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Oz
science forum Guru Wannabe
Joined: 30 Apr 2005
Posts: 155
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 Posted: Wed Jul 19, 2006 6:35 am Post subject:
Re: Two-slit experiment
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Timo A. Nieminen <timo@physics.uq.edu.au> writes
| Quote: | Don't confuse localisation with size. If a photon is "large", it should be able
to interact with and be detected by two spatially separated detectors at the
same time.
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In a sense it can, and in a sense it cannot.
Given exited enough detectors of course one can. Exited enough detectors
are by definition noisy and nobody can tell if two transitions are due
to the EM wave tripping two or whether one (or both) are noise.
We can only tell that on average the detector is best modelled by it
making quantum transitions. This is unsurprising given that detectors
are quantised.
--
Oz
This post is worth absolutely nothing and is probably fallacious. |
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Timo Nieminen
science forum Guru Wannabe
Joined: 12 May 2005
Posts: 244
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| Posted: Mon Jul 03, 2006 12:13 pm Post subject:
Re: Two-slit experiment
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On Mon, 3 Jul 2006, nightlight wrote:
| Quote: | Timo A. Nieminen wrote:
This being independent of wavelength
(but see below), low frequency isn't necessary. In fact, it's best to use
the highest frequencies available, so that the energy required for
detection is only a small fraction of the total energy. Put a gamma source
in the middle of some, preferably many, detectors. Each gamma photon can
go in any direction, the radiation field of each emission is spherically
symmetric (well, perhaps a dipole field, but spherically symmetric
averaged over many). Count, and look for coincidences. Has this been done?
I don't know offhand. You should look; if it hasn't been done, it could be
a cheap and useful entry into experimental physics for you.
Just detecting a particle-like anticorrelation in coincidences is not
by itself proof of anything non-classical or unusual in any way.
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The proposal is just to address the claim that the photon has a size equal
to the spread of its wavefunction, and that detection probability is
simply proportional to E. Yes, by itself, that doesn't prove anything
non-classical. For example, classical billiard ball photons will behave
this way. OTOH, I think there's already ample evidence that photons aren't
classical billiard balls (eg Hanbury Brown-Twiss).
| Quote: | Similarly, if you make gamma source produce coherent enough and equal
(in total energy) enough wave packet components in far away regions to
fully interfere when brought together, the coincidence measurements on
the remote packets will show the Poissonian coincidence rates (i.e.
each fragment will trigger or not trigger its detectors independently
form what the other remote detectors did i.e. the fragment A will not
suddenly vanish/collapse when the fragment B triggers its detector).
|
Have a weak enough source so that in some time interval longer than the
time required for the detector to click and recover, you only expect one
photon to be emitted, or else there's no point to the experiment. It's not
intended as a "collapse of the wavefunction" experiment.
| Quote: | Check the cited materials from my other two posts
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Will do.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
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Paul Danaher
science forum beginner
Joined: 25 Jun 2005
Posts: 26
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| Posted: Mon Jul 03, 2006 12:29 am Post subject:
Re: Two-slit experiment
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FrediFizzx wrote:
| Quote: | "Timo A. Nieminen" <timo@physics.uq.edu.au> wrote in message
news:Pine.WNT.4.64.0607010837130.1212@serene.st...
On Fri, 30 Jun 2006, Oz wrote:
Clearly (to me at any rate) the 'size' of a massive particle is
determined (like the photon) by its environment (typically
quantised). So an electron, say, can have a different physical size
when undisturbed in an orbital This can in some circumstances be
very large indeed when orbitals become macroscopic, for example in
conductors.
Don't confuse localisation with size. If a photon is "large", it
should be able to interact with and be detected by two spatially
separated detectors at the same time.
I don't think we actually know the answer to that "question" since
"large" photons might be radio wave photons and so far individual
detection of such photons is not possible. Do you know of any
experimental limits that we might have for this? IOW, what is the
lowest frequency at which individual detection is experimentally
possible with current technology?
FrediFizzx
|
This seems to bring up again the problem of the dual answers to my question
about how long it takes to absorb a photon. One answer was that the wave
function collapses instantaneously, another that it depends on the frequency
of the photon. Your "large" photon brings me back to my puzzle about when
absorption occurs - is it on the arrival of the leading edge of the wave
packet/probability density function, or at a point at which this reaches
some threshold value?
(Thank you for the further puzzles in the Diether paper you cite, with his
comment that the photon energy density volume for a radio wave could be as
big as a house or bigger.) |
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nightlight
science forum Guru Wannabe
Joined: 27 May 2005
Posts: 182
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| Posted: Mon Jul 03, 2006 12:29 am Post subject:
Re: Two-slit experiment
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Timo A. Nieminen wrote:
| Quote: | This being independent of wavelength
(but see below), low frequency isn't necessary. In fact, it's best to use
the highest frequencies available, so that the energy required for
detection is only a small fraction of the total energy. Put a gamma source
in the middle of some, preferably many, detectors. Each gamma photon can
go in any direction, the radiation field of each emission is spherically
symmetric (well, perhaps a dipole field, but spherically symmetric
averaged over many). Count, and look for coincidences. Has this been done?
I don't know offhand. You should look; if it hasn't been done, it could be
a cheap and useful entry into experimental physics for you.
|
Just detecting a particle-like anticorrelation in coincidences is not
by itself proof of anything non-classical or unusual in any way. After
all, kicking a ball into a fence with large holes in it will result in
the ball ending up exclusively on one side of the fence or the other.
And the distribution of the ball's stopping places may well be
symmetrical with respect to the fence.
You also need to show the interference if you bring the far away paths
back together. With gamma rays the state may be spherically
symmetrical, but it is not a pure state. It is a spherically
symmetrical mixture (since the recoil of the source nucleus can be used
to detect the direction of the gamma photon in individual emissions).
With optical photons any recoil (such as that of a heavy half-silvered
mirror) is negligible (i.e. comparable to the Heisenberg uncertainties)
to allow measurement of whether the photon was reflected or
transmitted. In that case the separate wave packet components retain
coherence and can thus interfere when brought together. If you were to
make the half-silvered mirror/beam splitter used with optical photons
light enough to undergo recoil sufficient to find out direction of the
photon, you will automatically lose the interference pattern. There is
a continuum of tradeoffs between the sharpness (visibility) of the
interference fringes and the certainty of detection (e.g. via recoil)
which way the photon went, with the perfect interference and the
perfectly certain recoil effect on its opposite extrema.
Similarly, if you make gamma source produce coherent enough and equal
(in total energy) enough wave packet components in far away regions to
fully interfere when brought together, the coincidence measurements on
the remote packets will show the Poissonian coincidence rates (i.e.
each fragment will trigger or not trigger its detectors independently
form what the other remote detectors did i.e. the fragment A will not
suddenly vanish/collapse when the fragment B triggers its detector).
Check the cited materials from my other two posts in this thread on the
experimental and theoretical status of this conjectured wave-particle
"duality" (with collapse of the remote wave packet) -- it has never
been observed experimentally or shown to exist theoretically even in
principle (within QED; the Glauber's theory of photo-detections and
photo-correlations in his 1964 Les Houches lectures was the high point
of such efforts on the theoretical side) despite over five decades of
attempts, the handwaving in the popular and pedagogical literature
notwithstanding. |
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Oh No
science forum addict
Joined: 06 Apr 2006
Posts: 82
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| Posted: Sun Jul 02, 2006 12:08 pm Post subject:
Re: Two-slit experiment
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Thus spake Oz <Oz@farmeroz.port995.com>
| Quote: | Absolutely. Perhaps a massive boson beam would be better. I guess that
probably means they would be entangled so as to get the long thin
coherent beam. Hmm....
|
This gets pretty confusing. Lasers are weird things, and I don't profess
to fully understand them, but I think they are pretty dependent on the
properties of photons as fundamental particles. IIRC It has been
remarked here, by those more qualified than I, that the properties of a
bose gas consisting of fundamental bosons are not the same as one
consisting of bosons which are themselves compound particles consisting
of fermions, the reason being that if compound particles were in exactly
the same state it would imply that the fermions of which they consist
would be in the same state, yielding a contradiction.
Looking through the derivation I gave it seems to me that the critical
distinction was that photons are annihilated when they are detected, so
that the amplitude for detection at x is <|A(x)|f>, a pure number. We
can add numbers, so we can get interference effects between different
photons. Fullerenes, for example are not annihilated, and the position
operator is |x><x| which yields |x><x|f>, a state. We still cannot
superpose states of different particles, so that means we can expect
interference effects between different photons, but not interference
effects between different fullerenes.
Regards
--
Charles Francis
substitute charles for NotI to email |
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Timo Nieminen
science forum Guru Wannabe
Joined: 12 May 2005
Posts: 244
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| Posted: Sun Jul 02, 2006 12:08 pm Post subject:
Re: Two-slit experiment
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On Sat, 1 Jul 2006, FrediFizzx wrote:
| Quote: | "Timo A. Nieminen" <timo@physics.uq.edu.au> wrote:
On Fri, 30 Jun 2006, Oz wrote:
Clearly (to me at any rate) the 'size' of a massive particle is
determined (like the photon) by its environment (typically
quantised). So an electron, say, can have a different physical size
when undisturbed in an orbital This can in some circumstances be
very large indeed when orbitals become macroscopic, for example in
conductors.
Don't confuse localisation with size. If a photon is "large", it
should be able to interact with and be detected by two spatially
separated detectors at the same time.
I don't think we actually know the answer to that "question" since
"large" photons might be radio wave photons and so far individual
detection of such photons is not possible. Do you know of any
experimental limits that we might have for this? IOW, what is the
lowest frequency at which individual detection is experimentally
possible with current technology?
|
The claim regarding electrons having different sizes depending on whether
"they are undisturbed in an orbital" reads to me as an identification of
size with spread of wavefunction. This being independent of wavelength
(but see below), low frequency isn't necessary. In fact, it's best to use
the highest frequencies available, so that the energy required for
detection is only a small fraction of the total energy. Put a gamma source
in the middle of some, preferably many, detectors. Each gamma photon can
go in any direction, the radiation field of each emission is spherically
symmetric (well, perhaps a dipole field, but spherically symmetric
averaged over many). Count, and look for coincidences. Has this been done?
I don't know offhand. You should look; if it hasn't been done, it could be
a cheap and useful entry into experimental physics for you.
But yes, there is a problem with trying to make sub-wavelength individual
photon detectors. Except for single atoms/molecules, but then you still
need an individual photon detector to detect the re-emission. IME, this is
in the near IR.
I guess that you're wondering about size of photons as it might depend on
wavelength. The above means that it's hard to answer experimentally. I
think that illuminating a group of atoms, all within a wavelength, and
only one of them absorbs and re-emits, is conclusive - the "size" of a
photon is no larger than an atom. Compton can be interpreted as saying
that the size of a photon is the size of an electron, ie zero AFAWCT.
But do consider the above gamma experiment. Data is good for you. All
theoreticians should be forced into labs at some point!
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
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FrediFizzx
science forum Guru
Joined: 01 May 2005
Posts: 774
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| Posted: Sat Jul 01, 2006 6:06 pm Post subject:
Re: Two-slit experiment
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"Timo A. Nieminen" <timo@physics.uq.edu.au> wrote in message
news:Pine.WNT.4.64.0607010837130.1212@serene.st...
| Quote: | On Fri, 30 Jun 2006, Oz wrote:
Clearly (to me at any rate) the 'size' of a massive particle is
determined (like the photon) by its environment (typically
quantised). So an electron, say, can have a different physical size
when undisturbed in an orbital This can in some circumstances be
very large indeed when orbitals become macroscopic, for example in
conductors.
Don't confuse localisation with size. If a photon is "large", it
should be able to interact with and be detected by two spatially
separated detectors at the same time.
|
I don't think we actually know the answer to that "question" since
"large" photons might be radio wave photons and so far individual
detection of such photons is not possible. Do you know of any
experimental limits that we might have for this? IOW, what is the
lowest frequency at which individual detection is experimentally
possible with current technology?
FrediFizzx
Quantum Vacuum Charge papers;
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.pdf
or postscript
http://www.vacuum-physics.com/QVC/quantum_vacuum_charge.ps
http://www.arxiv.org/abs/physics/0601110
http://www.vacuum-physics.com |
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Oz
science forum Guru Wannabe
Joined: 30 Apr 2005
Posts: 155
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| Posted: Sat Jul 01, 2006 6:06 pm Post subject:
Re: Two-slit experiment
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Oh No <NotI@charlesfrancis.wanadoo.co.uk> writes
| Quote: | Thus spake Oz <Oz@farmeroz.port995.com
You have been known to make errors, later corrected (like all of us).
I've given a demonstration again, in response to scerir. It is not
difficult, and nicely illustrates that observables, such as interference
effects, rely on the properties of operators, not just states, and thus
what is wrong with the view of superposition given in Dirac's koan.
|
Yes. Nicely done, I even mostly understood it <cough>.
| Quote: | Personally I vote for experimental results. My question is whether
anyone has any idea how it could be done? Personally I would bet you £50
it will show the same result as the photon experiment.
I'll take you up on that. Will you accept this as an electronic
handshake?
|
Earlier today I rescinded same....
| Quote: | The initial aim would be to produce extremely monochromatic beams of
electrons.
Ahem, you can't have an electron equivalent of a laser. They are
fermions and cannot all be in the same state.
|
Absolutely true, hence (luckily for me) no such experiment can be made.
| Quote: | Given that we are looking for exceedingly low beam intensity
I suspect that the problems associated with mutual repulsion of
electrons within a beam will be negligible (or am I being
oversimplistic?).
You are forgetting the exclusion principle, which is rather more
encompassing than charge.
|
Absolutely. Perhaps a massive boson beam would be better.
I guess that probably means they would be entangled so as to get the
long thin coherent beam. Hmm....
| Quote: | One is almost tempted to start with very low energy electrons, perhaps
separating them by time-of-flight (via a chopper)
No you wouldn't be allowed to do that either. Remember, when they do
this for photons the stipulation that only one photon comes through per
amount of time is statistical. In one of these low energy laser thingies
any photon can come through at any time, but it is only fed so much
energy so there is only one per amount of time.
|
This was to ensure a very precise *energy*, but I wasn't thinking very
carefully and imagining a neutron spallation source sort of thing which
is inappropriate.
--
Oz
This post is worth absolutely nothing and is probably fallacious. |
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Oz
science forum Guru Wannabe
Joined: 30 Apr 2005
Posts: 155
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| Posted: Sat Jul 01, 2006 6:06 pm Post subject:
Re: Two-slit experiment
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Oz <Oz@farmeroz.port995.com> writes
| Quote: |
Personally I vote for experimental results. My question is whether
anyone has any idea how it could be done? Personally I would bet you £50
it will show the same result as the photon experiment.
|
Bet rescinded....
It would need to be necessary to have two moving electron CLOUDS (that
is covering a large area) that emulate a laser beam. I'm fairly sure
that an electron beam does NOT have this characteristic.
--
Oz
This post is worth absolutely nothing and is probably fallacious. |
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Admral
science forum beginner
Joined: 07 Sep 2005
Posts: 22
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| Posted: Sat Jul 01, 2006 6:06 pm Post subject:
Re: Two-slit experiment
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Oz wrote:
| Quote: | Blackbird <fake@nospam.no> writes
[...]
I don't think that this is the same kind of interference. If you
add up two amplitude modulated waves of the same frequency, then
obviously the result will be garbled, but this has a different
explanation than the double slit experiment has.
Why? Radio waves are perfectly good EM waves just like light but with
different frequency.
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Sure, so I'll try to explain my point here a little better. Say we have a
vertical receiving antenna, and two MW transmitters that transmit waves of
the same frequency, but perfectly out of phase (relatively shifted by 1/2
the wavelength) at the location of the antenna. The waves transfer energy
inducing electrons in the antenna to accelerate. According to the theory,
this energy transfer (and thus the acceleration) is quantized, hence
"photons". Now, any random electron will from time to time absorb a photon
that either accelerates it in the "up" direction, or in the "down"
direction, and since we have two sources with cancelling phases, for any
finite (and sufficiently large) interval of time, the electron will absorb
approximately as many "up" as "down" photons. The electron will thus
exhibit a random walk, and no signal will be detected. This, however, does
not mean that the *photons* interfere with eachother. Interference, as in
the double slit experiment, would mean that photons from the two different
sources cancelled each other (or more precisely, they would be more likely
to show up at another location), thus there would be no energy absorbtion by
the electron whatsoever. |
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scerir
science forum beginner
Joined: 31 May 2005
Posts: 21
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| Posted: Sat Jul 01, 2006 1:19 pm Post subject:
Re: Two-slit experiment
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| Quote: | When the different possible photon paths,
from sources to detector, are indistinguishable,
then we have to add the corresponding amplitudes
before squaring to obtain the probability.
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Oz writes:
| Quote: | Hmmm.... how very convenient....
|
Try 'Quantum effects in one-photon and two-photon
interference'by L. Mandel (Rev.Mod.Phys.,vol.71,n.2,
page S274). It is online (use Scholar Google).
| Quote: | The second part of the koan (see below)
seems obscure (or it needs a reformulation),
since we have two-photon interference, that
is to say the interference of photons
emerging from _independent_ sources.
Which is precisely my point.
The below can be reformulated (I am absolutely confident mathematicians
can do this), basically by saying "take two independent sources, and
call them one source", which gives the right answer at some
philosophical cost.
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No, the actual meaning of interference changes here.
See Mandel's paper or, i.e.,
http://www.arxiv.org/abs/quant-ph/0603048
Regards,
s. |
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Timo Nieminen
science forum Guru Wannabe
Joined: 12 May 2005
Posts: 244
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| Posted: Sat Jul 01, 2006 1:19 pm Post subject:
Re: Two-slit experiment
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On Fri, 30 Jun 2006, Oz wrote:
| Quote: | Timo Nieminen <timo@physics.uq.edu.au> writes
On Thu, 29 Jun 2006, Oz wrote:
scerir <scerir@libero.it> writes
It seems that this experiment led to Dirac's famous koan
"each photon then interferes only with itself".
Except we know this is not correct. Experiments have been done where two
separate lasers fired through two separate slits produces an
interference pattern.
That just shows that each photon comes from both sources.
Hmmm....
As an explanation I think Mr Occham would find this improbable.
|
While William of Oakham/Occam would likely have found it improbable, due
to not knowing about either electromagnetic fields or photons, it is
not incompatible with his razor. As I wrote:
| Quote: | A photon is the
quantum of excitation of the EM field, the EM field is the sum of the
fields individually produced by the sources, so each photon comes from
both sources.
A contortion IMHO.
A much more plausible explanation is that photons are completely
wavelike.
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The EM field is completely wavelike. Much, even most, stuff about photons
comes from purely classical theory. However, by definition photons are
_not_ completely wavelike, being the quanta of excitation/de-excitation of
the field.
Your "much more plausible" completely ignores all of the observational,
experimental, and theoretical evidence for the existence of photons. But
yes, the original two-slit experiment did held overthrow the old
corpuscular theories of light and replace them with a wave theory of
light. But note well that the old corpuscules of light (proto-photons?)
were thought of as classical particles, and the modern photon is not a
classical particle.
| Quote: | One then looks to apparent quantum behaviour in the emitters
and/or detectors where of course one finds them.
|
One looks _at_ quantum behaviour in the emitters/detectors. Where else
will you find excitation/de-excitation of the EM field?
An October issue of Optics and Photonics News (iirc, in 2003) had a nice
special section on "What is a photon?". Read it. Also Lamb, "Anti-photon",
Applied Physics B from 1995.
| Quote: | NB I must logically also conclude that massive particles are also waves
and once again the quantised behaviour is due to something else.
|
Very de Broglie. It's been done. The "something else" is "that's the way
that nature works". If photons are waves, and massive particles are waves,
then why is the exchange of energy between matter and EM fields quantised?
Observably, it is. "Why" might be a deeper question than we can answer
(yet). Asking why hbar is non-zero and has the value we measure is like
asking why is c non-infinite with the value we measure(d).
| Quote: | Clearly
(to me at any rate) the 'size' of a massive particle is determined (like
the photon) by its environment (typically quantised). So an electron,
say, can have a different physical size when undisturbed in an orbital
This can in some circumstances be very large indeed when orbitals become
macroscopic, for example in conductors.
|
Don't confuse localisation with size. If a photon is "large", it should be
able to interact with and be detected by two spatially separated detectors
at the same time.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
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Oh No
science forum addict
Joined: 06 Apr 2006
Posts: 82
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| Posted: Sat Jul 01, 2006 1:19 pm Post subject:
Re: Two-slit experiment
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Thus spake Oz <Oz@farmeroz.port995.com>
| Quote: | Oh No <NotI@charlesfrancis.wanadoo.co.uk> writes
Thus spake Oz <Oz@farmeroz.port995.com
Now this has been demonstrated for photons. However the laser light used
for each beam (separate lasers) had extremely long coherence lengths
(times). To do this with electrons might be problematic (ie
"challenging") but would be interesting. Anybody any ideas how it could
be done?
It can't be done. You probably don't remember or didn't follow it, but
you induced me to calculate interference effects between wave functions
for different photons using qed. The same argument did not apply to
electrons, which are fermions and which are conserved in interaction.
You have been known to make errors, later corrected (like all of us).
|
I've given a demonstration again, in response to scerir. It is not
difficult, and nicely illustrates that observables, such as interference
effects, rely on the properties of operators, not just states, and thus
what is wrong with the view of superposition given in Dirac's koan.
You appreciate that there is a paradox here which needed resolution.
What Dirac says is trivially true of superposition of quantum states.
Hence it also would be true if we strictly observed superposition of the
wave function. But we do not. We observe the behaviour of the position
observable, and that is subtly different. In the instance of the
electron, it boils down to the same formula. In the instance of the
photon, it does not.
| Quote: |
Personally I vote for experimental results. My question is whether
anyone has any idea how it could be done? Personally I would bet you £50
it will show the same result as the photon experiment.
|
I'll take you up on that. Will you accept this as an electronic
handshake?
| Quote: | The initial aim would be to produce extremely monochromatic beams of
electrons.
|
Ahem, you can't have an electron equivalent of a laser. They are
fermions and cannot all be in the same state.
| Quote: | Given that we are looking for exceedingly low beam intensity
I suspect that the problems associated with mutual repulsion of
electrons within a beam will be negligible (or am I being
oversimplistic?).
|
You are forgetting the exclusion principle, which is rather more
encompassing than charge.
| Quote: | One is almost tempted to start with very low energy electrons, perhaps
separating them by time-of-flight (via a chopper)
|
No you wouldn't be allowed to do that either. Remember, when they do
this for photons the stipulation that only one photon comes through per
amount of time is statistical. In one of these low energy laser thingies
any photon can come through at any time, but it is only fed so much
energy so there is only one per amount of time.
Regards
--
Charles Francis
substitute charles for NotI to email |
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Oz
science forum Guru Wannabe
Joined: 30 Apr 2005
Posts: 155
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| Posted: Fri Jun 30, 2006 8:21 pm Post subject:
Re: Two-slit experiment
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bz <bz+spr@ch100-5.chem.lsu.edu> writes
| Quote: | What is usually heard there is the 'beat frequency' [hetrodyne] as signals
of two slighly different frequencies (or phases) are 'combined' in the
receiver's detector.
|
Indeed.
| Quote: | A signal arriving over multipaths can interfer with itself as the phase of
the multipath signals varies due to changes in path length as ionospheric
conditions vary.
|
No, I am NOT talking about that.
I am talking about two SEPARATE transmitters, which still interfere.
| Quote: | Of course a HUGE number of photon is involved as MW radio frequency photons
each carry very little energy.
|
So what? Its still photons from different sources interfering.
Or would you claim that the interference will reduce as amplitudes
reduce? Surely you aren't suggesting that?
--
Oz
This post is worth absolutely nothing and is probably fallacious. |
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Oz
science forum Guru Wannabe
Joined: 30 Apr 2005
Posts: 155
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| Posted: Fri Jun 30, 2006 8:21 pm Post subject:
Re: Two-slit experiment
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Oh No <NotI@charlesfrancis.wanadoo.co.uk> writes
| Quote: | Thus spake Oz <Oz@farmeroz.port995.com
2) There is also the interference of two sources each going through one
slit **when intensity is so low that the probability of finding two
'photons' in the apparatus at the same time is very low.
Now this has been demonstrated for photons. However the laser light used
for each beam (separate lasers) had extremely long coherence lengths
(times). To do this with electrons might be problematic (ie
"challenging") but would be interesting. Anybody any ideas how it could
be done?
It can't be done. You probably don't remember or didn't follow it, but
you induced me to calculate interference effects between wave functions
for different photons using qed. The same argument did not apply to
electrons, which are fermions and which are conserved in interaction.
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You have been known to make errors, later corrected (like all of us).
Personally I vote for experimental results. My question is whether
anyone has any idea how it could be done? Personally I would bet you £50
it will show the same result as the photon experiment.
The initial aim would be to produce extremely monochromatic beams of
electrons. Given that we are looking for exceedingly low beam intensity
I suspect that the problems associated with mutual repulsion of
electrons within a beam will be negligible (or am I being
oversimplistic?).
One is almost tempted to start with very low energy electrons, perhaps
separating them by time-of-flight (via a chopper) or even ballistically
as the take a parabolic path in a gravitational field (ok, VERY low
energy). From there one could pass them through two identical (but
separate) accelerators to the slit and target.
--
Oz
This post is worth absolutely nothing and is probably fallacious. |
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