Does Time Dilation Affect Observations in Baseball?

[Tranceform]

Homework Statement

A baseball player at home plate hits a pop fly straight up (the beginning event) that is caught by the catcher at home plate (the ending event). Which one or more of the following obeservers record(s) the proper time interval between the two events? (a) A spectator sitting in the strands (b) A spectator watching the game home on TV (c) The third baseman running to cover the play

Homework Equations

$$\Delta t=\frac{\Delta t_{0}}{\sqrt{1-\frac{v^2}{c^2}}}$$

The Attempt at a Solution

As I understood time dilution it occurs when an object is moving and the obeserver is not inertial with the movement of the object. In this case neither of the observers is moving with the object (the baseball) so no one of the observers should be able to records the proper time interval between the two events. Only a clock that was a attached to the baseball itself would do that. Please explain why this view is not correct.

 

[mfb]

In this case neither of the observers is moving with the object (the baseball)

Is time for the baseball relevant?

Check the problem statement - proper time of what is asked for?

 

[Tranceform]

Is time for the baseball relevant?

Check the problem statement - proper time of what is asked for?

Proper time between the two events. I guess then that since the events take place at the same place, the proper time is measured according to an observer inertial for those two places, which would be a stationary observer.

However if the time measured would have been only on the baseball going up (but not down), the proper time measured would have had to move along with the baseball?

 

[mfb]

Proper time between the two events. I guess then that since the events take place at the same place, the proper time is measured according to an observer inertial for those two places, which would be a stationary observer.

Right.

However if the time measured would have been only on the baseball going up (but not down), the proper time measured would have had to move along with the baseball?

What's the endpoint you consider here?
The highest point of the ball? Then neither is right, as proper time corresponds to the time you see in an inertial (not accelerated!) frame moving from one point to the other. As we do not consider general relativity here, the ball is accelerated.
Still the surface? Then see the original problem.

 

[HalfLostAndSearching]

Your understanding of time dilation is partially correct. Time dilation does occur when an object is moving, but it also occurs when an observer is moving relative to another observer. In this case, the third baseman running to cover the play is moving relative to the baseball and the catcher. Therefore, the third baseman would record a longer time interval between the two events compared to the other two stationary observers. This is because the third baseman is moving at a high velocity, and according to the equation for time dilation, their proper time (Δt) will be longer due to the factor of velocity (v) divided by the speed of light (c) squared. This means that the third baseman will perceive time to be passing slower than the other two observers. So, the third baseman will record a longer time interval between the two events than the other two observers.