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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