Abstracts Details

Previously, based on the law of energy conservation, we figured out that, the steady state elliptic motion of an electron around a given nucleus depicts a rest mass variation throughout. We happened to develop our theory, originally vis-?-vis gravitational bodies in motion with regards to each other, providing us, with all known end results of the General Theory of Relativity. 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 phenomenon we disclosed, is to consider a ?jet effect?. Accordingly, a particle on a given orbit through its journey, can be conceived to 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, in a closed system, stays constant throughout. The speed U of the jet, strikingly, points to the de Broglie wavelength , thus coupled with the period of time , inverse of the frequency , delineated by the electromagnetic energy content of the object of concern; is originally set by de Broglie equal to the total rest mass of the object (were the speed of light taken to be unity). This makes that, on the whole, the ?jet speed? becomes a superluminal speed , a fortiori excluding any transport of energy. We call it wavelike speed. This result, in any case, seems to be important in many ways. Amongst other things, it may mean that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, sense each other, with a speed greater than that of light, and this, in exactly the same manner, in both worlds. Note that what we do, well stays within the frame of Quantum Mechanics, since in fact, we ultimately land at the de Broglie relationship. Note also that, we well stay within the frame of the Special Theory of Relativity (STR). Our disclosure seems to be capable to explain the spooky experimental results recently reported, though without having to give away neither the STR, nor Quantum Mechanics, one for the other.

We present results of M?ssbauer experiment in a rotating system, whose performance was stimulated by our recent finding (*Phys. Scr.*, 77 (2008) 035302) and which consisted in the fact that a correct processing of K?ndig's experiment data on the subject gives an appreciable deviation of a relative energy shift (Delta E)/E between emission and absorption resonant lines from the standard prediction based on the relativistic dilation of time (that is (Delta E)/E = -v^{2}/(2c^{2}) to the accuracy c^{-2}, where v is the tangential velocity of absorber of resonant radiation, and c is the light velocity in vacuum). Namely, the K?ndig result we have corrected becomes (Delta E)/E = -kv^{2}/(2c^{2}), with k=0.596?0.006 (instead of the result k = 0.5003?0.006, originally reported by K?ndig). In our own experiment we carried out measurements for two absorbers with substantially different isomer shift, which allowed us to make a correction of M?ssbauer data regarding vibrations in the rotor system at various rotational frequencies. As a result we got the overall estimation k = 0.68?0.03.

An *arbitrary increase* of *rest masses* entering the *quantum mechanical description* of an atomic or molecular object, leads to the increase of the related *total energy,* and *contraction of the size* of the object at hand. Furthermore, this quantum mechanical occurrence yields the *invariance* of the quantity *[energy x mass x size ^{2}],* framing a

*fundamental architecture,*matter is made of. On the other hand, one can check that the latter quantity is Lorentz invariant, no matter one works on a non-relativistic or relativistic quantum mechanical basis. Thus, it appears that, the quantum mechanical invariance of

*[energy x mass x size*with respect to a hypothetical mass change, works as the

^{2}]*principal mechanism*of the

*end results*of the Special Theory of Relativity, were the object in consideration brought to a

*uniform translational motion,*or similarly the

*principal mechanism*of the end results of the General Theory of Relativity, were this object embedded in a

*gravitational field*

*(given that, in either case, it is question of a ?mass? change, which can well be considered as an input to the quantum mechanical description at hand)*. One can further show that, the occurrence we disclose holds, not only for the gravitational field, but generally for all fields, the object at hand interacts with.

PART I

Previously, based on the law of energy conservation, embodying the *mass & energy equivalence* of the Special Theory of Relativity (STR), thus inducing the *rest mass decrease of a bound object,* as much as the *static binding energy *coming into play, the first author developed a theory valid both for the atomic and celestial worlds, and yielding totally similar quantum mechanical deployments for both worlds. The application of the idea, however, to a rotating disc, which is Einstein's gedanken experiment, on which The Grand Master based his General Theory of Relativity (GTR), brings up two distinct effects: 1) Already, as observed by an observer located at the center of the disc and rotating with the same angular velocity as that of the disc, the clock placed at the edge, must, still owing to the law of relativistic law of energy conservation, embodying the *mass & energy equivalence *of the STR, experience, a *rest mass decrease* in the *centrifugal force field,* which in return, leads to a time dilation. 2) The clock according to an outside observer, further dilates by the usual Lorentz coefficient. The first effect is though as important as the second one. Einstein took into account the second one, but not the first one *(as he specifies his thoughts about the problem, in the footnote of page 60 of his book, The Meaning of Relativity).* The overall result is that, the time dilation an object placed at the edge of a rotating disc, would display, should be about *twice *as that predicted by Einstein. The law of conservation of angular momentum, constitutes a cross check of our finding. The recent measurements back us up firmly. At the same time and devilishly, the *inexact analogy* Einstein did set between the effect of rotational acceleration, and the effect of gravitation, leads to results which are the same as ours, up to a third order Taylor Expansion, thus well beyond any precision can intercept, with regards to *actual gravitational measurements.* The remedy of the mistake in uestion, leaves the GTR unfortunately, needless.

PART II

The present approach further leads to the derivation of de Broglie relationship, coming up to be coupled with the superluminal velocity U_{t}=(c^{2}/v) SQRT (1-v^{2}/c^{2}), where v is the velocity of the bound object, say an electron moving around a nucleus, or a planet moving around a star, with respect to the source of attraction or repulsion of concern. This suggests that an interaction, such as that delineated by an optical interception, can of course take place with an ?energy exchange? (in that case, "electromagnetic energy exchange"), but it can also occur without any energy exchange. We propose to call the latter "wave-like interaction". An interaction with energy exchange can not evidently occur with a speed exceeding the speed of light, whereas an interaction without any energy exchange occurs with the superluminal speed U_{t}, were the object moving with a speed v, with respect to the attraction or repulsion center. Note that the present approach is, in full conformity with the STR. Our disclosure, seems to be capable to explain the spooky experimental results newly reported. Thus, it is not that, Non-Locality and STR are incompatible. It is that the STR, allows a type of interaction faster than the speed of light, were there no exchange of energy.

As Galileo has formulated, one cannot detect, once embarked in a *uniform translational motion,* and not receiving any information from the outside, *how fast* he is moving. Why? No one that we recall of, has worked out the answer of this question, although the *Galilean Principle of Relativity (GPR),* constituted a major ingredient of the Special Theory of Relativity (STR). Thus, consider a quantum mechanical *object of clock mass?* M_{0} *(which is just a mass),* doing a *?clock motion?,* such as *rotation, vibration,* etc, with a *total energy* E_{0}, in a *space of size*. Previously we have established that, if the mass M_{0} is multiplied by an *arbitrary number*, then through the *relativistic *or* non-relativistic* quantum mechanical description of the object *(which ever is appropriate to describe the case in hand)* , the *size* R_{0} of it, shrinks as much, and the *total energy* E_{0}, *concomitantly,* increases as much. This *quantum mechanical occurrence* yields, at once, the *invariance* of the *quantity (total energy) x (mass) x (size) ^{2} *

*with regards to the*

*mass change*in question, the object being overall at rest; this latter quantity is, on the other hand, as induced by the

*quantum mechanical framework,*necessarily strapped to h

^{2}, the

*square of the Planck Constant.*But this constant is already,

*dimension wise,*

*Lorentz invariant.*Thus, any quantity bearing the dimension of h

^{2}, is Lorentz invariant, too. So is then, the quantity

*(total energy) x ( mass) x ( size)*Thence, the

^{2}, no matter how the size of concern lies, with respect to the direction of uniform translational motion, that would come into play.*quantum mechanical*

*invariance of the quantity (total energy) x (mass) x (size)*with regards to an

^{2}*arbitrary mass change,*comes to be

*identical*to the

*Lorentz invariance*of this quantity, were the object brought to a uniform translational motion

*.*It is this prevalence, which displays, amazingly, the

*underlying mechanism,*securing the end results of the STR, and this via quantum mechanics. The

*Lorentz invariant architecture, (total energy) x (mass) x (size)*more fundamentally, constitutes the answer of the

^{2}*mystery*drawn by the

*GPR.*In this article, we frame the basic assertions, which will be used in a subsequent article, to display the

*quantum mechanical machinery*making the GPR, and to draw the bridge between the GPR and the

*architecture,*we disclose.

Previously, based on the *law of energy conservation,* we figured out that, the steady state elliptic motion of an electron around a given nucleus depicts a *rest mass variation* throughout. We happened to develop our theory, originally vis-a-vis gravitational bodies in motion with regards to each other, providing us, with *all known end results of the General Theory of Relativity.* 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 phenomenon we disclosed, is to consider a *"jet effect".* Accordingly, a particle on a given orbit through its journey, can be conceived to 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. The *speed* of the jet, strikingly, points to the *de Broglie wavelength*, thus coupled with the inverse of the frequency, delineated by the *electromagnetic energy content* of the object of concern.This makes that, *on the whole,* the *"jet speed"* becomes a *superluminal speed*, *a fortiori* excluding any transport of energy. We call it *wavelike speed*. This result, in any case, seems to be important in many ways. Amongst other things, it may mean that, either gravitationally interacting macroscopic bodies, or electrically interacting microscopic objects, *sense* each other, with a speed greater than that of light, and this, in exactly the same manner, in both worlds. Note that what we do, well stays within the frame of *quantum mechanics,* since in fact, we ultimately land at the de Broglie relationship. Note also that, we well stay within the frame of the Special Theory of Relativity. Our disclosure seems to be capable to explain the *spooky experimental results* recently reported.

In this paper, we re-analyze the ingenious experiment by K?ndig (measurement of the transverse Doppler shift by means of the M?ssbauer effect) and show that a correct processing of experimental data gives a relative energy shift *DeltaE/E* of the absorption line different from the value of classically assumed relativistic time dilation for a rotating resonant absorber. Namely, instead of the relative energy shift *DeltaE/E* = −(1.0065?0.011)*v ^{2}/2c^{2}* reported by K?ndig (

*v*being the linear velocity of absorber and

*c*being the light velocity in vacuum), we derive from his results

*DeltaE/E*= −(1.192?0.011)

*v*. We are inclined to think that the revealed deviation of

^{2}/2c^{2}*DeltaE/E*from relativistic prediction cannot be explained by any instrumental error and thus represents a physical effect. In particular, we assume that the energy shift of the absorption resonant line is induced not only by the standard time dilation effect, but also by some additional effect missed at the moment, and related perhaps to the fact that resonant nuclei in the rotating absorber represent a macroscopic quantum system and cannot be considered as freely moving particles.

We show that, just like the gravitational field, the electric field too slows down the internal mechanism of a clock, which interacts with the field. This approach explains substantially, the retardation of the decay of the muon, bound to a nucleus.

The compatibility of Coulomb Force with the special theory of relativity (STR), is a well know fact. But, any compatibility is not a must. Thus, the following question arises: Would there a more fundamental level, shaping the known structure of Coulomb Force, perhaps based on the foundations of the STR? Yes, indeed: It is that electric charges are Lorentz invariant, just like the speed of light, is. What seems so far ignored is the following. Not only that the constancy of the speed of light is, an empirical evidence, but the Lorentz invariance of electric charges, is too. These two facts do not seem to imply each other. Thus, both of them (as well as, perhaps the Lorenz invariance of similar entities, such as nuclear charges), must be considered concomitantly, in order to insure the Galilean principle of relativity with respect to all inertial frames of reference, which is in effect, the underlying postulate of the STR. Actually the constancy of the speed of light, does not appear to insure all alone, the validity of this principle, and this is why, exactly, Einstein cared to state the second postulate of the STR (regarding the sameness of the laws of nature with regards to all inertial frames of reference), although he did not make any use of it, throughout. Once we have the two evidences of concern (i.e. the Lorentz invariance of electric charges and that of the speed of light), then we can right away, mathematically derive the known Coulomb Force, though reigning between two static charges, exclusively. By the same token, the spatial dependency of Newton Force too, regarding two static masses, becomes a mathematical requirement based on the STR, which seems to be something totally overlooked. So, both forces (still reigning between static, respectively, electric and gravitational charges only), are fundamental laws of nature, essentially imposed by the Galilean principle of relativity. In a subsequent article, however, we will show that, quite on the contrary to the general wisdom, neither Coulomb Force, nor Newton Force holds, if the ? electric or gravitational ? test charge in consideration, is in motion (the source charge being as usual, considered at rest, throughout). We show that, assuming the opposite (i.e. asserting that Coulomb Force, or Newton Force holds if the test charge, is in motion), constitutes a clear violation of the law of conservation of energy. Our approach removes the blockade toward a unification of fields, and the quantization of the gravitational field (hindered by the general theory of relativity).

We show that, just like the gravitational field, the electric field too slows down the internal mechanism of a clock, entering into interaction with the field. This approach explains substantially, the retardation of the decay of the muon, bound to a nucleus.

In a previous article, we have provided a whole new approach toward the end results of the General Theory of Relativity (GTR), based on just the energy conservation law, in the broader sense of the concept of ?energy? embodying the mass & energy equivalence of the Special Theory of Relativity (STR). Thus, our approach was solely based on this latter theory (excluding the necessity of assuming the principle of equivalence of Einstein). According to our approach, the rest mass of an object embedded in a gravitational field (in fact in any field the object interacts with) decreases as much as the binding energy coming into play. Thereby, based on a general quantum mechanical theorem we prove, its internal energy, weakens as much; thus the classical red shift and time dilation.

This theorem (we did not have any room to provide a general proof of, previously), basically says that, if in a relativistic or non-relativistic quantum mechanical description, composed properly, the mass of the object in hand is multiplied by an arbitrary number , then the total energy of it, is multiplied by , and its size is divided by . This number however may very well not be arbitrary. For example, it would specify how much the rest mass of the object is altered when this is embedded in a gravitational field, leading via quantum mechanics, strikingly at once, to the end results of the GTR. This manipulation further yields the invariance of the quantity [energy x mass x size2]. We conclude that, it is this quantum mechanical invariance, necessarily strapped to the square of the Planck Constant, which constitutes a given framework regarding the matter architecture, and insures the end results of the GTR.

Not only that our approach is incomparably simple as compared to the GTR, but it also avoids all incompatibilities (such as the breaking of the relativistic relationship E=mc2), or inconsistencies (such as the breaking of the energy conservation law, as well as the breaking of momentum conservation law), or blockades (such as the impossibility of the quantization of the gravitational field), thus opens a whole clean avenue toward a unification of fields, and understanding of the matter and the universe at all levels, with just the same set of tools.

Since we do not have to use the principle of equivalence of the GTR, amongst others, we could show that, just like the gravitational field, the electric field too slows down the internal mechanism of a clock, had this interacted with the field. This result explains substantially, the retardation of the decay of the muon, bound to a nucleus.

We base the present approach, on an alternative theory of gravitation, consisting essentially on the law of energy conservation broadened to embody the mass & energy equivalence of the Special Theory of Relativity, and remedying, known problems and incompatibilities, associated with the actually reigning conception. The mere rotation problem of say, a *sphere,* can well be undertaken, along the same idea. Accordingly, we consider the *problem of gravity created by a rotating celestial body.* Finally we apply our results to the case of a geosynchronous satellite, which is, schematically speaking, nothing but a clock placed on a considerably high tower. The approach ironically furnishes the >Newton's law of motion, which however we derive, based on just static forces, *and not an acceleration, governing a motion. (There is anyway no motion for a geosynchronous satellite, when observed from Earth.) *We predict accordingly that, the blue shift of light from a geosynchronous satellite *on an orbit of radius *r_{Gs} should be *softened *as much as omega^{2}/(2c^{2})(r_{Gs}^{2}-R^{2}) compared to what is expected classically; here omega is *Earth's self rotation angular momentum,* R *Earth's radius,* and c the *speed of light in empty space. *We hope, the validity of this unforeseen prediction, can soon be checked out.

In this article, we show that the analogy between the *effect of acceleration* and the *effect of gravitation*, making up the Classical (C) Principle of Equivalence (PE), which is the basis of the General Theory of Relativity (GTR), constitutes a *non-conform analogy*, i.e. it does not embody a *one to one correspondence between the two worlds* coming into play. This will constitute a starting point to show the inadequacy of the *Classical Principle of Equivalence* (CPE). On the basis of a *quantum mechanical theore*m previously established, we prove that, the CPE is further inaccurate. For one thing, it happens to constitute a *violation* of the *law of energy conservation*. More specifically, owing to the *law of energy conservation*, broadened to embody the *mass & energy equivalence* of the Special Theory of Relativity (STR), next to the *usual mass dilation* due to the movement in question, the force field too, is to alter the *rest mass* subject to an accelerational motion (*which happens something totally overlooked by the GTR*). This assertion is well compatible with the recent disclosure that the time dilation displayed by a rotating object is much greater than the one classically predicted on the basis of just the Lorentz factor, associated with the motion. Thence, we establish a Proper PE. The approach we present, leaves unnecessary the CPE, thus the GTR, and yields a *whole new theory about gravitation*, along with all end results of this theory, up to a third order Taylor expansion, yet with no singularity (*thus, no black holes*), and with an incomparable ease, with a *different metric* too. Our approach in fact is (*not restricted to gravitation, thus is*) extendable to all fields.

Previously, based on just the law of energy conservation, we figured out that, the gravitational motion depicts a *?rest mass variation?,* throughout. The same applies to a motion driven by electrical charges; this constituted the topic of the preceding article (Part I of this work). One way to conceive the mass exchange phenomenon we disclosed, is to consider a *?jet effect?.* Accordingly, an object on a given orbit, through its journey, *must eject mass to accelerate,* or *must pile up mass, to decelerate. *The speed of the jet, strikingly points to the de Broglie wavelength, coupled with the inverse of the frequency, delineated by the electromagnetic energy content, of the object. This makes that, *jet speed* becomes a *superluminal speed*. This result seems to be important in many ways. Amongst other things, it means 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, energy cannot of course go faster than light, but *information* can be carried without any basis of energy. Furthermore, our approach, induces immediately the quantization of the *?gravitational field?,* in exactly the same manner, the *?electric field?* is quantized.

Based on the law of energy conservation, we figured out that, the steady state electronic motion around a given nucleus generally depicts a rest mass variation throughout, though the overall relativistic energy remains constant. Note that our approach is, in no way, conflicting with the usual quantum mechanical approach. Quite on the contrary it provides us with the possibility of elucidating the ?quantum mechanical weirdness?. We happened to develop our theory originally vis-?-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. One way to conceive the phenomenon we disclosed 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. The speed of the jet, strikingly, points to the de Broglie wavelength, coupled with the inverse of the frequency, delineated by the electromagnetic energy content of the object of concern.This makes that, on the whole, the *jet speed* becomes a *superluminal speed*, yet excluding any transport of energy. Recent measurements appear to back up our conjecture. Here, furthermore may be a clue, for the *wave-particle duality. *

*Appl. Comput. Math.* 7(2) (2008), pp. 255-268. A complete description of space-time, matter and energy is given in Einstein's special theory of relativity. We derive explicit equations of motion for two falling bodies, based upon the principle that each body must subtract the mass-equivalent for any change in its kinetic energy that is incurred during the fall. We find that there are no singularities and consequently no blackholes.

A complete description of space-time, matter and energy is given in Einstein's special theory of relativity. We derive explicit equations of motion for two falling bodies, based upon the principle that each body must subtract the mass-equivalent for any change in its kinetic energy that is incurred during the fall. We find that there are no singularities and consequently no blackholes.

This article first consists in the quantum mechanical study of an *adiabatically* *compressed *particle, residing in an *infinitely high potential well,* which we will consider, as the basis of an *ideal gas.* Thus we prove in both non- relativistic and relativistic cases, that, all the *compression energy* is transformed into *extra kinetic energy* of the particle. The result may be intuitive, but does not seem trivial. Thus it shows a *full* *accordance *between *Quantum Mechanics, Newton's Second Law of Motion, the Law of Energy Conservation, Special Theory of Relativity*, and furthermore *Classical Thermodynamics* and *Kinetic Theory of Gases*. In effect, on the same basis, one can quantum mechanically derive, an essential relationship associated with an *ideal gas,* that is *Pressure x (Volume) ^{5/3}=Constant, *with regards to any set of adiabatic transformations, the gas at hand, would undergo. More important, by doing so, one as well, specifically derives the value of the

*Constant*making the RHS of this relationship,

*which has been otherwise left obscure since the time*

*Quantum Mechanics*came into the scene. Our finding means that, the

*ideal gas behavior,*is just a

*macroscopic*

*manifestation of Quantum Mechanics.*In other words i) it can be derived, by all means, based on the quantum mechanics of a single particle, ii) along that line, it excludes any interaction of the constituents, the gas, embodies. The latter is something known, for it is classically assumed, based on the Kinetic Theory of Gases. However we arrived at it, via the quantum mechanical approach we have deployed. Thus we end up with a

*precise definition*of an ideal gas:

*It is a gas,*

*where the behavior can be predicted based on the quantum mechanics of a single particle imprisoned in a box.*This is how

*the classical assumption*as to, it should be free of any interaction of its constituents, whatsoever, comes to find a deeper root.

In the previous article, we have shown that the spatial behavior of Coulomb Force, reigning between two static charges, exclusively, is *(not only compatible with, but is also)* imposed by the Special Theory of Relativity, more profoundly, the underlying Galilean Principle of Relativity. Herein we do the same for Newton Force reigning between two static masses, exclusively. In a subsequent article, how ever we will show that, quite on the contrary to the general wisdom, neither Coulomb Force, nor Newton Force holds, if the ? electric or gravitational ? test charge in consideration, is in motion *(the source charge, being as usual, considered at rest, throughout).* Assuming the opposite *(i.e. asserting that Coulomb Force, or Newton Force holds, if the test charge is in motion),* constitutes a violation of the relativistic law of conservation of energy. Our approach removes the blockade toward a unification of fields, and the quantization of the gravitational field *(hindered by the General Theory of Relativity);* it yields the same result, for any field, the object at hand, interacts with.

Previously we have shown that Coulomb Force, or Newton Gravitational Attraction Force *(or in short, Newton Force)* is imposed by the Special Theory of Relativity (STR), though for static *(electric or gravitational)* charges, exclusively. Thus, these forces *(for static charges)* happen to be deep-seated laws of nature. This unfortunately happens to be something totally overlooked chiefly for Newton Force. On the other hand, we have no sign that either force will work, for a moving *test charge,* the source charge being still at rest. In this article we are going to show that, although it remains a must to adopt Newton law, for static masses, as imposed by the STR, still to presume the validity of it, for a *moving test charge,* violates the *relativistic law of conservation of energy.* Thus, herein, we are going to provide the correct expression for Newton Gravitational Attraction Force exerted by a *source charge,* at rest, on a *moving test charge,* which right away leads to all measurable end results of the General Theory of Relativity.

Over the years, we were all taught, and did teach that Coulomb Force exerted by a source charge at rest on a test charge, is the same, whether the test charge is at rest, or in motion. Previously we have shown that the spatial behavior of Coulomb Force, or that of Newton Force, is a *must* imposed by the Special Theory of Relativity, though for static *(electric or gravitational)* charges, exclusively. In this article we will show that, to presume the validity of the Classical Coulomb Force for a moving test charge, violates the relativistic law of conservation of energy. Accordingly, we provide the correct expression for Coulomb Force exerted by a source charge, at rest, on a moving test charge. It is that, the Classical Coulomb Force in the latter case, is reduced by the inverse of the Lorentz dilation factor coming into play, or the same, the source charge appears to exert a greater acceleration on the moving test charge, if viewed classically. This approach, facilitates considerably, the formulation of the relativistic quantum mechanics. As regards to Newton Force, it allows us to reach the end results of the General Theory of Relativity, though through a totally different set up than that of Einstein, and incomparable ease, and thereby, the quantization of gravitation, just like the electric field, or in fact any field the object at hand interacts with.

Previously, we established a connection between the macroscopic classical laws of gases and the quantum mechanical description of molecules of an ideal gas (T. Yarman et al. arXiv:0805.4494). In such a gas, the motion of each molecule can be considered independently on all other molecules, and thus the macroscopic parameters of the ideal gas, like pressure *P* and temperature *T*, can be introduced as a result of simple averaging over all individual motions of the molecules. It was shown that for an ideal gas enclosed in a macroscopic cubic box of volume *V*, the *constant,* arising along with the *classical law of adiabatic expansion,* i.e. *PV ^{5/3} = constant*, can be explicitly derived based on quantum mechanics, so that the instant comes to be proportional to

*h*here

^{2}/m*h*is the Planck Constant, and

*m*is the relativistic mass of the molecule the gas is made of. In this article we show that the same holds for a photon gas, although the related setup is quite different than the previous ideal gas setup. At any rate, we come out with

*PV*, where

^{5/3}~ hc = constant*c*is the speed of light. No matter what the dimensions of the

*constants*in question are different from each other, they are still rooted to universal constants, more specifically to

*h*and to

^{2}*hc*, respectively; their ratio, i.e.

*V*interestingly pointing to the

^{1/3}~ h/mc,*de Broglie relationships*cast.

In this paper we find a connection between the macroscopic classical laws of gases and the quantum mechanical description of non-interacting particles confined in a box, in fact constituting an ideal gas. In such a gas, the motion of each individual molecule can be considered independently from all other molecules, and thus the macroscopic parameters of ideal gas, like pressure* P* and temperature *T*, can be introduced as a result of simple averaging over all individual motions of molecules. It is shown that for an ideal gas enclosed in a macroscopic cubic box of volume *V*, the *constant, in the classical law of adiabatic expansion expression*, i.e. PV^{5/3} can be derived, based on quantum mechanics. Physical implications of the result we disclose are discussed. In any case, our finding proves, seemingly, a *macroscopic manifestation of a quantum mechanical behavior, *and this in relation to classical thermodynamics.

A concise, *thoroughly scientific ethic system* is presented. We would like to call it, a *Cosmic Wholeness*, which can be taken as the basis for the definition of the *good* and the *bad*, and amongst other things, a sustainable energy consumption and development, a healthy environment, and a most stable World Peace.

Via Newton's law of gravitation between two static masses exculsively, and the energy conservation law, in the broader sense of the concept of energy embodying the relativistic mass & energy equivalence, on the one side, and quantum mechanics, on the other, one is able to derive the end results aimed by the General Theory of Relativity. The energy conservation law, in the broader sense of the concept of ?energy? embodying the relativistic mass & energy equivalence, is anyway a common practice, chiefly nuclear scientists make use of. Yet amazingly, besides it is not applied to gravitational binding, it also seems to be overlooked for atomic and molecular descriptions. Thus herein, next to the reestablishment of celestial mechanics, we propose to reformulate the relativistic quantum mechanics on the basis of Coulomb Force, but assumed to be valid only for ?static electric charges?; when bound though, the rest mass of an electric charge, must be decreased as much as the ?binding energy? it delineates.

Along the same line, one can remarkably derive the de Broglie relationship, for both electrically and gravitationally interacting objects. Our results, furthermore, seem capable to clarify the results of an experiment achieved long time ago, at the General Physics Institute of the Russian Academy of Sciences, but left unveiled up to now. The frame we draw amazingly describes in an extreme simplicity, both the atomic scale, and the celestial scale, on the basis of respectively, Coulomb Force (written for static electric charges, exclusively), and Newton Force (written for static masses, exclusively), in exactly the same manner. Our approach yields precisely the same metric change and quantization, at both scales, in question.

For simplicity, the presentation is made based on just two particles, one very massive, the other one very light, at both scales, without though any loss of

Herein we present a whole new approach which leads to the end results of the General Theory of Relativity, via just the law of conservation of energy *(broadened to embody the mass & energy equivalence of the special theory of relativity),* and quantum mechanics. Thus, we start with the following postulate.

**Postulate:** The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-?-vis the gravitational field of concern.

The decreased rest mass, is further dilated by the Lorentz factor, if the object in hand, is in motion in the gravitational field of concern. The overall relativistic energy must be constant on a stationary trajectory. This yields the equation of motion driven by the celestial body of concern, via the relationship exp(-alpha) x SQRT(1-v_{02}/c_{02}) = Constant, along with the definition alpha=G*M*/(rc_{02}); here *M* is the mass of the celestial body creating the gravitational field of concern; G is the universal gravitational constant, measured in empty space; it comes into play in Newton's law of gravitation, which is, in our approach, assumed to be valid for static masses only; r points to the location picked on the trajectory of the motion, the center of *M* being the origin of coordinates, as assessed by the distant observer; v_{0} is the tangential velocity of the object at r; c_{0} is the ceiling of the speed of light in empty space; v_{0} and c_{0} remain the same for both the local observer and the distant observer, just the same way as that framed by the special theory of relativity.

The differentiation of the above relationship leads to our equation of motion, i.e.

d__v___{0}/dt = -(G*M*/r^{2}) (1-v_{02}/c_{02}) __r__/r;

__r__ is the outward looking unit vector along r; the latter differential equation is the classical Newton's Equation of Motion, were v_{02}/c_{02}, negligible as compared to unity; this equation is valid for any object, including a light photon.

Taking into account the quantum mechanical stretching of lengths due to the rest mass decrease in the gravitational field, the above equation can be transformed into an equation written in terms of the proper lengths, yielding well the end results of the General Theory of Relativity, though through a completely different set up.

Via "Newton's law of gravitation" between two "static masses", and the "energy conservation laf", in the broader sense of the concept of "energy" embodying the "relativistic mass-energy equivalence", on the one side, and "quantum mechanics", on the other, we were able to derive the end results of the general theory of relativity. Yet we ended up, seemingly, with the violation of the principle of equivalence, the basis of the general theory of relativity. Thus, through a straightforward approach, we found m_{gravitational} = m_{inertial} / gamma^{2}, where gamma is the usual Lorentz dilation factor. In the aim of establishing a theory fully compatible with the special theory of relativity, Mie in 1912 had reached the same conclusion, though through an "inverse problem set up". Not having postulated an "alternative principle of equivalence", he failed to carry his theory any further, which presumably led Einstein to ignore Mie's theory. We have happened to achieve what Mie, apparently could not, and have well ended up with the "end results" of the general theory of relativity, via just Newton?s laf of gravitation and energy conservation law, thus without being in the need of the principle of equivalence.

Herein, a full quantum mechanical deployment is provided on the basis of the frame drawn in the previous Part I. Thus it is striking to find out that occurrences taking place at both atomic and celestial scales, can be described based on similar tools.

Accordingly, the gravitational field, is quantized just like the electric field. The tools in question in return are, as we have shown, founded on solely the energy conservation law.

The relativistic quantum mechanical equation we land at for the hydrogen atom, is equivalent to the corresponding Dirac's relativistic quantum mechanical set up, but is obtained in an incomparably easier way. Following the same path, a gravitational atom can be formulated, in a space of Planck size, with particles bearing Planck masses.

Previously, based on the energy conservation law *(in the broader sense of the concept of energy, thus embodying mass),* as imposed by the *special theory of relativity,* we had proposed to alter the *rest mass* of a an object of mass m_{infinity} *(measured at a place free of gravitational field),* gravitationally bound to a host celestial body of mass M_{infinity} (*still measured at a place free of surrounding gravitational field*), practically infinitely more massive as compared to the rest mass m_{infinity} . Accordingly, m_{infinity} was to be decreased, as much as the binding energy coming into play, in between the two masses of concern.

This manipulation, together with a *quantum mechanical theorem* we had established *(indicating that if the mass of a wave-like object is decreased by a given amount, its internal energy is concomitantly decreased as much),* did essentially yield the end results of the general theory of relativity, though through a completely different set up than that of this latter theory.

Herein we remove the restriction that the host body is infinitely more massive that the test mass, and we end up with a generalized expression for the *total binding energy,* coming into play.

Were the original masses m_{infinity} and M_{infinity} set free to fall onto each other, our approach yields the classical linear momentum conservation law.

In our previous article we arrived at an *essential relationship* for the *classical vibration period* of a diatomic molecule. It is that the *cast* of this relationship, [period of time] ~ [mass] x [size of space of concern]^{2}, is essentially imposed by the *special theory of relativity;* this is how we originally arrived to it, although we have derived it, *quantum mechanically,* in Part I of this work.

The above relationship holds generally. It *essentially* yields T~r^{2}, for the *classical vibrational period,* versus the *square of the internuclear distance* at different *electronic states of a given molecule,* which happens to be an *approximate relationship* known since 1925, but not disclosed so far.

In this article, we determine the *quantum mechanical mulitplier* appearing next to the Planck Constant in the epression in question to be r/r_{0}, for *electronic states configured similarly,* r being the *internuclear distance at the given electronic state,* and r_{0} the *internuclear distance at the ground state.*

Note that, not much is reported about the quantum numbers of complex systems, in the literature.

We consider the quantum mechanical description of a diatomic molecule. We apply to it, the Born & Oppenheimer approximation, together with the cast [total energy x mass x size**2 ~h^{2}] *(we established previously),* written for the electronic description *(with fixed nuclei);* here, "mass" is the* electron mass.*

Our approach yields an *essential relationship* for the *classical* *vibration period,* in terms of the [square root of the reduced mass of the nuclei] x [the square of the internuclear distance], at the given *total electronic energy.* The quantum multiplier that comes into play, next to the Planck Constant, in this latter expression, is determined in the subsequent part. The approach yields a *whole new systematization* regarding all diatomic molecules.

We draw the *classical* *vibration period*versus [the square root of the reduced mass of the nuclei] x [the square of the internuclear distance], for different chemical families, yielding indeed a smooth behavior. The plots are further bettered, along the determination of the quantum multiplier of concern, throughout the subsequent articles.

In a previous article, i.e. Part I of the present work, we arrived at an *essential relationship* for T, the *classical vibration period* of a diatomic molecule in terms of [the reduced mass of the nuclei] x [the square of the intranuclear distance].

In a subsequent article, i.e. Part II of the present work, we have established that the quantum m?ltiplier taking place next to the Planck Constant, in this relationship, turns out to be the ratio of the internuclear distance of the molecule at the given excited state, to the internuclear distance of the molecule at the ground state, provided that these states are configured similarly. Furthermore based on the analysis of H_{2} spectroscopic data, we found out that the *ambiguous states* of this molecule are configured like the ground states of alkali of hydrides*, *and the ground state of Li_{2}, respectively. Conversely, this suggests that, we can describe, the ground state of any of these molecules, on the basis of an *equivalent* H_{2} excited state.

Via this interesting finding, herein we propose to associate the quantum multiplier in question , with the bond's electrons of the *ground state* of any diatomic molecule belonging to *a given chemical family, *in *reference* to the *ground state of the diatomic molecule, still belonging to this family,* bearing the *lowest classical vibrational period, *since the proportionality constant, depending only on the *electronic configuration,* will accordingly stay nearly constant, throughout.

This allows us to draw a whole new systematization of diatomic molecules, given that the proportionality constant appearing in the above relationship, being *purely dependent on just the electronic structure of the molecule,* stays *constant* for *chemically alike molecules.*

Thus, our approach discloses a *simple architecture* about diatomic molecules, otherwise left behind a much too cumbersome quantum mechanical description. This architecture, telling how vibrational *period of time, size,* and *mass *are installed; is Lorentz invariant, and can be considered as the mechanism about the behavior of the quantities in question, in interrelation with each other, when the molecule is brought to a uniform translational motion, or transplanted into a gravitational field, or in fact any field it can interact with.

Herein we present a whole new approach to the derivation of the *Newton's Equation of Motion.* This, with the implementation of a metric imposed by *quantum mechanics,* leads to the findings brought up within the frame of the general theory of relativity* (such as the precession of the perihelion* *of the planets, and the deflection of light nearby a star).* To the contrary of what had been generally achieved so far, our basis merely consists in supposing that the gravitational field, through the *binding process,* alters the *?rest mass?* of an object conveyed in it. In fact, the special theory of relativity already imposes such a change. Next to this fundamental theory, we use the classical Newtonian gravitational attraction, reigning between two *static masses.* We have previously shown however that the 1/r^{2} dependency of the gravitational force is also imposed by the special theory of relativity.

Our metric is *(just like the one used by the general theory of relativity)* altered by the gravitational field *(in fact, by any field the ?measurement unit? in hand interacts with);* yet in the present approach, this occurs via *quantum mechanics.* More specifically, the *rest mass* of an object in a gravitational field is decreased as much as its *binding energy* in the field. A *mass deficiency* conversely, via *quantum mechanics* yields the *stretching *of the size of the object in hand, as well as the *weakening *of its internal energy. Henceforth one does not need the "*principle of equivalence*" assumed by the general theory of relativity, in order to predict the occurrences dealt with this theory.

Thus we start with the following interesting postulate, in fact nothing else, but the *law conservation of energy,* though in the broader *relativistic sense* of the concept of *?energy?.*

**Postulate:** The rest mass of an object bound to a celestial body amounts less than its rest mass measured in empty space, and this, as much as its binding energy vis-?-vis the gravitational field of concern.

This yields the interesting equation of motion driven by the celestial body of concern, and this already in an integral form.

The differentiation of this relationship leads to the general equation of motion. The resulting differential equation is the *classical Newton's Equation of Motion,* were the velocity of the object, negligible as compared to *the speed of light in empty space.*

The stretching of lengths in a gravitational field is equivalent to the slowing down of light, throughout, as referred to a distant observer. Based on this, the above differential equation can be transformed in regards to the distant observer. The mathematical manipulation in question, together with the related solution, will be undertaken in our next article.

Consider a *quantum mechanical clock *in the *rest frame of reference. *This can be a molecular, or an atomic, or a nuclear entity, of *?clock mass?* M_{0}, doing a regular *?clock labor?,* in a space of*. ?size?* R_{0}, throughout a *?period of time? *T_{0}. In our previous work we established that, in a *real (not artificially gedanken) wave-like description,* if the clock mass M_{0} of the object is increased by the *arbitrary number*, then its size R_{0} shrinks as much, and the total energy E_{0} of the object, is increased as much, or the same the period of time To is shortened as much. This occurrence induces the* quantum mechanical invariance *of the quantity E_{0}M_{0} R_{0}^{2} This quantity happens further, to be girdled to h^{2}. Note that E_{0}M_{0} R_{0}^{2} happens to be an invariant of the special theory of relativity.

This is in fact how space* (size), *mass (*clock mass*), and time *(period of time)* associated with a wave-like object, come to be interrelated to draw a *?given matter architecture?,* through a given *orchestration of charges.* The laws related to such a structure, are developed in our previous work. Thus, *?mass and space size ought to be structured as inversely proportional to each other?, *i.e. if mass in a wave-like object, is, say hypothetically increased, then, the space size in question, should decrease as much. *Mass and period of time too, ought to be structured as inversely proportional to each other?,* etc.

The *mass increase* we introduce above, may very well be not hypothetical, and this is indeed what one experiences, when a clock is removed out of a gravitational field; its *rest mass, *according to the special theory of relativity, would be increased as much as its *?binding energy with the field of the gravitational body of concern?. *Its period of time *(were this a wave-like clock),* according to our quantum mechanical findings, should then shorten as much. Strikingly, this is a quite known occurrence in the scope of the general theory of relativity. It is thus beautiful to discover that, *quantum mechanics, *due to the *matter architecture *we disclose, works as the* internal machinery of the occurrence regarding the period of time change, predicted by the general theory of relativity. *Yet according to our approach, the same phenomenon would occur, in exactly the same way, for *ionized wave-like clocks* in an electric field, or for wave-like clocks bearing an electric dipole, still in an electric field, or for wave-like clocks bearing a magnetic dipole, in a magnetic field. Similarly, when a muon is bound to a proton, its half life would *quantum mechanically* increase as much as its *binding energy. *These are occurrences,* substantially *identical to that predicted by the general theory of relativity, with however the difference that, now the effect in question, is caused, in a field, other than the gravitational field. Notwithstanding, there is an *important discrepancy* we arrive at; i.e. when a clock is bound to a gravitational field; its size stretches and its mass decreases, on the contrary to what the general theory of relativity predicts *(though the changes in question, thus except their directions, are exactly the same).* Note that no *mass measurement* within the frame of the frame of the general theory of relativity is so far achieved; we propose to clear out the problem, via a technique now available, i.e. by measuring the *Rydberg Constant* at two altitudes of difference of about 1000 m, on Earth.

One important result we derive is that, there seems to be no* singularity *for the time behavior in increasingly concentrated matter, thus there are no *?black holes?. *An other important result yet, is our prediction about the *possibility of the presence of a singularity* for an electric charge binding an electric clock: for instance, a nucleus bearing a charge of about 125e seems to stop the disintegration of a muon bound to the ground state of the outcoming muo-atom. Whether this is so or not, needs to be investigated. Further it is interesting to note that our approach makes possible the* ?presence of different times?, *at a fixed location in space.