ON NEW CONCEPTS OF WEIGHT AND GRAVITY AND THEIR BEARING ON RELATIVITY AND BIOCHEMISTRY

 

By Elie Agur

 

© E. Agur, Amsterdam, 2007

 

e.agur@wxs.nl

 

 

ABSTRACT

 

This paper presents a new concept of weight which distinguishes between self-weight and acquired weight and subsequently leads to a new definition of gravity. It is based on the assumed existence of mass-energy fields that extend from all material particles. These are the interactions of the fields which create the weight of bodies and bring about gravity.

Besides an enlargement of the Newtonian view, and a new interpretation of Galileo’s law of falling bodies, this paper touches upon a number of other topics, including that of the expansion of the universe.

However, its chief importance is probably with regard to protein conformations, the most enigmatic subject in modern biochemistry. A solution is offered to the rapidity and uniqueness of their folding.

 

Not being a professional physicist I cannot offer a full-fledged theory, yet the issues put forward here and their proposed solutions may, I believe, prove quite significant nonetheless.

 

 

THE MASS-ENERGY FIELD

 

This theory postulates that each subatomic particle has its own field. The frequency of the field is related to the mass-energy relationship of the particle which can be expressed as

In this equation e is in ergs c in centimeters (2.997x1010), m in grams and M, which is introduced here as a constant of mass, has the value of G/2x103, that is 3.336x10-11 in the cgs system (where G is the constant of gravitation); u, the field’s frequency, is given in Hertz.

From the above, the equation u=mc can easily be derived (see section THE DENOTATION OF THE CONSTANTS). The magnitude of u falls off at d2. As shall be explained presently these are the interactions of fields inside bodies which create weight and attraction. The wavelength of a field in centimeters is inversely equal to the particle’s mass in grams: uλ=c together with u=mc give λ=1/m.

 

 

 

 

SELF-WEIGHT AND ACQUIRED WEIGHT

 

According the pervasive view, based on Newtonian mechanics, weight is an acquired property of a body. That view holds that there is no need to differentiate between a body’s self-weight and its acquired weight since no body is supposed to possess ‘self-weight’ and thus ‘acquired weight’ is by definition a body’s ‘weight’. This view enabled Newton to conclude that the force of gravity acting on a body constitutes its entire weight.

Since the premises of the present theory are different from those of Newton, the question of weight has to be undertaken from a different perspective, and it necessarily leads to a new description as well as definition of weight.

 

The above description of the mass-energy field emanating from each subatomic particle means that the interacting fields of a body act on each of the body’s atoms in exactly the same way they act on atoms of other bodies. A body represents thus a unity of interacting fields, in the majority of cases on a huge scale. The reference to a body as a ‘unity’ is made on the grounds of its fields being all subjected to a unified motion (or state of rest) and their convergence at a single center – the body’s center of mass, or, in an atom, its nucleus.

 

However, there is no physical reason to deprive a body of possessing, in isolation from any other body in the universe, the same property its fields create when interacting with other bodies, namely weight, since the physical cause of weight, that is the interactions of mass-energy fields, exists, obviously, in a state of isolation as well, and the only pertinent difference is that the vector of weight is directed towards the body’s own center of mass. This state of affairs means that the ‘self-weight’ of a body cannot be measured from outside the body. It is concealed, as it were, inside the body and does not contribute to its fields’ interactions with other bodies, or for that matter, measurement instruments placed between it and other bodies.

The equation that describes ‘self-weight’ is w(s) =mG. 

We realize at the outset that G, Newton’s constant of gravity, is relegated here to a different physical function, that of the constant of weight, and this has to do with the view presented here, that gravity should be described as the motion of bodies due to the acquired weight created in them by the mass-energy fields of other bodies. The important aspect of G, given the physical context of this theory, is that we can surmise with some certainty that as the fields have their frequencies, G itself is a frequency-constant, and this is quite an important departure from Newtonian physics, where G is not assigned any physical meaning in itself, let alone given a frequency content.

 

In order to make it clear that ‘self-weight’ means “weight created by a body and contained within that body,” I believe that a small circle attached to the above equation would do. Thus: w(s) =(m1G)o. This would make it possible to indicate the ‘acquired weight’ due to the influence of another body by a small arrow attached to its part in the equation:

 giving the complete equation of weight

 

Self-weight may have escaped our attention thus far not merely because it did not fit in with the accepted concepts of classical physics, or even that it could not be detected independently, but mainly because of its minute, virtually negligible values, with regard to most bodies on Earth and their gravitational interactions with each other.

 

 

GALILEO’S LAW OF FALLING BODIES

 

The contents of the foregoing chapter enable us now to conclude that all bodies fall at an equal acceleration towards the Earth’s center regardless of their mass, shape and material composition, since

 

is uniform for all of them, where m2 is the mass of the Earth.

 

Einstein based his general relativity on the principle that the uniform acceleration of falling bodies testified to the equality of inertial mass and gravitational mass. He then could claim that the effects of gravity and acceleration were physically identical, and that one could not make any meaningful distinction between them. 

 

The present theory ascribes the uniform fall to more elementary causes: The (composite) field of the attracting body, and the fact that self-weight, in view of its vector being directed towards the center of mass of the falling body itself, has no influence on the acceleration of the body’s fall.

 

 

INERTIAL MOTION

 

A body will maintain its uniform motion in a straight line as long as its center of mass - which is the focal point of the convergence of all the fields of the particles making up that body - will not change its location, and that its mass-geometry will not alter – which is identical to the change of location of the center of mass under the same conditions.

 

 

GRAVITY

 

In his treatment of gravity Newton had to adhere to the concept of identical symmetry since gravity in his view had to conform to the third law of motion: Both forces had to be of the same magnitude, and proportional to the masses of the two bodies involved.

It would be a futile attempt to try to create a model of how such forces come into being and how they operate under the contradictory constraints of being infinitely flexible yet infinitely rigid in order to react immediately to any change of motion of any of the bodies and simultaneously maintain a straight line from each of the bodies’ center of gravity to the other one’s. Newton was thus obliged to introduce the concept of the infinite speed of gravity’s operation, since in no other way could he account for its operation under these, and other, constraints. 

He preferred not to enter the discussion as to the physical nature of these forces and treated the subject, in the most thorough way possible, mathematically and geometrically only.

 

The theoretical framework presented here does away with the concept of identical symmetry. Since Newtonian forces are substituted by mass-energy fields which create both self-weight and acquired-weight, identical symmetry cannot be maintained. The combined field of a body (that which creates its self-weight) has precedence over the operation of all other bodies’ fields on it in time and space.

The impact of the field of a large body (m2, say the Earth) on a small body (m1, say a stone) is given by

 

whereas the impact of the stone’s field on the Earth is given by

Contrary to the Newtonian concept the two forces cannot be described by an identical equation, even if the mathematical outcome is the same.

 

The meaning of ‘force’ in this context is that of the local magnitude of a second body’s field exerted on the first one’s and contributing to the change of that body’s geometry of mass. That change induces the advance of its center of mass, which, if the body be unobstructed in its motion, will cause it to accelerate.

 

 

THE DENOTATION OF THE CONSTANTS G, M, c AND c2

 

In Newtonian mechanics G is the constant of gravity. In the present theoretical framework, in which gravity is not considered to be a force proper, G is a constant of weight, to be distinguished from the constant of mass (M). There is a simple mathematical relationship between these two constants (see above) and both could be used as constants of frequency related to the mass-energy field. Moreover, one could relate M to c as well as c2, to which special relativity does not attach any intrinsic meaning.

 

Based on the algebraic principle that if ab=1 then a/b=a2 and b/a=b2, we can deduce that since Mc=1 then c/M= c2 and M/c=M2. c2 (as well as M2) stand here for a forthright relationship between the speed of propagation of the mass-energy field and the physical constant which determines the magnitude of the field’s frequency in relation to the mass of its particle. It is obvious, of course, that the above relations give c2=1/ M2, too.

From this we may infer that Newton’s gravitation could be formulated for two particles, with reference to the field, thus:

 or, in our way:

and there are quite a number of variations possible of these equations using the above constants.

 

 

PROTEIN FOLDING

 

The most intractable problem in modern biochemistry, and one which does not seem to be solvable in accordance with the laws of nature as known to us thus far, is the rapidity with which proteins attain their globular (i.e. active) form, and the uniqueness of that form, which, based on considerations of their chemical bonds, should not have been unique to each protein, but, following probabilistic considerations, should have been one among quite a large number of possible conformations.

Obviously, Newtonian gravitation cannot offer any solution to this problem, since the gravitational forces acting between a protein’s atoms are far too weak to account for this process, and general relativity is wholly irrelevant to this.

However, the theory offered here circumvents the problem of Newtonian gravitation, and comes up with a solution which might prove to be the only feasible one, short of invoking occult powers, in explaining these phenomena.

 

As mentioned above the combined mass-energy field of a body has precedence over the operation of all other bodies’ fields on it in time and space. This means that the gravity acting between very small bodies (i.e. atoms in this case) has a very short delay (obviously in the range of picoseconds) in operating on atoms changing their state of motion. This holds good for larger bodies as well, yet with them is this delay insignificant. The implication of this delay is that when one separates the two factors of gravitation – self-weight (m1G)o and acquired weight (m2/d2)↓ – all the atoms of an unfolded protein operate gravitationally with regard to any moving atom momentarily without regard to the constant of gravity, which practically means a force hundreds of millions of times stronger than what is ascribed to gravitation under so-called normal circumstances.  

 

Due to their chemical activity the proteins’ atoms change their position constantly. This case has no parallel in the macro physical world where motion comes about mostly due to mechanical forces. The situation in the micro physical world is thus different in that the two kinds of force are independent of each other, and can operate non-simultaneously. 

It takes time from the instance an atom starts moving under an electro-chemical force until gravitation creates mutually attractive forces between that atom and all the atoms of the polypeptide, operating under the equation

 .

Taking into account a length of some 25,000 atoms for an average-length protein and the fact that many of the atoms move at the same time, the computational work to sort out these mutual attractions is quite staggering indeed.

However, the cardinal point is that while the single atom’s composite field remains intact during its motion, it takes time until the fields of all other atoms re-interact with it, and adjust when it reaches relative stability. As the present theory is based on the concept of the separation between self-weight and acquired-weight and the attraction acting between these units, G is here an inherent attribute of self-weight, which implies that during any instance of time that it takes the fields to re-interact, all the other fields act with respect to the single atom - whose self-weight is fixed – as an independent factor. The strength of that force is, then,

 

(including that of Earth).

This explains the fact that proteins take between seconds to minutes to fold to their natural conformation instead of thousands of years, and have only one possible conformation.

 

In a now classical experiment carried out by Christian Anfinsen some fifty years ago, he proved by denaturing an enzyme whose three-dimensional structure was thus completely disrupted, and its amino acid subunits maintained their linear sequences only, that under normal physiological conditions the protein could nonetheless fold properly. This indicated that even if the pathways of folding were not necessarily unique, no final folding of the protein was possible besides a single one.

It should be pointed out that the theory presented here makes it clear that the process of folding is a non-linear one since at any stage of the folding, the slightest shift of the atoms making up an amino acid unit can bring about a large-scale change of that unit as well as of other parts of the polypeptide, which in turn may bring about other changes until the final equilibrium is reached with regard to the mutual gravitational attractions as well as the chemical bonds and the van der Waals’ forces acting between the incessantly dynamic atoms.     

Chemical interactions between atoms and molecules might have restrictive influence on the moving atom. Without them atoms moving under gravitation alone might in some cases wreak havoc on the structure of the molecule in view of their far too high momentum.

 

‘CONDITIONAL WEIGHT’ OUTSIDE BODIES

 

According to the present theory there should be no difference in the values of the interacting mass-energy fields inside bodies and outside them, meaning - in space. Thus every point in space has a ‘conditional weight’ which amounts to

The equation, which has apparent affinity with the Newtonian g-equation, indicates the total amount of mass bearing on each point in space. Theoretically these are all the masses in the universe, practically these are the masses contributing to local gravity. This weight is not actual but conditional since it is not related to a body yet, and, moreover, the above equation has to be modified once a body interacts with any local fields, since a parallelogram of the various fields bearing on the body at a certain place which create vectors of weight of different magnitudes and directions, has to be taken into account.

Conditional weight reaches its highest values at the center of galaxies as a result of the convergence of all the galaxy’s mass-energy fields there, provided the distribution of masses in the galaxy is, on that large scale, quite even.

Without having recourse to the creation of black holes, this theory offers a “rough substitute” for it, which provides a reasonable explanation, in a very general way, to the assumed cataclysmic events which take place at the center of galaxies.

 

 

MASS MODIFICATION

 

The combined mass field of a body is subject to changes of magnitude with regard to two factors: A - the amount of a body’s matter,  B – The body’s state of motion.  In the first case the magnitude is the outcome of the addition or reduction of the fields’ lines. In the second case the magnitude reflects the growth or diminishment of the fields’ frequencies and accordingly the diminishment or growth of their wave-lengths. The field’s wave-length is subject to change in accordance with Lorentz transformations:

 

 

THE ADVANCE OF THE CENTER OF MASS (COM) IN THE DIRECTION OF MOTION

 

It is quite a perplexing fact that this phenomenon has not been given due attention to so far, since it is directly related to the Lorentz transformations, hence to special relativity.

According to the accepted model bodies contract in the direction of motion by the factor . This means, according to the theory presented here, that the geometry of mass of bodies undergoes change in accordance with their motion, and that a body’s center of mass undergoes a relative progression in the direction of motion by the same factor () if it stays at the same position it was in the body at rest.

Yet in order to maintain its inertial as well as its accelerated motion, a body has to reciprocate by an absolute advance of its center of mass in the direction of motion by the same rate.

The advance of the center of mass is, thus

When the value inside the brackets is 1 the center of mass is situated at the center of a body at rest which is symmetrical of shape and materially homogeneous.  When the value inside the brackets is 2 the center of mass is found at the edge of the body with regard to its original size.

The advance of the center of mass in the direction of motion is the most significant element in the mechanism of motion of bodies, regardless of its actual scope (which in conventional velocities is very minute indeed).

 

 

THE ROTATIONAL MOTION OF PLANETS

 

All planets assume a rotational motion about their axis since this is the only mechanism which can keep their matter cohesive. A rotational motion about an axis sees to it that the center of mass constantly changes position within the body and the body’s geometry of mass does not stay fixed. A heavenly body moving at a constant straightforward motion for millions of years on end would gradually lose all its rear matter (meaning eventually all its matter) in view of the incongruence between its mass-geometry and its matter. Its mass would ever be greater in the frontal part of the body in the direction of its motion.

 

 

THE PRECESSION OF MERCURY

 

As explained earlier, the main difference between this theoretical framework and the Newtonian theory is in that Newtonian mechanics places the body’s mass in its entirety (as if) at a single dimensionless point, whereas the view presented here is that mass has the nature of a field related to each particle within a given body, and it is the convergence of all the fields at a certain point which creates a center that can be referred to as a center of a body’s mass. It should be pointed out that Newton confined his view to “centers” with regard, among other things, to the analogy he created between the mechanism of gravity and the third law of motion. The combined force of two bodies acting on each other from opposite sides, yet having the same magnitude, could rationally be explained only if those attracting forces emanated from single points which represented the total masses of bodies in proportion to the forces (to be) created.

By its very nature the Newtonian view is bound to deal with an idealized description of gravity, since here gravity acts from one single point to another single point. As Einstein pointed out Newtonian gravitation does not possess the tools to deal properly with the phenomenon of the precession of planets, which his theory did to a very high degree of accuracy, notably with regard to the precession of Mercury.

 

When we enlarge the Newtonian view to include the whole body in gravitation, we have to take into account structural elements of bodies, namely their geometrical shapes and material composition, since gravity is no longer idealized but reflects the particularities of the whole body. As far as gravity is concerned a “body” stands for the totality of the particular fields of the particles making it up.

In many cases these particularities would not have any meaningful impact on the total effect of gravity, yet in Mercury’s case they might play an important role.

Mercury is a most compact planet, and is the one closest to the sun. Chief among its numerous structural features is the Caloris Bassin which is an extremely large crater, having a circumference of about 1300km and being ringed by ranges of mountains of, on average, about 2000m above the planet’s surface. This structural element cannot be ignored when calculating the effects of the sun’s gravity on it, and calculations should show whether that structural feature can account for the discrepancy in its precession.

In general precession of planets can be explained by the slight incongruence of mass between a planet’s frontal part and rear part with regard to its direction of motion, and as a result the difference in the magnitude of gravity acting on those parts respectively.

 

 

THE INFLUENCE OF GRAVITY ON LIGHT RAYS

 

It might well be that mass-energy fields cause electromagnetic fields to undergo a change when interaction with them (if such an interaction indeed takes place), which is analogous to the refraction of light rays when passing from one medium to another, in accordance with the field’s magnitude. 

 

 

UNIVERSAL EXPANSION AND THE AMOUNT OF MATTER IN THE UNIVERSE

 

This theory offers quite a simple explanation of the cause of universal expansion, and one which enables its straightforward application to the question of the amount of matter, clear and dark, in the universe.

Mass-energy fields should be regarded as extending infinitely in time and space. The growing rate of the expansion of the universe is thus directly correlated to the rate of growth of the total amount of the fields emitted by all particles in the universe, all fields propagating at the speed of light.

This factor should enable us to gauge the amount of matter in the universe quite accurately, considering the fact that there is no particle, be it of observable or dark matter, which does not have its field.

It is noteworthy that the field which brings gravity about is the same which causes universal expansion, casting thus some doubt on the necessity of a cosmological constant to balance off the apparent contradiction of the effects of gravity and expansion.

 

 

THE TWO COMPONENTS OF TIME

 

It ensues directly from special relativity that the amount of time of a unit time is inversely proportional to its clock time.  When the clock time indicates zero as a system reaches the speed of light, the durational time of an observer at that system relative to an observer at a stationary system is infinite, that is inversely proportional to the stationary system’s observer’s clock time.

We may conclude that this law governs all phases of clock-time dilation (actually “diminishment”) and is subject to an identical yet inverse rate of change. So that when the clock’s time diminishes by duration, the complementary component of time, simultaneously dilates by .

 

Total time, that is the integrated time of the clock and the duration of its units, is not subject to change as a function of a change of velocity, that is to say: relativity does not apply to it.

 

(c) indicates clock time, (d) indicates duration.

 

The above misunderstanding of the nature of time is probably one of the most curious in the history of science.

If time dilates, where is the mathematical description of its dilation? Einstein’s equation is that of the clock time’s diminishment - the very opposite of dilation, that is. And if the clock’s time diminishes, what is that which dilates when the relative velocity of a system grows?

I know of no other example in physics where the verbal description of a phenomenon completely contradicts its physical meaning. A shameful case indeed.