**3. Schrödinger's equation**

One of the most important equations in quantum mechanics must be the Schrödinger equation as given by [4, 5]:

$$\frac{\partial^2 \Psi}{\partial x^2} + \frac{8\pi^2 \text{m}}{h^2} (E - V)\Psi = \mathbf{0} \tag{1}$$

where is the Schrödinger wave function, m is the mass, E is the energy, V is potential energy, and *h* is Planck's constant. The description of Schrödinger equation shows that changes of a physical system over time, in which quantum effects take place, such as wave-particle duality, are significant. However, the derivation of Schrödinger equation was based on point-singularity dimensionless atomic model submerged in a timeless empty space. And we have seen that there is a contrasting paradox, by which the model used in deriving the famous Schrödinger equation is incorrect, since a time-dependent atomic structure was, by not knowing it, embedded in an absolute empty timeless subspace, for which the evaluated Schrödinger equation is also a timeless equation [5]. We note that the intention of using the timeless subspace Bohr model was inadvertent, since Bohr's atomic model has been successfully accepted, in fact for over a century, and we are still using this model. This may be the reason that causes us to overlook the basic assumption, of which a time-dependent (temporal) subspace should not be embedded in a timeless subspace, since they are mutually exclusive. Nevertheless, the essence of Schrödinger equation is to predict a particle probabilistic behavior, as a dynamic particle, by means of a wave function. In other words, the outcome is not deterministic but a distribution of possible outcomes. But the question is: Is Schrödinger equation a physically reliable equation to derive its wave equations? The answer is "no," as remained to be shown in the following:

Since the derivation of Schrödinger equation is based on point-singularity approximation which is not a perfect assumption, it is an acceptable good approximation for this hypothesis. But it is the timeless subspace of the Bohr's atomic model embedded, which produces timeless solutions (i.e., t = 0) that are not acceptable within the temporal (time-dependent) subspace. In other words, the solution as derived from Schrödinger equation is expected to be timeless since Schrodinger equation is a time-independent equation. Thus we see that Schrödinger's quantum mechanics is a time-independent mechanics or timeless (i.e., with respect to the absolute empty timeless subspace) mechanics, which does not exist within our temporal universe!

As quoted by Feynman [6], "He think he can safely say that nobody understands quantum mechanics. So do not take his lecture too seriously…." Yet, after we understood the flaw of Schrödinger's cat, which has haunted quantum physicists for decades, we shall take a closer look at the paradox of the Schrodinger's cat. And at that moment, we may change our mind to saying that we have learned the inconsistency of Schrödinger's timeless (i.e., t = 0) quantum mechanics, as applied within our temporal universe (i.e., t > 0).

However, as I attempt to derive a wave dynamic where a particle is assumed situated within a temporal subspace, I am not sure that I will not be buried by complicated mathematical formulation (e.g., I have not attempted to do it yet at the time being). But I anticipate that the new result would not be paying off at least for the time being; it will have a better one than the Schrödinger equation that has already provided. But I am sure the solution will obey toward the causality condition (i.e., t > 0).

**111**

less environment.

**5. Schrödinger's cat**

*Schrödinger's Cat and His Timeless (t = 0) Quantum World*

As has been done by using the Schrödinger equation to evaluate the particle wave function, one may need to reinterpret the solution to meet the causality constraint as imposed by our temporal universe. Otherwise, the evaluated solution would not be useful for practical application, in which we see that instant quantum entanglement [7] is one of the typical examples that was derived from the classic Schrödinger superposition principle. And we can see that the "instant" (i.e., t = 0) entanglement between particles is "fictitious" and it would not happen within our temporal space. As we know that within our temporal universe time is distance and distance is time, any particle entanglement cannot happen instantly without a price

As we look back to the particle model embedded in an empty subspace for deriving the classic Schrödinger equation, without such a simplistic model, viable solution may not be able to obtain even using tons of complicated mathematic manipulation. Although those assumptions alleviate (somewhat) the complexity in analysis, it also introduces incomplete results that may not exist within our universe. Thus by knowing Schrödinger's quantum mechanics, it is a time-independent (or more precisely a timeless quantum computing machine) mechanics which was the consequence of using the assumed particle model within a timeless subspace. Since in practice timeless substance cannot exist within our temporal universe, we see that the flaw of Schrödinger cat as well the whole quantum space is due to the assumption that the embedded subspace is absolutely empty, in which we see that one cannot simply insert a timeless quantum machine into a time-dependent

The Pauli exclusive principle [8] states that two identical particles with the same quantum state cannot occupy the same quantum state simultaneously, unless these particles exist with a different half-spin. While quantum entanglement [7] occurs when a pair of particles interacts in such a way that the quantum state of the particles cannot be independently described, even when the particles are separated by a large distance, a quantum state must be described by the pair of particles as a whole. In view of Pauli exclusive principle, the entanglement between particles does exist, but the separation between the particles has to be limited, since the particles are situated within a time-dependent subspace (i.e., t > 0) [8]. Again we see that the flaw of instant entanglement comes from the assumption that the exclusive principle was derived within the timeless subspace, in which we see again that temporal and timeless subspaces cannot coexist. In other words, time-dependent particles

Before we move away from the timeless issue, we would point out that practically all of the fundamental principles in science, such as Paul's exclusive principle, Schrödinger's superposition principle, Einstein's energy equation, and others, are timeless principles, of which they were hypothesized "inadvertently" within a time-

One of the most intriguing cats in quantum mechanics must the Schrödinger's

decades. Let us start with the Schrödinger's box as shown in **Figure 3**; inside the box

cat, in which it has eluded the particle physicists and quantum scientists for

**4. Pauli exclusive principle and particle entanglement**

cannot coexist within a timeless subspace.

*DOI: http://dx.doi.org/10.5772/intechopen.86970*

to pay (e.g., time or distance).

(i.e., t > 0) subspace.

*Advances in Quantum Communication and Information*

One of the most important equations in quantum mechanics must be the

where is the Schrödinger wave function, m is the mass, E is the energy, V is potential energy, and *h* is Planck's constant. The description of Schrödinger equation shows that changes of a physical system over time, in which quantum effects take place, such as wave-particle duality, are significant. However, the derivation of Schrödinger equation was based on point-singularity dimensionless atomic model submerged in a timeless empty space. And we have seen that there is a contrasting paradox, by which the model used in deriving the famous Schrödinger equation is incorrect, since a time-dependent atomic structure was, by not knowing it, embedded in an absolute empty timeless subspace, for which the evaluated Schrödinger equation is also a timeless equation [5]. We note that the intention of using the timeless subspace Bohr model was inadvertent, since Bohr's atomic model has been successfully accepted, in fact for over a century, and we are still using this model. This may be the reason that causes us to overlook the basic assumption, of which a time-dependent (temporal) subspace should not be embedded in a timeless subspace, since they are mutually exclusive. Nevertheless, the essence of Schrödinger equation is to predict a particle probabilistic behavior, as a dynamic particle, by means of a wave function. In other words, the outcome is not deterministic but a distribution of possible outcomes. But the question is: Is Schrödinger equation a physically reliable equation to derive its wave equations? The answer is "no," as

Since the derivation of Schrödinger equation is based on point-singularity approximation which is not a perfect assumption, it is an acceptable good approximation for this hypothesis. But it is the timeless subspace of the Bohr's atomic model embedded, which produces timeless solutions (i.e., t = 0) that are not acceptable within the temporal (time-dependent) subspace. In other words, the solution as derived from Schrödinger equation is expected to be timeless since Schrodinger equation is a time-independent equation. Thus we see that Schrödinger's quantum mechanics is a time-independent mechanics or timeless (i.e., with respect to the absolute empty timeless subspace) mechanics, which does not exist within our

As quoted by Feynman [6], "He think he can safely say that nobody understands quantum mechanics. So do not take his lecture too seriously…." Yet, after we understood the flaw of Schrödinger's cat, which has haunted quantum physicists for decades, we shall take a closer look at the paradox of the Schrodinger's cat. And at that moment, we may change our mind to saying that we have learned the inconsistency of Schrödinger's timeless (i.e., t = 0) quantum mechanics, as applied within

However, as I attempt to derive a wave dynamic where a particle is assumed situated within a temporal subspace, I am not sure that I will not be buried by complicated mathematical formulation (e.g., I have not attempted to do it yet at the time being). But I anticipate that the new result would not be paying off at least for the time being; it will have a better one than the Schrödinger equation that has already provided. But I am sure the solution will obey toward the causality

*<sup>h</sup>*<sup>2</sup> (*<sup>E</sup>* <sup>−</sup> *<sup>V</sup>*)<sup>ψ</sup> <sup>=</sup> <sup>0</sup> (1)

\_\_\_ψ <sup>∂</sup>*x*<sup>2</sup> <sup>+</sup> <sup>8</sup>*π*<sup>2</sup> \_\_\_\_\_m

**3. Schrödinger's equation**

Schrödinger equation as given by [4, 5]:

remained to be shown in the following:

temporal universe!

condition (i.e., t > 0).

our temporal universe (i.e., t > 0).

<sup>∂</sup><sup>2</sup>

**110**

As has been done by using the Schrödinger equation to evaluate the particle wave function, one may need to reinterpret the solution to meet the causality constraint as imposed by our temporal universe. Otherwise, the evaluated solution would not be useful for practical application, in which we see that instant quantum entanglement [7] is one of the typical examples that was derived from the classic Schrödinger superposition principle. And we can see that the "instant" (i.e., t = 0) entanglement between particles is "fictitious" and it would not happen within our temporal space. As we know that within our temporal universe time is distance and distance is time, any particle entanglement cannot happen instantly without a price to pay (e.g., time or distance).

As we look back to the particle model embedded in an empty subspace for deriving the classic Schrödinger equation, without such a simplistic model, viable solution may not be able to obtain even using tons of complicated mathematic manipulation. Although those assumptions alleviate (somewhat) the complexity in analysis, it also introduces incomplete results that may not exist within our universe. Thus by knowing Schrödinger's quantum mechanics, it is a time-independent (or more precisely a timeless quantum computing machine) mechanics which was the consequence of using the assumed particle model within a timeless subspace. Since in practice timeless substance cannot exist within our temporal universe, we see that the flaw of Schrödinger cat as well the whole quantum space is due to the assumption that the embedded subspace is absolutely empty, in which we see that one cannot simply insert a timeless quantum machine into a time-dependent (i.e., t > 0) subspace.
