The h Bar

11:15 AM

I'm wondering how are fundamental formulas or relationships in Physics established and justified. How did Galileo justify them in the past? I'm sure the inventor did many experiments, but how can he or she generalise the finite number of observations to a Physics law? Or are these laws not necessarily an accurate description of our world?

Can anyone help me? :)

John Rennie

11:25 AM

← 2 messages moved from Problem Solving Strategies

ACuriousMind

@yh05 That's the classic problem of induction. Our "Physics laws" are not statements that we know beyond all doubt to be true forever and in all cases - in fact, we know many of them to be "wrong" (or rather, not fully accurate). You probably learned Newton's laws and classical mechanics, but since Einstein we know that's only accurate at low speeds compared to the speed of light.

But that doesn't make classical mechanics useless - it's still good enough to predict and analyze a large number of situations

All models are wrong, some are useful.

yh05

So the laws can't be justified to be true and accurate for all (infinitely many) cases. Then why do the inventor (Example, Galileo) establish such laws and we accept these laws and use them?

ACuriousMind

11:44 AM

@yh05 Because it works. We don't believe in physical laws because someone said so, but because in our experience, they actually do model the world correctly in many cases.

Sometimes they're wrong, and then we correct them after we've figured out how to.

yh05

How do we check and confirm that it works? What do you mean by in many cases?

ACuriousMind

@yh05 We use the laws to predict what will happen if we run an experiment (or operate a machine, or whatever), and compare what we observe to the prediction.

When the prediction matches the actual result (within errors), it "worked"

Take the laws of electricity: We use them to build power grids and all sorts of amazing applicances. If we had gotten the physics of electricity wrong, these things wouldn't work as we intended them to

yh05

12:02 PM

There are Physics laws that are expressed using mathematical equation. How can we check and confirm that they work? Because it will take infinitely many experiments to do so.

ACuriousMind

@yh05 Are you trying to say that in order to show that $y(x) = x$ holds for all $x$ I need to measure infinitely many pairs $(x,y)$?

If so, then you're right, but that doesn't mean that finitely many experiments cannot increase my confidence that that relationship holds. Statisticians have developed many techniques to quantify how well a particular (finite) dataset fits to such an ideal function.

John Rennie

@yh05 we don't try to prove laws. We try to disprove them.

@yh05 I can't think of any physical law that has been proven, but I can think of lots that haven't been disproven even after a hundred years of trying.

yh05

In what situations do we disprove a physical law? For a physical law that is expressed as a mathematical equation, how do we decide whether we should discard the law if we conduct an experiment and obtain a number different from what is expected from the law?

John Rennie

12:18 PM

@yh05 Well suppose you measure the gravitational force between two bodies of mass $M$ and $m$ and you find it is not equal to $F = GMm/r^2$. That disproves the law. Yes?

Slereah

Hello

Fun fact in the late 19th century people tried out a variety of alternative gravitation laws

$$F(r) = \frac{GMm}{r^{2 + \alpha}}$$

That sort of stuff

Due to a variety of cosmological concerns

None of those works out great though

yh05

12:46 PM

@JohnRennie Yes.

But do we really obtain the exact equality from experiments?

ACuriousMind

No, of course not. What we obtain from experiment is that the results are consistent with that equality being true within experimental errors.

yh05

How do we decide if the results are consistent with the mathematical equality as described by the law?

And how can we be sure that all (past and future) experiments always produce consistent results as well?

ACuriousMind

@yh05 As I said, statisticians have developed many tools to analyze how well a particular dataset follows a particular mathematical relationship, called measures of goodness of fit

yh05

How is this done before Statistics is developed?

ACuriousMind

1:02 PM

E.g. if your predicted relationship is linear, then most intro physics lab will have you perform least squares regression

@yh05 Poorly :P But even without sophisticated statistical tools you can certainly compare your measured dataset against what your equation predicts, and if you're not "too far off", it's good.

The meaning of "not too far off" is of course dependent on the application domain - even with statistics. E.g. high-energy physicists use standards for "significant observations" that are much stricter than what most other fields use - but that's also because HE physicists also typically have much more data to work with.

Slereah

Statistics wasn't use that much in physics until the 20ht century, IIRC

They just went with their guts :p

yuvraj singh

Today my grandma was saying, you wear black cloth, so won, t get cold, when I try it, it works, can anyone tell me why thus happen,

Sorry for grammatical errors.

yh05

2:04 PM

What is the "not too far off"? How can a finite number of "not too far off" result generalise a law to hold true in all (past and future) situation? This seems to me that the Physicist assumes what to be discovered as pre-existing and so seeing some instances of the law at work must reveal that pre-existing law (created by god or whatever superior being(?) ).

Slereah

2:18 PM

Well that's how the human brain works in the end

Bayesian inference~

we try to notice patterns out of what we see

Secret

2:38 PM

A class in programming is a blueprint for making objects, which are like custom types that are made in terms of other predefined types along with functions
A universe which obeys the simulation hypothesis will mean all types are composed of some fixed collection of predefined types

Such is sufficient to enable emergence as new behaviour results from combining arrangement of these types
However, there may be types that are inherently unspecifiable in terms of code. There existence of at least one of these will disprove the simulation hypothesis

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