Abstract

There are currently eight connected major unanswered questions in astrophysics. The most important of these are:

• How can dark matter be explained and described?
• How can dark energy be explained and described?
• How can the theories of symmetry and the Higgs field be used to calculate the masses of the fundamental particles? 

A self-consistent theory that consists of many parts has been developed that answers these questions quantitatively. These parts have been collected into a self-consistent set, which will be referred to as Model W1 or in these Aquater Papers simply as Model 1. The unique features of this model are:

• There are two spaces in the universe, particle space and quantum vacuum space. A potential barrier separates them. One space contains visible matter, and the other space contains dark matter.

• There is a cycling of mass-energy between these spaces through the black holes that connect them. Particles pass from our space through black holes where they are converted into super particles that operate with unified force. They then pass into the high-energy vacuum space where they become dark matter operating behind the potential barrier.

• Dark matter particles interact with each other and form a slowly building and moving bubble centered on a galaxy. Corridors of dark matter forming a cosmic web, which guide the development of new galaxies connect the bubbles of dark matter to each other.

• There, behind a potential barrier, the dark matter particles gain energy, build up in number and eventually exceed the ability of the barrier to contain them. They then explode back into particle space as a big bang. This process repeats to make a long series of new universes.

• After the big bang exhausts itself, super particles continue to tunnel through the barrier into particle space. The super particles are unstable and break down into particles with extreme kinetic energy. In doing so, they give up potential energy into particle space. The potential energy gradually builds up to become the dark energy that we observe as the cause of our accelerating, expanding universe. The extreme energy protons are observed as cosmic rays with energy between the energy of force unification and the Planck energy, which is beyond the GZK cutoff. 

In order to answer these questions, it became necessary to work out a means to calculate the mass of the proton and the fundamental particles that make it up from the theories of Symmetry and the Higgs field. In working out this quantum mass portion of Model 1, it was noticed that there is an application of this theory to the problem of the instantaneous transfer of state for entangled particles. This application will be analyzed in this paper.

  

The Problem

There is a set of experiments that show that an extremely fast transfer of state is possible over distances too large to allow for transfer of state information at 2.99 x 10¹⁰ cm/sec. These experiments appear to violate special relativity. In order for this transfer to happen, the particles involved must be entangled (see reference 3). The accepted theory for transfer of state information requires the exchange of virtual photons, which must happen at the speed of light, so this exchange should be impossible. Einstein referred to it as “spooky action at a distance”. Here, we ask how this can happen and not violate special relativity.

In order to attack this problem, we must first understand how particles and photons travel through the vacuum. In reference 1, AP4.7M, it was shown that the speed of photons and particles (v_o) is controlled by the changes in the photons, particles and Plank granules as photons and particles pass through the vacuum. Thus v_o can vary with the energy of the photon involved according to the equation:

            v_o = nl_p/ Nt_p ½[(1 – E_ke/(V₀– E_smo -E_ke)]   

                  = 2.99 x 10¹⁰ / ½[(1 + E_ke/(E_ke+ E_smo -V₀] cm/sec (if n/N ~1) 

            Where:

            V₀ = potential energy for the space of interest

            l_p = Planck length

            t_p = Planck time

            E_ke = photon and particle kinetic energy

            E_smo = Rest mass energy of particles

            l_p/ t_p = c = 2.99 x 10¹⁰ cm/sec

            n = number of vacuum granules along the travel length

            N = number of disruptions along a travel length caused by a potential energy edge 

In order to progress further, we must also establish the state functions of particles. To do this, we start with the particle wave function (Kane, 90), and multiply by the Higgs factor to get the mass state (ref 4, AP4.7W). We get the following expression.

The Fermion mass state is:

            Let m_e be a particular Electromagnetic mass state, then:

            m_e = (space factor)x(spin factor)x(U(1) factor)x(SU*(4) Higgs factor)

            Then the particular Isospin mass state is:

            m_i = (space factor)x(spin factor)x(U(1) factor)x(SU(2) factor)x

                      (SU*(4) Higgs factor)

            Then the particular Quark mass state is:

            m_q= (space factor)x(spin factor)x(U(1) factor)x(SU(2)factor)x

                      (SU(3) factor)x(SU*(4) Higgs factor)

 

The Boson mass state is:

Let m_ib be a particular Isospin boson mass state is:

            m_ib = (space factor)x(spin factor)x(SU(2)factor)x(SU*(4) factor)

            Then the particular Higgs boson mass state is:

            m_ih = (space factor)x(spin factor)x(SU(4)factor)x(SU*(4) factor)

The Photon energy state in particle notation is:

            E_ph = (space factor)x(polarization factor)x(U(1) factor)x(kc factor)x

                         (SU*(4)(Higgs) factor)

We see that the factors SU(2) and SU(3) which contain the mass charge have been omitted in the expression for the photon, because the photon does not have a mass charge. The Higgs field changes the refractive index of the Planck granule instead. Note also that there is a relationship between the Higgs field and Planck’s constant. This relationship will be investigated in a separate paper.

We see also that the particle state S_p is the first set of particle factors without the SU*(4) Higgs factor. We are aware that a more elegant quantum notation is available for these factors, but we maintain this notation to emphasize the similarity in the factors.

We see further that for photons (where E_smo= 0), energy is not required to penetrate the Planck granules, and the speed of 2.99 x 10¹⁰ cm/sec is automatically assumed, although for extremely low energies (cryogenic temperatures), it can be lower. The refractive index is determined by the photon energy. When the photon energy nears the Planck energy, the refractive index of the photon is 1, the photon passes through the granule without noticing it and n/N becomes large, making the photon velocity large. Note that this change in c makes the value of the Planck length at high energy remain constant in spite of relativistic foreshortening at this speed, as required by quantum mechanics.

For massive particles, the particle must alter the angular momentum quantum numbers of the Higgs field inside the granule as it enters, and this requires energy. Thus, a force must push the particle until it reaches the Planck energy, then it can pass the Planck potential energy barrier made by the Higgs field, and reach the speed of light. This is why massive particles resist achieving the speed of light. The Planck energy is huge, so the energy required for a particle to reach light speed is huge. Note, however, that if that amount of energy is supplied, the massive particle does pass the barrier, and n/N becomes large, and again the particle velocity becomes large. We see that the mass of a particle does not become infinite at light speed; it only becomes equal to the Planck mass.

In Appendix A, we note that as a particle or photon passes through a field of Planck granules, a decelerating Higgs field with certain quantum numbers will be formed. This decelerating Higgs field will interfere with the constant ambient Higgs field in space, and be reduced while simultaneously reducing the ambient Higgs field for those same numbers. This effect is screening, and it gives a finite range to the decelerating massive particles. For photons, the screening is for the refractive index. It is the refractive index that is that is reduced by the passing photon. We can model this effect by saying that the screening Higgs field generates an “effective refractive index” for the passing particle.

We note finally that quantum mechanics and general relativity both say that there is no special frame of reference in these theories. If two particles or photons have the same precise states, their position in finite particle space is not specified. The space factor only defines the position with reference to a Planck granule. For photons, the phase is defined. For massive particles, the angular momentum quantum numbers are defined. Since all Planck granules are the same throughout particle space, we cannot determine which granule a particle or photon is next to. When a particle or photon is split and the daughter particles travel through particle space to different points in space, the daughters don’t know their new positions relative to each other. The only thing they know is that they have the same quantum state, and there is a corridor connecting them with correct quantum numbers. Note, however, that in order to pass through a Planck granule and not change its state, the particle must change the state of the granule. The particle/photon has the charge, so it changes the state of the granule, not vice-versa. Granules have no charge. A charge could identify them and make them particles. Thus the key state factor in this translation to a new position is the space factor.

For photons, the space factor is the phase of one photon in a granule relative to the phase of another photon in its granule. For a massive particle, it is the orientation of one particle in a Higgs field of a granule relative to the orientation of the Higgs field of the primary particle. This orientation shows up in the quantum numbers that define the relative spherical harmonics of orientation between the granule and the particle. A particle passes through a granule field by penetrating each granule, granule by granule. As a specific particle is passed through the field, they generate a Higgs field that cancels the field of the granules in the column of travel, but only for the specific particle quantum numbers used. Thus the granules in the column act like one granule afterward for the specific particle, and n/N becomes large and the speed of travel is large. In addition, the column guides a traveling particle (or photon) to a correct space position with the proper quantum numbers. Thus, the two separate particles act like they are one particle, and end in the proper relationship to each other (i.e.-they have the same space quantum numbers), when the state collapses. The corridor will remain open as long as it is not disturbed by other particles passing through. This disturbance would be more common at the higher temperatures and densities in the earth’s atmosphere. 

At this point, we may say that we have discovered two guiding principles for particle travel through particle space. Note that the discovery of these principles was impossible until it was shown that a particle or a photon (including its mass) can be completely described by a set of quantum numbers (ref 4, AP4.7W). 

Guiding principles

1. If the quantum numbers of two separated particles (photons or massive particles) are exactly the same, the particles are indistinguishable, or entangled,
2. If there is an open corridor marked with the quantum numbers of the two particles in the Planck granules between the two particles, quantum information can travel between the two particles attaqched to virtual photons at a speed greater than 2.99×10¹⁰ cm/sec. 

In the remainder of this paper, we will use these principles to describe how instantaneous transfer of state can happen and not violate special relativity, or Bell’s inequality.

 

The Solution

There appears to be a way to accomplish a transfer of state with a speed that exceeds 2.99×10¹⁰ cm/sec. Consider the following experiment, where a subatomic particle decays into an entangled pair of connected particles (see reference 5) in the following way.

1. A spin zero particle decays into two spin 1/2 particles in this system. The two new particles are kicked out in opposite directions at close to 2.99×10¹⁰ cm/sec using decay energy. The two new particles have the same quantum numbers, because of their common origin, but the spin of each particle is in a suspended state until one is tested by experiment.
2. The particles then move through a Planck granule field to different, widely separated points in space, thus ensuring that a corridor exists between them in the Planck granules that is marked with a common set of quantum numbers.  
3. One of the particles is tested for spin, and this test collapses the state of both particles, because the quantum numbers are the same, and so they are entangled.  Since the total spin of the system before and after the decay must be zero (conservation of angular momentum), one daughter particle must have spin +1/2, and the other must have spin –1/2. 
4. If we measure the spin of one particle, and the measured value is +1/2, then two virtual particles are formed, one at each daughter particle’s position in the following way. The virtual particle at the original test site sends a signal to the second particle site (defined by the space factor quantum numbers) at the speed of light c to form the second virtual particle with the opposite spin –1/2. Since the Planck granules in the corridor between particles are marked with the same numbers as the virtual particle, the intervening Planck granules are unobservable, so the n/N ratio is large and the speed of light c is dramatically increased. Thus the delay time for the formation of the second particle is reduced. The mass in massive particles is then formed with the correct spin by interacting with the Higgs field, which is everywhere. Note that only quantum information is transmitted between sites, so the energy required to push a massive particle through a Planck granule field is not needed.

We see that the state and the particles are transferred from point to point at what appears to be a speed faster than the speed of light, but it doesn’t violate special relativity, because it actually travels at the speed of light. In addition, it does not appear to violate Bells inequality. 

It is important to note that, as stated in reference 5, “While it is true that a pure bipartite quantum state must be entangled in order for it to produce non-local correlations, there exist entangled states that do not produce such correlations, and there exist non-entangled (separable) quantum states that present some non-local behavior.” Reference 5 continues, “In short, entanglement of a two-party state is necessary but not sufficient for that state to be non-local.” Model 1 predicts this odd situation because there are two steps in a non-local correlation.

• If the two particles do have precisely the same quantum numbers, but the high-speed corridor has been disturbed by the penetration of other particles with different quantum numbers, the particles will be entangled, but the two virtual particles cannot communicate their state. A non-local correlation cannot be accomplished.
• If the two particles do not have precisely the same quantum numbers because of a disturbance of one particle, but the high-speed corridor has been formed by one particle, a high-speed exchange of quantum numbers can be accomplished, but the two particles are not entangled, so a non-local correlation cannot be accomplished.

Finally, we should note that we have given as our example, a massive particle non-local correlation, because it is the most difficult. The same results and limitations will result if we used a photon being split into a pair of daughter photons by an optical splitter, except that the Higgs field is not required to give mass to the resulting daughter particles. 

Now let us investigate possible practical means of using non-local correlations. The only known means of getting two particles that are entangled are:

• Obtaining two daughter particles from the decomposition of a mother particle.
• Passing a photon through an optical splitter.

Neither of these methods is very practical for use in transmitting:

• Information at speeds faster than 2.99×10¹⁰ cm/sec.
• Massive objects at speeds faster than 2.99×10¹⁰ cm/sec.

The reason is that we cannot choose which state the daughter particle collapses into when we test the state of one particle. 

We ask if some practical apparatus can be constructed to obtain a non-local correlation. To accomplish such a correlation, we need a scanner and a precursor object that prepares a high-speed corridor as follows:

• The scanner scans and registers an object’s quantum numbers at its source.
• Make a second object with exactly the same quantum numbers, but in a complementary state (as with the spins). Note that now we know the state of the new particle, because we made it.
• The second object is accelerated in the direction desired, using sub-light speed techniques (reaction motors) to a high speed, coast at the high speed until near the desired destination, and then decelerate to the same rest frame that it started with-i.e. obtain the same space quantum numbers as those at the objects source. This generates a high-speed corridor.
• Then check the state of the second object. This should collapse its state, and the two new objects should be in a complementary state at each end of the high-speed corridor. If we change the state of the second object, it should change the state of the first object. We can exchange information between the ends of the corridor.

The problem is that no such quantum scanner is currently available, so we cannot make an object with the correct quantum numbers and states.

 

Summary and Conclusions

There is a set of experiments that show that a very fast transfer of state can take place over distances too large to allow for transfer of information at the normal speed of light. In order for this transfer to happen, the particles involved must be entangled. In this paper, we have found that Model 1 predicts that a transfer of state can take place faster than the normal speed of light based on the following guiding principles.

1. If the quantum numbers of two separated particles (photons or massive particles) are exactly the same, the particles are indistinguishable, or entangled,
2. If there is an open corridor marked with the quantum numbers of the two particles in the Planck granules between the two particles, quantum information can travel between the two particles attaqched to virtual photons at a speed greater than 2.99×10¹⁰ cm/sec.

 We note the irony that after decades of thinking Einstein was wrong, we find that in a sense, he was right. There was something missing in our prior understanding of quantum mechanics.

 

Appendix A

The Inertial Effects of Mass Through the Higgs Field

The inertial effects of mass such as maintenance of velocity and resistance to acceleration can be modeled by a screening effect from the Higgs field (see Shumm, 293-299) that explains inertial mass formation. To explain this effect, we compare it with the screening effect of electrons on photons. If a photon passes through a medium filled with free electrons, its oscillating electric field oscillates the electron charges, and they generate opposing photons that tend to interfere with the oscillation of the original photon field. Thus the electric field in the medium will oppose the constant oscillation of the original photon field, and reduce it. This tendency is called screening, and it gives a finite range to a photon in conducting media. We can model this effect by saying that the screening electric field generates an “effective mass” for the photon even though the photon has zero mass and infinite range. This screening range is similar to the range of a field with massive exchange particles, shown in the equation (see Kane, 29).

           φ = φ_o /4πr exp(-mr) (natural units)

Note that the field is significant in size only out to a range of r ~ 1/m (natural units), where m is the “effective mass”.

We have shown above that the Higgs field interacts with the mass charge in a particle to form mass. Then if a decelerating quark passes through a medium (particle space) filled with a relatively uniform Higgs field (see above), a decelerating Higgs field will be formed. This decelerating Higgs field will interfere with the constant ambient Higgs field in space, and be reduced while simultaneously reducing the ambient Higgs field. This marking of both fields is limited to the quantum numbers in the particle charge. Again this effect is screening, and it gives a finite range to the decelerating quark. Note that this effect happens only for decelerating particles with mass charge. We can model this effect by saying that the screening Higgs field generates an “effective mass” for the accelerating quark as shown above, that operates on massive particles. As will be shown below, all of the mass of the fundamental particles can be accounted for by the interaction of the mass charge of the particle with the Higgs field. There does not appear to be any free inertial mass to a quark (or any massive particle) other than the Higgs “effective” mass.

Now if a force is applied to the particle over a distance giving energy to the particle, the particle will regain its original mass-energy at its prior velocity .We see, then that the particle has inertial properties, and follows Newton’s laws.

Note that the Planck granule has a very high potential energy 1.22×10¹⁹ GeV formed from the Higgs field. If a massive particle enters the Planck granule at the speed of light, it will obtain a Planck mass (not an infinite mass). This fits with the need for an energy of ~1.22×10¹⁹ GeV in order for a super particle to pass the barrier shell. It will need a Planck energy quantum to obtain the speed of light. A photon, however, will go immediately to the speed of light in each granule, because it has no mass charge. Every time a particle passes through a Planck granule, it must pay the energy price. The only way to increase the speed of travel is for a particle not to sense some of the Planck granules it passes. If the particle energy is high enough, this can happen.

A photon will sense the Planck granule and travel at speed c through it, but not require energy to enter or leave it, because it has no mass charge. If the photon has close to the Planck energy, it will carry a Higgs field close to a Planck granule field, cancel that field, and not see the granule. Then it would travel faster than c.

A massive particle with a Planck energy would also cancel the Higgs field, and not see the granule, and travel faster than c.

 

References

1. L. H. Wald, “AP4.7M VARIABLE LIGHT SPEED IN MODEL 1” www.Aquater2050.com/2015/12/
2. B. A. Schumm, Deep Down things, Baltimore, MD and London, England, The Johns Hopkins University Press, 2004.
3. https://en.wikipedia.org/wiki/Quantum_entanglement
4. L. H. Wald, “AP4.7W ORIGIN OF THE HIGGS FIELD FOR MODEL 1” www.Aquater2050.com/2016/11/
5. https://en.wikipedia.org/wiki/Quantum_entanglement#Methods_of_creating_entanglement