**7. Essence of a subatomic model**

*Advances in Quantum Communication and Information*

time-dependent (i.e., t > 0) equation, of which we will see that Schrödinger's wave functions of the dual-state radioactive particle can be shown as 1 (t) and <sup>2</sup> (t + t), respectively, where t represents a time delay between them. Since time is distance and distance within a temporal subspace, we see that the quantum states will not occur at the same time (i.e., t = 0). Furthermore, the degree of their mutual superposition states can be shown as a time ensemble of < 1 (t) 2\*(t+t)>, respectively, where \* denotes the complex conjugate, in which we see that a perfect degree of mutual superimposition occurs if and only if t = 0, which corresponds to

*Schrödinger's box with a timeless radioactive particle. Notice that timeless radioactive particle cannot exist in a* 

Now let us go back to the half-live cat in Schrödinger's box, where the radioactive particle is assumed within a timeless sub-box as shown in **Figure 5**, in which we see that a timeless (i.e., t = 0) radioactive particle is situated inside the time-dependent (i.e., t > 0) box, which is "not" a physical realizable postulation for Schrödinger's cat. The fact is that a timeless (t = 0) subspace cannot exist within a time-dependent

the timeless (i.e., t = 0) quantum state of the radioactive particle.

is not a physical realizable principle within our temporal universe!

less virtual subspace similar to what mathematics does.

(t > 0) space (i.e., the box). Thus we have shown that again the paradox of

Schrödinger's is not a paradox, since the postulated superposition is timeless, and it

However, by replacing the timeless particle with a time-dependent (i.e., t > 0) particle shown in **Figure 5**, then we see there is a match in time as a variable with respect to the box. Then Schrödinger's cat can only either be dead or not be dead but not at the same time, in which we see that there is nothing to do whether we open the box or not to cause the fundamental principle to collapse. In other words, a dead cat or a live cat has already been determined before we open up the box. And the occurrence of the particle's quantum states is not simultaneously by means of the fundamental principle of Schrödinger, in which we have shown that superposition principle does not exist within our temporal space and it only exists within a time-

At last, we have found the flaw of Schrödinger's cat, where Schrödinger was not supposed to introduce a timeless radioactive particle into the box. This vital mistake that he committed is apparently due to an atomic model in which subspace is assumed to be absolutely empty as shown in **Figure 1**, in which we see that a timeless (i.e., t = 0) particle is wrongly inserted into a temporal (i.e., t > 0) box. I believe we have finally found the root of the paradox of Schrödinger's cat, for which we shall leave the cat behind with a story to tell; once upon a time, there

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**Figure 5.**

*temporal (i.e., time-dependent) subspace.*

was a half-life cat!

With high degree of certainty, most of the fundamental laws of science embraced the singularity approximation which includes the atomic models embedded within a timeless subspace. As we look at any conventional atomic model, we might inadvertently assume that the background subspace is an absolutely empty space. And this is the consequence of Schrödinger's timeless quantum mechanics, since any physical atom (i.e., t > 0) cannot be situated within a timeless (i.e., t = 0) subspace. Although singularity model works very well for scores of quantum mechanical application until the postulation of Schrödinger's cat emerged. Since the paradox of the half-life cat is the core of the fundamental principle, it has been argued for over eight decades by Einstein, Bohr, Schrödinger, and many others since Schrödinger disclosed the postulation at a Copenhagen forum in 1935. This intrigues us to look at Schrödinger's equation which was developed on an empty (i.e., t = 0) subspace platform, in which we see that superposition position collapses as soon as we open Schrödinger's box. This must be the apparent justification for Schrödinger to preserve the fate of his fundamental principle. Otherwise his timeless fundamental principle cannot survive within our temporal universe (i.e., t > 0). In short, we see that the hypotheses of Schrödinger's cat are a fictitious postulation, and we have proof that it does not have a viable physical solution, since any timeless radioactive particle cannot coexist in a temporal box, and we have seen that Schrödinger have had inadvertently introduced in the box (**Figure 6**).

#### **Figure 6.**

*A time-dependent cat is in a temporal (time-depending) box, in which we see a temporal radioactive particle is introduced within Schrodinger's temporal box.*
