Re: Photon Duality (Feynman doesn't know why, do you?)
From: Prescott (whatishiggs_at_yahoo.com)
Date: 03/19/05
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Date: 19 Mar 2005 15:46:30 -0800
I wrote this thread the way it is because I read a thread a
couple of years ago where the "experts" in sci.physics.research
answered that there is no mystery to the particle duality. They
answered like there is nothing that was not explained... The
following are samples of their replies. For those offering
alternative theories. Pls. let me know what you think of the
following. It basically says you guys are treating it as
classical object and thinking in terms of everyday objects when
it's nothing like that in the quantum world and there is simply
no mystery. I'm surprised when Wormley replies Feynman may be
right. I expect him to mention that there is no mystery and you
guys are simply misinformed. Maybe he is better than dogma laden
physicists. Anyway. Guys like you (offering alternative models)
are banned from sci.physics.research because only "experts" are
allowed there. The following are samples of their replies to the
questions about the mystery of particle duality: (Comments
welcomed. Let's get to the bottom of this whether there is mystery
or not)
Sample # 1
"There is no riddle and there is nothing mysterious about it. The
problem is that people try to force the subatomic world to be
similar to the macroscopic of daily life, and in reality it is
totally different. Under some circumstance a particle such as
photon or electron can be most closely mathematically modeled as
a particle, and under other circumstances, it can be most closely
mathematically modeled as a wave, but in reality it's totally
different from either a macroscopic particle or macroscopic wave.
People say it's both a wave and particle, but really it's neither
a wave nor a particle. It's a subatomic entity totally unlike
anything in the macroscopic environment. Nothing can "can cause
the light to become particle or wave" because really it's neither
a wave nor a particle, and it's doesn't change from one thing to
another thing. You can put it in a situation where the closet
mathematical model will be to approximate it as a particle, and
then you can put it in another situation where the best
mathematical model will be to approximate it as a wave. Of
course, in reality, it's not like anything you've ever seen in
the macroscopic environment. This does not make it mysterious.
It's just different than what you're use to. There is nothing
mysterious about it. The whole idea of particle-wave duality
comes from clinging to a classical view of the world. Feynman
referred to this by saying "Your old-fashioned ideas are no damn
good!"
Sample # 2.
"Although many people are taught about "wave function collapses"
it is possible to do quantum physics without this idea. For
example, the McGraw Hill Encyclopaedia of Science and Technology
never mentions the words "wave function collapses" although
several of its 20 volumes concern quantum physics. It should be
understood that "wave function collapses" are purely a
mathematical device and relate only to the conditional
probability of where something is, where the condition is our
knowledge. When our knowledge changes then the "wave function
collapses" but the "real physical system" continues to develop
exactly as it did before. I have often seen the Young's two slit
experiment described in this way in books: A screen with two
slits is placed between a monocromatic light source and a screen.
When both slits are open an interference pattern is seen on the
screen showing the wave nature of a photon. When detectors are
placed at both slits that can detect photons then an event is
recorded at one or the other slit but not both. This shows the
particle nature of the photon. Now, firstly, this is an almost
truth and contains a huge assumption that masks the actual truth.
To see this requires some calculations about the probability of
detection of a photon. With a typical arrangement of light source
in this experiment probably less than one millionth of the light
emitted passes through each slit. This means that each detector
has one chance in a million of detecting (as a particle) any
given wave passing through the slit. Therefore there is one
chance in a trillion that both detectors will register at the
same time. Therefore in the typical Young's slit experiment if we
detect one thousand events at each slit there is only one chance
in a thousand (even supposing the totally "wave" nature of light)
that we will detect a single common event - which we would then
quite reasonably put down to coincidence. What is the huge
assumption? - It is that because detections happen at only one
detector it is because the "wave" is now behaving like a
"particle" without realising that it is the low probability of
individual event detection that makes events happen at only one
slit. Using a brighter light source does not help. However, if a
dimmer light source is used and the light source were to be
surrounded by a parabolic reflector and lenses used to focus the
light into a tight beam so that a larger proportion, say 10% of
the emitted photon, went through each slit, then we would detect
10% of events in both slits at once. Has anyone ever checked what
I am saying here? Yes, in a different arrangement using half
silvered mirrors, in 1956 (from memory) Twiss and Brown found
that detecting a photon at one place (as a "particle") makes
absolutely no difference to the probability of detection at
another place. For any emitted photon the detection events (over
all possible directions) are a poisson distribution with a mean
of one. I fear you read a misleading book. Unfortunately, the
most popular books about quantum theory use an old predecessor
version of the now established quantum theory, namely the so
called "wave-particle dualism theory" by Einstein and de Broglie,
developed from 1900 (Planck's radiation formula) over Einstein's
famous article from 1905 about light quanta to de Broglie's
thesis about "matter waves" (if I remember right, that was 1923).
Nowadays we have a much more clear concept at hand, namely
quantum theory which was found 1925 by Heisenberg, Born and
Jordan in its "matrix mechanics" version and 1926 by Schr"dinger
in it's "wave mechanics" version. The best formulation of the
quantum theory (QT) is that by Dirac (1926-1927) which is
independent from special representations. It is an abstract
mathematical formalism which, as far as we know, enables us to
describe the behaviour of nature, from the smallest known
entities ("elementary particles") to the bulk matter surrounding
us. In other words: Today, there are no experimental evidences
that the QT might be wrong. The price we have to pay for this
success is an abstract mathematical picture of the world, at
least compared to Newtonian mechanics. Nevertheless the physical
concept underlying QT is not that difficult: The QT only takes
into account the fact that all we can learn about objects (say
the possition of an electron) is due to measurements. For these
measurements we have to make the electron interacting with the
measurement apparatus, such that we can read off the position of
the electron from it. For instance you may think about an
detector which is placed on a certain position and which
registers the electron. So far this is not different from
classical physics, but now we must take into account the
observation that matter appears to be "atomistic". Especially the
electric charge is always an integer number of a smallest charge,
the charge of a proton (for positively charged matter) or an
electron (for negatively charged matter). NB: The charge of an
electron is exactly the negative of that of a proton. The
interaction of the electron with the measurement device,
necessary to determine its positition, is (mainly) due to
electromagnetic interactions. Thus to have this interaction for
position measurement we can use light (electromagnetic waves). To
create this light we need other moving charges which are at least
as strong as the electron's charge itself since there are no
smaller (free) charges in nature. Further the wavelength of the
light, used to determine the position of the electron, must be at
least of the same order of magnitude as the position resolution
we want to have for the electron. On the other hand Maxwell's
theory of electromagnetism tells us that light carries a momentum
which is the larger the smaller its wavelength is. The
interaction of the light with the electron thus gives the
electron a momentum which is the larger the more precise we like
to know its position. It is impossible to determine this momentum
transfer to the electron, i.e., after the (precise) measurement
of the electron's position we know very little about its
momentum. One can also think about the measurement of the
momentum of the electron. It comes out that the more precise we
like to determine the momentum of the particle the less precise
we know its position. This example of the Heisenberg uncertainty
relation (Delta x Delta p>\hbar/2) shows that, due to the
atomistic nature of matter, that it is impossible to make the
disturbance of the measured object by the necessary interaction
with the measurement apparatus, arbitrarily small. This means
that not all possible observables of an object are sharply
determined the same time. For instance, as we have argued above,
it makes no sense to say an electron (or any other object) has
the same time a precisely determined position and momentum. Only
one of those "incompatible" observables can be determined
precisely. The other observable is then necessarily undetermined.
The QT describes precisely the outcome of experiments in the
"atomistic" world and what we can say about observables of
objects which are not determined precisely, because another
observable, which is incompatible with it, is measured precisely.
Finally we look on the double slit experiment. First we have to
get clear, how this experiment is done: Let's assume we put the
double slit somewhere and shine on it with laser light. Then one
findes an interference pattern on the wall opposite to the slits.
Now we look on this experiment from the point of view of quantum
theory: The laser sends out an electromagnetic wave with a
precisely determined frequency. From the point of view of quantum
theory electromagnetic waves are described by light quanta, i.e.,
if we dim the laser light as much as we can, we have only one
light quantum coming out of it. This light quantum (also called
photon) has a precisely determined momentum. As we discussed
above for the electron, its position is completely unknown. Thus
it is impossible to know through which of the slits it will go.
Neither do we know where on the wall it will appear. The only
thing what we can calculate from the principles of quantum theory
is the probability to find the photon on a certain position on
the wall. To test this prediction of quantum theory, we simply
have to do our one-photon experiment a large number of times and
to count, how many photons appear on a certain position on the
wall. It comes out that we obtain exactly the same interference
pattern as appears due to Maxwell's classical theory of light.
The interesting thing is know, what happens if we look at the
double slit through which of the slits the photons come. For this
we have to detect the photons at the slits. Quantum theory tells
us that the more precise we like to know through which slit the
photons go, the less sharp is the contrast of the interference
pattern. To give finally a short answer: The modern quantum
theory describes nature in a consistent way. No wave-particle
dualism is needed, and physical entities like "elementary
particles" or "electromagnetic waves" are neither particles or
waves in the classical sense but described by an abstract
mathematical formalism as "quanta". For a good introduction read
the first chapter of J. Schwinger, Quantum Mechanics, an
formalism for atomistic measurements, Springer It does not use
any mathematics, but is a precise description why quantum theory
is necessarily as it is, because matter appears to be
"atomistic". The further chapters of the book then develop the
mathematics of quantum theory from these physical considerations.
It's not an easy book, but a very good one for physicists who
already learnt quantum theory in the introductury lecture.
Sample # 3
> The question is: > is it allowed to say that each
photon goes through both slits
? Not really. If we model a laser beam as a coherent state, the
photon number of the state is indeterminate. When people talk
about the number of photons in a coherent state, they usually
mean implicitly some kind of time-average, e.g: how many photons
per second on average (i.e: after integrating over a long time).
Descriptions of so-called "single-photon-at-a-time" experiments
can be a bit naive/misleading. Diming the laser light just means
that the expectation value of photon/sec is decreased - to the
point where the human eye+brain can resolve individual flashes on
a detector screen. But the photon number of the (dimmed) coherent
state nevertheless remains indeterminate. Therefore, it doesn't
really make sense to speak of "each photon". Also, phrases like
"goes through a slit" don't really make much sense in a QM
context. The term "goes through" implies a notion of translation
and hence momentum, while "a slit" implies a notion of position.
But we know from QM that we cannot meaningfully attribute exact
properties of momentum and position to a quantum state
simultaneously. > And: > is it allowed to say that each photon
interferes with it self
? It's better to think of the double-slit as a *filter*, which
takes one QM state and gives you another. I.e: it's like an
operator on the Hilbert space. In this case, it's convolving two
(approx) delta functions of position with the original state, to
yield a different state on the other side of the double slits. In
contrast, a detector is like a mapping from a QM state to a
number, i.e: you give it a state and it gives you back a number,
representing position in this case. So filters and detectors are
very different things.
Sample # 4
"> The question is: > is it allowed to say that each photon goes
through both slits ? > And: > is it allowed to say that each
photon interferes with it self ?
I'd not express it in this way. When learning quantum theory, it
is important, not to think about things in terms of classical
concepts. So you should not think about a photon as a classical
particle or a classical wave, but as a quantum. As I explained in
my previous posting, in the here considered double-slit
experiment, we have prepared photons with a certain momentum
(which, of course, is an idealisation, since we can do this only
approximatively, because each em. wave has a finite line width).
Then it does not make sense to speak of a photon as a classical
particle which has a certain position. So we should forget about
position at all. Thus, we have the following picture about the
photon: All we can say about the the photon is, what is described
by the quantum state. In our case, we know precisely its
momentum. Due to Heisenberg's uncertainty principle this excludes
necessarily a precise knowledge about its position. The quantum
state gives only probability distributions, where to find the
photon. This probability distribution can be calculated with help
of the quantum theoretical dynamics, where the slit is modelled
by boundary conditions (which, of course, is an idealisation
again, because it's not a completely microskopical description of
the slits, which is impossible, because they consist of
macroscopic matter, so that we can make the approximation and
treat it as boundary conditions). Now, we have a prediction about
the behaviour of the position of the photon in the double-slit
experiment, namely a probability distribution for the place,
where the photon will leave its track on the wall, but we have no
more information and, due to quantum theory, we cannot have any
more. Thus, to test the prediction from quantum theory, we need
to check, whether the probality distribution is the right one.
This can only be done by repeating the experiment a lot of times.
"Repeating" here means that one has to prepare a lot of photons,
which have to be independent of each other, and do the
double-slit experiment with them. Then we can count, how many
photons appear in a certain region of the wall, and this should
give the predicted probability distribution. Since physics is
about measureable facts about objects, this means that quantum
theory describes ensembles of independently prepared systems.
About each individual systems, we precisely know only those
observables, we have prepared in the preparation procedure. The
preparation procedure means to assign a certain quantum state,
described by a ray in the Hilbert space of the system (or,
equivalently, a operator of the form |psi><psi|, where |psi> is a
normalised Hilbert-space vector) or, if we do not (or can not)
prepare the system such, that a complete set of compatible
observables have precisely determined values, by a statistical
operator R (which is positively semi-definite with Tr R=1). First
of all, quantum theory tells us, which observables are
compatible, i.e., which observables can be determined precisely
at the same time: Each observable is described by a self-adjoint
operator in Hilbert space, and the possible outcomes of
measurements is given by the spectrum of this operator. Tow
observables are compatible if and only if the associated
operators commute. A set of compatible operators is a set of
pairwise commuting operators, describing observables such that,
if you determine the values of these observables precisely, the
system is prepared in a pure quantum state, i.e., the common
(generalised) eigenvector is unique. To make the things easier,
we look only on systems that are prepared in such a pure quantum
state. Now, if we have prepared the system in such a pure quantum
state, at time t0, and if we know the Hamilton operator of the
system precisely, we can predict its state for any later time. So
the state of the system is precisely determined at any time, but
it contains only information about the probability of the outcome
of further measurements, not more (nor less). An observable has a
determined value if and only if the state is an eigenvector of
the associated operator. If it is not an eigenvector, we know
only the probabilities to measure a certain value of the
observable, which has to be an eigenvalue of the associated
operator. What we have to learn, and admittedly it is very hard
to keep this in mind, is to forget our daily experience with
objects in the macroscopic world, where it seems clear that any
observable has a certain value. In the quantum world this concept
doesn't make any sense. It is another very interesting question,
why our daily experience is that of classical physics, when we
believe that the underlying natural laws are quantum laws. The
answer is, what is called decoherence, which explains why we
never see interference patterns, entanglement for "Schr"dinger's
cat". A very nice introduction in this topic is
http://arxiv.org/abs/quant-ph/-9803052
<http://arxiv.org/abs/quant-ph/9803052> -- "
Sample # 5
" The other road I'm sure the one taken by the "experts" is
this: Realize that, in the end, it's just a mathematical theory
to model what we see physically. Being a mathematical theory, it
ought to be self consistent, and everything we want to know
ought to be derivable in the theory. Now, in order for this
theory to explain what we see in everyday life, we must assign
interpretations. These interpretations ought to be simple and
ought to corres pond in a transparent manner to mathematical
objects in o ur theory. Of course to understand the process of
assigning interpretations and how they relate to the theory, one
must spend a lot of time thinking about this stuff and until you
see many of them you wont know what I mean. (Be warned that
sometimes we may need to change our thinking and restrain our
questions to the constraints of our theory). There are many
theories whose mathematical setup is not yet complete, or may
even be unattainable. Also, there are theories that are
consistent but are not g ood because they do not explain enough.
This being said, If you believe that quantum mechanics is a
mathematical theory, and that the theory should dictate our
questions and to a great extent our interpretation--as I suspect
it does for "professionals", then I venture that Quantum
Mechanics can be understood--in fact it's understood by many
experts. Now just what I mean cannot be really understood until
one sees an example of what I mean. Let's examine the "Double
Slit" pro blem. Ok, first we must ask, what are the assumptions
of the theory, and what does the theory say about this intuitive
double slit situatuation? I cannot tell you what other people
will say, but I can tell you what the theory I have in my mind,
Quantum Theory #1226789 says: You have states, and you have a
Hamiltonian that is dependent on the potential "the double slit
potential" in our case. There is a time evolution equation given
by v_t = e^{iHt}v_0 , v_t is the state at time t. The stat e
contains Physical information th at I can extract from the fact
that there are objects called observables, and each observable
and state determine a probability measure on the spectrum of the
operator. Now for the physical interpretation of this. When you
measure for a quantity experimentally, this is associated to
some operator now there is an experimental setup called "the
state" and each time you repeat the same experiment and you
setup things in exactly the same way you are in the same state.
No w if you measure a zillion times for position, you'll get the
distribution I mentioned before that corresponds to the position
operator. Then you can setup your experiment in the same way and
measure for momentum then you'll have the probability
distribution for the momentum operator. By the way for each
measurement I wait the same amount of time t after I setup the
experiment, so that I have "the state at time t" so for each
different t, for each observable I'm interested in, I'll have
the proba bility measure for that state at tim e t. However,
according to the interpretation I just assigned the probability
measure determined by a state operator pair, I cannot say that
"the state says I have a particle at such position and with such
momentum" In other words since I did a bunch of measurements of
position, and then a bunch of measurements of momentum at
different instances, When I look at the two probability
distributions, for position and for momentum I cannot say "when
*the part icle* had this position, it had that momentum" (This
could be done in a theory where you have a probability
distribution on position x momentum space, but this is not
standard Quantum theory). By the way I said *the particle*,
because even this notion is iffy, and I don't really need to
talk about it in my theory. I just have an experimental setup
which corresponds to a state, and I have probability
distributions which exist mathematically and can be compared to
those obtained from the exp erimental setup, and my theory
predicts how any of these probability distributions can
conceivably evolve in time. So I can check its usefulness
experimentally. So you see there are no particles of definite
position and momentum that take paths around barriers and so on.
>>From the setup of my theory Quantum Theory #1226789, its obvious
one cannot talk about these objects. [However there may be
another theory in which you can--but that's not standard quantum
theory.] Anyhow, getting to your double slit question, the
question which slit does it go through p icturing a classical
particle and picturing which slit it goes through is
hopeless.--at least according to quantum theory--That's why I
think accounts about this such as that in Feynman are bad. But
probably Feynman understood all this it's just that he was
trying to make it accessible to the general public. But, then
accessible to the general public does not mean that it makes
sense after second thought --Ie like mood poetry, it sets a mood
but when you try to examine the meaning, it doesn't make s ense.
Now one thing you can do is to try different initial states for
the double well, and see what this means in terms of the theory.
E.g., start with a state that has as its probability distribution
for position a gaussian located on one side of the double slit,
and that its probability distribution for momentum is also a
gaussian centered about a momentum that points towards the
double slit. By the way remember that from the point of vie w of
the theory, the double slit is a potential. Then using the
Hamiltonian that corresponds to this potential time evolve this
initial state and see what the probability distribution looks
like at a later time. (I recomend a good simulation to visualize
this --Try searching Google for "double slit applet"). Also try
the initial state where the whole probability distribution is
localized at on of the slits. I think this corresponds to the
statement in the popularizations where they say "if you knew
which hole the particle went through..." Anyways hope this
helps. And keep searching.
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