Re: Two-slit experiment


"Timo A. Nieminen" <timo@xxxxxxxxxxxxxxxxx> wrote in message
news:Pine.WNT.4.64.0608112139450.1416@xxxxxxxxxxxx
On Thu, 10 Aug 2006, Ron Baker, Pluralitas! wrote:

<snip>


Millikan's paper, Phys Rev 7, 355-388 (1916) is very worthwhile reading
on
the photoelectric effect in general.

I eventually found a copy but in looking for it I found this:
http://www.oufusion.org.uk/newswinter01/fusionnewswinter01.htm
An interesting quote from Einstein:
'...According to the concept that the light consists of energy
quanta of magnitude Rb?/N (i.e. h?) however one can
conceive of the ejection of electrons by light in the
following way. Energy quanta penetrate into the surface
layer of the body, and their energy is transformed, at least
in part, into kinetic energy of electrons. The simplest way
to imagine this is that a light quantum delivers its entire
energy to a single electron; we shall assume that this is
what happens. The possibility should not be excluded,
however, that electrons might receive their energy only
in part from the light quanta.'

In general the article is about how it is impossible to get the
sharp cutoff in the photoelectric effect that Millikan
described and everyone assumes.

Basically, yes. The electrons initially occupy a continuum of energy
states, and have whatever thermal energy they have. The incident light
adds to that, so there can't be a sharp cut-off. The experimentally
important thing is the width of the thermal energy distribution compared
to the incident photon energy. Also, on ejection, energy can be lost in
collisions on the way as well as due to the work function. Due to the
former, some assumed (as Millikan notes) that the most probable energy of
ejection was the most important parameter. But if the latter -
non-work-function losses - is usually larger than the thermal width, then
the maximum observed ejection energy is the most useful thing to measure
(again, as Millikan notes).


<snip>


Basically, to
say E = hf only makes sense for a monochromatic field, where there is an
f
to talk about.

('monochromatic field' sounds like a population to me.
Maybe you didn't intend that. Can a single photon be
a monochromatic field?)

In an idealisation, yes. In practice, no. The killer problem is that to be
monochromatic, the time of emission was sometime between -infinity and
+infinity - the probability of detecting the photon in any finite time
interval is zero. The practical equivalent is a monochromatic EM wave of
such low intensity that in whatever time interval you're interested in,
you are only likely to detect one photon, at most.

Theoretically, there is no problem.

Quantisation of the radiation field is, in essence, that energy is added
to or removed from a _monochromatic_ field in chunks of hf.

When hf is continuously variable the term 'chunk' doesn't seem
appropriate to me. It seems to imply only certain allowed sizes.
But perhaps that is not what you intended.

hf is only continuously variable insofar as f is variable. h is a
fundamental constant (so it seems). For exchange of energy between of
monochromatic field (or a mode of a total field) to be restricted to
chunks of hf does indeed imply only certain allowed sizes.

And this is a Schroedinger/quantum leap view, isn't it?


If I express the rest
of my view it sounds similar and is perhaps the same as your
intention. Towit: when energy is transfered from a massive
charged particle into radiation in the EM field any constraint
on the amount of energy is determined by the charged
particle and not by an intrinsic nature of the EM field
and that that EM radiation energy is somehow 'bundled' or has a unique
identity and acts as a unit and does not act with other such
quanta.

I don't believe it; I think it's a far more complex and irrational
explanation that this being a result of the nature of EM fields.

Hmm. I'm no Shakespear but I thought I was basically just
restating the collapse of the wave function.

One rule for EM fields vs many different rules for many different kinds of
matter giving the same result - which is simpler?

If 'one rule for EM fields' is what you have been saying
and 'many different rules for many different kinds
of matter giving the same result' is what you say I've
been saying then I disagree with your characterization
of both.

You don't have 'one rule'. You have two 'descriptions', i.e.
'photons' and wave functions that don't have a resolvable
relationship and you have rather arbitrary rules for when
you use one description or the other. You also have
things of spatial extent appearing
and disappearing instantaneously.

I don't know why you would say 'many different rules' or
'many different kinds of matter'. I don't see that I
said anything that implies that. What I have
been describing is pretty much a classical description
with the addition of the collapse of the wave function.


OTOH, perhaps there is no experimental way to distinguish between the two
opinions. Perhaps multi-photon states (not a state occupied by N photons
where N can be > 1, but where photons interact with matter in bunches of
N, N > 1. I'm not familiar with this stuff, some of it is entanglement and
some is what they call "non-classical interference".) might do it?

I don't know.


Given that no radiation field is actually monochromatic, is the above
definition of a photon useless? No more so than the concept of
monochromatic fields in classical EM. Often, the field is close enough
to
monochromatic, so we just pretend that it is - works for both the
quantum
and classical cases.

I don't object but what is the radiation field of a single photon?

For a single photon, and quasi-monochromatic? Approximately zero. For a
single photon in some unit of time, just the classical field that gives
the same expectation value. At least, this is the case for free space, no
boundaries.

For a cavity, sure, just stick an excited atom in it, and you can get a
single photon field.

Given a polychromatic field with a discrete spectrum, then you can just
write E_total = sum a_1 E_1 + a_2 E_2 + a_3 E_3 ...
where E_1,2,... are monochromatic fields, with frequencies f_1, f_2,
etc.
It's entirely reasonable to talk about the energy in field E_1, energy
in
E_2 etc - again, something done classically. Quantisation simply means
that the energy in field E_1 is exchanged with matter or matter+other
spectral components in chunks of h f_1.

Or less in the case of Compton scattering.

No, hf_1 is exchanged with the electron and the outgoing spectral
component (of frequency f_2), the latter of the two case above. Less
energy, if we consider the total field, but h f_1 if we consider only the
mode/spectral component of frequency f_1.

Maybe I spaced previously and didn't register your 'polychromatic
field' condition.


QED-wise, I don't think the question of whether or not it's the same
photon if you take h f_1 from field E_1 and add h f_2 to field E_2
really
makes sense.

That seems rather subjective or metaphysical.
Two marbles collide. It doesn't make sense to say that
all the kinetic energy of one at v1 went into the other and
then the other gave some of it back as v2.

Perhaps not. But then "+marble" isn't defined as an excitation of a
monochromatic mode of a field, "-marble" as the de-excitation. Marble
analogies for photons are perilous :); the QED photon - the most
successful photon we have - is very non-marble.

But yes, this is where we start to depart from physics and go to
philosophy. The maths works, but what does it _really_ mean? When that
questions comes up, it's philosophy time!

Indeed.


bound-bound have quantized allowed energy steps.
bound-free and free-bound have one sided limited
(> or <) allowed energy steps.
free-free is continously variable.

Yes, that's the point. And there's no resonant frequency involved since
the electron isn't bound. So why f1 in, f2 out, and delta_E = h delta_f,
even for free-free transitions?

It's a scale factor. Why is the ratio of D/E = 8.854e-12 C^2/Jm
in free space?


A photon or EM quantum is a united entity that has
an energy. You can call that 'quantized' but the 'EM
field' allows continuously variable values for the energy.
Bound electrons have discrete allowed energy values.
That is also called 'quantized'. (The photons they emit/
absorb are consequently similarly 'quantized' in allowed
energy values.) My point is that those two uses of
the word 'quantized' are actually and in reality two different things.
I think Nightlight was saying something similar (at least
in the post I saw).

When it comes to electrons and quantisation, I say that quantisation means
that you have 0, 1, 2, 3, or whatever electrons. Whether energy states are
discrete or form a continuum is a mere matter of boundary conditions. The
electron is the quantum of excitation of the Dirac field. I'm sure that
"discreteness" is called "quantized", at least some of the time (Is this
usual in QM? It's been a long time since I read serious QM. "Quantised" is
a different animal in quantum field theory and QED.)

Yes, the EM field is quantised in one sense, but not the other.

The transport of _all_ the energy of a single emission by an atom to a
single absorbing atom when this is classically impossible then has to be
either explained as a property of the field, or a property of the atom
interacting with a purely classical field. The absorbing atom could be
light-years away. To have the atom do this would be truly remarkable,
far
more so IMO than it being a result of quantisation of the field (still a
remarkable result).

Maybe we can create a couple new terms that might
help. How about 'quantumization' and 'quantization'?
'quatumization' refers to the unitary nature (while having
continuously variable allowed values) of the EM quantum.
Whereas 'quantization' refers to the discrete allowed
energy levels of confined matterial systems (and the consequent
restriction on the allowed energy they may exchange).

Well, I'd call the former "quantisation", since that's the word that I
encounter already in use, but then, I'm biased by my experience. Discrete
energy spectra are perfectly classical - they turn up, for example, in any
ideal EM resonator, so I'd hesitate to label them with something that
smacks of "quantum".

OK.
I see your view.


I'll have to read about this language when I have time. I agree, two
distinct terms would be good.

Yeah, I think so.

<unsnipping>

[TN] Not something you're going to
measure if you only have a single photon available.

[RB] That's my point. You can't say that an individual
photon has components

[TN] The photon doesn't have components, the wavefunction has components
of
different energies. Total probability = 1 if you have a single photon.



So the photon and the wavefunction are not
one and the same. Is one real and the other a
mathematical approximation? Or does reality shift
between being a photon and being a wavefunction?
If the components of the wavefunction change how
how is the photon affected?

I don't know.

I often find myself saying, "I don't know."
I think it is a sign of honesty.

Here you enter the realms of disputed pictures of what QM _really_ means.
The wavefunction is what we calculate; the photon is what we measure.
Perhaps this means that the photon is real and the wavefunction is
mathematical. OTOH, the photon is merely the quantum of excitation of the
wavefunction, so vice versa.

There is no escaping quantum weirdness. Reality is weird.


Even worse: the QED photon is basically defined in terms of monochromatic
modes, but Kramers-Kronig says that different sets of monochromatic modes
are equivalent in practice.

The key point is: if this is because this is how EM radiation fields
work,
then the field is quantised. If this is because all matter that the
fields
interact with work that way, then you'd see the same thing, but the
explanation is, IMO, far more complex and demanding of the suspension of
disbelief.

If you find meaning and some agreement in my
'quantumization'/'quantization' distinction then we may
be saying the same thing.

I agree with your distinction between the terms, though I'd choose
different words if I had my way.

I don't get things my way so if I can understand your
terminology I can deal with it.

But the core issue isn't the words: is it because, fundamentally, this is
the way EM fields work, or is it because this is the way matter works. I
think the former is the simpler. I suspect either is maintainable, at
least if one is willing to snub Ockam.

(The 'Pluralitas' in my handle is a reference to Ockam.)
But 'simpler' is subjective. You have this schizophrenic (nothing
personal intended) photon/wave function concept. To me
the collapse of the wave function, while still preposterous in 'common
sense', seems 'simpler'.
(And I consider my view to be regarding how EM quanta
work not how matter works. But looking at it from your view
I think I see how it might seem to apply more directly to matter.)


And finally, just to return to "is it the same photon?". Frequency
downconversion: one photon in, two identical photons out. Which one is
the
same individual photon as the original? (It's just the splitting amoeba
identity problem again!)

Interesting. I am not familiar with the downconversion
process you mention. Please describe it further if you
are so inclined.

Nonlinear optics. EM wave of frequency f goes in, EM wave of frequency f/2
comes out. 1 photon becomes 2. There's also the opposite, frequency
doubling, 2 in, one out at 2f. Which one of the original photons becomes
the final photon? What happens to the other?

Interesting. I could google on it too.


Let me know if you want me to try to find a tutorial paper or somesuch

If it is not much trouble, yes.

(and give me a week+; I'll be away for a bit).

Cool.

It has been an interesting exchange. I have enjoyed it.
You are one of the very few here who have
something intelligent to say.
I hope I haven't been too much of a bore.

--
rb


.

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