# Relativity - space time interval between 2 frames

1. Sep 5, 2010

### accountkiller

1. The problem statement, all variables and given/known data

In frame S, Herman drops a pizza at the same time that Pavel drops a marker. In frame S', Alice is moving relative to their S frame - What is the space time interval she sees?
A. S' > S
B. S' < S
C. S=S

2. Relevant equations

Lorentz transformations is what we've been learning, but there's no calculations here.

3. The attempt at a solution

This is my second week learning relativity, so it's a bit difficult to figure out where to start on a problem. First of all, what does "space time interval" mean? I'm still trying to wrap my head around the idea of space and time being essentially one entity. Does it mean I'm trying to figure out the time interval that Alice sees the two events occurring, Herman ordering and Pavel dropping? Or the distance?

I'd appreciate a nudge in the right direction.

2. Sep 5, 2010

### G01

The space time interval is defined as:

$$c^2\Delta t^2-\Delta x^2- \Delta y^2- \Delta z^2$$

Here "delta t" is the time between two events in a certain frame. While "delta x-y-z" is the spatial distance between two events in the same frame.

In this case, your two events are the dropping of the two objects.

Call S the value of the interval in Herman's frame. The question is asking if Alice's computed value of the interval, call this S' (measuring all times and distances in her frame) is greater than, less than, or equal to Herman's value for the interval.

Think back to the lectures or look up the space-time interval in your text. How does the interval transform when you change from one frame to another?

HINT: The space time interval in special relativity is analogous to the length of a vector in classical mechanics. How does the length of a vector in classical mechanics change when you move from one coordinate system to another?