Can signals travel faster than light?

According to the special theory of relativity, the velocity of light
(or, more generally, of electromagnetic radiation) in vacuum is a
fundamental property of time and space. The rules for combining
velocities, and the laws of mechanics, etc, ensure that nothing can
move with a velocity that exceeds this.
It would take us too far outside the scope of this book to explain
special relativity; we can, however, assert with confidence that it is
now firmly based on experimental observation and that it is a vital
ingredient of the structure of contemporary theoretical physics.
That its effects are not immediately obvious in our everyday
experience is due to the large size of the velocity of light,
c = 3 x 10' ms-'.
How then do we understand the fact that, according to quantum
theory, wavefunction reduction happens instantaneously over
arbitrarily large distances and, further, that such behaviour is
apparently confirmed by experiment?

The first thing to notice here is that we cannot actually use this
type of wavefunction reduction to transmit real messages from one
macroscopic object to another. To help us appreciate what is meant
by this statement we should distinguish the transmission of a
message between two observers from what happens when the two
observers both receive a message. For example, two people, one on
Earth and one on Mars, could make an agreement that they will
meet at a particular time either on Earth or on Mars. In order to
determine which, they might agree to measure spins, in a prearranged
direction, of electrons emitted in a particular EPR experiment.
If they obtained + 1/2 they would wait on their own planet,
whereas if they obtained -1/2 they would travel to the other’s
planet. The correlation between the results of their measurements,
noted in $5.4, would ensure that the meeting would take place. It
would be possible for them to make their measurements at the same
time, so they would receive the message telling them the place of
the meeting simultaneously. However this message would not have
been sent from one to the other.
We contrast this with the situation where the prior agreement is
that the person on Earth will decide the venue and then try to communicate
this to the person on Mars. How car, he use the EPR type
of experiment to transmit this message? The only option he has is
either to make a measurement of the spin of the electron or not to
make the measurement. A code could have been agreed: the
measurement of the spin of A along a previously decided direction
would mean that the meeting is to be on Earth, whereas no such
measurement would mean that Mars would be the venue. Thus, at
a particular time, he decides on his answer-he either makes the
measurement or he does not. Immediately the wavefunction of B
‘knows’ this answer; in particular, if it is Earth then B will have a
definite spin along the chosen direction, otherwise it will not.
The person on Mars, however, although he can observe the
particle B, cannot ‘read’ this information because he is not able to
measure a wavefunction. There is no procedure that the observer
could use that would allow him to know whether or not the spin
of B was definite or not.
The same conclusion is reached if we use, instead of a single
experiment, an ensemble of identical experiments. In this case,
if we decide on the venue Earth, then we would measure the spins
of all the A particles in the specified direction. This would

immediately mean that all the B particles had a definite spin in that
direction. Now, if these were all the same, e.g. if they were all
+ 1/2, then we could verify this by simply measuring them.
However, they would not all be the same, half would be + 1/2 and
half would be - 1/2, which is exactly the same distribution we
would have obtained if the spins were not definite, i.e. if the venue
had been Mars and no measurements of A had been made.
The situation could be very different if the quantum theory
description is incomplete and there are hidden variables. If these
could, by some as yet unknown means, be measured, then, since
measurements at A inevitably change these variables at B, the
possibility of sending messages at an infinite velocity would seem
to exist, in violation of the theory of special relativity. Such a violation
can be seen explicitly in some types of hidden-variable theories
where a quantum force is required to act instantaneously over
arbitrarily large distances. This contrasts with the known forces,
which in fact are due to exchange of particles and whose influence
therefore cannot travel faster than the velocity of light.
We here have another very unpleasant feature of hidden-variable
theories. It is not, however, possible to use this argument to rule
them out entirely. Special relativity has only been tested in experiments
that do not measure hidden variables; if we ever find ways
of measuring them then the theory might be shown to be wronggeneralising
results from one set of experiments to an entirely
different set has often led to mistakes.
Even within normal quantum mechanics the question of how a
wavefunction can reduce instantaneously, consistently with special
relativity, is one that requires an answer. To discuss it would take
us into relativistic quantum field theory, which is the method by
which quantum theory and special relativity are combined.
Although this theory has had many successes, it is certainly not
fully understood and at the present time does not appear to have
anything conclusive to say.