Transcript Albert Einstein and the Question of Reality

Dennis Blejer
October 21, 2006
Tagore on Einstein
“His is what might be called transcendental materialism,
which reaches the frontiers of metaphysics, where there can be
utter detachment from the entangling world of self.
To me both science and art are expressions of our spiritual nature,
above our biological necessities and possessed of an ultimate value.
Einstein is an excellent interrogator.”
Motivation
• Is the universe real? What is the nature of physical reality?
Read from: A. Einstein, Philosopher-Scientist, p 248 & p 5.
• “Any one who looks at the creation and wants to know about
it finds diverse manifestations. So he wants to know what force
is working behind it, who has made it possible, or what is that
force which has brought about such a gigantic creation in
existence and keeps it going?” - Shantananda Saraswati, 1965
• Physical science also asks “what are the basic elements of the
universe and how do they interact?” (Matter, energy, space, time, force)
• Albert Einstein figures prominently in the scientific discussion on
what is reality?
Outline
Let me tell you what I am going to tell you
• Motivation
• Locality, determinism, realism, and instrumentalism
• Physics circa 1900
• Einstein’s contributions to physical theory
• Quantum physics and the Copenhagen Interpretation
• EPR, Bell’s Theorem, Schrödinger's Cat, and Wigner’s Friend
• What is the world? (A. Watts, Shantananda (1965), Shankara
(Brihad.), and Plato’s allegory of the cave)
• Discussion
Locality, Determinism, Realism, and
Instrumentalism
• Locality: The notion that two systems that are distant from one
another cannot interact instantaneously. A finite amount of time is
required for one system to influence the other. Locality is related to
causality (A. Einstein)
• Determinism: The evolution of a system in space and time is
causally determined and can be predicted from scientific laws that
are expressed mathematically (A. Einstein)
• Realism: The notion that scientific investigation and the resulting
theories are dealing with things that actually exist, e.g., the atom
(read from Popper, p. 2.) (A. Einstein)
• Instrumentalism: The notion that scientific theories are not
statements about “reality”, but are only useful for predicting the
results of experiments (“There is no quantum world, only an
abstract quantum description”, N. Bohr)
Physics Circa 1900
• Newtonian Mechanics
– Motion of material objects with or without forces that take place in a
universe characterized by absolute space and time
– Conceptually simple (not mathematically!)
– Applicable to celestial mechanics (astronomy), motion of solids, liquids,
gases (rigid body mechanics, elasticity theory, fluid mechanics) and,
thermodynamics (heat and kinetic theory)
– Non-local, deterministic, and realistic (?)
• Electromagnetism (unified theory of electric and magnetic forces)
–
–
–
–
–
–
Motion of light and non-ionizing radiation
Field theory (dynamic and not conceptually simple)
Explained light as an electromagnetic wave (Maxwell)
Optics as a limiting case
Predicts radio waves and is the basis for much modern technology
Local, deterministic, realistic (???)
The Major Problems in Physics
(that Influenced Einstein)
• Poincaré, 1902, La Science et l’Hypothèse
– UV light ejects electrons from the surface of a metal
– Zigzag motion of pollen particles suspended in a liquid
– No ether drift (constancy of the velocity of light)
• Lord Kelvin
– The failure of the Rayleigh-Jeans law to predict the distribution
of radiant energy in a black body
• Ernst Mach, 1893, The Science of Mechanics
– Critic of Newtonian Mechanics
• No absolute space and time
• Ice skater and the stars
• Atomic Hypothesis
– Not completely accepted at the time
Blackbody Intensity as a Function
of Frequency
• The problem that started the quantum revolution
• Energy is quantized
Einstein
• Einstein accepts Planck’s notion that energy is
quantized to explain the photoelectric effect
• He accepts that the speed of light is constant,
independent of the motion of the source or receiver
• He accepts the atomic hypothesis to explain
Brownian motion
Einstein’s Contributions in 1905
His miracle year
• In 1905 Einstein is an unknown physicist working in a Swiss patent
office – at the age of 26 he publishes 5 papers, 3 of which are
seminal papers
– On a Heuristic Point of View about the Creation and Conversion of Light
(Photoelectric Effect, Nobel Prize, 1921).
“There is a profound formal difference between the theoretical ideas which
physicists have formed concerning gases and other ponderable bodies and
Maxwell’s theory of electromagnetic processes in so-called empty space.”
– A New Determination of Molecular Dimensions (doctoral thesis)
– On the Movement of Small Particles Suspended in Stationary Liquids
Required by the Molecular-Kinetic Theory of Heat (Brownian Motion)
– On the Electrodynamics of Moving Bodies (Special Relativity)
“It is known that Maxwell’s electrodynamics as usually understood at the
present time when applied to moving bodies, leads to asymmetries which do
not appear to be inherent in the phenomena.”
– Does the Inertia of a Body Depend on Its Energy Content? (E=mc2)
• Read from ‘Einstein 1905’
Einstein’s Contributions - Post 1905
• The Foundation of the General Theory of Relativity – 1916
– New theory of gravity that is local
• The Quantum Theory of Radiation – 1917
– Derives the Planck black body radiation formula from more
fundamental considerations
• Quantum Theory of Single Atom Ideal Gases – 1924
– Bose-Einstein statistics
• Can Quantum-Mechanical Description of Physical Reality
be Considered Complete? – 1935
– EPR paper
• Unified Field Theory and Cosmology
General Relativity
“In classical mechanics, and no less in the
special theory of relativity, there is an inherent
epistemological defect which was, perhaps for
the first time, clearly pointed out by Ernst Mach.”
“We shall soon see that the general theory of
relativity cannot adhere to this simple physical
interpretation of space and time.”
From
‘The Foundations of the General Theory of Relativity’,
A. Einstein, 1916
The Essence of General Relativity
• Einstein discovered in his
General Theory of Relativity that
gravity and acceleration are the
same phenomenon
• Read from ‘Principle of Relativity’
p 100, ‘But we arrive…’
g
Ball on left
falls due to
gravity
• Bending of light in a gravitational field
Ball on right
appears to fall due
to acceleration of
elevator upward
(no gravity)
Implications of the General Theory
• Light bends in a gravitational field
• Clocks measure time at different rates in a gravitational field
• Black Holes
– Requires the synthesis of general relativity and quantum mechanics
• Multiple universes
• Is the universe expanding?
General Covariance
General covariance
Wikipedia, the Free Encyclopedia
In theoretical physics… a physical law expressed in a
generally covariant fashion takes the same mathematical
form in all coordinate systems… The general principle of
relativity, as used in GR, is that the laws of physics must
make the same predictions in all reference frames.
Albert Einstein Quotes
• "I want to know God's thoughts; the rest are details."
• "Reality is merely an illusion, albeit a very persistent one."
• "The only real valuable thing is intuition.“
• “Physics is an attempt to grasp reality as it is thought
independently of it being observed.”
• "I am convinced that He (God) does not play dice."
• "The eternal mystery of the world is its comprehensibility."
• "Science without religion is lame. Religion without science is blind."
• "The most beautiful thing we can experience is the mysterious. It is
the source of all true art and all science. He to whom this emotion is
a stranger, who can no longer pause to wonder and stand rapt in
awe, is as good as dead: his eyes are closed."
Instability According to Classical Theory
Rutherford’s Atomic Model (1911)
Quantum Contributors
1. Schrödinger
1
2
3
2. Pauli
3. Heisenberg
4. Kramers
9
4
6
5
7
8
5. Dirac
6. Compton
7. De Broglie
10
11
12
8. Born
9. Bohr
10. Planck
11. Curie
12. Lorentz
13. Einstein
From: Einstein vs. Bohr
13
Quantum Mechanics in a Nutshell
• Quantization of energy
• Wave-particle duality
– Diffraction
Diffraction from a Dielectric Cylinder
• Wave behavior of light (electromagnetic radiation) was well established
Double Slit Diffraction
No interference
interference
interference
Wave-Particle Diffraction
Electrons behave as waves!
From: ‘The Story Book of Quantum Mechanics’
Electron Diffraction – One at a Time!
How to detect an electron (Uncertainty Principle)
How to measure position and velocity
Quantum Mechanics

 i
V
2m
t
2
2
• Schrödinger's Equation
– What does the wave function solution mean?
– First time in physics that founder’s explanation was not accepted
– Probabilistic interpretation
– Collapse of wave function upon measurement (flipping a coin)
Electron Orbitals
The shape of the five 3d orbitals
http://winter.group.shef.ac.uk/orbitron/AOs/3d/index.html
Copper-Oxygen Bond in Cuprite
(Cu2O)
Nature, September 1999
Zuo, Kim, O’Keeffe and Spence
Arizona State University/NSF
Copenhagen Interpretation
• Born’s probabilistic interpretation
- Physics and Philosophy, p. 46.
• Bohr’s Complementarity Principle
- Physics and Philosophy, p. 49.
• Heisenberg’s Uncertainty Principle
- Physics and Philosophy, p. 42.
• Conclusions
- Physics and Philosophy, p. 55.
• QM is non-local, non-deterministic, and non-realistic
- Einstein could not accept this interpretation!
Heisenberg Quotes on QM
•
All of my meager efforts go toward killing off and suitably replacing
the concept of the orbital path which one cannot observe.
– Heisenberg, letter to Pauli, 1925
•
The present paper seeks to establish a basis for theoretical QM
founded exclusively upon relationships between quantities which
in principle are observable.
– Heisenberg, 1st paper on QM
•
The more precisely the position is determined, the less precisely
the momentum is known in this instant, and vice versa.
– Heisenberg., Paper of 1925
•
Can nature possibly be as absurd as it seemed to us in these
atomic experiments?
– Physics and Philosophy
•
We regard quantum mechanics as a complete theory for which the
fundamental physical and mathematical hypotheses are no longer
susceptible of modification. (!!!)
– Heisenberg and Born, 1927
Nobody Understands Quantum Mechanics
Those who are not shocked when they first come across quantum theory
cannot possibly have understood it.
I… do not know what quantum mechanics is. I think we are dealing with
some mathematical methods which are adequate for description of our
experiment. Using a rigorous wave theory we are claiming something
which the theory cannot possibly give. We are away from the state
where we could hope of describing things on classical theories…
– Neils Bohr
I can safely say that nobody understands quantum mechanics. ...
Do not keep saying to yourself, if you can possibly avoid it, 'But how can it
be like that?' because you will get 'down the drain', into a blind alley from
which nobody has yet escaped. Nobody knows how it can be like that.
– Richard Feynman
Einstein Quotes on QM
• The theory yields a lot, but it hardly brings us any closer to the secret of
the Old One. In any case I am convinced that He does not throw dice.
– Einstein to Born, 1926
• Like the moon has a definite position whether or not we look at the
moon, the same must also hold for the atomic objects, as there is no
sharp distinction possible between these and macroscopic objects.
Observation cannot create an element of reality like a position, there
must be something contained in the complete description of physical
reality which corresponds to the possibility of observing a position,
already before the observation has been actually made.
• The laws of nature imply complete causality (radioactivity)
• The Heisenberg-Bohr tranquillizing philosophy – or religion? – is so
delicately contrived that, for the time being, it provides a gentle pillow
for the true believer from which he cannot very easily be aroused.
So let him lie there.
Einstein-Bohr Debates
• A series of discussions, debates, and
arguments, both formal and informal, took
place between Albert Einstein and Niels Bohr
in the post-Copenhagen Interpretation era on
the nature of physical reality and whether QM
is a complete theory
- Read from “Discussions with Einstein”, Niels Bohr, p. 1.
EPR Paper
• Can Quantum-Mechanical Description of Physical Reality
be Considered Complete?
– A. Einstein, B. Podolsky and N. Rosen, Physical Review, May 15, 1935
• Read first page of paper
“The EPR experiment was formulated on the basis that either an independent
reality did not exist or quantum mechanics was an incomplete theory.
Being a realist, Einstein firmly believed the latter.
The thought experiment addressed the problem of whether a particle could have
both a definite momentum and a definite position. E, P, and R, devised a
scheme in which it appeared that both these quantities could in principle at
least, be measured to any desired degree of accuracy – so contradicting the
uncertainty principle.
Two particles, A and B, interact and then separate until they are quite far apart.
It is possible to measure the momentum of particle A directly, and perform a
calculation to determine the momentum of particle B. While it is not possible to
know the position of particle A, because of the measurement performed on it, it
is possible to determine the position of particle B directly. Consequently, the
momentum and position of particle B can be determined, thereby,
circumventing Heisenberg and demonstrating the incompleteness of quantum
mechanics.”
- From: Quantum Reality, Manjit Kumar
Bohr’s Response to EPR and Bell’s Theorem
• Can Quantum-Mechanical Description of Physical Reality
be Considered Complete?
– N. Bohr, Physical Review, October 15, 1935
• Read first page
• Read “From Einstein’s Theorem to Bell’s Theorem: A History of
Quantum Non-Locality”, Section 4. 1935 (Bohr’s Reply)
Bell’s Theorem states that a violation of Bell’s Inequality is equivalent to a refutation of EPR
- From: The Copenhagen Interpretation of QM, Ben Best
“In the early 1980s, a version of the EPR experiment was performed in the laboratory.
For the present, the experiments appear to come down in favor of the Copenhagen interpretation
and against Einstein’s realism. But, accepting that the results of these experiments favour the
Copenhagen position involves rejecting one of three premises on which Einstein based his
position. These were that: inductive logic is valid; objective reality exists; it is impossible to travel
faster than light. …
The most popular interpretation of the experimental results is that while objective reality exists
independent of observation, the speed of light can be exceeded.
But difficulties then arise for the theory of relativity, since it is fundamental to this theory that
nothing can travel faster than light.”
- From: Quantum Reality, Manjit Kumar
Schrödinger's Cat
Is the cat both dead and alive?
From: Einstein versus Bohr, Mendel Sachs
Wigner’s Friend
From Wikipedia, the free encyclopedia
Wigner's friend is a thought experiment proposed by the physicist
Eugene Wigner; it is an extension of The Schrodinger’s Cat
experiment designed as a point of departure for discussing the
mind-body problem as viewed by the Copenhagen Interpretation of
quantum mechanics. In the Copenhagen Interpretation, the
collapse of the wavefunction is said to take place when a quantum
system is measured. Essentially, the Wigner's friend experiment
asks the question: at what stage does a "measurement" take place?
It posits a friend of Wigner who performs the Schrodinger’s
experiment while Wigner is out of the room. Only when Wigner
comes into the room does he himself know the result of the
experiment: until this point, was the state of the system a
superposition of "dead cat/sad friend" and "alive cat/happy friend,"
or was it determined at some previous point? Wigner designed the
experiment to highlight how he believed consciousness is necessary
to the quantum mechanical measurement process. The idea has
become known as the consciousness causes collapse
interpretation, or less flatteringly, the spiritual interpretation.
Quotes from Bell and Gell-Mann
• Well it does not really explain things; in fact the founding fathers of
quantum mechanics rather prided themselves on giving up the idea
of explanation. They were very proud that they dealt only with
phenomena: they refused to look behind the phenomena regarding
that as the price one had to pay for coming to terms with nature.
– Bell
• Bohr and Heisenberg brainwashed a whole generation of physicists
into thinking that the job was done 60 years ago’.
- Gell-Mann
What is a Thing?
• It’s a noun.
– As reported by Alan Watts
• Everything exists in name and shape only.
• Brahman is real, the world is an illusion, the
individual and the Absolute are not different.
– Shankara
Shankara
“Therefore the whole universe consisting of a series of
meditations and rites, means and ends, actions and
results – although, being held together by a stream of
work and impressions of innumerable beings in
combination, it is transient, impure, flimsy, resembling a
flowing river or a burning lamp, flimsy like a banana
stalk, and comparable to foam, illusion, a mirage, a
dream, and so on – appears, nevertheless to those who
have identified themselves with it to be undecaying,
eternal and full of substance.”
- Shankara, commentary on the Brihadaranyaka Upanishad, I.v.2
Shantananda Saraswati
“Take up anything and look into it seriously and
you will find that essentially it is nothing but a
manifestation of the same consciousness, bliss
and truth. Although in the physical manifestation,
color, form, tree, juice, skin, etc. are all related to
mango, yet essentially it is that formless
consciousness, a concept of that real knowledge
which is Sachidananda.”
- Shantananda Saraswati, Conversations with Mr. L. MacLaren, 1965.
Plato’s Republic, Book VII
This entire allegory, I said, you may now append, dear
Glaucon, to the previous argument; the prison-house is the
world of sight, the light of the fire is the sun, and you will not
misapprehend me if you interpret the journey upwards to be
the ascent of the soul into the intellectual world according to
my poor belief, which, at your desire, I have expressed
whether rightly or wrongly God knows.
But, whether true or false, my opinion is that in the world of
knowledge the idea of good appears last of all, and is seen
only with an effort; and, when seen, is also inferred to be the
universal author of all things beautiful and right, parent of light
and of the lord of light in this visible world, and the immediate
source of reason and truth in the intellectual; and that this is
the power upon which he who would act rationally, either in
public or private life must have his eye fixed.
Backup Slides
The Essence of General Relativity
• Einstein discovered in his General
Theory of Relativity that gravity and
acceleration are the same phenomenon
• Read from ‘Principle of Relativity’
p 100, ‘But we arrive…’
• Ball in box on left falls due to gravity
• Ball in elevator on right appears to fall
due to acceleration of elevator upward
(no gravity)
• Bending of light in a gravitational field
g
Cell Phone System Diagram
Texas Instruments
Observations of a Moving Compass by a Stationary Observer
and One Moving with a Compass
Both observers see the compass point towards the electrically charged sphere
• The two observers have different explanations for what is happening
- One claims a magnetic interaction, the other, an electric interaction
Moving observer
e─
Stationary observer
Read introduction to
“On the Electrodynamics
of Moving Bodies”
General Relativity
“Everything should be
1
G
as
R made
Rg  gas simple
8 T
2
c
possible,
but not simpler.”
Einstein's Field Equation (EFE) is usually written in the form:
v


4

Where








Rμν is the Ricci curvature tensor
R is the Ricci scalar (the tensor contraction of the Ricci tensor)
gμν is a (symmetric 4 x 4) metric tensor
Λ is the Cosmological constant
π is pi = 3.1415..., the ratio between a circle's circumference and diameter
G is the Gravitational constant
c is the speed of light in free space
Tμν is the energy-momentum stress tensor of matter
- Albert Einstein -
The EFE equation is a tensor equation relating a set of symmetric 4x4 tensors. It is
written here in terms of components. Each tensor has 10 independent components.
Given the freedom of choice of the four space-time coordinates, the independent
equations reduce to 6 in number.
The EFE is understood to be an equation for the metric tensor gμν (given a specified
distribution of matter and energy in the form of a stress-energy tensor).
DESPITE THE SIMPLE APPEARANCE OF THE EQUATION
IT IS, IN FACT, QUITE COMPLICATED.
This is because both the Ricci tensor and Ricci scalar depend on the metric in a
complicated nonlinear manner.
Einstein – Brief Sketch
By Leiwen Wu
• 1879: Einstein born Ulm, Germany.
• 1885 - 1925: Michelson and Morley began a series of puzzling
experiments which made the Newtonian Universe impossible.
• 1900: Max Planck shocked the physics community with the
concept of quantization
• 1905: The miracle year in physics: Einstein published papers on
Brownian motion as well as the seminal papers on his theory of
relativity. He developed the Special Theory of Relativity in which
he described how space and time are relative or related to each
other.
• 1915: Einstein extended his discussion of relativity to include
gravity and thereby explained the problem of Mercury. He
developed the general theory of relativity which dealt with gravity
and acceleration and a 4 dimensional space in which everything is
related to each other.
• 1919: Eddington confirms Einstein's prediction concerning
deflection of starlight.
• 1915 - 1925: Einstein was a co-leader in the birth and development
of quantum mechanics
• 1925 - 1935: Einstein and Bohr engaged in a fascinating series of
"debates" over the interpretations of physics especially the notion
of determinism (God does not play dice)
• 1930 - 1955: Einstein searches for a unified theory of the universe
• 1933 - Hubble and Humanson discover the recessional nature of
galaxies - Einstein's theories of the universe take shape.
• 1955: Einstein dies, Princeton, N.J.
Einstein’s Response to the
Uncertainty Principle
1. Imagine a box with a hole and a shutter that contains radiation.
2. Let the shutter be opened for a time T such that one photon
passes through the hole.
3. The box may be weighed before and after the event so the
photon’s mass may be determined.
4. From E = mc2 the energy of the photon may be determined.
5. Since there is no uncertainty in the energy of the photon the
product of the uncertainties in energy and time is zero (or as small
as one likes).
6. This violates the time-energy uncertainty relation.
From: Einstein, Bohr and the Quantum Dilemma
Einstein’s Thought Experiment
From: Einstein versus Bohr, Mendel Sachs
Bohr’s Response
It was quite a shock for Bohr… he did not see the solution at once.
During the whole evening he was extremely unhappy, going from
one to the other, and trying to persuade them that it couldn’t be true.
That it would be the end of physics if Einstein were right; but he
couldn’t produce any refutation…
The next morning came Bohr’s triumph.
Quote by Rosenfeld in Einstein, Bohr and the Quantum Dilemma
Bohr’s Response
• According to general relativity, a clock which is moved in the direction
of a gravitational field will change its rate. Thus the uncertainty in the
position of the pointer, and hence of the box, gives rise to an
uncertainty in the time interval. The uncertainty in momentum
corresponds to an uncertainty in energy, and when the detailed sums
are done, one obtains the result that the product of time uncertainty
and the energy uncertainty is at least as great as … the time-energy
uncertainty principle.
Quote by Rosenfeld in Einstein, Bohr and the Quantum Dilemma