How does Physics relate to Math

[uzair2010]

Hi everyone,

i have an essay to do on HOW DOES PHYSICS RELATE TO MATH

i need a little help to start the essay

i dont know where to start it from and what to write in it

CAN ANYONE PLEASE HELPPP MEEEEE

Thanx, Uzair

[Bignose]

A proper physics text should be chock full of math. By proper I mean a book designed to teach and/or discuss physcsis, not one of those popular science trying-to-teach-advanced-physics-concepts-using-analogies-and-pictures books.

 

Whether it is a very basic level high school algebraic-based physics, to a typical university level text full of calculus, to the advanced graduate level texts on string theory or general relativity or any of the other thousands of advanced physics topics, they will all have quite a lot of math in them. Just as one suggestion, check out Roger Penrose's The Road to Reality: A Complete Guide to the Laws of the Universe; it is going to have more math describing physics in it than you've probably ever thought possible.

[Klaynos]

I like to think of it as...

 

Maths is the language of physics...

 

It's the only true way you can get predictive theories...

[ajb]

You should also know that there has been much cross-fertilisation between mathematics and physics. Many ideas in mathematics arise from the study of physics; calculus and geometry are two prime examples.

 

What is also fascinating is applying physical ideas and notions to mathematical problems. This has been very important in developments in low-dimensional topology, differential geometry and knot theory where ideas from quantum field theory have been employed. Witten's reformulation of the Jones polynomial and Donaldson's theory are notable examples.

[ydoaPs]

Hi everyone,

i have an essay to do on HOW DOES PHYSICS RELATE TO MATH

i need a little help to start the essay

i dont know where to start it from and what to write in it

CAN ANYONE PLEASE HELPPP MEEEEE

Thanx, Uzair

 

Physics is our description of the universe. Mathematics is the language in which we made the description.

[the tree]

Classical mechanics, perhaps the most important part of physics in terms of practical application, came about in a bundle with calculus. Isaac Newton came up with calculus with the intent of describing physical laws but being maths it naturally turned out to have applications in economics, sociology etc etc. That's an example of something being born in physics but becoming a major part of maths.

 

Complex Numbers however, were thought up merely as a way of thinking about polynomials (and some other stuff) but many many years later they turned out to be absolutely essential in electrical engineering.

 

Again, when it came to thinking about polynomials, Group Theory came about with nothing but pure maths in mind (perhaps gun fights were also on Galois' mind at the time, but that's not entirely the point); yet well after our perception of the universe had been twisted beyond all recognition dozens of times since Group Theory was first proposed, it was used to predict "super-symmetry", the existence of previously unknown types of particle and it's now completely fundamental to String Theory.

 

Someone with greater knowledge of either subject could surely come up with more examples of one discipline spilling into the other.

 

Science in general requires maths to make predictions. Maths, could possibly survive without science giving it ideas all the time but real physical problems have inspired a lot of maths.

[uzair2010]

I asked my teacher if i can write the whole essay about: "MATHS IS THE LANGUAGE OF PHYSICS" and he said OK

Now, for bonus marks,i have to find something common in PHYSICS and COMPUTER ENGINEERING...can you guys help me with that please

and thanxxxxx a lottt all of you for the help with MATHS

[ajb]

 

Complex Numbers however, were thought up merely as a way of thinking about polynomials (and some other stuff) but many many years later they turned out to be absolutely essential in electrical engineering.

 

Complex numbers are also fundamental in quantum mechanics, solutions of the time dependant Schrödinger equation are necessarily complex. We need complex numbers to describe unitary evolution.

 

 

Again, when it came to thinking about polynomials, Group Theory came about with nothing but pure maths in mind (perhaps gun fights were also on Galois' mind at the time, but that's not entirely the point); yet well after our perception of the universe had been twisted beyond all recognition dozens of times since Group Theory was first proposed, it was used to predict "super-symmetry", the existence of previously unknown types of particle and it's now completely fundamental to String Theory.

 

By predict, you are referring to the no-go theorem of Coleman and Mandula(1967). It states that you can not combine internal symmetries and space-time symmetries in anything but a trivial way. Their work was based on classical Lie groups.

 

Haag, Lopuszanski, Sohnius (1975) showed that you can get round this if you include anticommutative generators of the symmetries, i.e. extend to a super Lie algebra.

 

Gol'fand and Likhtman were the first to extend the Poincare group to the super Poincare group in 1960, but as the cold war was raging this work was generally not appreciated or even known in the West.

 

None of the above works constructed a supersymmetric theory, I think the first was the superstring of Ramond, Schwarz and Neveu. I am not sure if they realised it was supersymmetric or just did not appreciate that fact. However, I think it was Wess and Zumino who really were the first to construct supersymmetric theories.

[the tree]

I asked my teacher if i can write the whole essay about: "MATHS IS THE LANGUAGE OF PHYSICS" and he said OK

Now, for bonus marks,i have to find something common in PHYSICS and COMPUTER ENGINEERING...can you guys help me with that please

and thanxxxxx a lottt all of you for the help with MATHS

I think your own title it about as heavy a hint as you can reasonably be given.

[fattyjwoods]

Well, physics talk about forces and stuff like that right?

 

Think about the distance, time graph.

 

To find the distance of something you multiply the speed and time.

To find the speed you divide the distance by the time

To find the time you divide the distance by the speed.