Can Quantum Jumps Same as Dimension Jumps ?

Main Question or Discussion Point

Can Quantum Jumps Same as Dimension Jumps ???

By going back to Bohr's stationary orbits of electrons, The idea of quantum jumps was born.

We can hypothesize that matter such as electrons are 4D objects and photons are 3D objects and the continuous space between orbits is a 2D continuum. So what happens when one electron jumps from one orbits to another orbit is that the 4D electron transforms to 3D energy and the 3D energy transforms to a 2D continuum then 2D continuum back to 3D energy and then back to a 4D electron at a lower or higher orbit whichever the case in question. And transformation of 2D continuous space (S) is given by:

$$S = cE$$

where c is the speed of light in vacuum and it acts as dimension lowering constant for energy (E).

And by dimensional analysis, the 2D continuous space is proportional to an arbitrary surface area with the proportionality constant as force per unit of time. Futhermore force per unit time is proportional to the time derivative of acceleration with mass as the constant of proportionality.

$$\frac {Force}{time} = m \frac {\partial a}{\partial t}$$

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If the surface area changes with time then the gradient of continuous space is given by

$$\nabla S = m \frac {\partial \vec{a}}{\partial t} \frac{\partial Area}{\partial t}$$

Futhermore for volume as a function of time, V(t) and given density $\rho$, the gradient of continuous space is given by

$$\nabla S = \frac {c^4 \rho_T}{\vec{r}} V(t)$$

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If we can define the ratio of instantaneous density to total density of the universe as a function of time given by

$$\frac{1}{\rho_T} \int_{0}^{\infty} \rho_i (t) dt = 1$$

then the instantaneous density is the sum of kinetic density and potential density given by

$$\rho_i = \rho_k + \rho_p$$

If the total mass of the universe is the sum of total potential mass and total kinetic mass

$$m_T = m_k + m_p$$

then instantaneous kinetic and potential volumes can be related to the total volume given by

$$\frac{m_T}{m_p} - \frac{V_k}{V_p} \left ( \frac{V_T - V_p}{V_k - V_T} \right ) = 1$$

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$$\frac{m_T}{m_p} \geq 1$$

and

$$\frac{V_k}{V_p} \left ( \frac{V_T - V_p}{V_k - V_T} \right ) < 1$$

if

$$\frac{m_T}{m_p} = 1$$

then

$$\frac{V_k}{V_p} \left ( \frac{V_T - V_p}{V_k - V_T} \right ) = 0$$

$V_k$ is the same as the instantaneous volume of radiation. $V_p$ is the instantaneous volume of matter. $V_T$ is the total volume of the universe at each epoch.

The gradient of continuous space becomes a function of instantaneous density and volume.

$$\nabla S = \frac{c^4}{\vec{r}} \int_{0}^{\infty} \rho_i (t) V(t) dt$$

From this, an integral force exist.

$$F = \frac{c^3}{\vec{r} \times \vec{r}} \int_{0}^{\infty} \rho_i (t) V(t) dt$$

This force is infinitely large because the term $\vec{r} \times \vec{r} = 0$. But if the r's are orthogonal and comparable to Planck length then the force is just simply large. If orthogonal r's is very large then the force is small.

Orthogonality seems to be a necessary condition for the force to exist. This implies that orthogonal forces must exist and the extremely high magnitude of this force must be able to quantize spacetime at the local infinitesimal region of a spacetime continuum.

For low velocity and small mass and together with the invariance, $\vec{a} \cdot \vec{r} = c^2$, this force becomes Newton's 2nd law of motion.

In post #7, the r's can become large only if the individual r's can be added collinearly together.

$$\vec{r} = \int_{0}^{\infty} \vec{r}_i$$

Collinearity implies that $\vec{r} = \alpha \vec{r}_i$ where $\alpha$ is an integer.

When the linear momentum is zero and when both density and volume are functions of energy and time, the square of mass is given by

$$m^2 = \int \int \frac{\partial \rho^2}{\partial t} \frac{\partial V^2}{\partial t} dt dt$$

Furthermore, the square of mass is a new constant of nature given by

$$m^2 = \left( \frac{h}{ac} \right)^2$$

where h is Planck's constant, a is Planck length and c is the speed of light.

Implication is the existence of real positive and negative root for mass given by

$$\pm \frac{h}{ac}$$

without the use of complex number.

The use of these roots is to constraint the value of

$$\frac {V_k}{V_p} \left( \frac{V_T - V_p}{V_k - V_T} \right)$$

or

$$\frac {V_k}{V_p} \left( \frac{V_p - V_T}{V_T - V_k} \right)$$

so that the expressions are always less than unity.

Why is the quantum of mass using $\pm \frac{h}{ac}$ numerically equal to the Planck mass using $\sqrt{\frac{hc}{G}}$?

If Planck's constant was determined first together with the speed of light and knowing the value of the Planck length, the value of the gravitational constant can be found by

$$G = \frac{a^2 c^3}{h}$$

In a planetary system where one of the earthlike planets is in a perpetual cloud cover, the inhabitants will never be able to have the opportunity of seeing the starry night sky. In this planet, there could be no Galileo nor Kepler and then nor Newton before Maxwell's and Planck's discoveries. Yet the scientists of this planet can derive the laws of electromagnetism and also quantum mechanics first and then discover the law of universal gravitation afterward.

Although Einstein's theories of relativity can clinch the final constancy of the speed of light, these are not necessary for the first order determination of the gravitational constant.

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Quite clever example of different paradigms and how they will guide our quests in different ways, but I was wondering if you did choose those examples to be discovered first(Maxwell equations without the displacement current concept and Plank's discoveries) because in the last analysis they have to do with more fundamental laws of nature than those of gravitation?

Regards

EP
Antonio Lao said:
In a planetary system where one of the earthlike planets is in a perpetual cloud cover, the inhabitants will never be able to have the opportunity of seeing the starry night sky. In this planet, there could be no Galileo nor Kepler and then nor Newton before Maxwell's and Planck's discoveries. Yet the scientists of this planet can derive the laws of electromagnetism and also quantum mechanics first and then discover the law of universal gravitation afterward.

Although Einstein's theories of relativity can clinch the final constancy of the speed of light, these are not necessary for the first order determination of the gravitational constant.

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Epsilon Pi,

Epsilon Pi said:
but I was wondering if you did choose those examples to be discovered first
I think all physical constants which are independent on other constants should appear in physical laws that are not depended on the sequential order of their discovery. For example, Planck's constant is depended on Boltzmann's constant therefore Boltzmann's constant must necessarily come first. Maxwell's theory of electromagnetism and quantum theory are in sequential order. One must follow the other since the later one uses some constants found in the earlier theory.

Unresolve relationships between mass, volume and density for some particles

Planck mass=10e(-5) gram, volume=10e(-99) cm^3, density=10e(+94) g/cm^3
proton mass=10e(-24) gram, volume=10e(-39) cm^3, density=10e(+15) g/cm^3
electron mass=10e(-28) gram, volume=10e(-39) cm^3, density=10e(+11) g/cm^3
photon mass=0 gram (?), volume= ?, density= ?

Epsilon Pi said:
I am now reading Thomas S. Kuhn's 'The Structure of Scientific Revolutions' to get some ideas about paradigm shift.

A TOE a futile intent?

By reading and reading T.S.K, I was wondering if the quest for a TOE, is not a futile one after all?
In this respect he wrote, in his classical, when arguing against Popper's falsification argument:
"...no theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect. On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any given time, define many of all the puzzles that characterize normal science. IF ANY AND EVEN EVERY FAILURE TO FIT WERE GROUND FOR THEORY REJECTION, ALL THEORIES OUGHT TO BE REJECTED AT ALL TIMES".(The Structure of Scientific Revolutions, p.146)

Must not we resolve then first the incommensurability problem we have between the existing paradigms, QM and GTR, before going with any intent? or at least making a great effort in this sense?

Just some inquisitive thoughts in my mind

Regards

EP

Antonio Lao said:
I am now reading Thomas S. Kuhn's 'The Structure of Scientific Revolutions' to get some ideas about paradigm shift.

Epsilon Pi said:
By reading and reading T.S.K, I was wondering if the quest for a TOE, is not a futile one after all?
If the derivation of a constant of a theory is independent from constants of other theories and furthermore if the theory can describe all other theories with consistency then this theory can be a TOE.

The theory of electromagnetism is the relative TOE to the theory of magnetism and the theory of electricity.

The theory of electroweak interaction is the relative TOE to the theory of electromagnetism and the weak nuclear force.

Although relative TOEs do exist, it is the belief that an absolute TOE can also exist. But as pointed out previously, the gravitational constant can be derived from knowing the speed of light and Planck's constant and maybe guessing by trials and errors the value of the Planck length (needed for determining some quantity of volume) which will require some sort of uncertainty principle (if the mass is quantized) between the concept of density and volume.

My hunch is that the resolution can simply be done in one dimensional space or the quantization of 1D space and 1D time.

The theory of quantized 1D spacetime can resolve the theory of mass by the combined theories of density and volume. This theory implies the existence of two kinds of mass: the potential and the kinetic. It can also clarify the concept of electroweak charges and color charges by invoking a principle of a directional invariance.

So a theory that can describe both mass and charge using the physically revised concepts of density and volume can be called an absolute TOE.

A rough formulation of this uncertainty between density and volume at time=0 is given by

$$3^{-9} gram \leq \Delta \rho^2 \Delta V^2 \leq 4^{-9} gram$$

or

$$\left| \Delta \rho^2 \Delta V^2 \right| \leq \frac{1}{\pi^9}$$