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PROCESS LINKED TO GRAVITY AFFECTING MASS-ENERGY


santiugarte

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pdf file attached

if you are interested in the proposed hypothesis, please contact me via e-mail

 

ABSTRACT

The proposal assumes that the distortion of space-time due to relative velocity (Special Relativity), and the distortion of space-time produced by gravitational fields (General Relativity) are linked to changes of state that affect to mass-energy.

The hypothesis proposes the existence of a process linked to gravity, this phenomenon would affect mass-energy. It would be required to add an additional condition (being a more restrictive scenario) keeping the field equations that define space-time curvature, but by adding the condition linked to the proposed phenomenon, the trajectory that would follow mass-energy in that curved space-time, changes with respect to the established by the officially accepted model. The effect is negligible if the distortion of space-time caused by a gravitational field does not have a significant value. The hypothesis proposed allows to calculate mathematically the discrepancy that would exist with respect to the current model. In case of being correct, the proposal would have important implications in diverse areas of science and its effect would be determinant in the study of black holes or questions related to Cosmology.

process linked to gravity.pdf

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All your equations are to the first leading order. They also do not apply the relevant equations under GR nor action under Euler-Langrene.

 

Try using the Einstein feild equations on particular the stress momentum terms.

 

Secondly this belongs under our speculation forum as it is a model proposal not a peer reviewed concordance (standard) model which the mainstream sections only allow.

Edited by Mordred
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Sorry as soon as I hit equation

 

[latex] e_t=ymc^2-mc^2[/latex] I see what you are trying to do but doing so incorrectly. (its not the kinetic energy formula) Your also not using the full form for e=mc^2 which is the invariant rest mass form. If you are discussing temperature/kinetic energy average then you need the full form with the momentum term.

 

I would also recommend you include the geodesic equations as well as the Poisson and principle of least action.

 

I realize your trying to do this under the SR regime but the correct methodology is under GR not SR in this case as the stress momentum tensor takes into account your hydrodynamic temperature influences and not SR.

 

From a professional standpoint you have a considerable amount of work left to do if you ever this proposal to get off the ground and into peer review standards where it can be considered plausible by the professional community.

 

They won't even consider your proposal without the Einstein field equations nor the above mentioned.

 

The very first things they will note is.

1) No EFE

2) No examination under action

3) no stress tensor

4) no hydrodynamic fluid equations

5) Not using the correct forms of key equations ie kinetic energy.

 

This is the key problem however.

6) no geodesic equations nor can they be derived under the equations in this article.

 

Unless you can derive the two primary geodesic equations timelike (null) and spacelike this is incomplete and insufficient.

That's just the start.

Edited by Mordred
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The equations proposed represent an additional condition.

 

The equation of motion (if there is no external force):

 

m(d2xμ/2) = fμ - m Γμνλ (dxν/)(dxλ /)

 

That is the equation for the geodesic in the curved space-time

 

What happens if we add the additional condition proposed. Then the system would not correspond to the equation of motion with no external force.

We know the geodesic that the particle or the body would follow if there is no external force, to know the trajectory of the particle adding the additional condition, we have to add the force corresponding to each space-time position of the trajectory (the equations proposed allow us to know that force corresponding to each space-time position)

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After reading your paper in your attempts to describe quantum processes and gravitational wave influences.

 

Why do you not have any of the pertinant equations of the two influences mentioned above?

 

Don't you think actually applying the equations would be important?

 

You haven't defined how a GW wave causes action nor how the quantum influences may be involved in terms of your creation/annihilation operators.

 

Sorry but that is incredibly lacking in the required details. When you mention a process is involved. One must show how it is involved via the appropriate equations.

 

You mention the higher equations but do not present them nor even apply them why?

You don't even have the Einstein field equations mentioned in your paper.

 

as a reader this comes across as knowing they exist but not knowing how they work or applies. it does not give any confidence you have attempted to fully apply the various standard models you mentioned.

 

May I also suggest you use an editor where you can properly latex your math. If anything your subscripts and superscript will be more presentable.

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Mass-Energy (α-state) interaction with GW + Energy ((dτ/dt)mc2-mc2))Mass-Energy (α-state)+Mass-Energy (β-state) = (dτ/dt)mc2

Mass-Energy at β-state depends on the factor q´=1-p´ that factor depends on the reference state and the referenced state to the previous one, so that if both are the same then, p´=1 and q´=0. The value of the factor p´= dt/

 

considering the probabilistic approach:

α-state corresponds to p´P´ being P´ the probability of a given event taking place. The interaction with gravitational waves generates the β-state (q´P´). that process requires energy ((dτ/dt)mc2-mc2)), depending on the factor q´ the probability at β-state would increase and consequently the amount of mass-energy at the β-state would increase, that is what is called generically “State B” which is characterized by the quantity of mass-energy at β-state

 

Concerning Special Relativity (hypothetically in absence of GF):

State A” reference

State B” relative velocity (repect to A)=0 then p´=1; q´=0

State B” relative velocity (repect to A)=v then p´=1/ϒ; q´=1- 1/ϒ

Energy between both states (energy required to pass from State A to State B)= ϒmc2-mc2

values of p´ between 0 and 1 ; p´=1 when relative velocity=0 and p´=0 when relative velocity=c

values of q´ between 0 and 1 ; q´=0 when relative velocity=0 and q´=1 when relative velocity=c

 

Concerning General Relativity (hypothetically with no relative velocities between states):

State A” reference, with associated time dt

State Bproper time (repect to A) if State A and B are the same then p´=1; q´=0

State B” proper time (repect to A) p´=dt/; q´=1- dt/

Energy between both states (energy required to pass from State A to State B)= (dτ/dt)mc2-mc2

values of p´ between 0 and 1 ; p´=1 when State A and B are the same and p´=0 when state B corresponds to the event horizon

values of q´ between 0 and 1 ; q´=0 when State A and B are the same and q´=1 when state B corresponds to the event horizon

 

Considering a combination of both GR and SR

State A” reference time dt

State Bwith proper time and velocity v relative to State A

Energy between both states (energy required to pass from State A to State B)= (dτ/dt)mc2-mc2 + ϒmc2-mc2

 

Note: taking into account that Kinetic energy is not invariant depending on the reference.

 

 

If we consider:

State A” reference time dt

State B1with proper time and velocity v1 relative to State A

We would have distortion of time between both states due to GR and SR with velocity v1

If we consider:

State A” reference time dt

State B2with proper time and velocity v2 (<v1) relative to State A

We would have distortion of time between both states due to GR and SR with velocity v2

 

The distinction between both B1 and B2 is the energy required to decelerate the object from v1 to v2

 

The proposal implies that the value of (dτ/dt)mc2-mc2 corresponds to a negative acceleration in the trajectory from A to B, so instead of velocity v1 would be v2

That is why I used this approach, in order to get a better understanding of the phenomenon. Using this approach is useful as well to obtain certain data, for expample we can easily calculate the velocity at State B or time distortions. We could force the object to follow the geodesic if we apply the compensate the energy required by the process, between the initial position and each space-time position.

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You really are missing the point. I've read these in your paper. They do not include the metrics I am referring to.

 

Ok start with the Newton approximation and model under GR. Get your paper to apply Noethers theorem under SO(1.3) Lorentz group as well as the Poisson group.

 

Establish your geometry and symmetry relations.

 

Start there. You need to properly model each state with the particle contributors modelled under their kinetic energy contributions via their equations of state. Yes kinetic energy and potential energy are describing specific states what of it ? You need to apply the relations of those states under some geometry. In this case you can describe each state (using your terminology) as a seperate geometry. Yet they overlap.

 

So do so.

 

Blooming bugger at least apply the correct equation with regards to the kinetic energy contributions. Which is also referred to as the energy momentum equation.

[latex] e^2=(pc^2)+(m_oc^2)^2[/latex]

 

where [latex]m_o[/latex] is your rest (invariant) mass under [latex]e=mc^2[/latex]

 

Establish a coordinate system (included in your article).

 

[latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex]

 

[latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex]

describe in under the above geometry or some similar established metric

 

the Principle of least action in the Standard view

 

Then apply where your proposal differentiates.

 

Include the energy momentum tensor under GR [latex] T_{\mu\nu}[/latex]

 

define the four velocity. [latex]u^\mu[/latex]

[latex]u^\mu=\frac{dx^\mu}{dt}=(c\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})[/latex]

 

this gives in the SR limit [latex]\eta u^\mu u^\nu=u^\mu u_\mu=-c^2[/latex]

the four velocity has constant length.

 

[latex]d/d\tau(u^\mu u_\mu)=0=2\dot{u}^\mu u_\mu[/latex]

 

the acceleration four vector [latex]a^\mu=\dot{u}^\mu[/latex]

[latex]\eta_{\mu\nu}a^\mu u^\nu=a^\mu u_\mu=0[/latex]

 

so the acceleration and velocity four vectors are

 

[latex]c \frac{dt}{d\tau}=u^0[/latex]

 

[latex]\frac{dx^1}{d\tau}=u^1[/latex]

 

[latex]\frac{du^0}{d\tau}=a^0[/latex]

 

[latex]\frac{du^1}{d\tau}=a^1[/latex]

 

Now your establishing the metric under SR for the lay person readers. Professionalism is also being established.

 

As your mentioning QM apply the QFT treatments. Use the metrics and describe how the Principle of least action falls under it. Which will Include your potential and kinetic energy terms. (the following will give a list of the equations under QFT.)

I am developing a list of fundamental formulas in QFT with a brief description of each to provide some stepping stones to a generalized understanding of QFT treatments and terminology. I invite others to assist in this project. This is an assist not a course. (please describe any new symbols and terms)

 

QFT can be described as a coupling of SR and QM in the non relativistic regime.

 

1) Field :A field is a collection of values assigned to geometric coordinates. Those values can be of any nature and does not count as a substance or medium.

2) As we are dealing with QM we need the simple quantum harmonic oscillator

3) Particle: A field excitation

 

Simple Harmonic Oscillator

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

s

the [latex]\hat{a}^\dagger[/latex] is the creation operator with [latex]\hat{a}[/latex] being the destruction operator. [latex]\hat{H}[/latex] is the Hamiltonian operator. The hat accent over each symbol identifies an operator. This formula is of key note as it is applicable to particle creation and annihilation. [latex]\hbar[/latex] is the Planck constant (also referred to as a quanta of action) more detail later.

 

Heisenberg Uncertainty principle

[latex]\Delta\hat{x}\Delta\hat{p}\ge\frac{\hbar}{2}[/latex]

 

[latex]\hat{x}[/latex] is the position operator, [latex]\hat{p}[/latex] is the momentum operator. Their is also uncertainty between energy and time given by

 

[latex]\Delta E\Delta t\ge\frac{\hbar}{2}[/latex] please note in the non relativistic regime time is a parameter not an operator.

 

Physical observable's are operators. in order to be a physical observable you require a minima of a quanta of action defined by

 

[latex] E=\hbar w[/latex]

 

Another key detail from QM is the commutation relations

 

[latex][\hat{x}\hat{p}]=\hat{x}\hat{p}-\hat{p}\hat{x}=i\hbar[/latex]

 

Now in QM we are taught that the symbols [latex]\varphi,\psi[/latex] are wave-functions however in QFT we use these symbols to denote fields. Fields can create and destroy particles. As such we effectively upgrade these fields to the status of operators. Which must satisfy the commutation relations

 

[latex][\hat{x}\hat{p}]\rightarrow[\hat{\psi}(x,t),\hat{\pi}(y,t)]=i\hbar\delta(x-y)[/latex]

[latex]\hat{\pi}(y,t)[/latex] is another type of field that plays the role of momentum

 

where x and y are two points in space. The above introduces the notion of causality. If two fields are spatially separated they cannot affect one another.

 

Now with fields promoted to operators one wiill wonder what happen to the normal operators of QM. In QM position [latex]\hat{x}[/latex] is an operator with time as a parameter. However in QFT we demote position to a parameter. Momentum remains an operator.

 

In QFT we often use lessons from classical mechanics to deal with fields in particular the Langrangian

 

[latex]L=T-V[/latex]

 

The Langrangian is important as it leaves the symmetries such as rotation invariant (same for all observers). The classical path taken by a particle is one that minimizes the action

 

[latex]S=\int Ldt[/latex]

 

the range of a force is dictated by the mass of the guage boson (force mediator)

[latex]\Delta E=mc^2[/latex] along with the uncertainty principle to determine how long the particle can exist

[latex]\Delta t=\frac{\hbar}{\Delta E}=\frac{\hbar}{m_oc^2}[/latex] please note we are using the rest mass (invariant mass) with c being the speed limit

 

[latex] velocity=\frac{distance}{time}\Rightarrow\Delta{x}=c\Delta t=\frac{c\hbar}{mc^2}=\frac{\hbar}{mc^2}[/latex]

 

from this relation one can see that if the invariant mass (rest mass) m=0 the range of the particle is infinite. Prime example gauge photons for the electromagnetic force.

 

Lets return to [latex]L=T-V[/latex] where T is the kinetic energy of the particle moving though a potential V using just one dimension x. In the Euler-Langrange we get the following

 

[latex]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/latex] the dot is differentiating time.

 

Consider a particle of mass m with kinetic energy [latex]T=\frac{1}{2}m\dot{x}^2[/latex] traveling in one dimension x through potential [latex]V(x)[/latex]

 

Step 1) Begin by writing down the Langrangian

 

[latex]L=\frac{1}{2}m\dot{x}^2-V{x}[/latex]

 

next is a derivative of L with respect to [latex]\dot{x}[/latex] we treat this as an independent variable for example [latex]\frac{\partial}{\partial\dot{x}}(\dot{x})^2=2\dot{x}[/latex] and [latex]\frac{\partial}{\partial\dot{x}}V{x}=0[/latex] applying this we get

 

step 2)

[latex]\frac{\partial L}{\partial\dot{x}}=\frac{\partial}{\partial\dot{x}}[\frac{1}{2}m\dot{x}^2]=m\dot{x}[/latex]

 

which is just mass times velocity. (momentum term)

 

step 3) derive the time derivative of this momentum term.

 

[latex]\frac{d}{dt}\frac{\partial L}{\partial\dot{x}}=\frac{d}{dt}m\dot{x}=\dot{m}\dot{x}+m\ddot{x}=m\ddot{x}[/latex] we have mass times acceleration

 

Step 4) Now differentiate L with respect to x

[latex]\frac{\partial L}{\partial x}[\frac{1}{2}m\dot{x}^2]-V(x)=-\frac{\partial V}{\partial x}[/latex]

 

Step 5) write the equation to describe the dynamical behavior of our system.

 

[latex]\frac{d}{dt}(\frac{\partial L}{\partial\dot{x}}-\frac{\partial L}{\partial x}=0[/latex][latex]\Rightarrow\frac{d}{dt}[/latex][latex](\frac{\partial L}{\partial\dot{x}})[/latex][latex]=\frac{\partial L}{\partial x}\Rightarrow m\ddot{x}=-\frac{\partial V}{\partial x}[/latex]

 

recall from classical physics [latex]F=-\triangledown V[/latex] in 1 dimension this becomes [latex]F=-\frac{\partial V}{\partial x}[/latex] therefore [latex]\frac{\partial L}{\partial x}=-\frac{\partial V}{\partial x}=F[/latex] we have [latex]m\ddot{x}-\frac{\partial V}{\partial x}=F[/latex]

This is the type of details you need. That is if you want your paper to go anywhere. Secondly energy does not exist on its own.... So you need to detail the particle contributors and their hydrodynamic contributions to the average kinetic energy.

 

For scalar models. Use the equation

 

[latex]w=\frac{\frac{1}{2}\dot{\phi}^2-V\phi}{\frac{1}{2}\dot{\phi}^2+V\phi}[/latex]

 

where the numerator is your potential energy and the denominator your potential energy term.

 

As you can see we already describe systems via strictly kinetic to potential energy clearly define where your model differentiates from the metrics already existing....

 

In the QFT Langrene above

 

 

[latex]L=\frac{1}{2}m\dot{x}^2-V{x}[/latex]

 

To the right of the- sign is potential energy to the left is the kinetic energy

 

Why would I need your model for something already available?????

 

 

 

 

 

Edited by Mordred
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Those are well known equations, the proposal focus on the changing issues with respect to the established model.

The Noether Theorem is preserved, considering the proposed process, when it is added a negative Kinetic energy term that offsets the increasing value of mass-energy from mc2 to (dτ/dt)mc2 (Note: as stated at the paper and on previous posts, Kinetic Energy is not invariant on references)

 

The principle of least action defines the trajectory, concerning a free fall body it would follow the Geodesic, The equation of motion (if there is no external force):

 

m(d2xμ/2) = fμ - m Γμνλ (dxν/)(dxλ /) equation for the geodesic in the curved space-time

 

The effect of the proposed process is similar to the one caused by an external force. So it has to be applied the negative Kinetic Energy term that takes place between the initial State A and all the space-time positions in its trajectory until reaching the final State B

 

Calculus or futher development of the proposal might be possible, nonetheless currently it shows some interesting properties and allows to obtain data and discrepancies with the etablished model, so that it might be tested.

The main point of the proposal is that a free fall observer would undergo a negative acceleration due to the effect of the proposed process. Altough that effect would be negligible if distortion of time has not a significan value.

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A negative acceleration great when all the datasets show an incredible degree of accuracy under the standard equations I provided. ie an increasing acceleration term as you approach a higher mass.

 

You really have your work cut out for you. First you need to show precisely what discrepancies your referring to under the standard equations.

 

GR does have an incredibly high degree of accuracy so which discrepancies are you referring to?

 

Little side note an added kinetic term would have temperature effects but lets skip by that for now. though by your descriptive a reduced temp.

Edited by Mordred
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The proposal adds an additional condition, that condition does not breach the weak equivalence principle.

 

Space-time position A Space-time position B

body with mass-energy m1 body with velocity v

body with mass-energy m2 body with velocity v

 

 

The proposed process is similar to the phenomenon corresponding to the kinetic energy.

Concerning SR:

Reference State A

State B with velocity v relative to State A.

Mass-energy of a body passing from A to B increases by the factor ϒ (relative to an observer at State A), that increase is at the expense of kinetic energy.

 

Concerning the proposed process:

Reference State A (dt)

State B with proper time

Mass-energy of a body passing from A to B increases by the factor (/dt) (relative to an observer at State A), that increase is at the expense of kinetic energy.

 

So what happens if we combine both. If there is E energy available between both states, then the proposed process would require part of that energy and the velocity of the body would be lower than the expected by the current officially accepted model. That would be the case on the transition from A to B, the reverse process would be an exhotermic one on the transition from B to A.

 

- Considering an hypothetically “pure Special Relativity scenario” for the observer passing from “State A” to “State B”.

The observer in transition from “State A” to “State B” with relative velocity v with repect of A, would have associated energy with reference to itself mc2 because the reference and the referenced states are the same.

The observer would experience a positive acceleration.

The energy associated with the previous reference would change, if an object is fixed at A while the observer passes form “State A” to “State B” the energy associated to the object changes from mc2 , when the observer was at “State A” to ϒmc2 , when the observer reaches the “State B”.

- Considering the proposed process for the observer in free fall from A to B

The observer in free fall would have associated energy with reference to itself mc2 because the reference and the referenced states are the same.

The observer would experience a negative acceleration, the observer would measure a negative acceleration linked or due to the proposed process (altough that value would be negligible insofar distortion of time due to the gravitational field does not change siginificantly).

The energy associated with the previous reference would change, if an object is fixed at A while the observer passes from “State A” to “State B” the energy associated to the object changes from mc2 , when the observer was at “State A” to (dt/)mc2 , when the observer reaches the “State B”.

- Considering the proposed process for the observer passing from B to A

The observer would have associated energy with reference to itself mc2 because the reference and the referenced states are the same.

The observer would experience a positive acceleration, the observer would measure a positive acceleration linked or due to the proposed process (altough that value would be negligible insofar distortion of time does not change siginificantly).

The energy associated with the previous reference would change, if an object is fixed at B while the observer passes form “State B” to “State A” the energy associated to the object changes from mc2 , when the observer was at “State B” to (dτ/dt)mc2 , when the observer reaches the “State A”.

 

 

In relation to the discrepancies, it is possible to calculate those discrepancies using the proposed equations.

Considering the GF corresponding to the Sun, the Schawarzschild metric outside the sphere

Taking as value 2GM/c2R= 0,00000424607412878786

The value of the discrepancy (increment per unit) between ϒ (ϒ = 1/√(1- v2/c2)) and ϒmod

(ϒmod = 1/√(1- v2mod/c2)) corresponding to a trajectoy between State A(far away from the gravitational source so that its effect is negligible) State B (the surface of the sun)

That discrepancy has a value of 0,000000000004507273

That would be the discrepancy for a body in free fall for the whole trajectory between State A and State B. That would be due to the energy required between both states, if the energy required from the initial State A to another one in the trajectory closer to the surface of the sun is compensated, then the discrepancy would be lower corresponding to the value of the energy required between those two states (the closer to the sun and the surface of the sun)

(Note: I have taken these data from a calculus I made a few months ago, I did not review the calculus today, but anyone can calculate that discrepancy on its own)

Edited by santiugarte
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Well considering the weak equivalence principle has been tested numerous times to a degree of accuracy to 1 part in [latex]10^{18}[/latex]

 

Which is far finer than the numbers you just posted. I would state that the experimental data doesn't reflect the discrepancy values you just posted.

 

As I stated you have your work cut out for you. Though you still haven't recognized that the quality of your article needs a huge overhaul as per the items I mentioned above. You have better details posted here than in your article where those details belong.

 

The error of margins you posted is several degrees of error greater than the experimental data.

 

Answer a simple question does this discrepancy show up under your model? or does it show up using the standard model?

 

Sounds like your model where it shows up. Which tells me something is wrong in your model. As the standard model is far more accurate than the numbers you posted.

 

I would be a far more accurate match to experimental data using the standard model as opposed to using your model. In other words you haven't improved anything but instead added a greater margin of error.

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The weak equivalence principle

"The trajectory of a point mass in a gravitational field depends only on its initial position and velocity, and is independent of its composition and structure."

 

As stated on the previous post, the proposed process does not breach that

 

Space-time position A Space-time position B

body with mass-energy m1 body with velocity v

body with mass-energy m2 body with velocity v

 

 

Two bodies with equal initial position and velocity but different composition or structure, would have the same velocity at State B. The proposed process cumplies that condition.

 

v represents the velocity corresponding to the current model.

vmod represents the velocity adding the proposed process

discrepancy is between v and vmod (and not between bodies with the same initial conditions)

Two bodies with equal initial position and velocity but different composition or structure, would have the save velocity at State B.

A body with mass m1 would have velocity vmod at State B

A body with mass m2 (with equal initial position and velocity than the body with mass m1) would have velocity vmod at the State B

 

The proposed process does not affect that condition

Edited by santiugarte
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I asked you specifically to define what the discrepancy is that you are trying to improve in the standard model.

 

You gave values that did not match.

 

Yet you are altering a key aspect kinetic energy term that makes up the above degree of accuracy then claim it doesn't affect the accuracy of GR.

 

I do not require lessons on what the standard model states. I need a detailed analysis that your model approximates the standard model in particular the freefall rate itself as per the standard model then the comaprison to your model.

 

Which quite frankly should have been in your paper to begin with.

 

Any good paper does a detailed comparison. Key word DETAILED. That has been what I have been trying to get you to include.

 

For instance when you claim your model shows negative acceleration as opposed to the increasing acceleration of the standard model.

 

Then lay the claim that this does not conflict you better have some very strong evidence. I do not see that reflected in your posts nor your paper as you have not done a detailed standard model series of tests to compare against.

 

I will not merely take your word on it. I will not struggle with the lack of latex in your article. A good article should be written in a clear and precise format that is easily read. I do not have issue with understanding any complex mathematics.

 

I am the reader it is up to you to provide a detailed analysis to sell me on your idea. A good article will be written for a target audience. If your target audience is the professional peer review standard then your well below the required details as per the suggestions I placed above.

 

I am more than well aware of how GR determines freefall geodesics. I can derive such under GR. Regardless of the particle contributors.

 

I specifically asked you to do the same USING your model and not merely posting the formula.

 

And for bloody sakes start applying the CORRECT energy momentum equation.

 

E=mc^2 is strictly the invariant mass under GR. IT DOES NOT include momentum.

 

The equation I posted above does.

Edited by Mordred
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Alright lets try this angle shall we.

The proposal assumes that the distortion of space-time due to relative velocity (Special Relativity), and the distortion of space-time produced by gravitational fields (General Relativity) are linked to changes of state that affect to mass-energy.

Equivalence principle m_i=m_g. Now explicitly show this.

 

Under SR and GR all forms of mass energy contribute to curvature. Via the equation

 

[latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex]

The hypothesis proposes the existence of a process linked to gravity, this phenomenon would affect mass-energy. It would be required to add an additional condition

Well good so does GR. though it does not require any additional terms if you use the correct formula. WHY do you think I keep mentioning it?

(being a more restrictive scenario) keeping the field equations that define space-time

Umm the momentum term of the above equation and the invariant mass of the above equation when applied to your four momentum determines your spacetime curvature.

 

You have already accounted for potential vs kinetic energy in terms of how total mass-energy density via the stress tensor curves spacetime. (at least in terms of energy equivalent contributions go.)

 

 

so my question is why do you think you need any adfitional kinetic energy terms?

, when it is added a negative Kinetic energy term that offsets the increasing value of mass-energy from mc2 to (dτ/dt)mc2

 

If you used the correct equation I posted above this is unnecessary

Shall I continue ?

 

[latex] e=pc^2[/latex] also happens to the the energy due to momentum of specifically all massless particles. (this technically includes kinetic energy, as energy is a property)

 

In essence

 

[latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex]

 

includes BOTH the invariant and variant mass that you claim needed adding to SR.

 

Your further statement of trying to account for changes in mass due to acceleration ie in an acceleration frame is already interconnected via SR and GR.

 

in essence you ignored a key equation that accounts for the kinetic energy term then tried to add that term in the above equation you provided by replacing p with

 

 

[latex]pc^2\rightarrow\frac{d\tau}{dt}c^2[/latex] in the last quoted section

 

As per my first reply when I hit this equation from your article

 

[latex] e_t=ymc^2-mc^2[/latex]

 

Considering an observer at State A, and an object at State A as well, with a associated energy [latex] E_a=mc^2[/latex]

If that object passes to State B, while the observer is sit at State A, the

value of the energy associated to that object relative to the observer fixed at State A,

changes to [latex] E_B=(\frac{d\tau}{dt})mc^2[/latex]

and the value of the energy required for that proccess to take place

would be [latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex]

Why two observers for the same coordinates? if you model potential vs kinetic energy seperately then apply them together you have an embedded geometry with two fields overlapping.

 

So where does the two observers come from????

 

An observer is an EVENT.....not a state an event is in essence a spacetime coordinate that is defined by total energy contributions via

 

[latex]e^2=(m_oc^2)^2+(pc^2)^2[/latex]

 

However as your in [latex]\mathbb{R}^4[/latex] you need to apply that to a multiparticle field under the four momentum and three velocity.

 

The rest of your article does not get any better....

 

Now back to this goofy equation

 

[latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex]

 

Great what about massless particles that definetely has kinetic energy but no invariant mass?

 

How does that equation work in a system of massless particles where you have no invariant mass? Brings us right back to that replacement I mentioned above. Except you also flipped the sign so you are no longer adding two forms of energy for total energy.

 

You are subtracting one from the other via your very OWN equations ????????

 

You have already defined [latex] E_a=mc^2[/latex] you are subtracting from total energy.

 

Why?

 

Oh right to correspond to your negative acceleration. Let's get back to that later. Under R^4 field treatment =not good

 

I assume you have rewritten the groups under Noether's theory in its definition of conservation of energy/momentum ? in R^4 ?

 

Is not your purpose to treat kinetic energy as the gamma factor ? If you did the derivitaves correct you should have gotten

 

[latex] E_t=\gamma m_oc^2[/latex]

 

Not this

 

[latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex]

 

Here study it for yourself.

 

https://www.google.ca/url?sa=t&source=web&rct=j&url=https://arxiv.org/pdf/1604.02651&ved=0ahUKEwiNq4-LpLrUAhVCwmMKHauqCew4ChAWCCMwAg&usg=AFQjCNEyL1NsYSdoH8evMNTVYjwRJO2ZPg&sig2=PV1eCsO8V5ctiLlNX1oqtQ

 

Start at section D and work down to equation 29.

 

I have no idea how you got this goofy equation. [latex] E_t= \frac{d\tau}{dt}mc^2-mc^2[/latex]

Edited by Mordred
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The proposed Hypothesis adds a new condition, so it can not be deduced from the currently established model. This v2 tries to better clarify the reasons or arguments that point towards that additional condition (not need to read v1).

The proposed process is the one that fits the behaviour of the Physical System to the features it shows considering the approach taken at this paper. This approach implies an invariant value: ndt=n´

The consequence of the process will be a force opposed to the free fall, which would be negligible insofar distortion of time does not reach a siginificant value.

v2process linked to gravity.pdf

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A hydrogen atom falling into a black hole should have the velocity of c when it reaches the event horizon. Will it's relative mass be infinite?

No it should not its velocity will always be less than c

The proposed Hypothesis adds a new condition, so it can not be deduced from the currently established model. This v2 tries to better clarify the reasons or arguments that point towards that additional condition (not need to read v1).

The proposed process is the one that fits the behaviour of the Physical System to the features it shows considering the approach taken at this paper. This approach implies an invariant value: ndt=n´dτ

The consequence of the process will be a force opposed to the free fall, which would be negligible insofar distortion of time does not reach a siginificant value.

I will look over it later though you do realize that the issues I raised are incredibly well tested and extremely accurate.

 

To this day I still do not understand why it is that everyone wishes to reinvent GR. When it is one of the most accurate snd tested models out there.

 

The most common reason usually ends up being "The OP didn't understand relativity past SR."

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