Difference between time / length equations for time dilation

In summary, time dilation refers to the difference in time intervals between two successive events in an inertial reference frame, measured on a single clock. The equation for time involves relating the spacetime coordinates of a single event as seen by observers in two inertial frames. It is important to note that events are not limited to a single point in space or time. Additionally, the term "moving frame of reference" is not accurate and should be avoided to prevent confusion.
  • #1
Pochen Liu
52
2
Homework Statement
What makes an event and when do I apply each equation to their respective situations
Relevant Equations
*attached
What is the difference between time dilation (t is the stationary reference frame)
t =
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Description:
If two successive events occur at the same place in an inertial reference frame, the time interval 􏰋t0 between them, measured on a single clock

And this equation for time, if we take t' as the moving reference frame.
245241

Description:
Relate the spacetime coordinates of a single event as seen by observers in two inertial frames, S and S' In terms of events, because I'm now confused as what classifies as an event. If you could provide a distinct example of when to use either equation that would be so helpful!
 

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  • #2
An event is simply a single point in space-time. Note that this is NOT a single point in space and it is NOT a single point in time.

Also be aware that the terminology "moving frame of reference" should NOT be used since it leads to confusion. Frames of reference don't move, objects do.
 

FAQ: Difference between time / length equations for time dilation

1. What is the difference between the time and length equations for time dilation?

The time equation for time dilation is t' = t/sqrt(1-v^2/c^2), where t' is the time measured in the moving frame, t is the time measured in the stationary frame, v is the velocity of the moving frame, and c is the speed of light. The length equation is L' = L*sqrt(1-v^2/c^2), where L' is the length measured in the moving frame and L is the length measured in the stationary frame. The main difference between the two equations is that the time equation involves a reciprocal while the length equation does not.

2. Why do we use different equations for time and length in time dilation?

The time and length equations for time dilation are derived from the principles of special relativity, which state that the laws of physics should be the same for all observers moving at a constant velocity. The equations are used to describe how time and length are affected by the relative motion between two frames of reference.

3. Can the time and length equations for time dilation be used interchangeably?

No, the time and length equations for time dilation represent different aspects of the same phenomenon. The time equation describes how time is affected by relative motion, while the length equation describes how length is affected. Therefore, they cannot be used interchangeably.

4. How do the time and length equations for time dilation relate to the concept of time and length contraction?

The time and length equations for time dilation are used to calculate the effects of time and length contraction. Time contraction is the phenomenon where time appears to pass slower for a moving observer compared to a stationary observer, while length contraction is the phenomenon where an object appears to be shorter in the direction of motion for a moving observer compared to a stationary observer. The equations are used to quantitatively describe these effects.

5. Are the time and length equations for time dilation only applicable to objects moving at the speed of light?

No, the time and length equations for time dilation can be applied to any object moving at any velocity. However, the effects become more significant as the velocity approaches the speed of light. At everyday speeds, the effects are negligible and can only be measured in high precision experiments.

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