Quantum Space-Time with Energy

Yajun Liu

Department of Mechanics Engineering, South China University of Technology, Guangzhou, China.

DOI: 10.4236/jhepgc.2025.112025                

Abstract

In this paper, we constructed a Space-Time with energy model just considering the velocity of the light C and the Plank constant h and $1/a_g$ ($a_g$ is the strength of gravition (m/s²)) This model will just provide a probability to combine the Gravitation and Electric-Magnetics field under a basic structure of quantum Space-Time with energy. We hope to throw a little bit of light on the big picture of uniting quantum mechanics and General relative theory.

Keywords

Quantum Time-Space with Energy, Unified Field Theory

1. Time Quantization

Time is a basic concept in physics. But till now, we have no idea how to use mathematical model to describe the structure of “Time”. In Newton’s system, Time is an independent existence with space. In Einstein’s system, Time and Space are bonded together just considering the Velocity of Light is a constant C (m/s). And then for a Quantum system, we consider the energy is discrete and then the “Time contentiousness” disappears in this system. But it is that the Dimension of Plank’s constant h (J·s) also includes the unit of Time. So, we think that if we may construct a Dimension system of Time-Space with energy based on two priori conditions: the velocity of light is a constant C and the unit of energy with Time is a constant h, Plank constant. And if we can quantize this Time-Space with energy system, maybe we can get a mathematical model to describe more physics details of the basic structure of Space-Time with energy and get a Unified Field Theory.

$\tau$ can be defined $d$ as

$\tau ~nh\left(\text{J}\cdot \text{s}\right)n~\left(1,2,3,\cdots \right)$

$h$ (J·s) is Planck constant. We can call $\tau$ as Time-been.

$t$ can be defined $d$ as

$t~n\left(\frac{c}{a_g}\right)\left(\text{J}\cdot \text{s}\right)n~\left(1,2,3,\cdots \right)$

$C$ is the velocity of Light (m/s), and $a_g$ is the Intensity of field of gravitation (m/s²). We can call $t$ as Time-to be.

And

$T~2n\left(\text{J}\cdot \text{s}\right)$

We call $T$ Time-being.

So we got a Time-space with Energy coordinate system (1/c-h(-T-c/ag)-1/c) shown as Figure 1(a).

$\langle T\rangle =\langle \tau \rangle +\langle t\rangle ~n\ast \left[\langle h\rangle +\langle \frac{c}{a_g}\rangle \right]$

We can define mass M as:

$M_0~\frac{h}{C^2}\left(\text{kg}\cdot \text{s}\right)$

$M~n^3\frac{h}{C^2}\left(\text{kg}\cdot \text{s}\right)$

and show as Figure 1(b).

At moments $T~2n\left(\text{J}\cdot \text{s}\right)$

$\tau =t$

$nh=nc/a_g$

$\frac{1}{a_g}=h/c\left(\text{J}\cdot {\text{s}}^2\cdot {\text{m}}^{-1}\right)$

So we have:

$M_0{a}_g~1/c\left(\text{s}\cdot {\text{m}}^{-1}\right)$

(a) (1/c-c/ag-h-T-1/c) Time-Space

(b) (h-c/ag-T) Time-energy Section

Figure 1. Time-Space with energy coordinate.

2. Quantum Time Space with Energy

We will define a space-time with energy as:

$M_0{a}_g~1/c\left(\text{s}\cdot {\text{m}}^{-1}\right)$

$T~2n\left(\text{J}\cdot \text{s}\right)$ $n~\left(1,2,3,\cdots \right)$

$S_0~\frac{1}{4}\ast h\ast \frac{c}{a_g}~{\left(\frac{1}{2}\ast h\right)}^2$ $S_n~n^{2}h\ast \frac{c}{a_g}~{\left(nh\right)}^2$

$\frac{S_n}{S_0}=4n^2$

$\frac{M}{M_0}~n^3$

3. Discussion

Galilei said that he can create the Universal only using Space, Time and Logarithm. Einstein said that a Unified Field Theory should be a geometrization one. And Roger Penrose pointed out that if we want to get the uniting of the Mass and Time-Space, we need the help of Complex Number [1]. The paper [2] discusses that a Unified field theory should be a model with Plank constant, gravitation and the velocity of Light. Wilczek [3] wants to use a concept called Quantum Time Crystals to define the Time space with energy.

In Newton’s system, Time is an independent existence with energy.

$S~E\ast t$

In Einstein’s system, Time and Space are bonded together just considering the Velocity of Light is a constant C (m/s).

$S~1\ast \left(\frac{C}{a_g}\right)$

$a_g$ is the strength of gravitation (m/s²).

And for a Quantum system, the energy is considered discrete and then the “Time contentiousness” disappears in this system. But It is that the Dimension of Plank’s constant h (J·s) also includes the unit of Time.

$S~{\left(E\ast t\right)}^2={\left(nh\right)}^2$

h is Plank constant, we can find that the Dimension of Plank’s constant h (J·s) also includes the unit of Time.

In our system, we can get

$S^{1/2}~E\ast t~\sqrt{h\ast \left(\frac{c}{ag}\right)}$

$S_n/S_0~4n^2$

$M_0{a}_g~1/c$

And we notice that if Goldbach conjecture $2n=p0+pn$ ($n$ is a nature number, and $p0$ , $pn$ are primer numbers)and Polignac’s conjecture $pn-p0=2n$ ($n$ is a nature number, and $p0$ , $pn$ are primer numbers) be proofed, then

$T~2n=\left(pn\pm p0\right)$

$\frac{S_n}{S_0}~4n^2={\left(pn\pm p0\right)}^2$

$\frac{M}{M_0}~n^3={\left(\frac{pn\pm p0}{2}\right)}^3$

Because of the randomness of prime numbers, this will be a model to explain the randomness of the nature and Quantum Entanglement.

4. Summary

In this paper, we constructed a Space-Time with energy model just considering the velocity of the light C and the Plank constant h. Our Model gives a definition of Quantum Space Time as

$m_0~\frac{h}{C^2}~{10}^{-50}\left(\text{J}\cdot {\text{m}}^{-2}\cdot {\text{s}}^3\right)$

$1/a_g~\frac{h}{C}~{10}^{-42}\left(\text{J}\cdot {\text{m}}^{-1}\cdot {\text{s}}^2\right)$

$S_0~\frac{1}{4}\ast h\ast \left(\frac{c}{ag}\right)\left({\text{J}}^2\cdot {\text{s}}^2\right)$

$T~2n\left(\text{J}\cdot \text{s}\right)$

$\frac{S_n}{S_0}~4n^2$

$\frac{M}{M_0}~n^3$

This model just provides a basic structure of quantum Space-Time with energy.

Data Availability Statement

No datasets were generated or analyzed during the current study.

Conflicts of Interest

The author declares no conflicts of interest regarding the publication of this paper.

References

[1]	Penrose, R. and Rindler, W. (1984) Spinors and Space-Time. Cambridge University Press. https://doi.org/10.1017/cbo9780511564048
[2]	Wagner, W., Gontchar, I.I., Gettinger, A.E., Litnevsky, L.A., Ortlepp, H. and Kamanin, D.V. (2002) Novel Features of the Fragment Mass Variance in Fission of Hot Nuclei. Physics of Atomic Nuclei, 65, 1403-1410. https://doi.org/10.1134/1.1501651
[3]	Wilczek, F. (2012) Quantum Time Crystals. Physical Review Letters, 109, 160401. https://doi.org/10.1103/physrevlett.109.160401