chat
karl robold
bit (Chinese in 16 bit). Is it thinkable, that social live in future
computer network fabrics is based on more complex artificial languages(
needing e.g. 128-bit encoding), which secure the idea of freedom, peace,
.... ?
======================================= MODERATOR'S COMMENT:
Karl, your recent posts seem to be drifting from the subject at hand. Can you explain how this relates to discrete physics?
karl robold
dan b. miller wrote:
>
> ======================================= MODERATOR'S COMMENT:
> Karl, your recent posts seem to be drifting from the subject at hand.
Can you explain how this relates to discrete physics?
>
as a beginner in discrete physics, i can't show direct strong relationship
to discrete physics for the above question, but originally i thought,
somebody, who
has a long occupation with discrete physics, knows some answers.
maybe i should pose the question in the following form:
has Digital Mechanics also good models for social dynamics, or are these
models exclusively used in physics?
daniel B miller
I suppose one could apply similar techniques to the study of social
dynamics or anything else, but in general we are applying these concepts
to the study of fundamental physical processes. Steven Wolfram's book,
"A New Kind of Science", does a pretty thorough job of applying the
logic of discrete systems to a number of fields of inquiry. While not
everyone agrees with his conclusions, it's a good place to start if
you're interested in applying these ideas to a wider range of problems.
Here at s.p.d, I think we are going to try to keep the discussion
revolving around physics.
>
>
Lubo? Motl
> dynamics or anything else, but in general we are applying these concepts
> to the study of fundamental physical processes.
Then I would be afraid that this newsgroup will become silent pretty
soon because every specific enough application of these ideas to the
questions in fundamental physics can be proved wrong faster than the
time necessary to write a posting about it.
For example, experiments show that all physical processes at distances
longer than 10^-17 meters are described by the Standard Model (plus
General Relativity) which are completely old-fashioned continuous
physical theories. Even when we discuss various discrete structure
behind physics - e.g. quantum foam in the case of quantum gravity -
there is always an equivalent continuous picture to derive these
results. Even as simple-minded theory as loop quantum gravity can be
derived from continuous objects, namely the metric written in
Ashtekar's new variables.
> Steven Wolfram's book,
> "A New Kind of Science", does a pretty thorough job of applying the
> logic of discrete systems to a number of fields of inquiry.
The problem is that these applications are not new, they are not
science, and they are not too kind either. ;-)
> Here at s.p.d, I think we are going to try to keep the discussion
> revolving around physics.
Do you have an example or evidence that these fundamentalistically
discrete ideas, admitting no continuous justification, are directly
related to physics? The best evidence I've heard so far goes as
follows: the picture resulting from the cellular automaton number XYZ
looks like tiger's skin, and because tigers are physical objects,
cellular automata must therefore describe physics. One can call it a
new kind of science, but as far as I am concerned, let me continue to
call it stupidity.
daniel B miller
...
> Do you have an example or evidence that these fundamentalistically
> discrete ideas, admitting no continuous justification, are directly
> related to physics? The best evidence I've heard so far goes as
> follows: the picture resulting from the cellular automaton number XYZ
> looks like tiger's skin, and because tigers are physical objects,
> cellular automata must therefore describe physics. One can call it a
> new kind of science, but as far as I am concerned, let me continue to
> call it stupidity.
>
and inability to understand the fundamental concepts involved makes your
opinion pretty much useless.
Lubos Motl
> You can call it what you want, but your obvious ignorance of the subject
> and inability to understand the fundamental concepts involved makes your
> opinion pretty much useless.
Note that besides these not-quite-nice and not-at-all reasonable cliches,
you have not given a simple argument and you have not answered a single
question or objection raised in my posting. The reason is that this
fundamentalist discrete way of thinking about physics is not able to
answer any questions. It is not (natural) science, it is not new, and as
you are repeatedly showing, it is not kind either.
Once again, the centuries or millenia of evolution of physics led to
General Relativity and the Standard Model that are continuous theories
that explain all physical phenomena at distances longer than 10^-17
meters. They have a lot of discrete features: quantum mechanics always
shows that the spectrum of many operators is discrete, for example.
Moreover, quantum gravity is holographic, which means that the Hilbert
space describing the interior of a region with surface area A (in the
units of the Planck area) has a finite dimension, namely exp(A/4).
Nevertheless the defining equations and the evolution, as given by
Schrodinger's equation, are always continuous and so far it seems that it
must be continuous.
One can play with various approximate discrete models. One can latticize
spacetime in lattice gauge theories, for example. Note that even in the
case of this approximation, the basic degrees of freedom that live on the
lattice sites are continuous. If one performs any numerical calculations,
these numbers themselves are approximated by numbers with a finite number
of digits. But all these things are just approximations or children's toy
models; the reality is based on continuous equations.
The discrete character of Nature can emerge in various contexts, but it
can never be *the* fundamental formulation because it would imply, among
many other wrong consequences, that all continuous symmetries must be
broken. We have a pretty good evidence that the rotational, translational,
Lorentz, SU(3) x SU(2) x U(1) etc. are symmetries of Nature. Until some
reliable experiments demonstrate that the laws of physics are *not*
rotationally invariant, for example, no serious scientist will believe any
theory that cannot be expressed in terms of continuous equations.
Trying to extend the validity of some entertaining pictures resulted from
simple programs to a unifying theory of physics is a too big leap to be
treated seriously. The reality is that the NKS-type of theories (if I can
use the word "theory" at all) is unable to describe as simple things as
classical electromagnetism - which is ignored by the self-confident NKS
"scientists", much like the rest of actual physics. Physics is a few
centuries and tens of thousands of papers further, however. The very fact
that the world is quantum-mechanical is enough to rule out all these naive
approaches to physics. Physics must be described by a Hilbert space with
operators - or equivalently by a probabilistically interpreted
path-integral. There is no evidence whatsoever that these basic principles
could be replaced by anything else, and all attempts to "undo" the quantum
revolution and return to a classical description have failed and the
probability that they could ever work is continously shrinking.
OK, let me imagine that the NKS-science will accept that the task is to
look for a quantum-mechanical theory. Wavefunctions and probabilities
predicted from them must be allowed to be continuous, and let me imagine
that the proponents of the NKS science will learn these basic points of
undergraduate physics in one sunny day, and they will try to make the
quantum-mechanical theory as discrete as possible.
Well, they will be still guaranteed to fail. Quantum field theory can be
understood as "second quantization" of the equations describing a
particle. Every quantization means that some new observables may become
discrete (their spectrum may become discrete), but at the same moment,
every quantization adds a new layer of continuity. A classical particle is
a discrete point-like object. Quantization converts it into an object
described by a continuous wavefunction that is (and must be) "smeared"
over an extended region of space. Such a wavefunction carries a comparable
amount of information as a classical field. A classical field is a very
concrete configuration, a discrete point in the configuration space.
Second quantization replaces this sharp point in the configuration space
by a wave functional - a function that is smeared over this
infinite-dimensional configuration space. Such a second quantized
wavefunction is even more continuous than anything before. Moreover, some
approaches to string theory can be interpreted as a result of a "third"
quantization, which makes the underlying wavefunction more continuous than
the wavefunction in all previous examples. Well, some people believe that
in some sense the full understanding of string theory will lead us to
infinitely many layers of quantization, to a recursively self-generated
theory. Don't get me wrong: of course that one derives a lot of discrete
and controllable quantities from this formalism, including
finite-dimensional Hilbert spaces. But it is pretty clear that the more
fundamental description we deal with, the more continuous it becomes, in
some very specific sense, and the more emergent the discrete results are.
Democritus et al. started with discrete atoms with hooks, but the
equations underlying physics have been becoming increasingly continuous
ever since. We've learned many things about the equivalence of various
discrete and continuous interpretations of some physical theories, but a
theory without a set of defining continuous equations will probably never
be accepted as a serious model for physics, and every person who knows
something about our actual knowledge of physics understands why my
statement is powerful and likely, given the current picture of the world
as painted by physics, even though the statement is not rigorously proved
yet.
All the best
Lubos
______________________________________________________________________________
E-mail: lu...@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Eray Ozkural exa
daniel B miller <dan...@cmu.edu> wrote in message news:<1090s3a...@news.supernews.com>...
If discrete physics can come to the point where it can accurately
predict cosmological or particle observations, as well as quantum
mechanics, then it is as successful a scientific approach as quantum
mechanics. There is no difference, philosophically, between looking at
numbers and looking at pictures. Pictures, after all, are just
numbers. You can do science with pictures or text, as you do with
numbers, ask a botanist or a linguist.
Best Regards,
--
Eray Ozkural
ueb
> On Wed, 28 Apr 2004, daniel B miller wrote:
>> You can call it what you want, but your obvious ignorance of the subject
>> and inability to understand the fundamental concepts involved makes your
>> opinion pretty much useless.
> Note that besides these not-quite-nice and not-at-all reasonable cliches,
> you have not given a simple argument and you have not answered a single
> question or objection raised in my posting. The reason is that this
> fundamentalist discrete way of thinking about physics is not able to
> answer any questions. It is not (natural) science, it is not new, and as
> you are repeatedly showing, it is not kind either.
Is that not the consequence of that today's physicists are too proud
to ask the simple question: "What quantities have discrete values ?"
> Once again, the centuries or millenia of evolution of physics led to
> General Relativity and the Standard Model that are continuous theories
> that explain all physical phenomena at distances longer than 10^-17
> meters.
The geometric theory, which unifies general relativity and electro-
magnetism, and predicts particle numbers, does not have such limits.
Unless numerical simulations indicate limits.
> They have a lot of discrete features: quantum mechanics always
> shows that the spectrum of many operators is discrete, for example.
Are operators real physical quantities ?
..
> Nevertheless the defining equations and the evolution, as given by
> Schrodinger's equation, are always continuous and so far it seems that it
> must be continuous.
I share your faith in the continuum. Do you see a way to prove it ?
> One can play with various approximate discrete models. One can latticize
> spacetime in lattice gauge theories, for example. Note that even in the
> case of this approximation, the basic degrees of freedom that live on the
> lattice sites are continuous. If one performs any numerical calculations,
> these numbers themselves are approximated by numbers with a finite number
> of digits. But all these things are just approximations or children's toy
> models; the reality is based on continuous equations.
You have no clue of numerical calculations. Note: If convergences for
more and more small time & length differences exist, these convergences
always differ from "conventional" solutions (non-numerically calculated).
Even my numerical simulations according to the Einstein-Maxwell
equations indicate the particle numbers in such fundamentally
different solutions.
> The discrete character of Nature can emerge in various contexts, but it
> can never be *the* fundamental formulation because it would imply, among
> many other wrong consequences, that all continuous symmetries must be
> broken.
And ? If it is so, we have to take notice of it.
> The very fact
> that the world is quantum-mechanical is enough to rule out all these naive
> approaches to physics.
That is no very fact but a very phantasy. It is neither cleanly
continuous nor consequently discrete, but a hotchpotch that fails
more and more.
> Physics must be described by a Hilbert space with
> operators - or equivalently by a probabilistically interpreted
> path-integral.
No, it must not.
> There is no evidence whatsoever that these basic principles
> could be replaced by anything else,
What do you take this confidence from ?
> and all attempts to "undo" the quantum
> revolution and return to a classical description have failed and the
> probability that they could ever work is continously shrinking.
This claim is plainly wrong. You must not bother your brain with
any shrinking probability. They _do_ simply work :-) , see
http://home.t-online.de/home/Ulrich.Bruchholz/
> OK, let me imagine that the NKS-science will accept that the task is to
> look for a quantum-mechanical theory. Wavefunctions and probabilities
> predicted from them must be allowed to be continuous, and let me imagine
> that the proponents of the NKS science will learn these basic points of
> undergraduate physics in one sunny day, and they will try to make the
> quantum-mechanical theory as discrete as possible.
> Well, they will be still guaranteed to fail.
Agree. Because each try to fit quantum mechanics to a serious theory,
must fail.
..
> We've learned many things about the equivalence of various
> discrete and continuous interpretations of some physical theories, but a
> theory without a set of defining continuous equations will probably never
> be accepted as a serious model for physics, and every person who knows
> something about our actual knowledge of physics understands why my
> statement is powerful and likely, given the current picture of the world
> as painted by physics, even though the statement is not rigorously proved
> yet.
What is the difference between the building block models of quantum
mechanics and cellular automata ? The latter are more consequent.
But I agree with you that continuous equations are fundamental.
Geometrical - not such from QM.
Ulrich
Ed Fredkin
snip
> ...you have not given a simple argument and you have not answered a single
> question or objection raised in my posting. The reason is that this
> fundamentalist discrete way of thinking about physics is not able to
> answer any questions. It is not (natural) science, it is not new, and as
> you are repeatedly showing, it is not kind either.
>
We have simple differences of opinion. Not all physicists agree on
all things. There's no reason for anyone to get huffy. The idea that
discrete models might be able to usefully address and answer
fundamental questions in physics is not foreign to competent
physicists. Feynman gave and 奏 Hooft is still giving serious
consideration to such models as cellular automata. Both Wolfram and
myself are physicists who might be wrong but who are not stupid.
The most powerful tool a good physicist has is a bag of tricks used to
quickly toss out ideas that are losers. It's a natural instinct to
avoid useless mental wandering. However the tool is not foolproof;
many physicists rejected early versions of quark theory (in the days
before color was invented). Others correctly realized that by
continuing to work with a "wrong" model that had a lot of explanatory
utility, a way might be found to get around the obvious difficulties.
Continuous mathematical models can work wonderfully well for discrete
systems. In fact, such models can be in as exact a correspondence as
possible. An example from mathematics is: n!<=>Gamma(n+1). We
have lots of so called "correct" continuous mathematical models in
physics that are modeling systems with discrete quantities (charge,
mass, fluid dynamics).
This field, called "Digital Mechanics," has many obvious difficulties.
One should note that it has overcome a number of difficulties during
the last 40 years. While vastly inferior to current accepted models
based on the continuum, DM does have answers down pat to some
questions that aren't answered by the Standard Model. No one, on
either side of a continuous vs. discrete basis for physics, has either
God or all the known experimental data on his or her side.
Let's try to dedicate one thread to one question. We can all be civil
and perhaps some of us can learn, some can explain, some can be amused
and everyone has the priviledge of ingnoring it all.
Ed F
ueb
> If discrete physics can come to the point where it can accurately
> predict cosmological or particle observations, as well as quantum
> mechanics, then it is as successful a scientific approach as quantum
> mechanics. There is no difference, philosophically, between looking at
> numbers and looking at pictures. Pictures, after all, are just
> numbers. You can do science with pictures or text, as you do with
> numbers, ask a botanist or a linguist.
First, I agree. May I remark that neither discrete nor continuous
physics can predict quantum mechanics, because it is a conglomeration
of _methods_ . Pretty dubious methods, as gravity experiments as well
as results from numerical simulations (that I already named you in
another reply to you) demonstrate.
BTW, particle observations are not quantum mechanics. Each serious
physical theory must *predict* particles.
Ulrich
Lubo? Motl
> Is that not the consequence of that today's physicists are too proud
> to ask the simple question: "What quantities have discrete values ?"
I think that this is a very good question, but it also seems to me
that the physicists are asking this question very often - at least a
sufficient fraction of the physicists. It is important to keep in mind
that it is a question, and the answer for specific observables can be
both YES as well as NO.
> The geometric theory, which unifies general relativity and electro-
> magnetism, and predicts particle numbers, does not have such limits.
> Unless numerical simulations indicate limits.
By "geometric theory", do you mean the Kaluza-Klein theory, or string
theory, or something else? I wrote about the limit 10^-17 meters
because we don't know what's exactly happening at shorter distance
scales. The Standard Model may be applied to even shorter distances,
but it is not guaranteed that this theory will work in this realm,
too.
Many things can be modified at very short distances, or equivalently
very high energies, and even something similar to the discreteness of
some unexpected kind can be relevant at very short distances.
> Are operators real physical quantities ?
Operators are gadgets into which you insert a complex vector (a state
in the Hilbert space), and you obtain another vector. For special
choices of the vectors, the result will be the same vector up to an
overall multiplication by a number. In that case, the number is called
the "eigenvalue" and the vector is the "eigenvector". The set of all
possible eigenvalues of an operator is called the spectrum.
According to quantum mechanics, measurable real quantities such as the
energy, position, or momentum are represented by *Hermitean* operators
- which are operators whose all eigenvalues are real and the
corresponding eigenvectors are orthogonal. Operators are observables
in quantum mechanics, and they are more subtle than simple
number-valued observables in classical physics. More concretely, they
can have discrete spectrum. For example, the energy spectrum of an
electron in the Hydrogen atom has both discrete as well as continuous
part. The discrete part of the spectrum describes the bound states of
the atom - 1s, 2s, and so forth - while the continuous part describes
the ionized atom. Both of them exist in the real world.
The discrete character of the Hydrogen spectrum is a derived concept.
The wavefunction for the discrete eigenstates has a finite number of
zeroes. The last zero must be approached at x=infinity (or the
boundary of the region where the particle propagates) because a
nonzero value would make the wavefunction non-normalizable (the
probabilities computed from such a non-convergent wavefunction would
be infinite). This constraint that "the last zero of psi(x) exactly
hits x=infinity" guarantees that the energy must be one of the
discrete eigenvalues.
> I share your faith in the continuum. Do you see a way to prove it ?
Not really, especially because so far I don't see a rigorous enough
way to state the theorem that we would like to prove. ;-)
> You have no clue of numerical calculations.
Feel free to think so if it makes you happier.
> Note: If convergences for
> more and more small time & length differences exist, these convergences
> always differ from "conventional" solutions (non-numerically calculated).
Right.
> Even my numerical simulations according to the Einstein-Maxwell
> equations indicate the particle numbers in such fundamentally
> different solutions.
Hmm.
> And ? If it is so, we have to take notice of it.
Yes, but the fact is that all observations that anyone has ever done
indicate that it is *not* so, and these continuous symmetries do work
so far.
> > The very fact
> > that the world is quantum-mechanical is enough to rule out all these naive
> > approaches to physics.
>
> That is no very fact but a very phantasy. It is neither cleanly
> continuous nor consequently discrete, but a hotchpotch that fails
> more and more.
I am not sure what you meant by "it", so I can't respond.
> > Physics must be described by a Hilbert space with
> > operators - or equivalently by a probabilistically interpreted
> > path-integral.
>
> No, it must not.
Certainly, physics today knows of no working non-equivalent
alternative that would be able to deal with the effects discovered
after the birth of quantum physics.
> > There is no evidence whatsoever that these basic principles
> > could be replaced by anything else,
>
> What do you take this confidence from ?
Seven decades of our investigation of quantum mechanics, seven decades
of failed attempts to create non-quantum alternatives to describe
quantum phenomena, seven decades that have been increasingly
convincing us that quantum mechanics and its mathematical as well as
interpretational characteristics must be taken seriously, thousands of
papers that show how amazingly accurate this theory is, many
experiments that show that even the mind-boggling consequences of
quantum mechanics are true in the real world, thousands of my hours
that I spent thinking about this issue, and increasingly unreasonable
and un-professional proposals of the people who would like to reject
the principles of quantum mechanics. Is not it enough for one to make
some expectations?
Be sure that when I was 16, I also wanted to replace quantum mechanics
by a deeper deterministic theory.
> This claim is plainly wrong. You must not bother your brain with
> any shrinking probability. They _do_ simply work :-) , see
> http://home.t-online.de/home/Ulrich.Bruchholz/
This is a contribution to the last reason among those listed above -
reasons to be quite certain that quantum mechanics must be taken as it
is.
> What is the difference between the building block models of quantum
> mechanics and cellular automata ?
I don't know where to start - it is like asking what is the difference
between a cat and a can of Coke. Quantum mechanics works with
probabilities and complex Hilbert spaces, while cellular automata
don't - they work with discrete deterministic systems.
All the best
Lubos
ueb
> No one, on
> either side of a continuous vs. discrete basis for physics, has either
> God or all the known experimental data on his or her side.
Is this seeming opposite really so incompatible ?
There is a geometric theory unifying general relativity and "classical"
electrodynamics, expressed by the known Einstein-Maxwell equations.
First, we have the data from GR and EM. But only a discrete approach
of these tensor equations lets see particle numbers. Such discrete
approach reveals discrete solutions, which are nothing else than
particles. The discrete values of the integration constants are
the particle numbers.
If time and space are indeed fundamentally discrete, the computations
will indicate it, as I already told.
Ulrich Bruchholz
http://home.t-online.de/home/Ulrich.Bruchholz/
daniel B miller
[snip]
> Certainly, physics today knows of no working non-equivalent
> alternative that would be able to deal with the effects discovered
> after the birth of quantum physics.
>
>>>There is no evidence whatsoever that these basic principles
>>>could be replaced by anything else,
>>
>>What do you take this confidence from ?
>
>
> Seven decades of our investigation of quantum mechanics, seven decades
> of failed attempts to create non-quantum alternatives to describe
> quantum phenomena, seven decades that have been increasingly
> convincing us that quantum mechanics and its mathematical as well as
> interpretational characteristics must be taken seriously, thousands of
> papers that show how amazingly accurate this theory is, many
> experiments that show that even the mind-boggling consequences of
> quantum mechanics are true in the real world, thousands of my hours
> that I spent thinking about this issue, and increasingly unreasonable
> and un-professional proposals of the people who would like to reject
> the principles of quantum mechanics. Is not it enough for one to make
> some expectations?
>
> Be sure that when I was 16, I also wanted to replace quantum mechanics
> by a deeper deterministic theory.
>
in experimental and theoretical physics implies a lack of determinism.
Anyone with an intuitive grasp of the nature of simple finite systems
realizes that any apparently probablistic theory can be replaced by a
fully deterministic (and finite) one, given that the deterministic
theory will have to operate at a scale far enough below our observations
to allow the statistical nature of the process to emerge. Perhaps that
scale is around 10**-17 meters, or it could be much smaller. All the
symmetries of translation, rotation, and the rest can easily be
accomodated by such a theory. Even features that are unsettling to our
physical intuition, such as superpositions, EPR, and all the rest, can
and will be shown to be consistent with a deterministic, finite, and
discrete theory.
In any case, believing that, because a statistical theory does not
quickly succumb to the search for its causal roots, that such roots must
not exist, strikes me as completely unscientific. To me, it's
reminiscent of the consistent dualist belief in the animus professed by
most biologists up until evidence produced in the last century made such
a position untenable. Similarly, the idea that there can be effects
without causes will undoubtedly be seen as one of the strange artifacts
of an age in which a good deal was known about how things appear, but
almost nothing was understood about *why* things appear as they are.
Finally, the tools of continuous mathematics are tools of analysis, not
synthesis. When one shows that constraints imposed on a set of
parameters are consistent with physics, one is simply stating one's
observations in a precise and unambiguous form. One is not, in this
case, saying anything about how the world actually works. For this, one
needs to move beyond mathematics, into the realm of processes. There is
nothing unscientific or unduly speculative about searching for such a
process, and there is nothing in the canon that prohibits such a process
from existing. The fact that most people, including most working
scientists, believe that such a prohibition exists is a curious but
ultimately irrelevant fact, most likely due to the historical quirk that
Quantum theory was developed before the advent of computers and a fuller
understanding of information theory, computation, and complexity (ie the
Church/Turing thesis and so on).
Statistical theories must always reduce to deterministic ones. To
believe otherwise is to believe in magic, and is the antithesis of
responsible science.
-dbm
PS: nothing in this post implies that any of the existing 'hard' results
of QM or the Standard Model will be 'disproved'. They will merely be
seen as what they are, statistical descriptions of an underlying reality
that consists of a discrete, finite, and deterministic process.
Similarly, understanding the nature of atoms and molecules did not
invalidate chemistry or thermodynamics. Even the Copernican model did
not make the complex machinations of the Ptolemaic system any less
accurate (though it did render them obsolete, as the new system was
vastly more accurate and powerful, not to mention a whole lot simpler
and more elegant.)
Lubos Motl
> Absolutely nothing about QM and the last 70 or more years of progress
> in experimental and theoretical physics implies a lack of determinism.
This is a very popular, and very incorrect, misconception. It is
widespread among the laymen as well as among the badly informed and badly
educated scientists. The history is nevertheless very exciting.
In fact, many physicists in the past - even some of the greatest
physicists like Einstein - were victims of this deterministic prejudice
and they tried to prove that at the deepest possible level, Nature works
according to some deterministic rules and quantum mechanics had to be
merely an approximate description. The results of their effort was just
the opposite: their investigation, initiated by Einstein, Podolsky, Rosen,
and continuing in the works of Bohm, Bell, Aspect, and others, have led to
the experimental test of violation of Bell's inequalities - i.e. a proof
that no such deterministic sublayer of explanation can exist.
Bell proved a mathematical theorem that *every* theory working according
to such classical rules, and respecting at least some approximate forms of
locality and reality, will imply that the phenomena in the world will
satisfy certain inequalities - these inequalities are saying that the
correlations between different observables will belong to some interval.
(I recommend everyone Brian Greene's "The Fabric of the Cosmos", whose
chapter 4 is a very good, entertaining and rather complete treatment of
quantum entanglement and Bell's inequalities. It also covers all major
ways how people look at these issues.)
Quantum mechanics was known to lead to stronger correlations (which is why
Einstein started to investigate these matters), and its prediction was
proved experimentally beyond any doubts (the type of experiments initiated
by Aspect et al. is, so far, the most impressive confirmation of
quantum-predicted correlations). Although Einstein, Bell, and others
believed that the measured correlations had to satisfy Bell's
inequalities, the reality showed clearly that these inequalities are not
only violated in Nature, but they are exactly equal to the numbers
predicted using the standard orthodox quantum mechanics.
This fact excludes the possibility that the world is desribed by any
deterministic local automaton, one that is analogous to "life". The
Lorentz invariance - even if it is an approximate one - makes highly
non-local fundamental laws also very unlikely. Whoever tries to ignore
violation of Bell's inequalities in the real world and construct theories
that would necessarily imply that Bell's inequalities are satisfied, can
be safely classified as a crackpot.
> Anyone with an intuitive grasp of the nature of simple finite systems
> realizes that any apparently probablistic theory can be replaced by a
> fully deterministic (and finite) one, given that the deterministic
> theory will have to operate at a scale far enough below our observations
> to allow the statistical nature of the process to emerge.
There are many chaotic phenomena in Nature that have origin in
classical statistical physics, but there are also inherently quantum
phenomena that *cannot* have such a classical, deterministic origin.
The discussion whether one can find a "deeper" deterministic theory
underlying quantum phenomena used to be thought to be a philosophical
debate which would never be answered scientifically.
Happily, the results of Einstein, Podolsky, Rosen, Bell, and others showed
that these two possibilities may be distinguished by experiment - and in
fact, once the experiment is done, the local deterministic description of
the world can be safely ruled out.
In principle, academically speaking, there could still be a non-local
deterministic description of the world that is more fundamental than the
standard quantum mechanics. There are many reasons to think that it would
violate the principles of relativity and it would have other problems, but
even if one imagines that these problems are fixed in some way, it is
absolutely clear that such non-local laws can't look like anything in the
"New Kind of Science" and the knowledge of NKS would be useless to
understand anything about such a theory.
(Note added: this post has been submitted, approved, accidentally deleted
by a confused moderator, and resubmitted with a couple of additions. LM)
ueb
deterministic. The Einstein-Maxwell equations, that I take as
fundamental, do not involve determinism, because they have only
10 independent equations for 14 components.
Ulrich
ueb
> ueb wrote in message news:<o35s6c...@Muse2.private.de>...
>> Is that not the consequence of that today's physicists are too proud
>> to ask the simple question: "What quantities have discrete values ?"
> I think that this is a very good question, but it also seems to me
> that the physicists are asking this question very often - at least a
> sufficient fraction of the physicists.
Who ? These should understand what I did.
> It is important to keep in mind
> that it is a question, and the answer for specific observables can be
> both YES as well as NO.
I meant actually *what* observables. Of course, the greater the values,
the more these appear continuous.
>> The geometric theory, which unifies general relativity and electro-
>> magnetism, and predicts particle numbers, does not have such limits.
>> Unless numerical simulations indicate limits.
> By "geometric theory", do you mean the Kaluza-Klein theory, or string
> theory, or something else?
The theories, named by you, introduce additional dimensions. There
is no evidence for such dimensions. - I mean the geometric theory
of gravitation and electromagnetism, formally expressed by the
known Einstein-Maxwell equations. It unifies general relativity
and "classical" electrodynamics.
> I wrote about the limit 10^-17 meters
> because we don't know what's exactly happening at shorter distance
> scales. The Standard Model may be applied to even shorter distances,
> but it is not guaranteed that this theory will work in this realm,
> too.
Is your limit a minimal radius or a shortest difference ?
Thanks for your careful explanation.
Since the real world is not (mathematically) complex, these nice
descriptions must be pure images, particularly if these aim to
real eigenvalues for discreteness. Do physicists see that so too ?
>> I share your faith in the continuum. Do you see a way to prove it ?
> Not really, especially because so far I don't see a rigorous enough
> way to state the theorem that we would like to prove. ;-)
>> You have no clue of numerical calculations.
> Feel free to think so if it makes you happier.
You have snipped the cause of this remark. ;)
>> Note: If convergences for
>> more and more small time & length differences exist, these convergences
>> always differ from "conventional" solutions (non-numerically calculated).
> Right.
>> Even my numerical simulations according to the Einstein-Maxwell
>> equations indicate the particle numbers in such fundamentally
>> different solutions.
> Hmm.
You just comment the most important statement with "Hmm".
In which, you are a lot more polite than your colleagues, who immediately
forget speaking at such statement, and treat it like leprosy or aids.
>> And ? If it is so, we have to take notice of it.
> Yes, but the fact is that all observations that anyone has ever done
> indicate that it is *not* so, and these continuous symmetries do work
> so far.
>> > The very fact
>> > that the world is quantum-mechanical is enough to rule out all these naive
>> > approaches to physics.
>>
>> That is no very fact but a very phantasy. It is neither cleanly
>> continuous nor consequently discrete, but a hotchpotch that fails
>> more and more.
> I am not sure what you meant by "it", so I can't respond.
Ok, forget it then. But may I ask two humble questions ? -
1.) How do you claim that the world be "quantum-mechanical" ?
Is not quantum mechanics a method to describe the world ?
How does quantum mechanics become a property of the world ?
2.) How do you claim that the other approaches be "naive" ?
You may want that the other approaches are ruled out. But nature
does not know your desire.
>> > Physics must be described by a Hilbert space with
>> > operators - or equivalently by a probabilistically interpreted
>> > path-integral.
>>
>> No, it must not.
> Certainly, physics today knows of no working non-equivalent
> alternative that would be able to deal with the effects discovered
> after the birth of quantum physics.
For that reason, it is time for physics to experience such
alternative.
>> > There is no evidence whatsoever that these basic principles
>> > could be replaced by anything else,
>>
>> What do you take this confidence from ?
> Seven decades of our investigation of quantum mechanics, seven decades
> of failed attempts to create non-quantum alternatives to describe
> quantum phenomena, seven decades that have been increasingly
> convincing us that quantum mechanics and its mathematical as well as
> interpretational characteristics must be taken seriously, thousands of
> papers that show how amazingly accurate this theory is, many
> experiments that show that even the mind-boggling consequences of
> quantum mechanics are true in the real world, thousands of my hours
> that I spent thinking about this issue, and increasingly unreasonable
> and un-professional proposals of the people who would like to reject
> the principles of quantum mechanics. Is not it enough for one to make
> some expectations?
> Be sure that when I was 16, I also wanted to replace quantum mechanics
> by a deeper deterministic theory.
Your mistake was to search for a _deterministic_ theory. But the
alternative theory, that works, is not deterministic. The Einstein-
Maxwell equations do not involve determinism with 10 independent
equations for 14 components.
With this mistake, it could take seven decades. The eighth decade
will bring the change.
>> This claim is plainly wrong. You must not bother your brain with
>> any shrinking probability. They _do_ simply work :-) , see
>> http://home.t-online.de/home/Ulrich.Bruchholz/
> This is a contribution to the last reason among those listed above -
> reasons to be quite certain that quantum mechanics must be taken as it
> is.
Come down from your high horse, and see for yourself.
Ulrich
Tim Tyler
> > Absolutely nothing about QM and the last 70 or more years of progress
> > in experimental and theoretical physics implies a lack of determinism.
>
> This is a very popular, and very incorrect, misconception. [...]
> Bell proved a mathematical theorem that *every* theory working according
> to such classical rules, and respecting at least some approximate forms of
> locality and reality, will imply that the phenomena in the world will
> satisfy certain inequalities - these inequalities are saying that the
> correlations between different observables will belong to some interval.
>
> (I recommend everyone Brian Greene's "The Fabric of the Cosmos", whose
> chapter 4 is a very good, entertaining and rather complete treatment of
> quantum entanglement and Bell's inequalities. It also covers all major
> ways how people look at these issues.)
>
> Quantum mechanics was known to lead to stronger correlations (which is why
> Einstein started to investigate these matters), and its prediction was
> proved experimentally beyond any doubts (the type of experiments initiated
> by Aspect et al. is, so far, the most impressive confirmation of
> quantum-predicted correlations). Although Einstein, Bell, and others
> believed that the measured correlations had to satisfy Bell's
> inequalities, the reality showed clearly that these inequalities are not
> only violated in Nature, but they are exactly equal to the numbers
> predicted using the standard orthodox quantum mechanics.
>
> This fact excludes the possibility that the world is desribed by any
> deterministic local automaton, one that is analogous to "life". [...]
No it doesn't.
See:
``So where did Bell and Eberhard go wrong? They thought that all theories
that reproduced the standard predictions must be non-local. It has been
pointed out by both Albert [A] and Cramer [C] (who both support
different interpretations of QM) that Bell and Eberhard had implicity
assumed that every possible measurement - even if not performed - would
have yielded a single definite result. This assumption is called
contra-factual definiteness or CFD [S]. What Bell and Eberhard really
proved was that every quantum theory must either violate locality or
CFD. Many-worlds with its multiplicity of results in different worlds
violates CFD, of course, and thus can be local.''
- http://www.hedweb.com/everett/everett.htm#bell
The MWI is a determinisitic, local theory.
The idea that such theories are ruled out by experimental tests of
Bell's inequality is incorrect - as explained above.
--
__________
|im |yler http://timtyler.org/ t...@tt1lock.org Remove lock to reply.
ueb
from Lubos Motl]
That is the best explanation re determinism, I saw.
Does indeterminism not simply mean lack of rules, regardless
whether continuous or discrete ?
Many scientists (under them Einstein) made the fundamental
mistake not to accept such lack of rules. They tried to save
the determinism by means of obscure "matter", that promised
unambiguous solutions.
Are you aware that quantum mechanics is not the ultimate
solution of that, because of oddities like unmeasurable forces
and lots of unseen quantities ?
BTW, if you believe that the geometric theory, proposed by me,
would "ignore violation of Bell's inequalities in the real world",
it is not so. That theory does even not imply that Bell's
inequalities are satisfied.
Ulrich
daniel B miller
There are other candidates besides full-blown MWI that are finite and
discrete but could reproduce EPR-type observations, as well as Lorenz
invariance. I for one have my doubts that what we percieve as local is
in fact local in the computational space in which low-level physics
operates.
None of these considerations in any way preclude either determinism or
fully discrete models. Proposing that non-local correlations imply a
lack of determinism is simply sloppy thinking.
-dbm
Lubos Motl
> > L.M.: ...
> > This fact excludes the possibility that the world is described by any
> > deterministic local automaton, one that is analogous to "life". [...]
>
> No it doesn't. See:
>
> ``So where did Bell and Eberhard go wrong? They thought that all theories
> that reproduced the standard predictions must be non-local. It has been
> pointed out by both Albert [A] and Cramer [C] (who both support
> different interpretations of QM) that Bell and Eberhard had implicity
> assumed that every possible measurement - even if not performed - would
> have yielded a single definite result. This assumption is called
> contra-factual definiteness or CFD [S]. What Bell and Eberhard really
> proved was that every quantum theory must either violate locality or
> CFD. Many-worlds with its multiplicity of results in different worlds
> violates CFD, of course, and thus can be local.''
Once again: the local deterministic cellular automata are ruled out - and
we were lucky because the quotation you have chosen is not only fine, but
it is essentially equivalent to mine - in fact it is stronger. You see
that the quotation above says that the local theories satisfying
contra-factual definiteness are ruled out. I only said that local
deterministic theories are ruled out. Determinism is stronger than CFD,
and therefore my statement was weaker.
CFD only requires some notion of "real existence of the answers before we
try to measure them"; determinism also requires that, plus something else.
At any rate, local cellular automata satisfy both locality as well as CFD,
and therefore they are ruled out as a theory of Nature. This is what
science is good for - we can actually disprove incorrect conjectures.
This shows the power of human thinking and creativity. Without such
progress, we could still believe that the atomic theories as proposed by
Democritus et al. might be the exact description of Nature; we could
continue to believe that we live on a gigantic turtle; we could still
believe that the world exactly obeys some "improved" classical Newton's
equations; or we could even believe that the world is a discrete computer
with a simple, discrete deterministic program. By finding the right
questions and by measuring the answers as Nature tells them, we are
actually able to learn a lot about Nature: we can easily exclude the whole
classes of theories and find the necessary characteristics that every
good and complete theory must have.
> - http://www.hedweb.com/everett/everett.htm#bell
> The MWI is a determinisitic, local theory.
First of all, MWI is not a theory; MWI is philosophy, and it has not been
completed into a full scientific selection mechanism. The only way to make
predictions using something like MWI is to say that MWI, if properly
defined, should be equivalent to the standard probabilistic quantum
mechanics, but no one knows a deeper mechanism that would lead to the
correct probability distributions. If MWI is not a well-defined theory,
then we cannot say whether it really satisfies CFD or not. It is certainly
not a theory of the usual type, and it is not an example of a cellular
automaton.
Lubos Motl
> That is the best explanation re determinism, I saw.
> Does indeterminism not simply mean lack of rules, regardless
> whether continuous or discrete ?
That's a very good point - or a very good question. There are various
levels of determinism. The word "deterministic" usually means "satisfying
Laplacian (classical) determinism". According to the Laplacian
determinism, the Universe is a huge clockwork that acts according to very
strict and unique rules analogous to mechanics (e.g. Newton's equations),
and it leaves no room for freedom in the motion of the objects, or for
uncertainty. Until the early 20th century, people believed in Laplacian
determinism. Usually they worked with continuous theories, but discrete
theories could have been considered, too. Our world in the classical limit
however happens to be more continuous than discrete. The more classical
approximation we adopt for description of the real world, the more
continuous the measurable quantities become.
Quantum mechanics changed the role of determinism, and it showed that the
only thing that is predictable are the probabilities of various outcomes.
These probabilities can be calculated from the wavefunction, and the
wavefunction satisfies a very well-defined equation (Schrodinger's
equation). The evolution of the wavefunction is as deterministic as the
evolution of the Universe was according to the Laplacian determinism.
However the wavefunction is not a real object that can be directly
measured. It is only an auxilliary tool that we use to compute the
probabilities that something else will happen. The deterministic
evolution of the wavefunction is a manifestation of "quantum determinism"
- the evolution is deterministic, but the wavefunction itself is not the
answer itself: the answers are obtained indirectly through a probabilistic
interpretation of the wavefunction.
The individual events became slightly unpredictable as quantum mechanics
became the accepted description; however the statistical averages and
other numbers remained totally exactly calculable - in fact, quantum
theories gave the most precise (verified) predictions in the history of
science. For example, the magnetic moment of the electron can be
calculated and experimentally verified with the accuracy of 15 decimal
digits or so.
> Many scientists (under them Einstein) made the fundamental
> mistake not to accept such lack of rules. They tried to save
> the determinism by means of obscure "matter", that promised
> unambiguous solutions.
Right.
> Are you aware that quantum mechanics is not the ultimate
> solution of that, because of oddities like unmeasurable forces
> and lots of unseen quantities ?
No, I am not aware of ghosts that control our lives. If something is
unmeasurable (in principle), then it does not exist, and Bell's
inequalities are an example that we are able to show that a certain type
of ghosts and spirits (local hidden variables in this case) can't exist.
The inexpensive cliche "the world is so complicated and full of
unmeasurable and unpredictable things" has never led to any progress in
science, and I guess that it never will.
Lubos Motl
> There are other candidates besides full-blown MWI that are finite and
> discrete but could reproduce EPR-type observations, as well as Lorenz
> invariance.
No, there are no discrete, exactly Lorentz-invariant models (this is a
manifest oxymoron because the Lorentz group is continuous - and Ed Fredkin
understands very well that the Lorentz group must be broken at some level
if the discrete models were correct), and there are certainly no such
models that would also allow EPR-like observations.
> I for one have my doubts that what we percieve as local is
> in fact local in the computational space in which low-level physics
> operates.
The world "local" has a unique meaning in mathematics, and in physics it
is almost always used as "local in the position space or spacetime". The
question whether a theory is local in spacetime is the essential question.
A physical theory can work with an auxilliary space - e.g. the stringy
worldsheet - that has its own notion of "locality", but these are
irrelevant technicalities that don't affect the questions whether
(spacetime) locality must be broken for a deterministic theory if it
reproduces the EPR predictions of quantum mechanics. The answer is that
any such a deterministic theory would have to be non-local (in spacetime),
regardless of your hidden layer of "computational locality".
> None of these considerations in any way preclude either determinism or
> fully discrete models. Proposing that non-local correlations imply a
> lack of determinism is simply sloppy thinking.
What you call sloppy thinking is a mathematical theorem: correlations
outside a certain interval imply that the underlying theory is either
non-deterministic (in fact, violating CFD), or non-local. The correlations
outside these intervals have been measured experimentally, and combining
that with the theorem implies that the world must either violate CFD, or
it must be non-local. I personally use the words "sloppy thinking" for the
approach to questions that avoids mathematical rigor and mathematical
theorems.
Quantum field theory (or string theory, if you want me to include
gravity), the state-of-the-art description of the real world, has a
precise answer which things are violated and in what sense. It is a
quantum theory, and therefore it is not classically deterministic, but it
does allow quantum correlations. The dynamical laws - e.g. the
Heisenberg's evolution equations for the operators in quantum field theory
- are totally local and causal (or at least approximately, in the case of
string theory), but the nonlocal character of the wavefunction itself
nevertheless allows measurements that "look" non-local.
Tim Tyler
>
> > > L.M.: ...
> > > This fact excludes the possibility that the world is described by any
> > > deterministic local automaton, one that is analogous to "life". [...]
> >
> > No it doesn't. See:
> >
> > ``So where did Bell and Eberhard go wrong? They thought that all theories
> > that reproduced the standard predictions must be non-local. It has been
> > pointed out by both Albert [A] and Cramer [C] (who both support
> > different interpretations of QM) that Bell and Eberhard had implicity
> > assumed that every possible measurement - even if not performed - would
> > have yielded a single definite result. This assumption is called
> > contra-factual definiteness or CFD [S]. What Bell and Eberhard really
> > proved was that every quantum theory must either violate locality or
> > CFD. Many-worlds with its multiplicity of results in different worlds
> > violates CFD, of course, and thus can be local.''
>
> Once again: the local deterministic cellular automata are ruled out - and
> we were lucky because the quotation you have chosen is not only fine, but
> it is essentially equivalent to mine - in fact it is stronger. You see
> that the quotation above says that the local theories satisfying
> contra-factual definiteness are ruled out. I only said that local
> deterministic theories are ruled out. Determinism is stronger than
> CFD, and therefore my statement was weaker.
Perhaps you missed this bit on the page:
``Q13 Is many-worlds a deterministic theory?
Yes, many-worlds is a deterministic theory [...]''
- http://www.hedweb.com/everett/everett.htm
> CFD only requires some notion of "real existence of the answers before we
> try to measure them"; determinism also requires that, plus something else.
> At any rate, local cellular automata satisfy both locality as well as CFD,
> and therefore they are ruled out as a theory of Nature. [...]
The use of cellular automata as modelling tools says absolutely nothing
about whether what is being modelled is a universe or a multiverse.
Model the universe with CA and you have a "definite" model.
Model the multiverse using a CA and you don't.
> > The MWI is a determinisitic, local theory.
>
> First of all, MWI is not a theory; MWI is philosophy, and it has not been
> completed into a full scientific selection mechanism. The only way to make
> predictions using something like MWI is to say that MWI, if properly
> defined, should be equivalent to the standard probabilistic quantum
> mechanics, but no one knows a deeper mechanism that would lead to the
> correct probability distributions. If MWI is not a well-defined theory,
> then we cannot say whether it really satisfies CFD or not. It is certainly
> not a theory of the usual type, and it is not an example of a cellular
> automaton.
The MWI is a theory - in every sense of the word. See:
``Q36 What unique predictions does many-worlds make?
A prediction occurs when a theory suggests new phenomena. Many-worlds
makes at least three predictions, two of them unique: about linearity,
(See "Is linearity exact?"), quantum gravity (See "Why quantum
gravity?") and reversible quantum computers (See "Could we detect other
Everett-worlds?").
- http://www.hedweb.com/everett/everett.htm#unique
The problem with the MWI as a theory is not that it does not make
its own bunch of predictions - but rather that its predictions are
in a realm where they are challenging to test.
daniel B miller
Lubos Motl wrote:
> On Mon, 3 May 2004, daniel B miller wrote:
>
>
>>There are other candidates besides full-blown MWI that are finite and
>>discrete but could reproduce EPR-type observations, as well as Lorenz
>>invariance.
>
>
> No, there are no discrete, exactly Lorentz-invariant models (this is a
> manifest oxymoron because the Lorentz group is continuous - and Ed Fredkin
> understands very well that the Lorentz group must be broken at some level
> if the discrete models were correct),
I'll rephrase: there are candidates which easily approximate Lorenz
invariance in the limit as our observations cover a wider range of
distances and timescales.
> and there are certainly no such
> models that would also allow EPR-like observations.
>
see below.
>
>>I for one have my doubts that what we percieve as local is
>>in fact local in the computational space in which low-level physics
>>operates.
>
> The world "local" has a unique meaning in mathematics, and in physics it
> is almost always used as "local in the position space or spacetime". The
> question whether a theory is local in spacetime is the essential question.
> A physical theory can work with an auxilliary space - e.g. the stringy
> worldsheet - that has its own notion of "locality", but these are
> irrelevant technicalities that don't affect the questions whether
> (spacetime) locality must be broken for a deterministic theory if it
> reproduces the EPR predictions of quantum mechanics. The answer is that
> any such a deterministic theory would have to be non-local (in spacetime),
> regardless of your hidden layer of "computational locality".
I agree. Read my post again. What I am saying is that a deterministic
theory is not ruled out by Bell's inequality; only local, deterministic
theories are (presumptively) ruled out.
>
>>None of these considerations in any way preclude either determinism or
>>fully discrete models. Proposing that non-local correlations imply a
>>lack of determinism is simply sloppy thinking.
>
>
> What you call sloppy thinking is a mathematical theorem: correlations
> outside a certain interval imply that the underlying theory is either
> non-deterministic (in fact, violating CFD), or non-local. The correlations
> outside these intervals have been measured experimentally, and combining
> that with the theorem implies that the world must either violate CFD, or
> it must be non-local. I personally use the words "sloppy thinking" for the
> approach to questions that avoids mathematical rigor and mathematical
> theorems.
Neither of us has introduced any rigor, mathematical or otherwise, in
this discussion. It is an english-language conversation at this point,
and anything you or I, or anyone for that matter, says about this stuff
must of course be fleshed out with a great amount of rigor to become
scientifically interesting.
>
> Quantum field theory (or string theory, if you want me to include
> gravity), the state-of-the-art description of the real world, has a
> precise answer which things are violated and in what sense. It is a
> quantum theory, and therefore it is not classically deterministic, but it
> does allow quantum correlations. The dynamical laws - e.g. the
> Heisenberg's evolution equations for the operators in quantum field theory
> - are totally local and causal (or at least approximately, in the case of
> string theory), but the nonlocal character of the wavefunction itself
> nevertheless allows measurements that "look" non-local.
I believe this is exactly what Tim T has been trying to explain to you.
There is nothing about the idea of developing a deterministic,
discrete theory of physics that says we need to retain CFD or Locality.
The fact that specific ideas put forward by Fredkin, Wolfram or others
do in fact attempt to retain normal (3D spatial) locality, or avoid
multiple worldlines, only speaks to these specific models, not to the
general class of discrete and deterministic models.
What is sloppy here is that you are taking specific examples of a class
of models, claiming to have evidence that these models are fatally
flawed (we can get back to this evidence later, I'm accepting it here
for the sake of argument), and using this as 'proof' that all such
models of this class must be wrong. This is the fallacy of composition,
which is prototypical sloppy thinking. It's also the kind of negative
claim that history has proven to be very risky to make (ie, Von
Neumann's 'proof' re: hidden variable theories). Sloppy thinking backed
up by presumptive mathematical rigor is just mathematically rigorous
sloppy thinking. Mathematics is secondary to logic; if our logic is
flawed, mathematics can't help us.
-dbm
Tim Tyler
> Lubos Motl wrote:
> > On Mon, 3 May 2004, daniel B miller wrote:
> >>I for one have my doubts that what we percieve as local is
> >>in fact local in the computational space in which low-level physics
> >>operates.
> >
> > The world "local" has a unique meaning in mathematics, and in physics it
> > is almost always used as "local in the position space or spacetime". The
> > question whether a theory is local in spacetime is the essential question.
> > A physical theory can work with an auxilliary space - e.g. the stringy
> > worldsheet - that has its own notion of "locality", but these are
> > irrelevant technicalities that don't affect the questions whether
> > (spacetime) locality must be broken for a deterministic theory if it
> > reproduces the EPR predictions of quantum mechanics. The answer is that
> > any such a deterministic theory would have to be non-local (in spacetime),
> > regardless of your hidden layer of "computational locality".
>
> I agree. Read my post again. What I am saying is that a deterministic
> theory is not ruled out by Bell's inequality; only local, deterministic
> theories are (presumptively) ruled out.
Adjacent points in our universe are also adjacent in the MWI multiverse -
since the multiverse is a superset that contains our universe entirely.
The MWI /is/ a local theory. It proposes no action-at-a-distance -
not even between points in what we regard as "our" spacetime.
What is does suggest is more along the lines that points in space are very
rich - and contain much more information than they appear to at first
glance.
Local, deterministic theories are not ruled out be experimental tests
of Bell's inequality. What *are* ruled out are local, deterministic
theories that exhibit contra-factual definiteness. By not assuming
contra-factual definiteness, one can retain a deterministic local
model - if one so wishes.
Lastly, let's not forget that Bell's inequality has been the subject
of experimental tests - and that some people are still arguing over
the results of those experiments.
http://freespace.virgin.net/ch.thompson1/ - for example - thinks that
Bell's inequality has never been properly tested.
I don't agree with Caroline - but talking as though arguing with
Bell's inequality is an argument with established maths and physics
is questionable: let's not completely lose sight of the fact that the
experimental tests of Bell's inequality are still the subject of
debate in some quarters.
ueb
> Right.
First: Thanks for your explanations :-)
Second: I fully agree with your last sentence.
Your nice explanations show me that here are more misunderstandings
than contrasts. For example, you are the first who calls the wave
function an auxiliary tool. Correspondingly, one must see strong and
weak forces or the additional dimensions of string theory as such
auxiliary tool too. However, the persons, I heard speak of that,
did as though such tool be total reality and absolute truth. -
What concerns the geometric theory of gravitation and electromagnetism,
as proposed by me, so quantum physicists see only full ignorance
of real indeterminism, and of facts like the violation of Bell's
inequalities. But they do simply not know it, and are too proud to
see for themselves. - In this theory, the Einstein-Maxwell equations
do not imply fundamental determinism with 10 independent equations
for 14 components. Thus, this theory leads at best to a criticism
of _methods_ in quantum mechanics like the use of mentioned
auxiliary tools. The geometric theory deals solely with directly
observable quantities, i.e. mentioned tools are not needed. It even
predicts particle numbers, as I already told.
With it, the proposed geometric theory might be the only one
real alternative to quantum mechanics, and you and your colleagues
should take it *very* seriously.
Ulrich Bruchholz
http://home.t-online.de/home/Ulrich.Bruchholz/
akha...@yahoo.com
> discrete but could reproduce EPR-type observations, as well as Lorenz
> invariance.
Would you please specify "other candidates" in more details?
> I for one have my doubts that what we percieve as local is
> in fact local in the computational space in which low-level physics
> operates.
Do you actually mean: "what we perceive as non-local is in fact local
in the computational space" or "what we perceive as local is in fact
non-local in the computational space"?
akha...@yahoo.com
> Democritus et al. started with discrete atoms with hooks, but the
> equations underlying physics have been becoming increasingly continuous
> ever since.
General public knows about atoms not from Democritus. They were
reintroduced and prevailed a century ago.
> We've learned many things about the equivalence of various
> discrete and continuous interpretations of some physical theories,
Discrete and continuous interpretations are not equivalent in all
aspects. That is where advantages of discrete technique could be
tangible.
> but
> a theory without a set of defining continuous equations will probably never
> be accepted as a serious model for physics, and every person who knows
> something about our actual knowledge of physics understands why my
> statement is powerful and likely, given the current picture of the world
> as painted by physics, even though the statement is not rigorously proved
> yet.
Hypotheses are not to be rigorously proven.
Alex
>
> All the best
> Lubos
daniel B miller
>>There are other candidates besides full-blown MWI that are finite and
>>discrete but could reproduce EPR-type observations, as well as Lorenz
>>invariance.
>
> Would you please specify "other candidates" in more details?
Some day, yes.
>
>
>>I for one have my doubts that what we percieve as local is
>>in fact local in the computational space in which low-level physics
>>operates.
>
>
> Do you actually mean: "what we perceive as non-local is in fact local
> in the computational space" or "what we perceive as local is in fact
> non-local in the computational space"?
I mean the first -- what we percieve as non-local could be local in the
computational space.
Ed Fredkin
Lubos wrote:
> ...If something is
> unmeasurable (in principle), then it does not exist, and Bell's
> inequalities are an example that we are able to show that a certain type
> of ghosts and spirits (local hidden variables in this case) can't exist.
there are constraints on the exact nature of the "certain kinds of
hidden variables". For example, we know that there is not a simple
hidden variable that contains the "true" direction of the spin of a
particle. But there are other kinds of hidden informational processes
(as opposed to simple variables) that can result in the kinds of
correlations predicted by QM. For example, in a CA type of model,
there can be information that is functionally related to the spatial
and temporal evolution of the "particles" (an informational process is
at work as the particle moves through space-time) so as to allow for
correlated measurements with another particle that has the same spin
state (and the same informational process). Such systems could be
consistant with the laws of QM and with experimental results.
What seems certain is that there is nothing in QM that rules out
hidden informational processes that produce the long range
correlations predicted by QM. In a CA model of physics, nothing just
moves as in ordinary models of physics. Motion of a particle in a CA
is a complex process that entails information about the motion, an
ongoing informational process that actually moves the particle
according to the information that specifies the motion and that also
moves that information along with the particle.
I have described this in a blunt manner, when what seems obvious is
that much of the information is represented by temporal and spatial
wave structures (made up out of bits) as opposed to IEEE floating
point numbers.
The ideas of digital mechanic may seem crazy, but they're not stupid.
Ed F
Serg
>
> > That is the best explanation re determinism, I saw.
> > Does indeterminism not simply mean lack of rules, regardless
> > whether continuous or discrete ?
>
> That's a very good point - or a very good question. There are various
> levels of determinism. The word "deterministic" usually means "satisfying
> Laplacian (classical) determinism".
There exist treatment of EPR paradox wich called "common future
hypothesis" It basically say that EPR expalned by boundary conditions
in the future. Now I remember your very interesting explanation of
stringy treatment of black hole information loss paradox - "black hole
singularity final state" which seems similar (for layman like me) -
also boundary condition in the future. Are there some coomon ground
here ?
No if there is, if the accept that kind of boundary condition as
legitimate, then the can make a trik - instead of CA use dicrete
CA-like objects, which have not only initial but also final (or
time-dependent) conditions (for example allowing some freedom in
initial conditions), which reproduce EPR-like behavior. In fact that
is very close to Palmen Petrov EPR CA model.
ueb
> The ideas of digital mechanic may seem crazy, but they're not stupid.
If people are very partial to their realm, they quickly do as though
other be stupid. But that might rather be misunderstandings ... ;)
Can one not better understand all that stuff with the quite simple
definition of indeterminism as lack of rules ? (I already told Lubos
of it.)
Since computers are fully determined systems, one must treat the computer
to additional (or even new) conditions in order to model the world.
If one is happy, this model becomes pretty similar. But one can only
simulate properties of the world that are independent on the additional
conditions.
Take as example my simulations of particles according to the Einstein-
Maxwell equations: I confined myself to time-independent and rotary-
symmetric solutions. That led to 6 independent equations for 8 components
(from metric tensor and electromagnetic vector potential). Thus, I
formulated two additional conditions. In that, I am fully aware that
these conditions are totally arbitrary. I chose these conditions
1.) for convenience,
2.) according to geometric possibilities.
There are significant indications from previous results that
1.) discrete solutions exist, and
2.) the integration constants for these solutions are identical
with particle numbers.
Ulrich Bruchholz
Eric A. Forgy
> daniel B miller <dan...@cmu.edu> wrote:
> > Absolutely nothing about QM and the last 70 or more years of progress
> > in experimental and theoretical physics implies a lack of determinism.
>
> This is a very popular, and very incorrect, misconception. It is
> widespread among the laymen as well as among the badly informed and badly
> educated scientists. The history is nevertheless very exciting.
[snip]
> In principle, academically speaking, there could still be a non-local
> deterministic description of the world that is more fundamental than the
> standard quantum mechanics. There are many reasons to think that it would
> violate the principles of relativity and it would have other problems
Has anyone looked at these issues from the perspective of discrete
physical models? After all, a discrete theory must be non-local almost
by definition, i.e. physics "here" depends on what is going on "near
here", i.e. nearest neighbors, etc., unlike continuum theories.
Eric
PS: "Near here" does not necessarily mean "geometrically close by". It
could refer to a topological sense of nearness, i.e. two geometrically
distant points in spacetime could be topologically identified, e.g.
was it Wheeler who postulated that fermions could be modeled as points
identified in a topological space?
PPS: I always wondered if EPR could be explained by some kind of
topological perturbation similar to the postulation that fermions are
geometrically separated points that are topologically identitied?
PPPS: I am severely lacking of sleep at the moment, so if this doesn't
make sense, let me know and I'll try to clarify when I am a little
more coherent :)
PPPPS: To completely confuse things, maybe I'll try to give an example
of what I mean by "topologically identifying geometrical separated
points".
Consider Minkowski space M and choose a reference frame so we can
split M into E^3 x R, where E^3 is Euclidean three space. We can solve
the source-free Maxwell's equations in this space giving a distribtion
of E and B. Now if we pick two points p1 and p2 in E^3 and "identify
them", i.e. consider the quotient space [E^3], where each point p in
E^3 that is not p1 or p2 gets mapped to a point in [E^3] denoted [p]
whereas both points p1 and p2 get mapped, i.e. "glued", to the same
point [p1] = [p2]. This space is no longer Hausdorff. If we solve the
source-free Maxwell's equations in this space, the fields E and B will
look precisely like they would in the original space E^3 if there were
oppositely charged point charges located at p1 and p2. The flux lines
that flow into point [p1] flow out of [p2] (since the are identified)
so that although there is no net flux in [E^3] there appears to be a
net flux (about the two points) if viewed as if the space were really
E^3.
Now to bring this back to the topic of this newsgroup, take everything
I just said and replace it with "discrete" versions of M and E^3 and
the same idea follows through. It is even simpler in the discrete case
though. There it is like you have a lattice with nodes and you simply
label the nodes with the same label as if they were really the same
node :)
I better give up there for now :)