Re: Quantum Cryptography can not work

Sebastian Gottschalk wrote:
Quadibloc wrote:

If the other photon doesn't know ahead of time what to do when
measured - independently of what measurements are made on the other
photon - as the disproof of hidden variables through Bell's inequality
shows it doesn't - then information must have been transferred.

No. Because entangled photons simply share a common quantum state. Such
quantum state isn't subject to distance and general relativity, and nothing
has to be transferred.

But we have no way of understanding what has happened
except in terms of a hidden transfer of information.

We have. It's called "state". Actually, one can easily emulate it by adding
another (very small) dimension.

The entangled photons share a common quantum state.

Yes, this is true.

But then that state is modified, at two different locations,
independently, by two observations.

These observations are in a spacelike relation to each other, so no
information can be transferred between them by any known conventional
means.

When the polarizations of the photons are measured in terms of the
same axis, they are always found to have equal and opposite
polarizations. This is required by conservation of angular momentum.
So far, so good.

If the polarizations are measured in terms of two axes 90 degrees
apart, then there is no correlation between the two measurements. This
is entirely what we might expect.

When the polarizations of the photons are measured in terms of two
axes at any other separation, the correlation is that which would be
produced if one measurement had been performed first, and then the
photon, in a polarization eigenstate, was measured again with the
other tilted polarizer.

Since this correlation is the same for either order, this cannot be
used as a signalling method. What is the problem?

If the photons are measured by polarizers both tilted by 5 degrees, we
*always* have equal and opposite polarities.

And if the photons are measured by polarizers not tilted, again we
*always* have equal and opposite polarities.

***

There is no conceivable superposition of states, no possible set of
values for the wave function, of the particle pairs emitted by the
particle source, that will provide this result, if we have *two
completely separate and independent particles* which happen to have
separate and independent wave functions, each of which separately and
independently collapses to a spin eigenstate on the occasion of each
of the two measurements.

***

So each particle can't simply be in *one* quantum state of *its own*.
When that state collapses to an eigenstate for one particle, it has to
collapse *simultaneously* for the other, even if that other one is far
away.

If that *hadn't* happened, it might be we have a particle source that
is biased, so that it really emits pairs of particles whose spins are
up and down. So when we measure for up and down spin, we always find
equal and opposite spins. But if we turn our polarizers, then the
spins *would stop being correlated*. Or, if our particle source is not
biased, the correlation between the particles would never be complete,
no matter which way our polarizers are turned.

Wait! There's one possibility that avoids transfer of information
faster than light.

Maybe quantum mechanics is wrong. Maybe the particles cheat, and they
carry around little books with them that tell them what to do under
any possible measurement!

This is called hidden variables. But then, for an angle theta between
the two polarizers, the chance of a mismatch has to increase at least
as fast as theta. In fact, the chance of a mismatch is much lower,
being proportional to theta^2.

If the observation of each of the two particles was totally,
completely, abjectly subject to time, distance, and special
relativity, then the wave function of each particle has to collapse
*as a separate event*, and perfect correlation between the two
particles for *all angles of measurement* is not possible.

To say that the "quantum state is not subject to distance" is just
another way of saying that it *can* get away with transferring
information - internally, and for its own use, in a way hidden from
our prying eyes. Or maybe it's doing something else - but then it's
doing something else that *we don't understand* - and, in fact,
something else that can't even be explained by anyone in meaningful
terms.

To me, it's easier to say we can think about the quantum state shared
by the two entangled particles as a thing which is *internally*
connected and communicating over the long distance, using a method
that is faster than light, than simply to say, well, it always is
consistent over this long distance... by a method we are forbidden to
think about at all. Because it's an absolute mystery, and we know
nothing about it, so we hae no right to assume it is built of things
that make sense to us!

It's all right to suggest caution. It's all right to suggest that a
model of the quantum state as having virtual tachyons zipping all over
the place internally - or, better yet, virtual FTL particles that are
always going forwards in time relative to the one frame of true rest -
may be wrong, since we can't (yet) look inside the quantum state, and
we know nothing about it. But to suggest that it is sinful and even
wicked to speculate on the internals of the quantum state using the
only concepts which our poor weak minds can speculate with... well,
*that* is something I'm not comfortable with.

I would rather say, _at least_ to people who are uncomfortable with
quantum mechanics and entanglement, if not to working physicists, that
we _can_ model entanglement by means of internal, hidden FTL transfer
of information... so as to show that it is not a brutal absurdity that
is impossible to express in terms meaningful to the human mind... than
to just say - that's the way it is, quantum mechanics and relativity
are beautiful (and, of course, verified by experiment) and so, you
poor dumb sod, you have no right to demand it make sense to your
uneducated mind that probably can't even solve a differential
equation, your duty is simply to believe and worship us!

Better to say that an X force *could* exist than to either say it
*must* exist (which I agree is going too far) or to fall into the
opposite trap of saying that until more evidence is in, such thought
is poisonous to the mind. I detest anything that even begins to appear
to smack of authoritarianism and dogmatism.

Just because the original thinkers of the past were victims of
authoritarianism and dogmatism themselves from the hidebound classical
thinkers does not mean that, now that experiment has vindicated them,
they should turn around and emulate the sins of their past foes!

John Savard

.

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