Operational definition of 'before'

[Johnny5]

Long ago, I was talking with Tom Mattson about something, and he asked me what I meant, and I never did finish explaining to him what I meant.

 

Part of what I said was, that I operationally defined the binary relation 'before,' on the set of moments in time.

 

Since I didn't finish then, I will now.

 

An operational definition is a non-verbal experiment which somehow assigns meaning to some term.

 

The term here is 'before'

 

A little thought, and you will see that if you are an adherent to "absolute time" and "absolute simultaneity," that before is a binary relation on the set of moments in time.

 

At any rate...

 

Suppose you go to the moon, and drop two objects of different mass, say two spheres of equal radii, from the same height above the surface of the moon, simultaneously in the rest frame of the moon.

 

You will discover that they hit the ground simultaneously.

 

Thus, you can use that experiment to operationally define the term 'simultaneous' if you wish. It is your sensory perception which lets you know that you released them simultaneously.

 

You can use an experiment to operationally define 'before' instead.

 

Suppose you release one object in the rest frame of the moon.

 

It will fall to the surface of the moon, and strike the ground.

 

The moment in time you released the object is before the moment in time at which the object struck the ground.

 

Thus, an experiment serves to operationally define the term before.

 

You can then link that operational definition to a clock in the rest frame of the moon. In other words, a clock maps numbers onto moments in time in a frame.

 

But logically, the term 'before' is undefined. So you have this kind of thing going on:

 

Undefined term: before

 

Now you can construct a logical definition of simultaneity:

 

Definition: For any moment in time X, and any moment in time Y:

X simultaneous to Y if and only if (not(X before Y) and not(Y before X))

 

PS: Galileo pioneered free-fall experimentation, his experiments led him to definitions of speed, and acceleration. They can be found here:

 

Dialogue Concerning Two New Sciences by Galileo

 

 

In texts and figures on the third day pp: 153-160 Galileo defines uniform motion. In subsequent pages Galileo goes on to discuss accelerated motion.