Laws of Physics

Question

Here is a thought.

Let us assume the there is an infinite uni-directional line of balls. And it is being jumbled up again and again, randomly. (say by 'God'!)

I in my limited experience/capacity can 'observe' only 10 balls. And I see that the positions of balls alternate in pairs. Say if balls are numbered 1 to 10, ball at position 1 takes 2 position and 2 comes to 1's position and this keeps repeating. And similarly for balls (3,4) to (9,10) - I call this pattern a 'Law' - "Balls alternate with their immediate following neighbor if they are at odd position or with their immediate preceding if they are at even position". (That such a pattern will be there is guaranteed by the fact the line of balls is infinite and jumbling is random - an assumption about infinity and randomness)

Assume suddenly I'm able to observe 20 balls and the above rule breaks - so I come up with another cleverer rule that applies to all 20 balls and claim this is the 'new' universal law.

But in reality / in totality there is 'no' pattern - there is 'no' law - there are just local patterns that emerge in this game which is actually 'random'.

Is the above a valid way of looking at Physics? What are the arguments against it? How can we be sure that there are universal laws without having the capacity to observe the entire universe?

Answer 1

One of the key aspects of a theory is to specify its domain of validity in which it is self consistent. In your example of when we observe just $10$ balls, we have a “law” that is valid in that domain. So you may ask what the is point of the “law” when it isn’t valid for $20$ balls? Well, in the domain of validity we can use that law and build a framework and all will be well and good. For example Newton’s laws are not valid in the atomic scale, so it isn’t universal. But are they of no use? Definitely not!

But if you begin with the assumption of existence of some property (pattern) of your infinite chain of balls that is independent of where you start looking at it, and show that this predicts all other local patterns with as little additional assumptions, then that “law” is more fundamental. These are called symmetries of the system.

This is something amazing about the way nature is! Some laws that we conjured up to explain local behaviour somehow can be extrapolated to understand phenomena that the laws weren’t derived from, or to make new predictions that are then observed to be true!

How can we be sure that there are universal laws without having the capacity to observe the entire universe?

At the end of the day science is empirical. Thus our laws are actually hypothesis that haven’t been disproven yet. And a sign of a good law is the measure of its (domain of) applicability. Any self-consistent theory that doesn’t make observable predictions is technically not science.