Relationship between mass and speed of light

10th Nov,2012

Tetsuya Nagai

 

It has been observed officially that the light is bent under gravity.

 

From general relativity

                          (1)

 Where  is the speed of light in vacuum.

Where is the curvature of light when light passes through distance  away from mass .

G is the gravitational constant.

 

In general relativity the bending of  light has been explained by the distortion of space.

However instead of the distortion of space, can't we explain the  bending of light as a phenomenon that derived from the changing of the speed of light depend on location in a vacuum?

 I try to explain the bending of light with using non- distorted axis of space-time as following.

 

 

 

I assume that the total amount of the Laplacian of is proportional to the mass, and have the following relationship.

 

 

                (2)

 

where is a constant

from(2)

 

                 (3)

 In following figure is the traveling direction of the light.

 

The light will pass through the distance  away from the mass on the axis .

 

is a vector.

 

 

 

                 (4)

                (5)

 

                            (6)

Where  is the angle between and axis

 

 

                     (7)

Where is standard speed of light in vacuum.   

 

 

   (8)

 

          (9)

Therefore

              

=                         (10)

 

From (1)(10)

 

                          (11)

 

From (2)(11)

          (12)

Therefore total amount of the Laplacian of is proportional to mass.

As a result I found a relationship between the mass and the speed of light.

 

Also I try to seek the relationship between the gravity and light speed.

 

From(3)and (11)

      (13)

 

 

From the law of universal gravitation.

@@@(14)

Where  is the gravitational acceleration.

 

From(13)(14)

 

@@@(15)

 

 

 

Therefore the gradient of  is four times the acceleration of gravity and the opposite direction.