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Two-slit experiment
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bz
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Joined: 24 Mar 2005
Posts: 833

PostPosted: Fri Jun 30, 2006 12:20 am    Post subject: Re: Two-slit experiment Reply with quote

Oz <Oz@farmeroz.port995.com> wrote in
news:T1db1MScyioEFwLk@farmeroz.port995.com:

Quote:
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.

Furthermore this happened even if "the probability of two photons being
in the apparatus at one time approached zero".

In any case anyone who has listened to MW radio knows that separate
radio transmitters on the same frequency can readily cause interference
patterns.


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.

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.

Of course a HUGE number of photon is involved as MW radio frequency photons
each carry very little energy.
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Admral
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Joined: 07 Sep 2005
Posts: 22

PostPosted: Fri Jun 30, 2006 12:20 am    Post subject: Re: Two-slit experiment Reply with quote

Oz wrote:
Quote:
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.

Hmm. Interesting. Do you have a reference to a paper or webpage?

Quote:
Furthermore this happened even if "the probability of two photons
being in the apparatus at one time approached zero".

To mee, this indicates that somehow the photon must interfere with itself.

Quote:
In any case anyone who has listened to MW radio knows that separate
radio transmitters on the same frequency can readily cause
interference patterns.

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.
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bz
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Joined: 24 Mar 2005
Posts: 833

PostPosted: Fri Jun 30, 2006 12:20 am    Post subject: Re: Two-slit experiment Reply with quote

nightlight <nightlight@omegapoint.com> wrote in
news:1151472082.880906.31520@p79g2000cwp.googlegroups.com:

Quote:
If you do know of some experiments or a QED derivation (but
not some handwaved elementary/popular QM stories) that can
distinguish double slit/beam splitter photo-detection trigger
statistics from the trivial classical phenomena such as dripping
faucets in the Poissonian limit p->0, you are welcome to cite it.

I don't know of any that have definitely done so, but I believe the 'single
photon' lasers that are designed to only produce a single photon at a time,
have the potential of being the basis of such an experiment.

Some are based on the idea that a single excited molecule can only produce
a single 'lase' photon per incoming excitation photon.
<http://lfw.pennnet.com/Articles/Article_Display.cfm?Section=ARTCL&ARTICLE_ID=257230&VERSION_NUM=3&p=12>

The 'buzz' in secure communications is the use of an 'untappable' stream of
single photons, where the loss of even a single photon, due to attempts at
tapping into the circuit, would render the stream of encrypted data as
clearly compromised.

Of course, simply attenuating a stream of photons from a candle or laser
until the frequency of photons detected is so low as to 'assure' single
photon events, really gives no such assurance. So the availability of
inexpensive sources of true 'single photon' streams will undoubtably lead
to some interesting observations on dual slit experments.

As for producing streams of guaranteed 'single electron' or 'single He
molecules', that may or may not be easier than guaranted single photon
streams.

I expect that given a stream of true single photons, each photon will only
excite a single grain on a photographic film(or a single element on a ccd).
The PATTERN of excited grains, over time, dependent on the slit
arrangement.
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Oh No
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Joined: 06 Apr 2006
Posts: 82

PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

Thus spake scerir <scerir@libero.it>
Quote:
It seems that this [Taylor's] experiment led
to Dirac's famous koan "Each photon then
interferes only with itself."

Oz writes:
Except we know this is not correct.
Experiments have been done where two
separate lasers fired through
two separate slits produces an
interference pattern.

Yes, but this does not mean that Dirac's
koan is wrong.
Even a photon emitted by two sources (in such
a way that you cannot say which of the two sources
emitted the photon) interferes only with itself.
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.
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.

s.

"Each photon then interferes only with itself.
Interference between two different photons
can never occur."
- P.A.M. Dirac, Principles of Quantum Mechanics,
Clarendon, Oxford, 1930, p.15.


Dirac's koan is wrong. He wrote this when quantum mechanics was in its
infancy and quantum electrodynamics had hardly even been born. He was
thinking, quite naturally, of the structure of one particle Hilbert
space in which the quantum superposition, |f>+|g>, appears in the
addition of states of one particle. It makes no sense to add the state
of one particle to the state of another, because they are strictly
described by states in different Hilbert spaces. However in quantum
electrodynamics we have to think of the wave function not in terms of
the probability for where a photon is, but rather the probability for
where a photon is annihilated (detected) and we get a different result.

As a concession to ASCII I shall ignore spin and simplify the formula as
much as possible, and just show the bones of the argument. The photon
field operator is,

A(x) = |x> + <x|

where I am using ket notation for operators, so that |x> creates the
state |x>, and <x| annihilates the same state.

The photon wave function in the state |f> is

<|A(x)|f> = <x|f>

so that |<x|f>|^2 is the probability for detection of a photon at x.


Now consider a two photon state |f;g> = |f>|g> + |f>|g>. For simplicity
I am assuming no entanglement, and that the photons are distinguishable
at some time in the past (they come from different sources) so that
<f|g>=0.

When one of the photons is detected the other remains as it was, but we
don't know which one is detected and which one remains. Then the final
state is either |f> or |g>, i.e. it is |f> + |g>, so the probability for
detection at x is given by

(<f|+<g|) A(x) |f;g> = (<f|+<g|)(|x> + <x|)|f;g>)

= (<f|+<g|)(<x|f>|g> + <x|g>|f>)

where I have lost the inner product between states of different numbers
of particles (it is zero). Using <f|g> =0 and <f|f>=<g|g>=1 this comes
down to

<x|f> + <x|g>

Which shows the superposition between states of different photons.

+++++

This argument does not work for electrons. I shall ignore spin. For
electrons the field operator is

Psi(x) = |x> + <x^|

where |x> creates an electron and <x^| annihilates a positron. The
thing we detect is the current

j(x) = Psi+(x)Psi(x) = (|x^> + <x|)(|x> + <x^|)

This is "normally ordered" so that <x||x> is replaced by |x><x|,
otherwise the theory is divergent before you start.

Ignoring positrons and pair creation j boils down to

j(x) = |x><x|

which is the position operator (more strictly j^0 is charge, but here I
have lost the spin indices).

Now when an electron is detected both particles remain in the final
state, so the probability of detection at x is given by

<f;g| j(x) |f;g> = <f;g| |x><x| |g;f>

= (<f|x><g| - <g|x><f|)(<x|g>|f> - <x|f>|g>)

Again the <f|g>=0 and <f|f> = <y|y> =1 so this reduces to

= |<f|x>|^2 + |<g|x>|^2

So in this case we do not have interference, but simply the sum of two
amplitudes.



Regards

--
Charles Francis
substitute charles for NotI to email
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nightlight
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PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

Quote:
I don't know of any that have definitely done so,

The authors of the controversial AJP 2004 paper would
have surely cited such work as 'definite' if there were
one by that time. You can read the discussion
of their experiment at the link given and see exactly
by what means they got their sub-Poissonian
distribution: they tweaked delays on the double
trigger coincidence circuit until the pulse fell
well out of the acceptance time window of their
coincidence unit (ORTEC TAC/SCA 567). With
those settings they could have as well saved
$8-10K spent on laser and PDC (BBO) crystal,
used candle light instead and got exactly
the same "mysterious" single photon collapse.
When such means are needed to demonstrate
"single photon" and its "collapse", after
five decades of attempts, odds are that the
conjectured phenomenon does not exist.

As explained in that earlier thread, this conjectured
phenomenon is simply an operational misinterpretation
of how the elements of formalism (Glauber's correlation
functions) map to the empirical facts (the photo-detection
events). You can read more on this point in an earlier
sci.physics.reasearch post:

http://groups.google.com/group/sci.physics.research/msg/7ee770990a31bd3f

with some more detail on Glauber's theory:

http://www.physicsforums.com/showpost.php?p=529314&postcount=16
http://www.physicsforums.com/showpost.php?p=535516&postcount=61
http://www.physicsforums.com/showpost.php?p=538215&postcount=73


Quote:
but I believe the 'single photon' lasers that
are designed to only produce a single photon
at a time, have the potential of being the
basis of such an experiment.

The most ideal laser produces at best only the
'coherent light' which is fully described by
Maxwell's EM equations. That was known since
early 1960s, when Sudarshan proved an equivalence
theorem which established complete classicality
of such light.

Quote:
Some are based on the idea that a single excited
molecule can only produce a single 'lase' photon
per incoming excitation photon.
http://lfw.pennnet.com/Articles/Article_Display.cfm?Section=ARTCL&ARTICLE_ID=257230&VERSION_NUM=3&p=12


All that they are creating is the Poissonian light in
the limit p->0, as they plainly say at the link you
gave. Poissonian photon statistics is indistinguishable,
even in principle, from the statistics of classical
EM wave being thresholded via AD conversion to single
bit precision, then counted as: 1 is trigger, 0 is
a non-trigger. In the classical EM model, when you
place two detectors in the two paths after the beam
splitter (or behind the two slits in the double-slit
experiment), each detector triggers based solely
on the EM energy incident on its cathode within
the sampling window and entirely independently
of whether the detector in the other path triggers
("collapses" the wave function) or not. There is no
remote collapse in the classical model, just the
local collapse via self-focusing of the local
EM field due to the resonant absorption of the
incident EM energy by the oscillating electron
cloud of the cathode. See more on this model
of photo-detection in the paper (and the more
detailed papers from the same group cited there):

V. Bykov
"Photons, photocounts and laser detection of
weak optical signals" Ann. Fond. L. de Broglie,
V 26, n. spec. 1, 115-134 (2001)
http://www.ensmp.fr/aflb/AFLB-26j/aflb26jp115.htm

The same Poissonian "glitch" plagues all PDC sources,
which are the main "non-classical" light source in
recent couple decades. Namely the laser pump
(which is a 'coherent light' source, thus it has
Poissonian photon number statistics) generates at
best the Poissonian number of PDC pairs in any
sampling window, hence one cannot observe anything
about the PDC pairs photo-counts or their
correlations that is not perfectly modeled
by classical EM field with ZPF (zero-point field)
boundary conditions. This was demonstrated in a
series of papers by T. Marshall, E. Santos
and collaborators (you can see few of these
preprints at arXiv, e.g. quant-ph/9711042,
quant-ph/0202097):

http://arxiv.org/find/quant-ph/1/AND+au:+Santos_E+au:+Marshall_T/0/1/0/all/0/1

On PDC pair state & photon statistics, see references
[16] and [17] (Teich's online papers) here:

http://www.physicsforums.com/showpost.php?p=544829&postcount=122

One needs to be careful with the wishfully loaded
terminology and imagery used in Quantum Optics and
read between the lines in papers claiming Bell inequality
violations or other "non-classicality" obtained from PDC
sources (or any other optical photon sources explored for
these purposes) -- the "non-classicality" claimed so far is
always modulo "fair sampling" conjecture, i.e. the assumption
that they can somehow subtract away the Poissonian noise.

This immovable Poissonian wall is euphemistically labeled
"detection loophole" within Bell inequality tests, since
the Poissonian distribution of photo-electrons implies
an unavoidable tradeoff between the rate of 'dark counts'
and the detector efficiency. This tradeoff then precludes
the Bell's inequality violations, even in principle, by
the actual counts. So far, after over three decades of
attempts, only the fictitious counts, the counts in which
the Poissonian statistics was willed away (via ever more
creative euphemisms), have managed to "violate" Bell's
inequality (or other classical inequalities). For more
on the present status of the experiments see preprints:

http://arxiv.org/find/quant-ph/1/AND+au:+Santos_E+abs:+bell/0/1/0/2004/0/1


Quote:
The 'buzz' in secure communications is the use of an
'untappable' stream of single photons, where the loss
of even a single photon, due to attempts at tapping
into the circuit, would render the stream of
encrypted data as clearly compromised.

That's a marketing hype. (I hope you didn't invest your
retirement into any of that "magic" technology.) Check
at the very link you posted on what the "single photon"
in this jargon means. It is simply a highly attenuated
Poissonian source:

--- quote --

It is possible to simulate a single-photon source by
strongly attenuating light pulses that initially contain
many photons so only a single photon remains. That approach
is widely used in quantum cryptography experiments, but
is inherently very inefficient. [ed. this is a red herring;
yes, it is inefficient, but that aspect is its least problem,
since it is also a perfectly classical source] ...
...
Outlook

"The field is evolving very rapidly," says Yamamoto.
But there are formidable challenges to overcome in
developing practical single-photon emitters. The number
of time slots filled by emitted photons is at best only
a few percent. "We should improve the number to 50%,"
says Yamamoto. Even with so few time slots filled, the
probability of finding two photons in an occupied time
slot is about 1% -- too high to be acceptable. He also
stresses the need to improve waveform overlap to
virtually 100%, so photons can interfere with one
another for quantum applications.

--- end quote ---

In other words, any detections are few percent, say 5%,
while two photons occur in 1% of slots. With Poissonian
distribution the probability of k detections (or
photo-electrons) in a sampling time slot is:

P(k,A) = A^k exp(-A) / k! ... (1)

where 'A' is average detections per slot. The probability
of non-detections is then:

P(k=0,A) = exp(-A) ... (2)

hence the probability of one or more detections is:

P(k>0,A) = 1 - exp(-A) ... (3)

Take their P(k>0,A) = 0.05, which yields A = -ln(0.95) = 0.05
detections per time slot on average. With this A, you can
compute the probabilities:

P(k=0,A) = exp(-A) = 0.95 = 95%
P(k=1,A) = A*exp(-A) = 0.0487 = 4.9%

P(k>1,A) = 1 - P(k=0,A) - P(k=1,A) =
= 0.00127 = 0.1 %

P(k=2,A) = A^2 exp(-A) / 2 = 0.00125 = 0.1%


Now, they acknowledge 1% is two photon detections, which
is about ten times worse than the ideal Poissonian source
would yield for their A: P(k=1,A)=0.1%. In other words,
they haven't even reached the sharpest "single photon"
statistics allowed by classical EM, let alone got
beyond it. Even the ancient perpetuum mobile inventors
had been closer to making it over their pesky hurdle
than this.

Quote:
So the availability of inexpensive sources of true
'single photon' streams will undoubtably lead to
some interesting observations on dual slit experments.

The guys you linked to aren't even close to just a
very stable classical source. I have yet to see a genuine
theoretical/QED model of a realistic process which would yield
sub-Poissonian distribution using a perfect laser (Poissonian
or super-Poissonian) pump to drive some nonlinear generator
of single photons. Merely randomly blotting out events from
a Poissonian source always yields another Poissonian source,
just a sparser one (with smaller average A). It can't yield
the sub-Poissonian (hence non-classical) statistics, since
whatever the interaction Hamiltonian does to a single
photon state (sharp Fock state), it will do exactly the
same to the coherent superposition from the laser pump
(which is a superposition of single photon states with
Poissonian distribution of photon number observable),
hence the generator will yield at best a Poissonian
photon number output.

Quote:
I expect that given a stream of true single photons,
each photon will only excite a single grain on a
photographic film(or a single element on a ccd).


The "single photon" is infinite in spatio-temporal
extent (e.g. infinite plane wave). Coincidence
measurements and counts correlations are operationally
vacuous for such objects (since there is no element
of the formalism with localized properties that could
map into a time-space 'coincidence window' on the
empirical side).

Note also that EM vacuum fluctuations (or ZPF in
Stochastic electrodynamics) contain 1/2 vacuum photons
per EM mode. The E field of these vacuum photons superposes
its effects on film grains or ccd elements, with the
effects of the 'signal' field, no matter how stable the
'signal' field may be.

Finally, recall that "photons" are a mathematical
artifact of perturbative QED (where photons are
quanta of free EM field, introduced perturbatively
one by one, to mediate interactions between matter fields).
There are infinitely many different bases and coordinate
axes one can pick, thus different modes, hence different
'photons', superposing into the same given state.

There are also non-perturbative formalisms, empirically
equivalent to QED (up to at least alpha^5 order,
i.e. 8+ digits of precision), which eliminate EM
from the equations altogether and express the whole
dynamics in terms of (delayed/advanced) interactions
between fermion/matter fields. There are no photons
in such formalisms. See for example Barut's "Self
Field Electrodynamics". Barut references with brief
summary were discussed in couple recent
sci.physics.research posts:

http://groups.google.com/group/sci.physics.research/msg/386f48731520d145
http://groups.google.com/group/sci.physics.research/msg/bb1225c256c34c02
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Oz
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Posts: 155

PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

Blackbird <fake@nospam.no> writes
Quote:
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.

Hmm. Interesting. Do you have a reference to a paper or webpage?

It was posted here, probably on one of the "length of a photon" threads.
More likely one of the longer-standing resident experts will know
anyway.

Quote:
Furthermore this happened even if "the probability of two photons
being in the apparatus at one time approached zero".

To mee, this indicates that somehow the photon must interfere with itself.

Maybe, however bear in mind that each laser points at only ONE slit.
The light beams (one from each laser-slit) is only combined in the
apparatus.

single
SLIT
| <D
LASER>----------------------------<E
| <T
<E
| <C
LASER>----------------------------<T
| <O
<R

So neither laser beam goes through two slits yet a two-slit diffraction
pattern is observed.

Quote:
In any case anyone who has listened to MW radio knows that separate
radio transmitters on the same frequency can readily cause
interference patterns.

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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Oz
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PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

scerir <scerir@libero.it> writes

Quote:
Yes, but this does not mean that Dirac's
koan is wrong.

hmmm...

Quote:
Even a photon emitted by two sources (in such
a way that you cannot say which of the two sources
emitted the photon) interferes only with itself.

Hmmm....
given the experiment.

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.

Hmmm.... how very convenient....

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.

"Each photon then interferes only with itself.
Interference between two different photons
can never occur."
- P.A.M. Dirac, Principles of Quantum Mechanics,
Clarendon, Oxford, 1930, p.15.

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PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

Timo Nieminen <timo@physics.uq.edu.au> writes
Quote:
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.


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. One then looks to apparent quantum behaviour in the emitters
and/or detectors where of course one finds them.

All detectors I know about rely on an irreversible energy step which is
by nature quantum.

Quote:
It is an excellent demonstration that photons aren't like classical
billiard balls.

I would agree, they are waves.

NB I must logically also conclude that massive particles are also waves
and once again the quantised behaviour is due to something else. 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.

The only real problem I have with this is why masses (which one could
say is the wavelength in the time direction) for free elementary
particles is most certainly quantised. If the particles were in a box of
fixed length in the time direction then of course there would be no
problem at all. Ideally some interaction between mass and box-size
should result in only a few integral solutions that express the
particles that we see.

Clearly this is grossly oversimplified because really we should exchange
the word 'energy' for 'mass' in all the above and there are at least two
broad energy systems, that is electromagnetic and colour, and we don't
seem to have very good theoretical constructs unifying them.

--
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PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

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?

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PostPosted: Fri Jun 30, 2006 8:21 pm    Post subject: Re: Two-slit experiment Reply with quote

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.

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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Oh No
science forum addict


Joined: 06 Apr 2006
Posts: 82

PostPosted: Sat Jul 01, 2006 1:19 pm    Post subject: Re: Two-slit experiment Reply with quote

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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Timo Nieminen
science forum Guru Wannabe


Joined: 12 May 2005
Posts: 244

PostPosted: Sat Jul 01, 2006 1:19 pm    Post subject: Re: Two-slit experiment Reply with quote

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.

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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scerir
science forum beginner


Joined: 31 May 2005
Posts: 21

PostPosted: Sat Jul 01, 2006 1:19 pm    Post subject: Re: Two-slit experiment Reply with quote

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.

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.

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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Admral
science forum beginner


Joined: 07 Sep 2005
Posts: 22

PostPosted: Sat Jul 01, 2006 6:06 pm    Post subject: Re: Two-slit experiment Reply with quote

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.

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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Oz
science forum Guru Wannabe


Joined: 30 Apr 2005
Posts: 155

PostPosted: Sat Jul 01, 2006 6:06 pm    Post subject: Re: Two-slit experiment Reply with quote

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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