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What Does It Mean?
From the “Afterword” of D J Griffith’s Introduction
to Quantum Mechanics
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Da Big Question





Did the physical system “actually have” the
eigenvalue in question prior to the
measurement? (REALIST)
OR
Did the act of measurement “create” the
eigenvalue (constrained by the wavefunction)?
(ORTHODOX)
OR
Can we completely duck the question?
(AGNOSTIC)
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Realist View

If the realist view is true, QM is an
incomplete theory because:

Even if you know everything that QM has to
tell you about the system, you STILL cannot
determine all of its features!
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Orthodox Position
Measurement forces the system to
“make a stand” helping create an
attribute that was not there previously
 Since repeated measurements yield the
same result, the act of measurement
collapses the wavefunctions.
 This is strange but not mystical

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Agnostic Response
I refuse to answer
 I ignore these problems

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EPR Paradox

1935- Einstein, Podolsky, and Rosen came up
with the EPR Paradox
 Designed to prove that the realist postion is
the only possible one
 A simplified version goes like this:

Assume that a pion at rest decays into an electron
and positron


p0->e- + e+
The positron and electron fly off in opposite
directions and the pion has spin=0
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EPR Cont’d

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Since pion is spin 0,
then electron and
positron are in singlet
configuration |00>
So if the positron is spin
up then electron must be
down or vice versa.
QM can’t tell you which
you will get, but that they
will be correlated
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     
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Movin’ On Up to the Big Time, the
Deluxe Apartment in the Sky!

Now move the electron far apart (pick
one)
10 meters
 10 light years

Now say you measure electron spin
down, then IMMEDIATELY you know
that the positron is spin up
 BTW, this is an INSTANTANEOUS
knowledge!

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The 3 views again
Realist: This is not surprising, the
positron was always up since the decay
 Orthodox: Hmmm… electron was
neither up or down until measurement.
The measurement caused the wave
function to collapse and that “knowledge”
was transmitted instantaneously across
the gulf to the corresponding particle.
 Agnostic: I don’t have an opinion

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EPR Says
Orthodox view is “spooky action at a
distance”
 Ergo, says EPR, the realist have it
correct and the spins were
predetermined at the decay
 Of course, this is all predicated on the
argument that nothing, not even
information, can go faster than the speed
of light– called the principle of locality

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Bell’s Thm

EPR did not doubt that QM is correct, just
incomplete
 Some other “hidden variable” is needed to
completely quantify the system.


The hidden variable could be a single number or a
whole collection of numbers; it doesn’t matter
J. S. Bell proved that ANY hidden variable
theory is INCOMPATIBLE with QM
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The Gedunken

Instead of having the electron and positron
detectors along the same direction, allow them
to be rotated independently
 The first detector measures the component of
the electron spin in the direction of unit vector
a and the second along the direction of b
 For simplicity, we will record the spins as +1
(up) and -1(down)
p0
ea
e+
b
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The Results of the Experiment
electron positron product
+1
-1
-1
+1
+1
+1
-1
+1
-1
+1
-1
-1
-1
-1
+1
…
…
…


Bell proposed to
calculate the average
value of the product of
the spins called P(a,b)
If detectors are parallel,
then we have original
EPR configuration so
always +1 and -1 and
therefore P(a,a)= -1
(and so is the average)
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However
If they are anti-parallel, then P(a,-a)=+1
 For any arbitrary orientation then
P(a,b)=-a ·b
 This result is IMPOSSIBLE for any
hidden variable theory

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Why?

Assume, that the hidden variable is called k
 k varies in some way that we neither
understand nor control from one decay to the
next
 Suppose that the outcome of the electron
measurement is independent of the orientation
(b) of the positron detector. b is chosen after
the decay but before measurement of electron
and thus is hindered by speed of light (locality
condition).
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Let’s do some math
So there is a function A(a,k) which gives
the result of the electron measurement
and B(b,k) which gives the result of the
positron measurement
 A(a,k)=+/- 1 and B(b,k)=+/-1
 When detectors are aligned, the results
are perfectly anti-correlated A(a,k)=B(b,k) for all k

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So
P(a, b)    (k ) A(a, k ) B(b, k )dk
Where rho is the probability density of k
Now let’s eliminate B(b,k) by using our
correlation function
P(a, b)     (k ) A(a, k ) A(a, k )dk
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If c is an other unit vector then
P(a, b)  P (a, c)     (k )[ A(a, k ) A(b, k )  A(a, k ) A(c, k )]dk
Since [ A(b, k )]2  1 :
P(a, b)  P (a, c)     (k )[1  A(b, k ) A(c, k )] A(a, k ) A(b, k )dk
Since  1  [ A(a, k ) A(b, k )]  1 and
 (k )[1  A(b, k ) A(c, k )]  0
P(a, b)  P (a, c)    (k )[1  A(b, k ) A(c, k )]dk
P(a, b)  P (a, c)  1  P(b, c)
Bell’s Inequality:
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|P(a,b)-P(a,c)|<= 1+P(b,c)
It is easy to show that P(a,b)=-a·b (the
QM prediction) is incompatible with Bell’s
Inequality
 Suppose all three vectors, a, b, and c lie
in a plane with c at 450 to a and b (a
perpendicular to b)
 Then P(a,b)=0 and P(a,c)=P(b,c)=-.707
 Obviously .707 is not greater than 10.707 (.293)

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But What does it Mean?

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If EPR is correct, then QM is completely WRONG!
On the other hand, NO hidden variable is going to
rescue us from the nonlocality that Einstein considered
preposterous
Many experiments were performed to test Bell’s
inequality: the results were compatible with QM and
incompatible with Bell’s Inequality
In other words, the realists are wrong and there is
spooky action at a distance
Or in the lingo: there is the possibility of superluminal
influences
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Supernaturally Superluminal

A causal influence that propagates faster than
light is bad news

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Faster than light things: any geometric point

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Because relativity says that anything going faster
than light is going backward in time!
We don’t get upset that geometric points move
faster than light
So is this influence casual or is just information
like a geometric point?
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Two types of influence
Causal: subluminal or luminal
 “ethereal”: neither energy or information
and for which the only evidence is a
correlation in the data of two different
subsystems

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Here, kitty, kitty ….
What is a measurement and why is it so
different from other physical processes?
And how can we tell when a
measurement has occurred?
 Schroedinger attempted to answer this in
his famous thought experiment formally
titled “The cat paradox”

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The Cat Paradox
A cat is placed in steel chamber, together with the following
hellish contraption: In a Geiger counter there is a tiny
amount of radioactive material so tiny that maybe within 1
hour one of the atoms decays but equally probable none of
them decays. If one decays then the counter triggers and via
a relay activates a little hammer which breaks a container of
cyanide. If one has let this entire system for one hour, then
one would say the cat is living if no atom has decayed. The
first decay would have poisoned it. The wave function of the
entire system would express this by containing equal parts of
the living and dead cat. At then end of an hour, the wave
function of the cat has the form of
1

( Alive  Dead )
2
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It’s ALIVE! It’s Dead! Etc. etc.
So according to the paradox, the cat is
trapped between life and death: a linear
combination until
 You look! And the cat is:

ALIVE: You saved it by measuring it
 DEAD: You killed it by measuring it

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Schroedinger thought this whole blame
game was nonsense
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Out of the Paradox
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Most widely accepted answer: the Geiger counter is
the measurer, not you and it will make the statistical
determination, not you
Wigner and others say that it is the intervention of
human consciousness that constitutes measurement
in QM
Wigner was Dirac’s brother in law and was associated
with the Maharishi Institute and the Natural Law party.
Unfortunately, the term measurement seems to imply
human intervention but it does is not necessarily so
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My Answer to All These Difficult
Dilemmas
I refuse to answer.
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