Time Gradients

 

Gravitational fields will generally be referred to in this discussion as time gradients. It is an established fact that time will vary as a function of the distance from an object that is generating the ‘gravitational field’. A time gradient can be considered as a field illustrated by lines connecting areas that have equal clock rates, as shown in figure 1.

 

Figure 1

 

The clock rate for a line close to the object is slower than the clock rate for a line further away from the object, changing as a function of the distance. The lines are closer together near the object than they are further away. A time gradient (TG) can be characterized by its density – a denser TG has lines that are closer together at a given distance from an object than a less dense TG. The denser areas of a TG represent slower clock rates than the less dense areas.

 

A TG is continuously generated by an object and thus is considered as traveling with that object. When a reference frame (RF, or system) is related to one object, then the TG associated with that object is considered as traveling with the RF also. Or when a RF is related to two or more objects that may or may not be at rest with respect to each other, then the TG generated by the group of objects is considered as traveling with the RF. The term 'traveling with' should perhaps be phrased as 'continuously generated by' since the TG field does not actually travel with an object. Since the TG field is continuously generated by an object, the field surrounding an object having a uniform velocity would essentiallyremain the same and thus would appear to be traveling with the object.

 

When light is traveling in a RF, the local clock rate in the area where the light is traveling will be primary in determining the natural forward speed of the light in that area relative to the RF. If an object is associated with a RF, then the object’s TG must also be associated with the RF. If the RF is considered as being an inertial one, then its area must be small enough so that the TG in the RF can be considered as essentially being flat (i.e. no change in clock rate) throughout the RF. Such areas are unlikely to actually exist unless ‘flat' is defined with respect to our ability to measure differences in clock rate.

 

A time gradient and a gravitational field can be considered to be equivalent. It has been established that a grivitational field implies a time gradient. That a time gradient implies a gravitational field would appear to be an inevitable conclusion. Light will curve in a gravitational field. This curving is associated with a change in speed of the light as a function of position in a gravitational field. A change in the speed of light is associated with a change in time as shown by the Maxwell equations. Thus light will curve in a time gradient. It follows that a time gradient and a gravitational field must be equivalent in that respect.