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When people do a study of, for
example, the double-slit experiment,
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and they approach the double-slit experiment
in the traditional way, one particle at a time,
00:00:06
a wave function that we can pretend
is moving in three-dimensional space,
00:00:09
but this is really just an artifact of the
fact that configuration space for one particle
00:00:13
looks three-dimensional. It looks like you
should treat the particle as a wave as it
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goes through the slits to get the correct pattern
over many repetitions of landing sites. You know,
00:00:24
we don't actually see a wave on the other side.
What we see is dots, many, many landing sites
00:00:28
over many repetitions of the experiment. The
wave is inferred. But when you measure where
00:00:33
the particle is at the end of the experiment,
or you measure which hole it goes through,
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you get a definite result, and that makes it
look more like a particle. So there's this idea
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that sometimes things are particle-like and
sometimes they're wave-like depending on what
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feature of the system we're trying to study.
This became known as wave-particle duality.
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This is further complicated by the fact that
there are waves of a different kind in physics.
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Electromagnetic waves, for example. Light is a
disturbance in the electromagnetic field that
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propagates like a wave through three-dimensional
space. And those are waves. I mean, like I said,
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I teach Jackson electromagnetism. We talk about
waves moving through three-dimensional space.
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It's very easy to confuse the waves of a field,
like the electromagnetic field, with the wave
00:01:22
functions or Schrodinger waves of quantum
mechanics. But they're not the same thing. And
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this has bled into the wave-particle duality. When
Planck in 1900 and Einstein in 1905 and various
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people were proposing that light came in quanta,
discrete particle-like quanta called photons,
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the wave that they were imagining was the wave
corresponding to photons was a three-dimensional
00:01:51
electromagnetic wave, a wave of the familiar
kind of wave. The wave functions that Schrodinger
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introduced in 1926 were not like those waves.
They were not three-dimensional waves in physical
00:02:06
space of a field. They were these abstract,
complex-valued functions in a high-dimensional
00:02:14
configuration space. And when you measured them,
they collapsed. Now, if you're in an MRI machine
00:02:21
and they've turned on a very strong magnetic
field, you don't have to worry that if you do
00:02:26
the wrong measurement you're going to collapse the
magnetic field in the MRI machine. It's not that
00:02:30
kind of field. The waves they're beaming at you
are not those kinds of waves. So you have to make
00:02:36
a distinction between the old waves, the waves of
a field, and Schrodinger waves. And I want to make
00:02:42
super clear that in the indivisible stochastic
approach to quantum mechanics that we've been
00:02:47
talking about, I'm saying Schrodinger waves are
not real things. These abstract things that live
00:02:51
in this high-dimensional configuration
space, those are not physically real.
00:02:57
But classical waves or the waves of a field, which
are a different, conceptually different kind of a
00:03:02
wave, those are perfectly valid. And if you're
studying a system that's not made of particles
00:03:07
but a system made of fields, you're going to
see wave-like behavior as well, but those are
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a different kind of wave. And these are the kinds
of subtleties that I think get lost when someone
00:03:16
just says wave-particle duality. So again, just
to summarize, the relationship between a photon,
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a particle of light, and an electromagnetic
wave is not like the relationship between an
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electron and a Schrodinger wave function for
the electron. Now what makes this even more
00:03:33
confusing is that electrons do have fields also.
There's a so-called Dirac field that plays a very
00:03:39
important role in the standard model. And this
is a field, a field in three dimensions for the
00:03:45
electron. But the Dirac field for the electron
is not the Schrodinger wave for an electron. So
00:03:54
these are super subtle distinctions, but it's
important to keep them in mind. What makes
00:03:59
it even more confusing is that particles like
electrons, which are called fermions, these are
00:04:03
particles that have an intrinsic half-integer
spin. They're the particles that obey a Pauli
00:04:07
exclusion principle. You can't put them all in the
same energy state. They make chemistry possible by
00:04:12
not having all the atoms collapse at the ground
state. Electrons are like this, quarks, protons,
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neutrons. Although they have fields associated
with them, the fields associated with them are
00:04:21
not classical fields like the electromagnetic
field. The fields are much more bizarre and weird.
00:04:28
And I'm not gonna have time to talk very
much about them except to say that one of the
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limitations of Bohmian mechanics is that it has
a great deal of difficulty dealing with the kinds
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of fields associated with fermions. And that's
one reason why Bohm mechanics has difficulty,
00:04:41
the Bohm pilot wave theory. I'm getting way ahead
of myself, but I just wanted to just clarify
00:04:46
what's going on in wave particle duality. So in
the indivisible stochastic approach, there are no
00:04:52
Schrodinger waves as part of the fundamental
physics. Of course, you can, when you go to
00:04:55
the Hilbert space picture, you can mathematically
write down wave functions and use them, write down
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Schrodinger waves, but they're not physically
there. You don't need them to explain the
00:05:03
interference patterns. The indivisible stochastic
dynamics itself generically predicts that you'll
00:05:08
have what look like over many repetitions of the
experiment, dots that look like they're following
00:05:13
some kind of wave equation. But there is no wave
actually involved in those experiments. But I'm
00:05:18
not saying that field waves, the waves in fields
are not there. That's a different kind of wave.
00:05:25
So speaking of these waves, you mentioned quantum
field theory indirectly with Dirac. Does your
00:05:32
approach illuminate any aspect of quantum field
theory or the standard model? We've been talking
00:05:37
about quantum mechanics, sure, especially in part
one and part two. What about QFT? Yeah. So one of
00:05:43
the nice things about Bohm's pilot wave theory
is that it works really beautifully for systems
00:05:49
of fixed numbers of finitely many non-relativistic
particles. That's a lot of qualifications. Doesn't
00:05:55
work so easily for fields. You end up either
having to do very complicated things or maybe even
00:06:02
reducing stochasticity of some kind. It gets kind
of messy and there's a lot of difficulty handling
00:06:07
fermionic fields in particular, the fields
associated with particles like electrons. One of
00:06:14
the advantages of this approach is although, okay,
so let me just say something very quickly about
00:06:21
Bohmian mechanics. Now this is different because
this is also related. In Bohmian mechanics for,
00:06:26
again, systems of fixed numbers of finitely many
non-relativistic particles, we have deterministic
00:06:30
equations. There's a pilot wave that guides
the particles around. The wave function, the
00:06:35
pilot wave obeys the Schrodinger equation. Then
another equation called the guiding equation is
00:06:39
how the wave function, the pilot wave guides the
particles around. And everything is deterministic.
00:06:44
There's no fundamental probabilities. There
are some initial uncertainties in the initial
00:06:49
configuration of the system. And these evolve to
become the Born rule probabilities later. But the
00:06:55
dynamics is fundamentally deterministic and is
not generating the probabilities in a fundamental
00:07:00
law-like way. This picture is in some ways very
elegant, provided you're okay with a pilot wave
00:07:08
living in a high dimensional configuration
space. Although I should say that Goldstein,
00:07:13
Durer, and Zanghi have already proposed the idea
that the Bohmian pilot wave is law-like and not
00:07:20
a physical thing. So there are other ways to read
this theory. The problem is it helps itself to a
00:07:26
lot of very special features of models that
consist of fixed numbers of finitely many
00:07:31
non-relativistic particles. Features that are
unavailable when you go to more general systems
00:07:36
like fields. So you end up having to write down
a very different looking model, including in some
00:07:42
cases models that you need to now deal with
stochasticity and indeterministic dynamics.
00:07:47
And they just don't really work very well when
you try to go beyond. One of the other things
00:07:52
that Bohmian mechanics requires is a preferred
foliation of space-time. So last time we spoke
00:07:57
we talked about how in special relativity there's
no preferred way to take space and time and divide
00:08:02
it up into moments of time, like different ways
to do it. The guiding equation, the equation
00:08:07
that takes the pilot wave and explains how the
pilot wave, obeying the Schrodinger equation,
00:08:10
how the pilot wave guides the particles
around, they call the guiding equation,
00:08:14
depends on there being a preferred foliation
of space-time, a slicing of space into moments
00:08:20
of time. That's also not really great. It
works fine in the non-relativeistic case,
00:08:24
but we want to do relativistic physics like we
often do when we want to do quantum field theory,
00:08:27
which is the kind of models we use when we want to
deal with special relativity and quantum mechanics
00:08:32
together, as in the standard model. Preferred
foliation is really difficult to deal with,
00:08:37
not impossible, but it'd be nice if we didn't
need it. In the indivisible stochastic approach,
00:08:44
there's no guiding equation. There's no pilot
wave. It's not that you solve the Schrodinger
00:08:49
equation, get a pilot wave, and then take the
pilot wave and plug it into a guiding equation,
00:08:52
which depends on a preferred foliation and then
the guiding, none of that happens. There's just
00:08:56
the indivisible stochastic dynamics, which
can be represented in Hilbert space language,
00:09:02
but the dynamics is just directly happening.
There's no middleman. There's no pilot wave
00:09:08
and guiding equation in the middle. This means
the theory is not going to be deterministic. I
00:09:12
think one question in the comments is, is
this fundamentally deterministic or not?
00:09:15
It's indeterministic. It's not a deterministic
theory, but because there's no guiding equation,
00:09:19
there's no preferred foliation. Because we're
not relying on all these special features of
00:09:25
the particle case, it's perfectly easy to now
generalize this to more general kinds of systems.
00:09:31
Have you done it? Have I done it? Good question.
There's this thing called time. Time is bounded
00:09:40
and limited. Is it? It is, amazingly. In your
framework? At least in my life. Okay. And when
00:09:48
we get to open questions like research directions,
which maybe people watching this may be interested
00:09:52
in because, I mean, the best part of a new
formulation or picture or model or whatever is,
00:09:57
are there things people can work on? There are
things people can work on. This is one of the
00:10:00
things people can work on. So it is, the term here
is straightforward in principle to generalize this
00:10:08
to quantum fields because there's no, none of the
obstructions are there like they were before. One
00:10:12
of the problems with Bohmian mechanics is
your wave function has to live in a space,
00:10:17
configuration space. And fermionic particles don't
have a familiar kind of configuration space. This
00:10:23
is what makes it so hard to do Bohmian mechanics.
But there's no pilot wave here so you just don't
00:10:26
even have that obstruction. So many of the things
that would have obstructed us from just applying
00:10:30
this to any kind of system are just, they're just
not there anymore. So if you want to deal with a
00:10:34
field theory, you just replace particle positions
with localized field intensities. These become
00:10:40
your degrees of freedom. And then you just apply
the stochastic laws to them and it works the usual
00:10:44
way. The problem with quantum field theory is
that quantum fields in general is that they have
00:10:49
infinitely many degrees of freedom, infinitely
many moving parts. At every sort of point in space
00:10:54
in the most sort of, you know, I mean, this is
a whole renormalization story of effective field
00:11:00
theory. But like at a simplest sort of like bird's
eye view, you have a degree of freedom at every
00:11:04
point in space, infinitely many of them. And this
makes them very mathematically difficult to deal
00:11:08
with. Even in the traditional Hilbert space or
path integral formulation, quantum field theories
00:11:13
are really mathematically tricky. And there
are very few, if any, I think there are none,
00:11:18
rigorously defined quantum field theories that
are also empirically adequate. Like none of the
00:11:24
quantum field theories that make up the standard
model have been rigorously defined. This means
00:11:29
that anytime you mention quantum field theory,
you're going to run into mathematical difficulties
00:11:33
that are just because quantum field theory is
mathematically very complicated. So I think
00:11:39
there's a research direction for an enterprising
student to not only formulate quantum field theory
00:11:46
in this language, but also see does it make any
of the mathematical difficulties easier? Do any of
00:11:52
them become harder? Like what exactly does it look
like when you do this super carefully? And that's,
00:11:58
I would say, an open research question. But
many of the obstructions that are in the way in,
00:12:03
for example, Bohmian mechanics are no longer in
the way here. New update! Started a Substack.
00:12:09
Writings on there are currently about language
and ill-defined concepts as well as some other
00:12:14
mathematical details. Much more being written
there. This is content that isn't anywhere else.
00:12:19
It's not on Theories of Everything. It's not on
Patreon. Also, full transcripts will be placed
00:12:24
there at some point in the future. Several people
ask me, Hey Curt, you've spoken to so many people
00:12:29
in the fields of theoretical physics, philosophy,
and consciousness. What are your thoughts?
00:12:34
While I remain impartial in interviews,
this Substack is a way to peer into my
00:12:39
present deliberations on these topics. Also,
thank you to our partner, The Economist.
