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

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 cannot coexist within a timeless subspace.

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 timeless environment.

### **5. Schrödinger's cat**

One of the most intriguing cats in quantum mechanics must the Schrödinger's cat, in which it has eluded the particle physicists and quantum scientists for decades. Let us start with the Schrödinger's box as shown in **Figure 3**; inside the box

#### **Figure 3.**

*Inside the box we equipped a bottle of poison gas and a device (i.e., hammer) to break the bottle, triggered by the decaying of a radioactive particle, to kill the cat.*

we have equipped a bottle of poison gas and a device (i.e., a hammer) to break the bottle, triggered by the decaying of a radioactive particle, to kill the cat. The box is assumed totally opaque of which we do not know that the cat will be killed or not, as imposed by the Schrödinger's superposition principle, until we open the box.

With reference to the fundamental principle of superposition of quantum mechanics [4], the principle tells us that superposition holds for multi-quantum states in an atomic particle, of which the principle is the "core" of quantum mechanics. In other words, without the superposition principle, it will not have Schrödinger's quantum mechanics. In view of this principle, we see that the assumed two states of radioactive particle inside the box can actually simultaneously coexist, with a cloud of probability (i.e., both one thing and the other existed at the same time).

Since the hypothetical radioactive particle has two possible quantum states (i.e., decay or non-decay) that existed at the same time, which is imposed by the virtue of superposition principle in quantum mechanics, this means that the cat can be simultaneously alive and dead, before we open the box.

But as soon as we open the box, the state of superposition of the radioactive particle collapses, without proof! In an instant, we have found that after the box is opened, the cat is either alive or dead, but not both. This paradox in quantum mechanics has been intriguing particle physicists and quantum scientists over eight decades, since the birth of Schrodinger's cat in 1935, as disclosed by Erwin Schrödinger who is as famous as Albert Einstein in modern physics.

Let us momentarily accept what the fundamental principle holds, such that superposition of a dual-quantum state radioactive particle exists within the box. This tells us that the principle has created itself a timeless (i.e., t = 0) quantum subspace or time-independent quantum space. However, timeless subspace cannot exist within our temporal universe, in which we see that any solution (i.e., wave function) as obtained by Schrödinger equation contradicts the basic superposition principle, such that a timeless quantum subspace exists within our temporal (i.e., time-dependent) universe. This conjecture tells us that the hypothetical radioactive material cannot actually exist within the box, since both quantum states (i.e., decay or non-decay) cannot occur at the same time within a time-dependent subspace. We stress that time is distance and distance is time within a temporal subspace.

**113**

**Figure 4.**

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

Nevertheless, it remains a question to be asked: Where is the source that produces the timeless radioactive particle? Why is Schrodinger's superposition principle timeless (i.e., t = 0) for which the particle's quantum states exist simultaneously (i.e., t = 0)? A trivial answer is that it has to be coming from a timeless subspace where the particle model embedded is shown in **Figure 5**. As we continue searching the root of paradox of the Schrödinger cat, we will provide an equivalent example to show that the paradox of the half-life cat is not

Let us replace the binary radioactive particle with a flipping coin in the

So as one flips a coin before it is landed, it is absolutely uncertain that the coin will land either as a head or as a tail. Suppose we are able to "freeze" the flipping coin in the space at time t'; then the flipping coin is in a timeless mode subspace at time t', which is equivalent to a two-state timeless particle frizzed as time equates to t'. Then as soon as we let the flipping coin continuingly flip down at the same instance time t = t', there should be "no" lost time with respect to the time of the coin itself, but "not" with respect to the time of the box. In other words, there is a section of time t that the box has gone by. So there is a time difference between the coin's time and box's time. That is precisely why we cannot tell if the cat will die or be alive, as Schrödinger himself assumed his fundamental principle is correct. As soon as we open the box, we have to accept the physical consequence that the cat is either dead or alive, but not both. Then I guess Schrödinger creates a logic to save his fundamental principle that superposition of the radioactive particle quantum states suddenly "collapses" as we open the box, without any physical proof. Otherwise the core of quantum mechanics fails to live up with the physical reality. Nevertheless as we see it, the failure of the fundamental principle is due to the fact that a timeless flipping coin "cannot be coexisted" within a time-

We further note that it is possible to alleviate the timelessness of superposition, if we appropriately add the temporal constraint (i.e., t > 0) in deriving the Schrödinger equation. We can change the timeless Schrödinger's equation to a

*A flipping coin analogy is substituted in the box for Schrödinger's cat paradox.*

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

**6. Paradox of Schrödinger's cat**

Schrödinger's box shown in **Figure 4**.

dependent (i.e., t > 0) box.

a paradox.

*Schrödinger's Cat and His Timeless (t = 0) Quantum World DOI: http://dx.doi.org/10.5772/intechopen.86970*

Nevertheless, it remains a question to be asked: Where is the source that produces the timeless radioactive particle? Why is Schrodinger's superposition principle timeless (i.e., t = 0) for which the particle's quantum states exist simultaneously (i.e., t = 0)? A trivial answer is that it has to be coming from a timeless subspace where the particle model embedded is shown in **Figure 5**. As we continue searching the root of paradox of the Schrödinger cat, we will provide an equivalent example to show that the paradox of the half-life cat is not a paradox.

## **6. Paradox of Schrödinger's cat**

*Advances in Quantum Communication and Information*

*the decaying of a radioactive particle, to kill the cat.*

we have equipped a bottle of poison gas and a device (i.e., a hammer) to break the bottle, triggered by the decaying of a radioactive particle, to kill the cat. The box is assumed totally opaque of which we do not know that the cat will be killed or not, as

*Inside the box we equipped a bottle of poison gas and a device (i.e., hammer) to break the bottle, triggered by* 

Since the hypothetical radioactive particle has two possible quantum states (i.e., decay or non-decay) that existed at the same time, which is imposed by the virtue of superposition principle in quantum mechanics, this means that the cat

But as soon as we open the box, the state of superposition of the radioactive particle collapses, without proof! In an instant, we have found that after the box is opened, the cat is either alive or dead, but not both. This paradox in quantum mechanics has been intriguing particle physicists and quantum scientists over eight decades, since the birth of Schrodinger's cat in 1935, as disclosed by Erwin

Let us momentarily accept what the fundamental principle holds, such that superposition of a dual-quantum state radioactive particle exists within the box. This tells us that the principle has created itself a timeless (i.e., t = 0) quantum subspace or time-independent quantum space. However, timeless subspace cannot exist within our temporal universe, in which we see that any solution (i.e., wave function) as obtained by Schrödinger equation contradicts the basic superposition principle, such that a timeless quantum subspace exists within our temporal (i.e., time-dependent) universe. This conjecture tells us that the hypothetical radioactive material cannot actually exist within the box, since both quantum states (i.e., decay or non-decay) cannot occur at the same time within a time-dependent subspace. We stress that time is distance and distance is time

can be simultaneously alive and dead, before we open the box.

Schrödinger who is as famous as Albert Einstein in modern physics.

imposed by the Schrödinger's superposition principle, until we open the box. With reference to the fundamental principle of superposition of quantum mechanics [4], the principle tells us that superposition holds for multi-quantum states in an atomic particle, of which the principle is the "core" of quantum mechanics. In other words, without the superposition principle, it will not have Schrödinger's quantum mechanics. In view of this principle, we see that the assumed two states of radioactive particle inside the box can actually simultaneously coexist, with a cloud of probability (i.e., both one thing and the other existed

**112**

within a temporal subspace.

at the same time).

**Figure 3.**

Let us replace the binary radioactive particle with a flipping coin in the Schrödinger's box shown in **Figure 4**.

So as one flips a coin before it is landed, it is absolutely uncertain that the coin will land either as a head or as a tail. Suppose we are able to "freeze" the flipping coin in the space at time t'; then the flipping coin is in a timeless mode subspace at time t', which is equivalent to a two-state timeless particle frizzed as time equates to t'. Then as soon as we let the flipping coin continuingly flip down at the same instance time t = t', there should be "no" lost time with respect to the time of the coin itself, but "not" with respect to the time of the box. In other words, there is a section of time t that the box has gone by. So there is a time difference between the coin's time and box's time. That is precisely why we cannot tell if the cat will die or be alive, as Schrödinger himself assumed his fundamental principle is correct. As soon as we open the box, we have to accept the physical consequence that the cat is either dead or alive, but not both. Then I guess Schrödinger creates a logic to save his fundamental principle that superposition of the radioactive particle quantum states suddenly "collapses" as we open the box, without any physical proof. Otherwise the core of quantum mechanics fails to live up with the physical reality. Nevertheless as we see it, the failure of the fundamental principle is due to the fact that a timeless flipping coin "cannot be coexisted" within a timedependent (i.e., t > 0) box.

We further note that it is possible to alleviate the timelessness of superposition, if we appropriately add the temporal constraint (i.e., t > 0) in deriving the Schrödinger equation. We can change the timeless Schrödinger's equation to a

**Figure 4.** *A flipping coin analogy is substituted in the box for Schrödinger's cat paradox.*

#### **Figure 5.**

*Schrödinger's box with a timeless radioactive particle. Notice that timeless radioactive particle cannot exist in a temporal (i.e., time-dependent) subspace.*

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

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 (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 is not a physical realizable principle within our temporal universe!

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 timeless virtual subspace similar to what mathematics does.

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 was a half-life cat!

**115**

and "yes."

**Figure 6.**

**8. Timeless quantum world**

*is introduced within Schrodinger's temporal box.*

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

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**).

Fundamental principle of quantum mechanics tells us that superposition of a multi-quantum-state particle holds if and only if within a quantum environment, by which it creates itself a timeless quantum subspace, but quantum subspaces cannot exist within our temporal universe. Then there is a question being asked: Can those quantum subspaces be utilized in our temporal universe? The answer is "no"

*A time-dependent cat is in a temporal (time-depending) box, in which we see a temporal radioactive particle* 

The "no" part answer is that if time component in application is an issue, such as applied to "instant" quantum entanglement [9] and "simultaneous" quantum

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

**7. Essence of a subatomic model**
