Time Dilation Equation: Clarifying Variables

[Dgonzo15]

Hello, I've recently come across the equation for time dilation, which is t=t(p)*γ, which is
t=t(p)*(1/√(v^2/c^2)). Can someone please clarify what each of these variables mean?

 

[Zmunkz]

I think you are missing a ( 1- ... ) in your denominator.

In any case:

t=time measured to pass in the moving frame
t(p)=proper time measured to pass in a still frame
v=speed of the moving frame measured from the still frame
c=speed of light in a vacuum

 

[Dgonzo15]

From what I know, v is the speed of the reference frame which the light is on--is this what you meant?

 

[Zmunkz]

Yes -- I've not seen it phrased like that, but I think you are saying the same thing. In textbooks it is often a train or a spaceship said to be moving at some speed. That speed is given relative to a reference frame, and represents "v" in the equation.

 

[sardar]

Sure, I would be happy to clarify the variables in the time dilation equation for you.

The variable t represents the time experienced by an observer in a particular frame of reference. This is the time that is measured by a clock in that frame of reference.

The variable t(p) represents the proper time, which is the time experienced by an observer who is at rest in a specific frame of reference. This is the time that is measured by a clock that is also at rest in that frame of reference.

The variable γ represents the Lorentz factor, which is a mathematical term that describes the relationship between time and velocity in special relativity. It is calculated as 1/√(1-v^2/c^2), where v is the relative velocity between the observer and the object being observed, and c is the speed of light.

Overall, the time dilation equation shows that time is relative and can be affected by factors such as velocity. As an object moves faster, time slows down for that object relative to a stationary observer. This is a fundamental concept in the theory of special relativity.