The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism!

[icarus2]

One of humanity's ultimate questions is "How did the universe come into existence?"

Since energy is one of the most fundamental physical quantities in physics, and particles and the like can be created from this energy, this question is "How did energy come into existence?" It is related to the question you are asking.

Cosmology can be largely divided into a model in which energy has continued to exist and a model in which energy is also created. Each model has its strengths and weaknesses, but in the model that assumes the existence of some energy before the birth of our universe, "How did that energy come into existence?" Since the question still exists, the problem has not been resolved and, therefore, I do not personally prefer it.

In order to explain the source of energy in our universe, there have been models that claim the birth of the universe from nothing, or a Zero Energy Universe. However, the key point, the specific mechanism of how being was born from nothing, is lacking, presupposes an antecedent existence such as the Inflaton Field, or is described in a very poor state. *The nothing mentioned here is not a complete nothing, but a state of zero energy.

I would like to suggest a solution to this ultimate problem.

 

1. Changes in the range of gravitational interactions over time

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

a

[math] {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} [/math]

b

<math> {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} </math>

c

[tex] {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} [/tex]

Since there is an attractive component (Mass-energy) and a repulsive component (Gravitational potential energy or Gravitational self-energy), it contains elements that can explain the accelerated expansion and decelerated expansion of the universe.

In the case of a uniform distribution, comparing the magnitudes of mass energy and gravitational potential energy, it is in the form of -kR^2. That is, as the gravitational interaction radius increases, the negative gravitational potential energy value becomes larger than the positive mass energy.

2. The inflection point at which the magnitudes of mass energy and gravitational potential energy are equal

The inflection point is the transition from decelerated expansion to accelerated expansion.

If R < R_gs , then the positive mass-energy is greater than the negative gravitational potential energy, so the universe is dominated by attractive force and is decelerating.

If R > R_gs, then the negative gravitational potential energy is greater than the positive mass-energy, so the universe is dominated by the repulsive (anti-gravity) force and accelerated expansion.

Therefore, by matching R_gs with the time of accelerated expansion in the early universe, we can create a new inflation model.

3. When entering accelerated expansion within the Planck time

This means that, in Planck time, a universe born with an energy density of ρ_0 passes through an inflection point where positive energy and negative gravitational potential energy (gravitational self-energy) become equal. And, it means entering a period of accelerated expansion afterwards.

4. Birth and Expansion of the Universe from the Uncertainty Principle

4.1 The Uncertainty Principle - Inflating in Planck time

During Planck time, fluctuations in energy

During Planck time, energy fluctuation of ΔE=(1/2)m_pc^2 is possible.

However, when the mass distribution of an object is approximated in the form of a spherical mass distribution, Δx from the uncertainty principle corresponds to the diameter, not the radius. So Δx=2R'=cΔt, this should apply.

In this case, from the values obtained above in "When entering accelerated expansion within the Planck time", the density is quadrupled, the radius is 1/2 times, and thus the mass is (1/2) times. Therefore, the mass value is M'=(5/6)m_p

It means,

If Δt occurs during the Planck time t_p, the energy fluctuation ΔE can occur more than (1/2)m_pc^2. And, the energy of the inflection point where the mass distribution enters accelerated expansion is (5/6)m_pc^2.

In short,

According to the uncertainty principle, it is possible to change (or create) more than (1/2)m_pc^2 energy during the Planck time,

If an energy change above (5/6)m_pc^2 that is slightly larger than the minimum value occurs, the total energy of the mass-energy distribution reaches negative energy, i.e., the negative mass state, within the time Δt where quantum fluctuations can exist.

However, since there is a repulsive gravitational effect between negative masses, the corresponding mass distribution expands instead of contracting. Thus, the quantum fluctuations generated by the uncertainty principle cannot return to nothing, but can expand and create the present universe.

 

4.2. The magnitude at which the minimum energy generated by the uncertainty principle equals the minimum energy required for accelerated expansion

In the above analysis, the minimum energy of quantum fluctuation possible during Planck time is ΔE≥(1/2)m_pc^2, and the minimum energy fluctuation for which expansion after birth can occur is ΔE≥(5/6)m_pc^2. Since (5/6)m_pc^2 is greater than (1/2)m_pc^2, the birth and coming into existence of the universe in Planck time is a probabilistic event.

For those unsatisfied with probabilistic event, consider the case where the birth of the universe was an inevitable event.

Letting Δt=kt_p, and doing some calculations, we get the k=(3/5)^(1/2)

To summarize,

If Δt ≤ ((3/5)^(1/2))t_p, then ΔE ≥ ((5/12)^(1/2))m_pc^2 is possible. And, the minimum magnitude at which the energy distribution reaches a negative energy state by gravitational interaction within Δt is ΔE=((5/12)^(1/2))m_pc^2. Thus, when Δt < ((3/5)^(1/2))t_p, a state is reached in which the total energy is negative within Δt.

In other words, when quantum fluctuation occur where Δt is smaller than (3/5)^(1/2)t_P = 0.77t_p, the corresponding mass distribution reaches a state in which negative gravitational potential energy exceeds positive mass energy within Δt. Therefore, it can expand without disappearing.

In this case, the situation in which the universe expands after birth becomes an inevitable event.

 

[Abstract]

There was a model claiming the birth of the universe from nothing, but the specific mechanism for the birth and expansion of the universe was very poor.

According to the energy-time uncertainty principle, during Δt, an energy fluctuation of ΔE is possible, but this energy fluctuation should have reverted back to nothing. By the way, there is also a gravitational interaction during the time of Δt, and if the negative gravitational self-energy exceeds the positive mass-energy during this Δt, the total energy of the corresponding mass distribution becomes negative energy, that is, the negative mass state. Because there is a repulsive gravitational effect between negative masses, this mass distribution expands. Thus, it is possible to create an expansion that does not go back to nothing.

Calculations show that if the quantum fluctuation occur for a time less than Δt = ((3/10)^(1/2))t_p ~ 0.77t_p, then an energy fluctuation of ΔE > ((5/6}^(1/2))m_pc^2 ~ 0.65m_pc^2 must occur. But in this case, because of the negative gravitational self-energy, ΔE will enter the negative energy (mass) state before the time of Δt. Because there is a repulsive gravitational effect between negative masses, ΔE cannot contract, but expands. Thus, the universe does not return to nothing, but can exist.

Gravitational Potential Energy Model provides a means of distinguishing whether the existence of the present universe is an inevitable event or an event with a very low probability. And, it presents a new model for the process of inflation, the accelerating expansion of the early universe. This mechanism also provides an explanation for why the early universe started out in a high dense state. Additionally, when the negative gravitational potential energy exceeds the positive mass energy, it can produce an accelerated expansion of the universe. Through this mechanism, inflation, which is the accelerated expansion of the early universe, and dark energy, which is the cause of the accelerated expansion of the recent universe, can be explained at the same time.

 

* The above is a summary of some of the key arguments of the paper, and for more details, please refer to the paper linked below.

# The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism

https://www.researchgate.net/publication/371951438

# Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field

https://www.researchgate.net/publication/360096238

Edited July 5, 2023 by icarus2
When editing, I can't see the text, so I can't edit it.

[exchemist]

22 minutes ago, icarus2 said:

One of humanity's ultimate questions is "How did the universe come into existence?"

Since energy is one of the most fundamental physical quantities in physics, and particles and the like can be created from this energy, this question is "How did energy come into existence?" It is related to the question you are asking.

Cosmology can be largely divided into a model in which energy has continued to exist and a model in which energy is also created. Each model has its strengths and weaknesses, but in the model that assumes the existence of some energy before the birth of our universe, "How did that energy come into existence?" Since the question still exists, the problem has not been resolved and, therefore, I do not personally prefer it.

In order to explain the source of energy in our universe, there have been models that claim the birth of the universe from nothing, or a Zero Energy Universe. However, the key point, the specific mechanism of how being was born from nothing, is lacking, presupposes an antecedent existence such as the Inflaton Field, or is described in a very poor state. *The nothing mentioned here is not a complete nothing, but a state of zero energy.

I would like to suggest a solution to this ultimate problem.

 

1. Changes in the range of gravitational interactions over time

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

a

ET=∑imic2+∑i<j−Gmimjrij=Mc2−35GM2R

b

<math> {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} </math>

c

[tex] {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} [/tex]

Since there is an attractive component (Mass-energy) and a repulsive component (Gravitational potential energy or Gravitational self-energy), it contains elements that can explain the accelerated expansion and decelerated expansion of the universe.

In the case of a uniform distribution, comparing the magnitudes of mass energy and gravitational potential energy, it is in the form of -kR^2. That is, as the gravitational interaction radius increases, the negative gravitational potential energy value becomes larger than the positive mass energy.

2. The inflection point at which the magnitudes of mass energy and gravitational potential energy are equal

The inflection point is the transition from decelerated expansion to accelerated expansion.

If R < R_gs , then the positive mass-energy is greater than the negative gravitational potential energy, so the universe is dominated by attractive force and is decelerating.

If R > R_gs, then the negative gravitational potential energy is greater than the positive mass-energy, so the universe is dominated by the repulsive (anti-gravity) force and accelerated expansion.

Therefore, by matching R_gs with the time of accelerated expansion in the early universe, we can create a new inflation model.

3. When entering accelerated expansion within the Planck time

This means that, in Planck time, a universe born with an energy density of ρ_0 passes through an inflection point where positive energy and negative gravitational potential energy (gravitational self-energy) become equal. And, it means entering a period of accelerated expansion afterwards.

4. Birth and Expansion of the Universe from the Uncertainty Principle

4.1 The Uncertainty Principle - Inflating in Planck time

During Planck time, fluctuations in energy

During Planck time, energy fluctuation of ΔE=(1/2)m_pc^2 is possible.

However, when the mass distribution of an object is approximated in the form of a spherical mass distribution, Δx from the uncertainty principle corresponds to the diameter, not the radius. So Δx=2R'=cΔt, this should apply.

In this case, from the values obtained above in "When entering accelerated expansion within the Planck time", the density is quadrupled, the radius is 1/2 times, and thus the mass is (1/2) times. Therefore, the mass value is M'=(5/6)m_p

It means,

If Δt occurs during the Planck time t_p, the energy fluctuation ΔE can occur more than (1/2)m_pc^2. And, the energy of the inflection point where the mass distribution enters accelerated expansion is (5/6)m_pc^2.

In short,

According to the uncertainty principle, it is possible to change (or create) more than (1/2)m_pc^2 energy during the Planck time,

If an energy change above (5/6)m_pc^2 that is slightly larger than the minimum value occurs, the total energy of the mass-energy distribution reaches negative energy, i.e., the negative mass state, within the time Δt where quantum fluctuations can exist.

However, since there is a repulsive gravitational effect between negative masses, the corresponding mass distribution expands instead of contracting. Thus, the quantum fluctuations generated by the uncertainty principle cannot return to nothing, but can expand and create the present universe.

 

4.2. The magnitude at which the minimum energy generated by the uncertainty principle equals the minimum energy required for accelerated expansion

In the above analysis, the minimum energy of quantum fluctuation possible during Planck time is ΔE≥(1/2)m_pc^2, and the minimum energy fluctuation for which expansion after birth can occur is ΔE≥(5/6)m_pc^2. Since (5/6)m_pc^2 is greater than (1/2)m_pc^2, the birth and coming into existence of the universe in Planck time is a probabilistic event.

For those unsatisfied with probabilistic event, consider the case where the birth of the universe was an inevitable event.

Letting Δt=kt_p, and doing some calculations, we get the k=(3/5)^(1/2)

To summarize,

If Δt ≤ ((3/5)^(1/2))t_p, then ΔE ≥ ((5/12)^(1/2))m_pc^2 is possible. And, the minimum magnitude at which the energy distribution reaches a negative energy state by gravitational interaction within Δt is ΔE=((5/12)^(1/2))m_pc^2. Thus, when Δt < ((3/5)^(1/2))t_p, a state is reached in which the total energy is negative within Δt.

In other words, when quantum fluctuation occur where Δt is smaller than (3/5)^(1/2)t_P = 0.77t_p, the corresponding mass distribution reaches a state in which negative gravitational potential energy exceeds positive mass energy within Δt. Therefore, it can expand without disappearing.

In this case, the situation in which the universe expands after birth becomes an inevitable event.

 

[Abstract]

There was a model claiming the birth of the universe from nothing, but the specific mechanism for the birth and expansion of the universe was very poor.

According to the energy-time uncertainty principle, during Δt, an energy fluctuation of ΔE is possible, but this energy fluctuation should have reverted back to nothing. By the way, there is also a gravitational interaction during the time of Δt, and if the negative gravitational self-energy exceeds the positive mass-energy during this Δt, the total energy of the corresponding mass distribution becomes negative energy, that is, the negative mass state. Because there is a repulsive gravitational effect between negative masses, this mass distribution expands. Thus, it is possible to create an expansion that does not go back to nothing.

Calculations show that if the quantum fluctuation occur for a time less than Δt = ((3/10)^(1/2))t_p ~ 0.77t_p, then an energy fluctuation of ΔE > ((5/6}^(1/2))m_pc^2 ~ 0.65m_pc^2 must occur. But in this case, because of the negative gravitational self-energy, ΔE will enter the negative energy (mass) state before the time of Δt. Because there is a repulsive gravitational effect between negative masses, ΔE cannot contract, but expands. Thus, the universe does not return to nothing, but can exist.

Gravitational Potential Energy Model provides a means of distinguishing whether the existence of the present universe is an inevitable event or an event with a very low probability. And, it presents a new model for the process of inflation, the accelerating expansion of the early universe. This mechanism also provides an explanation for why the early universe started out in a high dense state. Additionally, when the negative gravitational potential energy exceeds the positive mass energy, it can produce an accelerated expansion of the universe. Through this mechanism, inflation, which is the accelerated expansion of the early universe, and dark energy, which is the cause of the accelerated expansion of the recent universe, can be explained at the same time.

 

* The above is a summary of some of the key arguments of the paper, and for more details, please refer to the paper linked below.

# The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism

https://www.researchgate.net/publication/371951438

# Dark Energy is Gravitational Potential Energy or Energy of the Gravitational Field

https://www.researchgate.net/publication/360096238

The first problem with this is that energy is just a property of a system, not a free-standing entity in its own right. So starting with energy immediately begs the question “energy of what?”. In other words, it solves nothing, since you must first postulate some system, before you can speak of energy.

[studiot]

6 minutes ago, exchemist said:

The first problem with this is that energy is just a property of a system, not a free-standing entity in its own right. So starting with energy immediately begs the question “energy of what?”. In other words, it solves nothing, since you must first postulate some system, before you can speak of energy.

Jawohl, plus eins.

[Mordred]

I see your struggling to figure out which latex system this site uses. Here is a guide

https://www.scienceforums.net/topic/108127-typesetting-equations-with-latex-updated/

As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.

 In one of your equations you use the subscript \[i<j\]

I assume i,j,k are Euler coordinates with index 1 to 3 please confirm your usage .

2 hours ago, icarus2 said:

 

 

1. Changes in the range of gravitational interactions over time

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

 

Gravity results from the curvature term or more accurately via the stress energy momentum tensor, If I have a homogeneous and isotropic mass/energy distribution I wouldn't have a system with gravity when k=0. (zero curvature) (apply Newtons shell theorem) 

\[ {E_T} = \sum\limits_i {{m_i}{c^2}} + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R} \]

I have no idea what your using for i and j here the standard notation for i and j involve Euler coordinates judging from this equation your not using Euler coordinates please confirm. I should also not \(e=mc^2\) is not the full equation. This only involves massive particles not massless particles. You want the full energy momentum relation detials here

https://en.wikipedia.org/wiki/Energy–momentum_relation

Edited July 5, 2023 by Mordred

[icarus2]

On 7/6/2023 at 7:29 AM, Mordred said:

I see your struggling to figure out which latex system this site uses. Here is a guide

https://www.scienceforums.net/topic/108127-typesetting-equations-with-latex-updated/

As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.

 In one of your equations you use the subscript

i<j

 

I assume i,j,k are Euler coordinates with index 1 to 3 please confirm your usage .

Gravity results from the curvature term or more accurately via the stress energy momentum tensor, If I have a homogeneous and isotropic mass/energy distribution I wouldn't have a system with gravity when k=0. (zero curvature) (apply Newtons shell theorem) 

 

ET=∑imic2+∑i<j−Gmimjrij=Mc2−35GM2R

 

I have no idea what your using for i and j here the standard notation for i and j involve Euler coordinates judging from this equation your not using Euler coordinates please confirm. I should also not e=mc2 is not the full equation. This only involves massive particles not massless particles. You want the full energy momentum relation detials here

https://en.wikipedia.org/wiki/Energy–momentum_relation

 

I think this claim( It isn't something that exists on its own.) about potential energy is false. Potential energy should be treated as real energy, not virtual energy. Potential energy must have a specific value under specific circumstances.

1. In the calculation of potential energy, not only the calculation through the amount of change is successful. Calculations with own values(I don't know what to choose as the right word. own value?) also succeed. In other words, even if the calculation through the change is successful, it does not guarantee that it is correct.

U=mgh or U=-GMm/r

 

2. Looking at the electromagnetic potential energy similar to the gravitational potential energy,
+ + or - - : When the same kind of charge exists,

[math]{U_{ +  + }} =  + \frac{{k{q_1}{q_2}}}{r} + {c_1}[/math]
+ - : When charges of different species exist,

[math]{U_{ +  - }} =  - \frac{{k{q_1}{q_2}}}{r} + {c_2}[/math]

1)The situation where +Q+Q and +Q-Q exist seems to be a symmetrical situation, should c1, c2 exist?

2)Let's assume that the constants are the same as c1=c2,
+ + : When same kind charges exist, U=+kq1q2/r +c1
+ - : When charges of different kinds exist, U=-kq1q2/r + c1
Does this asymmetry look right?

 

3. In elementary particle physics, invariant mass includes either binding energy or potential energy, depending on how the system is defined.

It is well known that when proton-neutrons make up a nucleus, they have less mass than they do in their free state.

Since these protons and neutrons do not change their mass in the coordinate system of their center of mass, they are rest mass and invariant mass in this situation.

However, when they form one nucleon, the mass decreases by the difference in binding energy. In other words, the constant mass of one nucleon has a negative binding energy.

Now there's the matter of combining nucleons with other nucleons, then the individual nucleons have an invariant mass. This is because, in the coupling problem of two nucleons, individual nucleons are assumed to be invariant in the coordinate system of the center of mass of the individual nucleons. I think we need to think about the meaning of the fact that the binding energy is included in the rest mass of the composite particle.

In composite particles, binding energy is also a component of invariant mass. Should we treat these objects as objects that do not have any own value (fixed value), as objects that have values only when changes occur without substance?

Since almost all problems related to potential energy are problems of calculating the amount of change, the idea that the amount of change is important in potential energy and that only the amount of change has meaning has been established.

Even if the calculation through amount of change is successful, it does not guarantee that it does not have any energy value. The reason is that even if the energy has an own value, it still succeeds in explaining the problem by calculating the change.

U=mgh, U=-GMm/r : Both give the correct values in the change calculation problem.

4. Regarding gravitational potential energy, some physicists think differently than you.

I've talked a lot about potential energy, but the notion acquired by education is strong, and I'm not capable enough to break it. So, a little bit of other people's opinions.

1) Alan Guth said
The energy of a gravitational field is negative!
The positive energy of the false vacuum was compensated by the negative energy of gravity.

2) Stephen Hawking also said
The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

3) Gravitation and Spacetime (Book) : 25~29P

Different forms of energy as source of gravity : Gravitational energy in Earth

If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6×10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.

4) Explanation of GRAVITY PROBE B team
https://einstein.stanford.edu/content/relativity/a11278.html

Do gravitational fields produce their own gravity?

Yes.
A gravitational field contains energy just like electromagnetic fields do. This energy also produces its own gravity, and this means that unlike all other fields, gravity can interact with itself and is not 'neutral'. The energy locked up in the gravitational field of the earth is about equal to the mass of Mount Everest, so that for most applications, you do not have to worry about this 'self-interaction' of gravity when you calculate how other bodies move in the earth's gravitational field.

i,j, are subscripts used a lot in physics, and are not subscripts used only in the case of Euler coordinates.
And, in the symbol of summation, there is also an explanation of gravitational potential energy. So, I don't think anyone interprets it as Euler coordinates.

[math] \sum { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}} [/math]

When obtaining the potential energy of the mass system, the potential terms of all pairs are summed using the summation symbol. Then, since overlapping terms occur, i<j or a<b is used. It is used to avoid overlapping ordered pairs in ordered pairs.


In the major books I used, the notation "m_0" was always used to indicate rest mass. The same notation can be seen in the display of the wiki you linked to. When I use a rest mass, I use the notation m_0. The "m" I used is total mass, or equivalent mass.

[math]{E^2} = {({m_0}{c^2})^2} + {(pc)^2}[/math]


 

Edited July 9, 2023 by icarus2

[exchemist]

2 hours ago, icarus2 said:

 

I think this claim( It isn't something that exists on its own.) about potential energy is false. Potential energy should be treated as real energy, not virtual energy. Potential energy must have a specific value under specific circumstances.

1. In the calculation of potential energy, not only the calculation through the amount of change is successful. Calculations with own values(I don't know what to choose as the right word. own value?) also succeed. In other words, even if the calculation through the change is successful, it does not guarantee that it is correct.

U=mgh or U=-GMm/r

 

2. Looking at the electromagnetic potential energy similar to the gravitational potential energy,
+ + or - - : When the same kind of charge exists,

U++=+kq1q2r+c1
+ - : When charges of different species exist,

U+−=−kq1q2r+c2

1)The situation where +Q+Q and +Q-Q exist seems to be a symmetrical situation, should c1, c2 exist?

2)Let's assume that the constants are the same as c1=c2,
+ + : When same kind charges exist, U=+kq1q2/r +c1
+ - : When charges of different kinds exist, U=-kq1q2/r + c1
Does this asymmetry look right?

 

3. In elementary particle physics, invariant mass includes either binding energy or potential energy, depending on how the system is defined.

It is well known that when proton-neutrons make up a nucleus, they have less mass than they do in their free state.

Since these protons and neutrons do not change their mass in the coordinate system of their center of mass, they are rest mass and invariant mass in this situation.

However, when they form one nucleon, the mass decreases by the difference in binding energy. In other words, the constant mass of one nucleon has a negative binding energy.

Now there's the matter of combining nucleons with other nucleons, then the individual nucleons have an invariant mass. This is because, in the coupling problem of two nucleons, individual nucleons are assumed to be invariant in the coordinate system of the center of mass of the individual nucleons. I think we need to think about the meaning of the fact that the binding energy is included in the rest mass of the composite particle.

In composite particles, binding energy is also a component of invariant mass. Should we treat these objects as objects that do not have any own value (fixed value), as objects that have values only when changes occur without substance?

Since almost all problems related to potential energy are problems of calculating the amount of change, the idea that the amount of change is important in potential energy and that only the amount of change has meaning has been established.

Even if the calculation through amount of change is successful, it does not guarantee that it does not have any energy value. The reason is that even if the energy has an own value, it still succeeds in explaining the problem by calculating the change.

U=mgh, U=-GMm/r : Both give the correct values in the change calculation problem.

4. Regarding gravitational potential energy, some physicists think differently than you.

I've talked a lot about potential energy, but the notion acquired by education is strong, and I'm not capable enough to break it. So, a little bit of other people's opinions.

1) Alan Guth said
The energy of a gravitational field is negative!
The positive energy of the false vacuum was compensated by the negative energy of gravity.

2) Stephen Hawking also said
The matter in the universe is made out of positive energy. However, the matter is all attracting itself by gravity. Two pieces of matter that are close to each other have less energy than the same two pieces a long way apart, because you have to expend energy to separate them against the gravitational force that is pulling them together. Thus, in a sense, the gravitational field has negative energy. In the case of a universe that is approximately uniform in space, one can show that this negative gravitational energy exactly cancels the positive energy represented by the matter. So the total energy of the universe is zero.

3) Gravitation and Spacetime (Book) : 25~29P

Different forms of energy as source of gravity : Gravitational energy in Earth

If we want to discover whether gravity gravitates, we must examine the behavior of large masses, of planetary size, with significant and calculable amounts of gravitational self-energy. Treating the Earth as a continuous, classical mass distribution (with no gravitational self-energy in the elementary, subatomic particles), we find that its gravitational self-energy is about 4.6×10^−10 times its rest-mass energy. The gravitational self-energy of the Moon is smaller, only about 0.2 × 10^−10 times its rest-mass energy.

4) Explanation of GRAVITY PROBE B team
https://einstein.stanford.edu/content/relativity/a11278.html

Do gravitational fields produce their own gravity?

Yes.
A gravitational field contains energy just like electromagnetic fields do. This energy also produces its own gravity, and this means that unlike all other fields, gravity can interact with itself and is not 'neutral'. The energy locked up in the gravitational field of the earth is about equal to the mass of Mount Everest, so that for most applications, you do not have to worry about this 'self-interaction' of gravity when you calculate how other bodies move in the earth's gravitational field.

i,j, are subscripts used a lot in physics, and are not subscripts used only in the case of Euler coordinates.
And, in the symbol of summation, there is also an explanation of gravitational potential energy. So, I don't think anyone interprets it as Euler coordinates.

∑−Gmimjrij

When obtaining the potential energy of the mass system, the potential terms of all pairs are summed using the summation symbol. Then, since overlapping terms occur, i<j or a<b is used. It is used to avoid overlapping ordered pairs in ordered pairs.


In the major books I used, the notation "m_0" was always used to indicate rest mass. The same notation can be seen in the display of the wiki you linked to. When I use a rest mass, I use the notation m_0. The "m" I used is total mass, or equivalent mass.

E2=(m0c2)2+(pc)2


 

Well you would be wrong, then. Energy is just a property of a system denoting, as @Mordred says, the ability to do work. You won't find anyone with competent physical science training who claims energy can exist on its own. That sort of thinking is Star Trek, not science. There are many quantities in science like this: momentum, temperature, entropy, electric charge.....    Energy is just one of those.

In fact, your (1) illustrates the problem immediately. You can't talk about "change" without saying what is changing. And then you give a formula including mass. Mass of what? None of this makes sense until you specify some physical system to which it can be applied. 

 

[icarus2]

1 hour ago, exchemist said:

Well you would be wrong, then. Energy is just a property of a system denoting, as @Mordred says, the ability to do work. You won't find anyone with competent physical science training who claims energy can exist on its own. That sort of thinking is Star Trek, not science. There are many quantities in science like this: momentum, temperature, entropy, electric charge.....    Energy is just one of those.

In fact, your (1) illustrates the problem immediately. You can't talk about "change" without saying what is changing. And then you give a formula including mass. Mass of what? None of this makes sense until you specify some physical system to which it can be applied. 

 

 

The phrase I wrote is this.

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

[math]{E_T} = \sum\limits_i {{m_i}{c^2}}  + \sum\limits_{i < j} { - \frac{{G{m_i}{m_j}}}{{{r_{ij}}}}}  = M{c^2} - \frac{3}{5}\frac{{G{M^2}}}{R}[/math]

And, it is a matter of interpreting mass-energy as a being with mass or energy. It's just a summary of a 24-pages thesis.

And, in the introduction of the thesis, there are the following passages:
In addition, although there are electric charges, spins, and various physical quantities, it is necessary to analyze the problem of expanding the universe due to gravitational interactions because the object will be a being with at least energy (mass) even in various situations.


I'm sorry for you too. I didn't understand what you meant.
 

On 7/6/2023 at 7:29 AM, Mordred said:

 

As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.

 

I misunderstood this sentence(As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.) you wrote. I am so sorry.

The total energy E_{T} of the system
And, mass-energy means a being with mass or energy.

Edited July 9, 2023 by icarus2

[exchemist]

35 minutes ago, icarus2 said:

 

The phrase I wrote is this.

In Figure 1, if the mass-energy within the radius R_1 interacted gravitationally at t_1 (an arbitrary early time), the mass-energy within the radius R_2 will interact gravitationally at a later time t_2.

As the universe ages, the mass-energy involved in gravitational interactions changes, resulting in changes in the energy composition of the universe.

The total energy $E_{T}$ of the system is

ET=∑imic2+∑i<j−Gmimjrij=Mc2−35GM2R

And, it is a matter of interpreting mass-energy as a being with mass-energy. It's just a summary of a 24-pages thesis.

And, in the introduction of the thesis, there are the following passages:
In addition, although there are electric charges, spins, and various physical quantities, it is necessary to analyze the problem of expanding the universe due to gravitational interactions because the object will be a being with at least energy (mass) even in various situations.
 

I misunderstood this sentence(As mentioned energy is the property describing the ability to perform work. It isn't something that exists on its own.) you wrote. I am so sorry.

The total energy E_{T} of the system
And, it is a matter of interpreting mass-energy as a being with mass-energy. 

OK so you start with a "being" (I assume this is a language issue and you mean just an entity of some kind) that has energy as one of its properties.

But that means you don't start "from nothing", then.  

[Mordred]

22 hours ago, icarus2 said:

i,j, are subscripts used a lot in physics, and are not subscripts used only in the case of Euler coordinates.
And, in the symbol of summation, there is also an explanation of gravitational potential energy. So, I don't think anyone interprets it as Euler coordinates.

∑−GmimjrijE2=(m0c2)2+(pc)

The reason I asked about the use of Euler coordinates is that it is the most common method to describe Euclidean spacetime and subsequently it also is used for the basis vectors of GR for the infinitesimal invariant manifolds of a Riemannian  curvature.  The major element you haven't got in your mathematics is geometry nor any vectors. ( or more accurately no directional vector components) You also have no equations describing multiparticle systems.

 I have no issue with trying to describe a universe from nothing model.  However mathematically you truly are going about it the wrong way. That's understandable if your not very familiar with GR but in all honesty there is a far more versatile method under GR to develop your model. 

 You also can factor in much of your equations and subsequently greatly simplify the calculations using geometric units. Commonly referred to as normalized units.

https://en.wikipedia.org/wiki/Geometrized_unit_system

you can readily set c=g=h=K=1 

under geometry you can then apply the FLRW metric. However for the universe beginning or as close as possible without singularity issues at \(10^{-43}\) seconds one would need to have a scalar field in which all particles are in thermal equilibrium this field has no invariant mass as it is prior to electroweak symmetry breaking. This is something your theory runs counter to. As there is no invariant mass (rest mass) at this time.

Then there is also no gravity. Yes gravity can self interfere example gravity waves however if the stress energy momentum term at this time is has only one entry. typically  \(T^{00}\) for a scalar field however one can substitute the scalar field equation of state. One example being a method used by Guth in one his papers.

\(\rho=T^{00}=\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\nabla_i\phi)^2+V\phi\) where \(V\phi)\) is the potential energy density. negative pressure in this is when the potential energy dominates a scalar field leading to what is commonly described as repulsive gravity. Its a bit of a misnomer as it involves pressure.

\(p=\frac{1}{2}\dot{\phi}^2+\frac{1}{2}(\nabla_i\phi)^2-V\phi\)

this is valid when you have a system with no rest mass or invariant mass such as that prior to electroweak symmetry breaking for the volume at that same time. I am very familiar with Allen Guth's modelling methods. I have studied his works for years.

in spacetime tensor form for the stress energy momentum tensor you fill the energy density term at T_{00} the pressure terms on the diagonal.

\[T=\begin{pmatrix}\rho&0&0&0\\0&p&0&0\\0&0&p&0\\0&0&0&p\end{pmatrix}\]

 

 If you truly want assistance helping you to properly toy model your universe proposal and are willing to revamp your article using the higher mathematics (in particular those more applicable to multiparticle systems). Then I have no issue in helping you lean how to go about it. Let me know if you want to learn how to properly model a universe spacetime. 

For example Guth applies what is known as the scalar field equation of state to describe the potential energy and the kinetic energy terms. Under this method vacuum energy is a result of the kinetic energy terms exceeding the potential energy terms. 

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

see the scalar field equation of state here.

Anyways let me know if your interested in significantly improving your understanding as well as your papers

here is an older post I have done detailing Higgs inflation I didn't bother adding more to is as it didn't generate any discussion or interest lol

However the mathematical formulas used here are largely applicable to what you are attempting to do further equations can be found here where I have been setting myself reminder notes of key equations I will need. LOL it may look grandiose but the truth is all of these equations are covered in the first and second years of cosmology and particle physics. Every equation can be readily found in introductory level textbooks.

 

This should give you a better understanding of the type of mathematical weight you will need to send a good impression of your articles in the academic circles. Using the formulas you have so far ( not trying to be offensive) screams that you are lacking in understanding the more suitable mathematical methods. Key aspects you will need being geometry and under that geometry a setting for invariance which includes the conservation laws. You also need to incorporate thermodynamics, this is essential. hence the equations of state  methodology 

Edited July 10, 2023 by Mordred

[icarus2]

On 7/9/2023 at 8:46 PM, exchemist said:

OK so you start with a "being" (I assume this is a language issue and you mean just an entity of some kind) that has energy as one of its properties.

But that means you don't start "from nothing", then.  

That part introduces beings with energy just to explain the characteristics of gravitational potential energy.

The situation in which universe exists after birth from zero energy is the content of chapter 4.1 ~ 4.2.

Of course, it is not completely nothing because it assumes the existence of principles of physics such as the uncertainty principle, but the term "nothing" is sometimes used in that it starts from zero energy.

Edited July 10, 2023 by icarus2

[Mordred]

Ok so your article already includes zero point energy. Keep in mind I am only going off what is shown here on this forum so its good to know.  So my question still remains are you looking to improve your articles ?

the other question is how are you accounting for the vacuum catastrophe that results from zero point energy ?

 

Edited July 10, 2023 by Mordred

[icarus2]

On 7/10/2023 at 12:28 PM, Mordred said:

The reason I asked about the use of Euler coordinates is that it is the most common method to describe Euclidean spacetime and subsequently it also is used for the basis vectors of GR for the infinitesimal invariant manifolds of a Riemannian  curvature.  The major element you haven't got in your mathematics is geometry nor any vectors. ( or more accurately no directional vector components) You also have no equations describing multiparticle systems.

 I have no issue with trying to describe a universe from nothing model.  However mathematically you truly are going about it the wrong way. That's understandable if your not very familiar with GR but in all honesty there is a far more versatile method under GR to develop your model. 

 You also can factor in much of your equations and subsequently greatly simplify the calculations using geometric units. Commonly referred to as normalized units.

https://en.wikipedia.org/wiki/Geometrized_unit_system

you can readily set c=g=h=K=1 

under geometry you can then apply the FLRW metric. However for the universe beginning or as close as possible without singularity issues at 10−43  seconds one would need to have a scalar field in which all particles are in thermal equilibrium this field has no invariant mass as it is prior to electroweak symmetry breaking. This is something your theory runs counter to. As there is no invariant mass (rest mass) at this time.

Then there is also no gravity. Yes gravity can self interfere example gravity waves however if the stress energy momentum term at this time is has only one entry. typically  T00 for a scalar field however one can substitute the scalar field equation of state. One example being a method used by Guth in one his papers.

ρ=T00=12ϕ˙2+12(∇iϕ)2+Vϕ where Vϕ) is the potential energy density. negative pressure in this is when the potential energy dominates a scalar field leading to what is commonly described as repulsive gravity. Its a bit of a misnomer as it involves pressure.

p=12ϕ˙2+12(∇iϕ)2−Vϕ

this is valid when you have a system with no rest mass or invariant mass such as that prior to electroweak symmetry breaking for the volume at that same time. I am very familiar with Allen Guth's modelling methods. I have studied his works for years.

in spacetime tensor form for the stress energy momentum tensor you fill the energy density term at T_{00} the pressure terms on the diagonal.

 

T=⎛⎝⎜⎜⎜ρ0000p0000p0000p⎞⎠⎟⎟⎟

 

 

 If you truly want assistance helping you to properly toy model your universe proposal and are willing to revamp your article using the higher mathematics (in particular those more applicable to multiparticle systems). Then I have no issue in helping you lean how to go about it. Let me know if you want to learn how to properly model a universe spacetime. 

For example Guth applies what is known as the scalar field equation of state to describe the potential energy and the kinetic energy terms. Under this method vacuum energy is a result of the kinetic energy terms exceeding the potential energy terms. 

https://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

see the scalar field equation of state here.

Anyways let me know if your interested in significantly improving your understanding as well as your papers

here is an older post I have done detailing Higgs inflation I didn't bother adding more to is as it didn't generate any discussion or interest lol

However the mathematical formulas used here are largely applicable to what you are attempting to do further equations can be found here where I have been setting myself reminder notes of key equations I will need. LOL it may look grandiose but the truth is all of these equations are covered in the first and second years of cosmology and particle physics. Every equation can be readily found in introductory level textbooks.

 

This should give you a better understanding of the type of mathematical weight you will need to send a good impression of your articles in the academic circles. Using the formulas you have so far ( not trying to be offensive) screams that you are lacking in understanding the more suitable mathematical methods. Key aspects you will need being geometry and under that geometry a setting for invariance which includes the conservation laws. You also need to incorporate thermodynamics, this is essential. hence the equations of state  methodology 

First of all, thank you for your sincere advice.

Actually I lack knowledge and skills. My research is a personal hobby. It is true that I need to study more to make my hobby more meaningful. However, on the other hand, should I have to study hard to enjoy my hobby? Even if I study, there is still a high entry barrier, and I am not sure if I will overcome the entry barrier.

As for my current interests, I have some interest in publishing my research on arXiv or mainstream journals. arXiv requires endorsements from other scientists. Even with the endorsement of another scientist, the administrator will delete it arbitrarily. I've had that process a few times, so, now I don't even try.

I think this paper contains very cool ideas and is worthwhile. By any chance, do you have any intention of summarizing the content of my thesis in half and submitting it to a journal as a corresponding author?

I can also solve the vacuum catastrophe problem!
However, the result may not be what you expect. However, it is a solution that did not exist before, and it will be a pioneer of a new path.

Vacuum catastrophe problem has not yet been added to this thesis. I will update this post with that in a week or less.

Once again, thank you for your goodwill.

Edited July 13, 2023 by icarus2

[Mordred]

Lol I get the offer to be a co author quite often. My reply is always the same. In that I have no issue with assisting someone with their models by pointing out better methods, supplying corrections etc I have no interest in receiving credits for doing so. The real reward is helping someone improve in their understanding. However thanks for the offer.

You and I look at physics as a hobby a bit differently each week I try to find a new challenge or model to study as a good hobby to my way of thinking is something that has the goal of continual improvement. Yes I recognize that in regards to physics its not an easy task.

Anyways I look forward to see how you handle the vacuum catastrophe. 

 

[icarus2]

3.6. The Vacuum Catastrophe Problem or Cosmological Constant Problem

The vacuum catastrophe problem or the cosmological constant problem is a problem in which there is a large difference between the theoretical prediction of vacuum energy proposed by quantum field theory and the observed value. It is known that there is a difference of about 10^120 between theoretical predictions and observed values.

Strictly speaking, the vacuum energy model is only one of the dark energy models, so the observed (or estimated from observed results) dark energy density may not be the density of vacuum energy.

Therefore, the actual vacuum energy density can be the dark energy density, or zero, or negative. However, if the density of vacuum energy is greater than the dark energy density, it will have a larger effect than the dark energy term, so it can be excluded by observational results. Therefore, the upper limit of the observed vacuum energy density is approximately the dark energy density, and there is still a difference of more than 10^120 times between the theoretical prediction value and the actual vacuum energy density value.

 

First, looking at the claims of the vacuum energy model,

    

 

Since there is energy ΔE or u_{vac}, which is one of the sources of gravity, and there is time Δt for gravity to propagate, the gravitational self-energy must also be considered in this problem. So, to look at the mainstream estimates in terms of my model, let's do some calculations.

We have an equation for calculating the total gravitational potential energy in the case of a spherical, uniform distribution. This value is called the gravitational self-energy.

In the vacuum energy model, calculations were performed as a regular hexahedron with one side L. If we consider a spherical space inside a regular hexahedron, the value of the vacuum energy density will be the same in this case. Since there is an expression for gravitational self-energy already calculated for spherical space, to utilize it, let's consider a spherical energy (mass) distribution with \(R = \frac{L}{2}\).

According to the mass-energy equivalence principle, it is possible to define the equivalent mass (m = E/c^2) for all energies. Therefore, in this paper, the terms equivalent mass energy or mass energy or mass are sometimes used for objects with positive energy.

3.6.1. Vacuum energy in space R = L/2 

[math]{E_{vac}} = \frac{{4\pi {R^3}}}{3}{u_{vac}} = \frac{{4\pi {{(\frac{L}{2})}^3}}}{3}(\frac{{2{c^7}}}{{\hbar {G^2}}}) = \frac{{4\pi {{(\frac{\hbar }{{2{m_P}c}})}^3}}}{3}(\frac{{2{c^7}}}{{\hbar {G^2}}}) = \frac{\pi }{3}{m_P}{c^2}[/math]

[math]{E_{vac}} = \frac{\pi }{3}{m_P}{c^2} \simeq + 1.047{m_P}{c^2}[/math]

 

3.6.2. The gravitational potential energy of the vacuum energy of space R = L/2 

[math]{U_{gs}} = - \frac{3}{5}\frac{{G{M^2}}}{R} = - \frac{3}{5}\frac{{G{{(\frac{\pi }{3}{m_P})}^2}}}{{\frac{L}{2}}} = - \frac{3}{5}\frac{{G{{(\frac{\pi }{3}{m_P})}^2}}}{{(\frac{\hbar }{{{2m_P}c}})}} = - \frac{{2{\pi ^2}}}{{15}}{m_P}{c^2}[/math]

[math]{U_{gs}} = - \frac{{2{\pi ^2}}}{{15}}{m_P}{c^2} \simeq - 1.316{m_P}{c^2}[/math]

 

3.6.3. The event horizon created by vacuum energy \({E_{vac}} = \frac{\pi }{3}{m_P}{c^2}\) 

[math]{R_S} = \frac{{2GM}}{{{c^2}}} = \frac{{2G(\frac{\pi }{3}{m_P})}}{{{c^2}}} = \frac{{2\pi }}{3}{l_P} \simeq 2.094{l_P}[/math]

3.6.4. The radius R_gs at which the magnitudes of positive mass energy and negative gravitational potential energy are equal 

[math]|\frac{{{U_{gs}}}}{{{E_{vac}}}}| = |\frac{{ - \frac{3}{5}\frac{{G{{(\frac{\pi }{3}{m_P})}^2}}}{R}}}{{\frac{\pi }{3}{m_P}{c^2}}}| = | \frac{{\frac{\pi }{5}\frac{{G{m_P}}}{{{c^2}}}}}{R}| = 1 [/math]

[math] {R_{gs}} = \frac{\pi }{5}{l_P} = 0.628{l_P} [/math]

3.6.5. Physical meaning of calculated R values

[math]
{E_T}(t = \Delta t) = {E_{vac}} + {U_{gs}} = \frac{\pi }{3}{m_P}{c^2} - \frac{{2{\pi ^2}}}{{15}}{m_P}{c^2} \simeq  - 0.269{m_P}{c^2} < 0
[/math]

Initially, since the negative gravitational potential energy is greater than the positive mass energy, the mass distribution at \({R_0} = \frac{L}{2}\) will expand.

If there is no additional mass influx (or if mass is held constant), when the expanding mass distribution passes \(R_{gs}\), the negative gravitational potential energy equals the positive mass energy.

When the mass distribution becomes larger than R_gs, since the positive mass energy is greater than the negative gravitational potential energy, the system switches to the positive mass state, and thus the situation in which the attractive force acts. Thus, the mass distribution will contract back to R_gs.

Mass energy is of the form E=Mc^2 and remains constant. On the other hand, the gravitational potential energy is of the form \({U_{gs}} = - \frac{3}{5}\frac{{G{M^2}}}{R}\), which decreases as R increases. Therefore, when the mass distribution expands, only the negative gravitational potential energy term decreases, so the system switches to the positive mass state after R=R_gs. The reduced gravitational potential energy will be converted into kinetic energy.

For example, if the mass in the system is constant and R (R is the radius of the mass distribution) doubles from R_0 to 2R_0, it can be seen that the gravitational self-energy is reduced by a factor of 1/2.

[math] {U_{gs}}(R = {R_0}) = - \frac{3}{5}\frac{{G{M^2}}}{{{R_0}}} [/math]

[math] {U_{gs}}(R = 2{R_0}) = - \frac{3}{5}\frac{{G{M^2}}}{{2{R_0}}} = \frac{1}{2}{U_{gs}}(R = {R_0}) [/math]

R < R_gs : system is in negative energy (mass) state. Since the repulsive force component is greater than the attractive force component, the mass distribution expands.

R > R_gs : The system is in a positive energy (mass) state. Since the attractive force component is greater than the repulsive force component, the mass distribution undergoes deceleration expansion and contraction.

Therefore, the mass distribution becomes stable at R=R_gs while oscillating around R=R_gs. The point where R=R_gs is the point where the total energy of the system is zero.

One of the important characteristics is that it vibrates (repeating acceleration and deceleration expansion) based on R=R_gs, and finally stabilizes at R=R_gs. This is because the R=R_gs point is the point where the positive and negative energy components are equal, and the total energy of the system is zero. Although we are analyzing the process in detail, the time interval between these events is approximately t_P ~ 10^{-44}s.

As a rough estimate, if there is no additional mass density generation within the 1l_P(Planck length, approximately 2(0.50(l_P))) range, the mass distribution will converge to R_gs where the positive mass energy equals the negative gravitational potential energy. As a result, the mass distribution returns to the zero-energy state because the magnitudes of the positive mass energy and the negative gravitational self-energy in R_gs are equal.

Also, since the event horizon R_S=2.09(l_P) formed by the mass distribution of R_0 is greater than R_gs=0.63(l_P), the mass distribution exists inside the event horizon. Therefore, the mass distribution does not escape the event horizon, converges to R_gs, and finally returns to nothing.

And, as a problem of consideration, when a stellar black hole forms, the space-time outside the black hole is affected and curved during the process of forming the black hole. By the way, after forming the black hole, if the location of the mass distribution changes inside the black hole, does this also affect the space-time outside the black hole? 

It is estimated that gravity due to changes in the distribution of mass inside the black hole will not be able to escape the black hole.
Even when gravity due to changes in the mass distribution inside the black hole affects the geometry of space-time outside the black hole, the effect is zero or very close to zero because of the gravitational properties of negative gravitational potential energy and positive mass energy described above.

As in previous theoretical calculations, if the vacuum had an enormous energy of \({u_{vac}} \approx {10^{111}} \sim {10^{114}}J{m^{ - 3}}\), it should be observable around us. However, we are not detecting the presence of these enormous energies from the vacuum.
Even if quantum fluctuations occur in vacuum according to existing theoretical assumptions, since ΔE and Δt exist, their own gravitational interactions must also be taken into account. Therefore, considering the gravitational self-energy, the vacuum energy density is likely to be zero, unless the frequency of quantum fluctuations in the vacuum is extremely high.

If the frequency of occurrence of quantum fluctuations is less than approximately 1 within the range of radius l_P during the 5t_P(rough estimate), it can be estimated that the total energy of the quantum fluctuations produced will be in the zero energy.

For example, as a rough estimate, let's assume that 1 quantum fluctuation occurs within a radius of 1(l_P, Planck length ) in 100(t_P) time. Even in this case, it suggests a return to the zero energy state by the above mechanism.This is the case assuming an enormous number of quantum fluctuations. This situation corresponds to the assumption of approximately 10^147 ( 100{t_P} ~10^{-42}s, 2(1{l_P}) ~ 10^{-35}m, Volume ~ 10^{-105}m^3) quantum fluctuations per second, in a space of 1m^3.

Thus, vacuum energy is not a source of dark energy.
 

If the problem is a simple situation that cannot explain the difference in density of 10^120, the possibility remains that the difference in density can be explained by some mechanism at some point in the future.
 

The real problem with vacuum energy model is,

First, that positive energy density (positive inertial mass density) and negative pressure are logically contradictory because the source of pressure is momentum or kinetic energy.

Second, even in the case of light with the greatest momentum or kinetic energy component relative to the total energy, the pressure is \(P = \frac{1}{3}\rho \). The claims of the vacuum energy model require a being with a momentum or kinetic energy three times (\({P_\Lambda } = - {\rho _\Lambda } = - 3(\frac{1}{3}{\rho _\Lambda })\)) greater than that of light.

Third, it is a problem related to the logic of \({\rho _\Lambda } + 3{P_\Lambda } = {\rho _\Lambda } + 3( - {\rho _\Lambda }) = - 2{\rho _\Lambda }\). Mass density ρ and pressure P are properties that an object has. Also, mass density ρ and pressure P are the sources of gravity. However, even if the volume does not expand or contract and maintains a constant size, it means that the gravitational force of \({\rho _\Lambda } + 3{P_\Lambda } = - 2{\rho _\Lambda }\) is applied. That is, it suggests that the object (or energy density) has a gravitational force with a negative mass density of -2ρ_Λ. This is different from a vacuum, which we think has a positive energy density +ρ_Λ.

Fourth, it also seems that there is a problem in applying dU = - PdV to vacuum energy.

And, there are models that are 10^120 more accurate than the vacuum energy model.
 

The Birth Mechanism of the Universe from Nothing and New Inflation Mechanism

https://www.researchgate.net/publication/371951438

 

Edited July 19, 2023 by icarus2

[icarus2]

On 7/20/2023 at 7:22 AM, icarus2 said:

Mass energy is of the form E=Mc^2 and remains constant. On the other hand, the gravitational potential energy is of the form Ugs=−35GM2R , which decreases as R increases. Therefore, when the mass distribution expands, only the negative gravitational potential energy term decreases, so the system switches to the positive mass state after R=R_gs. The reduced gravitational potential energy will be converted into kinetic energy.

For example, if the mass in the system is constant and R (R is the radius of the mass distribution) doubles from R_0 to 2R_0, it can be seen that the gravitational self-energy is reduced by a factor of 1/2.

*Revision

Mass energy is of the form \(E=Mc^{2}\) and remains constant. On the other hand, the gravitational potential energy is of the form \({U_{gs}} = - \frac{3}{5}\frac{{G{M^2}}}{R}\), and the absolute value decreases as R increases. Therefore, when the mass distribution expands, only the absolute value of the negative gravitational potential energy term decreases, so the system switches to the positive mass state after \(R=R_{gs}\). The reduced gravitational potential energy will be converted into kinetic energy.

For example, if the mass in the system is constant and R (R is the radius of the mass distribution) doubles from \(R_0\) to \(2R_0\), it can be seen that the absolute value of the gravitational self-energy is reduced by a factor of \(\frac{1}{2}\).

Edited July 22, 2023 by icarus2

[Mordred]

Been a bit busy with work will look through this when I can give it the proper attention. At first glance it's not bad but I will have to look at it closer

[icarus2]

A combined model of the uncertainty principle and gravitational potential energy provides an explanation for how the universe was born and expanded in a dense state.

[math] \Delta E\Delta t \ge \frac{\hbar }{2}[/math]

From the energy-time uncertainty principle,

If, [math]\Delta t \approx {t_P} = 5.391 \times {10^{ - 44}}s[/math]

[math]\Delta E \ge \frac{\hbar }{{2\Delta t}} = \frac{\hbar }{{2{t_P}}} = \frac{1}{2}m{}_P{c^2}[/math]

Δx=ct_p=2R’ : Since Δx corresponds to the diameter of the mass distribution

Assuming a spherical mass distribution and calculating the average mass density (minimum value),

[math]\frac{1}{2}{m_P} = \frac{{4\pi {{R'}^3}}}{3}{\rho _0} = \frac{{4\pi {{(\frac{{c{t_P}}}{2})}^3}}}{3}{\rho _0}[/math]

[math]{\rho _0} = \frac{3}{\pi }\frac{{{m_P}}}{{{l_P}^3}} = \frac{3}{\pi }{\rho _P} \simeq 4.924 \times {10^{96}}kg{m^{ - 3}}[/math]

It can be seen that it is extremely dense. In other words, the quantum fluctuation that occurred during the Planck time create energy with an extremely high density.

The total mass of the observable universe is approximately 3.03x10^54 kg (used to ρ_c=8.5x10^-27 kg/m^3), and the size of the region in which this mass is distributed with the initial density ρ_0 is

R_obs-universe (ρ=ρ_0) = 5.28x10^-15 [m]

This value is approximately the size of an atomic nucleus.

Not all models can account for the high dense state of the early universe. Also, not all models can provide repulsion or expansion to overcome the very strong gravity in this high-density state. So it's a decent result.

[ Verifiability ]

As a key logic to the argument of this paper, gravitational potential energy appears, and the point where the magnitude of the negative gravitational potential energy equals the positive mass energy becomes an inflection point, suggesting that the accelerated expansion period is entered.

[math]{R_{gs}} = \sqrt {\frac{{5{c^2}}}{{4\pi G{\rho _0}}}} [/math]

Since we can let R_gs be approximately ct(for a space with uniform energy (mass) density) or cΔt/2(with the uncertainty principle applied, if the energy (mass) distribution enters an accelerated expansion within Δt), there is a strong constraint equation between the density and the time the universe entered accelerated expansion. Therefore, it is possible to verify the model through this.

It is necessary to create an early universe accelerating expansion model to which the ideas in this paper are applied. When such precise models come out, there will be more factors that can verify the model's accuracy.

Edited August 5, 2023 by icarus2

[icarus2]

In the post just above,
Even if there was no energy before the Big Bang, enormous amounts of energy can be created due to the uncertainty principle. In a region smaller than the size of an atomic nucleus, the total mass-energy that exists in the observable universe can be created.

In the early universe, when only positive mass energy is considered, the mass energy value appears to be a very large positive energy, but when negative gravitational potential energy is also considered, the total energy can be zero and even negative energy.

Considering not only mass energy but also gravitational potential energy, the total energy of the system is

According to the uncertainty principle, during Planck time, energy fluctuations of more than (1/2)m_pc^2 are possible. However, let us consider that an energy of ΔE=(5/6)m_pc^2, slightly larger than the minimum value, was born.

1) If, Δt=t_p, ΔE=(5/6)m_pc^2,

The total energy of the system is 0.

In other words, a mechanism that generates enormous mass (or energy) while maintaining a Zero Energy State is possible. 

2) If, Δt=(3/5)^(1/2)t_p, ΔE≥(5/12)^(1/2)m_pc^2,

The total energy of the system is 0. In other words, a mechanism that generates enormous mass (or energy) while maintaining a Zero Energy State is possible. This is not to say that the total energy of the observable universe is zero. This suggests that enormous mass energy can be created from a zero energy state in the early stages of the universe.

In this way (If we are limited to what is explained in this post~), the total energy of one quantum fluctuation is zero energy. Since individual quantum fluctuations are born in a zero energy state, and as time passes, the range of gravitational interaction expands, when surrounding quantum fluctuations come within the range of gravitational interaction, accelerated expansion occurs by this method. This method uses the minimum value of energy fluctuations. On the other hand, at energies greater than the minimum, expansion can occur even from a single quantum fluctuation.

Through this model, we can simultaneously solve the problem of the origin of enormous energy and the problem of accelerated expansion in the early stages of the universe.

Edited September 6, 2023 by icarus2

[hoola]

If, as Tegmark and others say, everything is mathematics, wouldn't a more appropriate question be: why mathematics? How could math develop if in a true void nothing exists, even math or the concepts therof?

[icarus2]

On 10/7/2023 at 2:02 PM, hoola said:

If, as Tegmark and others say, everything is mathematics, wouldn't a more appropriate question be: why mathematics? How could math develop if in a true void nothing exists, even math or the concepts therof?

Mathematics began as human intellectual activity to describe phenomena that exist in nature and the universe. Therefore, mathematics and the universe have a very deep connection, and events that occur in the universe can generally be described through mathematics.

However, in mathematics, if a proposition is true within a defined axiomatic system, then this proposition is true and has value. In other words, because mathematics reflects human intellectual activity, even things that are imaginary can become true. On the other hand, the universe is true to exist and has value. Therefore, mathematics and the universe are not completely the same thing.

[icarus2]

If the universe was nothing at the beginning, how did this state of nothing then create what is the universe?

We don't yet know what the answer is. However, because it is an important issue, I am writing my personal opinion.

Let's start with the following equation:

A = A

Before the universe was birthed, the concept of A did not even exist. This A is an concept created by intellectual creature called humanity, 13.8 billion years after the creation of the universe. Also, mathematical terms, including =, are concepts created by humans born after the birth of the universe.

If we move "A" from the left side to the right side,

0 = A - A = 0

To make the idea clearer, let's express this a little differently.

0 = (+A) + (-A) = 0

This equation can be conceptually decomposed as "0", "0=(+A)+(-A)", "(+A)+(-A)=0", "0=0".

1)"0" : Something did not exist. Nothing state.

2)"0 = (+A) + (-A)" : (+A) and (-A) were born from "nothing". Or "nothing" has changed to +A and -A. Something state.

3)"(+A) + (-A) = 0" : The sum of (+A) and (-A) is still zero. From one perspective it's "something state", from another perspective it's still “nothing state”.

4)"0 = 0" At the beginning and end of the process, the state of “nothing” is maintained.

5) "B = 0 = (+A) + (-A) = 0" : The intelligent life form called humanity defines the "first nothing" as B. B may be total A, which is the sum of all A, or it may be a new notion.

In other words, “nothing” can create something +A and something -A and still remain “nothing” state. And, the newly created +A and -A create new physical quantities and new changes. For example, in order for the newly created +A and -A to be preserved in space, a new relational equation such as a continuity equation must be created.

∂ρ/∂t + ∇·j=0

 

Let's look at how pair production occurs from photon (light).

B = 0 = (+Q) + (-Q) = 0

The charge of a photon is zero. When photon do pair production, photon do not conserve charge by creating beings with zero charge, but by creating +Q and -Q to preserve zero. That is, in all cases, in all circumstances, in order to satisfy or maintain “nothing”, this equation of the form (+Q) + (-Q) = 0 must hold. This may be because "0" is not representative of all situations and is only a subset of (+Q) + (-Q) = 0.

At the beginning and end of the process, the total charge is conserved, but in the middle process +Q and -Q are created. Due to the electric charge generated at this time, new concepts including electromagnetic fields and electromagnetic forces are needed.

According to Emmy Noether's theorem, if a system has a certain symmetry, there is a corresponding conserved physical quantity. Therefore, symmetry and conservation laws are closely related.

Conservation of spin, conservation of particle number, conservation of energy, conservation of momentum, conservation of angular momentum, conservation of flux... etc.. New concepts may be born from conservation laws like these.

Let’s look at the birth process of energy.

https://icarus2.quora.com/The-Birth-Mechanism-of-the-Universe-from-Nothing-and-New-Inflation-Mechanism

E_T = 0 = (+E) + (-E) = Σmc^2 + Σ(-Gmm/r) = 0

“E_T = 0” represents “Nothing” state.

Mass appears in “Σ(+mc^2)” stage, which suggests the state of “Something”.

In other words, “Nothing” produces a negative energy of the same size as that of a positive mass energy and can produce “Something” while keeping the state of “Nothing” in the entire process (“E_T = 0” is kept both in the beginning of and in the end of the process).

Another example is the case of gauge transformation for scalar potential Φ and vector potential A in electromagnetic fields.

Φ --> Φ - ∂Λ/∂t

A --> A + ∇Λ

Maxwell equations of electromagnetism hold them in the same form for gauge transformation. After all, the existence of some symmetry or the invariance that the shape of a certain physical law must not change requires a gauge transformation, and this leads to the existence of new physical quantities (Λ, ∂Λ/∂t, ∇Λ) that did not exist in the beginning (Φ, A).

This can be interpreted as requiring the birth of a new thing in order for the conserved physical quantity to be conserved and not change. The condition or state that should not change is what makes change.

Why was the universe born? Why is there something rather than nothing? Why did the change happen?

B = 0 = (+Q) + (-Q) = 0

E_T = 0 =(+E) + (-E) = Σmc^2 + Σ-Gmm/r = 0

∂ρ/∂t + ∇·j=0

Φ --> Φ - ∂Λ/∂t

A --> A + ∇Λ

It changes, but does not change!

It changes in order not to change!

What does not change (B = 0) also creates changes in order not to change in various situations (Local, Global, phase transformation, translation, time translation, rotation transformation ...). This is because only the self (B) that does not want to change needs to be preserved.

The change of the universe seems to have created a change by the nature of not changing. The universe created Something (space-time, quantum fluctuation, energy, mass, charge, spin, force, field, potential, conservation laws, continuity equation...) to preserve Nothing. By the way, as this something was born, another something was born, and the birth of something chained like this may still preserve the first "nothing", and in some cases, the first "nothing" itself may also have changed.

[swansont]

59 minutes ago, icarus2 said:

I am writing my personal opinion.

!

Moderator Note

Your opinion is not what is important. What we want is a model and to see how the evidence supports it.

 

[Mordred]

There is one major fundamental question that universe from nothing models based on zero point energy cannot answer.

Zero point energy uses the quantum harmonic oscillator. We all agree on this. However in order to have a harmonic oscillator one requires a particle field to oscillate.

 It would  be impractical to apply virtual particles as the initial temperature is to extreme. All particles have sufficient kinetic energy terms that they are all in thermal equilibrium and relativistic.

Energy as previously mentioned is a property so doesn't exist on its own.

So using the zero point energy the best one can do with it is describe conditions at the moment of BB. I should note zero energy universe models suffer the same problem.

Edited April 10 by Mordred

[Mordred]

I realize that you likely aren't familiar with the QFT treatment of the harmonic oscillator but the treatment has a elegance about it that shouldn't be ignored so I am going to demonstrate.

first QFT uses creation ad annihilation operators. It also employs the Hamilton as the energy of a simple harmonic oscillator in this case 

\[\hat{H}=\hbar\omega(\hat{a}^\dagger\hat{a}+\frac{1}{2})\]

now as this involves both matter and antimatter it is a complex field with both positive and negative frequency modes each in essence two overlapping fields each with a number density. Key note in QFT position and momentum are operators and its solutions are canonical just mention that for completeness.

the creation and annihilation operators for the harmonic oscillator can be rewritten as

\[\hat{a}=\sqrt{\frac{m\omega}{x}}(\hat{x}+\frac{i}{m\omega}\hat{p})\]

\[\hat{a}^\dagger=\sqrt{\frac{m\omega}{x}}(\hat{x}-\frac{i}{m\omega}\hat{p})\]

the number operator becomes

\[\hat{N}=\hat{a}^\dagger\hat{a}\]

giving us a simplified Hamilton

\[\hat{H}=\omega(\hat({N}+\frac{1}{2}\]

with eigenstates of the Hamilton being

\[\hat{H}|n\rangle=\omega(n+\frac{1}{2}|n\rangle\]

where \(|n\rangle\) is the number states for the number operator \[[\hat{N},\hat{a}]=-\hat{a}\] and  \[[\hat{N},\hat{a}^\dagger]=\hat{a}^\dagger\]

the annihilation operator  drops \(|n\rangle\) by 1 and the creation operator increase \(|n\rangle\) by one.

\[\hat{a}|n\rangle=\sqrt{n}|n-1\rangle\]

\[\hat{a}^\dagger|n\rangle=\sqrt{n+1}|n+1\rangle\]

with ground state \(\hat{a}|0\rangle=0\)

now the interesting thing about the ground state is that it has no particles but the field is still there. (a field is a mathematical construct) so don't confuse it with any realism arguments please. As its rather lengthy to go over how the wave vector k is derived I will skip that for now in particular detailing the Fourier transforms involved. However we can step up from the vacuum to a wave vector state with the following 

\[|\vec{K}|\rangle=\hat{a}^\dagger\vec{k}|0\rangle\]

for a single particle state we can expand this to multiple particle states for example

\[|\vec{k_1},\vec{k_2}....\\vec{k_n}\rangle=\hat{a}^\dagger(\vec{k_1}),\hat{a}^\dagger(\vec{k_2})....\hat{a}^\dagger(\vec{k_n})|0\rangle\]

where \(\omega_i=\sqrt{\vec{k}_i^2+m^2}\) the RHS this is just the invariant QFT derivative of\( E^2=(pc)^2+(m_0c^2)^2\) using the Klein Gordon equations with the four momentum/four velocity. From this we see a creation operator with \(\hbar\hat{a}^\dagger(k_i)\) and energy \(\hbar\hat{a}^\dagger\omega\) for clarity.

we further need the negative and positive frequency parts. (now that we have wave vectors with our invariant  energy momentum relations)

given as

\[\varphi^+(x)=\int{\frac{d^3k}{(2\pi)^{3/2}}\sqrt{\omega(k)}}\hat{a}(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}\]

\[\varphi^-(x)=\int{\frac{d^3k}{(2\pi)^{3/2}}\sqrt{\omega(k)}}\hat{a}^\dagger(\vec{k})e^{-i(\omega_kx^0-\vec{k}\cdot\vec{x})}\]

since \(\hat{a}(\vec{k})|0\rangle=0\) the positive frequency part is composed of the negative frequency parts while the creation operators comprise the negative frequency parts.

now here is the elegance, I have just modelled the zero point energy field with the harmonic oscillator that I can further calculate the particle number densities as well as provided the mathematics for each states wavevectors. One can then take this and using the QFT version of the Bose-Einstein statistics and fermi-Dirac statistics apply the above to obtain number density of any particle particle species knowing the black body temperature. Further more all the above is invariant and under the Hamilton.

This simply demonstrates a far better tool to model a universe from Nothing as I also correlated the momentum space via \(d^3(k_i)\) so already am in a field treatment and as were applying the four momentum and four velocity have Lorentz invariance.

 

 

 

Edited April 11 by Mordred

[Mordred]

All the above can be found in Quantum field theory Demystified by David McMahon. Though its also found in any decent introductory textbook. David's book is done in a manner to keep QFT as straight forward as possible which is why I chose his format here. However there is a problem with the above. If you run the positive and negative frequency parts over all of momentum space you will  end up with infinite energy levels. So one must apply constraints via renormalization to prevent that.

Furthermore one can correlate this for the effective equations of state for the FLRW metric by examining how it relates via the Two statistics I mentioned (Bose-Einstein, Fermi-Dirac). The FLRW metric isn't particularly useful to describe the quantum regime hence QFT supplies those details.

Edited April 11 by Mordred