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The Trouble with the Math-Physics Connection

Albert Einstein, "as far as the laws of
mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."

Two shortcomings of mathematics in modeling physical phenomena:

1. The correspondence of mathematical points to particles.

In mathematics a line drawn in space can be thought of as an infinite set of points. A mathematical object like a small microscopic sphere can move on the continuous line point by point. Math has no problem with this.

In physics a real object like an electron does not move (like a mathematical object) through all the point positions of a line path. DWT postulates that the electron hops from a point position to another point position, the distance between the point positions is the wavelength of the electron and the time it takes to make the hop is the period of the electron. In DWT a particle must hop (over points) in space and time to exist and manifest as a thing that has a wavelength. The hop of the electron is how the electron inhabits space-time, the space is the wavelength and the time is the period. An electron is not complete at a point because its existence requires a small chunk of space and time. Without the wavelength and period there is no particle. The electron is more like a musical note than a classical object. An experiment has been outlined in Section 14 to test this conjecture using Buckyballs instead of electrons.

This intrinsic motion of particles tripped up both Zeno and Newton. Zeno was fooled because real particles do not have to move through all the points of the continuum to get to a new position. Newton was fooled because real particles do not have a velocity at a point. Newton tried to get around this via his calculus, but to get a velocity at a point the Δx’s and Δt’s needs to go below the wavelength and period of the particle and this is not possible in real physics at least according to DWT. However, a velocity can be calculated for the particle over a “wavelength”. This does not render calculus useless, but it limits it’s Δx’s to values no smaller than the wavelength of the particles. Again see
Section 12 (paradoxes) for more info.

This faulty modeling of particles as point like things moving smoothly in the continuum of space-time is what has hidden gravity from being seen on the quantum level. It also puts a kink into all differential analysis that pertains to physical phenomena, like the Hamiltonian and the Riemann curvature tensor. See
Section 17 for a simple model of quantum gravity that is in basic agreement with the Standard Model of Particle Physics.

2. The assumption that 1 + 1 = 2 in the world of experience.

1 + 1 = 2 is something that is taken for granted and is held to be true in both math and physics. I do not believe it is true in physics. I will try to explain, here goes:

a. How do you add things that are physical? The grade school teacher will demonstrate by taking an apple from far away and present it to the class, then the teacher will bring another apple from far away and put it close to the first apple and say "One apple plus another apple is two apples." This is the physical interpretation of addition. It is very useful and essentially correct but it needs a minor correction when considering the apples as real objects with mass. I will explain in a moment.

b. How do you add things that are mathematical? The math instructor will say consider an apple (an ideal massless object in the imagination) and call it a 1. Now consider another apple and call it a 1. The 1 and the 1 can be added to produce 2 which can be considered to be the sum of the two idealized apples. This 1 + 1 = 2 is completely correct for idealized apples. The math is perfect when there is no real mass and no space-time.

c. What is wrong with the physical 1 + 1 = 2 ? The answer is the space-time that the apples exist in. When the apples that have mass are brought together to demonstrate their sum they have to move thru space and time. When one real apple’s mass (call it a 1) is added to another real apples mass (call it a 1) the result of the addition is 1 + 1 > 2.

Two equations and their physical  interpretation:

1.  The deBroglie equation λ = h/(mv): This equation is usually interpreted to show that a particle like an electron can be associated with a wavelength and thus the electron can also be viewed as a wave. The Bohr interpretation of quantum mechanics would say that the electron has two complementary aspects, one as a particle the other as a wave. And the aspect of the electron we see is determined by the type of experiments we perform.

DWT does not agree with this interpretation and says instead that an electron is not at times a wave and at other times a particle, it behaves as a whole consistently with all its properties. The way to see this is to visualize the motion of the electron as a hopping over the distance λ = h/(mv) in a time T=λ/v. This motion is a speculation but as outlined in
section 14 it can be tested experimentally.

2.  Newton’s Law of gravity F = G[m1m2/d2]: This equation has been criticized in physics
      for having spooky action at a distance.

            Spooky action at a distance: The equation F = G[m1m2/d2] as been interpreted to be an    
            instantaneously force of gravity because the equation has no time component. This means
            that if a star moves a force will be felt immediately on the earth due to this movement. This
            bothered most physicists and Einstein in particular. He removed the problem by postulating
            that the gravitational force the earth experiences from the star’s motion is due to
            a space-time disturbance caused by the star. This space-time disturbance travels to the
            earth (and is not instantaneous). Now there is no spooky action at a distance.

            Quantum mechanics prefers to remove spooky action at a distance with another mechanism. 
            It postulates the existence of mediating particles called gravitons. It is now a physical particle
            called a graviton that brings the force of gravity to the earth from the binary-star. As developed
section 36 DWT believes this mediating particle for gravity to be λ-hopping neutrinos.

            Some may consider gravitons spooky, but once they are recognized as a special form of        
            λ-hoppers, they can explain a lot of phenomena:

            1. Dark Matter: See section 20

            2. Dark Energy:  See section 19

            3. How mass bends spacetime: See section 17

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