26
votes
3answers
687 views

A “Hermitian” operator with imaginary eigenvalues

Let $${\bf H}=\hat{x}^3\hat{p}+\hat{p}\hat{x}^3$$ where $\hat{p}=-id/dx$. Clearly ${\bf H}^{\dagger}={\bf H}$, because ${\bf H}={\bf T} + {\bf T}^{\dagger}$, where ${\bf T}=\hat{x}^3\hat{p}$. In this ...
26
votes
6answers
2k views

Formalizing Quantum Field Theory

I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or ...
26
votes
4answers
1k views

Is there a Lagrangian formulation of statistical mechanics?

In statistical mechanics, we usually think in terms of the Hamiltonian formalism. At a particular time $t$, the system is in a particular state, where "state" means the generalised coordinates and ...
26
votes
3answers
761 views

Does quantum mechanics violate the equivalence principle?

I have a question about equivalence principle in quantum mechanics. Consider a Schroedinger equation under gravitional field $$\left[ - \frac{1}{2m_I} \nabla^2 + m_g \Phi_{\mathrm{grav}} \right]\psi ...
25
votes
12answers
4k views

How does a half-life work?

Carbon-14 has a half-life of 5,730 years. That means that after 5,730 years, half of that sample decays. After another 5,730 years, a quarter of the original sample decays (and the cycle goes on and ...
25
votes
8answers
3k views

What justifies dimensional analysis?

Dimensional analysis, and the notion that quantities with different units cannot be equal, is often used to justify very specific arguments, for example, you might use it to argue that a particular ...
25
votes
11answers
5k views

What is the simplest way to prove the Earth is round?

Assume you've come in contact with a tribe of people cut off from the rest of the world, or you've gone back in time several thousand years, or (more likely) you've got a numbskull cousin. How would ...
25
votes
10answers
4k views

Why is acceleration expressed as m/s/s?

I'm a philosophy student (I, regrettably, don't know calculus or much physics). Last year I spent some time learning how work, power, speed, velocity, energy, force, and acceleration relate. But I was ...
25
votes
11answers
1k views

Negative probabilities in quantum physics

Negative probabilities are naturally found in the Wigner function (both the original one and its discrete variants), the Klein paradox (where it is an artifact of using a one-particle theory) and the ...
25
votes
9answers
2k views

Why are the laws of thermodynamics “supreme among the laws of Nature”?

Eddington wrote The law that entropy always increases holds, I think, the supreme position among the laws of Nature. If someone points out to you that your pet theory of the universe is in ...
25
votes
4answers
4k views

Why is a new moon not the same as a solar eclipse?

Forgive the elementary nature of this question: Because a new moon occurs when the moon is positioned between the earth and sun, doesn't this also mean that somewhere on the Earth, a solar eclipse ...
25
votes
3answers
3k views

Where does the light go when I turn off the light switch?

As above... Surely it must go somewhere? My child asked me this question and it was a difficult one to answer.
25
votes
6answers
3k views

Why is there no absolute maximum temperature?

If temperature makes particles vibrate faster, and movement is limited by the speed of light, then temperature must be limited as well I would assume. Why there is no limits?
25
votes
3answers
374 views

Continuum theory from lattice theory

I am looking for references on how to obtain continuum theories from lattice theories. There are basically a few questions that I am interested in, but any references are welcome. For example, you can ...
25
votes
5answers
2k views

Hamilton's Principle

Hamilton's principle states that a dynamic system always follows a path such that its action integral is stationary (that is, maximum or minimum). Why should the action integral be stationary? On ...
25
votes
3answers
1k views

Why are there no asteroids or meteoroids with relativistic speeds?

Cosmic rays can have energies going into the $10^{20}$ eV domain. Asteroids and meteoroids originating in the solar system are probably limited in their speed because they all started out from the ...
25
votes
4answers
9k views

What are the precise statements by Shouryya Ray of particle dynamics problems posed by Newton which this news article claims have been solved?

This recent news article (here is the original, in German) says that Shouryya Ray, who moved to Germany from India with his family at the age of 12, has baffled scientists and mathematicians by ...
25
votes
4answers
877 views

How do the “hot Jupiter” planets get so close to their host star?

Many of the extrasolar planets to date are Jovian sized planets that orbit very very close to their parent star. Traditional planetary formation models say that it is extremely unlikely (if not ...
25
votes
1answer
3k 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 ...
25
votes
10answers
2k views

What is spontaneous symmetry breaking in QUANTUM systems?

Most descriptions of spontaneous symmetry breaking, even for spontaneous symmetry breaking in quantum systems, actually only give a classical picture. According to the classical picture, spontaneous ...
25
votes
1answer
1k views

Why does this object periodically turn itself?

See this video about 30 sec in. http://www.youtube.com/watch?v=dL6Pt1O_gSE Is this a real effect? Why does it seem to turn periodically? Can it be explained by classical mechanics alone? Is there a ...
25
votes
10answers
1k views

What is the difference between a measurement and any other interaction in quantum mechanics?

We've learned that the wave function of a particle collapses when we measure a particle's location. If it is found, it becomes more probable to find it a again in the same area, and if not the ...
25
votes
7answers
1k views

Why are differential equations for fields in physics of order two?

What is the reason for the observation that across the board fields in physics are generally governed by second order (partial) differential equations? If someone on the street would flat out ask ...
25
votes
5answers
3k views

Why is the bell, well, bell shaped?

What is the significance about the bell shape, when its hit at the rim it rings/produces sound better than other shaped objects? If so could anyone explain a little bit on it. EDIT: From the ...
25
votes
1answer
550 views

State of Matrix Product States

What is a good summary of the results about the correspondence between matrix product states (MPS) or projected entangled pair states (PEPS) and the ground states of local Hamiltonians? Specifically, ...
25
votes
5answers
522 views

What are some critiques of Jaynes' approach to statistical mechanics?

Suggested here: What are the justifying foundations of statistical mechanics without appealing to the ergodic hypothesis? I was wondering about good critiques of Jaynes' approach to statistical ...
25
votes
4answers
789 views

How much information about the scale of a waterfall can be obtained from its sound?

Is it possible to constrain the height, volume flow, or distance of a waterfall from the quantitative analysis of a high-quality recording of its sound? As an aside, the simulated sounds of fluid ...
25
votes
3answers
1k views

Why do the planets' orbital distances fall on an exponential curve?

Background: I was recently reading a book on the planets to my son and I noticed a pattern in the distributions of the planets. The planets' distances roughly follow an exponential distribution. ...
25
votes
9answers
2k views

What is the Earth truly rotating about/revolving around?

Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
25
votes
1answer
565 views

Best current bounds on nonconservation of momentum?

It's not straightforward to test conservation of momentum experimentally, and many experiments that seem like tests really aren't. For example, in a Newtonian system of identical particles that ...
24
votes
10answers
6k views

Discreteness and Determinism in Superstrings?

So Gerard 't Hooft has a brand new paper (thanks to Mitchell Porter for making me aware of it) so this is somewhat of a expansion to the question I posed on this site a month or so ago regarding 't ...
24
votes
6answers
5k views

How do whisky stones keep your drink cold?

From a discussion in the DMZ (security stack exchange's chat room - a place where food and drink are important topics) we began to question the difference between how ice and whisky stones work to ...
24
votes
6answers
2k views

Canonical everyday-life example of a technology that could not work without humans mastering QM in analogy to the application of GR in GPS?

The GPS is a very handy example in explaining to a broad audience why it is useful for humanity to know the laws of general relativity. It nicely bridges the abstract theory with daily life ...
24
votes
7answers
4k views

What is the difference between a white object and a mirror?

I was taught that something which reflects all the colors of light is white. The function of a mirror is the same, it also reflects all light. What's the difference? Update: But what if the white ...
24
votes
3answers
2k views

Can I use an antenna as a light source?

Can I use a normal metal antenna to emit visible light?
24
votes
10answers
6k views

About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
24
votes
4answers
2k views

Why does wet skin sunburn faster?

There is a popular belief that wet skin burns or tans faster. However, I've never heard a believable explanation of why this happens. The best explanation I've heard is that the water droplets on the ...
24
votes
5answers
2k views

Why is information indestructable?

I really can't understand what Leonard Susskind means when he says that information is indestructible. Is that information that is lost, through the increase of entropy really recoverable? He ...
24
votes
1answer
3k views

Was Titanic's captain's decision correct?

I just saw a documentary on Titanic. Someone in that documentary told Captain Smith "Shall we close the water tight doors, sir?" and the Captain replied "No, let it be open. Let the water ...
24
votes
4answers
5k views

If both radio waves and gamma rays can travel through walls

and they are on opposite ends of the electromagnetic spectrum, then why can't light travel through walls which is right in the middle of the spectrum? This question has already been asked here. ...
24
votes
2answers
1k views

Why is gravity such a unique force?

My knowledge on this particular field of physics is very sketchy, but I frequently hear of a theoretical "graviton", the quantum of the gravitational field. So I guess most physicists' assumption is ...
24
votes
3answers
1k views

Wind generators - why so few blades?

Why commercial wind generators usually have just 2-3 blades? Having more blades would allow to increase power OR decrease diameter. Decreased diameter would also reduce stress due to different wind ...
24
votes
3answers
1k views

From where (in space-time) does Hawking radiation originate?

According to my understanding of black hole thermodynamics, if I observe a black hole from a safe distance I should observe black body radiation emanating from it, with a temperature determined by its ...
24
votes
12answers
3k views

How can anything ever fall into a black hole as seen from an outside observer?

The event horizon of a black hole is where gravity is such that not even light can escape. This is also the point I understand that according to Einstein time dilation will be infinite for a ...
24
votes
4answers
1k views

Why does everything spin?

The origin of spin is some what a puzzle to me, everything spin from galaxies to planets to weather to electrons. Where has all the angular momentum come from? Why is it so natural? I was also ...
24
votes
3answers
2k views

When water climbs up a piece of paper, where is the energy coming from?

Take a glass of water and piece of toilet paper. If you keep the paper vertical, and touch the surface of the water with the tip of the paper, you can see the water being absorbed and climbing up the ...
24
votes
3answers
341 views

Renormalization Group for non-equilibrium

For equilibrium/ground state systems, a (Wilson) renormalization group transformation produces a series of systems (flow of Hamiltonians/couplings $H_{\Lambda}$ where $\Lambda$ is the cut-off) such ...
24
votes
4answers
5k views

What causes ballpoint pens to write intermittently?

After a while, a ball point pen doesn't write very well anymore. It will write for a little distance, then leave a gap, then maybe write in little streaks, then maybe write properly again. It seems ...
24
votes
1answer
610 views

Sigma Models on Riemann Surfaces

I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action ...
23
votes
8answers
14k views

Why CAN we see the new moon at night?

I understand that the Moon's phases are determined by its position in orbit relative to the Sun. (See: Full Story on the Moon). The "shadow" is not cast by the Earth (a common misconception - this is ...

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