SEVEN USES FOR QUANTUM ENTANGLEMENT
ABSTRACT: An important feature of two-particle systems is quantum entanglement
(QE). Actions carried out on one QE particle seem to affect its distant
partner instantly as through they were never separated. Schrödinger
called quantum inseparability not one but the process in which quantum theory
differs most from classical expectations.
QE is necessary for premeasurement, for establishing the von Neumann chain
between system and observer, useful for achieving decoherence by interaction
with the environment. Attribute coupling and context coupling seem to imply
a new type of connection. stronger than classical correlation. The necessarily
non-local nature of this connection is established by Bell's theorem, limited
to Reality and Theory by Eberhard's Proof.
Quantum entanglement combined with simple ESP or PK powers leads immediately
to a primitive type of time machine.
SEVEN USES FOR QUANTUM ENTANGLEMENT
According to conventional wisdom, the single-particle wavefunction |A>
encodes all knowable info concerning the (statistical) results of any possible
measurement carried out on an ensemble of similarly prepared examples of
A: A1, A2, A3, etc. For this one-particle state, the crucial Quantum Reality
Questions take the form: 1) What is the physical state of a single system
A whose mathematical representation is |A>? (How can we best conceptualize
the nature of one unobserved quantum system?) 2) What is a measurement?
(How does one physical state A produce human-observable indications of its
attributes?). These unsolved questions--the core of physicists' quantum
reality crisis--become even more acute when we move up in complexity to
quantum two-body systems.
Consider system A which can possess two possible attributes a1 and a2 and
system B which possesses two attributes b1 and b2. If these systems are
independent their combined wavefunction |C> is written in product form
|C> = |A>|B>. Now let us imagine that both A and B exist in some
equiprobable superposition of their attributes. In this case the product
|C>ind = (|a1> + |a2>) (|b1> + |b2>)
= |a1> |b1> + |a1> |b2> + |a2> |b1> + |a2>
Suppose some (unspecified) process now causes the cross terms to vanish.
The resulting wavefunction |C>ent is the simplest example of an entangled
state . There is no reference frame in which this entangled system can be
factored into a product of two states.
|C>ent = |a1> |b1> + |a2> |b2> 2)
The physics of this deceptively simple two-state has much to teach us about
the nature of quantum theory and the world. The remainder of this essay
is a brief review of seven indispensable features of quantum entanglement.
In order to perform a measurement on an invisible system A, we must find
some visible system B such that when A has the attribute a1 then B will
display the attribute b1; Also when A is a2 then B is b2. Systems such as
B are necessary for making a measurement on A but not sufficient. To complete
the measurement the attribute(s) of system B (which I will call a "probe")
must somehow end up as the contents of some human consciousness.
Suppose the probe B to be in neutral state |b0> and the system A to be
in a superposition state |A> = |a1> + |a2>. After interaction the
probe-system wavefunction finds itself in the entangled state |C>:
|C> = |a1> |b1> + |a2> |b2> 3)
We see that "probing" a superposed quantum state places the probe
itself in a superposition. If the probe is macroscopic such a superposition
is called a "Schrödinger Cat" after the Austrian physicist
Erwin Schrödinger who imagined in 1935 splitting a cat by entangling
it with a quantum system. In terms of this entangled Cat the two Quantum
Reality Questions take the form: 1) What is the real status of the S-Cat
(probe B) when its description is a superposition? 2) How and why do we
observe only one term (either b1 or b2) but never both? (Why are S-Cats
In order for the attributes of probe B to appear in human consciousness
the probe must be connected to the brain of the observer by a chain of two-state
systems D, E, F, G where D may be photons, E the state of the observer's
retina, F the state of the observer's optic nerve and G the state of some
portion of the visual cortex. In order for an observation of system A to
occur these intermediate systems must have the convenient "probe property"
that during interaction their two states, |d1 and |d2> for instance,
become correlated with the appropriate B probe states |b1> and |b2>.
For a true measurement to occur an unbroken chain of entanglement must extend
from the invisible quantum system A to some part G of the observer's brain:
|M>ent = |a1>|b1>|d1>|e1>|f1>|g1> + |a2>|b2>|d2>|e2>|f2>|g2>
This multistate entanglement is called the "von Neumann chain"
after John von Neumann's famous analysis of the "measurement problem".
Von Neumann asked: where in this chain does the wavefunction "collapse"
from the superposition represented by Eq 4) into one or the other term of
the entanglement to agree with the fact that we always perceive that system
A is either in state |a1> or |a2> but never both? Von Neumann reluctantly
concluded that, since all the links of the chain are physical objects, they
must obey Schrödinger's equation which treats both terms of the superposition
even-handedly (no collapse). Thus either some physical objects are not subject
to the S-equation (a speculation that is entirely groundless at present)
or some process outside of physics accomplishes the collapse. The most logical
candidate for a collapse-inducing non-physical process is human consciousness.
Thus, in the von Neumann picture, two parallel von Neumann chains are reduced
to one by the action of consciousness--mind is a necessary part of physical
reality, a conclusion developed further by Fritz London, Edmund Bauer, Eugene
Wigner, Henry Stapp, Amit Goswami and Casey Blood.
For concreteness imagine system A to be a single photon split by a beamsplitter
into two paths a1 and a2. The two paths are then brought together on a phosphor
screen and the states |a1> and |a2> represent the possibility of the
photon appearing in region 1 or region 2 on the screen. Assume that regions
1 and 2 overlap so that there is opportunity for interference. Assume further
that conditions are such (path length, coherence length, screen resolution,
etc) that interference fringes are actually observed.
|A> = |a1> + |a2> 5)
To test for interference we form the density matrix |A><A| from the
wavefunction (Eq 5) and look for cross terms:
|A><A| = |a1><a1| + |a2><a2| + |a1><a2| +
The last two terms represent interference twixt paths a1 and a2.
Now suppose that on its way to the screen photon a2 interacts with a system
B in an maximally non-disturbing way such that: 1) the initial state |b1>
and the final state |b2> of B have the same energy, so no energy is extracted
from photon A; 2) the phase of photon A is likewise undisturbed by this
interaction: as B goes from state |b1> to state |b2>, the photon goes
from state |a2> to |a2>, that is, it is left entirely unmolested.
Whether such a gentle interaction is physically realizable may be questionable,
but in the spirit of a Thought Experiment let's imagine photon A to be probed
by B in such a maximally undisturbing manner and simply calculate the consequences.
When photon traverses path a1, B remains in state |b1>; when photon traverses
a2, system B is placed in state |b2> while system A is (magically?) left
undisturbed. This (non-disturbing for A) interaction places states A and
B in a mutually entangled state |C>ent.
|C>ent = |a1>|b1> + |a2>|b2> 7)
To calculate the possibility of interference we form the density matrix
and look for cross terms.
|C><C| = |a1>|b1><a1|<b1| + |a2>|b2><a2|<b2|
+ |a1>|b1><a2|<b2| + |a2>|b2><a1|<b1| 8)
To isolate the photon variables a from the "probe" variables b,
we take the partial trace of the density matrix over the b variables:
|C><C|photon = <b1|C><C|b1> + <b2|C><C|b2>
If the probe states |b1> and |b2> are orthogonal (<b1|b2> =
0), this reduces to:
|C><C|photon = |a1><a1| + |a2><a2| 10)
This is the density matrix for an incoherent superposition of states |a1>
and |a2>. We see that interference vanishes whenever a system becomes
entangled with a pair of orthogonal states. Thus this special sort of interaction
(entanglement) is sufficient to destroy interference despite the facts that:
1) systems |b1>, |b2> need not be macroscopic--just orthogonal; 2)
system B need not be observed; 3) system A is "undisturbed" by
One strategy for attacking the measurement problem (Zurek, Hartle, Gell-Mann)
is to search for types of interactions that will "decohere the wavefunction"
so that interference terms vanish leaving the system in a state described--as
in Eq 10--by an incoherent mixture of diagonal density matrix elements with
no cross terms. Since no interference terms are present, the probabilities
generated by this sort of density matrix are formally equivalent to classical
(dice-style) probabilities. It is then easy for some thinkers to convince
themselves that the reality which these matrix elements represent has become
a classical-style reality--that, in other words, decoherence itself is sufficient
to "collapse the wavefunction".
This argument is dubious at best: even if incoherent, the elements of the
density matrix continue to represent possibilities not actualities: an explicit
collapse mechanism still seems necessary. (I have expressed this objection
elsewhere by saying that no amount of mixing can convert black sand and
white sand into grey sand). And even if decoherence can be somehow be construed
as collapse, what states does the system collapse into? Is unpolarized light
(a typical incoherent mixture of two states) "in reality" a classical
mixture of H and V photons? Or is it a classical mixture of R and L photons?
In typical decoherence/collapse schemes Entanglement-with-the- Environment
is invoked to achieve the necessary decoherence. However this analysis shows
that systems far less complicated than the entire environment suffice to
eliminate the system's phase: for example, solid entanglement with even
a single atom will completely erase the photon's phase. In light of this
result it is a marvel that interference experiments are possible at all!
Consider the photon in path a1 interacting with a mirror containing trillions
upon trillions of light-responsive atoms. As it bounces off this mirror
its phase will be completely destroyed if it entangles (even in a non-destructive
manner) with just one of the many myriads of mirror atoms. Mirrors are truly
marvelous (as are lenses) in that they are macroscopic objects that can
strongly interact with and change a photon's state of motion without the
slightest hint of entanglement.
This analysis of photon phase loss shows that it is entanglement not "disturbance",
nor "observation" that destroys the interference pattern during
measurement. "Disturbance" is a red herring: even interactions
purposely designed (as above) to be maximally non-disturbing can destroy
interference. Likewise with observation. Altho some mind could in principle
observe system B and infer the state of entangled system A, no such observation
is necessary for A's interference terms to vanish.
An independent particle's wave function possesses intrinsic amplitude and
phase representing the probability of results of measurements made on that
particle alone. On the other hand, an entangled particle does not possess
its own wavefunction. The two-particle system is in a definite quantum state
but the particles themselves are not. Each partner in the entanglement is
described by conditional not intrinsic probabilities. Participation in quantum
entanglement entails a kind of "loss of self" for each participant,
a phenomenon not unheard of in certain intimate human connections.
In an entangled state the attributes of system A are coupled one-to-one
with the attributes of system B. Thus the observation that system B is in
state b1 gives certain knowledge that system A is in state a1. If systems
A and B are spatially separated, entanglement allows us to discover the
properties of a far-away system by observations made locally. This ability
is not initially surprising because it is similar to situations of classical
correlation. If I seal a silver coin in one envelope and a gold coin in
another and send one envelope to Seattle, the other to Sydney, the moment
she opens her Seattle packet, she knows the state of the coin in Sydney.
But quantum systems are more subtle than coins because of the "meter
option"--each observer's ability to choose at the last moment what
attribute to measure. The wavefunction tells us not what a system is, but
how it will appear to be in any conceivable experimental context. Until
you have provided a particular context, the wavefunction is silent not only
about the values of particular attributes, but even about what kinds of
attributes the system may be said to possess.
For instance consider a system consisting of two polarization-correlated
photons P and p which are moving apart from one another at the speed of
light and are observed with polarization meters located (say) on Earth and
Pluto. These meters can be adjusted to measure an infinite number of polarization
dichotomies, for instance H-or-V (Horizontal or Vertical) or D-or-S (Diagonal
or Slant) or R-or-L (Right or Left circular Polarization). When both meters
are set to provide an H/V context the entangled photon wavefunction |C>
can be written:
|C> = |H>|h> + |V>|v> 11)
An observation of H-polarized photon P on Earth tells us instantly that
Pluto photon p will be measured to have polarization h. However we could
have chosen to measure D/S polarization at both stations where |D> =
|H> + |V> and |S> = |H> - |V>. In terms of this measurement
context the same coupled photon state can be written:
|C> = |D>|d> + |S>|s> 12)
Recalling the decohering feature of entanglement, we can write the density
matrices on Pluto for these two cases: 1) measuring H/V on Earth; 2) measuring
D/S on Earth:
Case 1: |C><C|Pluto = |h><h| + |v><v|
Case 2: |C><C|Pluto = |d><d| + |s><s|
These results seem to imply that if I make a H/V measurement on Earth the
photons on Pluto turn into an incoherent mixture of h and v photons. If
I make a D/S measurement on Earth, the Pluto photons obediently become an
incoherent d/s mixture.
Now mathematically these two expressions are exactly equivalent, but what
about "reality"? Does changing the context on Earth actually cause
a physical change in the distant photons on Pluto?
In 1963 Irish physicist John Stewart Bell investigated the question of the
effect of distant measurement contexts on local realities. Bell assumed
that change of context on Earth does not change photon properties on Pluto
and derived a simple condition that the Earth/Pluto polarization results
must satisfy if this so-called "locality assumption" is correct.
Quantum-mechanical calculations and experiments done at Berkeley (Clauser),
Paris (Aspect) and elsewhere show that the Bell condition is strongly violated.
Thus Bell's locality assumption is false. In light of Bell's result one
can reasonably conclude that a change in context on Earth instantly changes
photon facts on Pluto. Berkeley physicist Henry Stapp has called Bell's
theorem "the most profound result in science".
Using Immanuel Kant's convenient three-fold division of knowledge into Appearance,
Reality and Theory where Appearance is the sum of what we perceive--both
inner and outer; Reality the more-or-less hidden causes behind Appearance,
and Theory the stories we make up about both Appearance and Reality, we
can place Bell's theorem in its proper context. Bell's theorem is not about
Appearance nor Theory; it is about Reality. Bell's theorem states that no
model of Reality in which photons on Pluto are unaffected by change of context
on Earth can explain the quantum facts.
Bell proves that Reality is "non-local". What about Theory and
Simple inspection shows quantum theory to be non-local. The unitary transformation
(representing a change in Earth context) produces an immediate change in
the distant waveform representing the Pluto photons. So Theory is non-local.
What about Appearance? (It should be noted here that Bell's theorem is based
only on logic and experimental facts: thus if quantum theory should someday
be superceded by another kind of mathematical story, Bell's theorem would
still be valid.)
Looking at the Pluto photons we see a random mixture of two types of polarization
(whichever polarization pair we chose to measure) no matter what polarization
context is chosen on Earth. Thus Appearance (in this situation at least)
is stubbornly local.
Generalizing from this simple two-photon case, Berkeley physicist Philippe
Eberhard proved that (if quantum mechanics is correct) all Quantum Appearances
must be local. Here the term "Quantum Appearances" means "statistical
A quantum measurement consists always of individual events (which we might
call "primary datums" (PDs) out of which one can form many kinds
of statistical averages (SAs). One of the unquestioned dogmas of quantum
theory is that the PDs are utterly random, lawless, totally outside the
laws of physics or any other laws. Only the statistical averages (SAs) are
subject to laws, and these laws are what we call quantum theory.
Eberhard's Proof shows that no change on Earth can change a statistical
average on Pluto. So quantum theory is statistically local.
It seems intuitively obvious that any statistically local theory could easily
be given a local PD underpinning. One of the surprises of Bell's theorem
is that for entangled quantum states no such local PD underpinning is even
One way of understanding the subtle relationship between locality, non-locality,
SDs and PDs is to imagine that the PDs--the raw quantum jumps--actually
are non-local: a change in Earth context actually does (in "reality")
change individual quantum events on Pluto. However these Plutonian events
are random so this Earth-induced "change" involves replacing one
inscrutable random sequence by another sequence equally random. No statistical
test can distinguish between these two sequences: "Although there are
many kinds of order, there is only one kind of randomness". Thus (in
this way of thinking) it is easy to send faster-than-light messages from
Earth to Pluto using quantum entanglement. However these messages cannot
ever be decoded because they are encrypted into utterly random-appearing
sequences to which only nature holds the key..
MIND OVER MATTER
Eberhard's Proof shows that altho Earth and Pluto may be instantly connected
in Reality, it is impossible in the world of Appearance using current physical
processes to send faster than light messages via the quantum entanglement
channel. However suppose we introduce processes that lie outside of conventional
physical measurements. In particular could one apply ESP or PK locally to
a quantum-entangled system and use this combination of local mind power
and distant quantum links to send signals FTL in the realm of Appearance?
Physicist Helmut Schmidt in San Antonio has shown that certain individuals
seem to be able to alter quantum-random sequences with their intentions.
If this is a real (PK) effect, one could use it to send FTL messages to
Pluto by simply setting both contexts to H/V. When Helmut on Earth signals
a dash by mentally increasing H events on Earth, the increased h events
on Pluto would represent a decodable message. Thus local PK plus entanglement
would suffice to send FTL messages.
The time-machine aspects of such an FTL transmission scheme would not go
unnoticed and perhaps the fact that the "Schmidt effect" will
lead to temporal paradoxes is a sufficient argument to deny its existence.
But also perhaps not. The Schmidt effect plus quantum links may represent
the simplest time machine that could be constructed with 20th-century technology.
Consider the following quantum facts: when an H photon encounters an H/V
detector it will certainly register H; when the same photon encounters a
D/S detector it will randomly register as D 50% of the time and 50% of the
time as S. Now suppose the existence of the following kind of (local) ESP
ability. For a incoming photon entering a H/V detector the psychic guesses
H, V or "don't know". We further suppose that when the photon
is either D or S (that is, undecided in terms of H/D polarization) that
the psychic has no edge over nature: he/she can only predict the results
of events which are certain to happen. Then, for those events where the
psychic scores greater than chance, the folks on Pluto know that the Earth
context is H/V; otherwise the Earth context is S/D. Thus a certain kind
of local ESP on Pluto in combination with a quantum link to Earth would
produce a human-usable FTL connection over grand distances. Again the possibility
of using this link as a time machine would not go unnoticed.
So local quantum-event PK on Earth can send FTL messages to Pluto as a pattern
of deviation of H/h events from 50% . Likewise a certain variety of local
ESP on Pluto can decode FTL messages from Earth encoded as a pattern of
H/V and D/S contexts.
Most of the information collected here is well-known. What is new is its
assembly in one place under the rubric of quantum entanglement. I have shown
how essential QE is for the Premeasurement process (the formation of Schrödinger
cats), in the Measurement process itself (establishing a von Neumann chain
between system and observer), in the process of Decoherence which makes
quantum possibilities look (at least formally) like classical probabilities
(Entanglement Decoherence), in the suggestive property of Coupled Contexts
in which distant influences seem to propagate instantly across spacetime
(at least in Theory).
Bell's theorem uses entanglement to show that Reality as well as Theory
is non-local while Eberhard proves that, if quantum mechanics is correct
and complete, Appearances must remain stubbornly local. Finally I show that
quantum Appearances are balanced so precisely on the edge of non-locality
that the application of simple kinds of local ESP or PK suffices to make
the Appearances themselves as non-local as the Reality which supports them.
In this mind-over-matter context quantum entanglement might be exploited
to construct a crude sort of stone-age time machine.