Re: What evidence is there for a continuous space-time?

zzbunker_at_netscape.net
Date: 02/07/05 

Date: 6 Feb 2005 21:34:08 -0800

Mike wrote:
> examachine@gmail.com wrote:
> > [cross-posting to sci.physics]
> >
> > [This is one of those commonly occuring discussions on continuous
vs.
> > discrete worlds.]
> >
> > Hi Jeffrey,
> >
> > Thank you for your extensive and challenging argumentation. Let me
> > start by saying that I don't think there is enough evidence to
settle
> > this ages-old question either way. All we can hope to do is to
stack
> > our analytical cards, and review the known facts that might be
> related,
> > but I'm aware that this is one of those topics that tend to be
> decided
> > according to personal preference, rather than to truth, which we
> don't
> > have access at the present. (But I do think it will be known
> decisively
> > one day)
>
> Slow down. This is sci.physics and we don't settle anything by
> personal preference; there is this thing called the scientific
method.
> :-)
>
> If the universe is discrete a la quantum theory then the smallest
piece
> of space-time is measured at the Planck scale. So what experiment
can
> we run to test the hypothesis that the universe is discrete at the
> Planck scale?
>
> Enter the ESA's Planck satellite, due to be launched in 2007.
> Physicists have good reasons to believe that the early universe
> underwent a period of rapid inflation. If true then Planck-scale
> features may have been amplified to the point that their imprint is
> visible today in the cosmic microwave background (CMB).
>
> So rather than speculate on how many angels can fit on the end of a
> pin, just wait for the hard data that will answer the question.

  Well, that's where physicists whole rationale falls
  apart as usual. The Nobelean wait and see.
  Since physicists as usual have no evidence
  of quantum mechanics in it's entirety of
  being even close to a reality, just as
  Einstein told them in 1920s. Since the
  early universe and quantum mechanics themselves are entirely
  dismal artifacts of Euclid and have nothing whatsoever
  to do with gravitational effects of sattelites and the Earth.
  So the hard data will never be forthcoming until
  you can convince the idiots of that.
  Since to explain data itself of any kind, you
  need evolutionary biology, not a mathematician practicing
  for a new and improved auto-exploding Nobel Prize.

>
> See http://www.esa.int/esaSC/120398_index_0_m.html
>
>
> >
> > Jeffrey Ketland wrote:
> > > <examachine@gmail.com> wrote
> > >
> > > >> You believe that you can obtain a contradiction from the
> sentence
> > > >>
> > > >> (*) There are (at least) aleph_0 physical entities.
> > > >>
> > > >> Be our guest. Derive it.
> > > >>
> > > >
> > > > This would be a physical contradiction.
> > >
> > > I still do not see the "physical contradiction" that you are
> > asserting to
> > > hold.
> > >
> > > Moreover, the proposition (*) follows logically and trivially
from
> > General
> > > Relativity, at least if spacetime points/events are counted as
> > physical
> > > entities (actually, it follows, again trivially, from Euclid's
> > > axiomatization of physical geometry: what Einstein called "the
> first
> > example
> > > of a precise physical theory" (quote from memory)).
> >
> > Maybe it's also an idealized theory in addition. That is obviously
> how
> > we are taught geometry in elementary school.
> >
> > > > One interpretation of the uncertainty principle is that beneath
> the
> > > > planck scale, there is simply nothing, no, nothing. Same goes
for
> > time,
> > > > energy, etc.
> > >
> > > Heisenberg's principle (the product of uncertainties in position
> and
> > > momentum is bounded below by hbar) follows from:
> > >
> > > (i) the one-particle wavefunctions are represented by elements of
> > L^2[R^3];
> > > (ii) [Q, P] = -ihbar;
> > > (iii) Parseval's Theorem.
> > >
> > > I am not familiar with any "interpretation" of Heisenberg's
> principle
> > which
> > > says "beneath the Planck scale there is simply nothing". What
> happens
> > below
> > > the Planck scale, *no one* knows. We can only guess.
> >
> > Maybe the residents of sci.physics will have something to say about
> > this. [Main reason why I'm cross-posting]
> >
> > > Moreover, any operator representation of the commutation
relations
> > [Q, P]
> > > = -ihbar actually *requires* that the spectrum of the position
and
> > momentum
> > > operators Q and P be *continuous*. This is a theorem of
functional
> > analysis.
> >
> > The question is something else: is functional analysis physics?
> >
> > > > Or perhaps you would like me to believe that there is such a
> thing
> > as
> > > > infinitisimal periods of time.
> > >
> > > Manifolds---by definition---lack "infinitesimals". On a manifold
> > model of
> > > physical spacetime, spacetime is locally diffeomorphic to R^n.
And
> > R^n is
> > > archimedean.
> > > Perhaps you are thinking of Robinson's non-standard models of
> > analysis?
> >
> > No, I don't necessarily require hyperreals. Having actual infinite
> > divisibility, that there are spatial points, existing on my
> fingertip,
> > so many that cannot even be named is bad enough.
> >
> > Saying that there is actually space to fit infinitely many replicas
> of
> > the entire universe in 1mm cube is bad enough. I think you skipped
> > that part. That has absolutely nothing to do with the relative
> success
> > of a few theories so far: there are so many of them, some of them
are
> > founded on discretizations of space-time.
> >
> > Geometry is an abstraction. We are taught that the geometric notion
> of
> > a point has no corresponding reality: first of all it has no
> extension.
> > You want us to consider that the real space is like that,
consisting
> of
> > size-less points, e.g. points that do not extend in space. Surely,
> that
> > does not sound physical.
> >
> > Theoretical realism is something that is not going to work. For the
> > very reason that reality changes day by day and by the textbooks
that
> > stand on your bookshelf if you insist on that. Instrumentalism does
> > work. And for all our purposes and intents that's how we actually
> > operate most of the time (at least while doing physical sciences!).
> > Otherwise, we would be left motionless whenever two theories
> > contradict, which is quite often the case than it seems to
outsiders.
> >
> > The only way to describe the quantum world is not via continuous
> > functions, there is Heisenberg's matrix mechanics etc. And before
we
> > delve into generalizations of things, abstractions of the particle
> > world, and formulas on textbooks, and mathematical physics I remind
a
> > simple fact: we run simulations of quantum physical configurations
> and
> > they work. If these guys crucially depended on ACTUAL INFINITY in
the
> > geometry of ANY SINGLE ENTITY, think how well they would predict?
But
> > they predict well, the monte-carlo methods, etc. work extremely
well.
> >
> > In fact, if any of your claims about the geometry of space-time
were
> > true, I would expect cosmology simulations, or a class of
simulations
> > to be impossible. So far I've never heard someone say: "We just
can't
> > simulate any of this, because it requires infinite time and space
to
> do
> > it, even a slight portion of it!"
> >
> > There may be simpler terms to discuss this.
> >
> > You say "by definition". Defined according to *which* physical
fact?
> In
> > a physical theory, ultimately each "axiom" must depend on
> observation.
> > AFAICT, the arbitrary and in my opinion irresponsible use of R^n is
> not
> > justified in that fashion. That's mathematics, not physics. (So
> instead
> > of mathematical physics, I suggest that we must pursue physical
> > mathematics to do physics.)
> >
> > Pushing arbitrary "a priori" models sometimes works, sometimes does
> > not.
> >
> > Showing that general relativity or another theory of physics
> _requires_
> > R^n rather than Q^n or Z^n cannot be achieved simply by saying that
> "so
> > far this predicted well". That's an entirely different story. First
> you
> > should look analytically, for instance why do you insist on R
rather
> > than Q? Then, why do you insist on continuity, just because it
takes
> us
> > to certain perfect Pythagorean forms?
> >
> > I seriously suspect that some of the mindset in physics community
is
> a
> > leftover from Platonism, which the nominalist me would not agree
> with.
> >
> > In the second half of the 20th century, Konrad Zuse seriously
> > considered the idea that the universe is merely a digital computer.
> You
> > can find some elaboration of that idea in Fredkin's site:
> > www.digitalphilosophy.org although his views are not conclusive.
> >
> > Zuse and Fredkin convince me to a great extent. And they also
satisfy
> > the spirit of William of Occam in me, that wants to get rid of
these
> > posits like infinite number of physical constitutents residing in a
> > finite volume, which is a point I think you did not satisfactorily
> > answer.
> >
> > A flaw I see you in your argument is this: you constantly point out
> to
> > formulas in textbooks, while I demand empirical evidence. If you
say
> > that it is entirely impossible to distinguish a continuous,
> uncountable
> > space from a discrete, countable space via experiments, then I will
> > think either
> > - The theories are insufficient
> > - The simpler case, that is the second, is correct.
> >
> > Neither of which support your argument.
> >
> > The only real source of the Infinite Nature hypothesis is religions
> and
> > outdated metaphysics AFAICT. There is no such thing as an
arbitrarily
> > small or arbitrarily large quantity in any physical experiment, or
> > description that I can think of.
> >
> > That the nature is finite does not mean that the humans are capable
> of
> > conceiving it fully, but knowing whether it is finite or infinite
> could
> > be one of the things we should be able to understand. Modern
> cosmology
> > does not seem to suggest that our space-time is infinite, but you
are
> > now saying that in fact, it is infinite even if there is only
finite
> > volume. So we should be able to imagine time periods that are
> > 2^{-50000000000000} _Planck units_, spatial extents that are
> > 2^-{2^{-100}} Planck units, and accept all of these because R^n
looks
> > neat on paper? Also accept that all of such space-time differences
> > *actually* occur whenever there is a motion? I doubt that very
much.
> > This takes us to imagining these nonsensical fractal worlds. Do you
> > mean that there are variable material contingencies at such small
> > space-time scales? Perhaps entire worlds of their own? Or do you
want
> > to mean, they are uniform? Which is it? One has to make a choice.
If
> > you say "yes there is change", I'll come up with a smaller
space-time
> > contingency scale each time and I'll ask you. You can imagine that
> > either this means you should stop at a scale K, and accept the
finite
> > nature hypothesis, or admit infinitely complex worlds beneath the
> > Planck scale (basically saying that electrons are in fact universes
> as
> > complex as ours on their own, that's a necessary outcome, don't
laugh
> > :) ). I don't believe there is any other alternative.
> >
> > So, yes, I think the R^n model of physical space can be rejected as
> > superfluous on metaphysical grounds and existing physical
knowledge.
> >
> > > >Do you also want me to believe that
> > > > particles are actually made of continuous functions, or perhaps
> > actual
> > > > fractals? Are you suggesting to me that wave functions, as some
> > > > unobservable but existing real-valued functions exist elsewhere
> > > > elsewhen? Come on. I really think you could use a fair amount
of
> > > > instrumentalism in your approach to the textbooks that sit on
> your
> > > > shelf. The use of real-valued continuous geometry may just be a
> > > > coincidence, not truly a "shadow" of reality, maybe it's just
an
> > > > ancient leftover from days of muddy thinking.
> > >
> > > These are our best scientific theories. If you have better, then
> the
> > onus is
> > > one you to provide one.
> >
> > No, I don't mean to say *I* have better ones, but I think the
concept
> > of a real number has nothing to do with reality.
> >
> > > There is exactly no sense in which
> > > --- General Relativity;
> > > --- quantum field theory;
> > > --- gauge theories
> > > are examples of "muddy thinking".
> >
> > No, but their formulations could be improved, I believe.
> >
> > > > I think what you would really like me to believe is that, since
> the
> > > > space is continuous and real-valued as your textbooks assert
> > without
> > > > any kind of evidence, the whole universe could just fit on my
> > > > fingertip. It's a coincidence that it doesn't.
> > >
> > > You believe that it is a coincidence that our best theories are
so
> > > fantastically and hugely successful?
> >
> > Not so fantastically. There are still things that we do not
> understand
> > well.
> >
> > I am pointing out to the usual paradoxes which arise from admitting
> an
> > infinite space-time in a finite volume.
> >
> > Basically, if that were true, then I imagine there would be process
> > that would make the environment non-denumerable, which is I think
> > something you must argue for. Do you mean that there can be no
> complete
> > computer simulation of any quantum system whatsoever? Then, why do
> our
> > simulations work? Are they only approximations to the "infinite
> > reality"?
> >
> > In particular, there would be certain motions, even in Newtonian
> > mechanics, which would result in hyper-Turing computations, like
> > solving the halting problem in a finite volume. Do you mean that is
> > possible?
> >
> > > If our best scientific theories are so
> > > dramatically wrong, as you seem to believe, then why are they so
> > > surprisingly predictive, explanatory, etc.? It is your beliefs
> which
> > require
> > > the existence of fantastic coincidences and miracles.
> > >
> > > [snip]
> > >
> > > > AFAICT, neither general relativity or some continuous
formulation
> > of
> > > > quantum physics can assert that the space is continuous. As you
> > said
> > > > the assumption is trivial, it is given without any argument
> > whatsoever.
> > >
> > > 1. It is trivial that our best theories assume that spacetime is
> > continuous.
> > > This is demonstrated not by a priori reason, but by looking at a
> > textbook.
> >
> > So you mean textbooks magically show us the truth in whatever
> > assumption or definition they include.
> >
> > If that is true, then there should be ABSOLUTELY NO foundational
work
> > in physics, which was the position of the church against Galileo if
> you
> > remember. I don't believe that is an attitude a scientist can
accept.
> >
> > > 2. It is also clear that our best theories are fantastically
> > successful,
> > > hugely explanatory and highly predictive.
> >
> > That is not to say that we have a grand unified theory of course!
> >
> > You do not even explain what happens below the Planck scale, you
> assume
> > *something* happens, and then tell me "we don't know what happens".
> How
> > is that for being highly predictive?
> >
> > > 3. Science (or, all serious science since Galileo) does indeed
> > proceed
> > > "without any argument whatsoever". Correct. Science is based on
> > making bold
> > > guesses, conjectures, hypotheses, etc., about the structure of
the
> > world.
> > > These are not derived from observation. Exactly the opposite.
> > Scientific
> > > theories are "free creations of the human mind", as Einstein put
> it.
> >
> > This seems to me an inadequate theory of physical science. I cannot
> > imagine a physics that does not at some point depend on
observation.
> > You made Einstein sound as if he never observed gravity or
processed
> > any sensory input whatsoever.
> >
> > > Now, let's see how your radical and unwarranted scepticism copes
> with
> > some
> > > standard examples from theoretical physics. For example, consider
> > > symmetries: Noetherian symmetries (and their relation to
> conservation
> > laws)
> > > and gauge symmetries (which are related to the existence of
certain
> > kinds of
> > > gauge bosons, like the photon, etc.). In the Noetherian case, we
> > obtain a
> > > deep explanation for conservation laws. In the gauge theory case,
> we
> > obtain
> > > an interesting way of predicting the existence of new particles
> > (e.g., W and
> > > Z particles).
> > > This is all based on Lie groups (e.g., the Poincare group, gauge
> > groups like
> > > U(1), SU(3), etc.). I.e., continuous groups.
> > > But you reject all this for a priori philosophical reasons. Why?
> >
> > It is not as easy as it seems, I think.
> >
> > Continuity may always be an illusion when you observe a complex
> > discrete system. Then the symmetry becomes merely an approximation
to
> > the behavior of a complex discrete system... Perhaps you've seen a
> > circle on a high-resolution computer display which is quite common
> > nowadays. That proves absolutely nothing about whether the space is
> > continuous or discrete. It just shows that the theory is
> > self-consistent.
> >
> > Also, R is not the only "continuous" number line... Why R? Why not
*R
> > or Q?
> >
> > That is to say, the reasons you cite are all "a priori
philosophical
> > reasons" themselves.
> >
> > > > PS: I really don't believe that renormalization "proves" to us
> > > > infinitely many things are happening in a finite volume, that
too
> > is
> > > > schizophrenia. If you don't understand the complexity of
> something,
> > > > just say there are infinitely many. If you don't understand the
> > real
> > > > units of space-time, just say it's infinitely divisible.
> > >
> > > Nobody really understands the physical meaning of
renormalization.
> I
> > was
> > > taught to think of charge renormalization in terms of some sort
of
> > > polarization of the vacuum. I was also told that it is a "useful
> > trick",
> > > which nobody really understands.
> >
> > Well, last time I've read about it, I think I saw the explanation
> that
> > it accounted for infinitely many interactions, possibly occuring in
> > some imaginery subset of R^n, after all that would be possible in
> such
> > an infinite everywhere space-time.
> >
> > Regards,
> >
> > --
> > Eray Ozkural
> >
> > PS: Also, I don't think the Copenhagen interpretation has any
> relevance
> > to our discussion, while it could be thought of an example for
> "things
> > that exist but cannot be observed / understood, even in principle".
I
> > view that as a shortcoming in the theory of particle physics, like
> > Einstein I would have required everything to have an explanation, a
> > cause, a reason, including non-determinism.

Relevant Pages

  • What evidence is there for a continuous space-time?
    ... is functional analysis physics? ... because it requires infinite time and space to do ... Then, why do you insist on continuity, just because it takes us ... space from a discrete, countable space via experiments, then I will ...
    (sci.logic)
  • What evidence is there for a continuous space-time?
    ... is functional analysis physics? ... because it requires infinite time and space to do ... Then, why do you insist on continuity, just because it takes us ... space from a discrete, countable space via experiments, then I will ...
    (sci.physics)
  • Re: What evidence is there for a continuous space-time?
    ... If the universe is discrete a la quantum theory then the smallest piece ... > The question is something else: is functional analysis physics? ... because it requires infinite time and space to ... Then, why do you insist on continuity, just because it takes ...
    (sci.logic)
  • Re: What evidence is there for a continuous space-time?
    ... If the universe is discrete a la quantum theory then the smallest piece ... > The question is something else: is functional analysis physics? ... because it requires infinite time and space to ... Then, why do you insist on continuity, just because it takes ...
    (sci.physics)
  • Re: What evidence is there for a continuous space-time?
    ... >> Saying that there is actually space to fit infinitely many replicas ... >> world, and formulas on textbooks, and mathematical physics I remind ... because it requires infinite time and space ... Then, why do you insist on continuity, just because it ...
    (sci.logic)
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