# Can Quantum Jumps Same as Dimension Jumps ?

#### Antonio Lao

If this is multiplied by square of time rate of change of area, the result is the square of energy.

and the Einstein's field equations can be made equivalent to square of energy by the product of a factor as the speed of light in vacuum.

$$c \left[ R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R \right] = - 8 \pi \frac{a^2 c^4}{h} T_{\mu \nu}$$

In empty space at time=0, and considering vacuum fluctuation, the field equations become

$$cR_{\mu \nu} = \left(\psi_i \cdot \psi_j \right) \left(\phi_i \cdot \phi_j \right) \geq h^2$$

#### Epsilon Pi

Is it not a classical point of view, after all?

Hi Antonio and thank you very much!

An absolute TOE ? you really mean that? are you serious? in the same mansion of science?
Where is in your... -how would I say without trying to devaluate your great and noble intent- the duality of wave-particle, where is its rationalization?
It seems to me that the uncertainty principle is the one principle that identify in most cases QM, but where is in that description the duality of wave-particle, of space and time, ect?
Are you not seing things just a from classical point of view, or paradigm, just as those classical concepts such as mass and charge?

My best regards

EP

Antonio Lao said:
If this is multiplied by square of time rate of change of area, the result is the square of energy.

and the Einstein's field equations can be made equivalent to square of energy by the product of a factor as the speed of light in vacuum.

$$c \left[ R_{\mu \nu} - \frac{1}{2} g_{\mu \nu} R \right] = - 8 \pi \frac{a^2 c^4}{h} T_{\mu \nu}$$

In empty space at time=0, and considering vacuum fluctuation, the field equations become

$$cR_{\mu \nu} = \left(\psi_i \cdot \psi_j \right) \left(\phi_i \cdot \phi_j \right) \geq h^2$$

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#### Antonio Lao

Epsilon Pi said:
Where is in your... -how would I say without trying to devaluate your great and noble intent- the duality of wave-particle, where is its rationalization?
$$\Delta \psi \Delta \phi \geq h$$

is the Heisenberg's uncertainty principle of wave-particle duality.

#### Antonio Lao

But the expansion of $cR_{\mu \nu}$ give the following integral equations.
Let $\zeta$ be the product of Planck length and the speed of light c.

$$\left(m^2 - ma_m dt^2 \right) \left(n^2 - na_n dt^2 \right) \int \int a_m a_n dt dt \geq \zeta^2$$
$$\left(m^2 - ma_m dt^2 \right) \left(l^2 - la_l dt^2 \right) \int \int a_m a_l dt dt \geq \zeta^2$$
$$\left(n^2 - na_n dt^2 \right) \left(l^2 - la_l dt^2 \right) \int \int a_n a_l dt dt \geq \zeta^2$$

m, n, l are the quantum number of spacetime metrics.

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#### Epsilon Pi

no, that principle does not describe the wave-particle duality; according to what I have learned it was the Schrodinger wave equation -the fundamental and complementary equation- the one that described so well the wave nature of matter-energy, i.e., of physical reality.
As I have understood things the uncertainty principle has to do with that impossibility we have to have an exact, as it were, an absolute description of physical reality.
That reality is after all always paradigm-determined, isn't it?

Best regards

EP
Antonio Lao said:
$$\Delta \psi \Delta \phi \geq h$$

is the Heisenberg's uncertainty principle of wave-particle duality.

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#### Antonio Lao

The $a_i$ where i=m, n, and l are the infinitesimal accelerations due to orthogonal forces.

#### Epsilon Pi

Regards
EP
Antonio Lao said:
The $a_i$ where i=m, n, and l are the infinitesimal accelerations due to orthogonal forces.

#### Antonio Lao

Epsilon Pi said:
As I have understood things the uncertainty principle has to do with that impossibility we have to have an exact, as it were, an absolute description of physical reality
If this is the case, then I was wrong all this time in believing that the product of uncertainty in wavelength (a property of wave) and the uncertainty in momentum (a property of particle) is greater than or equal to Planck's constant.

#### Antonio Lao

Anyway, by doubling the uncertainty, multiplied by itself, and at time=0, which is the singularity of the big bang, I get an uncertainty in the square of a time rate of change of an infinitesimal area.

$$\frac{dA}{dt} = ac$$

Where A is area, a is Planck length and c is the speed of light.

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#### Epsilon Pi

Yes, but this talks about the impossibility we have to have an "ABSOLUTE description" of physical reality.
On the other hand it is Schrodinger wave equation the one that talks us about the wave nature in a precise mathematical description, even though, of course, and here I recognize your point, both:
- the uncertainty principle and
- additionally the Schrodinger wave equation

are fundamentals in describing QM; you cannot describe mathematically, in congruent way, the one without the other.

Regards

EP

Antonio Lao said:
If this is the case, then I was wrong all this time in believing that the product of uncertainty in wavelength (a property of wave) and the uncertainty in momentum (a property of particle) is greater than or equal to Planck's constant.

#### Antonio Lao

The uncertainty is between change in area and change in frequency of a wave.

$$\Delta A \Delta f \geq ac$$

#### Epsilon Pi

I thought uncertainty was related with that impossibility we have to measure, at the same time, two entities that cannot be reduced one to the other such as, wave and particle, or time and space, or momentum and position? a reason why its description had to be done with a complex differential equation such as the Schrodinger wave equation.

Regards

EP

Antonio Lao said:
The uncertainty is between change in area and change in frequency of a wave.

$$\Delta A \Delta f \geq ac$$

#### Antonio Lao

Schroedinger's equation is non-relativistic. Dirac's equation is relativistic. The transition is the energy formulation from

$$E =\frac{p^2}{2m}$$

to

$$E^2 = c^2 p^2 + m^2 c^4$$

I derived the the square of mass by assuming that linear momentum is zero.

#### Epsilon Pi

I really thought Schrodinger's wave equation was an equation that described the behavior of an entity such as the electron that sometimes can have the velocity of light; so just in those cases should we make the corresponding relativistic formulation or correction?

Regards

EP
Antonio Lao said:
Schroedinger's equation is non-relativistic. Dirac's equation is relativistic. The transition is the energy formulation from

$$E =\frac{p^2}{2m}$$

to

$$E^2 = c^2 p^2 + m^2 c^4$$

I derived the the square of mass by assuming that linear momentum is zero.

#### Antonio Lao

Epsilon Pi said:
thought uncertainty was related with that impossibility we have to measure, at the same time, two entities that cannot be reduced one to the other such as, wave and particle, or time and space
For 1D spacetime quantization, there exists uncertainty in the transformation of 1D space to 2D space (surfaces) to 3D space (volumes) and the product of this uncertainty with inverse uncertainty of time which is uncertainty in frequency of wave is greater or equal to product of Planck length and speed of light. Actually, it is the absolute value of the uncertainty because a negative part also exists as well.

#### Antonio Lao

The area uncertainty comes from its degree of freedom to become 1D or 3D. Like a incremental plane contracting to a line by motion or transforming into a volume. We are not certain how this incremental area would want to do, becomes 1D or 3D?

#### Epsilon Pi

An ABSOLUTE value of UNCERTAINTY? How can you talk about an ABSOLUTE value of UNCERTAINTY? Is not this a great contradiction?

Regards

EP
Antonio Lao said:
Actually, it is the absolute value of the uncertainty because a negative part also exists as well.

#### Antonio Lao

Epsilon Pi said:
How can you talk about an ABSOLUTE value of UNCERTAINTY? Is not this a great contradiction?
$$\left| ? \right| \geq n$$

is the same as

$$? \geq n$$

and

$$? \leq -n$$

The uncertainty approaches zero from left and right.

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#### Antonio Lao

Epsilon Pi said:
I really thought Schrodinger's wave equation was an equation that described the behavior of an entity such as the electron
Schrodinger's equation was capable of resolving the one-electron hydrogen (neutral atom) spectra. But Dirac's equation is the one for the multiple electrons atoms because of charge and spin in fine structure spectra.

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#### Antonio Lao

The positive and negative uncertainties as depicted by the uncertainty in frequency can resolve the concavity and convexity of quantized spacetime structures. One structure, from 2D surface to 1D string to 0D vacuum, resulting in the reality of the graviton with mass=0. The other structure, from 2D to 3D, and quickly to 4D and then bypassing 3D, 2D, and 1D jumps to 0D vacuum, resulting in the reality of the Higgs boson.

#### Antonio Lao

A clearer inequality formulation for the uncertainty in the quantum of mass is

#### Epsilon Pi

Thank you for your reply! You really have touched a point that concern me the most!
No, the fault of the quest for -what you now call the principle of duality, term, that I have used somewhere to identify: a binary logic, bilateral symmetry as was defined by Hermann Weyl, according to whom, all the theory of relativity rests on it- lies on that need to have a symbolism in which the third is included -not excluded as with the binary logic- or else the use of complex numbers that makes it possible to rationalize duality.
Of course, for our own convenience we have to reduce, in some cases, time to space, by defining a close system and then we will have a mathematical conception of time similar to that of space, that not only has the problem you have described, but additionally, it is a conception of time not in agreement with irreversible processes or the two arrows of time: in this wrong conception of time it can flow in both directions: positive and negative.
Now, thanks to your answer it is even more quite clear for me, why we have such a great difficulty in modern physics to even try to see things in a different way

Regards

EP

Antonio Lao said:
The fault of the quest for the principle of duality lies in the analysis of periodic functions. Given a period T time units, the inverse of T is the frequency. But what is the meaning of time inverse?

Time inverse can appear to be just a velocity magnitude with the distance factor normalized and turned into a dimensionless quantity.

But distance can only be normalized if we assume that there exist a maximum distance to gauge it to.

$$\frac{1}{d_{max}} \int_{-\infty}^{+\infty} d_i = 1$$

#### Antonio Lao

Epsilon Pi said:
in this wrong conception of time it can flow in both directions
You might have just rescued me from falling into the trap of further futile analysis in the quantification of the double time integrals

$$\int_{0}^{-\infty} \int_{+\infty}^{0} E(t) E^{*}(t) dt dt$$