked me for stopping "this accusation".
I repeatedly swallowed the insulting reproach I would not understand
what I am talking about. Having thoroughly dealt with fundamentals
for nearly half a century, I am sure that real-valued cosine transform
with arguments omega t in IR+ is equivalent to complex Fourier transform
with arguments extending from -oo to +oo except for the arbitrary
choice of a reference point.
Perhaps, you have to apologize for simply not believing that.
No matter whether or not you decide passing this challenge to the public,
I expect you to seriously check and confirm or disprove this claim of mine.
>>Why not reject the reality of future spacetime?
>
> Because it makes absolutely no difference to the laws of physics.
The environment of initial values cannot be derived from the laws.
>>Small is a relative property.
>
> It is made precise in mathematics.
The only reasonable reference I am aware of is to be found in
the unity:
delta x delta y > 1.
Regards,
Salviati
Salviati
> Thus spake neur...@yahoo.com.au
> Did I? That was naughty. I shall take it as a slapped wrist.
>> These are very different animals mathematically.
Yes, old engineers like me prefer to understand Galilei style mathematics
rather than Cantor's paradise. Discrete and continuous realms exclude
and mutually complement each other.
> Point (in the context of particle) should be taken as an abstraction of
> physical reality.
Yes, with emphasis on getting an ideal model and loosing reality.
> It needs to be used as a primary concept for the
> mathematical structure referring to physics (much as with Euclid, but
> not using Euclid's axioms).
A point is something that does not have parts.
Are there really approachable points in space or time according to
Euclid? No.
0.999... = 1.000... is not valid for rational numbers but merely for
(ir)real ones, for what Weyl called the sauce of continuum.
>One could take it as "element" in a set
> theoretic presentation.
Here you are are resorting to the core of Cantor's admittedly
untennable definition of an (infinite) set.
> Oh, I agree that you were doing what all the good mathemagical
> physicists do. I am the one out of step. It's just that by being out of
> step, I think I can try to focus on something a little different from
> usual, and I think it is advantageous.
What hinders you to go back to the old Galilei's
really rigorous thinking? Galilei did not claim having got from god
directly a hypothesis that cannot be proven wrong but also not
proven correct. He did not call for a conveninent axiom as did Dedekind.
>>And yes, thinking fuzzily is much easier than thinking
>>clearly. (Ha!)
>
> Oh I don't think so. Once one has a mathemagical structure,
Do you intend joking? What do you mean by "mathemagical"?
>everything
> about that structure becomes clear (with a little work). It is much
> harder to think about how that structure applies to nature.
Who understands Buridan's donkey, which I consider a purely mathematical
problem, should be able to reveal mistakes in mathematical physics, too.
> Because we
> do not start off by knowing, a priore, what nature is, this is
> necessarily fuzzy and one has to think very long and hard to make it
> clear.
Yes, but do not forget: Fully understanding something might be easy
if compared to getting accepted, even if one has just to convey that
a function of only positive argument does not really need a complex
representation because this merely adds arbitrarily chosen redundancy.
Regards,
Salviati
Oh No
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>> Point (in the context of particle) should be taken as an abstraction of
>> physical reality.
>
>Yes, with emphasis on getting an ideal model and loosing reality.
>
>> It needs to be used as a primary concept for the
>> mathematical structure referring to physics (much as with Euclid, but
>> not using Euclid's axioms).
>
>
>>One could take it as "element" in a set
>> theoretic presentation.
>
>Here you are are resorting to the core of Cantor's admittedly
>untennable definition of an (infinite) set.
Not at all, since I do not invoke the axiom of infinity. (As it happens
the axiom of infinity has been proven to be tenable. What you mean is
that it does not model physics. That is a different assertion
altogether).
>> Oh, I agree that you were doing what all the good mathemagical
>> physicists do. I am the one out of step. It's just that by being out of
>> step, I think I can try to focus on something a little different from
>> usual, and I think it is advantageous.
>
>What hinders you to go back to the old Galilei's
>really rigorous thinking?
We were talking of Lie algebras. There is no thinking more rigorous than
that of pure mathematicians.
>
>>>And yes, thinking fuzzily is much easier than thinking
>>>clearly. (Ha!)
>>
>> Oh I don't think so. Once one has a mathemagical structure,
>
>Do you intend joking? What do you mean by "mathemagical"?
do you not understand joking?
>
> >everything
>> about that structure becomes clear (with a little work). It is much
>> harder to think about how that structure applies to nature.
>
We were talking of Lie algebras. Do you know what they are?
Oh No
>
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>news:lxWYMkDl...@charlesfrancis.wanadoo.co.uk...
>> Thus spake Salviati <eckard.b...@arcor.de>
>
>
>>>I am sure that the fathers of qm did not see the possibility that complex
>>>representation exp(i wt) is redundant if one excludes negative elapsed
>>>time
>>>from reality.
>>
>> The founding fathers of quantum mechanics were neither stupid nor
>> uneducated. It is time you stopped making this accusation, since, as has
>> been explained to you many times, it only indicates that you do not
>> understand what you are talking about. I must apologise for not having
>> read this post accurately, or I would not have passed it.
>
>I never wrote that the fathers of quantum mechanics were stupid or
>uneducated.
What you did write was equivalent.
>Nobody asked me for stopping "this accusation".
You have repeatedly been asked.
>I repeatedly swallowed the insulting reproach I would not understand
>what I am talking about. Having thoroughly dealt with fundamentals
>for nearly half a century, I am sure that real-valued cosine transform
>with arguments omega t in IR+ is equivalent to complex Fourier transform
>with arguments extending from -oo to +oo except for the arbitrary
>choice of a reference point.
So is everyone else. But what you say has no relevance.
>Perhaps, you have to apologize for simply not believing that.
Now you are accusing me of being stupid or uneducated.
>No matter whether or not you decide passing this challenge to the public,
>I expect you to seriously check and confirm or disprove this claim of mine.
Why? It is irrelevant. Your claims that it is relevant have only
demonstrated that you do not know what you are talking about. We are not
doing signal processing here.
>
>>>Small is a relative property.
>>
>> It is made precise in mathematics.
>
>The only reasonable reference I am aware of is to be found in
>the unity:
>delta x delta y > 1.
>
That has nothing to do with it. Study analysis.
Salviati
> Thus spake Salviati
>>Here you are are resorting to the core of Cantor's admittedly
>>untennable definition of an (infinite) set.
>
> Not at all, since I do not invoke the axiom of infinity. (As it happens
> the axiom of infinity has been proven to be tenable.
The axiom of infinity has been borrowed from Archimede's obvious
and unrefutable insight that there is no limit to counting.
I consider it not just tenable but even unavoidable for spectral
analysis.
Fraenkel himself admitted already in 1923 that Cantor's definition
of an (infinite) set is untenable and cannot be replaced by a correct
substitute.
Hilbert and Zermelo defended by means of several further axioms
Cantor's "naive" belief. Perhaps the crucial role plays the first one,
the axiom of extensionality together with the axiom of infinity and
the joining assertion "there is as set with ...".
Hilbert frankly asmitted that the axiomatic method manages to
maintain the "belief in certain Zusammenhaenge" that were naively
believed so far.
> What you mean is
> that it does not model physics. That is a different assertion
> altogether).
I appreciate that you at least seem to agree on the need for
putting consequences wrt physics in question.
>>What hinders you to go back to the old Galilei's
>>really rigorous thinking?
>
>
> We were talking of Lie algebras. There is no thinking more rigorous
> than that of pure mathematicians.
Maybe, Galilei was not pure enough ;-).
What about the consequent thinking of mathematicians, let me
remind of the not really resolved fundamental crisis and of the
fact that Goedel died due to starvation because he feared to
loose his life by poison.
Did Sophus Lie apply his algebra to qm?
As far as I know, not even Karl Schwartzschild claimed having
found anti-worlds beyond infinite space and time.
>>
>>>>And yes, thinking fuzzily is much easier than thinking
>>>>clearly. (Ha!)
>>>
>>> Oh I don't think so. Once one has a mathemagical structure,
>>
>>Do you intend joking? What do you mean by "mathemagical"?
>
> do you not understand joking?
Sometimes joking is helpful. However, I do not appreciate Gauss
mocking about the Boeoter in the arrogant attitude of those who
feel not uneducated. Since my command of English is very shaky
and limited, I prefer a language that is as factual and blunt as
possible while nonetheless sometimes subtle between the lines.
Regards,
Salviati
neur...@yahoo.com.au
Prince Charles wondered anew:
> What is the face behind the mask?
Google for "cherry petite". (Anyone under 18yrs should NOT
do this.) She's not me, but a couple of seriously cheeky
freshmen recently asked in a tutorial whether I was
moonlighting at that website, because of a certain
resemblance.
(Bet you *really* think of me later this evening, now!)
> ... Are you sure you want me to work on puns? ...
No, try to work on being funny. (Hee hee!)
> Point (in the context of particle) should be taken as an
> abstraction of physical reality. It needs to be used as a
> primary concept for the mathematical structure referring to
> physics (much as with Euclid, but not using Euclid's
> axioms). One could take it as "element" in a set theoretic
> presentation.
That's fine. General topology begins from basic set theory.
>> And yes, thinking fuzzily is much easier than thinking
>> clearly. (Ha!)
> Oh I don't think so. Once one has a mathemagical structure,
> everything about that structure becomes clear (with a little
> work). It is much harder to think about how that structure
> applies to nature. Because we do not start off by knowing, a
> priore, what nature is, this is necessarily fuzzy and one
> has to think very long and hard to make it clear. My problem
> with heading straight for an abstract structure, like Lie
> algebra, is that I think one can then focus clearly on the
> structure and sweep the difficult bit under the carpet. I
> want to focus on the fuzzy bit, and make that clear, rather
> than focus on something which is already clear.
Still not clear what you mean by "the fuzzy bit". (I was
using the phrase "fuzzy thinking" to mean logically
incomplete or self-inconsistent.)
>>> My intuition is that a particle is a sizeless entity, a
>>> point, having neither length nor breadth. I see no need to
>>> embed a point into a geometry if some other structure
>>> (Feynman graphs) better portrays physics.
>> This is another reason to choose more rigorously between
>> "points" or "volumes of infinitesimal size" in your
>> foundations.
> I feel sadly misunderstood. Doubtless I was ambiguous. It is
> difficult not to be. I cannot talk of a volume of
> infinitesimal size without imposing a whole lot of
> mathematical structure which I think plays no role in
> modelling the fundamental structures of physical reality.
> More literally a point is sizeless in the sense that it has
> no structure by means of which size can be conferred (as
> distinct from having zero size, which would mean that the
> concept of size makes sense and has value zero).
Do you consider that points are associated with a notion of
"nearness" to each other? If so, then this should be
expressable as a family of open sets (and hence a topology,
though necessarily metrizable). That's probably a step in
the right direction.
My guess is that you think of "nearness" of 2 points in
terms of the results of measuring their positions (which
involves a mapping from some algebra to R^n)? If so,
you have a "weak topology" (or maybe "weak-* topology").
>> I've encountered a few fire-breathing dragons in my time.
>> The boy dragons invariably turn out to be pussy cats in
>> disguise!
> I have a friend who claims that delightful young
> princesses are really dragons in disguise...
I suppose I must concede that we all turn into (undisguised)
dragons after a few decades. (In my part of the world, many
people now feel that Germaine Greer's inner reptile is now
plain to behold!)
----
LOL from the not-yet-dragon Princess!
Oh No
>
>Prince Charles wondered anew:
>
>> What is the face behind the mask?
>
>Google for "cherry petite". (Anyone under 18yrs should NOT
>do this.) She's not me, but a couple of seriously cheeky
>freshmen recently asked in a tutorial whether I was
>moonlighting at that website, because of a certain
>resemblance.
>
>(Bet you *really* think of me later this evening, now!)
Were you trying to raise the heartbeat, or give an old wizard a heart
attack?
>> ... Are you sure you want me to work on puns? ...
>
>No, try to work on being funny. (Hee hee!)
If you can make yourself laugh, I won't need to. (Hee hee hee!)
> > Point (in the context of particle) should be taken as an
> > abstraction of physical reality. It needs to be used as a
> > primary concept for the mathematical structure referring to
> > physics (much as with Euclid, but not using Euclid's
> > axioms). One could take it as "element" in a set theoretic
> > presentation.
>
>That's fine. General topology begins from basic set theory.
>
>
>>> And yes, thinking fuzzily is much easier than thinking
>>> clearly. (Ha!)
>
>> Oh I don't think so. Once one has a mathemagical structure,
>> everything about that structure becomes clear (with a little
>> work). It is much harder to think about how that structure
>> applies to nature. Because we do not start off by knowing, a
>> priore, what nature is, this is necessarily fuzzy and one
>> has to think very long and hard to make it clear. My problem
>> with heading straight for an abstract structure, like Lie
>> algebra, is that I think one can then focus clearly on the
>> structure and sweep the difficult bit under the carpet. I
>> want to focus on the fuzzy bit, and make that clear, rather
>> than focus on something which is already clear.
>
>Still not clear what you mean by "the fuzzy bit".
I mean the bit concerning the relationship of the mathematical structure
to the objects which exist in nature. We were talking of "particle",
meaning, imv, an object which exists in nature. I was rejecting the
notion that "particle" can be placed in direct correspondence with
"member of Lie algebra". While we can only say what something is not, it
remains fuzzy. The problem, as I see it, actually does not lie so much
with saying what it is, but in the psyche, with the unwanted
connotations which all words have. We can never fully anticipate the
connotations which someone else may bring to a word, and it is difficult
to control the connotations we apply to a word. These connotations make
things fuzzy.
>(I was
>using the phrase "fuzzy thinking" to mean logically
>incomplete or self-inconsistent.)
Yes. I would take logically incomplete to include ill-defined. There is
a fundamental difference in the psyche of a mathmo, as compared to that
of a physicist (well, there are many). Dr George Jaroszkiewicz, of
Nottingham uni once said that physics is much harder than maths, and
remarked that when mathmos wander in to physics courses, they generally
leave because physics is largely based on fuzzy, or imperfectly defined
ideas. Mathmos cannot cope with that. What is really surprising to a
mathmo is that physicists seem to proceed with them as though they do
not even see the problem. I guess that is what you mean by saying that
thinking fuzzily is easier. I suspect it depends on who you are.
>>>> My intuition is that a particle is a sizeless entity, a
>>>> point, having neither length nor breadth. I see no need to
>>>> embed a point into a geometry if some other structure
>>>> (Feynman graphs) better portrays physics.
>
>>> This is another reason to choose more rigorously between
>>> "points" or "volumes of infinitesimal size" in your
>>> foundations.
>
>> I feel sadly misunderstood. Doubtless I was ambiguous. It is
>> difficult not to be. I cannot talk of a volume of
>> infinitesimal size without imposing a whole lot of
>> mathematical structure which I think plays no role in
>> modelling the fundamental structures of physical reality.
>> More literally a point is sizeless in the sense that it has
>> no structure by means of which size can be conferred (as
>> distinct from having zero size, which would mean that the
>> concept of size makes sense and has value zero).
>
>Do you consider that points are associated with a notion of
>"nearness" to each other? If so, then this should be
>expressable as a family of open sets (and hence a topology,
>though necessarily metrizable). That's probably a step in
>the right direction.
It is a step too far. The notion "open set" is abstracted from the
properties of R^n (it may have other application). R^n is a mathematical
construct. I want to restrict the structure associated with "particle"
so that it reflects only physical behaviour. At a primitive level, I
only really want to include a concept of "interaction" between
particles. Then I want to use "interaction" to develop a concept of
nearness.
>
>My guess is that you think of "nearness" of 2 points in
>terms of the results of measuring their positions (which
>involves a mapping from some algebra to R^n)? If so,
>you have a "weak topology" (or maybe "weak-* topology").
Measurement actually involves a substantial complexity of interaction.
It introduces a weak topology, but again we are talking about a relation
on members of the dual space. As per my previous objection, vector space
(and hence also the dual) refers to statements we can make about the
possible results of measurement (as per Von Neumann). It does not refer
directly to the concept I want to define "particle".
The next part of my answer seemed to merit a new thread, so that is what
I have done.
>> I have a friend who claims that delightful young
>> princesses are really dragons in disguise...
>
>I suppose I must concede that we all turn into (undisguised)
>dragons after a few decades. (In my part of the world, many
>people now feel that Germaine Greer's inner reptile is now
>plain to behold!)
Perhaps you are right then. A young princess would be perfect. By the
time she is a dragon, I will be past caring. Or preferably dead of the
heart attack she brings on.
Salviati
> Thus spake Salviati <eckard.b...@arcor.de>
>>
>>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>>news:lxWYMkDl...@charlesfrancis.wanadoo.co.uk...
>>> Thus spake Salviati <eckard.b...@arcor.de>
>>
>>
>>>>I am sure that the fathers of qm did not see the possibility that
>>>>complex
>>>>representation exp(i wt) is redundant if one excludes negative elapsed
>>>>time
>>>>from reality.
>>>
>>> The founding fathers of quantum mechanics were neither stupid nor
>>> uneducated. It is time you stopped making this accusation, since, as has
>>> been explained to you many times, it only indicates that you do not
>>> understand what you are talking about. I must apologise for not having
>>> read this post accurately, or I would not have passed it.
>>
>>I never wrote that the fathers of quantum mechanics were stupid or
>>uneducated.
>
> What you did write was equivalent.
Merely for the feeling of you and perhaps many others. I apologize for
feeling forced to hurt those who idolized these persons and their ideas.
>
>>Nobody asked me for stopping "this accusation".
>
> You have repeatedly been asked.
The facts I am referring to are checkable, and I maintain claiming they
are correct.
I did not accuse Heisenberg for possibly saving my life by
wrong calculation of the critical mass.
I also did not accuse Schroedinger for what he did with Itha.
I just substantiated mounting evidence for possible mistakes.
>>I repeatedly swallowed the insulting reproach I would not understand
>>what I am talking about. Having thoroughly dealt with fundamentals
>>for nearly half a century, I am sure that real-valued cosine transform
>>with arguments omega t in IR+ is equivalent to complex Fourier transform
>>with arguments extending from -oo to +oo except for the arbitrary
>>choice of a reference point.
>
> So is everyone else.
Does this mean (a) that everyone else is sure about that
or what (b) do you mean?
> But what you say has no relevance.
Given you are ready to accept (a) the equivalence between
cosine transform in IR+ and FT in IR and (C, respectively,
then I would like to know for what reasons you refuse sharing
my conclusions. After that we will see how relevant they are.
>>Perhaps, you have to apologize for simply not believing that.
>
> Now you are accusing me of being stupid or uneducated.
No. You are just challenged to refute factually.
>
>>No matter whether or not you decide passing this challenge to the public,
>>I expect you to seriously check and confirm or disprove this claim of
>>mine.
>
> Why? It is irrelevant.
We will see that. See above.
> Your claims that it is relevant have only demonstrated that you do not
> know what you are talking about. We are not doing signal processing here.
Signal processing and qm have common foundations.
Isn't this spf?
>>>>Small is a relative property.
>>>
>>> It is made precise in mathematics.
>>
>>The only reasonable reference I am aware of is to be found in
>>the unity:
>>delta x delta y > 1.
>>
> That has nothing to do with it.
Why not? It explains in an unexpected manner why uncertainty
also holds without complex numbers.
> Study analysis.
I cannot accept this as a factual counterargument.
Regards,
Salviati
Oh No
>> But what you say has no relevance.
>
>Given you are ready to accept (a) the equivalence between cosine
>transform in IR+ and FT in IR and (C, respectively, then I would like
>to know for what reasons you refuse sharing my conclusions. After that
>we will see how relevant they are.
I have previously given my reasons in some depth. If you haven't read
them, I suggest you do so. I am not going to do so again. In short, what
you say does not apply to quantum theory. You should study quantum
theory properly before misapplying a simple and well known result, or
you must continue to accept the accusation that you don't know what you
are talking about.
>>>Perhaps, you have to apologize for simply not believing that.
>>
>> Now you are accusing me of being stupid or uneducated.
>
>No. You are just challenged to refute factually.
Why would I refute a simple and well known result?
>> Your claims that it is relevant have only demonstrated that you do not
>> know what you are talking about. We are not doing signal processing here.
>
>Signal processing and qm have common foundations. Isn't this spf?
They use some superficially similar maths, but that is about as far as
it goes. You appear to have been misled by the superficial similarity of
some of the formulae into thinking the underlying structure is the same.
It isn't.
>>>>>Small is a relative property.
>>>>
>>>> It is made precise in mathematics.
>>>
>>>The only reasonable reference I am aware of is to be found in
>>>the unity:
>>>delta x delta y > 1.
>>>
>> That has nothing to do with it.
>
>Why not? It explains in an unexpected manner why uncertainty also holds
>without complex numbers.
>
>> Study analysis.
>
>I cannot accept this as a factual counterargument.
You do not need an argument to know what I mean by small. You need to
look at relevant material. I have told you where to find it.
Oh No
It is necessary that an ordering of events for the first particle makes
sense. I have called this a primitive notion of proper time in a related
thread "Particles as sole building blocks of matter"
>> >>>Is a nucleus separate from its electron cloud,
>> >>>without describing "orbital" parameters? Or an
>> >>>atom from similar atoms in different molecules?
>> >>>Pauli exclusion within a molecule seems
>> >>>to say there is no separation...
>>
>> >> Pauli exclusion does not apply between nucleus
>> >> and electron.
>>
>> >But it does between electrons. It applies between
>> >"like" members of a bound system, but has yet to
>> >be extended beyond the molecular level (that I
>> >know of). Is Pauli exclusion responsible for the
>> >resultant states of the two entwined particles?
>>
>> We get entanglement with bosons also.
>
>Is there any rule that says bosons can't be part of a system? What if
>the only requirement for "sub system hood" is that the members yield
>"binding energy" to the system at large?
I only meant that they do not obey the Pauli exclusion principle.
dlzc
On Aug 27, 9:40 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
> Thus spakedlzc<dl...@cox.net>
> >On Aug 25, 1:55 am, Oh No <N...@charlesfrancis.wanadoo.co.uk> wrote:
...
> >> Hmmm. OK, "pass" was not intended to invoke
> >> the connotation of passage through something.
> >> One may only say that a photon can be emitted
> >> by one particle and absorbed by another, and
> >> then that a photon is emitted by the second and
> >> obsorbed by the first.
>
> >What separates the two particles of the system,
> >that the emission by "first" and receipt of
> >"acknowledgement" by "first" is not
> >simultaneous?
>
> It is necessary that an ordering of events for the
> first particle makes sense. I have called this a
> primitive notion of proper time in a related
> thread "Particles as sole building blocks of matter"
Sequence provides "causality", but not the "proper separation" between
emission and receipt of detection by remote member. There is
something inherent to "system" that creates a spatial separation.
...
> >> We get entanglement with bosons also.
>
> >Is there any rule that says bosons can't be
> >part of a system? What if the only requirement
> >for "sub system hood" is that the members yield
> >"binding energy" to the system at large?
>
> I only meant that they do not obey the Pauli
> exclusion principle.
Spin? Can two bosons with identical spins be entangled?
David A. Smith
Oh No
>> It is necessary that an ordering of events for the
>> first particle makes sense. I have called this a
>> primitive notion of proper time in a related
>> thread "Particles as sole building blocks of matter"
>
>Sequence provides "causality", but not the "proper separation" between
>emission and receipt of detection by remote member. There is
>something inherent to "system" that creates a spatial separation.
Yes. See my other post for more detail.
>...
>> >> We get entanglement with bosons also.
>>
>> >Is there any rule that says bosons can't be
>> >part of a system? What if the only requirement
>> >for "sub system hood" is that the members yield
>> >"binding energy" to the system at large?
>>
>> I only meant that they do not obey the Pauli
>> exclusion principle.
>
>Spin? Can two bosons with identical spins be entangled?
>
Two particles in identical states cannot be entangled. This is called
something else - a pure state I think, but I have a memory like a sieve
and would have to look it up. This can apply to Bosons, but not to
Fermions. However, we can have an entangled state of two different boson
states (taking into account other properties than spin)
neur...@yahoo.com.au
Prince Charles, although in the middle of a heart-attack,
continued to ponder the mysteries of physics:
>> Still not clear what you mean by "the fuzzy bit".
> I mean the bit concerning the relationship of the
> mathematical structure to the objects which exist in nature.
OK, yes. The relationship is not necessarily a bijection.
> We were talking of "particle", meaning, imv, an object which
> exists in nature. I was rejecting the notion that "particle"
> can be placed in direct correspondence with "member of Lie
> algebra".
Actually, I was suggesting that the set of measurable
properties of a particle can be can be placed in direct
correspondence with a Lie algebra.
>> (I was using the phrase "fuzzy thinking" to mean logically
>> incomplete or self-inconsistent.)
> Yes. I would take logically incomplete to include
> ill-defined. There is a fundamental difference in the psyche
> of a mathmo, as compared to that of a physicist (well, there
> are many). Dr George Jaroszkiewicz, of Nottingham uni once
> said that physics is much harder than maths, and remarked
> that when mathmos wander in to physics courses, they
> generally leave because physics is largely based on fuzzy,
> or imperfectly defined ideas. Mathmos cannot cope with that.
> What is really surprising to a mathmo is that physicists
> seem to proceed with them as though they do not even see the
> problem.
Maybe it's just a question of how math (resp physics) a
physicist (resp mathmo) knows. A physicist would never
tolerate a blatant error in a simple integration, but many
tolerate a whole raft of errors of a functional analytic
nature because those are much more subtle.
> I guess that is what you mean by saying that thinking
> fuzzily is easier.
Not really. -- I meant that it's easy to come up with fuzzy
ideas, but communicating them sensibly to someone else
requires more discipline.
> The next part of my answer seemed to merit a new thread, so
> that is what I have done.
I'll rendezvous over there later.
----
LOL from Princess Baby-Dragon, bringer of heart attacks!
Oh No
>
>Prince Charles, although in the middle of a heart-attack,
>continued to ponder the mysteries of physics:
It's all right. It was just a small overdose of Princess Heart
Stimulant.
>
>>> Still not clear what you mean by "the fuzzy bit".
>
>> I mean the bit concerning the relationship of the
>> mathematical structure to the objects which exist in nature.
>
>OK, yes. The relationship is not necessarily a bijection.
>
>> We were talking of "particle", meaning, imv, an object which
>> exists in nature. I was rejecting the notion that "particle"
>> can be placed in direct correspondence with "member of Lie
>> algebra".
>
>Actually, I was suggesting that the set of measurable
>properties of a particle can be can be placed in direct
>correspondence with a Lie algebra.
I think one needs to be quite precise about what this means. The lie
algebra models statements we can make about measurement. Measurements
have to do with how the particle interacts with other matter, in quite
complex circumstances. They do not make sense for a particle in
isolation.
>>> (I was using the phrase "fuzzy thinking" to mean logically
>>> incomplete or self-inconsistent.)
>
>> Yes. I would take logically incomplete to include
>> ill-defined. There is a fundamental difference in the psyche
>> of a mathmo, as compared to that of a physicist (well, there
>> are many). Dr George Jaroszkiewicz, of Nottingham uni once
>> said that physics is much harder than maths, and remarked
>> that when mathmos wander in to physics courses, they
>> generally leave because physics is largely based on fuzzy,
>> or imperfectly defined ideas. Mathmos cannot cope with that.
>> What is really surprising to a mathmo is that physicists
>> seem to proceed with them as though they do not even see the
>> problem.
>
>Maybe it's just a question of how math (resp physics) a
>physicist (resp mathmo) knows. A physicist would never
>tolerate a blatant error in a simple integration, but many
>tolerate a whole raft of errors of a functional analytic
>nature because those are much more subtle.
>
> > I guess that is what you mean by saying that thinking
> > fuzzily is easier.
>
>Not really. -- I meant that it's easy to come up with fuzzy
>ideas, but communicating them sensibly to someone else
>requires more discipline.
Its easy to come up with false ideas. I am more concerned with
eliminating fuzziness in accepted ideas.
> > The next part of my answer seemed to merit a new thread, so
> > that is what I have done.
>
>I'll rendezvous over there later.
Looking forward
>LOL from Princess Baby-Dragon, bringer of heart attacks!
>
bring em on.
Salviati
> Thus spake Salviati
>>
>>Given you are ready to accept (a) the equivalence between cosine
>>transform in IR+ and FT in IR and (C, respectively, then I would like
>>to know for what reasons you refuse sharing my conclusions. After that
>>we will see how relevant they are.
>
> I have previously given my reasons in some depth. If you haven't
> read them, I suggest you do so. I am not going to do so again.
Sounds as if you easily understood the equivalence.
Otherwise you would not belittle it as follows:
> Why would I refute a simple and well known result?
Many experts had, some are still having problems to
understand why we do not need sine and cosine
within IR+.
> In short, what you say does not apply to quantum theory.
I am still having problems to find the point where classical
physics ends and qm (not quantum theory) begins.
I remember of Schulman's borderline at about 10^-7 cm,
and I cannot yet see any specific qm within the purely
classical work by H. A. Kramers.
Also, the praxis of guessing a complex "Ansatz" exp(-iwt)
is very common in electrical engineering.
So the qm arose from what Heisenberg used
within his cooperation with Kramers in 1925:
"A quantum interpretation ... in which derivatives are
replaced by differences divided by h, ...".
The decisive i was not mentioned, perhaps because
this is the old trivial trick of electrical engineers.
However, h is just a coefficient that could be
choosen equal to one.
>>Signal processing and qm have common foundations. Isn't this spf?
>
> They use some superficially similar maths, but that is about as far as
> it goes.
If so, then you might be able pointing me to work that retraceably
explains the difference.
>You appear to have been misled by the superficial similarity of
> some of the formulae into thinking the underlying structure is the same.
> It isn't.
Who structured that structure and how?
Regards,
Salviati:
... in ultima conclusione, gli attributi di eguale
maggiore e minore non aver luogo ne gl'infiniti,
ma solo nelle quantità terminate.
IR>|>IR+>|>IR
Oh No
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>news:f4bXCBBx...@charlesfrancis.wanadoo.co.uk...
>> Thus spake Salviati
>
>physics ends and qm (not quantum theory) begins.
>I remember of Schulman's borderline at about 10^-7 cm,
>and I cannot yet see any specific qm within the purely
>classical work by H. A. Kramers.
It is not any specific distance, but has more to do with whether
measurement of position is possible in principle. My own work in
Cosmology applies qm over astronomical distances.
>Also, the praxis of guessing a complex "Ansatz" exp(-iwt)
>is very common in electrical engineering.
>So the qm arose from what Heisenberg used
>within his cooperation with Kramers in 1925:
>"A quantum interpretation ... in which derivatives are
>replaced by differences divided by h, ...".
>
Quantisation like this was a heuristic.
>
>>>Signal processing and qm have common foundations. Isn't this spf?
>>
>> They use some superficially similar maths, but that is about as far as
>> it goes.
>
>If so, then you might be able pointing me to work that retraceably
>explains the difference.
I have pointed you at
http://www.teleconnection.info/rqg/RelativisticQuantumTheory
which explains the structure of quantum theory. Please observe that no
fourier transform is taken over time.
>
>>You appear to have been misled by the superficial similarity of
>> some of the formulae into thinking the underlying structure is the same.
>> It isn't.
>
>Who structured that structure and how?
It wasn't any one person, but Dirac is credited with much of the work of
creating a single structure - as distinct from papers exploring parts.
Von Neumann axiomatised the structure, i.e. gave a precise description
in terms of a small number of formal rules.
Salviati
> Thus spake Salviati >
> It is not any specific distance, but has more to do with whether
> measurement of position is possible in principle. My own work in
> Cosmology applies qm over astronomical distances.
Do you need h in cosmology?
>>Also, the praxis of guessing a complex "Ansatz" exp(-iwt)
>>is very common in electrical engineering.
>>So the qm arose from what Heisenberg used
>>within his cooperation with Kramers in 1925:
>>"A quantum interpretation ... in which derivatives are
>>replaced by differences divided by h, ...".
>>
> Quantisation like this was a heuristic.
As far as I understood, they changed to the Hamiltonian
point of view while sticking on their usual attributing.
In particular, Dirac wrote that frequency is always positive
while it is actually positive and negative in usual complex domain.
>>>>Signal processing and qm have common foundations. Isn't this spf?
>>>
>>> They use some superficially similar maths, but that is about as far as
>>> it goes.
>>
>>If so, then you might be able pointing me to work that retraceably
>>explains the difference.
>
> I have pointed you at
>
> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
>
> which explains the structure of quantum theory. Please observe that no
> fourier transform is taken over time.
Perhaps you refer to this sentence:
"One may ask why we are using complex numbers to construct the propositions
of quantum theory. So long as we are talking about measurements of position
at a particular time, real numbers would work just as well. In fact, real
numbers would be in some ways more precise, because complex numbers
introduce an extra level of freedom."
What about IR+ instead of IR? No matter whether we choose Laplace's point of
view where a creator switched on all initial conditions at t=0 or we prefer
the opposite point of view backward with t_elapsed=0, analysis of what
happened and prediction of what might happen mutually complement but exclude
each other. For that reason, I maintain: Something that has been completely
desribed within IR+ does not change its content if represented within IR or
even within (C. In that case the complex numbers do NOT introduce an extra
level of freedom but merely redundant ambivalence.
You continued:
"The reason for using them lies in what happens when we want to compare a
measurement at one time with a measurement at another, for example, when we
want to talk about motion."
Then you wrote:
" Taken together with linearity and complex conjugation,..."
Sorry, even someone like me being familiar with complex calculus has some
problems to clearly understand why and how you need complex numbers when
talking about motion.
>>>You appear to have been misled by the superficial similarity of
>>> some of the formulae into thinking the underlying structure is the same.
>>> It isn't.
>>
>>Who structured that structure and how?
>
> It wasn't any one person, but Dirac is credited with much of the work of
> creating a single structure - as distinct from papers exploring parts.
As far as I know, Dirac's brackets just intend to unify in a simple manner
the pictures by Heisenberg and by Schroedinger after Schroedinger managed to
show the equivalence. Did they really contribute something new to qm?
> Von Neumann axiomatised the structure, i.e. gave a precise description
> in terms of a small number of formal rules.
Perhapd you refer to 1932. Didn't v. Neumann in 1935 confess that he lost
his belief in Hilbert space?
The integal that you wrote when introducing plane waves strongly reminds of
Fourier transform. For what reason did you use exp(i yp)?
By the way, to my knowledge there is almost nothing plane in nature.
Plane waves are smelling to me like engineering for freshmen.
Oh No
>"Oh No" <No...@charlesfrancis.wanadoo.co.uk> schrieb im Newsbeitrag
>news:xOK1ZwBp...@charlesfrancis.wanadoo.co.uk...
>> Thus spake Salviati >
>> It is not any specific distance, but has more to do with whether
>> measurement of position is possible in principle. My own work in
>> Cosmology applies qm over astronomical distances.
>
>Do you need h in cosmology?
It hasn't made an appearance as yet
>
>>>Also, the praxis of guessing a complex "Ansatz" exp(-iwt)
>>>is very common in electrical engineering.
>>>So the qm arose from what Heisenberg used
>>>within his cooperation with Kramers in 1925:
>>>"A quantum interpretation ... in which derivatives are
>>>replaced by differences divided by h, ...".
>>>
>> Quantisation like this was a heuristic.
>
>As far as I understood, they changed to the Hamiltonian
>point of view while sticking on their usual attributing.
>In particular, Dirac wrote that frequency is always positive
>while it is actually positive and negative in usual complex domain.
Dirac was correct. Please do not repeat a misapplication of what you
know of signal processing.
>
>> Please observe that no
>> fourier transform is taken over time.
>
>Perhaps you refer to this sentence:
>"One may ask why we are using complex numbers to construct the propositions
>of quantum theory. So long as we are talking about measurements of position
>at a particular time, real numbers would work just as well. In fact, real
>numbers would be in some ways more precise, because complex numbers
>introduce an extra level of freedom."
>
>What about IR+ instead of IR? No matter whether we choose Laplace's point of
>view where a creator switched on all initial conditions at t=0 or we prefer
>the opposite point of view backward with t_elapsed=0, analysis of what
>happened and prediction of what might happen mutually complement but exclude
>each other. For that reason, I maintain: Something that has been completely
>desribed within IR+ does not change its content if represented within IR or
>even within (C. In that case the complex numbers do NOT introduce an extra
>level of freedom but merely redundant ambivalence.
Please do not repeat a misapplication of what you know of signal
processing. We are discussing quantum theory and your comments have no
relevance.
>
>You continued:
>"The reason for using them lies in what happens when we want to compare a
>measurement at one time with a measurement at another, for example, when we
>want to talk about motion."
>Then you wrote:
>" Taken together with linearity and complex conjugation,..."
>
>Sorry, even someone like me being familiar with complex calculus has some
>problems to clearly understand why and how you need complex numbers when
>talking about motion.
I agree that this is deep and subtle. I use "motion" in a very general
sense. "evolution of state" would be better. States are defined at one
time, and we need a mapping on Hilbert space to take us to another time.
We also need to ensure that the theory is covariant. This can be done
very tidily by using a mapping which uses complex numbers. You will need
to read another couple of pages to get to that, in the simple case of a
non-interacting particle. Take note that the complex numbers which
appear in the theory have no physical meaning, but there use gives us a
way to ensure that the physical quantities calculated from it (namely
probabilities) have the required invariance property under Lorentz
transform.
>>>>You appear to have been misled by the superficial similarity of
>>>> some of the formulae into thinking the underlying structure is the same.
>>>> It isn't.
>>>
>>>Who structured that structure and how?
>>
>> It wasn't any one person, but Dirac is credited with much of the work of
>> creating a single structure - as distinct from papers exploring parts.
>
>As far as I know, Dirac's brackets just intend to unify in a simple manner
>the pictures by Heisenberg and by Schroedinger after Schroedinger managed to
>show the equivalence. Did they really contribute something new to qm?
At the very least they enable us to get away from the misleading idea
that a complex wave is something physically real.
>
>> Von Neumann axiomatised the structure, i.e. gave a precise description
>> in terms of a small number of formal rules.
>
>
>Perhapd you refer to 1932. Didn't v. Neumann in 1935 confess that he lost
>his belief in Hilbert space?
It is not clear what his reasons were, but as he replaced it by
something even more abstract, and also involving complex numbers (viz.
C* algebras), I think we can be sure that he did not share your
objections.
>The integal that you wrote when introducing plane waves strongly reminds of
>Fourier transform. For what reason did you use exp(i yp)?
That is a Fourier transform in space, not in time.
>By the way, to my knowledge there is almost nothing plane in nature.
>Plane waves are smelling to me like engineering for freshmen.
Please read through the mathematical background for vector spaces.
http://www.teleconnection.info/rqg/IntroductionToVectorSpace
As I have developed the theory, plane waves are a basis for vector
space. We can calculate for all states by calculating for plane waves.
There is no implication that plane waves are physically really.
Cl.Massé
>>I am still having problems to find the point where classical
>>physics ends and qm (not quantum theory) begins.
>>I remember of Schulman's borderline at about 10^-7 cm,
>>and I cannot yet see any specific qm within the purely
>>classical work by H. A. Kramers.
"Oh No" <No...@charlesfrancis.wanadoo.co.uk> a écrit dans le message de
news:xOK1ZwBp...@charlesfrancis.wanadoo.co.uk...
> It is not any specific distance, but has more to do with whether
> measurement of position is possible in principle.
In principle, it isn't a distance, but an action about hbar. The
uncertainty in the measurement of position then depends on the uncertainty
in the measurement of momentum. But we can't speak about a borderline since
CM and QM are two qualitatively different theories. The hope that CM be an
approximation of QM has confused many things. Macroscopic phenomena
described by QM but not by CM have been observed.
>>>>Signal processing and qm have common foundations. Isn't this spf?
>>> They use some superficially similar maths, but that is about as far as
>>> it goes.
>>If so, then you might be able pointing me to work that retraceably
>>explains the difference.
> I have pointed you at
>
> http://www.teleconnection.info/rqg/RelativisticQuantumTheory
>
> which explains the structure of quantum theory. Please observe that no
> fourier transform is taken over time.
Signal processing and QM have in common the mathematical treatment of a
wave, but QM has additional principles like the projection postulate.
--
~~~~ clmasse on free F-country
Liberty, Equality, Profitability.