**2. Flaws of a physical model**

*Advances in Quantum Communication and Information*

science would be useless for practical application.

scientific researches and their applications.

repeated by experiments.

**Figure 1**.

postulation, and his quantum mechanics as well as his fundamental principle of

One important aspect within our temporal universe (or time-dependent universe) [1, 2] is that one cannot get something from nothing: there is always a price to pay. For example, every piece of temporal subspace (or every bit of information) takes energy and time to create. And the created subspace (or substance) cannot bring back the section of time that has expensed for its creation. Every temporal subspace cannot be a subspace of an absolute empty subspace, and any absolute empty space cannot have temporal subspace in it. Any science proven within our temporal universe is physically real; otherwise, it is fictitious unless it can be

Science is a law of approximation and mathematics is an axiom of absolute certainty. Using exact math to evaluate inexact science cannot guarantee the solution exists within our temporal subspace. Science is also an axiom of logic; without logic

In addition, all the fundamental sciences need constant revision. For example, science has evolved from Newtonian mechanics to Einstein's theory of relativity and to Schrödinger's quantum mechanics. And the beauty of the fundamental laws must be mathematical simplicity, so that their complicated logics and significances can be understood easily. And the advantages have been very useful for extending

Nonetheless, practically all the particle sciences were developed from pointsingularity approximation and had been "unintentionally" embedding a pointsingularity atomic model [3] within an empty timeless subspace, as shown in

In which we see that, nucleus and electrons were shown by a dimensionless singularities representation. And we may not be aware that the model is not a physically real model, since the submerged background represents a timeless empty subspace. However, a timeless empty subspace cannot exist within our temporal universe! Although Bohr's atomic model have been used since the birth of Bohr's atom [3], its background has been mistakenly interpreted as an absolutely empty timeless subspace. Strictly speaking, as a whole it is not a physically correct model, and the solution

*An isolated Bohr's atomic model (or a timeless model); h is the Planck's constant, and v is the radiation* 

superposition is timeless, which behaves like mathematics does.

**108**

**Figure 1.**

*frequency.*

Basically all the models are approximated. For example, point-singularity approximation for an atomic model offers the advantage of simplicity representation, but it deviates away from a real physical dimension, which causes the accuracy in solution. Secondly, physical model embedded within a timeless (i.e., t = 0) subspace is absolutely incorrect, since every physical subspace is a temporal (i.e., t > 0) subspace, and it cannot be coexisted with a time-independent (or a timeless) subspace [1, 2]. Therefore as we can see, solution obtained from a physical model embedded within a timeless empty subspace shown in **Figure 2** is absolutely incorrect, and it bounds to have incomplete or fictitious solution. The fact is that one of the significant reasons other than the singularity approximation is the temporal or causality condition (i.e., t > 0) which is required as we applied within our temporal universe. Therefore as depicted in **Figure 1**, it is not a physical realizable model, since time-dependent (or temporal) atom cannot exist within an absolute empty timeless subspace. As shown, it produces physically nonexistent fictitious solutions, which is similar as plunging a temporal machine into a nontemporal subspace.

On the other hand as referenced to **Figure 2**, a temporal (time-dependent) atomic model which is embedded within a time-dependent (or temporal) subspace is a physical realizable model, in which we see that the temporal or causality requirement (i.e., t > 0) imposed by our temporal subspace is included. In fact our universe was created by a Big Bang explosion followed by the laws of physics, which is a temporal (i.e., t > 0) universe [1, 2]. Therefore, any physical system within our temporal space has to follow the law of time (or causality condition), so that every physical science has to be proven temporal (i.e., t > 0) within our universe (our home); otherwise it is a virtual fictitious science.

#### **Figure 2.**

*An isolated atomic model embedded in temporal subspace (or a temporal atomic model). f(x, y, z; t); t > 0 represents a function of three-dimensional space and time t as a forward variable.*
