Relativistic non-localization enables a moving particle such as a photon to exist at different positions in different frames at an instant and gives rise to an experimentally distinguished physics of relativity. A photon exists in a relativistic non-localized superstate until it is encountered by a detector which results in the collapse of the superstate so as to preserve the lightspeed across frames because the motion state of the detector affects the position of detection. But the current relativity inadvertently assumes the photons to be relativistically localized and invents the relativity of simultaneity. The relativistic non-localization, which is the nonlocality across frames, remained hidden so far under the mathematical elegance of Lorentz transform but is readily revealed by the real domain transform.
Relativistic non-localization enables a moving particle such as a photon to exist at different positions in different frames at an instant and gives rise to an experimentally distinguished physics of relativity. A photon exists in a relativistic non-localized superstate until it is encountered by a detector which results in the collapse of the superstate so as to preserve the lightspeed across frames because the motion state of the detector affects the position of detection. But the current relativity inadvertently assumes the photons to be relativistically localized and invents the relativity of simultaneity. The relativistic non-localization, which is the nonlocality across frames, remained hidden so far under the mathematical elegance of Lorentz transform but is readily revealed by the real domain transform.
This paper, the tenth in the series of ‘Rudiments of relativity revisited’, explores superluminal communication based on relativistic non-localization of new relativity. The new relativity preserves the lightspeed like the current one but also digs deeper into the mechanism behind this constancy. The relativistic non-localization as a superstate is one of the explanations: a photon exists in a superstate of relativistic non-localization, which collapses on detection such that the lightspeed is preserved in the frame of detection. Is it possible to trick this mechanism for the light to supersede its own speed using one or more cross-frame interruptions meant to collapse its superstate in one frame and relaying another burst of light to be detected in another? The two subsequently relayed light-bursts individually preserve lightspeed in their respective frames of detection, but the net result of the two cross-frame flights can be fast or slow travel in a vacuum. Various caveats, assumptions, and experiments to explore supra or infra luminal communication under new relativity are discussed.
In a previous note (1) we considered a rest mass mo at x=0 and t=to and argued this transforms to E’, p’ with x’/t’=v. Thus a single system may be Lorentz transformed to create particles with mo and all velocities. We suggested that all of these particles are on the same footing in a sense. In this note we try to investigate what this “footing” is. In particular, we suggest nonlocality. A particle with rest mass mo, likely occupies some region of space, but is treated as a point (i.e. x=0) which may be the center of mass.The idea of a particle considered as a point is carried over into special relativity i.e motion. In Newtonian mechanics the particle is also considered to be a point. We argue that even though a particle “system” with mo at x=0 and t=to is a point and that after moving there may still be an x’/t’ = v pertaining to one point representing the system, the localization of mo at x=0 may be transformed into a localization in every constant moving frame. This localization seems to be linked to the idea of x and t being independent in -Et+px just as a particle at x=0 and t=to at rest treats x and t as independent. Thus we argue that the localization is the “same footing” of particles with different v and hence momenta mov. The dot product -Et+px = A is -moto for the rest frame which tends to 0 for to→0 . For any frame, t=b/E and x=b/p yields the same A=0. Furthermore x=b/p and t=b/E is a recipe which holds in all frames and describes nonlocality or a “trapped” length associated with the moving particle. This trapped length is not associated with time because x and t are independent. In other words the system moves with a speed of v=x’/t’, but the particle is “trapped” within a wavelength of the order 1/p in the sense that there is a cycling probability as the particle moves through space ignoring time. One does not simply have a point at rest transformed into a point in motion describing all aspects of the moving particle. If one considers x=0 and x=1/p, particles with different p values may follow the same probability distribution associated with energy flow in the region of one wavelength. If one ignores the motion v=x’/t’, then since time is ignored it is as if one has a particle with different probabilities to be at different x points. In a bound quantum state, time is physically dropped and these probabilities are linked to actual densities. For a moving particle (in one direction) one must consider the point motion v=x’/t’, but also kind of periodic trapping of the particle in space (not linked to time). In order to quantify this for a quantum free particle, one may consider the idea of a particle system with a length proportional to 1/p which is consistent with P(x)=constant. In particular, one may take the square root of 1 so to speak to obtain exp(ipx) and exp(-ipx). This also follows from eigenvalue equations of A= -Et+px i.e. -id/dx exp(ipx) = p exp(ipx). It should be noted (as stated above) that exp(ipx) does not involve time. Thus the trapping is in space and may occur over a long period of time if the velocity is very slow i.e. 1/p is very large. In a sense the particle is trapped in a kind of periodic motion in space. There is locality in the sense of position x’/t’=v, but not in the sense of the trapped periodic motion. The nonlocality seems to exist one opposite scales than the usual point velocity. For example, if a particle has a very small velocity then x’/t’=v→0 i.e. one thinks in terms of a very small x’, but 1/p is very large.
This paper, the eleventh in the series of rudiments of relativity revisited, extends our efforts to speed up or slow lightspeed in a vacuum using relativistic non-localization of new relativity. In the previous paper namely ‘Ultra lightspeed travel using relativistic non-localization’ we had developed theory and experimental setups to realize supra and infra lightspeed travel. However, all the experimental setups were bulky to realize and their sensitivity was also low. In this paper, we design a highly sensitive interferometer and a lightspeed manipulator that work on the presumption that reflection or refraction may lead to the total collapse of the relativistic non-localized state of a photon, and the reflected or refracted beam bears no memory of the relativistic non-localized state of the incident beam.
After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators imply a kinematical non-locality and non-separability influencing the theory of relativistic entanglement and not connected with the standard quantum non-locality.
It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level. – John Bell [1] Introduction Bell's theorem establishes a contradiction between locality (and a few other assumptions) and certain predictions of quantum mechanics [2]. There have been two main issues surrounding the deep implications of this celebrated theorem. The first issue is basic, and it concerns whether the theorem really establishes that nonlocality is a necessary feature of any empirically viable theory and hence a feature of nature itself. One aspect of the issue concerns exactly what the underlying assumptions of Bell's theorem are. For example, some argue that these assumptions include the assumption of counterfactual definiteness [3–5], while others disagree [6–8]. The other aspect of the issue concerns which assumption should be dropped due to the resulting contradiction. Some believe that standard quantum mechanics may avoid nonlocality by denying counterfactual definiteness [3–5]. The second issue is much deeper, and it concerns how to make sense of the strange nonlocality when assuming that Bell's theorem establishes that our world is nonlocal. In particular, it has yet to be determined whether such quantum nonlocality is compatible with the theory of relativity, e.g., whether the nonlocality requires the existence of a preferred Lorentz frame [7, 9, 10]. It seems that “there is a preferred frame of reference, and in this preferred frame of reference things do go faster than light … Behind the apparent Lorentz invariance of the phenomena, there is a deeper level which is not Lorentz invariant” [11]. But it also seems possible that the existence of a preferred Lorentz frame is an illusion, since it cannot be detected according to standard quantum mechanics. A more subtle issue is whether quantum nonlocality permits superluminal signaling. It is widely thought that the answers to these questions will lead to a deeper understanding of Bell's theorem and quantum nonlocality. In this paper, we will present a new analysis of quantum nonlocality and its apparent incompatibility with relativity.
Thus far I have been primarily concerned with how an interpretation of quantum mechanics might, or might not, be local. This question is traditionally not sharply distinguished from the question of whether quantum mechanics is consistent with the theory of relativity. However, the two questions are indeed quite distinct, and should be recognized as such explicitly. The theory of relativity What does relativity require? As a first approximation, we may make the distinction by noting that the requirements of the theory of relativity are themselves unclear. Minimally, relativity seems to require that there be no way to distinguish one reference frame from another – i.e., that there be no experimental procedure that can determine which of two inertial observers is ‘really’ moving, or more generally that there be no way to discover an observer's absolute velocity. Most authors are willing to find in (special) relativity a stronger requirement: namely, Lorentz-invariance. They say that relativity requires that in fact there is no such thing as absolute velocity. This requirement goes beyond the minimum – it might be that there is an absolute rest frame (so that absolute velocities are given by motion relative to this frame) while there is no way to find it. (As I will discuss in chapter 9, exactly this situation occurs in Bohm's theory.)