Time Travel Safety Critical Systems: Particle and Body Acceleration Past the Speed of Light and Digital Quantum Teleportation

Some thoughts on Special Relativity:

(i) The Michelson-Morley experiment for classical electromagnetic wave propagation at speed of light in vacuum, c, generates Lorentz transformation with gamma^2 ~ 1 / 1 – v^2/c^2.

(ii) Considering the same argument about the equivalence of inertial frames, for any other wave equation, e.g., the scalar acoustic wave equation, with speed c_other, generates Lorentz transformation with gamma^2 ~ 1 / 1 – v^2/c_other^2.

(iii) Why ‘prefer’ one LT to the other ? They each apply to their own aspect of science, i.e., electromagnetic or acoustic wave propagation.

(iv) Then why attach the force-mass relation to one LT, rather than the other ? Why m = m(v) for c or c_other ?

(v) As neither Newtonian dynamics, nor SR dynamics, have an associated wave speed, why infer that there is any upper speed limit at all, on particle or body dynamics ?

(vi) If there exists a LT for each wave equation, then does there even exist such a thing as an inertial frame for all wave equations, in the sense of a (collection of) frame(s), all moving at constant relative velocities, in which all waves propagate always at their respective speeds, c_i, all different ? (Clearly, air resistance will not typically be negligible, in fast movement through air. But that is a secondary consideration, here.)

(vii) A key question then: what difference for rest frame of air, or in case of air carried with moving observer ? Thus, the early ether drag concepts.

(viii) Electromagnetism has waves. Gravity has waves. Are all gravity waves at speed c ? Don't know. If so, might we get a 'universal' inertial frame 'by accident' ? Do strong, weak, electro-weak forces, QED, QCD, ... , have wave equations ? If so, at what wave speeds ? All c again ? For matter waves, at any propagation speed, does the inertial frame and LT concept work as above, or not, if the matter wave transmission medium does have a unique rest frame ?

(ix) And in a fully quantum picture, with only free particle transmission and interconversion, no 'emergent' waves at all, why any upper speed limit on anything ?

(x) In the previous context, it is interesting to consider what 'non-locality' actually means. To experimental accuracy and limited measurement speed, it would presumably mean something like 'observably faster than light' transmission', or some such ? Explicit and direct demonstrations of non-locality ? None, probably ? Then indirect demonstrations like Bell's inequalities ?

Consider various possibilities for backwards-in-time travel:

(i) extant, self-consistent, 4D (or other) static space-time, with closed time (and perhaps space)-like loops.

(ii) extant, self-consistent, 4D (or other) static space-time, with (perhaps repeated) branching of that space-time at jump-back singularities.

In neither case, can you go back and ‘kill your own grandfather’, preventing your own birth.

(iii) tachyon particle or body backwards-in-time travel, by acceleration of particle or body to greater than the speed of light in vacuum, c, then Tolman’s ‘paradox’ (to the extent that it is consistent).

* Speed of light upper limit assumed non-applicable to particle or body, *but* Lorentz transform assumed with speed, c. Is that a consistent position ?

(iv) Digital Quantum Teleportation, instantaneous, non-local, digital signalling, across arbitrary distances, then Tolman’s ‘paradox’.

* Non-local, digital signalling, across arbitrary distances, *but* Lorentz transform assumed with speed, c. Is that a consistent position ? 

Tolman’s Paradox [wiki]

Tolman used the following variation of Einstein’s thought experiment [1][4]. Imagine a distance with end points A and B. Let signal be sent from A propagating with velocity, v_a, towards B. All of this is measured in an inertial frame where the endpoints are at rest. The arrival at B is given by:

Dt = t1-t0 = (B-A)/v_a.

Here, the event at A is the cause of the event at B. However, in the inertial frame moving with relative velocity v, the time of arrival at B is given according to the Lorentz transformation (c is the speed of light):

Dt’ = t1’-t0’

= (t1 – Bv/c^2) / gamma – (t0 – Av/c^2) / gamma

= (1 – v_a v/c^2) Dt / gamma,

gamma = sqrt(1 – v^2/c^2).

It can then be easily seen that if v_a > c, then certain values of v_a, v can make Dt' negative. In other words, the effect arises before the cause in this frame. Einstein (and similarly Tolman) concluded that this result contains in their view no logical contradiction; he said, however, it contradicts the totality of our experience so that the impossibility of v_a > c seems to be sufficiently proven.[1]

References:

1.      Einstein, Albert (1907). "Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen" [On the relativity principle and the conclusions drawn from it] (PDF). Jahrbuch der Radioaktivität und Elektronik. 4: 411–462. Retrieved 2 August 2015.

2.     R. C. Tolman (1917). "Velocities greater than that of light". The theory of the Relativity of Motion. University of California Press. p. 54. OCLC 13129939.

On the working assumption that v_a > c is already a thing, this says that information can be propagated backwards in time, in some reference frames. Those frames in which v_a > c, either by particle or body acceleration past the speed of light in vacuum, c, (to become ‘tachyonic’ particles or bodies), or for which non-locality and instantaneous transmission of actual information, occurs at an effective v_a > c, once finite measurement speed is accounted for, allow actual information transfer backwards in time.

Note, however, the implicit assumptions and contradictions (!). For the particle or body, accelerated past the speed of light to tachyonic, and for the effective faster-than-light, non-local, info-propagation, a Lorentz transformation is being assumed for the Tolman paradox, and based on the standard limiting speed, c. These look inconsistent. It may be that the Lorentz transformation is inapplicable. And no backwards-in-time possibility actually arises.

For sake of argument, assume consistency of the above, in some appropriate forms, to complete the discussions.

Arguably, as soon as any information is sent backwards in time, the space-time continuum splits at the jump-back singularity. This conclusion is based on the butterfly effect for the coupled Earth atmosphere-ocean chaotic weather system. Once backwards-propagated information dissipates as heat in the atmosphere, a hurricane could develop on the other side of the world, which might not have developed otherwise. For speed of sound in air, around ~15+ hours later, assuming some initial exponential growth of small perturbation to make its impact detectable on the other side of the globe. Mostly, new hurricanes will not occur.

The above is a self-consistent picture. The typical contrasting picture, is the usual, also fully self-consistent one, with an assumed single time-line, no space-time splitting.

Safety Critical Systems

Particle or body acceleration past the speed of light [other blogs], are not precluded by the Michelson-Morley experiment. However, no such speed has ever been achieved experimentally. Digital Quantum Teleportation [other blogs] suggests instantaneous signalling across arbitrary distances with zero attenuation, thus effective, greater than the speed of light, actual info-transfer. This has also not been demonstrated experimentally.

However, if either is achievable, is it possible that backwards-in-time travel of actual information might be possible. If so, the result could be (allowing for the possible formulation inconsistencies flagged above), splitting of the 4D (or other) static space-time continuum.

For safety critical systems, e.g., the Earth, what reasonable assumptions to adopt when contemplating implementing any approach which might imply backwards-in-time travel, e.g., *any* non-local signalling.

Experiments are required.

As a related example, how often are calculations of possible mini-black-hole formation, say, revised against increasing Large Hadron Collider energies ? What reasonable assumptions to weigh against any risk of the Earth being swallowed by a mini-black-hole ? Are LHC safety assumptions re-visited regularly, or could experiments such as those above, be regarded as reckless ? I do not know. I will hunt around on the web for some further information.