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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´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. v2process linked to gravity.pdf

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

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 dτ Mass-energy of a body passing from A to B increases by the factor (dτ/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/dτ)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)

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/dτ2) = fμ - m Γμνλ (dxν/dτ)(dxλ /dτ) 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.

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/dτ 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 B” proper time dτ (repect to A) if State A and B are the same then p´=1; q´=0 “State B” proper time dτ (repect to A) p´=dt/dτ; q´=1- dt/dτ 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 B” with proper time dτ 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 B1” with proper time dτ 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 B2” with proper time dτ 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.

The equations proposed represent an additional condition. The equation of motion (if there is no external force): m(d2xμ/dτ2) = fμ - m Γμνλ (dxν/dτ)(dxλ /dτ) 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)

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