The question concerning information in a physics model requires a few things. Other than being scientifically-rigorous, and correct, despite it not actually being the true theory behind the phenomena, it does require an elegant base – a theory that will have to satisfy information’s possible identities.

Non-locality attempts to explain this strange phenomenon, but it does lead to the question if information itself and its true nature; it could after all act like a local field, rather than one obeying Bells Rule. Howsoever, we could also assume the field of information has [parts] which move at superluminal speeds.

The reason why we would want to hypothesize this is because of a well-known phenomena, Quantum Entanglement; the simultaneous resolution of particle polarization. Entanglement caused a stir in the academic world, because the quantum model we have suggests that information is exchanged between particles in time equal to t<r<c=0. So if we have two photons at billions of light years distance between each other, how can information be exchanged to inform each particle-observer of each others state?

Information, by common sense of what we can work with, informs us that information would need to travel at superluminal speeds, many magnitudes of ‘’c’’. Information at this speed would oscillate throughout the real time barrier, as seen by themselves, to us, they are moving in imaginary time every time a resolution in the wave function had transpired. Each time the wave function is collapsed, it required information getting to the point of collapse in equally necessary tachyonic speeds.

Bell's Conclusions say, ''Universe is Non-Local.''

But now, we are given other solutions, like Bells Theorem, but the idea of superluminal information cannot be so justifiably removed, since the quintessential nature of quantum mechanics, is the idea that no stone should be uncovered. It turns out that it is possible to have a non-local universe, where its information does travel faster-than-light. There is absolutely nothing that could escape that notion, because entanglement may still be a very clever interaction of information using matter as a conduit; a type of medium itself. This medium should capture this information, from coming from the future.

This is of course, the Transactional Interpretation of quantum mechanics, where there is a retarded and advanced wave, one that comes from the future, and the other from the past and they meet up in the present where their parts square. You can say mathematically, that they are the complex-conjugates of each other whose components square and yield a positive result.

Faster-Than-Light Communication

This would require that the property of the collapse is found from the absolute square of the quantum field of information;

∫ |ψ|^2=1

The field of information can be imagined to be like any other quantum field that it has infinite range, and must encompass large distances over space time. It will also be pretty homogenous next to smooth in distribution over that space. But this space is no ordinary space. This space it moves through is the imaginary dimension of space (which is time). Tachyons move in the imaginary time dimension, and since they never wield use of the real time dimension, it finds itself oscillating throughout the fourth.

If information moved at superluminal speeds, it would require a similar existence, but in a virtual state; totally imaginary, but it is there. Imaginary is just one of those buzz-words in physics terminology where the media get confused about. Whilst it is called an imaginary dimension, it is still quite real as it does contain an asymmetric relation to the three space dimensions. In fact, it is part of its geometry.

Using Dirac notation we can state the wave state of something is given by:

|ψ> = ∑ |i>Ψ_i

And concerning the collapse of the wave function, or the general probability is given as:

<\ψ O|E\Ψ*>

Where ‘’O’’ stands for Offer Wave (as in Dr Cramer’s Transactional Interpretion), and ‘’E’’ stands for Echo Wave. Superluminal Waves may be describable under sine waves, if derived from group velocity equations describing wave length interactions.

Without the group velocity, particles would be found to move faster than light on their own, if it wasn’t to be distinguished from the phase velocity because;

v_ph v_gr = c^2

where v_ph = v_gr

Solutions of wave equations, can lead to equations describing wave-particles to be moving at superluminal speeds:

v = b/a = √(c^2 + (w/a)^2)

But the distinction between a group velocity and a phase velocity removes the superluminal qualities for a wave form. It can be derived from these solutions of a wave equation, that describe two waves travelling at tachyonic speeds;

u = A cos( ax - bt )

c^2 a^2 - b^2 + w^2 = 0

Which seems analogous to the echo quantum wave vector and the offer quantum wave vector and if these two wave solutions are to refer to them, somehow the magical mathematical quantity of vph vgr = c2 changes their superluminal dualities. Of course, the waves do not take the mathematical form of two perfect conjugates such as (a+ib)(a-ib), but they do contain an almost similar premise to the collapse theory in general. The quantity of movement could be given as (ip), where (i) is the imaginary number i=sqrt -1. Whilst they are called imaginary, again they are very real.

ik/√ 1-β^2=ip

Here, (k) is some property of the information field, and (ip) is the virtual momentum within it. Often we forget that the very constituents of matter itself even on the macroscopic scale, are all formed from different forms of information embedded in the vacuum of space time. It’s quite a lot of information as well, with something like 10^80 particles in count. But admittedly, it is still quite small on the scale of spacetime itself. In fact, matter only takes up 1% of all spacetime.

Lord Rayleigh showed that the velocity U satisfied:

I/U=∂(nv)/∂v

So that U=v, and that that group velocity of waves in a 4-momentum system xyzt is equal to the speed of light, so this applies to Luxon Particles.

Over the years, it has been favourable by most to assume that relativity necessarily posited a limit in the motion of things, and this was assumed at light speed. In fact, for a piece of matter to move at light speed it would require more energy than is available in the universe due to:

E = mc^2/√(1 - v^2/c^2) = imc^2

So the energy (E) is equal to the ‘’mass due to inertia’’ (imc2) with the equality also with relativistic velocities mc^2/√(1 - v^2/c^2). Matter simply could not accelerate to the speed of light, so people in general gave up serious talks on superluminal entities.

The information we speak of however, is the kind associated with some virtual, and non-tangible property; so implication of the energy-limit is not accountable. These waves are totally virtual and as I showed, could be describable under sine wave mathematics.

Conclusion

I have decided, upon my own interpretation of quantum physics which is hardly new at its core, that quantum information may indeed be posited to move at superluminal speeds. It does suggest as well, that this information is not physical and so does not require a physical carrier, but does however require matter as a medium.

We may have two electrons that share this information through angular momentum, and with this adequate theory of quantum mechanics, allow information between two particle-observers to experience each others entangled forms through faster-than-light communication via ethereal quantum wave mechanics.

I hope with the passing years, the idea of information being exchanged without a physical carrier is taken seriously, as it could open many new doors to physics, and the phenomena that plague it without the need of a spooky action at a distance.

References

[1] M. Fayngold, Special Relativity and Motions Faster than Light, Wiley-VCH, 2002

[2] Miloslav Dušek 1999 Instantaneous Action at a Distance in Modern Physics : Pro

and Contra, ed Viv Pope (Commack: Nova Science) 391.

[3] Zeilinger, Anton 1999 Rev. Mod. Phys. 71 288.

[4] Ruhla, Charles 1999 The Physics of Chance (Oxford: Oxford) 158.