Question re: time dilation equations

In summary, the kinematic and gravitational time dilation equations have different symbols for the numbers that represent the physical quantities. The difference is that t0 represents the time at which an observer is located very far away from the subject, while t' represents the time at which the observer is located on the surface of the Earth as viewed by the subject.
  • #1
mathyou9
8
0
For both time dilation equations (kinematic and gravitational) I have often seen

[tex]\Delta t^\prime = \frac{\Delta t}{\sqrt{1-(v/c)^2}}[/tex]

and

[tex]\Delta t' = \frac{\Delta t}{\sqrt{1-\frac{2GM}{rc^2}}}[/tex]

I'll calls these equations as "Set A"

------------------------

And at other times as

[tex]\Delta t = \frac{\Delta t_0}{\sqrt{1-(v/c)^2}}[/tex]

and

[tex]\Delta t = \frac{\Delta t_0}{\sqrt{1-\frac{2GM}{rc^2}}}[/tex]

I'll calls these equations as "Set B"

---

I'm no physics (or mathematics) major (just a dilettante; that's why I'm asking.) Why use t' (on the left side of the equals sign for "Set A" equations) but t0 (on the right side of the equals sign for "Set B" equations)? I realize an equation is only good as far as you can interpret it. And so I know these are the same equations, but why the difference?

Thanks. :)
 
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  • #2
It would be nice if all physicists agreed on the symbols used to represent physical quantities in equations. Unfortunately they don't. In case of apparent conflict, you need to read the text surrounding the equations carefully, to find out how each author defines his symbols.
 
  • #3
jtbell said:
It would be nice if all physicists agreed on the symbols used to represent physical quantities in equations. Unfortunately they don't. In case of apparent conflict, you need to read the text surrounding the equations carefully, to find out how each author defines his symbols.
Of course. Universality of equation symbology would be nice, but that'll never happen. :-)

---

Completely tangential to my OP: I can easily plug numbers into the kinematic time dilation equation without even thinking about it. But I've never really involved myself with the gravitation time dilation equation until recently. I'm still trying to get a firm grasp on it. With that said, can anyone provide me an example of the numbers to use in the gravitational time dilation equation regarding someone on the surface of the Earth as viewed by an observer very far away from earth?

Thanks, your response(s) are much appreciated.
 

1. What is time dilation and how does it relate to Einstein's theory of relativity?

Time dilation is a phenomenon in which time passes slower for objects or individuals in motion compared to those at rest. This concept was first introduced by Albert Einstein in his theory of relativity, which states that the laws of physics are the same for all observers in uniform motion.

2. How is time dilation calculated and what are the equations used?

Time dilation is calculated using the equations derived from special relativity, which include the Lorentz factor, time dilation formula, and velocity addition formula. These equations take into account an object's velocity and the speed of light to determine the amount of time dilation experienced.

3. Can time dilation be observed in everyday life?

Yes, time dilation can be observed in everyday life, although the effects are usually very small. For example, GPS satellites have to take into account the time dilation caused by their high speeds in order to accurately measure time and provide accurate location data.

4. Does time dilation only occur at high speeds?

No, time dilation can occur at any speed, but its effects become more noticeable at speeds closer to the speed of light. However, even at everyday speeds, such as those of airplanes, time dilation is still present but to a very small degree.

5. Are there any practical applications of time dilation?

Yes, time dilation has several practical applications, such as in GPS technology as mentioned earlier. It is also important in understanding the behavior of particles at high speeds in particle accelerators and in the development of theories on the structure of the universe.

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