Is nature discrete?
Gerard Westendorp
1. Nature is discrete and there are experiments that prove
it isn't continuous.
2. Nature is discrete but there are no experiments that prove
it isn't continuous.
3. Nature is continuous and there are experiments that prove
it isn't discrete.
4. Nature is continuous but there are no experiments that prove
it isn't discrete.
In general, I believe that there are equivalent ways to
describe nature, and that there are no experiments to
decide which of these equivalent ways is "real". For
example, you can chose different Lorentz frames.
So perhaps we can never know if nature is discrete.
On the other hand, as Planck showed when he invented quantum
mechanics, nature has a discrete spectrum of energy states.
So this seems like real experimental evidence for discreteness.
The trouble with quantum mechanics is that it allows
superpositions of these discrete states, which makes things
more complicated.
Gerard
Eray Ozkural exa
> On the other hand, as Planck showed when he invented quantum
> mechanics, nature has a discrete spectrum of energy states.
> So this seems like real experimental evidence for discreteness.
As Ed Frenkin said, all fundamental properties in physics seem to come
in small integers, which should provide a lot of intuitive confidence
for the digital physicist.
> The trouble with quantum mechanics is that it allows
> superpositions of these discrete states, which makes things
> more complicated.
Interesting thought. I'll try to abstract away from the idea of
superposition to something else. Here is an odd way in which continuum
might exist. Maybe integer functions of the form f : Z -> {0,1} exist
in the physical sense and not merely through imagination. Such reality
would be consistent with all the digital observations we are making,
for it may be harder to identify the reality of functions, due to
merely physical reasons... Such a realist approach would be consistent
with Godel, but of course Godel denied the possibility of a mechanical
mind among other things so his point of view is not popular nowadays.
The proper objection to this argument would be a way to show, by a
physical experiment, that uncomputable functions do not exist in
nature. I can imagine this might be directly related to the
statistical properties of the universe, assuming their existence would
be violating basic observations (in astronomy, cosmology...) and so
forth. If such uncomputable functions did not have any "energy", we
would not really count them as physical anyway. [*]
By the way, an AI researcher would definitely like Godel to be wrong.
Regards,
--
Eray Ozkural
[*] Note however, that digital philosophy does not _seem_ to deny an
"underlying reality", it simply does not deal in what is not physical.
And a modern skeptic would most likely find it closer to his heart
that if something is not physical, it does not exist.
ueb
> I guess there are 4 possibilities:
> 1. Nature is discrete and there are experiments that prove
> it isn't continuous.
> 2. Nature is discrete but there are no experiments that prove
> it isn't continuous.
> 3. Nature is continuous and there are experiments that prove
> it isn't discrete.
> 4. Nature is continuous but there are no experiments that prove
> it isn't discrete.
You well sort the possible answers :-)
> In general, I believe that there are equivalent ways to
> describe nature, and that there are no experiments to
> decide which of these equivalent ways is "real". For
> example, you can chose different Lorentz frames.
> So perhaps we can never know if nature is discrete.
Well possible.
> On the other hand, as Planck showed when he invented quantum
> mechanics, nature has a discrete spectrum of energy states.
> So this seems like real experimental evidence for discreteness.
No. One must first ask the question: What quantities have discrete
values ? Above fact is no evidence for fundamental discreteness.
(The integration constants of PDEs have discrete values, if for
example a margin exists.)
> The trouble with quantum mechanics is that it allows
> superpositions of these discrete states, which makes things
> more complicated.
Forget quantum mechanics for that reason. Let us rather collect
the facts:
1.) The known Einstein-Maxwell equations deal exclusively with
measurable quantities, not more and not less. The tensor components
are the field quantities (gravitation + electromagnetism).
However, mass, spin, charge, and magnetic momentum are the first
integration constants, which can have discrete values and must
not be superposed. Also Planck's constant can be explained
from a single wave solution.
2.) There are lots of experimental evidence for the predictions
from the Einstein-Maxwell equations, and that a lot better than
for *single* predictions from any quantum model.
Note that these tensor equations predict also particle numbers
(which are discrete values of above mentioned integration constants),
http://home.t-online.de/home/Ulrich.Bruchholz/
3.) These tensor equations mean first a continuum.
But the practical computations always take discrete coordinates
for granted. My simulations demonstrate clearly, that any convergence
to very small differences does _never_ match solutions according
to "conventional" methods (though the initial conditions come from
"conventional" solutions).
Thus, there is no clear answer. May be, one has to newly define
the term "continuum" ? Searching for a simplifying model (that
replaces the complicated computations), such like "digital physics"
could meet nature better than quantum mechanics ?
Ulrich Bruchholz
info at bruchholz minus acoustics dot de
Thomas Lee Elifritz
> I guess there are 4 possibilities:
>
> 1. Nature is discrete and there are experiments that prove
> it isn't continuous.
>
> 2. Nature is discrete but there are no experiments that prove
> it isn't continuous.
>
> 3. Nature is continuous and there are experiments that prove
> it isn't discrete.
>
> 4. Nature is continuous but there are no experiments that prove
> it isn't discrete.
Actually no, experiments don't 'prove' anything, they produce
evidence.
Proof is mathematical, science is demonstrative.
The mathematical evidence is demonstrably both continuous and
discrete, and the empirical physical evidence is demonstrably dual.
http://www.av8n.com/physics/scientific-methods.htm
Thomas Lee Elifritz
http://elifritz.members.atlantic.net
charliew2
Eray Ozkural exa <er...@bilkent.edu.tr> wrote in message
news:fa69ae35.0403...@posting.google.com...
(cut)
>
> By the way, an AI researcher would definitely like Godel to be wrong.
>
> Regards,
>
> --
> Eray Ozkural
This is getting off the subject a bit, but here goes. I've done a bit of AI
programming, and seen the field grow somewhat over the years. In principle,
I agree with Godel's argument, as programming functions at their most basic
level are still the rapid opening and closing of switches, albeit by a
"smart" program.
In addition, even though "smart" programs can actually write their own code
(e.g., higher level implementations of LISP programs), there is one more
"fly in the ointment" regarding this problem. In the early years of AI
research, people defined "intelligence" as the ability of program "x" to
demonstrate skill "y". As advancements led to programs that could
demonstrate this ability, our definition of "intelligence" seemed to change.
Thus, there is a two-fold problem with this area of research: 1) The skill
level necessary to demonstrate true artificial intelligence is very high ;
2) People have a very difficult time in coming to a consensus such that
intelligence can be well defined.
R. Troedler
i much appreciate your distinctions, because it emphasises the
difference between nature and our theories.
most people here stick to talk about how nature IS, and that seems
dangerous to me, because they may loose sight of the possibility of
more than one correct theory.
lets start with a mathematical metaphor (that may be near to
discretists).
if a researcher finds out herself to live on a conway-game-of-life
checkerboard, she won't be able to test whether this is the basic
layer, or 'run' on a turing-machine, or at some continuous-world
computer.
or, more generally, living in any cellular automata universe, if some
evolution rules can simulate each other, how would she find out which
one be the right?
thus we have a bunch of somethings that we can hope to cast in
mathematical structure:
classes of worlds (world models), that are indistinguishable from
inside.
(btw., the word 'classes' suggests indistinguishablitity to be an
equivalence relation. take care, that has to be proven first.)
does anybody know about research in that direction? about what it
means for a discrete world to contain observers that want to test
theories about this world?
i still dont know what an observer may be in, say, a cellular
automaton, or in one of wolframs developing networks.
the theory of (special) relativity has been build from an analysis of
what a measurement is (time differences and distances); much insight
into quantum theory can be gained from an analysis what a measurement
is.
so i think it worthwile to analyse the possibilities of an observer in
discrete worlds.
if we, for example, find out that all (computational complete)
discrete worlds are indistinguishable from inside, that would be a
highly interesting result. what would in imply? i think it implies
that we have the choice.
coming from the other side, we can try to analyse how to proof the
world to be continous.
is this possible in a finite number of steps?
if this can be disproved in complete generality, we again have the
choice.
in that case we can choose the discrete model we like best, and never
be proven wrong.
(of course we will never be able to prove it right, but thats true
about every scientific theory.)
any volunteers to do the above requested proofs? ;-)
yours, troedler
dan miller
> hello gerard, and all,
>
...
>
> or, more generally, living in any cellular automata universe, if some
> evolution rules can simulate each other, how would she find out which
> one be the right?
Obviously, any rule that gives the right answer is as 'right' as any
other. There are two considerations we might use in choosing one over
another: 1) practical: choose the one that your hardware runs the
fastest. After all, the practical use of physics is primarily to make
predictions, so the fastest way to caculate your predictions is the
best. 2) epistemological: choose the one that seems most elegant, most
fundamental, etc. (choose your adjective). Frankly, as a pragmatist, #1
is what I am primarily interested in, though thinking about #2 may
have some important philosophical implications.
>
...
>
> does anybody know about research in that direction? about what it
> means for a discrete world to contain observers that want to test
> theories about this world?
>
> i still dont know what an observer may be in, say, a cellular
> automaton, or in one of wolframs developing networks.
An observer is simply an agent that exists within the simulation. I
like to think in terms of computer programs playing games. Let's say
you build your CA world, and within it you create some sort of virtual
machine that has a virtual computer for a 'brain' (Not to imply anything
like human consciousness, just on the level of say a Sony AIBO running
computer code).
Now, design a game where this virtual robot needs to make correct
predictions in order to win points. How will we program the robot to
win the most points?
-dbm
Gerard Westendorp
[...]
> On the other hand, as Planck showed when he invented quantum
> mechanics, nature has a discrete spectrum of energy states.
> So this seems like real experimental evidence for discreteness.
>
> The trouble with quantum mechanics is that it allows
> superpositions of these discrete states, which makes things
> more complicated.
>
Maybe I should formulate this a bit better.
According to quantum mechanics, when you do a measurement
the possible outcomes are limited to eigenvalues of the
operator called the observable. These are often discrete.
The so-called 'continuous' eigenvalues are really also
discrete. For example, momentum eignevalues are continuous
only in an infinite volume, but as soon as you put them in
a finite volume, the spectrum becomes disctrete.
But how do these states evolve in time, when
no one is watching? (ie doing a measurement on them)
The answer, at least according to present understanding,
is that the state becomes a superposition of eigenstates.
When a new measurement is done, you once again get
one of the eigenvalues.
So our measurements outcomes are discrete, but the case
for nature itself is more subtle.
Gerard
Gerard Westendorp
[..]
> lets start with a mathematical metaphor (that may be near to
> discretists).
> if a researcher finds out herself to live on a conway-game-of-life
> checkerboard, she won't be able to test whether this is the basic
> layer, or 'run' on a turing-machine, or at some continuous-world
> computer.
hmm,
probably, some universal Turing machine somewhere has already simulated
the universe!
[..]
>
> thus we have a bunch of somethings that we can hope to cast in
> mathematical structure:
> classes of worlds (world models), that are indistinguishable from
> inside.
Well known examples are "fundamental symmetries", like
rotation, translation, gauge invariance.
If a computer runs a model of nature, you could always
add a vector to all coordinates, and you would get an
equivalent model.
In the case of translation symmetry, there is an
isomorphism between the models that you obtain by switching
the choice of origin.
But in the case of Gauge theories, it is a bit more
complex. You can switch models by switching choice
of gauge. But you can also use models that explicitly
depend on gauge and models that are manifestly gauge
invariant.
For example, a model that does not use the vector
potential (A) but uses only the directly observable field
(B).
So in the first example (translation) there is a nice
group of transformations that relates the various
equivalent models. But in Gauge example, you leave out
certain degrees of freedom that you say are
"unobservable".
A CA model of the universe could have a huge amount
of Gauge degrees of freedom. In other words, the number
of variables of the simulation could be much greater
than the number of variables that an "internal" observer
living inside the CA would be able to observe. This could
mean for such an internal observer that his world seems
fundamentally probabilistic, while the CA itself is
deterministic.
Hope I am being intelligible...
[..]
> in that case we can choose the discrete model we like best, and never
> be proven wrong.
That's also how I look at it.
Gerard
ark
> I guess there are 4 possibilities:
>
> 1. Nature is discrete and there are experiments that prove
> it isn't continuous.
>
> 2. Nature is discrete but there are no experiments that prove
> it isn't continuous.
>
> 3. Nature is continuous and there are experiments that prove
> it isn't discrete.
>
> 4. Nature is continuous but there are no experiments that prove
> it isn't discrete.
>
>
> In general, I believe that there are equivalent ways to
> describe nature, and that there are no experiments to
> decide which of these equivalent ways is "real". For
> example, you can chose different Lorentz frames.
We are asking question: is Nature discrete? If so, then we assume that
the answer "Yes" is one of the possibilities that need to be seriously
considered, at least at the beginning. If so, then we should be very
suspicious concerning those concepts and those standard theories that
have been derived under assumption that Nature is a continuum. One
such theory is the Special Theory of Relativity, together with Lorentz
transformations. So, let's forget about Lorentz transformation and
about space-time metric. If so, then space separates from time. If so,
we have two questions that are, a priori, independent:
1) is space discrete?
2) is time discrete?
We should consider these two possibilities, their combinations, and
try to re-think derivation of Lorzentz transformation (or something
replacing them)
separately for each case.
Suppose, for instance, that a viable theory is possible with discrete
time and continuous space. And another viable theory with continuous
time and discrete space. These two theories may cover different areas
of experience. Theory with discrete space and discrete time may, for
instance, prove to be inconsistent (it needs a lot of hand waving
arguments and arbitrary, doubtful (as in Eddington) assumptions). Is
such a situation possible? Why not?
Now, let us think about quantum theory. Normally time evolution there
is assumed to be continuous. But we have GRW and EEQT where time
evolution is a piecewise deterministic processes, with pieces of a
continuous, non-unitary evolution, interrupted by discrete quantum
jumps ("collapses"). Can it be that we can totally eliminate the
continuous part, and that the only reason for time "to flow" will be
"quantum jumps"?
I consider such a possibility vialable.
ark
Arkadiusz Jadczyk
http://www.cassiopaea.org/quantum_future/homepage.htm
ueb
agree with. But the situation may be more subtle ...
ark wrote:
> Now, let us think about quantum theory. Normally time evolution there
> is assumed to be continuous. But we have GRW and EEQT where time
> evolution is a piecewise deterministic processes, with pieces of a
> continuous, non-unitary evolution, interrupted by discrete quantum
> jumps ("collapses"). Can it be that we can totally eliminate the
> continuous part, and that the only reason for time "to flow" will be
> "quantum jumps"?
I have good reasons to claim that quantum jumps are nothing else
than transitions from one to another stable solution of generally
valid equations. There are good reasons too, that these equations
are the known Einstein-Maxwell equations. (You know of my simulations
according to them.) In which, it is useless to speculate how such
transitions may look, because nobody can simulate or even observe
them.
May be, one should not question "Is nature discrete ?" but "Is nature
continuous ?". First, above mentioned Einstein-Maxwell equations
have most and best experimental evidence, and do _not_ deal with
unobservable quantities (also not such declared as "observable"),
and unseen dimensions. They do even predict particle numbers. -
But we can never prove the assumption of arbitrarily small time
and length differences. However, there are chances to disprove it:
First, the results from simulations according to valid equations
using the proper method may become more and more precise with
more and more small differences (robust computation assumed).
If this tendency does not continue, we had detected a smallest
time and a smallest length.
Ulrich
http://home.t-online.de/home/Ulrich.Bruchholz/
ueb
ueb wrote:
> But we can never prove the assumption of arbitrarily small time
> and length differences.
But there is an overwhelming reason for this assumption:
The geometric view of nature, as founded in SR/GR, is the only one
taking the role of the observer into consideration.
ark wrote:
>> Now, let us think about quantum theory. Normally time evolution there
>> is assumed to be continuous. But we have GRW and EEQT where time
>> evolution is a piecewise deterministic processes, with pieces of a
>> continuous, non-unitary evolution, interrupted by discrete quantum
>> jumps ("collapses"). Can it be that we can totally eliminate the
>> continuous part, and that the only reason for time "to flow" will be
>> "quantum jumps"?
[ueb]
> I have good reasons to claim that quantum jumps are nothing else
> than transitions from one to another stable solution of generally
> valid equations.
I have difficulties to imagine that time does "flow". But I could
agree that time and quantum jumps are "married". Because nothing
would change without above mentioned transitions. Time has been
defined from changes, i.e. without changes no time.
Thus, the basis might be the continuum. Searching for simplifying
models, quantum mechanics proves successful less and less.
Purely discrete models are only consequent, because they consider
our possibilities.
Ulrich
Tim Tyler
> ueb wrote:
> > But we can never prove the assumption of arbitrarily small time
> > and length differences.
>
> But there is an overwhelming reason for this assumption:
> The geometric view of nature, as founded in SR/GR, is the only one
> taking the role of the observer into consideration.
A discrete theory could explain this just as well.
It would be inaccurate to think that relativity represents
"overwhelming" reason for favouring continuity.
--
__________
|im |yler http://timtyler.org/ t...@tt1lock.org Remove lock to reply.
ueb
> ueb wrote or quoted:
>> ueb wrote:
>> > But we can never prove the assumption of arbitrarily small time
>> > and length differences.
>>
>> But there is an overwhelming reason for this assumption:
>> The geometric view of nature, as founded in SR/GR, is the only one
>> taking the role of the observer into consideration.
> A discrete theory could explain this just as well.
> It would be inaccurate to think that relativity represents
> "overwhelming" reason for favouring continuity.
Ok, I'll not fight for this claim, because it is rather philosophical.
A real reason were, if a continuum theory predicts particle numbers.
The geometric theory of gravitation and electromagnetism (formally
expressed by the known Einstein-Maxwell equations) does it ! (See
http://home.t-online.de/home/Ulrich.Bruchholz/ )
BTW, it is not the favour. One must carefully distinguish basis and
method. Thus, I take the continuum as basis, for above reason.
As well, I'd favour a purely discrete method (dealing with discrete
time & length) rather than quantum mechanics (which is only a method
too).
Ulrich
charliew2
I'm not a physicist, but I have a problem with our current understanding.
If you are not observing the states of some experimental apparatus, you just
don't know what state it's in. Claiming that there is a superposition of
eigenstates for a non-observed experiment is a statement that can't be
validated. Why don't physicists just say that they don't know what is
happening when they aren't looking?
daniel B miller
...
>
> I'm not a physicist, but I have a problem with our current understanding.
> If you are not observing the states of some experimental apparatus, you just
> don't know what state it's in. Claiming that there is a superposition of
> eigenstates for a non-observed experiment is a statement that can't be
> validated. Why don't physicists just say that they don't know what is
> happening when they aren't looking?
>
probability distributions. The probabilities interfere in a
non-intuitive way that isn't the same as how probability theory would
predict if the situation were simply that we don't know all the facts.
There is a correlation between what we would expect to be independent
variables that cannot (yet) be explained with any simple theory of
particles and forces similar to those we use in the classical realm.
One of the clearest examples of this phenomenon is the two-slit
experiment. Here's a nice explanation:
http://online.physics.uiuc.edu/courses/phys150/fall03/slides/lect23/sld005.htm
Note that the interference pattern persists even when we are measuring
what would normally be considered individual particles, such as single
electrons or photons. We even see this interference when the particles
in question are apparently detected seconds or minutes apart!
the hanged man
> charliew2 wrote:
>> I'm not a physicist, but I have a problem with our current understanding.
>> If you are not observing the states of some experimental apparatus, you just
>> don't know what state it's in. Claiming that there is a superposition of
>> eigenstates for a non-observed experiment is a statement that can't be
>> validated. Why don't physicists just say that they don't know what is
>> happening when they aren't looking?
>>
> Because 'superposition of eigenstates' do not act like normal
> probability distributions.
As far as I can tell, you aren't really answering his question. It
is, of course, true that superpositions don't act like normal
probability functions. But I don't think that's at the heart of his
question, so let me put it another way.
Instead of talking about the "superpositions" as a state that
particles are in when we aren't looking at them, why not just say that
we don't know what is happening while we aren't looking, though we
have a nice formalism that will tell us what we will observe, with
certain probabilities, if we do certain future measurements?
--
Matt Brown (thehan...@askee.net) | "Reason is and ought to be
Philosopher, Web Designer, SysOp | the slave of the passions."
Philosophy Grad Student @ UCSD | - David Hume
http://thm.askee.net |
charliew2
daniel B miller <dan...@cmu.edu> wrote in message
news:1067jn5...@news.supernews.com...
(cut)
I'm familiar with the two slit experiment, but this is the first time that I
have seen a description of electrons being used. I do, of course, have a
few comments:
* The results of the two slit experiment say something about our knowledge
of this system. If you don't know which slit an electron passed through,
you get the familiar interference pattern. If you do know which slit the
electron passed through, you do not get the interference pattern. I don't
know what this implies from a reality or philosophical standpoint.
* As you stated, even when single electrons (or photons) go through the two
slit apparatus, an interfernce pattern is produced if you don't try to
detect which slit the electrons went through. This strongly implies that
you are measuring the wave properties of the electrons, and it strongly
implies that individual electrons are interfering with themselves. Somehow,
when you try to detect which slit the electron goes through, you are
interferring with the apparatus such that you are measuring the particle
properties of electrons, and no interference pattern is produced.
* It is obvious that all particles have wave properties and all waves have
particle properties (the wave-particle duality). You can't get the familiar
interference pattern with bullets because their wavelength is so small that
the two slit apparatus can't be used to produce an interference pattern. In
other words, the two slit apparatus only works for "particles" whose
wavelength is at least as big as the particle itself.
Apparently, the type of apparatus and the type of observation governs which
property is being measured. I don't know if it is possible to
simultaneously measure both the wave and particle properties of electrons (I
suspect it isn't). If this test was possible, it would be interesting to
see the results.
charliew2
the hanged man <thehan...@askee.net> wrote in message
news:slrnc67ocj.v3...@gehennom.net...
Matt,
I think you "got it". Thanks for the reply.
By the way, this is just one man's opinion. When I see physicists claim
that they know what is happening to a system that they are not observing, I
tend to "cringe". Something in this type of statement just doesn't make
sense (common sense or otherwise).
I will elaborate, so bear with me. I very recently looked at a suggested
link, which described the famous two slit experiment and Schrodinger's cat.
In the case of Schrodinger's cat, I KNOW that at the end of the experiment,
the cat is either alive or dead, as these are the only two possibilities. I
also know that the cat must be in one and only one of these two states, even
though I am not presently observing the cat. The fact that I am not
observing the cat at the end of the experiment does not change its fate
(i.e., it can't be both alive and dead, and it can't change from one state
to the other merely by observing it).
Once I actually observe the cat, I now have enough information to determine
which state the cat is in, but I do not have any power to change the status
of the cat merely by observing it. This seems to me to be part of the
problem with the thought experiments and actual experiments of quantum
mechanics. I maintain that there is a reality that exists, whether or not
it is observed. Before observation, a few or many possibilities exist,
depending on the circumstances, but we don't have enough knowledge to
determine which possibility is "real". The act of observation serves to
eliminate all but one of the possibilities, because a lot more knowledge is
gained from this observation. Despite this, there is no valid reason to
conclude that all possible states of a system exist while we are not
observing that system. In fact, such a statement may be true (although I
doubt it), but there is no scientific reason on which to base such a
conclusion, entirely due to the fact that the non-observation of such a
system means that we don't have the data necessary to draw that conclusion.
Based on this opinion, I maintain that there has been a real confusion in
the quantum mechanics world, relating to the differences between "reality",
probability, and observation.
daniel B miller
[snip]>
Your thinking is clear and logical. However it is based on a flawed
assumption, which is that there is no experimental difference between a
world where we simply don't have all the facts, and a world with Quantum
interference. There is a big, important difference. If the tenets of
Quantum Mechanics hold out indefinitely, things like quantum computation
will be possible. Quantum computing implies that we can utilize the
superposition of states to do information processing that cannot be done
in a 'simple' Universe with a single worldline.
Personally, I doubt this is the case. But it is important to realize
that the present state of affairs is not due simply to some naive
confusion about probability, reality, and observation, as you imply.
Believe me, if that were the case no one in their right mind would have
accepted QM as it is understood today, and there would have been no
reason to. I suppose it was once expected that the statistical nature
of QM would readily give itself up to a reasonable explanation in terms
of classical probability and statistics applied to some ensemble of
microscopic events, in a way similar to how thermodynamics was
eventually understood through the kinetic theory of atoms and molecules.
Unfortunately, such a picture has proven very, very, very hard to put
together. Most of the people I know who post to this forum believe in
their hearts as you do (as do I) that such a rational picture must
exist. However, I think once you absorb all the facts, it will become
clear that such a picture may have attributes that are not easily mapped
onto the world of our everyday experience.
And there are some (many, outside of this discussion) who believe, not
entirely without evidence, that there is an aspect of reality that
involves the 'superposition' of different possible realities in a much
more concrete sense than just the existence of various possibilites that
we don't have perfect knowledge about, such as is the case with standard
statistics and probability theory. They're probably wrong, but they're
not wrong in the simplistic way you allude to. Any theory that
supercedes Quantum Mechanics and its brethren will need to deal with
some very strange facts about how things behave in this world.
-dbm
akha...@yahoo.com
Dan is right.
A real confusion of QM is how to calculate probabilities.
Classical probabilities can be reduced to rules of simple
deterministic dynamics behind.
QM probabilities are postulated and nobody was able to show what logic
could generate such probabilities. It does not mean that determinism
should be forgotten.
Alex
charliew2
Ah, but my assumption is entirely true for Schrodinger's cat, because that
cat is a macroscopic entity. As such, it doesn't follow the standard rules
of QM. The act of observing an object this big has no meaningful impact on
the state of that object. The point? Analogies such as this probably don't
help in understanding QM principles, because they are, in a sense, comparing
apples to oranges.
If you want to talk about observing an object the size of an electron, that
is an entirely different matter. For objects this size, it appears to be
impossible to observe them without affecting their status.
> There is a big, important difference. If the tenets of
> Quantum Mechanics hold out indefinitely, things like quantum computation
> will be possible. Quantum computing implies that we can utilize the
> superposition of states to do information processing that cannot be done
> in a 'simple' Universe with a single worldline.
>
> Personally, I doubt this is the case. But it is important to realize
> that the present state of affairs is not due simply to some naive
> confusion about probability, reality, and observation, as you imply.
Help me out here. I have recently read about "spooky action at a distance",
and I still don't "get it". The article stated that particles were chosen
such that either two "A" type particles were emitted from a source, or two
"B" type particles were emitted from a source, in a random sequence.
Distant detectors were set up to look at pairs of particles. Every time one
detector saw a given particle type, the "distant" detector saw the same
particle type.
I may be missing something here, but if you choose the source to emit only
particle pairs of the same type, why would you expect even a remote
possibility of seeing a "mixed pair" of particles at distant detectors? In
other words, if you set up this experiment to guarantee detection of "like"
particle pairs, what is the point of questioning the result when you get
this exact outcome?
> Believe me, if that were the case no one in their right mind would have
> accepted QM as it is understood today, and there would have been no
> reason to. I suppose it was once expected that the statistical nature
> of QM would readily give itself up to a reasonable explanation in terms
> of classical probability and statistics applied to some ensemble of
> microscopic events, in a way similar to how thermodynamics was
> eventually understood through the kinetic theory of atoms and molecules.
> Unfortunately, such a picture has proven very, very, very hard to put
> together. Most of the people I know who post to this forum believe in
> their hearts as you do (as do I) that such a rational picture must
> exist. However, I think once you absorb all the facts, it will become
> clear that such a picture may have attributes that are not easily mapped
> onto the world of our everyday experience.
I'm no longer so sure that very small particles can be understood in
everyday terms. Since these small particles possess both wave and particle
properties, they behave in nonintuitive ways.
charliew2
<akha...@yahoo.com> wrote in message
news:5bdca6d3.04032...@posting.google.com...
> daniel B miller <dan...@cmu.edu> wrote in message
news:<106a9h2...@news.supernews.com>...
> > charliew2 wrote:
(cut)
> >
> > And there are some (many, outside of this discussion) who believe, not
> > entirely without evidence, that there is an aspect of reality that
> > involves the 'superposition' of different possible realities in a much
> > more concrete sense than just the existence of various possibilites that
> > we don't have perfect knowledge about, such as is the case with standard
> > statistics and probability theory. They're probably wrong, but they're
> > not wrong in the simplistic way you allude to. Any theory that
> > supercedes Quantum Mechanics and its brethren will need to deal with
> > some very strange facts about how things behave in this world.
> >
> > -dbm
>
> Dan is right.
>
> A real confusion of QM is how to calculate probabilities.
>
> Classical probabilities can be reduced to rules of simple
> deterministic dynamics behind.
>
> QM probabilities are postulated and nobody was able to show what logic
> could generate such probabilities. It does not mean that determinism
> should be forgotten.
>
> Alex
>
Classical probabilities are derived from objects so large, that they have no
apparent wave function. Despite this, people are still struggling with the
idea that classical probability theory can be applied to quantum objects.
Obviously, they can't. I suspect (but can't prove) that many of Einstein's
observations are correct. There should be deterministic dynamics behind
quantum mechanics. Defining the logic that can generate them may well be an
impossible task.
I do, of course, have a thought experiment in mind regarding this issue.
Here's the "proposal":
* Write a computer program which describes this situation, in very
simplified terms. The computer program can give you all of the information
that you need about the simulated quantum particle/wave.
* Code a wave/particle function for the object of interest. Note that the
function, designated f1, must contain both wave properties and particle
properties.
* Code an "apparatus" function for the device that you will use to observe
the quantum object. Note that this function, designated f2, must contain
both wave properties and particle properties.
* Write the program such that the following applies:
1) When you are not observing the quantum object, only function f1
applies.
2) When you are observing the quantum object, you must perform some sort
of mathematical operation between f1 and f2, because these functions are
interacting during the "observation" period.
3) The mathematical operation performed on f1 and f2 must ensure that when
you are looking for particle properties of the quantum object, the wave
properties are cancelled out in your "experimental" results (i.e., when the
observational apparatus is "looking" at the quantum object). Likewise, when
you are looking for wave properties of the quantum object, the particle
properties are cancelled out.
If such a program can be written, there are several observations that come
to mind:
* This model is deterministic, because the computer program can tell you
everything that you need to know about the quantum object at all times,
whether or not it is being observed.
* Functions f1 and f2 cannot be defined independently of each other.
* There is no unique mathematical form for either function f1 or f2.
* In such a system, it becomes obvious that questions relating to why you
don't see "particle" results from a "wave" apparatus, or vice versa, are
probably the wrong questions to ask.
Comments?
the hanged man
> By the way, this is just one man's opinion. When I see physicists claim
> that they know what is happening to a system that they are not observing, I
> tend to "cringe". Something in this type of statement just doesn't make
> sense (common sense or otherwise).
Well, many physicists don't make such claims. But we don't tend to
hear much from them because the physicists making the paradoxical
claims sound much sexier.
You have to be careful here, however. If you assume one unique
reality even when we aren't observing the system, then you run the
risk of running afoul of the theory in a way that goes against
experimental evidence. Hidden-variable theories that have this
reality are possible, though. Cf. Bohmian Mechanics. The problem
with Bohm's theory, of course, is that it is difficult if not
impossible to reconcile with relativity, with more modern physics, and
with discreetness.
Another possibility is to forget about this reality stuff, and think
entirely operationally or praxically. What you have are the concrete
measurement events, which represent a certain amount of knowledge,
that knowledge evolves over time based on certain conditions, giving
predictions for future concrete measurement events. The best you can
say about what happens in between is a transmission process of a
certain general sort. This interpretation is one of the few *local*
interpretations of the quantum theory (it is only nonlocal in the
sense of statistical correlations, not nonlocal actions at a
distance), and thus much more friendly to relativity, and much more
open to synthesis into a future, discrete theory.
--
Matt Brown (thehan...@askee.net) | "Are you gonna follow your soul
Philosopher, Web Designer, SysOp | Or just the style of the day?"
Philosophy Grad Student @ UCSD | - Dan Bern, "Soul"
http://thm.askee.net |
Gerard Westendorp
[..]
> Instead of talking about the "superpositions" as a state that
> particles are in when we aren't looking at them, why not just say that
> we don't know what is happening while we aren't looking, though we
> have a nice formalism that will tell us what we will observe, with
> certain probabilities, if we do certain future measurements?
>
Take the case of a spin 1/2 particle. When you measure its spin in
a predefined direction, say the z-direction, you get either
"UP" or "DOWN". Suppose you did the measurement and you found
"UP".
Then you know all there is to know about the spin. Next time
you measure it in the z-direction, you again get "UP", with
probability 1.
But when you switch direction to lets say the x-direction,
you get a superposition:
|UP_z> = sqrt(1/2)(|UP_x> + i |DOWN_x> )
This means you will get a 50% chance for UP in the x-direction,
and a 50% chance for DOWN.
But the superposition has nothing to do with ignorance. It
is necessary for a complete description. If
you changed the superposition of x-direction eigenstates, you
would no longer reproduce exactly the z-direction eigenstate.
Check out the Feynman Lectures on Physics, part III for
a lot of stuff with spin and superposition, including experiments
that have proven the weirdness of QM.
So although measurement outcomes are in this case discrete and
probabilistic, there are underlying dynamic equations that
appear continuous and deterministic.
To be more precise, the probability aspect only enters the game
when you do a measurement. And the continuous aspect is that
the space of allowed states is formed by pairs of complex numbers
whose sum of norms are 1. (This corresponds to the surface of a
4-dimensional sphere!)
Gerard
ueb
> Alex wrote in message
> news:5bdca6d3.04032...@posting.google.com...
..
>> A real confusion of QM is how to calculate probabilities.
>>
>> Classical probabilities can be reduced to rules of simple
>> deterministic dynamics behind.
>>
>> QM probabilities are postulated and nobody was able to show what logic
>> could generate such probabilities.
That is a strong argument against QM.
>> It does not mean that determinism
>> should be forgotten.
>>
>> Alex
>>
> Classical probabilities are derived from objects so large, that they have no
> apparent wave function. Despite this, people are still struggling with the
> idea that classical probability theory can be applied to quantum objects.
> Obviously, they can't.
The reason could be that "quantum objects", as people imagine in QM,
do not exist at all. Is there experimental evidence for the "wave
function" ?
> I suspect (but can't prove) that many of Einstein's
> observations are correct.
I can support it. See below.
> There should be deterministic dynamics behind
> quantum mechanics. Defining the logic that can generate them may well be an
> impossible task.
It _is_ an impossible task, because quantum mechanics as such is dubious.
> I do, of course, have a thought experiment in mind regarding this issue.
> Here's the "proposal":
> * Write a computer program which describes this situation, in very
> simplified terms. The computer program can give you all of the information
> that you need about the simulated quantum particle/wave.
> * Code a wave/particle function for the object of interest. Note that the
> function, designated f1, must contain both wave properties and particle
> properties.
[snip]
> Comments?
Yes. - Forget the (non-existent) wave/particle function.
The simple question is: What quantities have discrete values ?
With the yet simpler answer: The integration constants of the known
Einstein-Maxwell equations !
Consequently, I _have_ simulated particles according to these tensor
equations, http://home.t-online.de/home/Ulrich.Bruchholz/ .
In which, the particle numbers appear as values of the integration
constants for most stable solutions. I have listed the facts in the
article 514c3c...@Muse2.private.de (this thread).
If one wants to discretely model the world, purely discrete models
like digital physics or cellular automata could be a lot better than
quantum mechanics with all its unproven assumptions and postulates.
Ulrich
daniel B miller
...
I think this is the correct approach. However, you say:
> * Write the program such that the following applies:
> 1) When you are not observing the quantum object, only function f1
> applies.
What do you mean by 'you'? The apparatus in the program, or you, the
human programmer? For this thought experiment to be appropriate,
everything, including the observer, must be within the system being
simulated. After all, we as observers are in the same Universe as the
things we are observing, and are subject to all the same laws.
Only by making the program itself completely self-contained can we glean
knowledge about our situation as observers in our own Universe.
-dbm
charliew2
(cut)
>
> Check out the Feynman Lectures on Physics, part III for
> a lot of stuff with spin and superposition, including experiments
> that have proven the weirdness of QM.
>
Do you have a link, or a suggested Google search?
> So although measurement outcomes are in this case discrete and
> probabilistic, there are underlying dynamic equations that
> appear continuous and deterministic.
> To be more precise, the probability aspect only enters the game
> when you do a measurement. And the continuous aspect is that
> the space of allowed states is formed by pairs of complex numbers
> whose sum of norms are 1. (This corresponds to the surface of a
> 4-dimensional sphere!)
>
>
> Gerard
Quite interesting.
charliew2
ueb <Ulrich.B...@t-online.de> wrote in message
news:jsa64c...@Muse2.private.de...
Can your model approximately reproduce the effects of the two slit
experiment?
charliew2
The apparatus in the program. In a very real sense, the human programmer in
this simulated problem knows all and sees all, and he is outside of the
simulation (he has no effect on it). Pardon the confusion - I should have
been more explicit.
> For this thought experiment to be appropriate,
> everything, including the observer, must be within the system being
> simulated. After all, we as observers are in the same Universe as the
> things we are observing, and are subject to all the same laws.
That is why I suggested the program. A simulation of this sort lets you
"get away with" non-physical things, such that you readily draw the
conclusion that you can't get this kind of information in the real world,
exactly because you are a part of the same Universe whose laws you are
trying to discover.
>
> Only by making the program itself completely self-contained can we glean
> knowledge about our situation as observers in our own Universe.
>
> -dbm
Agreed. Some of the REALLY big questions in this scenario:
* Based on what we know about QM, is it possible to develop a program which
is simple enough to run on a modern computer, and that gives results that
approximately agree with experiment?
* Will this program be able to provide predictions that can be tested
against "reality" by a physical apparatus?
* How do you ever know that your computer model is approaching an accurate
description of the real world?
Is it likely that someone in this NG has the talent to write a simplified
version of a computer program such as I have outlined? If so, it would be
interesting to see this program's results.
the hanged man
> the hanged man wrote:
>> Instead of talking about the "superpositions" as a state that
>> particles are in when we aren't looking at them, why not just say that
>> we don't know what is happening while we aren't looking, though we
>> have a nice formalism that will tell us what we will observe, with
>> certain probabilities, if we do certain future measurements?
> But the superposition has nothing to do with ignorance. It
> is necessary for a complete description.
All of what you've said is right, but I think it is entirely
compatible with what I've said, so let me try to make myself more
clear.
I'm not sure how you measure spin, but I know I can measure
polarization with my sunglasses, so let's talk about polarization for
a second.
Say we have a polarizer, aligned in the y-direction. Now, when we
have a photon pass the polarizer, we know that it passed through, and
we know that if another polarizer is directly after the first, in the
same direction, all the photons that get through the first get through
the second. And we know that if we have an x-polarizer, none of them
will get through. And, likewise, we know that if we have one at
45-degrees, about half get through (I think. I may be forgetting some
subtle complication). Likewise, we know if we have a y, a 45, and an
x, some photons still get through, and this is an interesting quantum
effect.
Now, one way to describe the situation, and I take it this is your
preferred way, is to say that when the photon passes through the
polarizer, we learn that it has a certain state, which we can describe
with a wave function (or pick your favorite quantum formalism).
Knowing that the photon has this state, which is an unambiguous
"y-polarized" but also a superposition of "45-polarized" (in your
electron spin example, it was an unambiguous "UP-z" and a
superposition in x), we can predict how the state will change due to
other measurements, with accompanying probabilities for pass or
no-pass.
This seems to me to be a bizarre way to describe the situation.
It seems to me that when we run a photon through a polarizer, all we
learn is one bit (in the computational sense) of information: pass or
no-pass. Our wave function isn't a description of the photon's state
at all; it is a description of the measuring device, the direction of
the polarizer. So when we have a y and an x polarizer, we have a wave
function describing each, and when we put them together we learn that
it is impossible for photons to pass both. If we put a y and a 45
together, we learn that half of the photons will get through.
One can always describe quantum mechanics as saying that there are
weird objects in the world like superpositions and wave functions, but
it isn't necessary. Rejecting this doesn't mean rejecting the quantum
theory or thinking classically. Heisenberg and Bohr certainly didn't
think of quantum mechanics in the way you're recommending.
One can, more faithfully to the originators, describe quantum theory
as measurement processes and strange statistical results, without
having to reify parts of the formalism into bizarre claims about what
kind of entities are out in the world. Furthermore, I think that
thinking in this way is more useful for moving beyond quantum theory,
though I certainly haven't backed up that claim (and probably couldn't
to a degree that would satisfy).
--
Matt Brown (thehan...@askee.net) | "No, no, you're not thinking,
Philosopher, Web Designer, SysOp | you're just being logical."
Philosophy Grad Student @ UCSD | - Niels Bohr
http://thm.askee.net |
daniel B miller
[snip]>
>
>>For this thought experiment to be appropriate,
>>everything, including the observer, must be within the system being
>>simulated. After all, we as observers are in the same Universe as the
>>things we are observing, and are subject to all the same laws.
>
> That is why I suggested the program. A simulation of this sort lets you
> "get away with" non-physical things, such that you readily draw the
> conclusion that you can't get this kind of information in the real world,
> exactly because you are a part of the same Universe whose laws you are
> trying to discover.
>
>
[dan:]
>>Only by making the program itself completely self-contained can we glean
>>knowledge about our situation as observers in our own Universe.
>>
>
> * Based on what we know about QM, is it possible to develop a program
which
> is simple enough to run on a modern computer, and that gives results that
> approximately agree with experiment?
> * Will this program be able to provide predictions that can be tested
> against "reality" by a physical apparatus?
> * How do you ever know that your computer model is approaching an
accurate
> description of the real world?
You ask good questions. The answers aren't as simple as we would hope.
Certainly programs can and have been written that basically do as good
a job as possible of running through the complex equations of QM and
producing some sort of statistical result that one can compare with
experiments. However, it appears that no one has really put forth any
kind of 'process model', discrete or otherwise, that attempts to produce
the kinds of things we see at the quantum level with any kind of
precision. I would guess that common wisdom in the physics community is
that such a model is either impossible in principle, or so far beyond
our capabilities as to be a non-starter for a long time.
Of course there are various 'models' such as string theory and LQG, but
they seem more focused on explaining why we have such-and-such particles
and forces, or why the fundamental constants of QM are what they are,
rather than actually trying to build models in the computer science
sense of 'virtual reality at the quantum level'.
>
> Is it likely that someone in this NG has the talent to write a simplified
> version of a computer program such as I have outlined? If so, it
would be
> interesting to see this program's results.
>
Perhaps a combination of people in this NG can contribute to something
of this sort. Certainly what you are talking about is along the lines
of the work I'm doing at CMU with Ed Fredkin. There has been discussion
about releasing some of that work as an open source project. It's
preliminary right now but perhaps we could move it along faster with
more people contributing. At least it would be interesting to get some
feedback as we develop our models. I'd be curious to hear any opinions
out there on this idea.
-dbm
charliew2
> charliew2 wrote:
(cut)
> > Agreed. Some of the REALLY big questions in this scenario:
> >
> > * Based on what we know about QM, is it possible to develop a program
> which
> > is simple enough to run on a modern computer, and that gives results
that
> > approximately agree with experiment?
> > * Will this program be able to provide predictions that can be tested
> > against "reality" by a physical apparatus?
> > * How do you ever know that your computer model is approaching an
> accurate
> > description of the real world?
>
> You ask good questions. The answers aren't as simple as we would hope.
(cut)
Thanks. And yes, I realize that the answers aren't simple. If they were,
equations like the Schrodinger equation would be much easier to solve for
"normal" problems (i.e., for problems somewhat more complicated than the
hydrogen atom).
If you are wondering, even though I work in a different field, I've had to
work with some very highly dimensional computer models. In addition to
that, I actually followed my own advice on another problem at work, and I
coded up a tough statistical problem such that I new all of the answers in
my program before I calculated statistics on the results. The output from
this program was interesting, to say the least.
The main lesson from this: it's a LOT easier to know where you stand when
you have access to data that you normally can't get in the real world.
Take care, and thanks for a most interesting discussion.
ueb
> Can your model approximately reproduce the effects of the two slit
> experiment?
I don't know it, because I'm at the beginning. Up to now, I can
only simulate the simplest stationary fields. Your example means
transitions that are much too complicated to simulate them with
today's means. (It seems to be a special case where QM works. ;)
You should bear in the mind, that people take any reproduction
of particle numbers with "my model" as absolutely impossible,
despite of all achieved and presented results.
Ulrich
charliew2
me a book title. Thanks.
charliew2 <char...@ev1.net> wrote in message
news:106e3pu...@corp.supernews.com...
Gerard Westendorp
> Nnnnnnnever mind! A quick Google search informed me that you actually gave
> me a book title. Thanks.
[..]
>>>Check out the Feynman Lectures on Physics, part III for
>>>a lot of stuff with spin and superposition, including experiments
>>>that have proven the weirdness of QM.
Feynman Lectures on Physics is worth having on your book shelf.
One of, if not the, best physics book(s).
Gerard
Gerard Westendorp
[..QM description of photons and polarizers..]
> This seems to me to be a bizarre way to describe the situation.
Yes, quantum mechanics is bizarre! (But we both knew that of
course)
> It seems to me that when we run a photon through a polarizer, all we
> learn is one bit (in the computational sense) of information: pass or
> no-pass. Our wave function isn't a description of the photon's state
> at all; it is a description of the measuring device, the direction of
> the polarizer. So when we have a y and an x polarizer, we have a wave
> function describing each, and when we put them together we learn that
> it is impossible for photons to pass both. If we put a y and a 45
> together, we learn that half of the photons will get through.
>
But there are also a lot of interference experiments you can do,
that you can only predict by using amplitudes. (ie states weighed
by complex numbers called amplitudes)
The question of whether these amplitudes really mean anything
or if they are just mathematical constructs is a bit
philosophical. My experience is that it very rarely happens
that someone from one side convinces someone from the
other on this issue.
Gerard
the hanged man
> [..QM description of photons and polarizers..]
>> This seems to me to be a bizarre way to describe the situation.
>
> Yes, quantum mechanics is bizarre! (But we both knew that of
> course)
I agree. Let me rephrase: this description seems incoherent. Quantum
mechanics is indeed bizarre, but it doesn't have to be incoherent.
> But there are also a lot of interference experiments you can do,
> that you can only predict by using amplitudes. (ie states weighed
> by complex numbers called amplitudes)
I agree, but this can be understood as oddities in the logic or
statistics of nature without being understood ontically.
> The question of whether these amplitudes really mean anything
> or if they are just mathematical constructs is a bit
> philosophical.
I agree**. However, I think how you understand quantum theory can be
an aid or a barrier to your ability to work towards the next theory.
** Though, as a philosopher, I resist the implication that this makes
it unanswerable, meaningless, or bad.
charliew2
> Gerard Westendorp brought forth from the ugyldig:
> > the hanged man wrote:
> > [..QM description of photons and polarizers..]
> >> This seems to me to be a bizarre way to describe the situation.
> >
> > Yes, quantum mechanics is bizarre! (But we both knew that of
> > course)
>
> I agree. Let me rephrase: this description seems incoherent. Quantum
> mechanics is indeed bizarre, but it doesn't have to be incoherent.
(cut)
I'm not sure what description I would use to label quantum mechanics. It
definitely defies expectations. Of course, I have never seen a macroscopic
object refract. Everyday experience just does not suffice when you start
working with objects that simultaneously have both wave and particle
properties. Coming to grips with the implications of the wave/particle
duality seems to be the biggest "mind block" for understanding.
I have another question for the NG, which I don't have the expertise to
answer. Could it be that the Heisenberg uncertainty principle is another
way to say that you can't simultaneously observe the wave and particle
properties of a quantum object?
Gerard Westendorp
[..]
> I have another question for the NG, which I don't have the expertise to
> answer. Could it be that the Heisenberg uncertainty principle is another
> way to say that you can't simultaneously observe the wave and particle
> properties of a quantum object?
sort of.
[I don't know if I am an expert, but I like to pretend I am.]
There are various interpretations of qm, and I am probably taliking
in a variant of Everets many worlds interpretation.
The fundamental concept is neither wave or particle, but state.
A state is basically a large set of numbers, that completely describes
the system. States evolve deterministically in time.
Classical concepts like position, momentum, energy, are coded in
the state. To extract them, you need an operator. Each classical
concept has a so called observable, which is an operator to
extract the classical variable from the quantum state.
But unfortunately, the operators do not always give a single
number. Some states give a single number for certain observables.
In that case they are in an eigenstate of that observable.
But you cannot simultaneously have an eigenstate of all observables
that you want. Some exclude one another. That is Heisenbergs
uncertaintyy principle.
This is also the reason that some wave-like things exclude
particle-like things. The details depend on the experiment.
Now the real weirdness happens during a measurement or observation.
Determinism, causality, and locality break down, and you
suddenly end up in an eigenstate of whatever observable
corresponds to your experiment.
Personally I (and some others) think of quantum mechanics
a describing not just reality, but a kind of hyper-reality,
which is sort of a superposition of "ordinary" realities.
When you do an experiment, you get information that forces
you to refine the subset of possible realities to those
consistent with your measurement.
There are other interpretations, but the best I can do
is explain how I see it.
Suppose you wrote a simulation of the universe on a
computer. You have to simulate some internal observer,
who of course cannot directly
see the bits and bytes of the simulation, but only sees
certain filtered aspects of it. (like Plato's shadows)
But according to quantum mechanics, you would have to
simulate a whole bunch of observers, who each see a different
reality, without seeing each other, but who have to be simulated
together in order to do a deterministic simulation.
Gerard
ueb
..
> Everyday experience just does not suffice when you start
> working with objects that simultaneously have both wave and particle
> properties. Coming to grips with the implications of the wave/particle
> duality seems to be the biggest "mind block" for understanding.
In order to understand the reason of the seeming wave/particle
duality, I can only refer to my answer to your question for me
in this thread.
Particle means a stationary state, but waves occur with any changes,
i.e. at interactions.
Ulrich
the hanged man
> I have another question for the NG, which I don't have the expertise to
> answer. Could it be that the Heisenberg uncertainty principle is another
> way to say that you can't simultaneously observe the wave and particle
> properties of a quantum object?
I think this is a pretty good way to think of it, actually. The
Heisenberg uncertainty principle indicates that (for example) position
and momentum measurements don't commute, that is, you can't measure
them the same way, and the order you measure them matters. Now, when
doing position measurements on a photon or an electron, it behaves
much like a particle (it arrives at a detector as a discrete whole),
whereas in momentum measurements it acts more like a wave (two slit
interference stuff).