Math proofs in physics

How often do you use formal math-style proofs in physics?

I imagine it would mostly be in theoretical physics

Everywhere proofs using Leibniz differentials isn't simpler. Funwise and rigorwise, doing physics without math is like doing biology.

You don't do formal proofs in physics. Most physics professors will tell you 1/x is not a continuous function kek.

That pic is retarded, x requires y isn't the same as x = y, something like [math]x \impliedby y[/math] would be more accurate, which would give you the end result that being evil is a requirement for getting girls, thus proving the idea that nice guys dont get girls. So its still a lol XD math joke and the only reason to use girls = time * money is that the author of the pic is a retarded brainlet

this is the most retarded baby level bullshit level of proof i've ever seen and you should feel bad for wasting 24kb of your precious harddrive space to store it and feel even worse from the waste of electricity it took to upload it and have it stored on Veeky Forums and even worse further still for having us waste the electricity and bandwidth for having to store the image in our cache

fuck you cunt and learn how to do real math

You could though.

For instance, I could mathematically prove that change in direction of acceleration (but not parallel)does not mean a speed increase. Your acceleration is a vector with parallel and orthogonal components. if you work a little vector math on it, you eventually get down to an equation where acceleration and velocity depends on the parallel accel component which means 0 acceleration in parallel diretion = no change in speed

So Im asking how often physicists actually do that stuff

>x requires y isn't the same as x = y, something like [math]x\Leftarrow y[/math]
It would in fact be [math]x\Rightarrow y[/math], because if x requires y it means that it is sufficient to have x to have y but not that it is sufficient to have y to have x (which is what you wrote)

You would have to develop speed,acceleration,velocity, and orthogonal basis from first principles. Then you can prove properties based on those definitions and theorems. I've never seen a physics program that develops this way. They all use notions of vectors, vector functions and norm as the commonly knowledge analog. So there's nothing rigorous about the physics. Luckily, you don't need the same self consistency as math as long as you can justify your math through experiment.

mathematical physics is a real thing the experiments are to make sure the theory is correct

On a related note, I can't stand assholes that write "necessary and sufficient" instead of "if and only if"
One of the many reasons I hate statisticians

I'm not saying you don't use math in physics. I'm saying that the development of physical concepts aren't rigorously developed. Instead, it takes common notions or observation and explains it using math.

Contrast this with development of naturals, integers, reals from axiom. Then use those numbers to prove properties of sequences. Then use sequences to prove series and functions. In math, you could take something complex like the limit of a sequence and break it down to first order logic and set telations.

You can't do that with physics, because a majority of relations are empirical. There's no way to break them down to first principles because there are none.

>2018
>not saying 'or equivalently'

According to the first line, my dying grandfather should be swimming in pussy. Guess what: he isn't.

>There's no way to break them down to first principles because there are none.
Except there is. See Wightman axiomsof QFT, Atiyah axioms of TQFT and Seiberg-Moore axioms of CFT, etc.
The axioms of theories in physics are not any less mathematical. In fact all axioms in mathematics are more or less motivated or at least inspired by real world observations. There's just more freedom in what is considered "useful" axioms in mathematics than in physics.

Axioms are "first principles" because we say they are, not because they are. The axiomatic method is essentially 'if we say this, then that', but you are always under hypothesis.

You have to square both sides

What exactly is your point?
>Axioms are "first principles" because we say they are, not because they are.
Why can't we say whatever is [math]the[/math] first principle is the first principle? You do know that the Peano axioms are developed in order to reproduce one of the most basic real life observations about arithmetic and counting right? Or are you going to deny that basic rules of counting that you've (hopefully) learned in elementary school are "first principles because we say they are", and not because "they are"?
>The axiomatic method is essentially 'if we say this, then that'
And this is different from physics how? For instance: "if we say the laws of EM are invariant in all reference frames, then special relativity."
>but you are always under hypothesis.
What hypothesis? Physical hypotheses aren't any more "true" than mathematical hypotheses you know, since experimental observation is ultimately nothing more than induction and abduction. Read some Hume before you post please.

>What exactly is your point?
Some user said that there isn't any first principles, you said there was and they are axioms, my point is axioms are not first principles.

>Why can't we say whatever is *the* first principle is the first principle?
We already do, but anything we say can be a first principle. There are no first principles in the sense that if there were they would have to come before everything. The Peano axioms are very much primordial and basic but there is something under them that is more basic, primordial, 'first'.

>And this is different from physics how?
It's not necessarily, in fact it's the basis of all rational thought. I never even talked about physics; you're putting words into my mouth.

>Physical hypotheses aren't any more "true" than mathematical hypotheses you know
Yes that's true, that's exactly my point.

my bad.

Nothin' personel, friendo

>you said there was and they are axioms
No. I said there are axioms, period. I didn't say anything about first principles and as far as formal constructive QFTs are concerned, there's no difference between the two.
>There are no first principles in the sense that if there were they would have to come before everything
That's what axioms are. They come before everything in the theory. What do you think "everything" here means exactly? Do you take counting rules as more "basic" than the Peano axioms? Because in case you're not aware the latter implies the former so I don't see how the former can be more "basic" than the latter.
>I never even talked about physics
That's the topic of the OP. I had to assume that you were talking about physics or there's no point in talking with you.
>Yes that's true
So we agree? It seems you were arguing that physics doesn't have first principles a few posts prior but now you're arguing that it does and math doesn't. What exactly is your point pertaining to the OP again?

>No. I said there are axioms, period. I didn't say anything about first principles
Broeh, look at your own first post:
>"There's no way to break them down to first principles because there are none."
Except there is. See Wightman axiomsof QFT, Atiyah axioms of TQFT and Seiberg-Moore axioms of CFT, etc.

Nevermind my dude, I read the post you were replying to originally and I understand now. I guess I just wanted to disagree with you, but you provided good info.

Yeah I'm out studying Ayala's paper on the cobordism hypothesis in Starbucks so I couldn't reply for the past few hours, but I'm glad you've learned how to read in the meantime.

You've been arguing with someone else than you originally replied to.

>qft is all of physics
I will definitely look at your references but I doubt they are developed from first order logic. Without that, it's not good enough for me.

Yes you do, just in a less detailed way. Well at least most of my professors tell me we need to be rigorous, but it's stupid to re-invent the wheel or consider irrelevabt details. For example, using differentials to solve a problem is a heuristic to make computing integrals easy from a physical problem, lets say, the electric field of a distribution. To know which integral you need you use them, but in essense its just a compact way of writting a formal Riemann sum.

My issue with the OP is that they are fucking multiplying time and money. I get it's all for the joke at the end, but since when does the word and signify multiplication? Logically wouldn't it make more sense for it to be Time+Money?

It's good to be rigourous, especially in mathematical physics, but for the most part it's useless and counter-productive to do mathematics-styled proofs in physics.

you dont , even if its a physics textbook its not a 'proof in physics' its a mathematical proof . theoretical physics is just mathematics with the 'axioms' arising from experimentation\assumption ,like how at the beginning of every electrodynamics textbook they state the inverse square nature of the electric acceleration , the existence of attracting and repelling charges , the fact that these accelerations are independent and just add up (superposition). at that point in the first 3 pages all the physics of electrostatics is done and 90% of the text is all the mathematics which arises from these things .

a proof in physics is an experiment

I know what you mean. The problem is that your equations for charge distribution and electric potential and gauss's law are not based on axiomatic principles. If you can't take your problem and reduce it to set relations based purely on axiom and theory, it is non-rigorous.

I don't doubt the validity of the method of finding electric fields from direct sums, or for gauss's law, but it's all predicated on coloumbs law, which is strictly empirical. Therefore, there is no way to reduce the problem further.

In other words, it's not enough for the math of physics to be consistent, it must also be able to be built from the ground up. To my knowledge, no such attempt has been made.