DO NOT USE THIS TAG just because your question involves math! If your question is on simplification of a mathematical expression, please ask it at math.stackexchange.com The mathematics tag covers non-applied pure mathematical disciplines that are traditionally not part of the mathematical physics ...

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7
votes
0answers
81 views

Reading differential forms

When, usually in text of physics or concerning thermodynamical aspects of chemistry, I find notations such as$$\mathrm{d}f=g\,\mathrm{d}t$$ I always interpretate it as ...
0
votes
1answer
59 views

Will Gödel's theorem strike a death blow to the future of science? [duplicate]

According to Gödel's incompleteness theorem, no matter how many statements you prove, you will always have a set of statements not proved. Does this imply that some time in the future, scientific ...
1
vote
0answers
48 views

Representing propagators as Dirac delta functions [on hold]

I have found online, in particular on the wolfram site, http://mathworld.wolfram.com/DeltaFunction.html, certain identities that allow one to represent a delta function as limits. Of particular ...
6
votes
0answers
42 views

Experimental Hopf fibrations

Recently I read a paper where the authors experimentally constructed a Hopf fibration - that is, they created a quantum system where the nematic vector field of the system had a non-zero Hopf ...
1
vote
1answer
73 views

Does a continuum exist in reality? [closed]

There are uncountably infinite sets in mathematics. Such as the number of points in the interval [0,1] Or the set of all integer sequences. Do these have a physical reality? In case this helps : ...
1
vote
0answers
21 views

Calculating sieve screen size [closed]

I have a lot of mixed Lego, is it possible to calculate sieve screen dimensions to sort out particularly lego categories like bricks or plates ? So you can say if I use this screen size and ...
1
vote
2answers
58 views

Self similar functions

I'm trying to undestand the self-similarity as an invariance of a function under certain transformation. For example I think $$f(\lambda x)=\lambda^\epsilon f(x)$$ could be understood as a ...
1
vote
0answers
61 views

Intuitions for the simplest model in which the evolution of the laws of nature arises from the natural selection of structures [closed]

The problem I’m trying to solve can be described as To create the simplest model possible in which the evolution of the laws of nature arises from the natural selection of structures. This approach ...
1
vote
1answer
66 views

Problem arising from quantisation of e.m. field

In my studies on the quantisation of the electromagnetic field I've come across a small calculation that I wasn't able to reproduce. Remember the following: In the Gupta-Bleuler method to quantize ...
2
votes
0answers
50 views

Why are we allowed to decompose a function of two variables $f(x,y)$ into the form $\sum_n^\infty c_n(y)\psi_n(x)$? [duplicate]

I apologize if this is more mathematical than physical, but this issue always seems to come up when I am solving physics problems. Given a function of two variables $f(x,y)$ let us decompose it into ...
0
votes
0answers
43 views

Why do many equations need squared powers? [duplicate]

It seems that an equation factor must be “squared” as a convenient approximation to balance out some other series of factors invisibly . Might $E=mc^{1.95}$ work as well as $E=mc^2$? Might ...
2
votes
1answer
150 views

Are there any physical theories that use unsolved mathematics [closed]

In a talk Gödel and the End of Physics by Steven Hawking, he argues all mathematical problems are also physical problems for example: Given an even number of wood blocks, can you always divide them ...
1
vote
1answer
132 views

Why is the logarithm of the number of all possible states of a system differentiable?

Temperature of a system is defined as $$\left( \frac{\partial \ln(\Omega)}{ \partial E} \right)_{N, X_i} = \frac{1}{kT}$$ Where $\Omega$ is the number of all accessible states (ways) for the system. $ ...
1
vote
0answers
67 views

QFT and lack of rigour [duplicate]

How can physicists compute path integrals and such if there is no rigorous definition of it? If they can get an definite answer, there must be some method they used, so what is meant when ...
1
vote
0answers
55 views

Start learning Math for all my Physics [duplicate]

I know Physics but I don't know Math for this physics. Let me explain. When I say I know physics I mean I know stuff like Einsteins Special & General Relativity, Time Dilation, Gravitational ...
4
votes
0answers
70 views

Why are so many relationships in physics described by equations? [closed]

Consider $f$, some mapping between two ordered subsets of the natural numbers, $A$ and $B$. I see two ways $f$ can be expressed. The first way is an equation that defines $f$ (i.e. $f(A) = 2A$). ...
1
vote
1answer
72 views

Feynman's question on the mathematical machinery underlying nature [duplicate]

Physicist Richard Feynman said in his lectures "It always bothers me that according to the laws as we understand them today, it takes a computing machine an infinite number of logical ...
1
vote
1answer
131 views

$\pi$ and quantum mechanics [closed]

I read paper of Friedmann and Hagen Quantum Mechanical Derivation of the Wallis Formula for $\pi$ I am not a physicist but I know how to solve Schrödinger's differential equation for the hydrogen ...
0
votes
1answer
24 views

How to calculate turning acceleration from a compass? [closed]

I have degree and timestamp and want to calculate the turning acceleration. I what to trigger some code when the compass is turning fast. Is there a mathematic way to get an turning acceleration ...
0
votes
3answers
119 views

Can a particle have no instantaneous velocity at all points of the path taken but a finite average velocity?

I have a question on kinematics. Say the path traced by a particle is given by a Koch curve or Koch snowflake. Now consider the particle starts from some arbitrary point $A$ on the curve and ...
1
vote
2answers
156 views

How $\pi$ is derived from quantum mechanics

I came across this article New Derivation of Pi Links Quantum Physics and Pure Math in which they discuss about a recent discovery of deriving PI from physics. I am not a physicist or a mathematician ...
0
votes
0answers
44 views

Can we choose any dense subset of $\mathbb{R}$ to represent time?

Is there any particular reason for choosing time to be real? Is choosing time to be represented by say rationals going to give problems? Can someone give a physical reason that requires it to be ...
1
vote
1answer
53 views

Are there Non-conformal maps encountered in Physics?

We always encounter Conformal maps in Physics, may be they are easier to study, but are there Non-Conformal transformations encountered in Physics anywhere? if they are encountered, where are they ...
2
votes
1answer
74 views

Cancelling the partial of a coordinate, $\partial q$, with the element of a coordinate, $dq$ in Physics [closed]

I've seen in many books, things like this ( I will be simple ): $$\int \frac{\partial f}{\partial q} dq=\int df$$ where $f$ is a function of $q$ and other coordinates. I just axiomatically assumed ...
2
votes
2answers
154 views

Why is $\pi$ the value it is? [closed]

Why is the value of $\pi$ 3.141592...(etc.)? Is it a fundamental property of our universe? Or does it follow from our definition of what a circle is, or does it otherwise follow from the way we ...
2
votes
3answers
109 views

Why does Griffiths define the complex inner product differently? [closed]

I have just now noticed that Griffiths (in his book Introduction to Quantum Mechanics) defines the complex inner product as $\big<z,w\big>=\sum_{i=1}^n\overline{z}_iw_i$. In all mathematics ...
0
votes
0answers
37 views

Given a dimension of a known object in the image, how can we calculate the dimension of other objects in the same image ?

The question considers a very specific scenario in which we have an image with let us say, two rectangle objects. We know width and height of one object. How can we calculate the dimensions of the ...
0
votes
1answer
58 views

Causality and response functions

Referring to David Tong's notes on Electromagnetism, page 29 (of the PDF, numbered 183), section 7.5.4; It is proved that the frequency domain response function (in this case describing the ...
1
vote
2answers
66 views

See the opposite wall on a mirror [closed]

I'm in tenth standard. This is a higher-order-thinking-skills Q I found in a book. One is supposed to use laws of reflection ($\angle i = \angle r$). You can also use mathematical concepts like ...
1
vote
0answers
27 views

Mathieu equation and instabilities

Consider the Mathieu equation $$ \tag 1 y'' + (A -2q\cos(2t))y = 0, $$ How does it provide instabilities for small $q << 1, A > q$? I don't understand this because as the result of ...
0
votes
1answer
87 views

Book on gamma functions with applications in physics

I have heard that in my next semester, our quantum mechanics teacher will be giving a great emphasis on difficult integrals with the most of them having to do with gamma functions. Does anybody know ...
2
votes
2answers
212 views

Can all of physics be described by simple math? [closed]

Recently I was browsing through A Dynamical Theory of electromagnetic field by Maxwell and wondered because the paper did not seem to include any vector calculus or any vectors. I thought of the ...
0
votes
0answers
33 views

Mathematics involved in string theory [duplicate]

As an amateur mathematician and lover of the sciences I have a well working knowledge of classical mechanics, quantum mechanics, general relativity, quantization, and so on... But recently I've been ...
2
votes
1answer
89 views

How to prove that sum converges to integral using density of states?

Essentially, I would like to prove $$ \sum_k f(k) \to \int f(k) \rho dE \tag{1}$$ where $$ \rho = \frac{dk}{dE} \tag{2}$$ is the density of states and $k \to \infty$. The model is that there is a ...
1
vote
0answers
78 views

Any other mathematical fields in physics than $\mathbb{R}$ or $\mathbb{C}$? [closed]

In physics, we usually use the real number field $\mathbb{R}$ or the complex number field $\mathbb{C}$. Does any other field find use in physics too?
1
vote
2answers
128 views

Reference for mathematics of statistical mechanics

I'm looking for materials (books, articles, etc) which focus ONLY on the mathematics of statistical mechanics (as I have no background in physics). The materials may have some simple explanations or ...
2
votes
1answer
127 views

Why Newton wanted lines to be generated by continued motion of points rather than by apposition of parts?

The following passage has been extracted from the Newton's (John Stewart's English translated version) "Sir Issac Newton's two Treatises: Of the Quadrature of Curves, and Analysis by equations of an ...
1
vote
1answer
31 views

Formula relating sum of values of a function to its integral

I came across the above formula in some quantum mechanics lecture notes explaining the Casimir effect. Anyone seen it before if so could you please tell me its 'name'. B refers to the Bernoulli ...
13
votes
5answers
832 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
4
votes
2answers
54 views

Pointwise and uniform convergence. Examples from physics

I am a first-year mathematical student, and from a mathematical perspective I understand the difference between pointwise and uniform convergence of sequences and series of functions. However, I have ...
-2
votes
0answers
44 views

Subject is Maths that would complement Physics? [closed]

Suppose Math has 5 sub parts- Analysis: Analysis, Complex Analysis, Measure theory and integration,Functional Analysis Algebra: Group Theory, Vectors space-rings-modules, Galois, Algebra Number ...
2
votes
2answers
203 views

Mathematics needed for string theory [duplicate]

I'm interested in cutting edge string theory studied by research physicist. I'm wonder what mathematics is needed and how far am I in terms of mathematics background needed and how much more ...
-4
votes
3answers
132 views

Can pure mathematics alone give proofs in science [closed]

I reasoned in my last post that because of science's nature of induction and falsifiability, it is impossible to give a theorem in science, unlike in mathematics. It is because even when a scientific ...
0
votes
1answer
80 views

Numerically summing a divergent series [duplicate]

Say I have a closed form expression for a divergent series and I can calculate as many terms in it as I want. What options have I got to obtain a meaningful result for this divergent series?
1
vote
1answer
103 views

Trajectories piecewise smooth?

In my studies of calculus and real analysis I have found the proofs of several theorems, commonly used in physics, such as those concerning the conservativity of fields, for example like If ...
1
vote
0answers
42 views

Dirac delta function equation intuition and proof [duplicate]

What is the intuition and where should I find proof of this equation (do not know what its name is). It is used to derive Gauss law from Newton equation. $${\nabla \cdot \Bigg ( ...
6
votes
5answers
727 views

Is it possible to have infinite combinations in reality?

On a yoghurt advert, the voiceover claimed that you have infinite combinations with it. However, given that there is a finite amount of matter, is it possible to have infinite combinations with the ...
2
votes
0answers
87 views

Convert discrete sum to principal integral

I'm studying IQHE beginning with Laughlin's famous gauge argument. I referred to his Nobel Lecture, in which he mentioned a paper that enlightened him. It is Phys.Rev.B.23.5632(1981) which talked ...
1
vote
0answers
63 views

Is it possible to express continuous growth without using transcendental numbers? [closed]

Continuous growth is typically expressed using some variant on $A = Pe^{rt}$, I understand where $e$ comes from in general, it is the amount something grows in a given time interval, when continuously ...
3
votes
1answer
87 views

What really are perturbation expansions?

I'm unsure if this question belongs here or at Math.SE, but since I've got to it by reading some articles about Physics I'm going to post it here anyway. In this particular article (Theoretical ...