The next step I want to consider is the work from the mid thirties to about
the mid 60s. During this time, there were two developments that were
important to our discussion of the foundation of QM. The first was the
development of quantum field theory, or reletivistic quantum mechanics.
The second is the development of Bohm's hidden variable theory of QM.
Fortunately for us all, we don't need an expansive review of QED to obtain
the points relevant to this discussion. QED is a relativistic quantum
theory, consistent with special reletivity. Thus, it must be able to
explictly handle the SR requirement that there are no faster than light
signals.
This might seem very difficult, since we've established that, in QM, the
wave function can collapse over spacelike intervals. The answer lies in
what is a signal.
For example, we can make a spot on the moon travel faster than the speed of
light. Shoot a laser at the moon and change it's angle. One can make the
bright spot travel from one side of the moon to the other in a
microsecond....which is many times faster than the speed of light. But, no
signal travels from one side of the moon to the other. No information can
be sent on this moving point of light.
That is the key definition of a signal that we need to consider. Can
information be sent from one spot to another. With quantum superpositons,
can I make a measurement of one of the particles and know whether or not my
contemporary at the other end already made a measurement.
The reason this is critical is that, for spacelike events, A, and B; A is
before B in some reference frames, A and B are simulaneous in at least one
reference frame, and B is before A in some reference frames. So,. there is
no way one should be able to measure B and tell whether A has been
measured...if A and B are spacelike.
In reletivistic quantum mechanics, this is stated as "Spacelike operators
must commute." So, going back to our example of two spin 1/2 particles in
a spin zero state, if we have call the operator for measuring the spin of
particle 1: A and the operator for measuring the spin of particle 2: B, we
find that if we perform A then B on the wavefunction BA(|+-> +
|-+>)/sqrt(2) one gets |+-> half of the time and |-+> half of the time.
(the operator closest to the ket (which is what |>s are called) operates
first. If we perform B then A, we obtain exactly the same results. There
is no difference in the results if you perform A then B or B then A. So,
the operators do commute.
If one could pass information, one would have a real working ansible.
Fortunately, SF writers are able to modify the rules of QM, or we would
have missed out on some pretty good novels. But, such things, like db's
Uplift series are good fiction and bad science. :-)
This theoretical development was a real step forward in the completeness of
modern physics. Two theories of physics (SR and QM) are unified. A
significant question about the completeness of QM has been answered.
Still, there were a number of aestetic reasons why people wanted a more
"real" theory. One of them who had a hunch that there were hidden
variables that underlaid QM was David Bohm. In the '50s he developed a
hidden variable theory of QM.
It was considered fairly problematic at the time. There are several
reasons for this. First of all, a physicist is suspicious of any hidden
variable. Quarks were considered to be a mathematical convenience until
jets were observed. These high transverse momentum events showed structure
within protons and neutrons (the way the high angle scatters showed
pointlike electrons in the Rutherford scattering experiment.)
Now, quarks were very useful, even if they turned out to be a mathematical
convenience. One can see the deucouplet in terms of the combination of
three quarks:
uuu uud udd udd
uus uds dds
uss dss
sss
Where u is the up quark,
d is the down quark
and s is the strange quark
But, the order didn't need to come from structure within these hadrons; it
could have been just a property of the system. But, two things happened,
then. First, a fourth quark was predicted, and evidence for that fourth
quark was found. Second, as mentioned above, jets were found. At this
point, quarks became well established.
It may seem funny for physicists to worry about something that sounds
ontological; especially "shut up and calculate" physicists. Part of it, is
a question of permanence. Mathematical conveniences can be dropped in a
split second, when something slightly better comes along. Physicists do
not want to say "something exists" and then say it doesn't, and then say it
does, etc.
Second, physicists are suspicious of "really there, but you can't see it."
The reason for this is that it's quite straightforward to develop a
mechanism, such as the asymptotic freedom of quarks, to explain why these
real things can never bee observed independently. If one allows the
unconstrained existence of real but unobserved things in one's theory, then
one has almost unlimited license. One can make reality whatever one want.
Now, with the quarks, there was a constraint. They were constrained to
provide a system that explained the strange deucouplet. That was a big plus
in favor of the quarks. An even bigger plus was the fact that it
simplified the system.
Further, even apart from the jets and the fourth quark of electroweak,
there were other verifications. The zoo of particles could be explained as
higher order states of this three quark system. Thus, hundreds of
fundamental particles could be explained in terms of just three (and then
4, and finally 6). This simplification was a great plus.
So, we have the first hit against Bohm. It is a hidden variable theory.
The second hit is that it is, in many ways, the opposite of quarks. It
does not simplify; it complicates. Bohm's theory has a rather complicated
mechanism behind even the simplest of quantum mechanics: such as two
correlated polarized photons or two correlated spin � particles. As Paulie
said about Maxwell, any idiot can take something simple and make it
complicated; it takes a genius to take something complicated and make it
simple.
The third hit is that it doesn't work. Bohm never even got to the point of
constructing a toy model (a unrealistically small system in which the basic
features of a new theory or technique can be demonstrated.) He only had
arm waving generalities; he did not construct a system which allowed one to
turn the crank and obtain QM. This is in contrast with QED, where one can
turn the crank and obtain classical E&M or relativity, or statistical
mechanics, where one can obtain the results of thermodynamics.
All of these hits are basically non-lethal. It was still possible in the
'50s and early '60s to consider his hidden variable theory something that
would be a theory of real observables once we probed a bit deeper. But,
there was a big development in the mid-60s that eliminated hidden variable
theories from serious consideration. That will be in the next installment.
Dan M.
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