# Proof in physics

1. Aug 24, 2008

### evagelos

is a proof in physics equal in strength with that in mathematics?

in mathematics we have at one end an ordinary proof and at the other end a formal proof.

how would aformal proof in physics look like,an example would help.

I suppose that the validity of a proof in physics could be checked by an experiment but in the case that we have no experiment what happens??

Thanks

2. Aug 24, 2008

### Defennder

I don't understand your distinction between an ordinary and formal proof in mathematics. In physics, every experiment done to verify a theory is necessarily theory-laden, which means to say the results of the experiment requires interpretation through the lenses of some physical theory. It isn't as simple as what Popper's falsification principle in induction makes it out to be.

3. Aug 26, 2008

### evagelos

lets take in steps:

.................can we put a problem in physics into quantifiers form like we can do in mathematics??

4. Aug 26, 2008

### DaveC426913

No.

Physics attempts to describe reality. Our grasp of reality is arbitrarily blurry.

For example, you can never prove that F exactly equals ma because those are all measurements, which have margins of error and measurement. Nor could we ever hope to demonstrate - even in principle - that there isn't some tiny bit of energy leaking into some other dimension.

5. Aug 27, 2008

### evagelos

when you say...............no................you must have some arguments to support your
...........no

I an sorry but your argument about equality between F and ma is irrelevant to the above.

correct me if iam wrong

6. Aug 27, 2008

### DaveC426913

??

We do. It's called mathematics. Quantification, by definition, means applying numbers to something.

I do, otherwise you wouldn't have been able to address it :uhh::
How is it irrelevant? That is about as definitive and succinct an answer as you can get. And I can't think of any way to elaborate on it that isn't just repeating myself.

Is it possible you were thinking the correct answer was somehow trickier?

Maybe we can root out some of your assumptions and possible misconceptions. I think that may be the source of these odd questions to which you don't like the answers.

Perhaps you could give an example of something that physics seems to have "proven" - or could prove.

Last edited: Aug 27, 2008
7. Aug 27, 2008

### granpa

In math certain things are true by definition. we know they are true. In physics the best we can hope for is to know beyond a reasonable doubt (through experimentation)

8. Aug 27, 2008

### HallsofIvy

Notice, by the way, that all statements in mathematics are of the form "If A then B". We make no claim as to whether "A" or "B" itself is true, only that the implication is valid. That is fundamentally different from physics where all statements must be based on experimental evidence.

9. Aug 27, 2008

### evagelos

where is the "if A then B" form in the statement ; .....no object belongs to the empty set? Written in quantifier form

for all x ~xεΦ where Φ is the empty set.
Another statement which can be proved is:...nothing contains everything

10. Aug 27, 2008

### evagelos

an example of quantification in maths could be the following:

for all a : a>0====> (a^2)>0. a belonging to real Nos

a similar one in physics could be the following:

for all masses between 1 and 5 Kgs and for all forces F there exists a unique acceleration a

such that .......F= ma where F and a are vectors

Another one could be :

for all M masses and for all m masses and for all r distances between M and m there exists a force of magnitude ........F= [(KMm)/r^2] acting along the r direction.K a universal constant

11. Aug 27, 2008

### DaveC426913

OK, you've just stated (a special case of) Newton's 2nd law.

What's unsatisfactory about that?

12. Aug 28, 2008

### evagelos

so ,a problem in physics can be put in a quantifier form and in our case we have:

...................(m)[ 5>= m >= 1=====> (F)E!a( F=ma )]..........1

where (m),means for all m, E!a means there exists a unique a ,F and a are vectors.

Formula 1 can be proved using Newton's 2nd law, which law we can put in the following quantifier form:

.......... (m)[ mε( 0, 00)====>(F)E!a( F =ma)]

Where 00 means infinity and masses forces and reference frames all being Newtonian

13. Aug 28, 2008

### Defennder

There's one problem with the notion of proof: You never know when your theory might be superseded. Although this is often over-cited, Newton's laws were superseded by Einstein's. You can't make a generalising statement in physics which is essentially formally proven since there is always a possibility that it would be overtaken by a newer one.

In maths, once you have a proof, you can't be mistaken unless the proof is flawed.

P.S. You ought to cut down on the "...". It makes it look as though you were half-asleep while posting.

14. Aug 28, 2008

### DaveC426913

This is what I'm sayin'. Maybe he'll like it more coming from you.

15. Aug 28, 2008

### granpa

arent those things true by definition?

16. Aug 28, 2008

### evagelos

in the book of Patrick Suppes Axiomatic Set Theory in page 21, he proves as his 1st
theorem¨

~xεΦ

Paul R.Halmos in his book called Naive Set Theory, in page 6 he proves that:

'nothing contains everything'

So the statement that: that all statements in mathematics are of the form "If A then B".
is wrong

17. Aug 28, 2008

### humanino

I don't know those people but this is flat wrong. There is nothing in the empty set. Forget about obscure books you are the only one to have. Please define the empty set for us and show us how "anything" is in "nothing".

18. Aug 28, 2008

### granpa

or rather, isnt the first of those true by definition?

19. Aug 29, 2008

### evagelos

still that does not change the fact that the statement:

that all statements in mathematics are of the form "If A then B".'

Is wrong

20. Aug 29, 2008

### humanino

This is a disagreement on the interpretation of what mathematics are. Ultimately, you can have any mathematical statement implemented on a computer which uses (at least in principle) only NOR gates, and that is equivalent to only "if A then B" statements. But what is interesting about this interpretation (a contrario to other proposals here in this discussion, at least at the level they were presented) is that mathematics indeed does not care whether A is true or not. In particular, it is most often relevant to Nature and physics that A is strictly wrong, but approximately true in which case, if the statement "If A then B" is true and "B is relevant", then "If A then B" is useful even though A is strictly wrong.

Did I loose you by now, or do you agree ?