4
votes
1answer
3k views

How is Gauss' Law (integral form) arrived at from Coulomb's Law, and how is the differential form arrived at from that?

On a similar note: when using Gauss' Law, do you even begin with Coulomb's law, or does one take it as given that flux is the surface integral of the Electric field in the direction of the normal to ...
201
votes
19answers
69k views

A mirror flips left and right, but not up and down

Why is it that when you look in the mirror left and right directions appear flipped, but not the up and down?
32
votes
9answers
4k views

Rigor in quantum field theory

Quantum field theory is a broad subject and has the reputation of using methods which are mathematically desiring. For example working with and subtracting infinities or the use of path integrals, ...
29
votes
8answers
3k views

Why $\displaystyle i\hbar\frac{\partial}{\partial t}$ can not be considered as the Hamiltonian operator?

In the time dependent Schrodinger equation $\displaystyle, H\Psi = i\hbar\frac{\partial}{\partial t}\Psi$ , the Hamiltonian operator is given by $\displaystyle H = -\frac{\hbar^2}{2m}\nabla^2+V$ ...
28
votes
4answers
3k views

Which is more fundamental, Fields or Particles?

I hope that I am using appropriate terminology. My confusion about quantum theory (beyond my obvious unfamiliarity with its terminology) is basically twofold: I lack an adequate understanding of ...
16
votes
11answers
34k views

How do you start learning physics by yourself? [closed]

I think this question has its place here because I am sure some of you are "self-taught experts" and can guide me a little through this process. Considering that : I don't have any physics scholar ...
39
votes
5answers
3k views

Scattering of light by light: experimental status

Scattering of light by light does not occur in the solutions of Maxwell's equations (since they are linear and EM waves obey superposition), but it is a prediction of QED (the most significant Feynman ...
17
votes
7answers
8k views

How to learn physics effectively and efficiently [closed]

How do you effectively study physics? How does one read a physics book instead or just staring at it for hours? (Apologies in advance if the question is ill-posed or too subjective in its current ...
33
votes
1answer
5k views

What conservation law corresponds to Lorentz boosts?

Noether's Theorem is used to related the invariance under certain continuous transformations to conserved currents. A common example is that translations in spacetime correspond to the conservation of ...
31
votes
3answers
3k views

Why the galaxies forms 2D plane (or spiral-like) instead of 3D ball (or spherical-like)?

Question: As we know, (1) the macroscopic spatial dimension of our universe is 3 dimension, and (2) gravity attracts massive objects together and the gravitational force is isotropic without ...
13
votes
5answers
22k 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 ...
15
votes
1answer
2k views

Mathematically, what is color charge?

A similar question was asked here, but the answer didn't address the following, at least not in a way that I could understand. Electric charge is simple - it's just a real scalar quantity. Ignoring ...
17
votes
4answers
1k views

Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
18
votes
4answers
6k views

Is spacetime discrete or continuous?

Is the spacetime continuous or discrete? Or better, is the 4-dimensional spacetime of general-relativity discrete or continuous? What if we consider additional dimensions like string theory ...
15
votes
3answers
9k views

Your Mass is NOT from Higgs Boson

Your Mass is NOT from Higgs Boson? http://www.youtube.com/watch?v=Ztc6QPNUqls This guy can't be correct, right? He argues that because mostly of a nucleus' mass is made out of the space between ...
12
votes
6answers
3k views

Why is there a $\frac 1 2$ in $\frac 1 2 mv^2$?

For elastic collisions of n particles, we know that momentum in the three orthogonal directions are independently conserved:$$ \frac{d}{dt}\sum\limits_i^n m_iv_{ij} =0,\quad j=1,2,3$$ From this, it ...
26
votes
5answers
4k views

Why isn't Higgs coupling considered a fifth fundamental force?

When I first learned about the four fundamental forces of nature, I assumed that they were just the only four kind of interactions there were. But after learning a little field theory, there are many ...
14
votes
4answers
6k views

When is the Hamiltonian of a system not equal to its total energy?

I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
10
votes
3answers
3k views

What has been proved about the big bang, and what has not?

Ok so the universe is in constant expansion, that has been proven, right? And that means that it was smaller in the past.. But what's the smallest size we can be sure the universe has ever had? I ...
4
votes
2answers
355 views

Are all scattering states un-normalizable?

I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the ...
8
votes
7answers
1k views

Why do physicists believe that particles are pointlike?

String theory gives physicists reason to believe that particles are 1-dimensional strings because the theory has a purpose - unifying gravity with the gauge theories. So why is it that it's popular ...
6
votes
2answers
2k views

Noticing that Newtonian gravity and electrostatics are equivalent, is there also a relationship between the general relativity and electrodynamics?

In classical mechanics, we had Newton's law of gravity $F \propto \frac{Mm}{r^2}$. Because of this, all laws of classical electrostatics applied to classical gravity if we assumed that all charges ...
3
votes
4answers
3k views

Define Pressure at A point. Why is it a Scalar?

I have a final exam tomorrow for fluid mechanics and I was just looking over the practice exam questions. They do not provide solutions. But pretty much I have to define pressure at a point and also ...
13
votes
3answers
5k views

Why does the moon drift away from earth?

I once saw on TV that the moon is slowly drifting away from the earth, something like an inch a year. In relation to that the day on earth what also increase in time. I wonder why is that?
9
votes
4answers
1k views

Is there an accepted analogy/conceptual aid for the Higgs field?

Is there an accepted analogy / conceptual aid for the Higgs field? In Physics there are many accepted conceptual aids such as * Schrödinger's cat * Maxwell's Demon * I'm sure I'm missing ...
2
votes
1answer
941 views

Why path integral approach may suffer from operator ordering problem?

In Assa Auerbach's book (Ref. 1), he gave an argument saying that in the normal process of path integral, we lose information about ordering of operators by ignoring the discontinuous path. What did ...
12
votes
4answers
844 views

Why do all the planets of the solar system orbit in roughly the same 2D plane?

Most images you see of the solar system are 2D and all planets orbit in the same plane. In a 3D view, are really all planets orbiting in similar planes? Is there a reason for this? I'd expect that ...
11
votes
3answers
919 views

Temperature below absolute zero?

I saw this Nature article today, which cites e.g. arXiv:1211.0545. And it makes no sense to me. The temperature of a collection of particles is the average kinetic energy of those particles. Kinetic ...
3
votes
8answers
1k views

Does the (relativistic) mass change? Why?

I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place?
1
vote
4answers
973 views

What's so special about the speed of light? [duplicate]

What's so special about the speed of light? Why do many equations in physics include the speed of light in vacuum $c$? Why do so many thing depend upon it? Why can't it be the speed of sound? ...
5
votes
5answers
646 views

Does a photon instantaneously gain $c$ speed when emitted from an electron?

An excited electron looses energy in the form of radiations. The radiation constitutes photons which move at a speed $c$. But, is the process of conversion of the energy of the electron into the ...
75
votes
7answers
10k views

Why do people categorically dismiss some simple quantum models?

Deterministic models. Clarification of the question: The problem with these blogs is that people are inclined to start yelling at each other. (I admit, I got infected and it's difficult not to raise ...
47
votes
10answers
7k views

Can Maxwell's equations be derived from Coulomb's Law and Special Relativity?

As an exercise I sat down and derived the magnetic field produced by moving charges for a few contrived situations. I started out with Coulomb's Law and Special Relativity. For example, I derived the ...
102
votes
3answers
24k views

Why does Stephen Hawking say black holes don't exist?

Recently, I read in the journal Nature that Stephen Hawking wrote a paper claiming that black holes do not exist. How is this possible? Please explain it to me because I didn't understand what he ...
37
votes
11answers
16k views

How did Newton discover his second law?

I've always assumed/been told that Newton's 2nd law is an empirical law — it must be discovered by experiment. If this is the case, what experiments did Newton do to discover this? Is it related to ...
13
votes
5answers
2k views

Noether charge of local symmetries

If our Lagrangian is invariant under a local symmetry, then, by simply restricting our local symmetry to the case in which the transformation is constant over space-time, we obtain a global symmetry, ...
23
votes
6answers
2k views

Why do we still need to think of gravity as a force?

Firstly I think shades of this question have appeared elsewhere (like here, or here). Hopefully mine is a slightly different take on it. If I'm just being thick please correct me. We always hear ...
22
votes
7answers
5k views

Why do people still talk about bohmian mechanics/hidden variables [closed]

I was reading the Feynman lectures in physics and after thinking about it for a while it seems particularly unreasonable to talk about hidden variables. Let us say that the electron has some internal ...
13
votes
4answers
2k views

Introduction to string theory

I am in the last year of MSc. and would like to read string theory. I have the Zwiebach Book, but along with it what other advanced book can be followed, which can be a complimentary to Zwiebach. I ...
31
votes
6answers
4k views

Do electrons have shape?

According to the Wikipedia page on the electron: The electron has no known substructure. Hence, it is defined or assumed to be a point particle with a point charge and no spatial extent. Does ...
12
votes
7answers
3k views

Deterministic quantum mechanics

I came across a very recent paper by Gerard 't Hooft The abstract says: It is often claimed that the collapse of the wave function and Born's rule to interpret the square of the norm as a ...
28
votes
6answers
14k views

Is there an equation for the strong nuclear force?

The equation describing the force due to gravity is $$F = G \frac{m_1 m_2}{r^2}.$$ Similarly the force due to the electrostatic force is $$F = k \frac{q_1 q_2}{r^2}.$$ Is there a similar equation ...
7
votes
1answer
2k views

Schrodinger equation from Klein-Gordon?

One can view QM as a 1+0 dimensional QFT, fields are only depending on time and so are only called operators, and I know a way to derive Schrodinger's equation from Klein-Gordon's one. Assuming a ...
21
votes
5answers
2k views

How are forces “mediated”?

I hope this is the right word to use. To me, these forces seem kind of fanciful (except for General Relativity and Gravity, which have a geometric interpretation). For example, how do two charged ...
6
votes
1answer
1k views

Noether theorem and classical proof of electric charge conservation

How to prove conservation of electric charge using Noether's theorem according to classical (non-quantum) mechanics? I know the proof based on using Klein–Gordon field, but that derivation use ...
38
votes
6answers
4k views

If I am travelling on a car at around 60 km/h, and I shine a light, does that mean that the light is travelling faster than the speed of light?

The title says it all. If I was on a bus at 60 km/h, and I started walking on the bus at a steady pace of 5 km/h, then I'd technically be moving at 65 km/h, right? So my son posed me an interesting ...
15
votes
4answers
2k views

What is the physical meaning of a “complete” Hilbert space in QM?

What does the word "complete" means from the physical point of view? I do not understand what it physically means to say that a Hilbert space is a complete vector space.
15
votes
4answers
5k views

Is energy really conserved?

In high school I was taught energy was conserved. Then I learned that nuclear reactions allow energy to be converted into mass. Then I also heard that apparently energy can spontaneously appear in ...
7
votes
5answers
8k views

Recommendations for Statistical Mechanics book

I learned thermodynamics and the basics of statistical mechanics but I'd like to sit through a good advanced book/books. Mainly I just want it to be thorough and to include all the math. And of course ...
24
votes
4answers
2k views

Why does the sky change color?

Why the sky is blue during the day, red during sunrise/set and black during the night?

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