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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-1
votes
0answers
29 views

How many pieces of paper to the length of the observable universe? [on hold]

Correct me if I'm wrong, but if you fold a piece of paper to the point where it's a long stain of atoms, you would need 601 pieces of paper to get to a light-year. That would mean that you would need ...
1
vote
2answers
94 views

Is multiplication in physics purely mathematical or is there a physical explanation to it?

Here is what I mean: We always use mathematics in physics, which is pretty powerful, but I still need to ask whether multiplication in physics has a better explanation to what I already think. For ...
0
votes
1answer
57 views

Exact solution of Qubit Decoherence using Transfer Matrix

I'm going through a particular paper on decoherence: Exact Solution of Qubit Decoherence models by a transfer matrix method I'm having trouble understanding a particular step in the mathematics ...
4
votes
1answer
100 views

Integrating elements of a Lie group with respect to parameters of the corresponding Lie algebra

I am working with an operator $\textbf{M}$ that is represented by the Lie group SO(1,3), thus it can be written as, $$ \textbf{M} = \exp{\textbf{L}} $$ where, $$ \textbf{L} = \begin{bmatrix} ...
1
vote
0answers
31 views

Derivative with respect to a difference of independent variables

I am dealing with an equation from nonlinear acoustics (Khokhlova-Zabolotskaya-Kuznetsov equation) where a strange term (for me as a mathematician) is used. The equation looks like this $$ ...
2
votes
1answer
163 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 ...
1
vote
0answers
36 views

Relevance of pure mathematics vs statistics to physics [closed]

For someone currently studying physics, with an interest in experimental physics, would pure mathematics or statistics be more relevant?
0
votes
0answers
6 views

How does the Dirac delta function operate when its peak is at the boundary of an integral? [migrated]

As far as I can tell the Dirac delta function in an integral picks the value of the multiplying function at the peak provided the peak is within the boundary, i.e. $$\int^{a+e}_{a-e} \delta (x-a) ...
20
votes
9answers
2k views

How to interpret the units of the dot or cross product of two vectors?

Suppose I have two vectors $a=\left(1,2,3\right)$ and $b=\left(4,5,6\right)$, both in meters. If I take their dot product with the algebraic definition, I get this: $$a \cdot b = 1\mathrm m \cdot ...
4
votes
0answers
71 views

Mutual $E$ force due to charged coaxial rings [closed]

I found the following question in a good physics book I was solving and although this is a computer problem, I wonder if it can be done without using computers. $Q.$ Find the force of attraction ...
1
vote
0answers
44 views

Can someone help me to do the math? [duplicate]

This might seems off topic or something, but I am a middle school student and i'm really into Quantum Field Theory and String theory and every video on youtube or article on the internet shows only ...
1
vote
1answer
42 views

Book to study Dirac delta function from a physics point of view [duplicate]

I am a beginning physics graduate student. I am often bewildered by the strange properties of the Dirac delta function such as: $\delta (a x)= \frac{1}{a} \delta (x)$ The derivative of $\delta (x)$ ...
13
votes
3answers
2k views

Book covering differential geometry and topology required for physics and applications

I am a physics undergrad, and interested to learn Topology so far as it has use in Physics. Currently I am trying to study Topological solitons but bogged down by some topological concepts. I am not ...
1
vote
0answers
20 views

Can you help me solve this using the current value Hamiltonian? [closed]

Okay, so I am getting a little stuck on this question, I will post it and then tell you how far I get. $$ max - \int_0^2 (x^2 + u^2)e^{-0.03t}dt\, $$ $$ x' = x-2u $$ $$ x(0) = 3 $$ $$ x(2)free $$ ...
0
votes
1answer
42 views

Assumptions in physics for Helmholtz decomposition

A version of the Helmholtz theorem says that, under opportune assumptions on the vector field $\boldsymbol{F}:\mathbb{R}^3\to\mathbb{R}^3$ and on $V\subset\mathbb{R}^3$ the following identity holds: ...
24
votes
6answers
63k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors ...
1
vote
2answers
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
-1
votes
2answers
95 views

Disproving the mathematical universe hypothesis [closed]

The mathematical universe hypothesis is claimed by Lee Smolin to be falsifiable: [...] it is easy to disprove the mathematical-universe hypothesis. Simply exhibit one property of the natural world ...
5
votes
2answers
442 views

Proof of Ampère's law from the Biot-Savart law for tridimensional current distributions

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
votes
0answers
43 views

Seeking masters degree advice [closed]

I am graduating this semester with a bachelors in physics. My goal is to do theory in my graduate level course work. The problem I am in now is that I missed the deadline to take the physics GRE (I'm ...
1
vote
1answer
72 views

Why do people care about Mathieu groups and related things? (Something about monstrous moonshine)

Before I begin, let me say I don't know anything about what I am asking. This morning for somewhat random reasons I decided to google moonshine and related things. As it were I discovered my ignorance ...
0
votes
2answers
54 views

Can a laser beam be captured in prism?

is there a way to shoot a laser at a prism (or something) and have it glow when the laser hits it? I want to make a small box with a small hole in it. With the prism in the box, when the laser is ...
3
votes
1answer
73 views

Existence and Uniqueness of Newton's Laws

I'm reading Arnold's book on classical mechanics. This is kind of a dumb question, but I'm having problems understanding his explanation for existence and uniqueness of Newton's laws. On page $8$ he ...
-2
votes
2answers
62 views

What Are Logarithms? [closed]

I'm just starting out and have a limited area of mathematic study and have no idea how to do logarithms. I know that they're involved in physics and want to progress. Could someone help?
1
vote
0answers
50 views

Metric defining an sphere [closed]

I want to find for which cases this metric can define an sphere: $$\frac{1}{P^2}\left(\mathrm d\theta^2+\sin^2 \theta\; \mathrm d\phi^2\right)$$ where $P=\sin^2 \theta+K\cos^2 \theta$, with $K$ the ...
1
vote
3answers
82 views

Transition probability derivation

I have encountered this limit while learning time dependent perturbation and transition probability in Sakurai. How to show this limit? I tried to integrate around $x=0$ but didn't get anything ...
3
votes
2answers
97 views

Proof that 1d lattice displacement by phonons is given $u_{n\pm 1}(t) = A_ke^{i\omega_k t} e^{i knd}e^{\pm i k d}$

I looked in «Kittel - Introduction to solid state physics», Wikipedia and Google for the derivation that: A phonon of wavenumber $k$ displaces the $s$-th atom in a monoatomic 1d crystal lattice by a ...
1
vote
0answers
58 views

Why is this differential added instead of subtracted?

I was looking at a derivation of the Barometric formula which reads like this: Consider a flat disc of air of mass $\mathrm{d}m$ at distance $h$ above the ground of mass $\mathrm{d}m$ and ...
11
votes
3answers
646 views

If a theory of everything exists, is it necessarily unique?

There is a lot of interesting debate over whether a "theory of everything" (ToE) is allowed to exist in the mathematical sense, see Does Gödel preclude a workable ToE?, Final Theory in Physics: a ...
5
votes
1answer
81 views

Meaning of integral signs in classical physics

When I began studying physics, by myself, on a universitary textbook, F.J. Keller, W.E. Gettys , M.J. Skove, Physics, about one year ago, I believed that all the integrals that I was going to find in ...
-1
votes
1answer
50 views

Find the indicated quantities from the given data [closed]

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 ...
8
votes
0answers
146 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 ...
1
vote
1answer
198 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 ...
1
vote
1answer
136 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
56 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
votes
1answer
789 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
votes
1answer
66 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 ...
8
votes
0answers
60 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 ...
0
votes
0answers
102 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.)
69
votes
7answers
8k 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
vote
1answer
76 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
69 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
0answers
22 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
67 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
vote
2answers
64 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
votes
0answers
54 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 ...
7
votes
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 ...
0
votes
0answers
46 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
157 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
0answers
74 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 ...