Changes

The description of gravitation starts with the next section.

The description of gravitation starts with the next section.

===Gravitational force===

===How gravitational force is generated===

 

====Qualitative aspects of gravitational force====

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

[[Gravity|Gravitation]] has been for long time treated as mysterious force attracting objects one to another, approximately according to [[Newton's law]]. Even Newton didn't believe in existence of such force, the same as Einstein, who called it ''"spooky action at a distance"''.

After Einstein discovered his equation for the energy of a particle

After Einstein discovered his equation for the energy of a particle

:<math>E=mc^2</math> ...... (1)

:<math>E=mC^2</math> ...... (1)

where <math>c^2</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

where <math>C^2</math> is square of speed of light in vacuum adjusted by <math>(d\tau/dt)</math> (ratio of proper time to coordinate time<ref>

This ratio is expressed usually as  

This ratio is expressed usually as

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,  

:<math>d\tau/dt=\sqrt{-g_{oo}}</math>,  

where <math>(-g_{oo})</math> is time-time component of metric of spacetime, which means that <math>mc^2 \sqrt{-g_{oo}}</math> is not a constant but a function of time and we may take its non vanishing derivative with respect to time to calculate gravitational force.

 

in sign convetion used in mathematics, where distances in spacetime are considered to be positive numbers, or

 

 

 

:<math>g_{oo}</math> in both notations is time-time component of metric of spacetime, which means that <math>mc^2 \sqrt{g_{oo}}</math> is not a constant but a function of time and we may take its non vanishing derivative with respect to time to calculate gravitational force.

</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>.  

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.

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 (1) 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'', pushing mass <math>m</math> 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. We may say that gravitational force is a quantum effect of particle trying to assume its most probable position of its lowest enery.  

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.

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"''.  

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