**11. Remarks**

*Advances in Quantum Communication and Information*

**10. Quantum mechanical assessments**

world is timeless (i.e., t = 0).

quarter of a century, since 1935.

do it, since quantum mechanics is mathematics.

speaking, this is precisely why the dual-quantum states of the radioactive particle within Schrodinger's box are dysfunctional or impaired, within a temporal space.

The Schrödinger equation was developed on an absolute timeless subspace platform, for which all the solutions are timeless or time-independent. Since the fundamental principle of superposition was derived from the timeless Schrodinger equation, the corresponding quantum states' wave functions are also timeless with respect to the subspace that the particle is embedded in. Although wave function is time-dependent equation, it is with respect to the corresponding quantum state itself. This can be easily understood by an atomic model where the particle quantum states are represented by *h*n, where n = 1, 2, … N, number of quantum state, in which we see that each n-th wave function is time dependent with respect to *h*<sup>n</sup> quantum state. And it is not with respect to the subspace that the atomic model is embedded in, which is an empty subspace. Since time-dependent wave functions dictate the legitimacy of the superposition principle, the time dependency with respect to the particle's subspace is timeless, which is precisely the reason the fundamental principle of superposition is timeless and the whole Schrodinger's quantum

Since the whole quantum space is timeless, it cannot coexist within our temporal universe. In view of the logic of collapsing superposition principle as soon as we open up the Schrödinger's box, it must satisfy the physical reality that the cat cannot be alive and dead at the same time. Otherwise, the fundamental principle of superposition has proven itself to not exist within our temporal (i.e., t > 0) universe. It is apparent that Schrödinger's fundamental principle only exists within a timeless subspace. Personally I believe this must be the reason for him to justify the fate of his fundamental principle; otherwise, the principle is not able to survive. It must be Schrödinger himself that made the argument; otherwise, the paradox of his halflife cat has no physical foundation to debate by the world's top scientists over three

Since quantum mechanics is a virtual quantum machine as mathematics is, we have found that Schrödinger's machine is a timeless (or a virtual quantum) computer and it does not exist within our temporal universe. As we have seen, the Schrödinger equation was derived within an empty subspace; it is not a physical realizable model to use, since empty subspace and non-empty subspace are mutually exclusive. And we have seen that, as one plunges the timeless superposition principle within a temporal (i.e., t > 0) subspace and then anticipates the timeless superposition to behave "timelessly" within a temporal subspace is physically impossible. We have shown that only mathematician and quantum mechanists can

But this is by no means to say that timeless quantum mechanics is useless, since it has proven to us with scores of practical application that long solutions are not directly confronted with time-dependent or causality (i.e., t > 0) issue within our temporal universe. As quoted by the late Richard Feynman [12] that "nobody understands part of quantum mechanics," we have found the part of quantum mechanics nobody understands which must be from the "timeless superposition principle" that causes the confusion. And the root of timelessness quantum world is from the empty subspace that the atomic model was inadvertently anchored on. We are sure this discovery would change our perception as applying the fundamental principle to quantum computing and to quantum entanglement in communication, for which the "instance and simultaneous" (i.e., t = 0 and concurrent)

**120**

In conclusion, I have shown that the atomic model that Schrödinger used must be anchored within an absolute empty subspace. And it must be the underneath timeless subspace that caused the paradox of his half-life cat. The reason for overlooking the underneath timeless subspace must be due to the well-accepted Bohr's model that has been used for over a century, since the birth of Niels Bohr's atom in 1913 [3]. It has been very successfully used with excellent results for over a century. And it has never in our wildness dream that the underneath empty subspace causes the problem. In view of Schrödinger's time-dependent wave solutions, we have found the time dependency is with respect to the atomic particle itself but not with respect to the subspace the atomic model embedded in. In searching the root of the paradox of Schrödinger's cat, we found that a timeless radioactive particle should not have had introduced within a time-dependent (or temporal) Schrödinger's box. To alleviate the timeless radioactive particle issue, we have replaced a timedependent (i.e., t > 0) radioactive particle for which we have shown that the paradox Schrödinger's cat is not a paradox after all. We have also used science and math duality analogy to illustrate the outcome of a temporal excitation into a timeless system analog, as well as onto a temporal subspace, in which we have shown temporal space is a time-invariant space, while superposition principle is timeless and it is neither a time-invariant nor time-variant principle. It is however a no-time or timeless principle, which cannot be implemented within a time-invariant space. In short, we found the hypothesis of Schrödinger's cat is not a physical realizable postulation and his whole quantum world is timeless and behaves like mathematics does. Nonetheless, many of Schrodinger's timeless solutions are very useful until the implementation of fundamental principle that confronts with causality (i.e., t > 0) issue of our universe.
