Kokosar, J. (2006). The Variable Gravitational Constant G, General Relativity Theory, Elementary Particles, Quantum Mechanics, Time's Arrow and Consciousness. PHILICA.COM Article number 17.
The Variable Gravitational Constant G, General Relativity Theory, Elementary Particles, Quantum Mechanics, Time’s Arrow and Consciousness

Janko Kokosarconfirmed user (Independent Researcher)

Published in physic.philica.com

Firstly, the article shows that the gravitational constant G inside of a black hole is rapidly changing. It then shows how this variable quantity allows us to understand why elementary particles are formed by gravity. The analysis of dimensionless constants, formed from gravitational constant, Planck’s constant, the speed of light and the elementary particle masses offers additional arguments for the theory that elementary particles are formed by gravity. Some additional explanations of the time’s arrow are also presented. Time’s arrow is also linked to consciousness and quantum mechanics. Thus, a new explanation of consciousness is presented and the connection between consciousness and quantum mechanics and general relativity is also shown.





This article presents the problem of merging general relativity theory (GR) and quantum mechanics (QM) from an alternative point of view.

First of all, a gedanken experiment of quantum measurements of gravitational acceleration is analysed in section 2. This is also a new interpretation of the measurement of acceleration at the horizon of a black hole (BH). This interpretation states that the gravitational constant G inside of a BH is rapidly variable. Because G is variable, Planck's mass is also variable. This means that it can sometimes be smaller than the masses of the elementary particles, so it follows that elementary particles can be formed by gravity.

Dimensionless constants bi are formed from G, masses of elementary particles, mi, Planck's constant, h, and speed of light, c. It is shown in section 3 that the existence of the dimensionless constants bi is an additional argument that elementary particles are formed by gravity. A further argument that elementary particles are formed by gravity is the theory of Mark Hadley [1..6], which explains quantum logic with only four-dimensional time-symmetric geons. The significance of the constants bi for Hadley's theory is also shown in section 3.

Explanations of time's arrow are presented in section 6. Time's arrow is also linked to consciousness and QM. Therefore, a new explanation of consciousness, and the connections between consciousness and QM and GR are presented in sections 4, 5 and 7. Sections 2 and 3 are more physical and with calculations and other sections are more philosophical and less mathematical.




Various arguments that G is rapidly variable inside of BHs are given below.

Mark Hadley [1] shows the connection between GR and QM by the example of Einstein's equation of GR.




The quantity C is a proportionality constant, and tensor Tuv is the energy-momentum part of the equation, which forms the curvature of space-time described by tensor Guv. It is known that the energy-momentum part Tuv is quantized. Therefore, Page and Geilker [7] assumed that the quantum version of equation (2.1) equals:




This equation was obtained by replacing the energy-momentum tensor in (2.1) by the expectation value of the energy-momentum operator with respect to a quantum state Ψ. Hadley wrote that the left side of equation is incorrect, because it is in contradiction with QM - some physical quantities can be precisely determined in this way, which is in contradiction to QM. The expectation value can also be equal to a value that does not exist. For example, the mean spin of an electron is zero, but electron spin can only be equal to h/(4π) or -h/(4π). He corrected equation (2.2) and obtained:




Assuming that equation (2.2) is incorrect and equation (2.3) is correct, Guv is shown to be rapidly variable. One possible explanation for this is that the gravitational constant G is rapidly variable. Therefore, formula (2.3) is an assumption for preliminary conclusion that G is rapidly variable.

Let us consider more precisely how the derivations of Unruh radiation and Hawking BH radiation imply a variable G.

If we are moving under acceleration, we feel Unruh radiation. If we are moving under constant acceleration, a, Unruh radiation is the thermical radiation where the temperature, T, of this radiation equals [8]:




where k is Boltzmann's constant.

In other words, when classical acceleration and quantum field are connected, it appears radiation with temperature, T, which is proportional to acceleration, a.

The distribution of the energy of the photons dp/dW equals:




Let us assume that acceleration of an accelerated body can only be measured by Unruh radiation, and  let us consider a single moment in time when a single photon is perceived. The precise temperature of this radiation cannot be derived from the energy of one photon, because the measurement of temperature means to measure the mean of the energies of photons. Constant temperature means only the constant mean of the energy of radiated photons. The energy of a photon is triggered by an acceleration a. Thus, it cannot be assumed that acceleration a can be constant in small time intervals. QM states that if something cannot be noticed in any way, it does not exist. Therefore the uniform acceleration of a body is only an approximation, but in fact acceleration can change thermically, according to the formula:




where the energy of the photon, W = hν, is changing thermically and ν is the frequency of this photon. Of course the assumption of Unruh radiation as the only possibility of measurement is real only for very small accelerated bodies.

This example can be compared to the radiation of a BH. Acceleration a means gravitational acceleration, g, at the horizon of a BH. The BH emits radiation at temperature, T. But, if this BH is very small (close to Planck's mass), the temperature of the radiation may be the only possibility for measuring gravitational acceleration, g. I cannot imagine another means of measuring this acceleration. So, the constant acceleration at a BH horizon does not exist and the acceleration at BH horizon changes thermically.

Hawking radiation is only a semi-classical approximation. Therefore, the assumption above is also only a semi-classical approximation. But, this is also useful.

Hawking radiation is an assumption without experimental verification. Therefore, there are many possibilities for modification.

If g changes rapidly, then G changes rapidly. The radius r of a BH equals:




where m represents the mass of a BH. Because G is changing rapidly, it is expected that r is also changing rapidly. But, this is not the case. The radius of a BH, r, approximately represents the distance which must be traversed by a photon to reach the horizon where it returns inside of the horizon. If the BH is not extremely small, the average G in this journey is not very different from the ideal, mean G. This means r is not changing as fast as g and G, therefore G is changing approximately thermically.

Hawking radiation is also a semi-classical approximation, because the radius of a BH cannot be precisely determined and the reaction of a gravitational field when a photon flies away is not respected. Nevertheless, it is most likely that higher approximations would also give thermical radiation for a BH because if a multitude of small BHs can be in thermical equilibrium, the radiation must be thermical. (The third possible instance of a higher approximation is the above example, where G is changing approximately thermically.) Because thermical radiation is very basic in physics, I suppose that some derivation maybe exists, which is still simpler than [8].

Probably, G is changing thermically, approximately thermically or in some other way that it can sometimes reach arbitrarily high value. However, if G is changing, then Planck's mass is also changing. Planck's mass mpl equals:




If G can maybe reach an arbitrarily high value, then it follows that mpl can reach arbitrarily small values. Therefore, the value of this mpl can sometimes be smaller than the masses of elementary particles. This offers the possibility that elementary particles can be BHs.

The assumption that an acceleration can be measured only by Hawking radiation gives also variable G. Variable G enables BHs that are smaller than mpl. The acceleration g at the horizon of such BHs can only be measured by Hawking radiation. Therefore, this is an assumption which becomes fulfilling.

A problem of physics that it is not yet explained is how elementary particles can be BHs. One possibility is that G is very large at very small distances. The question is, why it is larger than normal. The possibility of a variable G is better supported by explanation than the possibility of an enlarged G at small distances.

Important elements of quantum gravity (QG) theories are also BHs remnants with mass mpl. But no one has ever seen one of these objects. I think that objects with this mass do not exist, but elementary particles, as BHs, exist.

If elementary particles are BHs, which radiate, then the decay of a particle is a BH radiation. It follows that electrons and protons are BH remnants.

A variable mpl also gives a variable Planck's distance, lpl, and a variable Planck's time, tpl. The quantities lpl and tpl are defined as:





So space-time is not grained, but it can achieve arbitrarily small distances and times. The limitation for perception at very small scales is only the probability of perception, which is very small as distances are very small.

A variable G can be obtained in still another way: Constant acceleration cannot be achieved without gravity, because the energy of a body can be entered in "steps" with photons or any other particles. (Gravity must not be used as a source of acceleration, because Unruh acceleration is an analogy for gravitational acceleration.) The principle of equivalence says that it is not possible to differentiate if we are in a homogeneous gravitational field or in an elevator with uniform acceleration. But I would add here: "If an elevator with constant acceleration does not exist, it is not necessary that a homogeneous gravitational field exists and also does not exist". So G is not constant in small time intervals.

An almost uniform acceleration in quantum regime can be achieved by many photons of very small energies. But, equal energies of large number of these photons cannot be achieved. They demand too much information. Including the second law of thermodynamics, entropy of these photons should be maximal. This means that their energy should be distributed thermically. So the most possible uniform acceleration in quantum regime can be achieved with many low-energy photons, where the energy is thermically distributed. Due to the equivalence principle, acceleration in gravitational field cannot be uniform, but it is rapidly thermically changing. This can be generalized that G of the black hole is rapidly thermically changing.

Variable G above was derived theoretically, but it can also be derived semi-empirically. If constant G is supposed, gravitational field of a single elementary particle (for instance neutron) cannot be detected, because change of a momentum (of any body) due to neutron's gravitational field is smaller than the uncertainty of momentum of measured body. (Alternatively, shift of trajectory is smaller than lpl.) The inability of existence of black holes, smaller than mpl also gives inability of measurement of gravitational field of a single elementary particle. If the neutron's gravitational field cannot be detected, the gravitational field of many particles also cannot be detected; otherwise this is in contradiction with principle of uncertainty. A possible and simple solution is that G is rapidly variable. It is possible to add possibility that G equals zero sometimes, that gravitational field is not negative (positive energy theorem), and we should suppose that uncertainty of G is maximally possible. This gives the same solution as with Hawking radiation above and with "acceleration with small photons" example. At the same time, this is one sort of test of Hawking radiation.

There is also an important difference between emitted and received momenta of gravitational field. In classical physics these two momenta are the same, but they are calculated somewhat differently. If G is variable, these two momenta are different. They are also different in quantum mechanics and so momentum in QM is uncertain. It is possible that variable G and QM are more clearly connected.

In the everyday life we are more accustomed to statistical quantities and entropy than to smoothness and absolute determinism, therefore statistical QM is more comprehensible than smooth GR; and QM should be base for GR and not oppositely.




Even if the variable G was ignored, there are also other arguments that elementary particles are BHs or in general, objects formed by gravity.

Every elementary particle has its own value of bi. This is known dimensionless constant, which can be written as:




where mi means mass of i-th elementary particle, for instance mass of the electron, the proton etc.. It is not easy to find any other dimensionless constants, where G is included but mis are excluded. The existence of dimensionless bis is an important fact. I believe and it is very likely that the existence of dimensionless bis means the existence of interrelations between constants inside of them.

The second important fact appears when constants inside of bis are changed. Let us change mis by one arbitrary factor and let us change the constants h, c and G by three arbitrary factors, but with the limitation that all bis remain equal. It is shown below that all physical laws also remain the same. One example is the following variation of constants:










The quantity γ is an arbitrary constant, for instance 10; quantities with index 1 are the same quantities after the change. Index i counts all elementary particles, known and unknown. A calculation shows that constants bi remain the same as before the change. Therefore, if the world behind a "glass wall" has so changed constants bi, physical laws behind the wall are the same.

The example in formulae (3.2 to 3.5) is experimentally and theoretically proven. This example can also be obtained in special relativity and in this case γ equals:




Someone measures mis, G, h and c is in a fast moving rocket with velocity v. Measurements are taken transversal according to direction of the rocket. We can see and know that time for him runs slower than for us. But this can be interpreted so that time runs for him at the same speed as for us, but because of acceleration we gave additional energy to the rocket, (energy is proportional to mass) so everything in the rocket is more massive and it moves slower. For explanation, see appendix A. This can be respected in calculation and gives modified values for mis G, h and c as seen in formulae (3.2 to 3.5). If he would measure longitudinally according to the direction of the rocket movement, the new relations for changed mis, G, h and c would be different. This variation of constants shows that the keys of relativity are not only c, distances and time, but also bis. Or more generalized, if the world behind the "glass wall" has equal values of bis, but different constants inside bis, it is logically that this world has the same physical laws as our world.

But, if the numbers bi define physical properties, this means connection between masses of elementary particles mi and G (of course, h and c are included in these connections.) So elementary particles are formed by gravity. The constants bi are also implicit relations between GR and QM, because they connect h and G. Constants bi are very simple relations, but they are overlooked in QG theories. Majority of QG theories are complicated, but the constants bi lead to a hint that this is not necessary.

According to special relativity theory, elementary particles are the smallest objects that can be standstill in any inertial system. Photons can never be standstill objects. (Exception is only if they are circulating, but this is another story.) Special relativity theory gives that time only flows inside of objects that can be standstill, not inside of photons. So elementary particles define time and in that way distances too.

Quantities lpl and tpl are defined as base for space. But space is also defined by elementary particle masses. For instance, ten times larger masses of elementary particles and ten times larger tpl give the same numbers bi and so the same physical laws. However, gravitational constant G hidden in quantities lpl and tpl creates space. So it can be strange to imagine that G cannot create elementary particles, especially because elementary particles also create space and time. Each of four quantities inside of the bis is important as building blocks of space-time, therefore bis are also important. To sum up, the numbers bi define and form space and time.

Elementary particles can be imagined as circulations of photons. This is not yet known to be false and this circulation is a very simple model, so it is promising. Circulation of light is possible only in curved space, but space can only be curved by gravity. Improvement of this model is Hadley's theory of four dimensional time symmetric geons [1..6]. So again, elementary particles are objects formed by gravity.

The fine structure constant α, with value 1/(137.03599911(46)) [10], is in principle close to 1 (regarding very small values of bis, which are by no means close to 1.) Value (46) means uncertainty on last two digits. Coupling constants for strong force are also close to 1. This directs us that quantities inside of these constants are interrelated and that elementary charge is consequence of Planck constant h. Quantities bi have similar structure of applied physical constants as fine structure constant. This also directs us that constants inside of bis are interrelated.

Above noted facts about the importance of bis of particles are very simple and important, but I have not found them in literature.

Mark Hadley found that GR with non-orientated time contains the same logic as QM. So, in his opinion, GR forms all QM. There are some unfinished things here and I am trying to explain some of them below.

If GR generates QM, then h can be calculated from G. So h and G must form one dimensionless number. As a possibility for such a number, numbers bi come in sight. It is not easy to find other dimensionless constants, which contain h and G. But many elementary particles exist, so it can be easier to say that G, h and c create masses of elementary particles and not that G, c and mi create h. It is possible that only one existent or nonexistent particle creates all other elementary particles, but this is not very simple and so it is not very possible. Therefore, it is very likely that h is one free parameter, which with G and c forms masses of elementary particles and laws of QM. It is also possible that it is undetermined which constants are cause and which are consequence.

But, this is approximately the same what Mark Hadley wrote. He also operates with geons and geons are elementary particles or connected with elementary particles. Geons have some masses, what are required parameters for dimensionless numbers bi.

Hadley did not answer, where jump from symmetrical to asymmetrical time appears. Nevertheless, if the wave function collapse as a free parameter is added to his theory, this can be explained. His symmetrical time gives possibility of explanation of multitude of possible states before the wave function collapse; and asymmetrical time explains state after the wave function collapse.

Hadley's theory does not consider variable G and Hawking radiation, but this is not in opposition with his theory, or it can also be in opposition, because his theory is not yet completed.

I think that consciousness is basic thing and it is connected with collapse in QM. This is presented in the next section. So GR is the consequence of QM. Hadley and also other theories of QG did not give enough space for consciousness. GR is not enough to explain consciousness, because GR is not enough subjective thing. Consciousness establishes the time's arrow, as it is explained in section 6, but Hadley did not explain the time's arrow.

But quantum logic obtained from GR is useful, because common points between GR and QM must be found to simplify QG calculations. Hadley also partially explained spin of fermions and charge of elementary particles.

I got motivation for variable G and for importance of bis from empirical formulae for bis of elementary particles [11, 12, 13 and 14]. For instance:





It is clear that formulae (3.7) and (3.8) are similar. Formula (3.7) and others in [11] are obtained unknowing formula (3.8) [12, 13, 14]. Therefore, this is a relation, which "offers itself", if we guess. Formula (3.7) indicates one sort of temperature inside of elementary particles, so it indicates entropy, and therefore it indicates time's arrow inside of elementary particles. Although neither of formulae (3.7) and (3.8) would be right, numbers bi still keep the importance.




Many interpretations of QM exist and it is not possible ultimately to confirm which is true. But from QM follows: "If something cannot be perceived in any way, this thing does not exist." If all possible methods cannot answer which QM interpretation is correct, all these interpretations are incorrect. Therefore QM should be a theory which allows only one interpretation. For instance, "Many worlds" interpretation is intuitively unattractive and Occam's razor of its gives bad results. But this is also a legal interpretation of QM. Occam's razor is useful for something, what is later possible to fully uncover, but QM is meant as completed and impossible further to uncover. Therefore it is very possible that QM should be modified. My model for modification is stated below.

Quantum measurement is the process triggered by consciousness. More precisely, triggered by measurement, but consciousness cannot be denied and live world is consequence of quantum measurements. Measurements give information, but the information is intended to observer not to dead measurement device.

Let us see the process of measurement of the electron spin.

The main, Copenhagen interpretation, of QM says that the electron has not determined spin before the measurement, there is only a superposition of spins h/(4 π) and -h/(4 π). After the measurement one of both spins appears. I suppose that measurer can decide which spin will appear.

This interpretation of QM demands some modifications in QM. These modifications can be visible above all in biological systems. These modifications demand additional explanation and this is explained in section 7.

Einstein said that he intuitively thought that god does not play dice. The model above for connection of QM and consciousness also agrees with Einstein's belief. Einstein's intuition cannot be ignored because it gave some top-level results of physics.

The above interpretation of QM indicates larger importance of consciousness than matter. Other areas of physics also indicate this.

Matter loses all its meaning if consciousness is excluded. It cannot be imagined how processes in matter form consciousness in the brain or how to build up a computer that has consciousness. Special relativity theory also indicates this. It gives priority to an observer regarding to absolute space. The principle of equivalence in GR equates gravitational field with lifting in an elevator. The reason is that the observer feels the same in the both cases. So this indicates that consciousness is more basic than space. Entropy is also important in physics, for instance it shows direction of the time's arrow. The entropy measures information and information is connected with consciousness. Time's arrow also demands consciousness.




It is known that QM and GR are not compatible. One or both theories must be modified.

QM operates with absolute time and this time does not allow compatibility with GR. Besides, absolute time does not give enough importance to observer. Hitoschi Kitada [15] offers explanation that absolute time does not exist and thereby absolute time of universe does not exist. He puts the observers as carriers of time. In principle, I agree with this. He supposes that the elementary time is time which is written in the Schrödinger equation. I suppose that elementary time is time that arises at the collapse of a wave function and it is possible that it is somehow really connected with time from the Schrödinger equation. (Time should be sensed in some way, otherwise it is not time.) Subjectivity is a common property of QM and GR. Therefore, they should be combined on this basis and this property should not be ignored.

As opposite example, Penrose [16] proposed that the collapse of a wave function can also be gravitationally induced. So he presents such a QM which does not always need consciousness. According to present knowledge about QM this is logical theory, but it is more likely that solutions for QG must be searched for with consciousness. Theory of everything must also include consciousness and QG is also sometimes named as theory of everything.

According to interpretation in section 4, influence of consciousness in QM is more basic than in GR (It is active in QM and passive in GR and special relativity), so I think that it is more necessary to modify GR than QM, but somewhat also QM.

Present rules and elementary formulae of QM and GR are simple and exactly this simplicity means also applicability. But according to main QG theories the union of both means loss of simplicity. For instance, generalized uncertainty relation in QG theories [17, 18] becomes more complicated. There is also a doubt in opposite direction: How one complicated QG theory becomes so simple in two main approximations (QM and GR). The third example is constancy of speed of light and the fourth example is principle of equivalence. These last two principles are not valid in the main QG theories, but these principles are basis of special relativity theory and GR.

However, the problem is that the main QG theories are complicated, but QG should be simple theory. My assumptions, described also in next sections are simple.

We should also know that the collapse of a wave function is an additional element besides QM. This collapse of a wave function is substitute for consciousness and it is possible to operate with it mathematically. It is connected with the time just like consciousness is connected with the time. The Wheeler-De Witt equation is only a generalization of the Schrödinger or Dirac equation but these two equations do not tell enough about the collapse of a wave function.

Including the special relativity theory, space-time is defined by elementary particles, as shown in section 3. (Time can run only in matter, which can be standstill. This matter is built up from the elementary particles.) If elementary particles do not exist, space-time does not exist. The same conclusion is obtained, if it is said that bis define space-time.

GR gives that space-time is defined by paths of light. So, the photons are auxiliary particles only. Because GR is background-free, empty space without matter does not exist. But nevertheless, curved space is not completely in accordance with elementary particles as builders of space-time and I will try to harmonize this. GR also gives that a clock can be put in an every point of an empty space. This is not in accordance with principle of uncertainty and principle that space-time is defined by elementary particles and not with empty space.

GR is background free. This is in accordance with the common wish that matter and space-time can be derived from elementary principles and as less as possible number of elementary principles. (For instances, polynomial's spaces and other spaces are known from mathematics, so it is no need that our space-time is elementary. Or Pythagoras theorem is maybe consequence of the energy conservation law.) But GR is not enough background free - three space dimensions are not explained and it is not explained why some events are close together and some events are remote. It is also not explained how precisely these events are connected. Because light stretches space-time, I suppose that three-dimensional light causes three dimensions of space.

By classical physics, light ray, which is created somewhere on a star, flies until it is not absorbed or reflected somewhere. But, Cramer's interpretation of QM gives that starting and ending points of light ray are checked first. When this "hand-shaking" happens, then light ray flies off [19]. It is according to Mach principle that single matter cannot exist in space. I add to Cramer that this "hand-shaking" does not only happen once on a way from star to eye, but on all virtual particles on this way. So I expect that average distance for "hand-shaking" is Planck's distance. (Cramer operates with symmetric time, similarly as Hadley.) So real photons became more similar to virtual photons.

These three views on:

  • 1. special relativity theory (particles as base for space),
  • 2. GR (generalization of "background free") and
  • 3. QM (Cramer's interpretation)

are united below in proposal of a new model of QG. As the first element of the model, there are some points, for instance small black holes (and elementary particles at the same time). These points create connections across the photons. At the same time three dimensions of the photons create three dimensions of the space.

The model, where interactions are momentary, regardless of distances, should be elementary. But in our space where some time is necessary to travel from one location to another, this space behaves as one sort of aether. This space is not empty, but it is filled with virtual particles. Time is proportional to distances and time behaves as one sort of aether. Because connections between points are indirect, this defines near and distant points, so interactions are not momentary and space is not infinitely dimensional.

My presumptions in 2nd and 3rd section give that circulating photons are simple and promising model for matter, so the question remains, what is before, circulating photons or particles. Particles demand photons, which build up them. Circulation of photons demands some space, but this disagrees with assumption that particles are more elementary than space. Space and particles are interrelated and I expect that at quantum level they become more and more similar. But, I think that interaction is more basic than space. Existence ob bis also shows interrelations and importance of the both, particles and space. The collapse of a wave function must also be included. Things before collapse are subjective, but after collapse are objective and materialized. The space-time is probably built up from objective and subjective things.

If people (or any other conscious measurers) could be so light that they can behave as quantum objects, our view of QM and GR would be different and unknown. (It can also be imagined that all elementary particles are lighter by one defined factor, as their real masses are. Therefore, all movements in our world would be much faster and quantum effects would be more obvious.) Simulation of this behaviour could contribute to clarification of QG. (In the model above, both QM and GR hint to unsmooth space.)




Cramer tried to explain the time's arrow as well [20]. He described many types of time's arrows and he determined connections between them. He admitted that all theories of the time's arrow are speculative. My model for the time's arrow is described below.

One of the time's arrows is a consequence of the collapse of a quantum wave function. Time in QM is symmetric, but when a measurement and so the collapse of a wave function happens, the time's arrow arises. Differently as by Cramer, this time's arrow is defined below as almost basic time's arrow.

Cramer operates with the subjective time's arrow. I put it here as the cause for the time's arrow of the wave function collapse. But Cramer puts it on the end of cause-consequence chain. The time measures consciousness as described in appendix A. (Therefore, consciousness is also measured by the time's arrow.)

One special time's arrow in micro world is known at decaying of particles KL. It is written in the section 3 that time arises at elementary particles. So it is logical that time's arrow also arises there. But how can the consciousness exist in elementary particles?! Because the problem is: "If the consciousness forms time, it also forms elementary particles." In section 7 it is presented how this is possible. It is an important question why quantum electrodynamics has time symmetry but decay of KL, which is triggered by weak force, has time asymmetry. The difference is that a field particle of quantum electrodynamics is the photon, but field particle of weak force is the weak boson. The photon is a particle inside of which time does not run. The weak boson is a standstill particle and time can run for it. So it has a germ of time's arrow and time asymmetry can be measured at decay of KL. So growth of entropy is only a consequence of time's arrow. ("If nothing is done, things go from bad to worse", as commercial for an insurance company said.)

Important time's arrow is also the cosmological time's arrow. It is very likely that all in our cosmos is connected, so it has the same direction of time's arrow. It is not possible to communicate with someone who travels in opposite time direction. Therefore, time's arrow at the collapse of a wave function can choose arbitrary plus or minus direction, but it is motivated by direction of time's arrow in the cosmos. (By the way, it is very likely that explanations of big bang need improvement. For instance, why is entropy at big bang very low?! Low entropy does not happen spontaneously.) Hitoshi Kitada [15] wrote that absolute time of universe does not exist and that only time for local observers exists. This is true in principle, but time also exists as connection between local observers, local observers are connected and this gives one direction of time's arrow of cosmos.

A BH behaves as an elementary particle. It does not have inner structure; it has only spin, mass and charge - the same as elementary particles have. It is formed by gravity and I suppose that elementary particles are also formed by gravity. A BH has temperature and entropy, so it also has time's arrow. It is very likely that elementary particles also have a germ of time's arrow and therefore of entropy. Maybe this germ of entropy in elementary particles is variable G and this is cause for variable gravitational energy. Exponent formula (3.7) [11] can also be explained as the consequence of one temperature proportional to the fine structure constant.




The option, that consciousness is a quantum effect, is a possibility that "offers itself". One reason is that quantum collapse is connected with consciousness and the second reason is that these ones are two incomprehensible effects and uniting gives one incomprehensible or comprehensible effect. The third reason is, if non-causality of QM would not exist, free will would not exists, etc..

Objections against consciousness as connected to QM are above all in fact that coherence length of quantum effects in the brain is too short and so a brain cannot work on a quantum level. The coherence length is short because brain temperature is high. For instance, temperature of Bose-Einstein's condensate is around 1 nK. But possible large coherence length in brain can be explained - It is supposed that a human body has also an astral body. I think that this body is built up of particles which have much lower mass than electrons. Known particles with smaller masses are electron-neutrino, muon-neutrino and tau-neutrino. Such small particles have enough large coherence length for brain processes at room temperature. This matter then triggers a whole biological system, so all brains and all organisms.

Therefore, this gives prediction that biological systems have additional mass which can be measured somewhat.

It is assumed in this article that an observer can determine which option of the wave function collapse will happen, if he can directly observe the wave function collapse. I suppose that the wave function collapse cannot be noticed directly with the present state of technology because a measurement device already triggers it. If a measurement device triggers collapse, it also has consciousness of some sort. Therefore understanding of conception of consciousness must be modified and I tried to explain this below.

The essence of consciousness is memory. If someone forgets every day, what he was doing a day before, he could become a new person. This phenomenon exists in psychiatry known as double personalities. Personalities of these double personalities can really be switched for some time and personality of that moment forgets memories of former personality.

It is important that consciousness exists in the brain. I think that the microtubules are not the essential reason for consciousness but the reason is that neurons have many more connections than other body cells. These connections are called synapses. Synapses cause considerable memorizing and processing of information. By supposition that consciousness is a quantum effect, this means that the brain is not something very special regarding other organs, except its connections. So consciousness can be searched for in organisms without the brains or nerve systems. So logic is a condition for consciousness. Logic can be defined as a tool for survival. Logic can also be found in one-cell organisms and in plants. It is possible to object that plants have automatic logic without consciousness, similar to computers. But computers do not work on a quantum level. If the brain functions on a quantum level, then all cells of biological world function on a quantum level. The brain is not necessary in the biological world, but the cell is necessary in the biological world. So consciousness is presented as built up from simpler elements.

If consciousness has a quantum cause, then movement of a hand is a consequence of the collapse of a wave function. If the collapse of the wave function is absolutely accidental and without reason, as it is defined, moving of any living being would be absolutely accidental. And second, if the collapse of a wave function is absolutely accidental, free will does not exist. Therefore this is another reason that the wave function collapse would be a thing of decision and would not be accidental. That is why the decision also appears as one sort of measurement. If the collapse of a wave function is accidental, the moment of the collapse should also be accidental. It is expected that the observer is a quantum object, who triggers collapse, so a quantum object would accidentally trigger collapse. Because the moment of the wave function collapse is not accidental, the wave function collapse is also not accidental. This is another reason for the different wave function collapse.

As first, it is important that the above model is not contradictory. Besides, it is possible to prepare experiments which can prove or disprove the model above.

It is also important to add an explanation of consciousness to the non-biological world because quantum collapse exists everywhere. But, if it is said that consciousness exists everywhere, this is not contradiction. It is only necessary to add that this non-biological consciousness does not have as long duration memory as the human being; this means duration is 10-xx s and not some 10 years. Because this memory is short lasting, it also gives less logic. But consciousness with less logic and with short lasting memory is still consciousness. It is important that this model does not contradict our knowledge about the inanimate world and the laws of physics.

So the above deduction can give us that measurer of electron spin can decide which spin [h/(4π) or -h/(4π)] will appear after the measurement. Such a kind of the wave function collapse is very similar to telekinesis, known from parapsychology. I think that movement of a hand or any muscle is a consequence of micro telekinesis. Our consciousness triggers the brain, the brain triggers nerves and they trigger the muscles. The first triggering in the brain is consequence of telekinesis, by my opinion. These are things, which can be checked.

This could be checked by making one big superposition of quantum states and after this a person triggers the wave function collapse so that he/she observes this superposition. Therefore, this can be like observation of the Schrödinger cat.

It is also possible to search for animals or organisms with very good senses (hearing, vision, smell, to get sight of polarised light etc.), so that this Schrödinger cat can be much smaller and accessible to our technology. There are organisms that detect one molecule - maybe there are organisms that detect a small number of polarised photons. Maybe Pavlov's conditional reflex can help us to find out what this organism feels.

It is possible to make a few photons of determined polarisation. One polarisation can be used for learning one behaviour (positive for this organism) and another polarisation can be used for learning another behaviour (because of negative impact on this organism). After this learning, photons with superposition of both polarisations will be send to this organism. After this, it should be measured the frequencies of appearance of the both polarisations. It is expected that this organism can influence these two frequencies, because it will choose more collapses that trigger behaviour positive to this organism.

Measurements on a biological level and quantum level are becoming more and more advanced and it is very likely that this will be possible one day.




There are many theories which try to explain QG. Some begin at QM or GR and try to be valid also at another theory (GR or QM). Let us name these approximations step-by-step. The second possibility is to begin with something completely new and then to approximate to QM and GR. Let us say that example of this is the superstring theory. It is considered as the best approximation to QG. But, it has not given enough results according to work applied to this theory. Calculated numbers are still far away from the possibility of testing. Advocates of this theory are still questioning themselves what these strings mean and how they explain our ordinary world. They do not know anything about consciousness. The same problems are at loop quantum gravity theory.

Step-by-step approximations give better results according to experiences from ordinary life. I admit that this does not mean to make QG theory and to test it, because the possibility of testing in QG is rare. So this means to make assumptions and to observe how they are harmonized among themselves and with known facts. Superstrings theory does not have enough self-harmonized assumptions.

The problem of theory of QG is also testing. Assumptions about consciousness in my article can be tested.

More attention should be given to assumptions of theory of QG, than to theories of QG. The larger number of possible options will give larger possibility for true option and so also for the true theory of QG. This article is full of new assumptions which can be used for construction of a new theory of QG. These assumptions are: variable G, a new explanation of the wave function collapse, new explanation of the time's arrow, a new explanation of consciousness, assumptions that constants inside of bis are interrelated, photons as building blocks for the space, elementary particles as formed by gravity, etc..

The problem despite such a number of assumptions is that they have not given the theory of QG in this article yet. A clear model for elementary particles is still missing in this article and this remains the main problem of this theory of QG.

Maybe this article does not show correct or enough developed theory of QG. But, main approaches to QG theory are still worse. I am solo, but "QG theory personnel" is big. It is very likely that the organization of this research is not good. I think that present-day priority given to superstring theory is the problem of psychology of crowd, when they mutually persuade each other in the correctness of the theory. Advantage of computer age is badly used for clearer explanations of base-theories of QG. (These are QM, quantum electrodynamics, GR, special relativity, problems of uniting QM and GR etc..) Every important formula in these theories can be explained better. (For instance, factor 2 at formula for "starlight deflected by gravity of the sun" is rarely explained clearly enough.) The most likely, better organization of QG theory research would give this theory in the near future. The theory of QG is important, because it will approximate us closer to answer on some ideological questions, closer to answers, what is consciousness, what is life and what are the grounds of everything. It will also appease our curiosity. Larger motivation for QG among people will help sooner to access this theory.




Time is relativistic also in our common non-relativistic world. Time runs faster for the fly than for the elephant and faster for the a warm lizard than for a cold lizard. Time running can also be explained in such a way that if everything is moving slowly, we feel slower running of time. This means, brain processes are slower and clocks can be slower. Cause for slow running of time are also proportionally larger masses of all particles and this happens in the theory of relativity. This is presented below as additional explanation, which does not change the formulae of special relativity, nor does it change elementary principles of special relativity. However, in special relativity it fails total explanation, why everything in a neighbouring inertial system is moving slower than here. So the far existing, orthodox, explanation is not enough, because time can be additionally relativized, as described above.

If we ignore almost all special relativity rules and only respect the equation




where m is relativistic mass and W is total energy of accelerating body, then the equation for increasing of energy of an accelerating body is:




where a means acceleration, x means distance and v means velocity.

Solution of equation (A.2) is




where m0 was mass at velocity zero and ln is logarithm with base e. The result is wrong, because real relation is




 (Yes, this is correct relation, not only (A.8) and that is explained in the next lines.)

But, additional supposition should be that longitudinal distances x1 in the rocket seen from the rocket are larger than the same distances x seen from a standstill system (Lorentz contraction):




If this is corrected in equation (A.2), the new equation is:




and the result is (A.4), what is correct.

Equation, similar to (A.6) is known from special relativity:




It is interpreted that longitudinal relativistic mass equals




but the same interpretation as in (A.5) is also possible and it additionally gives the same longitudinal and transversal relativistic mass. It is also important that mathematics here is free - by all means it is not necessary to glue γ only to m0 or to t.

Let us simplify that we observe movement of an object in the rocket in transversal direction regarding direction of rocket, so Lorentz contraction does not exist. We can see that transversal momentum of an object in rocket, seen from a standstill system equals the momentum of the object, seen from the rocket:




t has a time base seen from standstill observer. So the law of conservation of momentum compares values seen from the rocket and from the standstill system. Equality of momenta can be obtained also in longitudinal direction.

The above interpretation says that everything in rocket moves slower because of enlarged relativistic masses. At the same time common explanations are not forbidden. This means we can take moving rocket as standstill system and we use the same calculations. This does not disturb the constancy of light speed in all systems and relativity of simultaneity, because in the model above these two are not important.

Einstein dissuaded from relativistic mass, as did also Lev Okun [21]. But I did not find any argument against my formulae. But, once Einstein said that all solutions should be respect. This is a new solution, which also explains relativity inside of constants bi.

Evidently mass, energy and geometry are linked and geometry is not everything.


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Information about this Article
Peer-review ratings as of 17:50:42 on 20th Oct 2017 (from 4 reviews, where a score of 100 is average):
Originality = 57.03, importance = 58.55, overall quality = 61.07

Published on Tuesday 5th September, 2006 at 10:20:50.

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This work is licensed under a Creative Commons Attribution 2.5 License.
The full citation for this Article is:
Kokosar, J. (2006). The Variable Gravitational Constant G, General Relativity Theory, Elementary Particles, Quantum Mechanics, Time’s Arrow and Consciousness. PHILICA.COM Article number 17.

Peer review added 16th September, 2006 at 13:54:32

A very comprehensive article.

However, from what I understand, G is a very small quantity, close to 0.

As G cannot be negative, wouldn’t it have less probability of fluctuating down, than fluctuating up?

And if G fluctuates upwards, the force given by F=GMm/r2 will also increase, ultimately leading to the universe either contracting, or slowing its expansion.

However, we currently know that the universe is expanding.

Please correct me if I am wrong, as I only have up to high school physics.

Anyway, overall this is a ground-breaking article, if true, it is Nobel material.

Peer review added 25th March, 2007 at 09:28:16

There is a serious mistake in the article. To show it let us take the empty spacetime. Then all the components of the energy-momentum tensor are zero, but the diagonal components of the spacetime curvature tensor are non-zero. So, there is no such a relationship as that introduced by the author. Because of this fact my notes are very low.

Author comment added 10th April, 2007 at 11:33:09

Reviewer #997 think that he found a fault in the article. But he did not write, where it is. I suppose that he thought formula (2.1). Guv in formula (2.1) really means Ruv – ½ R guv, as it is written in Einstein’s formula. Formula (2.1) is evident also in reference [1] on page 61. Formula (2.1) is really Einstein’s formula. I tried to write it in a compact form, but I see that this is not clearly enough. The article is also full of new ideas and formulas. If all except one idea are wrong, the article can still be breakthrough. But #997 did not read all article, he read one formula and gave note. Because of all above reviewer #997 was not fair and serious.

#2144 wrote »As G cannot be negative, wouldn’t it have less probability of fluctuating down, than fluctuating up? As G cannot be negative, wouldn’t it have less probability of fluctuating down, than fluctuating up? And if G fluctuates upwards, the force given by F=GMm/r2 will also increase, ultimately leading to the universe either contracting, or slowing its expansion.«
My answer: Exponential distribution gives that G cannot be negative, but average force is constant, similarly as thermical energy of gas cannot be negative, but average energy is constant.

Additional peer comment added 24th April, 2007 at 05:08:22

The tensor in (2.1) is the Einstein’s tensor. The tensor which describes the geometrical features of the space-time is the metric tensor which is the natural way of dscription of the all space-time features. Using mathematical operations we can give Ricci’s tensor and Einsten’s tensor. Thus, because Einstein’s tensor is non-linear compostion of the metric tensor that can not be used as the basic thing for the description of the space-time. But if the author had meant Einstein’s tensor (called also Einstinen’s curvature tensor (e.g. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation) I would agree that equation of (2.1) is correct. But the name of the Einstein’s tensor was not mentioned at (2.1) so, there was a confusion. Concluding, I ask the moderator for cancelling my previous grades of the article. I hope they will be higher. If it would be impossible to cancel them, please, set the values of 5,5,5 (until the whole article will be fully understood). Thank you in advance.

Additional peer comment added 23rd February, 2008 at 10:19:50

I fully upkeep my first note 1,1,1 for the paper. The reasons are as follows:
1. There is a mistake between the gravitational tensor and the “big” tensor G that doesn’t describe the whoile parameters of space-time because we cant get the exact solutions from the “big” tensor G the g tensor, so we can’t obtain the R tensor for example. Thus, the author is not aware of he is writing about.
2. The second mistake is more serious. The author doesn’t define the vacuum state, which is different for different observators and therefor he can’t built in a properly way the Hilbert space for the quantum gravity. Even more childish is to set simple relation between the average value of G tensor between Phi states, when we don’t have the transition rules between vacuum state and multiparticle states. This thing is very coplicated in “flat” space in QED and what about QG? We can set the Cauchy problem in a proper way in calssical gravity, but this problem is much more complicated. The similar problem is in the QCD, where doesn’t exist any Hilbert space (isn’t known the way how to build it), but there are very important results got from it, so the theory (or just the way of doing the calculations) is valid (or important) anyway. Thus, if the basic relation is not valid (we can’t simply just do it, as we do it in QM,we don’t whether QM formalism is valid in QG or not, unless we prove that it is valid), so the whole relation is invalid.
3. We don’t know whether Unruh effect exists or not.
Conclusion: the arguments presented are very feable therefore upkeep my prevous notes. But authors intelectual potential is big, so I encourage him to try harder.

Author comment added 28th August, 2008 at 16:00:36

1. Formula 2.1 from reference [1] is caricature, it is short as possible and give a main idea. Do you think that caricatures are wrong pictures.
2. The essential question here is: where does variable G give contradicts against known facts? I did not get the answer and I really wish it.
“Even more childish is to set simple relation between the average value of G tensor between Phi states, when we don’t have the transition rules between vacuum state and multiparticle states. This thing is very complicated in “flat” space in QED and what about QG?”
From classical gravity it is known that gravity is not a force. So why to compare QG with QED or with QCD. QED is put in a flat space “or even in curved space”, but gravity built up space. So it is before QED calculations and it NOT NEED VIRTUAL GRAVITONS.
Example of different theory: “http://arxiv.org/PS_cache/physics/pdf/0504/0504062v9.pdf”, for which particles are more important than fields. I please for judgment of this reference.
The basic thing (before space) are gravitational coupling constants of elementary particles. What built them, are elementary laws of physics. An elementary particle is always in an inertial system. This defines Hilbert’s space and not accelerated systems etc..
3. I showed also other examples, beside Unruh radiation.

What is purpose of your “1, 1, 1”!

Author comment added 31st August, 2008 at 12:11:38

add to comment:
Formula (2.2) can be treated separately in accelerated system or in inertial system. In both cases formula (2.3) can be written and so variable G can be obtained.
So, it is not necessary to define Hilbert space in accelerated system.

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