(Atomic-sized particles / Particle waves / Quantum mystery)
In this section, Feynman discusses atomic-sized
particles, particle waves, and the central quantum mystery that are related to quantum mechanics
(instead of atomic mechanics). Perhaps this chapter is outdated to a certain
extent and some physicists may not agree with Feynman’s views of quantum
mechanics. For example, during an interview*, John Clauser
says that: “[w]ell, Columbia was dramatically bigger. But Columbia not only had
a counterpart to Feynman, i.e. T.D. Lee who certainly— Frankly, I think he was
a much brighter guy. I didn't particularly care for Feynman. I didn't really
like him very much. And frankly a lot of the stuff that he did and said was
wrong, especially in foundations of quantum mechanics.” However, Clauser was
willing to question these foundations, leading to his experiments with quantum
entanglement that eventually earned him a Nobel Prize.
Furthermore, in a Q & A session**,
Clauser reveals: “[w]hile I was performing the
1972 Freedman–Clauser experiment at UC Berkeley, Caltech's Richard Feynman was
highly offended by my impertinent effort and told me that it was tantamount to
professing a disbelief in quantum physics. He arrogantly insisted that quantum
mechanics is obviously correct and needs no further testing!” In short, Feynman
viewed Clauser’s effort as unnecessary, or “impertinent,” because Feynman
believed quantum mechanics was already proven and didn’t require further
validation. It seems to imply that
Clauser might miss the opportunity to perform the experiments that eventually
earned him the Nobel Prize.
However, in
a lecture on gravitation delivered to graduate students, Feynman explains: “…we
should always keep in mind the possibility that quantum mechanics may fail,
since it has certain difficulties with the philosophical prejudices that we
have about measurement and observation (Feynman et al., 1995, p. 15).” It is
possible that Feynman changed his views of quantum mechanics over time.
*Interview of John Clauser
by Joan Bromberg on 2002 May 20, Niels Bohr Library & Archives, American
Institute of Physics, College Park, MD USA,
www.aip.org/history-programs/niels-bohr-library/oral-histories/25096
**Q&A
(2022 Sep 20) with Caltech alumnus John Clauser on his experimental proof of
quantum entanglement: https://www.caltech.edu/about/news/proving-that-quantum-entanglement-is-real
1. Atomic-sized particles:
“In discussing these, we
will find that the “classical” (or older) theory fails almost immediately,
because matter is really made up of atomic-sized particles (Feynman et al., 1963, p. 37–1).”
It could be confusing for Feynman to explain that matter is really made up of atomic-sized particles. Firstly, the term particle is treated as a point-like entity with no spatial extension; this means that it has no size, shape, or internal structure. Secondly, the so-called particles like electrons could be described by probability clouds or wave packets that can spread out over space, i.e., they exhibit wave-like behavior, such as interference and diffraction, under certain conditions. Thirdly, the observed particle-like behaviors are manifestations of underlying fields that pervade space from the perspective of quantum field theory. Essentially, the notion of particles as idealized dimensionless objects is a mathematical construct that simplifies calculations, however, it is limited, not directly observable, and may be considered unsatisfactory from a philosophical or conceptual viewpoint.
Note:
In the next chapter, Feynman clarifies: “… the idea of a
particle is limited. The idea of a particle—its location, its momentum,
etc.—which we use so much, is in certain ways unsatisfactory (Feynman
et al., 1963, p. 38–1).”
Feynman was a “particle-guy” because he preferred
particle-based approach and developed methods (path integral formulation and
diagrams) that emphasize particles and their interactions. In his Nobel speech,
Feynman (1966) says: “Well, it seemed to me quite evident that the idea that a
particle acts on itself, that the electrical force acts on the same particle
that generates it, is not a necessary one – it is a sort of a silly one, as a
matter of fact. And, so I suggested to myself, that electrons cannot act on
themselves, they can only act on other electrons. That means there is no field
at all (Feynman, 1966, p. 32)…We also found that we could reformulate this
thing in another way, and that is by a principle of least action. Since my
original plan was to describe everything directly in terms of particle motions,
it was my desire to represent this new theory without saying anything about
fields (Feynman, 1966, p. 35).” However, characterizing him solely as a
"particle-guy" oversimplifies his nuanced view.
Feynman was later a “field-guy” who recognized the
essential role of fields, striving to simplify and unify the
understanding of quantum phenomena through his field theory. In Wilczek’s
(2008) words, “As for Feynman, he gave up when, as
he worked out the mathematics of his version of quantum electrodynamics, he
found the fields, introduced for convenience, taking on a life of their own.
He
told me he lost confidence in his program of emptying space when he found that
both his mathematics and experimental facts required the kind of vacuum
polarization modification of electromagnetic processes depicted - as he found
it, using Feynman graphs ... In describing this process, it becomes very
difficult to avoid reference to space-filling fields (p. 89).” Feynman’s
transition to a “field-guy” was driven by the realization that fields are
essential for accurately describing quantum phenomena, despite his initial
preference for particles.
2. Particle waves:
“There is one lucky break, however—electrons behave just like light. The
quantum behavior of atomic objects (electrons, protons, neutrons, photons, and
so on) is the same for all, they are all “particle waves,” or whatever
you want to call them (Feynman et al., 1963, p. 37–1).”
In a sense, it is potentially
misleading to say that atomic or subatomic objects are all “particle waves,” “wavicles,”
or whatever you want to call them. These terms may imply that the objects are simultaneously particles and
waves, which is paradoxical. Specifically, electrons are neither particles with
wave-like properties nor waves with particle-like properties, but they are now idealized
as “electron fields” (or “quantum fields.”) Generally speaking, the wave-like
and particle-like behaviors of atomic objects observed in experiments of quantum
mechanics can be understood as different manifestations of fields. For example,
interference patterns arise from the superposition principle applied to field
amplitudes, while discrete detection events correspond to the quantization of
these fields.
“Newton thought that light was made up of particles, but then it was
discovered, as we have seen here, that it behaves like a wave. Later, however
(in the beginning of the twentieth century) it was found that light did indeed
sometimes behave like a particle. Historically, the electron, for example, was
thought to behave like a particle, and then it was found that in many respects
it behaved like a wave. So it really behaves like neither. Now we have given
up. We say: ‘It is like neither’ (Feynman et al., 1963, p. 37–1).”
Currently, "field-particle duality" may
replace "particle-wave duality" for four reasons: 1. Alignment
with Quantum Field Theory: It reflects
the principles of quantum field theory, where “particles are avatars of fields
(Wilczek, 2021, p. 99).” 2. Unified Framework: It provides a coherent description of quantum phenomena, integrating
wave-like and particle-like behaviors with probability waves. 3. Experimental
evidence: It aligns with the
interference patterns of double slit experiment showing that particles emerge
from and interact through fields. 4. Conceptual consistency: It resolves the apparent paradox of
wave-particle duality and offers a clearer, more accurate ontological
perspective on the nature of quantum entities. For example, an electron can be
understood as a quantum excitation of the electron field and its motion is
influenced by the electromagnetic field and guided by its probability wave (or wave
function).
Defining quantum mechanics as “the description of
the behavior of matter in all its details and, in particular, of the happenings
on an atomic scale” can be considered inadequate. In short, it is not only
concerned with atomic-scale phenomena but also with subatomic particles (e.g., quarks
and gluons) and larger systems (molecules, superconductors, and macroscopic
systems exhibiting quantum behavior). To be more precise, quantum mechanics is
the description of the behavior and interactions of energy and matter from
subatomic particles to molecules, using principles that include uncertainty,
superposition, and probabilistic outcomes. In short, it incorporates the principle
of uncertainty and wave function to provide a framework for understanding the
uncertainties and statistical nature of quantum systems. The principles of
quantum mechanics are also important to the prospect of quantum computation,
quantum cryptography, and quantum teleportation.
3.
Quantum mystery:
“The gradual accumulation of information about atomic and small-scale
behavior during the first quarter of the 20th century, which gave some
indications about how small things do behave, produced an increasing confusion
which was finally resolved in 1926 and 1927 by Schrödinger, Heisenberg,
and Born (Feynman et
al., 1963, p. 37–1).”
Feynman’s above-statement oversimplifies the
historical development of quantum mechanics. For example, the Dirac equation is
crucial for understanding the behavior of electrons and the existence of
antimatter, but it was derived in 1928. On the other hand, the Aharonov–Bohm (AB)
effect was not known in 1927. In Feynman’s (1964) words, “It seems strange in
retrospect that no one thought of discussing this experiment until 1959, when
Bohm and Aharonov first suggested it and made the whole question crystal clear
(p. 15-12).” The effect reveals the profound and unexpected role of
electromagnetic potentials in quantum mechanics. This effect has become a key
example in quantum mechanics, showing the mysterious and counter-intuitive
nature of quantum phenomena. It should be worth mentioning that AB effect can
be considered as a quantum mystery and the investigation of the effect
remains far from completed.
“We choose to examine a phenomenon which is impossible, absolutely
impossible, to explain in any classical way, and which has in it the heart of
quantum mechanics. In reality, it contains the only mystery.
We cannot explain the mystery in the sense of “explaining” how it works. We
will tell you how it works. In telling you how it works we
will have told you about the basic peculiarities of all quantum mechanics (Feynman et al., 1963, p. 37–2).”
Another quantum mystery
is the spin-statistics relation. In a 1996 issue of Caltech’s Engineering
& Science magazine, Goodstein writes: “I said to him, ‘Dick, explain to me, so that I can
understand it, why spin one-half particles obey Fermi-Dirac statistics.’ Sizing
up his audience perfectly, Feynman said, ‘I’ll prepare a freshman lecture on
it.’ But he came back a few days later to say, ‘I couldn’t do it. I couldn’t
reduce it to the freshman level. That means we don’t really understand it’ (Feynman
et al., 1997, p. 52).” Interestingly, in a 1984 letter to David Mermin, Feynman
asked whether Mermin has a clear explanation of the relation of spin and
statistics. However, in the 1986 Dirac Memorial Lecture, Feynman explains the spin-statistics
rule as “[t]he effect on the wave function of the exchange of two
particles is the same as the effect of rotating the frame of one of them by
360° relative to the other’s frame (Feynman & Weinberg, 1999, p. 57).” In
addition, he illustrates the rule by twisting two ends of a belt as shown
below.
 |
| Source: (Feynman & Weinberg, 1999) |
Note: Feynman’s
letter to David Mermin concerns two quantum mysteries (quantum entanglement and
spin-statistics relation): “All my mature life I have been trying to distill
the strangeness of
quantum mechanics into simpler and simpler circumstances. I have given
many lectures of ever increasing simplicity and purity. I was recently very
close to your description (down to six states, instead of three, etc.) when
your ideally pristine presentation appeared. I have since copied it almost
exactly (with attribution, of course) in several recent lectures on the
subject. Thank you. I have been making a similar series of attempts to explain
the relation of spin and statistics. Can you do as well there? Perhaps if we
meet someday we can discuss it together and create a clear explanation of why
exchanging two particles implies a tacit rotation of the axes of one by 360
degrees relative to the other (Feynman, 2005, pp. 367-368).”
Perhaps Feynman would disagree with himself that there
is only one quantum mystery. Recently, some
researchers showed that the two quantum mysteries, wave–particle duality and
uncertainty principle, are equivalent using wave-particle duality relations and
entropic uncertainty relations (Coles, Kaniewski, & Wehner, 2014). However, wave–particle duality is not really a
mystery from the perspective of quantum fields. In his book titled More than one mystery, Silverman (2012) disagrees
with Feynman and suggests that there are three more quantum mysteries:
Aharonov-Bohm effect, spin-statistics relation, and quantum entanglement. In a
sense, these quantum mysteries are inter-related and could be reduced to one:
the need to sum probability amplitudes over all paths in the appropriate
configuration space. However, there could be more quantum mysteries, such as quantum
measurement problem and quantum reality, depending on how one classifies and
interprets the mysteries (or paradoxes).
In short, quantum entanglement refers to two or more
particles become correlated in such a way that the state of one particle
instantly influences the state of the other, regardless of the distance between
them. In a paper titled Simulating physics with computers,
Feynman discussed quantum entanglement, that is, another quantum mystery. In
Feynman’s (1982) words, “…. we always have had a great deal of difficulty in
understanding the world view that quantum mechanics represents. At least I do,
because I'm an old enough man that I haven't got to the point that this stuff
is obvious to me…… I cannot define the real problem, therefore I suspect
there's no real problem, but I'm not sure there's no real problem. So that's
why I like to investigate things. Can I learn anything from asking this
question about computers--about this may or may not be mystery as to what the world view of
quantum mechanics is? So I know that quantum mechanics seem to involve
probability--and I therefore want to talk about simulating probability. Well,
one way that we could have a computer that simulates a probabilistic theory,
something that has a probability in it, would be to calculate the probability
and then interpret this number to represent nature… (p. 471).”
Review
Questions:
1.
Do you agree with Feynman that matter is made up of atomic-sized particles?
2. Are atomic objects (electrons, protons, neutrons) all “particle waves”?
3. Is there only one
quantum mystery? Surely, Feynman was joking? Or what are the quantum mysteries?
The
moral of the lesson: Quantum entities exhibit particle-like or wave-like
properties depending on the experimental conditions, but they are neither
particle nor waves; currently they are idealized as quantum fields.
Note: Feynman was likely influenced by the views of John Archibald
Wheeler, his PhD supervisor, on quantum mechanics. In Wheeler’s words: “I think
of my lifetime in physics as divided into three periods. In the first period… I
was in the grip of the idea that Everything is Particles… I call my second period Everything is Fields… Now
I am in the grip of a new vision, that Everything is Information (Wheeler, 2010, p. 63-64).”
References:
1. Coles, P. J., Kaniewski, J., & Wehner,
S. (2014). Equivalence of wave–particle duality to entropic uncertainty. Nature
communications, 5(1), 5814.
2. Feynman, R. P. (1982). Simulating physics with
computers. International Journal of Theoretical Physics, 21(6-7),
467–488.
3. Feynman, R. P. (1966). The development of
the space‐time view of quantum electrodynamics. Physics Today, 19(8),
31-44.
4. Feynman, R. P. (2005). Perfectly reasonable deviations from the
Beaten track: The
letters of Richard P. Feynman (M.
Feynman, ed.). New York: Basic Books.
5. Feynman,
R. P., Goodstein, D. L., & Goodstein, J. R. (1997). Feynman's lost
lecture: the motion of planets around the sun. London: Vintage
6. Feynman, R. P., Leighton, R. B., &
Sands, M. (1963). The Feynman
Lectures on Physics, Vol I: Mainly mechanics, radiation, and
heat. Reading, MA: Addison-Wesley.
7. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.
8. Feynman, R. P., Morinigo, F. B., &
Wagner, W. G. (1995). Feynman Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley.
9. Feynman, R. P., & Weinberg, S.
(1999). Elementary particles and the laws of physics: The 1986 Dirac
memorial lectures. Cambridge: Cambridge University Press.
10. Silverman, M. P. (2012). More
than one mystery: explorations in quantum interference. New York: Springer
Science & Business Media.
11. Wheeler, J. A. (2010). Geons,
black holes, and quantum foam: A life in physics. New York: WW Norton &
Company.
12. Wilczek, F.
(2008). The lightness of being: Mass, ether, and the unification of
forces. New York: Basic Books.
13. Wilczek, F.
(2022). Fundamentals: Ten keys to reality. New York: Penguin.
