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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137 views

Rigorous proof of Ampère's law from the Biot-Savart law

Let us assume the validity of the Biot-Savart law for a tridimensional distribution of current:$$\mathbf{B}(\mathbf{x})=\frac{\mu_0}{4\pi}\int_V ...
-2
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1answer
34 views

Find the indicated quantities from the given data [on hold]

This is a vector application. A rope is hung at both ends from a horizontal beam, and a weight m is suspended from it as shown in the figure. The left part of the rope exerts a force G at P, while ...
7
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0answers
93 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 ...
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1answer
169 views

What is the relationship between completeness of wave functions and completeness of Hilbert space?

In the lecture, my prof said that completeness means that any wave function can be constructed using an infinite number of "other" basis wave functions. This is very intuitive since this is nothing ...
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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. $ ...
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0answers
48 views

Representing propagators as Dirac delta functions [closed]

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 ...
10
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1answer
776 views

String theory from a mathematical point of view

I have a great interest in the area of string theory, but since I am more focused on mathematics, I was wondering if there is any book out there that covers mathematical aspects of string theory. I ...
0
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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 ...
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0answers
43 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 ...
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0answers
100 views

Literature request for books / review papers on gravitation, gauge theories and related mathematics [duplicate]

Similar to this reference, are there more such references / works [including textbooks] available in the literature? (A list would be greatly welcomed and appreciated.)
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7answers
7k views

Number theory in Physics [closed]

As a Graduate Mathematics student, my interest lies in Number theory. I am curious to know if Number theory has any connections or applications to physics. I have never even heard of any applications ...
1
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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 : ...
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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 ...
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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
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 ...
1
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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 ...
2
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1answer
120 views

Description of charged sphere with Heaviside function in cylindrical coordinates

I need to describe density of charge of uniformly charged sphere (radius R, total charge Q, position of centre (0,0,0)) with Dirac delta function and Heaviside step function. The hard part is to ...
2
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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 ...
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11answers
2k views

Is it possible for a physical object to have a irrational length?

Suppose I have a caliper that is infinitely precise. Also suppose that this caliper returns not a number, but rather whether the precise length is rational or irrational. If I were to use this ...
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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
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0answers
68 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 ...
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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 ...
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0answers
71 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. $f(A) = 2A$). ...
14
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5answers
1k views

What happened with Hilbert's sixth problem (the axiomatization of physics) after Gödel's work?

I'll write the question but I'm not fully confident of the premises I'm making here. I'm sorry if my proposal is too silly. Hilbert's sixth problem consisted roughly about finding axioms for physics ...
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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 ...
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8answers
3k views

Why are sine/cosine always used to describe oscillations?

What I am really asking is are there other functions that, like $\sin()$ and $\cos()$ are bounded from above and below, and periodic? If there are, why are they never used to describe oscillations in ...
14
votes
17answers
3k views

Can pure maths create new theories in physics or does the “idea” ALWAYS come before the math?

I am in a debate with a friend about the value of string theory in physics. He is concerned that we are wasting valuable intellectual and financial resources on a path that is fanciful and can't ever ...
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
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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 ...
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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
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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
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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 ...
35
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11answers
2k views

Examples of number theory showing up in physics [duplicate]

Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the trivial to ask but often unhelpful ...
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 ...
68
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12answers
22k views

Best books for mathematical background?

What are the best textbooks to read for the mathematical background you need for modern physics, such as, string theory? Some subjects off the top of my head that probably need covering: ...
0
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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 ...
14
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5answers
32k views

What is the math knowledge necessary for starting Quantum Mechanics?

Could someone experienced in the field tell me what the minimal math knowledge one must obtain in order to grasp the introductory Quantum Mechanics book/course? I do have math knowledge but I must ...
0
votes
1answer
60 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
67 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 ...
5
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2answers
373 views

Resources for theory of distributions (generalized functions) for physicists

I am looking for tutorials, articles or books containing theory of distributions in context of mathematical physics. Please suggest.
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3answers
2k views

Can quaternion math be used to model spacetime?

Quaternions are commonly used to model 4 dimensional systems where the quaternion consists of a real 3 dimensional vector and an imaginary scalar. So on the surface Quaternions seem well suited to ...
1
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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
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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 ...
28
votes
11answers
12k views

What is the logarithm of a kilometer? Is it a dimensionless number?

In log-plots a quantity is plotted on a logarithmic scale. This got me thinking about what the logarithm of a unit actually is. Suppose I have something with length $L = 1 km$. $\log L = \log km$ ...
0
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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 ...