The Copenhagen interpretation of QM

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Jacques M. Mallah" <jqm...@is2.nyu.edu> wrote
>As for is an ontological view that
>>>important, yes. I have little tolerance for a Copenhagen-like view
>>>that observations are everything.
>
>>subtler than that. I would put forth the proposition that people who
>>start with a presupposition that a subset of realism is the only
>>possible valid philosophy might view things that way, but I read
Copenhagen
>>quite differently than that.

>There is not really any one Copenhagen view. The interpretation
>is defined by the writings of Bohr, which are more like an ink
>blot test to me, so it's not surprising that several different
>versions of 'Copenhagen' go under the same label.
>The version I described is a sketch of what I see as the main
>thrust of much of what is said under the label. I wouldn't
>mind if you described the way you see the Copenhagen interpretation.
>I certainly would say that some form of realism is the only
>possible valid philosophy, but I surely would rather deal with the
>actual rival than a straw man which I might have devised.

I appreciate the fact that you do not wish to argue against a straw man.

I think the best way to approach this is to first give the philosophical

background, and then discuss the Copenhagen interpretation in light
of that background.

PHILOSOPHICAL BACKGROND
The philosophy for which I am arguing, neo-Kantiant, was an attempt
to bridge the gap between two great philosophical traditions. One
was scholastic. In it where the classicists of the 15th-17th century,
and Thomas Aquinas, with the deepest roots in Aristotelian thought (and
to a lesser extent Agustinean and Platonic thought). The other was
empiricism. Included in this tradition are Locke, Hume, and Barclay.
The scholastic tradition thought some things are inherently known,
such as A or ~A. The empiricists argued that nothing is known
a priori, that everything comes from experience. And, since
the senses could mislead, one does not know anything with certainty.
In some ways, the scholastics were idealists, although Aristotle was
mostly a realist. Plato, of course, was an idealist.

Into this position stepped Kant. Kant examined the possibility of
certain knowledge. He asked the question "are a priori synthetic
judgments possible?" A priori means certain knowledge before,
and/or independent of experience/observation. For example, we know
that a triangle has three sides a priori. That is an a priori
analytical judgment because "having three sides" can be understood
by analyzing the definition of triangle. One drawback is that
there is no new information in this judgment. A posterori synthetic
judgments are also easy to show. That ant is black is one. New
information is contained in this judgment, because black cannot
be deduced from ant. However, this judgment is not certain. One
cannot deduce from observing 1,000,000 ants, all of which are
black, that all ants are black.

This leads to the question at the top of the previous paragraph: are
a priori synthetic judgments possible? Kant states that they are,
and gives an example: 2+3=5. He states, I think quite rightly,
that the concept of 5 cannot be obtained from analyzing 2 and 3.
New information is obtained from doing this addition. This is a
trivial example, but one could think of theorems proven from axioms
that would surprise even the person who wrote down the axioms.

I think that most of us now would agree that we know the validity
of theorems in mathematical systems a priori. Indeed, since Kant,
there has been a proliferation of systems that have no know
connection to the world of phenomenon. At the time, however, systems
tended to have correspondence with the outside world. Of particular
note was geometry, which was seen in the world and the axioms of
Euclid. At that time, it was thought that non-Euclidean geometry
was self-contradictory. I think a bit after that time "Euclid without
any Flaws" was written, supposedly showing that more than one
parallel line through a point contradicted the other postulates
of Euclidean geometry.

With this understanding, Kant bridged idealism and realism (which
was in the form of empiricism at the time) in his "Critique of Pure
Reason." There was a world apart from us, which is labeled "nomenon."
This nomenon consisted of things in themselves (to use a more modern
phrase" that exist independent of us. There was also the human mind,
which had basic forms, basic features. Logic, mathamatic, etc. are
not derived from experience, but are known a priori, because they
are part of the structure of the human mind.

Given this basis, Kant then explains phenomenon. Phenomenon is the
product of both the structure of the human mind and nomenon. Trees,
rocks, planets, etc. are not things in themselves, they are the
result of the interaction of our minds with nomenon. For Kant,
space and time are not properties of the nomenon, they are the
a prior forms of our intuition. (Intuition here is not like the
stereotyped "woman's intuition, or even scientific intuition, it is
the way we organize understand the world.)

It is likely that he was influenced by the perceived a priori nature
of space as Euclidean. In some circles, the fact that physical
space is now seen as non-Euclidean and that there is no absolute
space is seen as an argument against Kant's ideas. I think that
there is no argument that a Kantiant perspective needs to be
modified in light of special and general relativity. However, by
considering rotations in spacetime with translation, instead of
an infinity of spaces and times, and by allowing non-Euclidean
geometries, I think that a neo-Kantiant view can still be reasonable
in a relativistic frame.

Anyway, back to the main thrust toward Copenhagen. In the Kantiant
view, phenomenon does not exist without the human mind. This is not
idealism, it certainly is not solipsism, since there is stuff, the
nomenon, that exists apart from our minds. However, we our perceptions
are not of nomenon. They are of phenomenon that is a mixture of
how our mind works and the independent nomenon.

One obvious question is why do we all perceive the same things.
Why isn't there one type of space and time for me, and another one
for those folks who believe in absolute space and absolute time.
The answer is twofold. First, there is the same nomenon for all,
regardless of the form of the minds. Second, humans all have
the same basic form of mind. The structure of our minds is not
a matter of beliefs, it is how the mind works.

Let us consider two examples of this from mathematics. First,
we know that the Pythagoreans believed in only rational numbers.
They considered the existence of sqrt(2) as an irrational number
to be scandalous. I've read that they actually kept that hidden.
However, their beliefs did not make the square root of 2 a rational
number. One could argue from the correspondence to the world that
this was empirical, but taken simply as math, one can see within
the structure of ordinary arithmetic, sqrt(2) will be an irrational
number.

I've already alluded to the second example. During Kant's time,
most mathematicians believed that the parallel line postulate could
be proven from the other postulates of Euclidean geometry. However,
they did prove the opposite. In fact, I remember that the "Euclid
free from any flaws" actually contained much of the proof that the
parallel line postulate was not deducible from the other postulates.

So, in the Kantiant view, although much of the structure of the world
of phenomenon comes from the structure of our minds, we cannot
directly control the reality we live in. We can no more do this
than control which theorems are true and which are false.

COPENHAGEN INTERPRETATION
Now, we go on to understanding the Copenhagen interpretation.
At the time that Copenhagen was developed, it was apparent
that QM objects did not behave like classical things. In terms of the
wave/particle duality picture of the two slit experiment, for example,
one photon went through two slits and interfered with itself to
cause the diffraction pattern.

Now, quite rightly, you can say that is not what is really happening.
You could point to the superpositons and the collapse of the wave
function as the reality, and the wave-particle duality as merely one
of the first pictures of what is happening. This improved understanding
just heightens the difficulty of expressing QM in terms of normal
macroscopic things. For example, is possible to assume that balls have
both definite position and momentum at all times and that one can, by
knowing the initial velocity and position of a ball, predict both its
future
position and momentum as a function of time, provided one knows the
forces acting upon it. We both know this is not true in QM. The EPR
paper is a great example of the difficulty of resolving QM with
classical
realism.

So, given this, I believe that the Copenhagen school abandoned
classical realism as a prerequisite for doing physics. In this post,
I will not take the time to do the necessary due diligence to determine
the exact extent of the Kantiant influence on the Copenhagen school
(that's fodder for a history of science journal article). Rather,
I will consider a lesser task, view the Copenhagen interpretation
from a neo-Kantiant perspective.

In the development of the Copenhagen interpretation several things
were seen.

1) Wave functions often propagated in superpositions, it takes
a measurement to reduce a superposition to an eignenstate.

2) Correspondingly, superpositions are not the result of
measurement, eigenstates are.

3) Statements such as "when the spin is up at x, what is the spin
at x + 10 degrees" have no meaning. There is just a probability
of observing either up or down.

So, it was reasonable to say that we know that there are definite
values when we measure but we cannot assign definite values to what
we don't measure. Further, if we measure first one thing, then the
other,
and if the measurements do not commute, then the second measurement
destroys the knowledge we gained from the first measurement. For
example, if we measure momentum, and then position, we no longer know
momentum better than given by dx dp > h.

O.K., none of this is foreign to you. But I hope you can see where
juxtaposition of the philosophy and physics are heading. From a
neo-Kantiant perspective, we do not know the nature of nomenon:
existence apart from our minds. Our perception, our measurements
are all we have. The world of tables, books, rocks, electrons, etc. is
not independent of us. It is the world of phenomenon, which is the
product of both our minds and the stuff apart from us, the nomenon.

Thus, one is not surprised that observation/measurement is required for
the spin of quantum particles to exist in anything but a combination
(superposition) of opposite spins. There is no a priori reason for all
objects of phenomenon to follow the rules we have established for the
macroscopic world we live in. As we expand the envelope in interacting
with the nomenon, we start to see the breakdown in our conventional
organization of the world.

Indeed, this pattern could be seen going throughout physics. The
world view of 18th and 19th century physics was a very mechanistic
view. Phenomenon was described in mechanical analogs. The best
example of this was the description of light as waves in the aether
fluid.
I remember in E&M class discussing some of the mechanical models
Maxwell tried for the aether. As we now know, this has been doomed
to failure. One can see by the anti-relativity posts on the net, the
desire
to have E&M waves explained in terms of things that have analogies to
things we can sense directly: the medium of the aether corresponding
to the medium of water or air.

This distancing from everyday intuitive understanding has been
increasing
in this century. A good example of this has been the discussion I am
having
with David Elm on the logic of QM. He wants the underlying mechanism
for
QM, the gears and levers underlining the superposition reducing to
eigenstates. He asked me to explain why some of the time when up is
measured at angle x, down is then measured at x + 13 deg. I gave him
the superposition answer and he stated:

"This is just the math. What physical reality does it represent?"

I am going to respond with "that's the physics, there are no hidden
variables underlying this." I believe that neither one of us feels the
need to explain quantum physics in terms of macroscopic metaphors.
Theories of physics regularly give mathematical formulas as the
description
of what exists, what is measured. I would argue that this is a strong
example of the function of our mind in the structure of phenomenon.
Mathematical systems that begin as pure structures of our mind end
up being the best description of the world that we have.

A consideration of QED also adds to this understanding. Renormalization
is the best example of a sucessful mathamatical picture that has
unintuitive unobserved features that I can think of. Do particles
really have infinite charge, which results in vacuum polarization and
the finite charges that we measure? If renormalization gives the right
answer, do we need to worry about the ontological significance of
infinite charge?

If, tomorrow, we would find a formulation of QED that would do away
with the need for renormalization, it would probably be considered a
step forward, but would we think that we have a radically different
physics? I would argue that if the same predictions were given, it
would be considered a nice bit of simplification, but not a new theory.
I think Feynman himself was fundamentally in the "shut up and
calculate" camp. If the right predictions are made, it doesn't matter
what unmeasured features are in the theory. I cannot imagine rejecting
a unification of QM and GR because of the nature of the unobserved
variables within it.

So, to go back to your first point about "measurements being all there
is," I would argue that for the Copenhagen interpretation that
measurements/observation are not all there is; they are just all
we have. We live in a world of phenomenon. What exists apart from
that is an interesting question, but not one we can answer. Yes,
there is existence apart from us, but our perception is not directly
of that existence. Phenomenon is not the world of things in themselves
apart from us, it is the interface between those things and our minds.

This should provide a decent basis for a discussion of my view of
Copenhagen. It did take up a fair amount of bandwidth, but it could
be viewed as short in terms of the complexity, detail, and subtlty of
the philosophical system that is described (Kants, not mine :-) ) I cut
my answers to your post, but I can always post and/or send them later if
it becomes germane. For now, I think it suffices to present my
understanding of Copenhagen.

Dan M.

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Jacques M. Mallah" <jqm...@is2.nyu.edu> wrote

>The question of making a distinction between a priori and a
>posterori judgements is interesting, but is not the issue at hand, >and I'll try to avoid that tangent for now.


It is not totally a tangent, but I understand why you wish to focus on what you consider main issues. Indeed, I will also focus on only
part of what you posted. The important questions to be considered are what is the source of our knowledge, and how certain is the knowledge we obtain. For now, I will mention only one example of where it is important. By seeing hundreds, thousands, millions of black ants, and no red ones, someone could have summarized that all ants are black and not red. A reasonable person could see that that if only one area was checked, that could be too quick of a generalization.

However, in all of human history, there have been just a few million
sunrises. Nonetheless, the generalization that the sun rises in the
East is very reasonable. The difference has a lot to do with how can
we obtain certain knowledge.

>>With this understanding, Kant bridged idealism and realism (which
>>was in the form of empiricism at the time) in his "Critique of Pure
>>Reason." There was a world apart from us, which is labeled "nomenon."
>>This nomenon consisted of things in themselves (to use a more modern
>>phrase" that exist independent of us.

>I take it that the modern word is 'reality.' Of course we are part >of reality but I see no reason to distinguish that part from the >rest.


No, the modern word is not reality. All of our knowledge, certain or
otherwise, comes from perception. We know that we perceive things and
that we have a reflective self awareness of the "I" doing the perception. This reflective self awareness is not observable by others. Indeed, in your viewpoint, there is no objective reason to believe that it exits.

There is no free will, and all observed human behavior is only an
infinitesimal part of the sum total of the multiworld human behavior which includes every possible human behavior.

>>Logic, mathamatic, etc. are not derived from experience, but are >>known a priori, because they are part of the structure of the human
>>mind.

>I take it you are talking about postulates, such as A=B and B=C
>implies A=C.

That sort of thing, yes.

>>Given this basis, Kant then explains phenomenon. Phenomenon is the
>>product of both the structure of the human mind and nomenon. Trees,
>>rocks, planets, etc. are not things in themselves, they are the
>>result of the interaction of our minds with nomenon.

>I take it you are talking about what I would call conscious
>perceptions. It seems like the idea here is like the old 'you could
>really be a brain in a jar' idea. No one disputes that.

Its stronger and older than that. The denial of the ultimate reality
of the empirical world goes back to Plato's Republic. Have you read
the Republic? It is >2000 years old, and its "cave" analogy to reality
is one of the classic pieces in Western thought.
However, neither I nor Kant holds idealism like this. We do not hold
ideas to be the only true reality. Stuff does exist, apart from us.
Since we have only a posterori knowledge of this stuff, it is uncertain. Does that mean there is no certainty, as the empiricists state? No, you, I, and Kant do not believe that A=B, B=C, -> A=C comes from experience with observations.

>Re absolute space, I don't see it as relevant.

We do not need to link neo-Kantiant thought to a pre-relativistic
absolute space and absolute time. I think that we can substitute
absolute spacetime, if you will, with the usual rotations shown in
Goldstein. What is critical is that space, time, causality, are how
we order things in themselves. The world apart from the human mind
does not have space and time, they are part of how the human mind
organizes the world. The same is true for causality.

<snip>

>So you seem to agree that there exists an objective reality, which
>you call nomenon, as well as conscious perceptions that depend on >that >reality in some way.

Human minds are also objectively real, and separate from the nomenon
that they interact with in order to produce phenomenon.
<snip>

>>Thus, one is not surprised that observation/measurement is required >>for the spin of quantum particles to exist in anything but a
>>combination (superposition) of opposite spins.

>Now that you're suggesting that measurements affect reality, you
>should come up against the fact that the term 'measurement' is ill
>defined. The best you can say is 'I know it when I see it,' which is >good enough for anti-pornography laws, but not for physical laws.
>Who can make 'measurements' or 'conscious observations'? Can I?
>Can you? Can a robot? Can a rock?

There is no doubt that the exact point that the wave function collapses is not determined. We know when we observe, it is collapsed, as we know that it is not collapsed in experiments that utilize superpositions.

You claim that the uncertainty goes away with the MWI interpretation.
I do not think so. Your example can be extended to point that out.

>What about Shrodinger's cat? Or, better, a guy in a box measuring
>a spin up or down. It is possible in principle, to observe an
>interference pattern between the superposed states of the guy. If I >have no grounds to say that the guy in the box has conscious >observations, then I have none to say that you do either. And if I >do have grounds, then I have the same grounds for the 'spin up' and >'spin down' observations he makes, and it's certainly simpler to say >that both observations really occur.

Let us look carefully at that situation. Let us look at a very extreme example of this where we have a human "cat". We send a photon to a half silvered mirror. If it passes through, he dies. If it doesn't he lives.

Well, the photon reflects, and he observes that he is alive, or
it doesn't and he isn't around to observe. We look in and see him alive or dead. Everyone's observation is the same, all alive or all dead.

Now in MWI, there is no collapse of the wave function. Both alive and
dead are considered to be true. However, if we see him dead, we will
always live in a universe in which he died. If we see him alive, we
will always live in one in which he lives. I would argue that branching and splitting are very good words for this. This is a fundamentally different situation than a superposition. If, for example, we have wonderful optics and paths for the photon that were 3x10^10 meters long, we could have a man in a box knowing for 100 seconds that there was a superposition, and then finally living or dying.

>And if the wavefunction is not the reality, why is it so closely
>tied to what we percieve?

Because it is part of the structure of our minds as we interact with
nomenon. While it may be difficult to put a sliding scale for this
on a rigorous basis, I would argue that the wave function is further
from the nomenon than the observations themselves.

<snip>

>>I think Feynman himself was fundamentally in the "shut up and
>>calculate" camp. If the right predictions are made, it doesn't >>matter what unmeasured features are in the theory.

>Please refrain from dropping names. We are here to debate the
>issues on merit, not on which big name believed what.

I used him as an example of how theories of physics are
developed and used. My guess is that he would think that both of
our philosophical positions were nonsense. : ) A parallel example
would be to quote Maxwell's discussion of E&M in terms of an aether.
That does not support the aether theory but does support the theory
that physics was understood in a mechanistic framework in the 19th
century. My use of Feynmann was in this spirit.

>I would certainly say that unmeasured features do matter, and are
>really the most important part of the theory! For example, consider
>solipcism. Does it matter if you are the only being with conscious
>perceptions? Would you prefer if your loved ones had them too?

As a scientist, it would matter little, the physics would be
the same. Philosophy is the field that deals with ontology and
epistemology. As a side note, my loved ones wouldn't really be
loved if MWI were true. Remember in MWI, the statement I'm about
to kill them is always true if I can physically do it.

>Now, you might say that since other people can make the
>measurement, it does matter. But in that case you would have to >admit that whether or not the other branches of reality predicted by >the MWI exist or not also matters, because other people (the ones in >those branches) would be able to verify their existence. (Each one >could only verify his own branch.)

You do seem to accept branching with this statement. I would argue
that the branching of the wavefunction has all the problems of the
collapse; that they are just different interpretations of the exact
same phenomenon. Thus, MWI does nothing to solve the problems of
why and when does the wave function collapse, it just transfers it
to why and when does the wave function branch.

>>So, to go back to your first point about "measurements being all >>there is," I would argue that for the Copenhagen interpretation that
>>measurements/observation are not all there is; they are just all
>>we have. We live in a world of phenomenon. What exists apart from
>>that is an interesting question, but not one we can answer. Yes,
>>there is existence apart from us, but our perception is not directly
>>of that existence.

>Yes, but we can make models of what the reality could be, and some
>possible model must be the right one, as I said, and even though we >can't prove which one it is, there is evidence and Occam's razor to >guide us.

I think that even within our perceptions we have significant examples
of that not being true. Let us say we have a given data set that are
passed through a filter. This filter has strong patterns and reorganizes
the data according to its patterns. This reorganization includes
changing links, totally rejecting an unknown amount of data, and adding data. The question is, can we produce a model of the original data?

In the case of nomenon, I think it is even stronger. It would be
like having an undedicated man describe QED. Lots of squiggly lines and 'rithmatic might be the description. This may be much closer to QED than our models are to the nomenon.


Well, after a long wait, you finally have your answer. As you may
notice, I am also discussing this issue with someone who wants an FTL
aether. Its an interesting juxtaposition for me. I think the difference is that we don't seem to disagree on the physics, just the philosophy.


Dan M.

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