FLASH (FIRST LASER-AMPLIFIED SUPERLUMINAL
HOOKUP)
FLASH ATTEMPTS TO BREAK EINSTEIN'S LUMINAL SPEED LIMIT BY FINDING A
WAY TO DETERMINE THE POLARIZATION EIGENSTATE OF A SINGLE PHOTON.
In the classic EPR set-up two photons A and B are emitted back-to-back
at the speed of light from a common source. The photons travel to distant
detectors A and B where observers (Alice and Boris) measure their polarizations.
For photons polarization is a binary quantity YES or NO with respect to
an axis chosen by the observer. Polarization is measured by setting a calcite
crystal at a particular angle: photons polarized ALONG the crystal axis
will be bent UP (YES); photons polarized at right angles to the crystal
axis will be bent DOWN (NO). No other outcome is ever observed.
This two-outcome polarization interrogation can be performed along any of
an infinity of axes but for the FLASH device we are interested in only two
angles VERTICAL and DIAGONAL (45 degrees to vertical).
If we set the calcite vertical, UP photons are polarized VERTICALLY (V)
and DOWN photons are polarized HORIZONTALLY (H). If we set the calcite DIAGONALLY,
UP photons are polarized DIAGONALLY (D) and DOWN photons are polarized "SLANTWISE"
(minus 45 degrees). For a particular beam of photons we can choose either
to investigate the V/H polarization content of the beam or the D/S content
of the beam but not both. For brevity I will call the V/H calcite setting
"T" and the D/S calcite setting "X"
What makes the EPR setup so special is that the photon pair emitted by the
central source is in "the twin state". What this means is that
(in the quantum description at least) each particular photon is in an indefinite
state--it has no definite polarization. Each photon by itself has only a
definite PROBABILITY to be in a particular polarization state: furthermore
each of the infinitely many possible directions of polarization is equally
probable. But being in twin state requires that whenever polarization photon
A is found to be in a definite state, photon B will always be found in exactly
the same state. The quantum twin state resembles that of a woman bearing
identical twins but not knowing their gender. In the EPR case however each
twin is born to a different mother and the twins can emerge from their widely
separated wombs as one of four "genders" H, V, D, S depending
on how Alice and Boris set their calcites.
Most quantum experiments are probabilistic--many outcomes are possible and
the one result that actually occurs is considered to happen as a matter
of pure chance. But a certain subclass of quantum experiments are perfectly
predictable. Namely when you measure an "eigenstate" with its
"eigencrystal". ("Eigen" is German for "self"
or "unique") For example a beam of photons all of which are Vertically
polarized are said to be in a V eigenstate. This means that if you make
a "T" polarization measurement on a V beam, every photon in that
beam will be bent UP. One could say that the beam was made up entirely of
"V photons".
But suppose we measured the same beam of "V photons" with a "X"
calcite. Then we would get a probabilistic result because we are not using
an "eigencrystal" to measure the beam. In this case the output
of the X crystal is equal amounts of photons bending UP or DOWN in an apparently
random pattern. Similarly if we constructed a beam of "D photons",
they would all go UP when measured with a X calcite but only 50% would go
UP if measured with a T calcite.
When a photon is measured by its eigencrystal one outcome always occurs--perfect
certainty. When the same photon is measured by what might be called its
"gemeincrystal" ("gemein" = "many"), all outcomes
(in this case only two) occur with equal probability--perfect uncertainty.
The two calcite settings (called T and X) considered here are one possible
eigen/gemein pair of measurement devices. For each particular photon Alice
can choose one of these settings (T or X) --but not both--to interrogate
the photon as to its polarization state.
I will use this notion of eigen- and gemein-crystals to show how the EPR
twin-state situation can be used to transmit signals faster than light.
Given a faster-than-light signalling scheme, any high-school student who
has studied special relativity can then show you how to build a time machine
which is able to gain knowledge about future events before they happen.
If we have a BEAM OF PHOTONS all in the same eigenstate (either H, V, D
or S), it is easy to discover what that state is. We simply put a calcite
in the beam and turn it until all the photons go UP: the angle of the calcite
(V, H, S or D) when all the photons go UP is the same as the eigenstate's
polarization direction.
Now to send signals faster-than-light we need only this: a way of determining
the eigenstate not of a beam of identical photons but the eigenstate of
a beam consisting of ONLY ONE PHOTON.
Let's see how that works. We imagine an EPR setup with Alice doing the signalling.
She encodes a message in ZEROs and ONEs: To send ZERO she sets her calcite
at T and observes an H photon: Because the photons are in the twin state
Alice knows that Boris's distant photon is the same as hers--that, is, in
the H eigenstate.
To send ONE Alice sets her calcite at X and observes, say, a D photon. Then
she knows that Boris's photon (which may be a million miles away) is also
a D photon.
Suppose Alice and Boris have agreed that each binary bit (ZERO or ONE) will
be carried by one hundred photons. So if Alice is sending the signal 1001,
then Boris will receive photons #1-100 in eigenstates of D and S; photons
#101-300 in eigenstates of H and V and photons #301-400 in eigenstates of
D and S. If he can determine the eigenstates of only a fraction of the photons
in each of these groups of 100, Boris can decode Alice's message and receive
her signal faster-than-light.
In order to prevent this kind of ultrafast signalling, nature is going to
have to prohibit humans from learning the eigenstates of single particles.
But what sort of prohibition could this be? Here is a particle coming towards
me. One of its properties is that, if I set a calcite at a certain angle,
the particle will WITH CERTAINTY bend UP. Why should nature prohibit my
discovering this angle using purely local means? (The eigenstate of a single
photon is not completely forbidden knowledge after all. Boris could always
ask Alice what she measured and hence discover the eigenstate of his photon
before he actually verified it locally. Thus eigenstate.knowledge is not
wholly unavailable, but merely unavailable locally. Or is it?)
The FLASH proposal was one of several schemes concocted to measure the eigenstate
of a single photon. Since we can measure the eigenstate of a beam of identical
photons, why not simply "clone" each photon into say 6 identical
photons and estimate the polarization of this "beamlet" in obvious
ways. This method would certainly work if we could clone photons--six is
more than enough--even two identical photons would suffice to allow us to
distinguish T-type photons from X-type photons.
The FLASH device (FLASH stands for First Laser-Amplified Superluminal Hookup)
works by sending each photon into a Laser Gain Tube (LGT). LGT is a gas
of excited atoms that are ready to emit light of the same frequency as the
input photon. The atoms de-excite by two mechanisms: SPONTANEOUS EMISSION
where light is given off in a random direction and polarization, and STIMULATED
EMISSION where light is given off with identical direction and polarization
as the stimulating photon. The stimulated emission of the LGT makes it a
good candidate for a photon cloning device.
In the FLASH scheme Boris sends his photons into a LGT one-by-one and measures
the polarization of the beamlets of identically polarized photons that emerge.
After about a hundred tries he should be able to tell whether he is looking
at a random mixture of V and H photons (corresponding to a ZERO) or a random
mixture of D and S photons (corresponding to a ONE).Hence he could decode
Alice's message which she is sending "right now" a million miles
away--an example of instantaneous signal transmission: obviously faster
than light.
Nick Herbert submitted the FLASH proposal
to a major physics journal where it was rejected (but not refuted) by all
referees but published anyway because the editor thought it would stir up
thinking about quantum entanglement--of which the EPR two-photon twin state
is a simple example.
Shortly after publication of FLASH Wooters and Zurek published in Nature
a paper entitled "A Single Quantum
Cannot be Cloned" arguing that polarization-neutral laser amplifiers
cannot be built. However Mandel a few weeks later published an
explicit design for a polarization-neutral laser amplifier. Mandel in
addition showed that such an amplifier would produce just enough noise that
the polarization eigenstate of the input photon will be unmeasurable. For
example when you put, say, an H photon into Mandel's device, two H photons
come out--a single photon CAN be cloned--two times out of three. But one
time out of three when an H photon goes in, an H and a V photon come out.
This looks good--a signal-to-noise ratio of 2 to 1--but just this amount
of noise exactly suffices to prevent you from discovering the difference
between a random mixture of V, H photons (ZERO) and a random mixture of
S, D photons (ONE). Thus Alice can send Boris a faster-than-light message
but Boris cannot decode it.
Altho the FLASH proposal was refuted, it stimulated much discussion about
the intrinsic limits of quantum amplifiers: we know now that noiseless quantum
amplifiers cannot exist because if they did we would be able to build time
machines. In a small way FLASH led to the discovery of a new and unsuspected
natural law: NO PERFECT AMPLIFIERS.
Also to prevent time machines nature must enforce the law: NO
LOCAL KNOWLEDGE OF SINGLE-PARTICLE EIGENSTATES. Nick Herbert has investigated
many physical schemes for obtaining such knowledge without success. One
is tempted to ask: can we obtain this knowledge (which certainly exists
in nature: Alice for instance is aware of Boris's photon's eigenstate) by
psychic means? Can Boris "guess" the eigenstates of his photons
at a better-than-chance level. Then verify his guesses by setting his calcites
in a way that yields a different result than the 50/50 pattern of UP/DOWN
photon deflections that would be produced by Boris's uninformed guesses?
If psychics can "read" the internal state of elementary particles
before those particles are actually measured then (using the EPR setup to
produce coded and entangled eigenstates) we can send signals backwards in
time. EPR experiments. Photon eigenstates. Time travel. Psychic physics.
Questions of this sort certainly lie at the very fringes of human knowledge.
More information on quantum FTL signalling schemes may be found in Nick
Herbert's "Faster Than Light: Superluminal
Loopholes in Physics".
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