Changes

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.  

</ref>) and <math>m</math> is rest mass of a particle though the equation works also for ''[[relativistic mass]]'' with just the energy increased by kinetic energy of the particle, it turned out that this mysterious force of alleged ''attraction'' comes just as derivative of the above equation with respect to displacement of the particle <math>dx</math>.  

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause such force.  

It came from the fact that the time ''slows down in vicinity of any external mass'' just by right amount to cause force.  

:<math>F=-dE/dx</math> ...... (2)  

:<math>F=-dE/dx</math> ...... (2)  

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.  

where dx is displacement of particle in relation to the source of slowed time, that we call mass <math>M</math>.  

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (2) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation, and that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

With slowing down of time in vicinity of mass <math>M</math>, the energy of any particle in vicinity of mass <math>M</math> diminishes according to equation (2) since all movements of the particle are also slower so all of them contain less kinetic energy expressed by <math>E</math>. So there is certain apparent ''force'', towards mass <math>M</math> taken before Einstein for ''"attractive force"'' of ''"gravitational attraction"'' while it had been just a force of ''apparent attraction'': the tendency of particle <math>m</math> to move towards the most most probable position of this particle, position of its lowest energy. Something that the particle is ''pushed'' towards, without any prompting force, which also shows the quantum nature of Einsteinian gravitation.

 

It means that the force is only an '''inertial force''' with which particle presses towards its location of most probable position in spacetime. That's why introduction of [[curvatures of spacetime]] to physics the problem of gravitational force that Newton worried so much became moot.

 

 

Now we show also its quantitative aspects to be sure that it is really the ''"gravitational force"''.  

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative  

Since the energy of any particle is controlled by Einsteinian equation (1) then when time runs slower in vicinity of mass <math>M</math>, the energy <math>E</math> is diminished according to its derivative  

:<math>dE/dx=2mcdc/dx</math> ...... (3)

:<math>dE/dx=2mcdc/dx</math> ...... (3)

The above equation implies that  

The above equation implies that (if it is going to be the real ''"gravitational force"'' <math>F=ma</math>)

:<math>dc/dx=-a/c/2</math> ...... (4),

:<math>dc/dx=-a/c/2</math> ...... (4),

which may be derived from a rocket ship moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is the same as acceleration causing the same gravitational effect as the one given by equation (2) and remembering that dependence of bending of light ray in the rocket ship is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in flat space. And so the "gravitational force" is the same as in (3) and substituting (4) at the right place we get as the result  

which may be derived from a rocket ship model moving with acceleration <math>a</math> which according to the ''"[[principle of equivalence]]"'' of gravitation and acceleration is exactly the same as acceleration causing the same gravitational effect as the one given by equation (2). Remembering that dependence of bending of light ray in the rocket ship model is twice as big as the observed since the second half of bending comes from the [[curvature of space]] non visible in the flat space of our rocket ship model.

 

And so the ''"gravitational force"'' is the same as in (3) and substituting (4) at the right place we get as the result  

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

:<math>F=-dE/dx=2mcdc/dx=-2mca/c/2=ma</math> ...... (5).

And so the "gravitational force" comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the following equation  

And so the ''"gravitational force"'' comes out as <math>F=ma</math> and more accurately than the Newtonian force given by the following equation  

:<math>F_N=GMm/r^2</math> ...... (6),  

:<math>F_N=GMm/r^2</math> ...... (6),  

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).  

It is the whole mystery of ''gravitational force'' demystified by Einsteinian ''[[time dilation]]'' and the ''[[curvature of space]]''. Turning out to be the '''inertial force''', ''pushing'' the particle towards mass <math>M</math>, that allegedly ''attracts'' it but in fact only changes the rate of time around itself (slowing it down).  

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that together cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy  as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

In the end, the apparent gravitational force of equation (2) is caused by the [[curvature of space]] and the [[time dilation]] that combined, cause the effects of diminishing energy of objects immobilized in curved space. When they aren't immobilized (they are left in [[free fall]]), they follow their natural positions of the greatest probability of being there in the spacetime without producing any forces. As e.g. the Moon following its natural path around the Earth moving at each point of its travel with appropriate acceleration <math>a</math> compensating changes of its total energy  as given by (1). In this way no additional energy can be created or destroyed and the law of conservation of energy is satisfied automatically for all the moving objects of the universe.

===Einstein's universe===

===Einstein's universe===