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Physical interpretation of the semilinear Dirichlet problem

As a non-physicist student, I’ve been trying to gain some intuition on the problem I’m studying, namely \begin{equation}\begin{cases} -\Delta u + f(u) = h, \; \text{in } D \subset \mathbb{R}^n\\ u=0, \...
Spida's user avatar
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7 votes
1 answer
648 views

How can a scalar field have components and how do I interpret these components?

From lecture notes$^\zeta$ I've been reading that: Consider a real three-component scalar field $$\phi=\begin{pmatrix}\phi_1 \\\ \phi_2 \\\ \phi_3\end{pmatrix}\tag{a}$$ with Lagrangian $$\mathcal{L}=\...
Sirius Black's user avatar
26 votes
7 answers
4k views

Can spinors be explained or understood without group or representation theory?

Vectors, either as abstract mathematical elements of a vector space (in this case the definition of the vector is divorced from any notion of transformation), or as elements of tangent spaces on ...
Jagerber48's user avatar
1 vote
2 answers
94 views

Intuitive charge distribution

I often see it stated that excess charge will appear on the surface or excess charge will appear on the outside surface and it is causing me some intuitive confusion in some situations if it is always ...
axawire's user avatar
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13 votes
4 answers
2k views

What is an Intuitive example of a Gauge Symmetry?

Can anyone give an intuitive example of what a gauge symmetry is? I am new to this concept and would like to understand it better!
PhysicalScience's user avatar
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2 answers
74 views

What is the intuition behind difference in tension In two block problem

Consider a system of two blocks having masses $m_1$ and $m_2$ lying on smooth floor, where $m_2>m_1.$ They are attached by an ideal inextensible string. There are two different situations $1$ and $...
Dheeraj Gujrathi's user avatar
1 vote
0 answers
80 views

Similar to how there's field lines that make equations in Newtonian Gravity more intuitive, is there something that makes GR equations more intuitive?

One way I know to get intuition for the derivation of the force equation $$F=\frac{GM_1M_2}{r^2}$$ in Newtonian Mechanics is to imagine gravitational field lines, in combination with certain ...
Anders Gustafson's user avatar
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0 answers
53 views

Interpret momentum applied on a rod when holding it from one end

Yesterday I started wondering exactly how much more effort it takes holding a rod from one of it's edged instead of from it's centre. Picture a rod, held by your hand from under it's centre. The force ...
El Nitromante's user avatar
3 votes
0 answers
194 views

What weight does a scale show when you throw an object onto it?

Imagine you have a bucket (cross-sectional area $A$) on top of a scale. Into the bucket you begin to pour sand (density $\rho$) with a mass flow rate of $\dot{m}$. The total weight of the sand in the ...
S. Green's user avatar
0 votes
2 answers
305 views

Euler-Lagrange intuition

We know from euler-lagrange, that $S$ should be minimized, which in turn means (KE-PE) should be minimized at each smallest interval along the path. I'm not trying to understand the math here, it's ...
Giorgi's user avatar
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Intuition for Relative Phase of Energy-State Qubits

Consider a general qubit $|\Psi \rangle = \alpha |0 \rangle + \beta |1\rangle$. My understanding is as follows: If such a qubit is implemented using electron spin, for example, the computational basis ...
BewilderedFermion's user avatar
1 vote
1 answer
75 views

Can we design an experiment or an intuitive way to demonstrate tidal locking?

I was explaining the tidal locking phenomenon to a friend. First I started with the formation of solar system and how at the beginning the planets were actually like balls of magma-esque rocks. And ...
polfosol's user avatar
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-1 votes
3 answers
164 views

Temperature is discrete but not countable? [closed]

So I was reading a a question and top comment on math stack exchange that didn't make sense to me. you can measure the temperature of something, but you can't count it. Incidentally, I claim ...
More Anonymous's user avatar
1 vote
3 answers
80 views

What do the units of entropy quantify? [closed]

Entropy has the units $J\cdot K^{-1}$. Velocity has the units $m \cdot s^{-1}$. In the latter example, I know what the units are quantifying across all applications of the quantity of velocity. ...
user110391's user avatar
1 vote
0 answers
109 views

Resource for building "physical" intuition for mathematics [closed]

I stumbled across an intuition for the Laplace operator that suggests it can be considered "the difference between the value of a function at a point and the average value at "neighboring&...
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0 answers
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Intuition and the reason behind rotation operators or angular momentum operators NOT commuting?

So I was thinking about the fundamental reason why rotation operators don't commute so I started thinking about Euler rotations. I tried the experiment of the rotating frame, first around the x-axis ...
Kobamschitzo's user avatar
0 votes
1 answer
65 views

Intuition behind rotational analog's of motion [closed]

Whenever I think of rotational analog's of motion , like angular velocity ,angular displacement and mainly angular momentum , something doesn't click with my intuition. Like I cant understand how they ...
Naveen V's user avatar
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1 answer
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Is there a physical interpretation of the algebraic Bianchi identity?

The Riemann curvature tensor $R_{ijkl}$ satisfies several algebraic index symmetries: $R_{ijkl} = -R_{jikl} = -R_{ijlk}$ $R_{ijkl} = R_{klij}$ $R_{i[jkl]} = 0.$ I more or less understand how to ...
tparker's user avatar
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-1 votes
1 answer
124 views

Physical significance of multiplication [closed]

I have a question. Hope someone helps me. The multiplication sign in $p = m \times v$ is allowed . But... The addition sign in $p = m + v$ is not allowed. It is said that in order to add different ...
Curious55's user avatar
2 votes
3 answers
165 views

Why does resistance contribute to the AC impedance's real part for a single circuit, but to its imaginary part for an infinite transmission line?

A simple AC-driven RLC series circuit has equivalent impedance $$Z = R + i\left( \omega L - \frac{1}{\omega C} \right),$$ where $R$ is the resitance, $L$ is the inductance, $C$ is the capacitance, and ...
tparker's user avatar
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0 votes
2 answers
214 views

Would it be conceptually clearer to refer to the impedance of free space as the "reactance of free space" instead?

I'm aware that the impedance of free space (377 ohms in SI units) doesn't have a whole lot of physical significance, because in natural EM units impedance is dimensioness and (e.g. in Lorentz-...
tparker's user avatar
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1 vote
1 answer
99 views

Physical interpretation of an infinite eigenvalue

First, I am a mathematician with some basic knowledge in quantum mechanics, so I should be able to understand a few details, but I am more looking for a physical intuition of my problem. I am working ...
Spida's user avatar
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1 vote
2 answers
387 views

What is the physical meaning of sigma in the Laplace transform?

Let’s use a simple harmonic oscillator as an example. When we calculate the Fourier Transform (a special case of the Laplace transform) of that system we get a function that shows which frequencies of ...
Christian S's user avatar
0 votes
2 answers
297 views

Divergence of Rank-2 Tensor: Motivation/Intuition

I'm reading through a text on continuum mechanics (Intro to CM by Lai, Rubin, Krempl), and it defines the divergence of a rank-2 tensor $\mathbf{T}$ as follows: The divergence of $\mathbf{T}$ is ...
Jacob Wilson's user avatar
3 votes
0 answers
117 views

Why is the Lax-Jacobi identity useful in integrability?

I'm studying integrabilty and there is the so-called Lax-Jacobi identity, which is an implication of the classical Jacobi identity of the Poisson brackets of the Lax-Poisson structure: $$Cycl_{123} [...
Spida's user avatar
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2 votes
2 answers
672 views

How do I know whether waveguides support TE or TM modes?

I'm working through the formalism of waveguides, and I've seen many different situations with various boundary conditions: hollow metal rectangular waveguide, dielectric slab, dielectric rectangular ...
flevinBombastus's user avatar
1 vote
0 answers
63 views

Do these functions (parabolas with opposite parity) ever occur in physics? [closed]

Let's define $$f_n(x)=(n-1)\operatorname{Li}_n\left(e^x\right)-x\operatorname{Li}_{n-1}\left(e^x\right)$$ (the function $\operatorname{Li}$ is polylogarithm) $$f_{even_n}(x)=\frac{f(x)+f(-x)}2$$ $$f_{...
Anixx's user avatar
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3 votes
1 answer
248 views

Physical intuition behind the optical theorem

I am taking a course of QM (as part of my maths studies) and we saw the optical theorem in scattering theory. Namely, we have $$\sigma = \frac{4\pi}{k}\Im f(\vec{q}=0),$$ where $\sigma$ is the total ...
Spida's user avatar
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0 votes
1 answer
91 views

Intuition for Results of a Measurement of Entangled Spins

Suppose I have a source that produces pairs of spin-1/2 spins in the entangled state $$ \frac{1}{\sqrt{2}} \left( \mid\uparrow_z\uparrow_z\rangle + \mid\downarrow_z\downarrow_z\rangle \right). $$ The ...
flevinBombastus's user avatar
0 votes
2 answers
96 views

Understanding voltage as a relative measure between two bodies

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which (in a static electric field) is defined as the work ...
timtam's user avatar
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2 votes
0 answers
87 views

In what way is conditional quantum probability restrictive, and why?

This is close to a duplicate of https://mathoverflow.net/q/412327/ but with a different emphasis. Unlike the mathoverflow equivalent, here I want to ask for your informed intuition as physicists. To ...
Mehmet Coen's user avatar
1 vote
0 answers
136 views

Is this a reasonable intuition for the Higgs mechanism?

Though I've more or less come to terms with the math behind the Higgs mechanism, I'm trying to develop a rough intuition for it. Here's how I'm thinking: the Higgs field (like everything) likes to sit ...
Pedro's user avatar
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2 votes
1 answer
202 views

Physical intuition for coherent states look like classical

In my course on quantum mechanics, we have seen that coherent states look classical. Since the expectation value of the electric field is similar as for the classical expression. Furthermore they look ...
Mari3's user avatar
  • 163
7 votes
4 answers
763 views

$1/r^2$ force and "photon decay"

Background: My question is about the interpretation of the $1/r^2$ force in terms of the fundamental processes of the underlying QFT. We know that if the photon had mass $m$, then we may have a "...
Quillo's user avatar
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4 votes
3 answers
359 views

Why does a distant rotating body have angular momentum about the origin?

In a frame where the center of mass is stationary, the angular momentum of a body is invariant to translation of the origin. That is: $\mathbf{L} = \sum_i \mathbf{r_i} \times \mathbf{p_i}$ is constant ...
Ned Ruggeri's user avatar
0 votes
1 answer
214 views

Intuition behind phase difference in AC circuits

So I've been studying AC Circuits lately and I've come across a few things that I'm not able to digest. Let's take a pure inductive circuit for example. This is the first time I'm experiencing current ...
Soumil Gupta's user avatar
15 votes
9 answers
8k views

Why does something round roll down faster than something square?

Why does something round roll down faster than something square? That's a question given to me by my five year old son. So let's not get into detailed discussion about what is 'square' and what is '...
Sextus Empiricus's user avatar
0 votes
2 answers
97 views

Interpreting Stokes' theorem using the energy of a particle looping around a closed curve

We know that the work for a particle moving along a path $L=\partial S$ is $\int_{L} \vec{F} \cdot d\vec{s}$. Suppose the particle loops around this path once: $$ \int_L \vec{F} \cdot d\vec{s} = \int_{...
Babu's user avatar
  • 7,970
3 votes
6 answers
750 views

Intuition behind torque, rotational inertia and angular momentum

I'm reading about conservation of linear momentum and angular momentum. I understand the idea that angular momentum should be thought of as the "rotational analogue" of linear momentum, just ...
35T41's user avatar
  • 404
12 votes
2 answers
1k views

Are chaotic systems the same as dissipative systems in inverse time?

Lyapunov exponents define whether a system expands or contracts in phase space and can be used to determine whether a dynamical system is chaotic, conservative, or dissipative. If the volume expands ...
J.Galt's user avatar
  • 223
3 votes
5 answers
460 views

How should I understand work?

What is the intuitive meaning of work or analogy used to understand work? I'm able to understand math, but I can't grasp the idea of energy and work. For acceleration, say $+2\frac{\text m}{\text s^2}$...
Rambal heart remo's user avatar
4 votes
1 answer
150 views

What's the intuitive physical difference between the conservations of momentum and of the boost generator in SR?

This is a soft question about classical special relativity (although a related question applies even to nonrelativistic classical mechanics). The (connected) symmetry group of Minkowski space is the ...
tparker's user avatar
  • 48k
2 votes
1 answer
152 views

Why is torque assumed to be constant?

Consider a spanner: I was doing calculations on how much torque would be applied on the bolt. To do this, I considered how much force was being applied at the full length of the handle. Then, I ...
John Hon's user avatar
  • 2,346
2 votes
1 answer
487 views

What is an intuitive explanation for the change in internal energy being equal to the heat capacity times the change in temperature?

I read that the change in internal energy, $\Delta U$, is equal to the heat capacity at constant volume, $C_V$, times the change in temperature, $\Delta T$. So, in other words, we have that $\Delta U =...
The Pointer's user avatar
1 vote
1 answer
53 views

Intuition About the Impossibility of Acceleration to C in Relativity. Is my Intuition Getting in the Way

Bob is riding a bicycle on a highway into space. His sister Alice watches him leave, and each rotation of the pedals brings Bob an absolute 1% closer to the speed of light relative to Alice. Bob also ...
CuriousDunce's user avatar
2 votes
4 answers
948 views

Is there an intuitive way to view the concept of momentum?

Ideas like distance, velocity and force are very intuitive to understand because you can "see" their real-world applications and so one can come to understand them without having any ...
RandomUser's user avatar
6 votes
4 answers
2k views

Analogy for Lentz soliton

Analogy for Alcubeirre Warp Drive: Every explanation of warp drive in layman terms has this sentence in it: "The Warp Drive will contract space in thier front and expand space behind." (I ...
Rounak Sarkar's user avatar
0 votes
2 answers
141 views

Understanding distance from a line to a point at infinity (Jaan Kalda's handouts)

I'm reading page-7 of Jaan Kalda's Kinematics handouts, the following is written: Here we can use a small addition to the last idea: if the quickest way to a plane (in a 3-d problem) or to a line (in ...
Babu's user avatar
  • 7,970
2 votes
0 answers
42 views

Intuitive explaination for the influence of different mass-energy components on the CMB

So I'm going to be giving a talk to a local astronomy club, and I want to be able to give them an intuitive understanding of why the CMB tells us about both the geometry of the universe and the matter ...
levitopher's user avatar
  • 5,391
1 vote
2 answers
322 views

If the earth constantly exerts a force on air molecules downwards, then why do they not fall to the ground?

I'm sorry if this seems like a really stupid question but it has really puzzled me... The earth exerts gravitational force on all objects with mass, and gas has mass. I know that this force results in ...
Aniket Gupta's user avatar