Feynman and
Squeezed States
Y. S. Kim
Univ. of Maryland
Feynman’s Poem about Physical Laws
The artists of the Renaissance said that man’s main
Concern should be for man, and there are other
things of interest in the world. Even the artists
appreciate sunsets, the ocean waves, the march of
the stars across the heavens. There is then some
reason to talk of other things sometimes. As we look
into these things we get an aesthetic pleasure from
them directly on observation. There is also a rhythm
and a pattern between the phenomena of nature
which is not apparent to the eye, but only to the eye
of analysis; and it is these rhythms and patterns
which we call Physical Laws.
Feynman’s Interpretation of Physics
The adventure of our
science of physics is a
perpetual attempt to
recognize that the different
aspects of nature are really
different aspects of
the same thing.
Feynman published approximately 150
papers on many different subjects of
physics. Was he making his perpetual
attempts to combine them into one
paper?
Then how?
Did he know what he was talking about?
Who writes Interpretations?
About Philosophers
• Worker of all Lands
Unite.
• The philosophers
have interpreted
this world in
various ways.
The point however
is to change it.
Physicists change the world by
writing down one equation
• Newton: one differential
equation for both comets
and planets.
• Schroedinger: one
equation for both running
and standing waves.
• How about Feynman?
Where is his one
equation?
How about Maxwell?
• Four Equations =
One set of Equations
for electricty and
magnetism..
• Applicable to the
Lorentzian World.
Feynman, Washington, 1970
Based on Feynman’s 1970 Talk
Feynman said!
• For Scattering problems, use Feynman
diagrams.
• For bound-state problems, use harmonic
oscillators.
• However, there were no Lorentz-covariant
oscillators in 1970.
• People said Feynman was absolutely crazy.
• But, I became excited about what he said,
and studied his physics systematically since
then. I also became crazy.
Feynman
talked about
many things.
Use
harmonic
oscillators
for Step 1.
Feynman said
Feynman’s One Equation
In his 1971 paper,
Feynman wrote down
one partial differential
equation to cover
both comets and
planets.
Where is the
Squeezed State?
Feynman’s One Equation
Hydrogen Atom becomes the Hadron
(bound state of two quarks) in the
Lorentz-covariant world.
Hadrons – Running waves
Quarks inside – Standing waves
Harmonic oscillators
Feynman was successful in
solving the mysteries of Regge
poles, but totally failed in
providing Lorentz-covariant
solutions of his own equation for
harmonic oscillators.
From the Lorentzian point of
view, his paper is total mess.
Feynman’s One Equation
In order to handle
the differential
equation Feynman
wrote down, we
have to import both
Wigner and Dirac.
Two famous brothers in law
Feynman said
Running waves and Standing Waves
Wigner’s Little Group
• The space-time symmetry inside the hadron is
smaller than the Lorentz group. It is isomorphic
to O(3), three-dimensional rotation group.
1962. I had a private
audience with Dirac
like Nicodemus with
Jesus
I asked Dirac what I
should do in Physics.
Dirac told me to study
Lorentz covariance.
Americans should
study more about this
subject.
When Dirac was talking about
Americans, he was talking about
Feynman. He was talking with
Feynman two months before I talked
three months before I talked to him.
Thus, one way to fix Feynman’s
problem was to import Dirac’s work.
Dirac and Feynman in Poland (1962)
• Dirac: construct a
beautiful mathematics.
• Feynman: mathematical
instrument that will
produce numbers which
can be compared with
numbers observed in
the real world.
Back to two famous brothers-in-law
• Dirac: Modern physics is the physics of
harmonic oscillators.
• Wigner: Modern physics is the physics of twoby-two matrices.
Theory of Everything in Physics
The same formula leads to
Top: Squeezed State
Bottom: Entangled State
Waves in Relativistic World
• There are running waves and standing waves.
• Running waves can be approximated by plane
waves. Running waves can be made Lorentzcovariant through the Klein-Gordon equation.
Thus, the S-matrix and Feynman diagrams.
This is called Quantum Field Theory. Is the field
theory capable of solving standing wave or
bound-state problems?
We started writing papers on
Feynmanism from 1973
2003
Covariant Bound States
(Standing Waves)
• Bound States: Hydrogen
Atom or
Harmonic Oscillators.
• Feynman chooses osc.
wave functions to
understand the covariant
world.
• Hadron consisting of two
quarks. Overall
coordinate and spacetime separation.
Time
separation
Feynman said
This set of formulas is identical to the
set we see in the coupled oscillators
• Squeezed State
• Entangled State
Dirac’s Quantum World
Dirac 1927
Time-energy uncertainty
without excitations.
C-number T-E
uncertainty.
Space-time asymmetry.
Dirac’s
Light-cone
System
(1949)
Lorentz-squeezed Hadron
Squeezed States in
Quantum Optics
Parton Picture
Coherence
to
Incoherence
Lorentz-covariant
Picture of Feynman’s
Parton Model
Parton Distribution Function
Time Dilation
External signal
sees quarks as free
independent
particles.
Feynman’s
decoherence
Since Einstein’s energy-momentum
relation (1905)
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Phys. Rev.
Letters
Two different aspects
(quarks and partons) of nature
coming from one thing!
The adventure of our
science of physics is a
perpetual attempt to
recognize that the
different aspects of
nature are really different
aspects of the same thing.
Feynman was a Kantianist,
so was Einstein.
Entropy Problem
• First, let us look at what he says about the density
matrix. In his 1973 book, Feynman says
Here again, Feynman talks like
a philosopher
• Here again, we can use harmonic
oscillators to see what he really had in
mind.
• In his original paper he uses a single
oscillator.
• We should use coupled oscillators to
decode what he was saying.
Rest of the universe -Entanglement
• X variable: we do
physics with.
• Y variable: we do not
observe. – rest of the
universe.
Two worlds are entangled.
Time
separation
hidden in the
present
form of
quantum
mechanics
Back to Space-time physics
• Time separation variable between the
quarks exists, but they are not observed
deeply hidden in the present form of
quantum mechanics .
• It indeed belongs to Feynman’s rest of the
universe.
Feynman’s Interpretation of Physics
The adventure of our
science of physics is a
perpetual attempt to
recognize that the different
aspects of nature are really
different aspects of
the same thing.
New Words in Physics
• Frogs: most of are frogs.
• Birds; Feynman is a bird.
Birds see the world as one world.
To Feynman, quantum optics and the
quark model belong to one world.
For more details, visit the
following webpages.
• http://www.ysfine.com
• http://www.ysfine.com/feynman