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<DIV>There’s some good stuff here John. </DIV>
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<DIV style="font-color: black"><B>From:</B> <A
title=John.Williamson@glasgow.ac.uk
href="mailto:John.Williamson@glasgow.ac.uk">John Williamson</A> </DIV>
<DIV><B>Sent:</B> Monday, March 09, 2015 6:43 AM</DIV>
<DIV><B>To:</B> <A title=general@lists.natureoflightandparticles.org
href="mailto:general@lists.natureoflightandparticles.org">Nature of Light and
Particles - General Discussion</A> </DIV>
<DIV><B>Subject:</B> [General] The electron as a point particle: the
experimentalevidence.</DIV></DIV></DIV>
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<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Dear
Ladies and Gentlemen,</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">This is a
quick note in the spirit of a club both Martin and I belong to, the fanaten, a
science study club of which Martin and I were founder members a quarter of a
century ago. It is still going strong with regular mutual educational seminars.
I do not attend, or contribute, as often as I would like – because I no longer
live in Holland. This stuff could form the basis of talk to them at some point –
what do you think Martin? Within the context here, it is intended to be simply
educational. The main aim is to discuss whether or not the electron may, or may
not, be a point. The discussion here is primarily on the basis of two
experiments I carried out personally. There are many more in the literature –
including those an the difference between centre of charge and centre of spin
which have become current (see refs in other paper I sent – the one that is too
dangerous for arXiv!).</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Though
current work seems to focus on theory I should reveal that I do not see myself
as, primarily a theorist. Firstly, a natural philosopher, secondly an engineer,
and only thirdly a (not very good) theorist. I think my theory is ok, in theory.
It is just not very good in practice. I sometimes think I could make a sign
error in signing my name. Martin is much better – think I have only found a sign
error for him once!</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb"><SPAN
style="mso-spacerun: yes"> </SPAN>Anyway, for much of my career I was an
experimentalist and engineer. My job at Philips was to propose and design new
devices, to build and develop a measurement facility for them, to carry out the
actual experiments and to interpret the results. I designed a couple of devices
more than a quarter of a century ago. One of these was the “quantum point
contact”, the other the “single electron electrometer” or “single electron
pump”. These were pretty successful in taking science forwards at the time – the
first (mostly with Henk van Houten or Bart van Wees as “first” author) pretty
much took over the lions share of articles at solid state conferences at the
time. The second – driven by the excellent Leo Kouwenhoven – continues to make
significant impact today. In such experiments we looked at electrons in the
solid state. Often single electrons in the solid state. This is why I know so
much about them and the real meaning of their experimental properties in this
regime: I carried out a good number of the seminal experiments personally.
</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">The
attached paper is one of these. My usual-co-authors declined to be involved with
this particular one, partly because they found it a bit weird (and possibly even
dirty). Timmering made the device, Foxon and Harris grew the (best in the world)
material, and the excellent Kees Harmans was an all-round good guy from Delft .
My role was the initial conception of the device, the optimisation of the
measurement electronics and cryogenics, the (late night) experimental
measurements and the interpretation of the results. Having said this, my
initial<SPAN style="mso-spacerun: yes"> </SPAN>- and continuing -
interpretation, did not make it into the actual paper. Parts were taken out on
the insistence of more influential people in the group – mainly Henk, who said
that “mensen zullen het niet begrijpen” (people will have trouble understanding
it). Others were removed by referees. The final humiliation was that Physical
review insisted on changing the title to include the word “contours” in place of
the word “landscape”. The word “contours”, as you will note if you read it,
appears only once in the article: in the title. The abstract, luckily, remained
un-bowdlerised. <SPAN style="mso-spacerun: yes"> </SPAN>No matter- the
experiment itself was sound and I am still here to say now what I think it
really means. Also there is a typo at the bottom of page 7677 about the shifting
of odd models – just to poke a bit of fun.</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">The
experiment allowed the (landscape of the) lateral charge profile of single
quantum-confined electrons, at a current low enough that they came over one at a
time,<SPAN style="mso-spacerun: yes"> </SPAN>to inter-act with the
(landscape of the) locality of the quantum point contact. The electron landscape
was that familiar from quantum mechanics textbooks, with a single lobe for one
half wavelength , a double lobe for two, three for three and so on. The observed
quantised conductance depends on that number with 2 units of conductance (for
spin up and spin down) per quantum mechanical sub-band. What the experiment
shows, is that the charge profile of individual electrons in the solid state is,
experimentally, spread over a few tens of nanometres. This charge interferes
with that of the crystal charge distribution in such a way as to exclude certain
sub-bands from transmission. These objects are BIG. The effective electron
charge distribution is similar to that which one would expect from the
interpretation of wave-mechanics. In that interpretation the biggest electron in
a single crystal metal sliver is twice as big as the sliver (folded over on
itself as it moves back and forth in a single-wavelength standing mode).
Electrons in the solid state really do (experimentally) blow up to, literally,
macroscopic sizes.</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">If that
does not give the lie to the concept that the “electron is a point”<SPAN
style="mso-spacerun: yes"> </SPAN>- I do not know what will.</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Let me
come back to another field in which I was personally involved and the
experimental “proof” that the electron is measured to be a point in high-energy
scattering experiments. This belief is widely held- even amongst experimental
high-energy professionals. The theoretical wing believes implicitly this as one
of the major commandments about the fundamental nature of the electron.
Completely undeterred by the fact that they can all calculate that this cannot
be the case from simple energy considerations, they will consider any suggestion
to the contrary dangerous and delusional. I think the reason is that the
electron is considered a point in the (well tested) quantum electrodynamics.
Well tested it may be, but this is to confuse theory with reality. It is also to
place old classical theory of mundane things such as field and energy as of no
consequence when compared to big- sexy new field theory (QED). If you want a
good laugh you should listen to some of these guys trying to argue with me in
person. They lose. Fast. </SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">This is
because I am quite lucky in that, not only to I understand both QED and
classical physics, but also I was one of the physicists who carried out the
actual experiments. This means that I am in a position to not only suspect this
is all bullshit, but also to know precisely why. It then becomes no contest:
think Harrison Ford – they whip –me gun.</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">The fact
of the matter is that the electron is observed to be point-like and not to be a
point. That is the point. Any spherically symmetric distribution of
energy-conserving objects will act in this way. The energy conservation ensures
that the forces are inverse square and the corresponding potentials 1/r. Any
distribution of these- if itself spherically symmetric, has a point-like
interaction. <SPAN style="mso-spacerun: yes"> </SPAN>I teach this stuff in
second year maths. Its easy. It is in 19<SUP>th</SUP> century textbooks. It is
probably in Newton’s “Principia” – though I have not looked. That stuff has not
gone away just because Richard Feynmann thought of a (very neat!) way of
removing some calculational difficulties in electrodynamics</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">An analogy
is the gravitational interaction. It too is inverse square in force and hence
1/r in potential. Spherical objects, such as the earth (roughly) act under
gravitation as though their mass was concentrated at a point. If you do not
believe me just try doing the integrations – they are not hard. This is just
Newtonian gravitation. If you think this proves the earth is therefore a point
just try looking out of the window. It really is this stupid!</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Also what
goes into QED is not, essentially, that the electron is a point. What goes in is
that electrons emit photons with a certain probability (about 1/137). The point
bit arises because of problems in the interpretation of the detail of this – the
renormalisation scheme. This deals with the infinites by simple dividing them
out. We need something better. A reason that the required length scale is (as
Dirac pointed out) lambdac/4 pi. By a strange co-incidence this is just the
characteristic length scale in the Martin-John model. Funny huh?</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Ok … that
is enough for now. Need to get back to thinking about important things like
organising an exam on vectors and complex numbers ….</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">Cheers,
</SPAN></P>
<P class=MsoNormal><SPAN
style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">- John
Williamson.</SPAN></P>
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style="FONT-SIZE: 10pt; FONT-FAMILY: times; mso-ansi-language: en-gb">
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