1. Introduction

The history of physics involves two great revolutionary theories: relativity and quantum physics. Quantum mechanics and general relativity operate at different space and time scales; therefore, the main problem for unification of these theories is due to the "mystery" of the scale of variables.

Recently, a new approach [1–3] for the unification of general relativity and quantum mechanics was suggested, which involves reconciling relativity's black hole space and quantum entanglement. Science News [4, 5] announced that a new equation ER = EPR, generated from Einstein's papers [6, 7], may provide a possible path for connection of principles of general relativity with quantum mechanics. Maldacena and Susskind [2] suggested that two distant black holes of general relativity, connected through the interior wormhole (Einstein-Rosen bridge), could be interpreted as the entangled EPR's pairs of two black holes. Maldacena and Susskind [2] showed that the formula ER = EPR (bridge between Einstein-Rosen

(ER) wormhole [6] and Einstein-Podolsky-Rosen (EPR) entanglement [7]) can be the cornerstone of the new physics theory, connecting relativity and quantum mechanics through space-time wormholes.

We should concentrate our attention to the statement of quantum mechanical uncertainty to understand why the combination of general relativity with quantum mechanics does not generate a valid mathematical formulation, which is applicable

First, it is necessary to show that a particle may have a certain identity when the

change of energy in time (conservation of energy) has commutation with the change of energy, consumed in space phase of a particle (conservation of momentum). The mathematical description of momentum may be valid only if the emerged formulation comprises residing of energy-momentum exchange interac-

The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes…

Therefore, momentum "as the quantity of motion" alone without locality is uncertain and cannot give a proper mathematical description of this quantity in any physical theory. If momentum conservation has no commutation with the energy conservation within the space-time frame, it cannot describe an event in a proper way. However, without the space-time boundary, it is difficult to get commutation of energy-momentum conservation laws. Description of motion by a model, involving a certain local boundary of the dynamical space-time frame, generates a reference frame independent of the true momentum conservation principle.

Quantum mechanics states that position and momentum cannot have simultaneous reality, due to the application of the mathematical formulation of uncertainty, which conjugates position, independent from space-time and momentum

The Heisenberg uncertainty principle in not a mystery of nature; rather, it is an improper mathematical formulation, which does not involve missed local spacetime position and conjugation of a local position with the applied force, leading to

An event of measurement is not a simple displacement of a particle position in the abstract Hilbert space, but it is the change of space-time phases as an outcome of energy-momentum action-response interaction. Therefore, change of position of a system is not a linear transformation of the space dimension; it should describe commutation of local space-time frame with the action-response energy-

It is necessary to show that commutation of two parameters, such as local space-

time position and energy-momentum exchange interaction, is the only way for conservation of energy and momentum within the discrete space-time frame. The concept, describing entanglement of two pieces of space [6], does not explain the driving force behind why two equal pieces of space, separated by less than two black holes, may form entangled pairs. The two-space piece entanglement approach describes entanglement of two space pieces in abstract space, while space does not have independent existence, and it changes only within space-time frame. For description of entanglement of particles simultaneously in space and time, we need a proper structure of space-time frame. However, a description of events with the proper mathematical formulation involving dynamical space-time is the main problem associated with physical laws. As was shown by Merali [11], without knowing the origin of space-time, we will not understand physical laws. General relativity suggested the revolutionary idea that space-time and gravitational fields are the same, but an "Einstein's matter," which curves space-time, is an external entity and has no inner connection with the space-time frame. Another problem of

general relativity is that its space-time has no background frame.

Rovelli's statement [12] that space-time has a relation to the electromagnetic field is the modification of general relativity. The main problem of the Rovelli's statement is that he describes quanta as an independent identity, which cannot live in space-time. Rovelli's statement did not reveal a mathematical formulation, and its quanta have no commutation with the space-time frame. The other problem of this

for small- and large-scale interactions.

DOI: http://dx.doi.org/10.5772/intechopen.88722

the change of momentum.

147

momentum exchange interactions.

tion within boundary-mapped space-time frame.

and also independent from the action-response interaction.

Grant [5] suggested that the connection of entanglement with the space-time might help to understand the origin of space-time and its behavior at the small scales of quantum mechanics.

Siegfried [8] also discussed the ER = EPR equation as a possible approach for connection of space-time geometry of relativity with the quantum entanglement.

Van Raamsdonk [9] showed that the existence of space-time is due to the quantum entanglement in the corresponding quantum system.

Carroll suggested [10] a similar approach in accordance of which space can emerge from a quantum state. Caroll's comments on connection of space-time curvature with energy are similar to the statement of general relativity, but in this approach, origin of space connected with the quantum entanglement.

While a path to quantum gravity through the wormhole became a very hot topic for the generation of new physics, it could be very useful to return to the ER [6] and EPR [7] papers to summarize the basic principles on how the combination of outcomes from the ER and EPR papers may unify different scale interactions.

The main idea of the ER paper [6] is a presentation of the physical space by field equations where space involves two identical, equal halves, separated by the symmetry and connected by a Wormhole Bridge. The separated halves of space describe the same physical space. The idea of this approach is the application of space field equations for the description of quantum level interactions.

The ER bridge, which is also called a wormhole, denotes a shortcut connection between widely separated regions of space-time. In accordance with the hypothetical equation ER = EPR [1–3], an ER wormhole between two places of space could be considered as an entangled pair in quantum mechanics.

It is necessary to note that the ER paper [6], as was claimed by the authors, does not contain the quantum phenomena and the interaction between two identical pieces of space does not lead to the "quantization of gravity."

The EPR paper [7] gives an analysis of the basic principles of quantum mechanics such as the description of state by the wave function to predict a particle's behavior. It establishes the now well-known cornerstone of quantum mechanics that two physical quantities such as position and momentum of a particle cannot be precisely determined simultaneously and that these two quantities cannot have simultaneous reality. The authors showed that the quantum mechanical description of physical reality given by wave functions is also not complete and it is necessary to assign two different wave functions to the same reality.

It is necessary to note that the conjugation of statements of the ER [6] and EPR [7] papers does not reveal a non-hypothetical mathematical equation of a dynamical event, which may explain physical reality regardless of scale.

### 2. The main principles of ER and EPR papers

We can select important statements of these papers, which were the cornerstone [1–3] for the unification of relativity with quantum mechanics:


### The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes… DOI: http://dx.doi.org/10.5772/intechopen.88722

We should concentrate our attention to the statement of quantum mechanical uncertainty to understand why the combination of general relativity with quantum mechanics does not generate a valid mathematical formulation, which is applicable for small- and large-scale interactions.

First, it is necessary to show that a particle may have a certain identity when the change of energy in time (conservation of energy) has commutation with the change of energy, consumed in space phase of a particle (conservation of momentum). The mathematical description of momentum may be valid only if the emerged formulation comprises residing of energy-momentum exchange interaction within boundary-mapped space-time frame.

Therefore, momentum "as the quantity of motion" alone without locality is uncertain and cannot give a proper mathematical description of this quantity in any physical theory. If momentum conservation has no commutation with the energy conservation within the space-time frame, it cannot describe an event in a proper way. However, without the space-time boundary, it is difficult to get commutation of energy-momentum conservation laws. Description of motion by a model, involving a certain local boundary of the dynamical space-time frame, generates a reference frame independent of the true momentum conservation principle.

Quantum mechanics states that position and momentum cannot have simultaneous reality, due to the application of the mathematical formulation of uncertainty, which conjugates position, independent from space-time and momentum and also independent from the action-response interaction.

The Heisenberg uncertainty principle in not a mystery of nature; rather, it is an improper mathematical formulation, which does not involve missed local spacetime position and conjugation of a local position with the applied force, leading to the change of momentum.

An event of measurement is not a simple displacement of a particle position in the abstract Hilbert space, but it is the change of space-time phases as an outcome of energy-momentum action-response interaction. Therefore, change of position of a system is not a linear transformation of the space dimension; it should describe commutation of local space-time frame with the action-response energymomentum exchange interactions.

It is necessary to show that commutation of two parameters, such as local spacetime position and energy-momentum exchange interaction, is the only way for conservation of energy and momentum within the discrete space-time frame.

The concept, describing entanglement of two pieces of space [6], does not explain the driving force behind why two equal pieces of space, separated by less than two black holes, may form entangled pairs. The two-space piece entanglement approach describes entanglement of two space pieces in abstract space, while space does not have independent existence, and it changes only within space-time frame.

For description of entanglement of particles simultaneously in space and time, we need a proper structure of space-time frame. However, a description of events with the proper mathematical formulation involving dynamical space-time is the main problem associated with physical laws. As was shown by Merali [11], without knowing the origin of space-time, we will not understand physical laws. General relativity suggested the revolutionary idea that space-time and gravitational fields are the same, but an "Einstein's matter," which curves space-time, is an external entity and has no inner connection with the space-time frame. Another problem of general relativity is that its space-time has no background frame.

Rovelli's statement [12] that space-time has a relation to the electromagnetic field is the modification of general relativity. The main problem of the Rovelli's statement is that he describes quanta as an independent identity, which cannot live in space-time. Rovelli's statement did not reveal a mathematical formulation, and its quanta have no commutation with the space-time frame. The other problem of this

(ER) wormhole [6] and Einstein-Podolsky-Rosen (EPR) entanglement [7]) can be the cornerstone of the new physics theory, connecting relativity and quantum

Grant [5] suggested that the connection of entanglement with the space-time might help to understand the origin of space-time and its behavior at the small

Siegfried [8] also discussed the ER = EPR equation as a possible approach for connection of space-time geometry of relativity with the quantum entanglement. Van Raamsdonk [9] showed that the existence of space-time is due to the

Carroll suggested [10] a similar approach in accordance of which space can emerge from a quantum state. Caroll's comments on connection of space-time curvature with energy are similar to the statement of general relativity, but in this

While a path to quantum gravity through the wormhole became a very hot topic for the generation of new physics, it could be very useful to return to the ER [6] and EPR [7] papers to summarize the basic principles on how the combination of outcomes from the ER and EPR papers may unify different scale interactions.

The main idea of the ER paper [6] is a presentation of the physical space by field equations where space involves two identical, equal halves, separated by the symmetry and connected by a Wormhole Bridge. The separated halves of space describe the same physical space. The idea of this approach is the application of space field

The ER bridge, which is also called a wormhole, denotes a shortcut connection between widely separated regions of space-time. In accordance with the hypothetical equation ER = EPR [1–3], an ER wormhole between two places of space could be

It is necessary to note that the ER paper [6], as was claimed by the authors, does not contain the quantum phenomena and the interaction between two identical

The EPR paper [7] gives an analysis of the basic principles of quantum mechan-

It is necessary to note that the conjugation of statements of the ER [6] and EPR [7] papers does not reveal a non-hypothetical mathematical equation of a dynamical

We can select important statements of these papers, which were the cornerstone

a. Entanglement (connection) of two equal pieces of space through the

b. The common uncertainty principle of quantum mechanics is that when the momentum of a particle is known, its coordinate has no physical

ics such as the description of state by the wave function to predict a particle's behavior. It establishes the now well-known cornerstone of quantum mechanics that two physical quantities such as position and momentum of a particle cannot be precisely determined simultaneously and that these two quantities cannot have simultaneous reality. The authors showed that the quantum mechanical description of physical reality given by wave functions is also not complete and it is necessary to

quantum entanglement in the corresponding quantum system.

equations for the description of quantum level interactions.

considered as an entangled pair in quantum mechanics.

assign two different wave functions to the same reality.

2. The main principles of ER and EPR papers

event, which may explain physical reality regardless of scale.

[1–3] for the unification of relativity with quantum mechanics:

"Wormhole Bridge" of relativity theory [6].

reality [7].

146

pieces of space does not lead to the "quantization of gravity."

approach, origin of space connected with the quantum entanglement.

mechanics through space-time wormholes.

Advances in Quantum Communication and Information

scales of quantum mechanics.

approach is the locality of the quanta, while any particle or antiparticle cannot have independent existence.

The problem associated with these differential equations is that they describe the dynamical laws in abstract space with an independently moving interval of time. Another principle, which is related to the conservation of energy, is the Lagrangian action principle. For the action integral to be well defined, the trajectory has to be determined simultaneously in time and space coordinates. However, the

The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes…

Usually, the known mathematical formulations of dynamical laws either simplify space to conserve the details of time or simplify time to preserve the spatial dimension. The Lagrangian or Hamiltonian mechanics are the examples of such an approach, which was the reason for the replacement of differential equations of

To compose a unified theory, first, it is necessary to solve the locality problem of classical physics and quantum mechanics, which describe an event as a change of

3. Commutation of space-time with the principle of conservation

operator Δt/t<sup>1</sup> describes the fluctuation of time about instant of action.

sumed in space phase (event mass) and restored in time phase:

ΔS S1 Δt t1

ΔS Δt ¼ S1 t1

In our early studies [14–16], we suggested that the change of a function in relation to its local position (Δf/f1) could be a sufficient entity for the identification of change. The non-unitary function Δf/f1 with the fractional feature has a "quantum mechanical behavior": the classic operator in the form of Δf/f1 portion

describes the fraction of the change (spinning or vibration) of a function around its dynamical initial locality to repeat its origin. Similarly, the operator ΔS/S<sup>1</sup> describes the fluctuation of space with the applied force in relation to its origin, while the

In the conjugated space-time field frame, the position of a particle, localized within the space-time frame in relation to its origin, is not a point; it exists within a very certain discrete non-virtual space-time manifold, commuting dynamic energy, which is distributed within space and time fields. On this basis, the origin of spacetime is the energy, which generates space-time and holds its conservation within

In accordance with the above-described principle of conservation of energy within the space-time frame, the space-time becomes the resulting non-unitary inner product of energy distribution, which comprises the portions of energy con-

> <sup>¼</sup> Eap�Es Es

> > Eap Es �1

<sup>λ</sup> <sup>¼</sup> Eap Es

S<sup>1</sup> and t<sup>1</sup> are the space and time variables corresponding to the dynamic local boundary; Eap and Es are the energies of action and under action systems of interaction at conditions corresponding to the local boundaries of S<sup>1</sup> and t1. On this basis, the space and time phases, which "absorb" applied force and carry energy, attain features of an energetic field. The minimum portion of quanta generates an ele-

(2)

�1 (3)

(1)

Lagrangian action principle does not cover these requirements.

classical physics by Schrödinger's wave function.

DOI: http://dx.doi.org/10.5772/intechopen.88722

of energy

space and time phases.

at λ = 1, Eap = 2Es.

mentary space-time frame.

149

state of something without relation to something itself.

According to Rovelli's opinion [12], there is no difference between a gravitational field and space-time, and the locality of a particle can be defined with respect to the gravitational field. This approach is similar to the Newtonian concept that acceleration has a meaning with respect to the gravitation field. However, any field, particularly a gravitational field, cannot have an independent existence; therefore the relation of locality to the gravitational field leads to the uncertainty in quantum mechanics.

Smolin [13] developed quantum field theory and suggested that at the Planck scale, space exists in the form of fundamental discrete units instead of general relativity's continuous space-time frame. But quantum field theory, similar to Newtonian physics, do not have space-time structure, which interacts with the event. The origin of discrete space and the condition of its independent existence is also not clear.

Therefore, different views on space-time and the absence of the origin of the background of space-time frame in both theories is the main problem for reconciling these theories into the unified theory. One of the main problems of these theories also is the locality of a particle in the space-time frame.

Einstein showed that space and time are simply different dimensions of the same space-time continuum. By his opinion, energy and momentum are the same quantities of space-time, which has four dimensions. The relative quantity of energy and momentum depends on the observer.

The problem of this approach is that the dynamical nature of the space-time variables connected within the continuum framework, which did not allow distinction of the local properties of time and space identities. General relativity determines the dynamics of matter by the geometry of space-time and does not explain the origin of the mass and energy, which curves the structure of space-time. The problem of Newtonian physics, regarding how the moving body responds to action in relativity theory, also remains an open question.

Unfortunately, the basic formulation of general relativity does not provide the answers to these questions. That is why the theory of relativity itself became the "observer" between Newton's physics and quantum mechanics.

It is necessary to note that problems of founding a unified theory are due to the problems of energy conservation, which is not complete in the theory of relativity and quantum physics. The approaches related to the generation of a unified theory do not use the principle of conservation of energy as the basis for the unification of relativity and quantum physics. The theory of relativity has a problem with the conservation of energy, which leads to the problem of singularity at small scales. Quantum mechanics suggests that particles borrow energy for some time and then return them. However, quantum mechanics does not explain the origin of this energy, which is borrowed and conserved in the wave function.

It is clear that for the generation of unified theory, we have to find a proper mathematical formulation of the conservation of energy, covering the higher scale space-time of relativity and the small-scale quanta of quantum mechanics. The model connecting relativity and quantum mechanics should involve the dynamic local state of space and time variables which, independent of the energy input, can operate between the small scale of quantum physics and large scale of relativity.

The known statements of Noether's theorem on conservation of energy, being philosophical in nature, are not applicable for generation of a mathematical formulation of the space-time picture of a particle.

Lagrange and Hamilton have suggested the conservation of energy in the form of differential equations, which is widely used in classical and quantum mechanics.

#### The Hot Disputes Related to the Generation of a Unified Theory Combining the Outcomes… DOI: http://dx.doi.org/10.5772/intechopen.88722

The problem associated with these differential equations is that they describe the dynamical laws in abstract space with an independently moving interval of time.

Another principle, which is related to the conservation of energy, is the Lagrangian action principle. For the action integral to be well defined, the trajectory has to be determined simultaneously in time and space coordinates. However, the Lagrangian action principle does not cover these requirements.

Usually, the known mathematical formulations of dynamical laws either simplify space to conserve the details of time or simplify time to preserve the spatial dimension. The Lagrangian or Hamiltonian mechanics are the examples of such an approach, which was the reason for the replacement of differential equations of classical physics by Schrödinger's wave function.

To compose a unified theory, first, it is necessary to solve the locality problem of classical physics and quantum mechanics, which describe an event as a change of state of something without relation to something itself.
