phil 105 fall lecture xx

1. Relativity of Simultaneity and the Laws of Nature

It might seem that the relativity of simultaneity is just a weird fact about light, not to be taken literally – but that would be a misconception.

How can we give any substance to the ideas of distance, duration and simultaneity?

Via the laws that govern the development of events in time and space –
Huh?

That can mean a number of things, but one very direct way to understand it is to observe that what makes a time or distance measuring device – a 'clock' or 'ruler' – good is that it is strictly periodic or rigid according to the laws of physics.
Put another way, one way that laws give meaning to spatio-temporal ideas is that we implicitly use the laws to infer times and distances from our observations of clocks and rulers.

The speed of light is constant implies that the relativity of simultaneity is a fact about the laws:

What I mean is that the speed of light measured using any clocks and rulers that are good according to the laws, is the same in all frames.

So suppose that the laws allowed some criterion of simultaneity such that light reached both targets simultaneously in both frames.
Then in the frame of the ground

since the lamps light simultaneously, and the light from each arrives at the targets simultaneously, the time taken to reach each target is the same,
but the rear target is moving towards the light and the front target away, so the light travels further to reach the front target than the rear,
Hence the forward travelling light travels faster than the rear travelling light – contrary to the constancy of the speed of light.
Therefore, given the constancy of the speed of light the laws cannot allow absolute simultaneity.

So the relativity of simultaneity is not just a weird fact about light, and not just a matter of subjective psychology, or appearance, but goes 'all the way down' to the bottom of our grasp on time and space – it is written into the laws.

2. Spacetime

Since there is no fact about which events are simultaneous, there is no absolute way to divide universe into space and time, no absolute spatial slices 'at a time': there is only their inseparable mix – spacetime.

Spacetime (time up the page and space across the page) is divided up differently relative to different standards of rest. 1, 2 and 3 represent the worldlines of three different objects – the diagram shows which events are simulataneous relative to each.

We can pick any object (even hypothetical objects) as a standard of rest – so we can talk about the motion or rest of any other body relative to it.

So let 1 be such a body:

The horizontal lines represent events that are simultaneous relative to 1
The blue line represents the worldline of a 'particle of light'
2 and 3 represent two bodies in motion relative to 1 – but not each other.

Or let 2 be the standard of rest:

3 then is at rest relative to 2

The red dashed lines represent events that are simultaneous relative to 2 (and 3)
Clearly (distant) events that are simultaneous relative to 1 are not simultaneous relative to 2.
By convention, the planes of simultaneity are drawn so that the light worldline bisects the angle between them and the worldline of the reference body.

Phil 105: Science and Philosophy - Fall 2004 Lectures

!You will be sorely disappointed if you think that these are a substitute for attending class!

Topic Five: Spacetime

Lecture 22 – Spacetime (11/10/04): Thorne Ch 1