7.1 Symmetric principle

Why we have missed the timeless (t = 0) subspace paradigm issue is very "natural," since we are all human, imperfect and simple as it is. And we have "inadvertently" treated the shadow background of a scratch paper as a physical space, and it has never been in our minds that the background represents a virtual empty space. And this is precisely the reason that Schrödinger's quantum

Physical realizable paradigm (a) shows a Bohr atom situated within an empty space, which is "not" a physical realizable model, and (b) shows a Bohr atom situated within a temporal subspace, which is a physical

Nevertheless, it is possible to build a "temporal (t > 0)" quantum machine [10] similar to the one that Schrödinger has built. Instead, the quantum machine is built with a Bohr atomic embedded within a temporal (t > 0) subspace, as depicted in Figure 7(b), in which we see that any analytical solution that emerges from this physical realizable paradigm will be temporal (t > 0), for which I note that if one is searching a new particle in a timeless (t = 0) quantum world, it is "very likely" the newly discovered (i.e., analytical) particle is timeless (t = 0), since every particle is also a temporal particle within our universe, no matter how small it is; otherwise the particle cannot exist within our temporal universe. In case one "insists" that a timeless particle can coexist within our universe, it is equivalent of searching for a

As from the particle physics perspective, every substance within our universe is built by particles, of which our universe is compacted with particles, for which we see that our universe is granular instead of smooth and continuous. And it is a very convincing argument from a particle physicist's point of view: our universe is not

Since particle is temporal (t > 0) no matter how small they are, empty space cannot coexist within a temporal (t > 0) space, in which we see that there should be "temporal" substances between particles. And this is precisely why there are existent temporal substances throughout the entire universe, beyond particle forms. Otherwise gravitation fields, electric fields, magnetic fields, as well electromagnetic

With all these physical evidences, we see that there is a new branch of physics beyond the particle physics that is waiting for us to explore, for which the "micro limit" of physics should not have to be limited to the particle physics point of view,

timeless (t = 0) particle within our temporal universe.

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mechanics did.

Figure 7.

realizable model.

7. Granular universe

continuous and smooth.

134

waves cannot exist within our universe.

Symmetric principle has been used in theoretical physics for searching new particles and others, since the dawn of modern physics. Mathematically speaking those imaged properties of particles exist, but they are from an abstract mathematical standpoint.

Symmetric principle is based on a virtual empty space where time is treated as an independent variable as a Newtonian subspace. And this is precisely why the symmetric principle of science behaves as a mirror perception, such as positive versus negative or as groups in group theory, for example, positive time versus negative time, positive energy versus negative energy, matter versus anti-matter, and others. It is physical real versus mathematical virtual. But the fact is that all the mirror images such as negative time, negative energy, and anti-matter do not exist within our temporal (t > 0) universe. The fact is that those conjectures were derived from a mathematical or a Newtonian space standpoint; which is not existed within our temporal (t > 0) universe that has had or has had not!

Since time and space coexist, matter (i.e., subspace) is time, and time is matter. Without time we have no matter, and without matter it has no time, in which we see that there is an "asymmetric principle" in science with respect to physical real versus mathematical virtual, instead of the mirror image of mathematics.

Samples of asymmetric principle are:

Have time (t > 0) vs. no time (t = 0)

Having energy vs. no energy

Having matter vs. no matter

Physical real vs. virtually fictitious

Therefore we see that searching for any new particle, it is more reasonable to use the "asymmetric principle" instead of symmetric principle. It will be more "likely" found within our physical world, since timeless particles do not exist within our temporal (t > 0) universe.

### 7.2 Curving time–space

Within our temporal (t > 0) universe, every subspace takes an amount of energy ΔE and a section of time Δt to create, and it is not free, for which time is subspace and subspace is time, and we see that time is a "dependent" variable with the existence of space. Since we are still having a vague idea of interaction between gravity with time and knowing that gravitational field is produced by masses, gravitational field has to be embedded in a non-empty space which coexists with time. It is therefore "incorrect" to assume time as an "independent" variable, as we often do, for which I have a hard time to accept curving time–space dynamics, as based on a virtual mathematical space.

Since speed of time is settled by the velocity of light as our universe was created by a Big Bang explosion (a well-accepted paradigm) from the theory of relativity [5, 9], we have shown time is a dependent variable, instead of an independent variable, as within a Newtonian subspace, where time traveling is possible.

And this is the reason why space "cannot" be curved by time, since time is a "dependent" variable, of which we see that time is "physical real" since time and subspace coexist, in which we see that time is certainly "not" an illusion as some scientists claimed.

#### 7.3 Entropy and information

Aside from the virtual empty space paradigm, there are some serious mistakes that have been made on entropy theory of information by some theoretical physicists. Since information theory was developed by a group of mathematically oriented engineers, it was hardly appreciated by the physicists until it is connected with Boltzmann's second law of thermodynamics as given by

$$\mathbf{I} = \log\_2 \mathbf{N} \text{ bits} \tag{14}$$

such that the corrupted digital signal (e.g., by noise) can be refreshed, since digital signal can be repeated. For example, a compact disk (i.e., CD) can copy for thousands of time, and we have experienced that the latest copy is just as good as the

One of the important aspects for information transmission is that "reliable" information can be transmitted, such that information can be reached to the receiver with high degree of certainty. Let me take two key equations from information theory, mutual information through a "passive additive noise channel" as

where H(A) is the information provided by the sender, H(A/B) is the information loss (or equivocation) through transmission due to noise, H(B) is the informa-

However there is a basic distinction between these two equations: one is for "reliable" information transmission to the receiver, and the other is for "retrievable" information from the source (i.e., sender). Although both equations represent the mutual information transmission between sender and receiver; but the objective for using Eq. (19) is that "sender" "carries" an "active" role in achieving a reliable information transmission to the receiver, while using Eq. (20) is that "receiver" plays a more active role to deal with information that has been received. In which we see that; as for "reliable" information transmission is to increase the signal-tonoise ratio (i.e., ΔE) at the transmitting end. While for "retrievable" information after it has been received. In other words, one is to be sure information will be reached to the receiver "before" information is transmitted, and the other is to

In communication theory, basically we have two types communication strategies: by Norbert Wiener [17, 18] and by Claude Shannon [19]. However there is a major distinction between them; Wiener's communication strategy is that, if the information is corrupted through transmission, it may be recovered at the receiving end, but with a "cost," mostly at the receiving end, while Shannon's communication strategy carries a step further by encoding the information before it is transmitted, such that information can be "reliably" transmitted, also with a "cost" but mostly at the transmitting end. In view of the Wiener and Shannon information transmission strategies, mutual information transfer of Eq. (19) is kind of Shannon type, while Eq. (20) is for Wiener type, in which we see that "reliable" information transmission is basically controlled by the sender. It is to "minimize" the noise entropy

One simple way to do it is by increasing the signal-to-noise ratio, with a "cost" of

On the other hand, to recover the transmitted information is to "maximize" H (B/A) (the channel noise). Since the entropy H(B) at the receiving end is larger than

tion received by the receiver, and H(B/A) is the noise entropy of channel.

retrieve the information "after" information has been received.

H(A/B) (or equivocation) of the channel, as shown by

the entropy at the sending end, that is, H(B) > H(A), we have

higher signal energy (i.e., ΔE).

137

I A; B ð Þ¼ H Að Þ� H Að Þ =B (19)

I A; B ð Þ¼ H Bð Þ� H Bð Þ =A (20)

I A; B ð Þ≈ H Að Þ (21)

I A; B ð Þ¼ H Bð Þ� H Bð Þ =A ≈ H Að Þ (22)

original copy, while an analog magnetic tape cannot.

What Is "Wrong" with Current Theoretical Physicists? DOI: http://dx.doi.org/10.5772/intechopen.90058

given by [16]

and

and

$$\mathbf{S} = \mathbf{k} \text{ ln N joules per Kelvin} \tag{15}$$

where k is the Boltzmann constant, in which we see that information and entropy can be exchanged or traded, as given by the following symbolic representation:

$$\mathbf{I} \bullet \mathbf{S} \tag{16}$$

Without this connection, information would be very difficult to be applied in physics, since entropy is a well-accepted quantity in science.

However, the relationship of Eq. (16) does not mean that quantity of entropy (or equivalent amount of information in bits) is equaled to the information. It is the "cost" in bits (or equivalent amount of entropy in joules/kelvin) needed to generate the information, for example, a book of 1000 bits of information content (i.e., the cost), which means that there are 21000 possible copies of books having the same 1000 bits of information. There are also many objects available having the same bits of information, but not books.

As for quantum entanglement communication, it seems to me they have missed the essence of information transmission. For "efficient" information transmission, the sender (i.e., information source) is required to provide a highest information content (i.e., equip-probable state) of the source. For example, the more equalprobable or "uncertain" the ensemble signal is provided by the sender, the higher the information content from the source. For example, information content provided by the source (i.e., the sender) is given by

$$\mathbf{I} = -\log\_2 \mathbf{p}(\mathbf{a\_i}) \tag{17}$$

where p(ai) is the probability of an event ai from the source (i.e., sender) provider ensembles A = {ai}, I = 1, 2, … , N, in which we see that the largest information content provided by the source is P = 1/N (i.e., equal probability state).

As for a "binary" information source (i.e., 0, 1), for N = 2 it is the maximum entropy-coded binary source as given by

$$\mathbf{I} = -\log\_2 \mathbf{p} \\ \mathbf{(1/2)} = \mathbf{1} \text{ bit} \\ \tag{18}$$

in which we see that binary source information is the "lowest" information capacity for transmissions per unit time Δt, if we used digital transmission. Yet, the major advantage for using binary-digital transmission is for noise immunization,

What Is "Wrong" with Current Theoretical Physicists? DOI: http://dx.doi.org/10.5772/intechopen.90058

such that the corrupted digital signal (e.g., by noise) can be refreshed, since digital signal can be repeated. For example, a compact disk (i.e., CD) can copy for thousands of time, and we have experienced that the latest copy is just as good as the original copy, while an analog magnetic tape cannot.

One of the important aspects for information transmission is that "reliable" information can be transmitted, such that information can be reached to the receiver with high degree of certainty. Let me take two key equations from information theory, mutual information through a "passive additive noise channel" as given by [16]

$$\mathbf{H(A;B)} = \mathbf{H(A)} - \mathbf{H(A/B)}\tag{19}$$

and

subspace coexist, in which we see that time is certainly "not" an illusion as some

Aside from the virtual empty space paradigm, there are some serious mistakes that have been made on entropy theory of information by some theoretical physicists. Since information theory was developed by a group of mathematically oriented engineers, it was hardly appreciated by the physicists until it is connected

where k is the Boltzmann constant, in which we see that information and

Without this connection, information would be very difficult to be applied in

However, the relationship of Eq. (16) does not mean that quantity of entropy (or equivalent amount of information in bits) is equaled to the information. It is the "cost" in bits (or equivalent amount of entropy in joules/kelvin) needed to generate the information, for example, a book of 1000 bits of information content (i.e., the cost), which means that there are 21000 possible copies of books having the same 1000 bits of information. There are also many objects available having the same bits

As for quantum entanglement communication, it seems to me they have missed the essence of information transmission. For "efficient" information transmission, the sender (i.e., information source) is required to provide a highest information content (i.e., equip-probable state) of the source. For example, the more equalprobable or "uncertain" the ensemble signal is provided by the sender, the higher the information content from the source. For example, information content pro-

where p(ai) is the probability of an event ai from the source (i.e., sender) provider ensembles A = {ai}, I = 1, 2, … , N, in which we see that the largest

information content provided by the source is P = 1/N (i.e., equal probability state). As for a "binary" information source (i.e., 0, 1), for N = 2 it is the maximum

in which we see that binary source information is the "lowest" information capacity for transmissions per unit time Δt, if we used digital transmission. Yet, the major advantage for using binary-digital transmission is for noise immunization,

entropy can be exchanged or traded, as given by the following symbolic

I ¼ log <sup>2</sup> N bits (14)

I⬌S (16)

I ¼ � log <sup>2</sup> p að Þ<sup>i</sup> (17)

I ¼ � log <sup>2</sup> p 1ð Þ¼ =2 1 bit (18)

S ¼ k ln N joules per Kelvin (15)

with Boltzmann's second law of thermodynamics as given by

physics, since entropy is a well-accepted quantity in science.

scientists claimed.

and

representation:

of information, but not books.

vided by the source (i.e., the sender) is given by

entropy-coded binary source as given by

136

7.3 Entropy and information

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$$\mathbf{H(A;B)} = \mathbf{H(B)} - \mathbf{H(B/A)}\tag{20}$$

where H(A) is the information provided by the sender, H(A/B) is the information loss (or equivocation) through transmission due to noise, H(B) is the information received by the receiver, and H(B/A) is the noise entropy of channel.

However there is a basic distinction between these two equations: one is for "reliable" information transmission to the receiver, and the other is for "retrievable" information from the source (i.e., sender). Although both equations represent the mutual information transmission between sender and receiver; but the objective for using Eq. (19) is that "sender" "carries" an "active" role in achieving a reliable information transmission to the receiver, while using Eq. (20) is that "receiver" plays a more active role to deal with information that has been received. In which we see that; as for "reliable" information transmission is to increase the signal-tonoise ratio (i.e., ΔE) at the transmitting end. While for "retrievable" information after it has been received. In other words, one is to be sure information will be reached to the receiver "before" information is transmitted, and the other is to retrieve the information "after" information has been received.

In communication theory, basically we have two types communication strategies: by Norbert Wiener [17, 18] and by Claude Shannon [19]. However there is a major distinction between them; Wiener's communication strategy is that, if the information is corrupted through transmission, it may be recovered at the receiving end, but with a "cost," mostly at the receiving end, while Shannon's communication strategy carries a step further by encoding the information before it is transmitted, such that information can be "reliably" transmitted, also with a "cost" but mostly at the transmitting end. In view of the Wiener and Shannon information transmission strategies, mutual information transfer of Eq. (19) is kind of Shannon type, while Eq. (20) is for Wiener type, in which we see that "reliable" information transmission is basically controlled by the sender. It is to "minimize" the noise entropy H(A/B) (or equivocation) of the channel, as shown by

$$\mathbf{I(A;B)} \approx \mathbf{H(A)}\tag{21}$$

One simple way to do it is by increasing the signal-to-noise ratio, with a "cost" of higher signal energy (i.e., ΔE).

On the other hand, to recover the transmitted information is to "maximize" H (B/A) (the channel noise). Since the entropy H(B) at the receiving end is larger than the entropy at the sending end, that is, H(B) > H(A), we have

$$\mathbf{H(A;B)} = \mathbf{H(B)} - \mathbf{H(B/A)} \approx \mathbf{H(A)}\tag{22}$$

Equation (22) essentially shows us that information can be "recovered" after being received, again with a price: ΔE and Δt. In view of these strategies, we see that the cost paid for using Wiener type for information transmission is "much higher" than the Shannon type; aside from the cost of higher energy ΔE, it needs an extra amount of time Δt for "post processing." Thus we see that Wiener communication strategy is effective for a "noncooperating" sender, for example, applied to radar detection and others. On the other hand, Shannon type provides a more reliable information transmission, by simply increasing the signal-to-noise ratio so that every bit of information can be "reliably transmitted" to the receiver.

Therefore, we see that quantum entanglement communication is basically using Wiener communication strategy. The price will be "much higher and very inefficient," such as post processing. And it is "illogical" to require the received signal to be "more equivocal" (i.e., uncertain); the information recovery is better if it can be received at the receiving end, in which quantum entanglement communication is designed for extracting information as Wiener-type communication. However it is "not" the purpose for reliable information-transmission of Shannon.

> Schrödinger is based on hυ. Although singularity hυ has led him to a timeless (t = 0) quantum world, which was not due to mathematics, it is due to the background empty space. In other words, if he has had treated hυ as a band-limited radiation hΔυ, as shown in Figure 8(b), his "timeless" fundamental principle may not have emerged, in which I have shown that small changes from singularity bandwidth (i.e., υ) to band limited (i.e., Δυ) assumption could have altered the end results

(a) A conventional Bohr Atomic model and (b) the same Bohr model, except the quantum state energy is

Let me show a system analysis to illustrate the dynamic behavior when a timeless (t = 0) superimposing of wavelets (or particles) is plunging into a temporal (t > 0) subspace. For simplicity we assumed a set of two time-limited quantum state wavelets (or two particles) are plunging into a timeless (t = 0) space first, and then

Since empty space of Figure 9(b) is timeless, we see what its response does to the particles; all collapse at t = 0 within an empty space, which shows the behavior of superposition principle dose to particles. In other words, within a timeless environment all things existed at t = 0, and all things can also be found "simultaneously

Now, if we further plunge this timeless response into a temporal (t > 0) space of Figure 9(d), we see that the response shows "no sign" of preserving the original

A system simulation for timeless (t = 0) superposition within a temporal (t > 0) space (a) shows a set of time limited wavelets (or particles) plunge into a timeless space of (b); (c) shows the output response collapse at t = 0; (d) shows a temporal space representation; and (e) shows the corresponding response within a temporal

its output is submerging within a temporal (t > 0) subspace, as depicted in

and instantly" anywhere within the timeless (t = 0) subspace.

space, in which we see that output loses all the original input personality.

tremendously.

Figure 8.

Figure 9.

Figure 9.

139

8. Timeless and temporal

presented by a band-limited notation hΔv.

What Is "Wrong" with Current Theoretical Physicists? DOI: http://dx.doi.org/10.5772/intechopen.90058

wavelet (or particles) properties.

#### 7.4 Mathematics and physics

In view of all preceding evidences, we see that theoretical physics is mathematics, but mathematics is not physics since physics has to be physically real and should not be virtual as mathematics is. In other words, any analytical solution as obtained from any theoretical analysis has to comply with the boundary condition of our universe: causality (i.e., t > 0) and dimensionality; otherwise it is virtual as mathematics is. As we know that in mathematics; it needs to prove first that a mathematical postulation has a solution before searching for the solution. However, in theoretical physics it seems to me it does not have such a criterion, although theoretical physics is mathematics. Since now we have one criterion available, any solution emerging from theoretical analysis has to be shown "first" that it exists within the boundary condition of our universe. Otherwise it is a virtual solution as mathematics is.

When one is discussing the origin of science, it is inevitable not to talk about singularity approximation or singularity principle, in which sometime we underestimate the wisdoms of our predecessors. Practically all the laws of science are singularity approximated. Otherwise it is impossible mathematically to create a set of "simple and elegant" formulas for us to appreciate and to apply. Yet we tend to use the singularity approximated laws to interpret them as classical and deterministic, which undermines our predecessor's intelligence, in that they did not know there were approximated. And then we turn to using the singularity principle to evaluate the singularity approximated laws to obtain another singularity solution. It seems to me the ended singularity solution has the composition of two singularities' approximated results, for which I felt the solution will be even further deviated from the physical reality, aside from the nonphysical existing paradigm.

Let me pick a model for the illustration: the Bohr atomic model since we have used this model for over a century, shown in Figure 8(a).

We see it is a typical singularity approximated paradigm, no coordinate, no dimension, and no mass, and the entire Bohr atom is point singularity approximated. The only viable information provided by this model is the quantum state energy hυ, which is also singularity approximated, since υ has no bandwidth. However in practice every quantum state radiation has to be band and time limited.

Although mathematics can be regarded as entropy or information provider, my question is how much additional information from hυ Schrödinger can generate. In fact, he has had done an amazing task that nobody in quantum physics had done in the history of quantum mechanics, since all the viable information obtained by

What Is "Wrong" with Current Theoretical Physicists? DOI: http://dx.doi.org/10.5772/intechopen.90058

#### Figure 8.

Equation (22) essentially shows us that information can be "recovered" after being received, again with a price: ΔE and Δt. In view of these strategies, we see that the cost paid for using Wiener type for information transmission is "much higher" than the Shannon type; aside from the cost of higher energy ΔE, it needs an extra amount of time Δt for "post processing." Thus we see that Wiener communication strategy is effective for a "noncooperating" sender, for example, applied to radar detection and others. On the other hand, Shannon type provides a more reliable information transmission, by simply increasing the signal-to-noise ratio so that

Therefore, we see that quantum entanglement communication is basically using Wiener communication strategy. The price will be "much higher and very inefficient," such as post processing. And it is "illogical" to require the received signal to be "more equivocal" (i.e., uncertain); the information recovery is better if it can be received at the receiving end, in which quantum entanglement communication is designed for extracting information as Wiener-type communication. However it is

In view of all preceding evidences, we see that theoretical physics is mathematics, but mathematics is not physics since physics has to be physically real and should not be virtual as mathematics is. In other words, any analytical solution as obtained from any theoretical analysis has to comply with the boundary condition of our universe: causality (i.e., t > 0) and dimensionality; otherwise it is virtual as mathematics is. As we know that in mathematics; it needs to prove first that a mathematical postulation has a solution before searching for the solution. However, in theoretical physics it seems to me it does not have such a criterion, although theoretical physics is mathematics. Since now we have one criterion available, any solution emerging from theoretical analysis has to be shown "first" that it exists within the boundary condi-

every bit of information can be "reliably transmitted" to the receiver.

Advances in Quantum Communication and Information

"not" the purpose for reliable information-transmission of Shannon.

tion of our universe. Otherwise it is a virtual solution as mathematics is.

When one is discussing the origin of science, it is inevitable not to talk about singularity approximation or singularity principle, in which sometime we underestimate the wisdoms of our predecessors. Practically all the laws of science are singularity approximated. Otherwise it is impossible mathematically to create a set of "simple and elegant" formulas for us to appreciate and to apply. Yet we tend to use the singularity approximated laws to interpret them as classical and deterministic, which undermines our predecessor's intelligence, in that they did not know there were approximated. And then we turn to using the singularity principle to evaluate the singularity approximated laws to obtain another singularity solution. It seems to me the ended singularity solution has the composition of two singularities' approximated results, for which I felt the solution will be even further deviated from the physical reality, aside from the nonphysical existing paradigm.

Let me pick a model for the illustration: the Bohr atomic model since we have

We see it is a typical singularity approximated paradigm, no coordinate, no dimension, and no mass, and the entire Bohr atom is point singularity approximated. The only viable information provided by this model is the quantum state energy hυ, which is also singularity approximated, since υ has no bandwidth. However in practice every quantum state radiation has to be band and time limited. Although mathematics can be regarded as entropy or information provider, my question is how much additional information from hυ Schrödinger can generate. In fact, he has had done an amazing task that nobody in quantum physics had done in the history of quantum mechanics, since all the viable information obtained by

used this model for over a century, shown in Figure 8(a).

138

7.4 Mathematics and physics

(a) A conventional Bohr Atomic model and (b) the same Bohr model, except the quantum state energy is presented by a band-limited notation hΔv.

Schrödinger is based on hυ. Although singularity hυ has led him to a timeless (t = 0) quantum world, which was not due to mathematics, it is due to the background empty space. In other words, if he has had treated hυ as a band-limited radiation hΔυ, as shown in Figure 8(b), his "timeless" fundamental principle may not have emerged, in which I have shown that small changes from singularity bandwidth (i.e., υ) to band limited (i.e., Δυ) assumption could have altered the end results tremendously.

### 8. Timeless and temporal

Let me show a system analysis to illustrate the dynamic behavior when a timeless (t = 0) superimposing of wavelets (or particles) is plunging into a temporal (t > 0) subspace. For simplicity we assumed a set of two time-limited quantum state wavelets (or two particles) are plunging into a timeless (t = 0) space first, and then its output is submerging within a temporal (t > 0) subspace, as depicted in Figure 9.

Since empty space of Figure 9(b) is timeless, we see what its response does to the particles; all collapse at t = 0 within an empty space, which shows the behavior of superposition principle dose to particles. In other words, within a timeless environment all things existed at t = 0, and all things can also be found "simultaneously and instantly" anywhere within the timeless (t = 0) subspace.

Now, if we further plunge this timeless response into a temporal (t > 0) space of Figure 9(d), we see that the response shows "no sign" of preserving the original wavelet (or particles) properties.

#### Figure 9.

A system simulation for timeless (t = 0) superposition within a temporal (t > 0) space (a) shows a set of time limited wavelets (or particles) plunge into a timeless space of (b); (c) shows the output response collapse at t = 0; (d) shows a temporal space representation; and (e) shows the corresponding response within a temporal space, in which we see that output loses all the original input personality.
