Based on the law of energy conservation, the author shows that, the steady state electronic motion around a given nucleus in a non-circular orbit, depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach. Quite on the contrary it provides one with the possibility of bridging the Special Theory of Relativity and Quantum Mechanics, to finally achieve a natural symbiosis between these two disciplines, and furthermore, elucidating the “quantum mechanical weirdness”, simply based on the mere law of relativistic energy conservation. The author developed his theory, originally, vis-a-vis gravitational bodies in motion with regards to each other; hence, it is comforting to have both the atomic scale and the celestial scale described on just the same conceptual basis. The approach leads to the de Broglie relationship, and superluminal speeds, yet excluding any exchange of energy, making the basis of quantum mechanics.
Based on the law of energy conservation, the author shows that, the steady state electronic motion around a given nucleus in a non-circular orbit, depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach. Quite on the contrary it provides one with the possibility of bridging the Special Theory of Relativity and Quantum Mechanics, to finally achieve a natural symbiosis between these two disciplines, and furthermore, elucidating the “quantum mechanical weirdness”, simply based on the mere law of relativistic energy conservation. The author developed his theory, originally, vis-a-vis gravitational bodies in motion with regards to each other; hence, it is comforting to have both the atomic scale and the celestial scale described on just the same conceptual basis. The approach leads to the de Broglie relationship, and superluminal speeds, yet excluding any exchange of energy, making the basis of quantum mechanics.
Based on the law of conservation of energy, we have shown that, the steady state electronic motion around a given nucleus in a non-circular orbit depicts a rest mass variation, though the overall relativistic energy remains constant. This is, in no way, conflicting with the usual quantum mechanical approach. On the contrary, it provides us with the possibility of bridging the special theory of relativity and quantum mechanics, to finally achieve a natural symbiosis between these two disciplines, and furthermore, elucidating the “quantum mechanical weirdness”, simply based on the mere law of relativistic conservation of energy. Our theory was developed originally, vis-a-vis gravitational bodies in motion with regard to each other; hence, it is comforting to have both the atomic scale and the celestial scale described on just the same conceptual basis. One way to conceive the rest mass variation of concern is to consider a “jet effect”. Accordingly, a particle on a given orbit through its journey must eject a net mass from its back to accelerate, or must pile up a net mass from its front to decelerate, while its overall relativistic energy stays constant throughout. In other words, a minimal rest mass is transformed into extra kinetic energy through an acceleration process, and kinetic energy condenses into extra rest mass through a deceleration process. The tangential speed of the jet in question, strikingly points to the de Broglie wavelength. This, on the whole, makes the jet speed ‘’superluminal”, yet excluding any transport of energy. This conjecture coincides with the recent measurements (Kholmetskii et al., 2007; Salart et al., 2008), and provides a clue for the wave-particle duality, also insures their concurrent coexistence. An important consequence of the approach presented herein is that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, sense each other, with a speed much greater than that of light, and this, in exactly the same way. In which case, though, the interaction coming into play, excludes any energy exchange; thus, we would like to call it, “wave-like interaction”. The present approach ends up the existing schizophrenia, between different conceptions painting separately the micro world and the macro world, and unites these two worlds with an unequal, single and simple conception, based on just the law of relativistic energy conservation.
Key words: Special theory of relativity, electric interaction, tachyons, de Broglie relationship, superluminal or wave-like interaction, general theory of relativity, gravitation.
Historically, special relativity followed as a generalization of Newtonian mechanics and later quantum mechanics (both nonrelativistic and relativistic) was developed as a somewhat independent theory with some connections to Newtonian/special relativistic concepts such as energy and momentum and their conservation. For example, the Newtonian concept of a potential V(x) is used in quantum mechanics. Here we wish to consider the notion of a system seen from different frames moving with constant speed (-v) together with some basic physical ideas that are presumed to hold at any scale such as the idea of a push or pull changing the speed of a particle and the notion of speed itself. We argue that one may develop special relativistic equations in such a manner, but at the same time consider notions of dp/dt and dE/dx linked not only to Newtonian mechanical ideas, but at the same time to quantum mechanics, by generalizing these forms. We argue that one may start with the notion of energy, momentum and their conservation together with the generalizations of a linear force linked to finite dt=hbar/E and dx=hbar/p. This allows one to a priori write, based on conservation of energy for v<
Special relativity seems to be associated with linking physical relations as seen in one frame with those as seen in a frame moving at a speed relative to such a frame. A constant speed is often used for the moving frame. This suggests that classically there is a special frame for a particle with rest mass called a rest frame. In such a case, one simply introduces a parameter for rest mass and does not worry about the complicated motion and interactions which actually create the rest mass. It seems that even quantum mechanics, which considers a particle to be moving as one does not know its location, one uses the idea of a potential V(x) which in principle is associated with a very large rest mass, presumably at rest as no variables of such a rest mass appear in the Klein-Gordon or Dirac equations. It seems that one uses a preferred frame when solving relativistic quantum mechanical equations. Furthermore, given V(x) and a bound state with exp(-i E bound t), E applies to the overall bound system, not to a possible exp(ipx) constituent. The special relativistic invariant equation seems to exist at the system level, like with the rest mass and one may apparently calculate E in the special rest frame of the large mass and hence find a rest mass of the bound system, i..e large rest mass*cc + mo cc + E, mo is the rest mass of the single bound particle. As a result of the use of the special rest mass frame for the V(x) producing large rest mass, it seems that one does not have to worry about special relativistic constraints on the interaction with V(x), as only one frame is involved. In other words, a bound calculation is about finding a new rest mass for an overall new system. Then this system may be used in Lorentz boosts. One simplifies by working in the rest frame of the mass creating V(x). Perhaps surprisingly then, we note that exp(-iEt+ipx) for a free particle is Lorentz invariant and in fact must be Lorentz invariant for the following reason. Imagine that one wishes to create a probability for free particles which is linked with conservation of momentum. Any p must have the same real value weight because for free particles there is no bias for one p or the other. There is, however, a bias for a p1 and p2. It should have the same probability as a p3 and p4, if p1+p2 = p3+p4. (We use one dimension for simplicity.) As a result, exp(ip) seems to be a probability which respects these conditions. The problem is that one may have p=m1v1=m2v2 hence (E1,p) and (E2,p). With respect to momentum, it is irrelevant if one particle has E1 and the other E2, but not if one does a Lorentz boost. Then, in one case: p→ g(v) p + g(v) v E1 and in the second, p→ g(v) p + g(v)vE2. Here g(v) =1/sqrt(1-vv/cc). In other words, p is the same for each particle in one frame and not in the other which violates conservation of momentum because in frame 1 both particles can complete the same conservation of momentum equation, but in the second frame this is not the case, because each has a different momentum. Thus, exp(ip) cannot hold. One requires a linear form in p which is Lorentz invariant, i.e. exp(-iEt+ipx), we argue (and have done so in previous notes). We see now that momentum probability is linked with space in exp(ipx). The idea seems to be that for free colliding particles there is no preferred frame and the probabilities used must reflect this Lorentz invariance. As a result, we argue that a free particle probability in E,p arises because of Lorentz invariance, but then apply it to a V(x) problem and no longer worry about Lorentz invariance at the interaction level. V(x) with no associated rest mass variables assumes a rest frame for the V(x) producing mass. A Lorentz boost which then invalidates exp(ip), would only apply to the total rest mass of the bound particle system which has no overall momentum. It seems that one does apply the Lorentz transformation to the interaction of exp(ipx)’s with V(x). One is only interested in the overall bound system as a single entity for special relativity. As a result, one may only impose momentum considerations as V(x) is a spatial function and one must link it with exp(ipx). In fact, one may write V(x) = Sum over k Vk exp(ikx) to associate it with momentum hits linked with Vk energies, which already moves away from the idea of special relativity as Vk and k are not linked as a 4-vector. The idea of exp(ip1x)exp(i k1x) = exp(ip2x)exp(ik2x), however, seems to still hold (as it does for free particles), linking these two values (i.e. Vk1 and Vk2) with (p1+k)(p1+k) exp(i (p1+k)x). Lorentz invariance for a particle with rest mass seems to be linked with the idea that one ultimately has a rest frame for the particle. One then establishes a relation between the rest mass in one frame and its new E and p as seen by another frame. One does not, however, need to impose Lorentz invariance conditions on the interaction which creates the rest mass it seems. For example, exp(-iEt+ipx) is the Lorentz form used to describe a free particle, but exp(ipx) is the only portion used to describe its interaction with V(x) in the rest frame of the large mass creating V(x). Furthermore, exp(-iEt+ipx) ensures conservation of energy and p for a free particle, but in an interaction case, that does not happen as the potential may absorb energy.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Because he did not complete his theory its far-reaching, intuitively motivated derivations were never properly appreciated. It is the only theory based on a relativistically correct foundation, the time evolution of energy states, rather than the stipulation of energy eigenvalues in absolute time. Further development of his arguments based on the momentum reveals that although non-relativistic theory correctly predicts what it is possible to observe (the emissions) with remarkable accuracy it neglects the other half of natural phenomena, that which cannot be observed (the absorptions), thereby violating the conservation of energy. The deficiencies in non-relativistic theory are corrected by introducing Hamilton’s principle and deriving relativistic equations of motion. This allows quantum mechanical formalism in abstract space to be replaced by the superposition of particle field geometries in real space. Direct application of the calculus of variations to an electron cycle reveals that the wave function is incomplete because it requires twice the allowable action minimum.
An unconventional outlook on relationship between the quantum mechanics and special relativity is proposed. We show that the two fundamental postulates of quantum mechanics of Planck and de Broglie combined with the idea of comparison scale (explained in the paper), are enough to introduce relativistic description. We argue that Lorentz group is the symmetry group of quantum, preferred frame description. We indicate that the departure from the orthodox relativity postulate allows us, in easy way, to make special relativity and quantum mechanics indivisible whole.
It is often claimed that Einstein is wrong about quantum mechanics. However, when comparisons are made with respect to theoretical foundations rather than experimental results Einstein’s theories are found to be superior. Because he did not complete his theory its far-reaching, intuitively motivated derivations were never properly appreciated despite the fact that his is the only theory based on a relativistically correct foundation. The development of his arguments reveals that although non-relativistic theory correctly predicts what it is possible to observe (the emissions) with remarkable accuracy it neglects the other half of natural phenomena, that which cannot be observed (the absorptions), thereby violating the conservation of energy. The deficiencies in non-relativistic theory are corrected by applying Hamilton’s principle and deriving relativistic equations of motion. This allows quantum mechanical formalism in abstract space to be replaced by the superposition of particle field geometries in real space. Direct application of the calculus of variations to an electron cycle reveals that the wave function represents a non-conservative force and it is incomplete because it requires twice the allowable action minimum.