Question

For this problem, assume that any two frames have the same origin.

Consider two events with coordinates (t₁, x₁) and (t₂, x₂) in an inertial frame of reference S. The coordinates of these two events in an inertial frame S'moving to the right with speed u relative to frame Sare (t) and (a).
If we assume that the y and z coordinates are constant in the two frames, then x₂=x₁ is the space interval, more commonly known as distance, between the events as measured in frame S', and 21 is the space interval in the frame S. These two intervals are more commonly written Ax' and Ax, respectively. Similarly, t₂-t₁ is called the time interval between the events in frame S', and tot is called the time interval in frame S. These two intervals are more commonly written ∆x' and ∆x, respectively.
quantity is a mixture of space and time called the space-time interval s. To avoid possibly having to take the square root of a negative number, we usually talk about the square of the space-time interval, which is what you actually showed to be conserved in this part:
A pair of events are observed to have coordinates (0 s, 0 m) and (50.0 s, 9.00 x 10⁹ m) in a frame S. What is the proper time interval AT between the two events?
∆T=___

Answer 1

The question pertains to the calculation of the proper time interval (ΔT) between two events in special relativity, which is invariant across all inertial frames. However, the lack of velocity information for a specific reference frame where the events occur at the same location prevents a direct calculation using the provided event coordinates in reference frame S.

Step-by-step explanation:

The student is asking about the proper time interval (ΔT) between two events in the context of special relativity. Specifically, they have provided the coordinates of the two events in one reference frame, S, and are seeking to understand the time interval as measured in the frame in which the events occur at the same location. Proper time is a relativistically invariant quantity, meaning all observers in all inertial frames agree on its value for a given pair of events. In this case, the proper time interval is the elapsed time ΔT as measured in a reference frame where the two events occur at the same spatial location.

The formula relating space and time intervals in different reference frames is often derived from the Lorentz transformation, which respects the constant speed of light c. However, without additional context or specific velocities, we cannot use the Lorentz transformation to calculate ΔT directly from the given information about reference frame S.