Spacetime intervals

Good Evening

In the Special relativity course on the chapter about spacetime intervals, there is a form of the equation for the spacetime interval that looks like this: (Δt^2) > (Δx/c)^2 where the time interval that separates two causally related events A and B (A caused B) is greater than the time that light would need to propagate to reach event B from A, but if that's the case then doesn't that mean that the light bolt would "miss" event B since it will pass B's location before B happened?

Easy Math Editor

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`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
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Comments

@Brilliant Mathematics

David Stiff - 5 months, 4 weeks ago

@Quantum pixel You are interpreting this condition correctly. A light beam traveling from event A arrives at (and passes) the place where event B will happen before event B actually happens.

If $\Delta x$ is the distance between two events A and B, then $\Delta x/c$ is how long it takes a beam of light to travel from the position of one event to the position of the other because light travels with speed $c.$

The time $\Delta t$ between events A and B has no relationship to $\Delta x$ in general, but if event B follows from event A, then the time between the events is constrained. For example, event A might be someone picking up and glass, and event B is the glass breaking because the same person dropped it. In this case, $(\Delta t)^2 \geq (\Delta x/c)^2.$ This condition prevents such paradoxes as an observer (moving relative to the person in event A) who sees the glass break before it was picked up.

In the future, if you have concerns about a problem's wording/clarity/etc., you can report the problem. See how here.

Aaron Miller Staff - 5 months, 3 weeks ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$