Exclusion principle

CSGnet Archive CSG1997
1

[From Bill Powers (970713.0530 MDT)]

Martin Taylor, any other volunteers --

While procrastinating on the reorganization problem, I was reminded of
something in physics that has bothered me since I heard of it 50 years ago:
the Pauli Exclusion Principle. As I remember it, it proposes that no two
electrons (particles? atoms?) can be in the same quantum state at the same
time. I was never clear as to the scope of this apparently arbitrary rule.
Does it apply to the whole universe? And what does "at the same time" mean?
How does an electron in a wire in my computer know that an electron in the
Andromeda Galaxy has occupied a state into which my electron would
otherwise fall, so as to avoid violating the Exclusion Principle? Does the
principle apply to all of time as well as all of space?

Best,

Bill P.

2

[From Bruce Gregory (970713.0935 EDT)]

Bill Powers (970713.0530 MDT)

While procrastinating on the reorganization problem, I was reminded of
something in physics that has bothered me since I heard of it 50 years

ago:

the Pauli Exclusion Principle. As I remember it, it proposes that no two
electrons (particles? atoms?) can be in the same quantum state at the

same

time. I was never clear as to the scope of this apparently arbitrary

rule.

Does it apply to the whole universe? And what does "at the same time"

mean?

How does an electron in a wire in my computer know that an electron in

the

Andromeda Galaxy has occupied a state into which my electron would
otherwise fall, so as to avoid violating the Exclusion Principle? Does

the

principle apply to all of time as well as all of space?

The exclusion principle applies to simple (electrons) and compound (atomic
nuclei) objects with non-integer spin -- one-half in the case of
electrons. As
Pauli postulated it, it was arbitary but is now understood (but not by
me!).
Such particles are said to obey Fermi-Dirac statistics. Particles with
integer
spin, such as photons, obey a different statistics called Bose-Einstein
statistics. Bose particles can crowd into the same state, which makes
lasers possible and leads to the recent announcement of the creation of a
"Bose condensate" long predicted but only recently fabricated.

The question you posed about an electron here and one in the Andromeda
galaxy is the heart of quantum non-locality. A "practical" formulation is
one in
which two electrons are created in a state in which a measurement will
always find the electrons in different states (spin "up" and spin "down").
Prior to the measurement assuming either particle has a definite spin
orientation leads to erroneous predictions. However, after the spin of one
of the particles is measured, one can predict exactly what the spin of the
other particle would be found to be were it to be measured. How the
electron in the Andromeda galaxy instantaneously "knows" that you
have just measured the spin of its "twin" and found it to be spin up, and
so the Andromeda twin must adopt a spin down orientation, is the deep
mystery of quantum mechanics -- its non-locality. This non-locality is
what led Bohm to develop his widely unappreciated view of the existence
of "implicate" order. To me it suggests strongly that Nature has a very
different view of the world than we do.

Bruce

3

[From Bruce Gregory (970713.1215 EDT)]

Bill Powers (970713.0924 MDT)

But wait, doesn't the exclusion principle state that NO TWO electrons can
occupy the same state? So how does an electron in the Andromeda galaxy

know

it's the twin of one on the earth? And what if the universe contains 3
electrons -- doesn't that mean that one of them can't be in either the
spin-up OR the spin-down state? Maybe I've just misunderstood the

exclusion

principle all this time because of the way it was worded.

The problem hinges on the meaning of "state". Another way to say it
is that no two electrons can be characterized by the same set of
quantum numbers. Spin is only one of the quantum numbers assignable
to an electron. As a result countless electrons can have the same
spin orientation so long as they do not have the all other quantum
numbers equal. The most common example of the exclusion principle
applies to electrons in the ground energy state of an atom. Two electrons
can occupy this state. This duality was intially "explained" by
postulating that they must differ in some hitherto unexpected way. This was
Pauli's way out. The notion that this quantum number was associated
with "spin" was at first ruled out because a "spinning" electron would
have a equatorial velocity greater than the speed of light. By ignoring
this problem (by saying that it is an artifact of trying to build a
classical model of an electron) physicsts were able to assign two
different intrinsic moments of angular momentum (spin orientations) to
electrons. In order for these directions to be unique, they must be
parallel and anti-parallel to the electrom's "path" (or linear momentum
vector). It is not easy to "prepare" a set of electrons so that they
differ only in spin. Basically you have to create a situation where the
theory tells you this is the case. (Something along the lines of the
creation of an electron-positron pair from a gamma ray when it passes
close to aparticle).

Bruce

4

[Martin Taylor 970713 15:30]

[From Bill Powers (970713.0530 MDT)]

Martin Taylor, any other volunteers --
...
the Pauli Exclusion Principle. As I remember it, it proposes that no two
electrons (particles? atoms?) can be in the same quantum state at the same
time. I was never clear as to the scope of this apparently arbitrary rule.
Does it apply to the whole universe? And what does "at the same time" mean?
How does an electron in a wire in my computer know that an electron in the
Andromeda Galaxy has occupied a state into which my electron would
otherwise fall, so as to avoid violating the Exclusion Principle? Does the
principle apply to all of time as well as all of space?

Tricky questions. Consider all my answers to be tentative, here, no
matter the language in which they are couched...

The quantum state of an electron (or other entity) defines it
completely. Some quantum numbers deal with the orientation of the
electron with respect to a local magnetic field, for example.
Anything against which the electron can be referenced is a potential
source for a quantum number. Usually, the reference is to the atom
within which the electron is (largely) found, but it could be
the crystal lattice within which the electron is moving, or
whatever. I would guess that an electron in the Andromeda Galaxy
necessarily has different quantum numbers from one in our galaxy
just because it's in a different place.

As I understand it, the exclusion principle can be paraphrased as
saying that two electrons must always be distinguishable in some
way. That is to say that there must be _some_ measurement that
would say "this electron is not that electron." The problem is
that if you could have two or more electrons with the same set
of properties, all the electrons in the universe would coalesce
(eventually) at wherever their potential would be lowest.

The whole notion of quantum numbers strikes me as being what you
have called "descriptive" rather than "explanatory." It describes
what is observed (at some remove, of course), but seems to have
no application outside the domain for which the description was
originally invented.

What does "at the same time" mean? You are getting into relativity
here, and at the time of Pauli, quantum ideas and relativity ideas
had a hard time coexisting (maybe they still do?). However, in
the more restricted sense, of what happens within an atom or a
crystal, one electron cannot jump from a high-energy level to a
lower one while all the slots are filled in the lower one, but
if, say, a photon bumps a low-level electron to a higher energy,
another can move in to fill its place. I would guess that if "time"
were not translationarily symmetric with respect to the electron,
there would be a "time" quantum number as well. But I can't
imagine what that might mean.

As I say, take all the above with large grains of salt.

Martin

5

[From Bill Powers (970714.0649 MDT)]

Bruce Gregory (970713.1215 EDT)
Martin Taylor 970713 15:30 --

Thanks, gentlemen. I think Martin's commment that this is a descriptive
rule rather than an explanation tells me the most about the exclusion
principle.

I think that this is what bothered me about physics when I was exposed to
"atomic physics" in 1948. The descriptive rules of quantum phenomena
(although I could not have put it that way then) just seemed like an
entirely different sort of mental construct from all those I had
encountered in physics before then. Not that the observations bothered me;
what seemed to be missing was the thoroughness I had become used to. Until
I started trying to learn the new rules, I had always been able to envision
a continuous train of reasoning from first principles to the equations that
described more complex phenomena. Each part of each equation had a meaning
in terms of physical processes or relationships among them. But all that
seemed to stop with quantum physics.

The exclusion principle is a perfect example of what I mean. Some guy said,
"What if there's a rule that says no two electrons can be in the same state
at the same time?" This struck me then, and still does, as a giant leap
backward right into the ways of alchemy. Such a rule doesn't describe
properties of anything; it describes (if one has guessed approximately
right) the behavior of something. But I had always been taught that
behavior is the outcome of interactions between things that have properties
that are independent of their behavior. Where were the properties, the
interactions, that would lead to the observation that no two electrons
could share exactly the same state?

I guess I would say now that I couldn't see any model behind the exclusion
principle. That seems to be true of a lot of quantum physics; rules exist
only for the purpose of making predictions come out right, but they don't
follow from anything else -- not from observations, and not from deeper
principles that can be traced to observations. It's as though physics
jumped to a higher level of abstraction without filling in the levels between.

Of course all this probably reflects my ignorance more than anything else.
But I wonder whether, if I were able to follow all the mathematical
arguments and derivations, I would really be any closer to seeing where the
exclusion principle and other such ideas came from.

Best,

Bill P.

6

[From Bruce Gregory (970414,1020 EDT)]

Bill Powers (970714.0649 MDT)

Thanks, gentlemen. I think Martin's commment that this is a descriptive
rule rather than an explanation tells me the most about the exclusion
principle.

The question of what constitutes an explanation has been
considerably shaken by quantum physics. The exclusion principle
started as a descriptive rule, but it is now an integral part of
the formalism. That is, it follows from the mathematical basis
of the theory. You are looking for a 'gears and levers' level of
explanation. There does not appear to be one. If you dip into
Feynman's little book QED, you'll find him discussing exactly
this question and arguing that there are no such explanations
compatible with quantum theory. Bohm and few others including
Bell believed otherwise. They proposed models that did have a
mechanism in the form of "quantum potentials", but these ideas
never caught on. If you want to think further about this
approach Bohm (and Hiley) have a few books over the past ten
years that argue the case.

Bruce

···
7

[Hans Blom, 970714b]

(Bill Powers (970714.0649 MDT))

I think Martin's commment that this is a descriptive rule rather
than an explanation tells me the most about the exclusion principle.

Ultimately, all rules of physics are descriptive. They can be called
"explanatory" only in sofar as they describe one level in terms of a
different, lower level which we think we understand "intuitively".

The exclusion principle of quantum mechanics is such a case. It is, I
think, best reformulated as the equivalent of the earlier physics law
that says that no two material bodies can occupy the same space. Now
replace "space" by "state", its modern equivalent, and you have the
new rule.

But why is so "self-explanatory" that no two physical bodies can
occupy the same space? In mathematics, for instance, it is perfectly
admissible for two points to have exactly the same coordinates. We
think we "understand" where we simply accept an "obvious truth", it
appears to me.

The exclusion principle is a perfect example of what I mean. Some
guy said, "What if there's a rule that says no two electrons can be
in the same state at the same time?" This struck me then, and still
does, as a giant leap backward right into the ways of alchemy.

To paraphrase: Archimedes' law is a perfect example of what I mean.
Some guy said, "What if there's a rule that says no two material
bodies can be in the same space at the same time?"

Did this strike you then, and still does, as a giant leap backward
right into the ways of alchemy? Or is _this_ something that you can
accept as self-explanatory? If so, why this and not that?

Greetings,

Hans

8

[From Bruce Abbott (970714.1045 EST)]

Bill Powers (970714.0649 MDT) --

Of course all this probably reflects my ignorance more than anything else.
But I wonder whether, if I were able to follow all the mathematical
arguments and derivations, I would really be any closer to seeing where the
exclusion principle and other such ideas came from.

Bill, check out this web site; it may help, and even if it doesn't, I think
you'll enjoy it anyway:

    http://newton.umsl.edu/~philf/candles.html

This site is labeled "Candle Dances and Atoms" and is described by the
author as follows:

    This is a note for a modern physics class on why particles with
    half-integral spin obey the Pauli exclusion principle (i.e. no two
    can occupy the same quantum state).

It is accompanied by some cool graphics to help explain the Pauli exclusion
principle via topology.

Regards,

Bruce

9

[From Bruce Gregory (970714.1100 EDT)]

Hans Blom, 970714b

The exclusion principle of quantum mechanics is such a case. It is, I
think, best reformulated as the equivalent of the earlier physics law
that says that no two material bodies can occupy the same space. Now
replace "space" by "state", its modern equivalent, and you have the
new rule.

In this discussion, everyone should keep in mind that there are
particles (those described by Bose-Einstein statistics) that
_can_ and _do_ occupy the same state. Only Fermions
(including electrons) are proscribed from this behavior. There
are, by the way, "explanations" of why bosons can get away with
this while fermions cannot. Unfortunately these explanations are
less than intuitive unless you are a mathematician.

Bruce

10

[From Bruce Gregory (970714.1220 EDT)]

Bruce Abbott (970714.1045 EST)]

Bill, check out this web site; it may help, and even if it doesn't, I think
you'll enjoy it anyway:

    http://newton.umsl.edu/~philf/candles.html

Neat!

Bruce

11

[From Bill Powers (970714.1822 MDT)]

Hans Blom, 970714b--

Ultimately, all rules of physics are descriptive. They can be called
"explanatory" only in sofar as they describe one level in terms of a
different, lower level which we think we understand "intuitively".

There's another kind of "lower level" that's not just an intuitive matter,
but is based on definitions involving measurements. As an example, the
concept of mass involves two measurements: applied force and measured
acceleration. Inertial mass is defined as the ratio of force to
acceleration. Mechanics is built on such basic definitions. Even relativity
uses this definition.

The exclusion principle of quantum mechanics is such a case. It is, I
think, best reformulated as the equivalent of the earlier physics law
that says that no two material bodies can occupy the same space. Now
replace "space" by "state", its modern equivalent, and you have the
new rule.

But why is so "self-explanatory" that no two physical bodies can
occupy the same space? In mathematics, for instance, it is perfectly
admissible for two points to have exactly the same coordinates. We
think we "understand" where we simply accept an "obvious truth", it
appears to me.

It may seem self-explanatory that two material objects can't occupy the
same space, but we can at least say why this is true, in terms of a model
based on more fundamental notions. If we treat this idea as a philosophical
truth it has little justification, but if we think in terms of physical
operations and interactions, it has a great deal of practical -- i.e.,
experimental -- truth.

The exclusion principle is a perfect example of what I mean. Some
guy said, "What if there's a rule that says no two electrons can be
in the same state at the same time?" This struck me then, and still
does, as a giant leap backward right into the ways of alchemy.

To paraphrase: Archimedes' law is a perfect example of what I mean.
Some guy said, "What if there's a rule that says no two material
bodies can be in the same space at the same time?"

The difference is that we can offer an explanation for why two objects
can't be in the same space at the same time: we can't push hard enough,
without destroying the objects. The reason that objects displace water is
not that there's a rule saying they do, but that the interaction of the
objects and the water is such as to push the fluid water aside. There is a
simple mechanical explanation, or if you like, a more sophisticated one
involving electrostatic fields or other interatomic forces. And the rule
comes out of interactions between the objects.

Without an explanation that invokes an underlying model, a rule of nature
is like a rule of a game: it's given, and we play by it, but it stands
alone, unrelated to anything else. It isn't "true" in any sense.

Did this strike you then, and still does, as a giant leap backward
right into the ways of alchemy? Or is _this_ something that you can
accept as self-explanatory? If so, why this and not that?

Actually, no giant leap backward was required in Archimedes' time; he was
already there.

I looked up that thing on the topology of the exclusion principle. It seems
to jump into the middle of the subject. It's nice that there's an analogy
available, but of course if the principle had been about some other rule, a
different analogy, and a different mathematical representation, would have
been found. The question is still why the exclusion rule exists -- if it
really does.

Martin suggested that a difference in location might qualify as a
difference in quantum state. If that's true, two electrons at different
places in the same orbit would be in different states even if they had the
same spin. But if a difference in location is NOT enough, then we have to
worry about the fact that there are (I think) a hell of a lot more
electrons in the universe than distinct states for them to have.

Martin also agreed that relativity is a problem: what does it mean to say
that different electrons can't be in the same state _at the same time?_
"The same time" in what inertial frame? "The same time" with or without the
light-lag?

In all the examples I've seen, the exclusion principle is applied to
particles that are somehow involved in a single local system or process. It
would make a lot more sense to me if that were made a condition on the
principle, because then there might be some chance of seeing this principle
as emergent from a lower level of physical interactions. But when the rule
is stated without reference to any process, it implies things that are hard
to accept and raises all sorts of questions which -- so far -- nobody has
answered.

What frustrates me is that nobody but a full-fledged physicist could
possibly understand all these things well enough to see whether the entire
logical-mathematical system really hangs together. But people with that
much knowledge also have a considerable committment to physics as it exists
today; they are willing to expend considerable time and energy to convince
doubters that physics is on the right track, but very little of either to
see if it is really just a giant systematic delusion. True Believers are
not likely to be looking for a way to negate their beliefs!

Anyway, I doubt whether my own problems with physics will have any impact
on that science.

Best,

Bill P.

12

[Martin Taylor 970715 09:50]

Bill Powers (970714.1822 MDT)

Martin suggested that a difference in location might qualify as a
difference in quantum state. If that's true, two electrons at different
places in the same orbit would be in different states even if they had the
same spin.

You can't talk about an electron being in "a location" within its orbit
the way you can talk about a planet being at some specific point in its
orbit. The electron is everywhere in its orbit at all times, at least
insofar as any observation could determine. The "orbit" is better seen
as a smear of probability density for the electron, rather than as an
arc along which the electron progresses. Two electrons are in different
orbits when they have different probability distributions. The quantum
numbers describe the probability distribution, among the various
properties of the electron.

That's too crude to be taken literally, but probably not too far wrong
for the purposes of this discussion.

It may seem self-explanatory that two material objects can't occupy the
same space, but we can at least say why this is true, in terms of a model
based on more fundamental notions.

Yes. It's amusing that the notion of the Exclusion Principle may well
derive from the everyday observation that two objects can't occupy the
same space at the same time, while at the same time the application of
the Exclusion Principle "explains" this everyday observation. From the
viewpoint of the mundane everyday events of life, the "more fundamental
notion" that says why it is true is an unexplained phenomenon that
has its impact over a much wider range of observations. That's why
Hans said (in a passage I don't totally agree with) that all physics
depends on explanations at lower and lower levels, and ultimately rests
on a "pure" description of observations.

Martin

13

[From Bill Powers (970715.0855 MDT)]

Martin Taylor 970715 09:50--

You can't talk about an electron being in "a location" within its >orbit

the way you can talk about a planet being at some specific point >in its
orbit. The electron is everywhere in its orbit at all times, at >least
insofar as any observation could determine.

Then what's wrong with two electrons being "in the same place at the same
time?"

Best,

Bill P.

14

[From Bruce Gregory 9970715.1115 EDT)]

Bill Powers (970714.1822 MDT)

The difference is that we can offer an explanation for why two objects
can't be in the same space at the same time: we can't push hard enough,
without destroying the objects. The reason that objects displace water is
not that there's a rule saying they do, but that the interaction of the
objects and the water is such as to push the fluid water aside. There is a
simple mechanical explanation, or if you like, a more sophisticated one
involving electrostatic fields or other interatomic forces. And the rule
comes out of interactions between the objects.

This is what we mean by "gears and levers".

Without an explanation that invokes an underlying model, a rule of nature
is like a rule of a game: it's given, and we play by it, but it stands
alone, unrelated to anything else. It isn't "true" in any sense.

Not obvious. The laws of thermodynamics are more fundamental
than the models we use to illustrate them. They seem more like
"rules of the game."

I looked up that thing on the topology of the exclusion principle. It seems
to jump into the middle of the subject. It's nice that there's an analogy
available, but of course if the principle had been about some other rule, a
different analogy, and a different mathematical representation, would have
been found. The question is still why the exclusion rule exists -- if it
really does.

Why does the second law of thermodynamics exist?

Martin suggested that a difference in location might qualify as a
difference in quantum state. If that's true, two electrons at different
places in the same orbit would be in different states even if they had the
same spin. But if a difference in location is NOT enough, then we have to
worry about the fact that there are (I think) a hell of a lot more
electrons in the universe than distinct states for them to have.

Martin also agreed that relativity is a problem: what does it mean to say
that different electrons can't be in the same state _at the same time?_
"The same time" in what inertial frame? "The same time" with or without the
light-lag?

In all the examples I've seen, the exclusion principle is applied to
particles that are somehow involved in a single local system or process. It
would make a lot more sense to me if that were made a condition on the
principle, because then there might be some chance of seeing this principle
as emergent from a lower level of physical interactions. But when the rule
is stated without reference to any process, it implies things that are hard
to accept and raises all sorts of questions which -- so far -- nobody has
answered.

In the example developed by Bohm we create a situation in which
a pair of electrons emerges which we know from theory must be in
a "pure" state. This is a state in which measurement will reveal
one electron to be "spin up" and the other electron will be spin
down", but prior to the measurement of one of these electrons we
cannot say that one is spin-up and the other is spin-down
without conflicting with experimental evidence. Now we can let
the electrons get as far apart as we like and measure the spin
of one of them. Say it is spin up. We _know_ now that if someone
measures the spin orientation of the second electron with regatd
to a similar reference system, they will find it to be spin up.
A causal explanation would require that the measurement of the
spin of the first particle sends an instantaneous signal to the
second partle telling it to adopt a spin down orientation. No
one believes in these "instantaneous signals" (which, however
_cannot_ be used to send messages)so we avoid taking about any
possible mechanism. Bohn and a few others believe they have
found a way around this problem, but their approach has few
takers. (Which, needless to say, is no indication they are not
correct.)

What frustrates me is that nobody but a full-fledged physicist could
possibly understand all these things well enough to see whether the entire
logical-mathematical system really hangs together. But people with that
much knowledge also have a considerable committment to physics as it exists
today; they are willing to expend considerable time and energy to convince
doubters that physics is on the right track, but very little of either to
see if it is really just a giant systematic delusion. True Believers are
not likely to be looking for a way to negate their beliefs!

See comment on Bohm above.

Bruce

15

[Hans Blom, 970715e]

(Martin Taylor 970715 09:50)

You can't talk about an electron being in "a location" within its
orbit the way you can talk about a planet being at some specific
point in its orbit. The electron is everywhere in its orbit at all
times, at least insofar as any observation could determine.

Repeating your proviso "too crude to be taken literally, but probably
not too far wrong for the purposes of this discussion", one might
still make an analogy between planets and electrons. Remember that
there are severe and unavoidable measurement problems when attempting
to discover an electron's position. Now imagine that some strange
measurement equipment would allow us to (imprecisely) discover a
planet's orbit but not that planet's position within its orbit.
Imagine, for instance, that the planet cicles so rapidly that our
measurement is already fully outdated when we receive the planet's
radar echo back, so that at the moment we receive the echo the planet
could be anywhere -- but still in its orbit. The latter might be
established by the fact that we always get an echo back [remember,
the planet moves so rapidly that it frequently intercepts the radar
beam and thus always reflects some of it if the radar is pointed at
its orbit], and always after about the same delay. What could we say
we know about the planet's position? We might express our knowledge
by saying that the planet's "position" is a certain sun-centered
(probability) torus. To paraphrase you: The measured torus which to
the best of our ability describes the planetary "orbit" is best seen
as a smear of probability density.

Again: That's too crude to be taken literally, but probably not too
far wrong for the purposes of this discussion.

Greetings,

Hans

16

[From Bill Powers (970715.0951 MDT)]

Bruce Gregory 9970715.1115 EDT)--

Why does the second law of thermodynamics exist?

Interestingly, this law is subject to experimental disproof. If we ever
measured a warmer object in contact with a colder object actually getting
warmer, the law would be rejected.

In the example developed by Bohm we create a situation in which
a pair of electrons emerges which we know from theory must be in
a "pure" state. This is a state in which measurement will reveal
one electron to be "spin up" and the other electron will be spin
down", but prior to the measurement of one of these electrons we
cannot say that one is spin-up and the other is spin-down
without conflicting with experimental evidence. Now we can let
the electrons get as far apart as we like and measure the spin
of one of them. Say it is spin up. We _know_ now that if someone
measures the spin orientation of the second electron with regatd
to a similar reference system, they will find it to be spin up.
A causal explanation would require that the measurement of the
spin of the first particle sends an instantaneous signal to the
second partle telling it to adopt a spin down orientation. No
one believes in these "instantaneous signals" (which, however
_cannot_ be used to send messages)so we avoid taking about any
possible mechanism. Bohn and a few others believe they have
found a way around this problem, but their approach has few
takers. (Which, needless to say, is no indication they are not
correct.)

This is more like what I might be comfortable with. If you have two
electrons (that are part of the same set of proximal interactions) turning
up with opposite spins, then it is clearly something about the interactions
that creates the up-down relationship. Then, if you separate the electrons,
you would expect them to retain the same spins (barring any new
interactions). This is very different from asserting that two electrons,
one selected at random on Earth and the other in the Andromeda Galaxy,
would show any regular relationship between their spins, or that the act of
observing one would affect the state of the other.

What, by the way, constitues an "observation?" Does a human being have to
be aware of it, or is it sufficient that some physical apparatus respond to
the state of what is being observed? In other words, does an observation
take place when a physical device is affected, or when a human being, say a
week later, happens to glance at the dial and see what the reading is? What
if the human being sees the readout in passing, but only later realizes
what it said? Or what if the device records a complex set of effects, and
takes a week to calculate what the spin must have been? _When_ is an
observation?

Best,

Bill P.

17

[From Bruce Gregory (970715.1300 EDT)]

Bill Powers (970715.0951 MDT)

This is more like what I might be comfortable with. If you have two
electrons (that are part of the same set of proximal interactions) turning
up with opposite spins, then it is clearly something about the interactions
that creates the up-down relationship. Then, if you separate the electrons,
you would expect them to retain the same spins (barring any new
interactions). This is very different from asserting that two electrons,
one selected at random on Earth and the other in the Andromeda Galaxy,
would show any regular relationship between their spins, or that the act of
observing one would affect the state of the other.

It's a little trickier than this. If we assume that the
electrons emerge with a definite spin orientation, we make
incorrect predictions. It _seems_ as though the measurement
creates the orientation. The only way I know to think of this
is in terms of a polarizer. Say you pass a beam of light through
a horizontal polarizer. If you then pass the polarized beam
through a second polarizer set at 45 degrees to the first, some
of the light gets through. It is as if the second polarizer
forces some of the light into a new orientation (and absorbs the
rest). We believe that after passing through the first polarizer
_none_ of the light was in this new state which was somehow
created by the second polarizer. (We can test our assumption by
passing the beam through a second horizontal polarizer
immediately after the first horizontal polarizer and noting that
the intensity does not diminish, so none of the light is
polarized in the 45 degree plane.)

What, by the way, constitues an "observation?" Does a human being have to
be aware of it, or is it sufficient that some physical apparatus respond to
the state of what is being observed? In other words, does an observation
take place when a physical device is affected, or when a human being, say a
week later, happens to glance at the dial and see what the reading is? What
if the human being sees the readout in passing, but only later realizes
what it said? Or what if the device records a complex set of effects, and
takes a week to calculate what the spin must have been? _When_ is an
observation?

Very good question. Nobody knows. The problem is sometimes
referred to as "Wigner's friend." The friend looks at the
outcome of a quantum experiment, and Wigner looks at the
friend. Wigner computes the probability that the friend
observerse spin up and the probability that the friend observes
spin down. Who is the observer, Wigner or the friend? Wheeler
and others argue that a measurement occurs whenever an
irreversible process occurs such as the blackening of a silver
grain on a photograph. Others say there are no irreversible
processes at the quantum level. Still others maintain that
consciousness is required for the "collapse of the state
vector" (into either spin up or spin down). Feynman argues that
the state vector never collapses -- it is just a mathematical
device for calculating probability. You pays your money....

Bruce

18

From Bill Powers (970715.1216 MDT)]

Bruce Gregory (970715.1300 EDT)--

It's a little trickier than this. If we assume that the
electrons emerge with a definite spin orientation, we make
incorrect predictions. It _seems_ as though the measurement
creates the orientation. The only way I know to think of this
is in terms of a polarizer. Say you pass a beam of light through
a horizontal polarizer. If you then pass the polarized beam
through a second polarizer set at 45 degrees to the first, some
of the light gets through. It is as if the second polarizer
forces some of the light into a new orientation (and absorbs the
rest). We believe that after passing through the first polarizer
_none_ of the light was in this new state which was somehow
created by the second polarizer. (We can test our assumption by
passing the beam through a second horizontal polarizer
immediately after the first horizontal polarizer and noting that
the intensity does not diminish, so none of the light is
polarized in the 45 degree plane.)

Not sure this is a definitive example. Suppose you set up a circular
standing wave on a rope that passes between two vertically-oriented
closely-space rods (frictionless, of course). What gets past the rods will
be a vertically polarized wave. Then, if you place two more rods oriented
at 45 degrees farther along the rope, there will be a component of the wave
that gets through them, diminished in amplitude, resulting in a wave
polarized at 45 degrees. The final polarization was, indeed, "created" by
the second pair of rods, but only because of the interaction of the
vertically polarized wave with the slanted rods.

Of course the vertical wave would be undiminished by passing through a
second set of vertically-oriented rods, "proving" that there is no energy
in the 45-degree direction.

What I feel is missing from quantum mechanics are the interactions that
lead to the apparent rules.

What, by the way, constitues an "observation?"

Very good question. Nobody knows. The problem is sometimes
referred to as "Wigner's friend." The friend looks at the
outcome of a quantum experiment, and Wigner looks at the
friend. Wigner computes the probability that the friend
observerse spin up and the probability that the friend observes
spin down. Who is the observer, Wigner or the friend? Wheeler
and others argue that a measurement occurs whenever an
irreversible process occurs such as the blackening of a silver
grain on a photograph. Others say there are no irreversible
processes at the quantum level. Still others maintain that
consciousness is required for the "collapse of the state
vector" (into either spin up or spin down). Feynman argues that
the state vector never collapses -- it is just a mathematical
device for calculating probability. You pays your money....

Why does the process have to be irreversible? A meter with a
superconducting coil in it will return all the energy required to deflect
the needle against the (perfect) torsion spring when the input current goes
away, yet it could be read while it is deflected. So does someone have to
look at the meter -- and understand what the reading means -- in order for
an observation to have been made? If a dog looks at the meter, is that an
observation? If you're conscious of the meter reading -- "3.14" -- but
don't know the units, is that an observation?

It seems to me that there's a lot of silliness going on here.

I go with Feynman: probability is a calculation.

Best,

Bill P.

19

[From Bruce Gregory (970715.1550 EDT)]

Bill Powers (970715.1216 MDT)

Not sure this is a definitive example. Suppose you set up a circular
standing wave on a rope that passes between two vertically-oriented
closely-space rods (frictionless, of course). What gets past the rods will
be a vertically polarized wave. Then, if you place two more rods oriented
at 45 degrees farther along the rope, there will be a component of the wave
that gets through them, diminished in amplitude, resulting in a wave
polarized at 45 degrees. The final polarization was, indeed, "created" by
the second pair of rods, but only because of the interaction of the
vertically polarized wave with the slanted rods.

Agreed. Only in Q.M. the waves are photons and they are either
absorbed or not absorbed -- no diminished amplitudes allowed,
only different numbers of photons.

What I feel is missing from quantum mechanics are the interactions that
lead to the apparent rules.

You bet!

Why does the process have to be irreversible? A meter with a
superconducting coil in it will return all the energy required to deflect
the needle against the (perfect) torsion spring when the input current goes
away, yet it could be read while it is deflected.

The irreversibility arises because without it the wave-function
never collapses. Of course your example poses a problem. The
macroscopic world doesn't follow quantum rules. Why not?

It seems to me that there's a lot of silliness going on here.

I can't argue with that.

I go with Feynman: probability is a calculation.

Me too.

Bruce

20

[Martin Taylor 970715 16:00]

Bill Powers (970715.0855 MDT)]

Martin Taylor 970715 09:50--

You can't talk about an electron being in "a location" within its >orbit

the way you can talk about a planet being at some specific point >in its
orbit. The electron is everywhere in its orbit at all times, at >least
insofar as any observation could determine.

Then what's wrong with two electrons being "in the same place at the same
time?"

Nothing, except that by assuming they don't (invoking the Exclusion
Principle), we discover that the world we observe looks like the predicted
world, and if we assume that they can, the predicted world implodes
while the observed world doesn't.

There's nothing morally "right" or "wrong" about it.

Two electrons can't have the same set of quantum numbers that define
their orbits. The "place" can be seen as the coordinates defined by
the set of quantum numbers. When you look on the scale of an atom,
the relation to geometric place in the 3-D world gets quite blurry.
The electron almost certainly isn't in the Andromeda Galaxy, or even
in the next room, if it is bound to an atom in a glass of water I
hold. But the probability distribution of the electron orbit isn't
cut off at any finite distance. The "same place" involves having the
same probability distribution. That's what can't happen.

When you want to use everyday language, tuned to observations on the
scale of millimeters to kilometers, "place" is a precise term that can
be used as an analogy. But as with most analogies, if you carry it too
far, it fails you. To be precise at the small scale, you have to use
primitives appropriate to the scale, operated on by operators appropriate
to those primitives. And "place" in the everyday sense is not ordinarily
one of those useful primitives, when applied to a wavicle such as an
electron.

Martin