Questions tagged [mathematical-physics]
For questions regarding the mathematical aspects of physics.
98 questions
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Cases where a misunderstanding in mathematics led to misunderstanding of the physics?
Originally, I asked this question on Physics SE, but it was immediately suggested that I ask this question here. Quite soon afterwards, the question was closed on (see below).
Quite some time ago, ...
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How did Vladimir Arnold explain the difference in approaches between mathematicians and physicists?
In Vladimir Arnold's Problems for children from 5 to 15 he writes:
Note to problem 13. I tried to illustrate with this problem the difference in approaches to tasks by mathematicians and physicists, ...
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Did von Neumann consider his mathematical formulation of quantum mechanics to be essentially complete?
With my faulty memory, I recall reading someone claiming that von Neumann did not consider his Mathematical Foundations of Quantum Mechanics to be complete and did expect further work to correct it.
...
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Does the paper "W.F. Eberlein, Axiomatic charge conjugation, J. Math. Phys. (to appear)" exist?
I found the reference
Axiomatic charge conjugation, J. Math. Phys. (to appear)
in W. F. Eberlein, Models of space-time, Bull. Amer. Math. Soc. 71 (1965), 731-736, (pdf) however, I don't find the ...
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When did Claude Navier write the work "Sur Les Lois du Mouvement des Fluides"?
When did Claude Navier write the work "Sur Les Lois du Mouvement des Fluides"?
I can’t find this information on the internet.
"Sur Les Lois du Mouvement des Fluides" read at 1822
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Who is Rudolf Bach?
I've googled but have not found anything about mathematician Rudolf Bach. In Riemannian or semi-Riemannian geometry such as general relativity, Conformal geometry, Wave propagation theory such as ...
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How does the science community decide which scientist to credit for a particular discovery?
In the science community there are lots of cases where two or more scientists work on the same ideas or theories.
How is it decided which scientist to give credit for a particular discovery? What are ...
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Why Isaac Newton published his discoveries so much later than he discovered them?
Principia was completed in 1686 and published in 1687, but he discovered calculus, gravity and laws of motion long before (1665-1666 "Year of Wonders").Is this correct?
He wrote book Method ...
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What year was Navier-Stokes equations introduced?
In this video he is explaining what are Navier-Stokes equations. As I find these equations are evolution of Euler equations.
In this article they choose 1822. Do yo agree with this?
Who and when first ...
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Math concepts introduced by physicists and made rigorous later
I am looking for mathematical concepts (*) which have been introduced by physicists in a non rigorous way (e.g. without a formal definition, without rigorous proofs of the results, etc.) and used to ...
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How did Schrödinger do quantum mechanics with wave functions?
On my way to learn about the very beginning of quantum mechanics and its different formulations, starting with Heisenberg infinite matrices and Schrödinger's wave functions, I can really not find till ...
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Surface Integrals History
Can't find any information about who and when first used surface/surface area integrals. What was the original motivation? In it's modern form it depends on some relatively modern notations like ...
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Did Rayleigh or Ritz prove the Rayleigh–Ritz theorem?
The maximum eigenvalue of a real symmetric (or complex Hermitian) matrix is given as the maximum of the associated the quadratic form:
$$
\lambda_{\rm max}(A) = \max_{\|x\| = 1} x^*Ax. \tag{1}
$$
This ...
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Did physics resulted in invention of maths or vice a versa [closed]
Did physics resulted in invention of maths or Maths resulted in invention of physics ??
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Why is $T_{\mu\nu}$ the Standard Notation for the Stress-Energy-Momentum Tensor
My question is simple: why do we use $T_{\mu\nu}$ to denote the stress energy momentum tensor, and when was the concept of the stress energy tensor first (or roughly the first) introduced (and by whom)...
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The abstraction of mathematics from physics
When and how did mathematics come to be abstracted away from the physical world?
At first, mathematics would originate in its simplest form of counting and addition as to keep track of certain ...
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What was the first physical theory to be mathematically expressed?
Newton's theory of gravitation is expressed as a mathematical relationship between distances and masses. It can be deduced from Kepler's equations (which are also mathematical).
Are there even older ...
user16484
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Physical theories and Mathematics [closed]
I study pure mathematics. In pure mathematics, we begin from some axioms and obtain theorems. I am also interested in studying physics. I have some questions about the relationship between physical ...
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Complex potential in E227?
I have a reason to believe that Euler introduced the complex potential in his Continuation des recherches sur la theorie du mouvement does fluides, published in 1757. However, I am having hard time ...
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Who first proposed the idea of "resolution of the identity"?
Who first proposed the idea of "resolution of the identity" as used in the functional calculus of self-adjoint operators? Was it von Neumann?
In Japanese, it translates as "resolution ...
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Who established the current standard demonstration of Euler-Lagrange equation in calculus of variations?
Who established the current standard(*) demonstration of Euler-Lagrange equations in calculus of variations, that is, $\displaystyle\frac{\partial f}{\partial y}-\frac{d}{dx}\frac{\partial f}{\partial ...
follonic
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Who first used complex analysis to account for singularities in field theory?
In 1925, Frenkel wrote a paper titled Zur Elektrodynamik punktförmiger Elektronen, which used complex analysis to treat an electron as a point, and its corresponding potential function as an isolated ...
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Has physics ever given a physical significance to a mathematically abstract idea?
Consider a fundamental concept in maths that was created to 'solve' a problem that simply couldn't be solved by any other approach (or maybe for some other reason). Now let's assume that this concept ...
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Best history of Maxwell and his equations
I've done my B.S. in Electrical Engineering as well as mathematics but I'd like to get a proper, or complete history of Maxwell and the history of his derivation of the equations and the newness of ...
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In which work was Gibbs' Inequality introduced?
Gibbs' inequality
$$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$
is such a popular thing that I cannot find where it was introduced.
My findings
I ...
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Were Kepler's Laws of Planetary Motion the first formal definition of an ellipse?
It seems to me that Kepler's Laws necessitate some definition of an ellipse in terms of a coordinate system. I am wondering whether Kepler's Laws mathematically defined what an ellipse is, or if he ...
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Examples of Physical Discoveries with no Counterpart in Mathematics
Throughout the history of mathematics and physics, there has been many examples where mathematics was discovered first prior to its application in physics. Consider $i=\sqrt {-1}$ as an example, among ...
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Who discovered the wave equation?
https://link.springer.com/chapter/10.1007/978-1-4684-5772-8_2
says:
Using Newton's recently formulated laws of motion, Brook Taylor
(1685–1721) discovered the wave equation by means of physical ...
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Did Sophie Germain find a flaw in Euler's equations for elastic vibrations?
I am a playwright working on a play about Sophie Germain. When Sophie was competing for the prix extraordinaire to find effective formulas to describe the vibrations of elastic surfaces, she believed ...
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Background on the Stone-von Neumann theorem
I'm a mathematician.
I'm required to give a lecture on the Stone-von Neumann theorem. I already have all the mathematical details figured out, but I wish to make the lecture more interesting by giving ...
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How did we arrive at the rule of addition of vectors?
I wanted to ask about how they arrived to the rule of addition of vectors. How did they know that if we add the X's and Y's of two vectors they would get a third vector which has exactly the same ...
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What is the origin in the discrepancy between engineers' and physicists' notation of waves?
my question is very simple. Physicists use this notation in order to write a (for example) plane wave:
$$
\xi(z) = \xi^+ \mathrm{e}^{+\mathrm{i}kz} + \xi^- \mathrm{e}^{-\mathrm{i}kz},
$$
where $\xi^+$ ...
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Finding sources for "computers will become so powerful that special functions will become obsolete" as a zeitgeist
In Why are special functions special [Physics Today 54, 11 (2007); eprint], Michael Berry makes the following observations:
This continuing and indeed increasing reliance on special functions is a ...
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Were pictorial notations like Feynman diagrams for integrals used before Feynman?
In the book Mathews, Walker: Mathematical Methods of Physics, Addison-Wesley(1969),
there is a pictorial notation of the solution found by Fredholm about an integral equation.p.304, p.305This circle ...
user12897
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Is Hermann Weyl's book “Space, Time, Matter” (1923) on General Relativity still relevant?
I really liked Hermann Weyl's mathematical books and would like to get accustomed to general relativity from his perspective, but wonder if it's still relevant after almost 100 (!) years?
Can this ...
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Who made the first derivation of the angle to maximise projectile range, which turned out to be wrong?
I remember hearing once that the first "proof" that the angle to maximise projectile range gave the correct answer, 45 degrees, but was later found that the proof was wrong. I can't remember ...
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Who originally worked out the magnetic field produced by a solenoid and toroid?
Although, it seems very easy to find the magnetic field produced by a solenoid or a toroid, all we got to do is to make a suitable an Amperian Loop and take the $\mathbf B$ out of the integral and so ...
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Was Von Neumann and Birkhoff's original formulation of Quantum Logic related with projective geometry?
I was looking at how did von Neumann and Birkhoff formulate their Quantum Logic formalism back in 1936. To solve some questions, I contacted via email a philosopher who studied this topic.
I thought ...
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Who introduced the "dagger"symbol as conjugate transpose in quantum mechanics?
The $\dagger$ symbol is often used in quantum mechanics,and also often in general mathematics to represent the conjugate transpose operation.For Hermitian matrices we can write $$A^\dagger=A$$Who ...
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Who pioneered the study of the sedenions?
I found lots of background information about the discovery of both imaginary and complex numbers, and enough information about the first two types of hypercomplex numbers; quaternions and octonions (...
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Collection of open problems in Partial differential equations
Except Navier-Stokes equation, are there any other interesting open problems in partial differential equations?
I want to know the collection of problems, which are easy to understand but ...
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Where did Euler derive the wave equation in 3d?
Wikipedia claims that Euler was the first do derive the wave equation in 3d. In which of his writings can I find this?
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What was the real need of divergence and curl operators?
As I'm advancing my study in Electromagnetism I'm getting introduced to more mathematical operators which are exclusively used in Electromagnetism and Fluid Dynamics only.
Let me try to explain myself ...
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Does anyone know of any examples of the Magnus effect in a real battle?
I've read a lot about the Magnus effect altering the trajectories of cannonballs and musketballs. Robins noticed it with Musket balls and Magnus with canonballs, but presumably they weren't the first ...
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How were negative numbers first used in physics?
The use of negative numbers in most of today's calculations is natural. But how did the use of negative numbers began in physics? What physical quantity required the introduction of negative numbers ...
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What are the great works of Richard Phillips Feynman? [closed]
What are the prerequisites to read his book? Why Richard Phillips Feynman is so famous? What are great works of Richard Phillips Feynman?
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When were vectors invented?
Encyclopedia Britannica says,
In their modern form, vectors appeared late in the 19th century when Josiah Willard Gibbs and Oliver Heaviside (...) independently developed vector analysis to express ...
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Introduction of shape parameters in the formulation of probability distribution
I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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How did philosophers and scientists in the 18th century view mathematical explanation?
The 18th century saw a rise in the use of mathematical formalisms to account for natural phenomena. Works of Lagrange, Euler, d'Alembert, etc., were groundbreaking in the history of mechanics and ...
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Does the “O” in the google doodle for Olga Ladyzhenskaya have anything to do with her work?
Ladyzhenskaya is famous for fluid dynamics and partial differential equations, both of which are beyond my pay grade. And she worked on the Navier-Stokes equations. Does this circle with the arrows ...
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