[Bill S (OP)]

Thinking about the idea that if a quantum particle (quon, sensu Herbert) might be at one point now, and on the other side of the Universe an instant later, and that this would involve faster than light travel, I find myself wondering this.

My understanding of QM is that we cannot say anything about the state of a quon when it is not being observed.  An electron jumps from one energy level to another in an atom.  We can say that first it is in one, then the other, but cannot say anything about an “in between” state.  Would the same not apply to bigger jumps?  Could one not argue that a quon might be on Earth now and on the other side of the observable Universe an instant later, and that, because we can say nothing about the intervening instant, it makes no sense to talk of FTL travel, or any kind of travel.  We cannot even say that the quon exists in any sense that is meaningful to us between observations.

[JP]

My understanding of QM is that we cannot say anything about the state of a quon when it is not being observed.  An electron jumps from one energy level to another in an atom.  We can say that first it is in one, then the other, but cannot say anything about an “in between” state. 

This is incorrect.  Quantum mechanics allows you to predict the probability of where you will find it during the "in between state."  In this case, the probability of being in  one state decreases as the probability of being in the other increases.  If it starts entirely in one state, it can't jump the gap faster than light speed (though I imagine in an atom, this is too fast to test).

The catch is that the wave function tells you where a particle could be when you take a measurement.  If the particle starts at a point, its wave function can only travel away from that point at light speed.  The collapse of the wave function might seem to transmit information instantaneously, but it doesn't.  The information contained in the particle arrived with the leading edge of the wave function, which was limited to the speed of light.

So the proper way to ask the question about a particle at two distant points is to ask if you could start a wave function localized at point A and as the wave function spreads out if you could detect a particle at point B faster than light speed communication would allow.  The answer is no.

[Bill S (OP)]

Thanks again JP.  If I were 50 or 60 years younger I would give up reading pop sci books and set about learning some real physics. 

BTW, I found this a few days ago, in a physicist's answer to the question as to whether photons experience time:

"When something travels at the speed of light it really doesn’t experience any time."


http://www.askamathematician.com/2011/07/q-does-light-experience-time/comment-page-1/#comment-304613

Where does a hitch-hiker go for information? 

[JP]

Well, you can say "a photon doesn't experience time" as meaning we can't define an on-board clock for the photon, which is what the answer to that question says at the end.  But that's misleading, as for everyone else in the universe, we talk about their "experience" of time in relativity by comparing their onboard clocks to those of another observer (usually at rest) and you can't do this for photons.

[MrVat7]

Photon is a Pseudo particle, It just acts as both wake and a particle. For ordinary matter, they cannot exceed speed than light. Certain neutrinos have been proved to travel faster than light. Also Quantum entanglement is faster than light. 

[yor_on]

What neutrinos would that be Mrvat?

All clocks use photons/waves. That's the 'exchange particles' of 'force' in all interactions, also called 'virtual particles'. And I think there might be a slight confusion when discussing light, and clocks, to me depending on the observer definition. When you measure something you must use a clock, and that clock is your local one, the 'wrist watch'. That's the way we get to a speed of light in a vacuum, and 'repeatable experiments', by using a local definition of a time.

You can't measure without that clock. You might want to experiment with using some other, 'non local' clock, but assuming Lorentz transformations to hold true you then will need to translate it into local time, or redefine your local 'time' (and everyone else's clocks) to fit whatever other definition you use. A repeatable experiment always use a local clock. It's the simplest, most natural way, to do it.

So we have a speed of light in a vacuum, defined locally from the observer. But intrinsically it makes no sense of defining a a time to light. It has two states that I know of, its/the 'recoil' shown in matter, as it leaves, by JP explained as a result of conservation laws. Then nothing until its annihilation, there is no way to follow a 'photon path', although you might want to argue 'weak experiments' shows it to have one.
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Strictly defined a photon has only one I think, its 'energy'. And that one you find in its annihilation, the energy measured being a result of your detector (eye) interacting with the photon. That as a photon can red and blue shift, losing or gaining energy depending on your relation. Using waves to define it you also have a definition of 'wave packets'. http://galileo.phys.virginia.edu/classes/252/Wave_Packets/Wave_Packets.html
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I think one way to think of a wave packet is as a description of several waves superimposed in a specified space. At most places those waves take each other out (quench), but at some specific point, defined by the waves/particles probability of existing statistically, it reinforces itself itself into a point like existence, then thought of as a 'particle'. But, black body radiation also shows that light behaves as if it only have certain discrete energies, not encompassing a whole spectrum, which make a particle behave differently from a wave. There is no discreteness to a wave, think of a rubber band undulating, you can stretch it to make different 'wavinesses', but it's a smooth phenomena. It doesn't 'jump' from one value to another. That's why light is defined to have a duality, it's not as simple as solely defining it as waves.

[JP]

Photon is a Pseudo particle, It just acts as both wake and a particle. For ordinary matter, they cannot exceed speed than light. Certain neutrinos have been proved to travel faster than light. Also Quantum entanglement is faster than light. 

Modern quantum theory suggests that all particles behave as both waves and particles. 

Neutrinos don't travel faster than light.  The (in)famous OPERA result that perported to show this was later amended--there was an error in their equipment: http://en.wikipedia.org/wiki/Faster-than-light_neutrino_anomaly   

No particles we've found so far travel faster than light--there is a theoretical particle called a tachyon that could, but few physicists believe it could exist, sor if it did exist, that it could ever interact with normal, sub-luminal matter or light.  For instance, you could set up an experiment to detect tachyons.  If it didn't detect a tachyon, it would emit a tachyon.  But if it emitted a tachyon, that tachyon would travel back in time, be detected and prevent itself from being emitted in the first place!

Quantum entanglement is "faster" than light, as are certain types of velocities of pulses.  A shadow can appear to move faster than light.  But none of these things transmit information faster than light.  Every time one of these superluminal effects has been examined carefully, it has been found that an server can only send information to another observer at the speed of light or less.