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Some Additional Notes on The Klein-Gordon Equation

The following are some ideas that occurred to me after I wrote my notes on the K-G E: Mass is a mathematical construct from the human perspective on the particle. From this perspective the particle state is real and can be represented by,

c |ψi = m M ~ |~ω i

(1)

where |ψi is a general state vector which, when operated on by a real operator, will produce a specific real state vector (e.g.|~ω i,) where the vector sign,in this equation, is shown for clarity, but is not necessary since the state vector is a vector anyway. |ωi is the real particle state vector representing a particle having a rate of time, ~ω , a vector which makes the mass (and it’s energy) a vector too. Representing ω ~ in it’s operator form gives,

ω b=i

∂ ∂t

(2)

the time operator. This time operator operates in all dimensions of reality, rotating any vector by π2 . This time operator operating on the particle state vector gives,

ω b |ωi = −i~ ω |λ, ωi

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(3)

an imaginary vector state residing in an imaginary dimension of Reality. This vector state can be written as,

   ~r |Îť, Ď&#x2030;i = exp i â&#x2C6;&#x2019; ~Ď&#x2030; t Îť

(4)

From equation (3) we can see that the imaginary state vector comes from the real state vector:

|Îť, Ď&#x2030;i = i |Ď&#x2030;i

(5)

Equation (4) represents the stationary particle wave-state when the following photon orbital relationship applies: ~ ~r. ~c = Ď&#x2030; ~Ă&#x2014;

(6)

Equation (4) also represents a traveling wave whose states vector is also imaginary.

It should be clear that the particle state is stationary in space and time since the orbiting photons orbit around a fixed point in space, and that the rate of time for the particle is referenced to that fixed point in space.

It should also be clear that the Copenhagen Conventionâ&#x20AC;&#x2122;s ideas about relative reference frames are debunked. All matter and their motions are referenced to a fixed frame of reference in both time and space.

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Equation (5) shows that the displacement of a particle occurs only in imaginary dimensions of Reality. This means that the Human Perception of motion is an illusion. We only see motion as a time average of a body’s particle displacements. Particle displacements are: ~r |ωi = |0i

(7)

~r |λ, ωi = ~λ |λ, ωi .

(8)

where the displacement of the particle is the wavelength of the particle’s photon wave-state:   ~ ~λ = 2πr ω . (9) ω

Ron Poteet 11/25/10

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Additional notes on the Klein-Gordon Equation
Additional notes on the Klein-Gordon Equation

some additional notes on the Klein-Gordon Equation