# All Questions

7k views

### Is a hard drive heavier when it is full?

Browsing Quora, I saw the following question with contradicting answers. For the highest voted answer: The bits are represented by certain orientations of magnetic fields which shouldn't have ...
2k views

### Path integral vs. measure on infinite dimensional space

Coming from a mathematical background, I'm trying to get a handle on the path integral formulation of quantum mechanics. According to Feynman, if you want to figure out the probability amplitude for ...
1k views

### The Impossibility ( or Possibility) of Solving $N$-Body Problem

One can obtain the solution to a $2$-Body problem analytically. However, I understand that obtaining a general solution to a $N$-body problem is impossible. Is there a proof somewhere that shows this ...
1k views

I realise that there are already a few questions looking for general book recommendations, but the motivation and type of book I'm looking for here is a little different, so I hope you can indulge me. ...
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### Before a once-warm lake starts to freeze, must its temperature be 4°C throughout at some point?

This is a problem I just started puzzling over, and I felt this would be a good forum to check my reasoning. So here are the relevant observations followed by my question: Water achieves its maximum ...
2k views

### Mechanics around a rail tank wagon

Some time ago I came across a problem which might be of interest to the physics.se, I think. The problem sounds like a homework problem, but I think it is not trivial (i am still thinking about it): ...
1k views

### Is 3+1 spacetime as privileged as is claimed?

I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. ...
3k views

### Why is it hard to solve the Ising-model in 3D?

The Ising model is a well-known and well-studied model of magnetism. Ising solved the model in one dimension in 1925. In 1944, Onsager obtained the exact free energy of the two-dimensional (2D) model ...
806 views

### On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $\mathcal N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the ...
2k views

### Why does one experience a short pull in the wrong direction when a vehicle stops?

When you're in a train and it slows down, you experience the push forward from the deceleration which is no surprise since the force one experiences results from good old $F=m a$. However, the moment ...
2k views

### Where does the extra force generated by a lever come from?

Given an object being pulled down to earth by a force of 1000 lb: If a machine were to lift it off the ground for me, and I grabbed on to the rope before it was released, there is no way in the world ...
8k views

### With Newton's third law, why are things capable of moving?

I've got a rather humiliating question considering newton's third law "If an object A exterts a force on object B, then object B exerts an equal but opposite force on object A" -> $F_1=-F_2$ ...
4k views

### Why can't we feel the Earth turning?

The Earth turns with a very high velocity, around its own axis and around the Sun. So why can't we feel that it's turning, but we can still feel earthquake.
1k views

### What keeps mass from turning into energy?

I understand the energy and mass can change back and forth according to Einstein. It is fluid; it can go from one to the other. So, what keeps mass from just turning into energy? Is there some force ...
2k views

### Why does a supernova explode

This is really bugging me. When you look up some educational text about stars life, this is what you find out: Gravity creates the temperature and pressure to start fusion reactions. The fusion ...
1k views

### Can I survive a free fall using a ramp and a rope?

Can I survive a free fall by carrying a very light and resistant ramp using a rope? Note: lets assume the ramp is a little bit heavier at the bottom and I am very skilled at making it always land ...
1k views

### Floating a ping pong ball in the air just using a pen!

Caution: Apparently this problem is harder than it seems! There is a well known phenomena, which I first learnt about when I was a 10 years old kid. You can levitate a ping pong(or whatever ...
2k views

### A No-Nonsense Introduction to Quantum Field Theory

I found Sean Carroll's "A No Nonsense Introduction to General Relativity" (about page here. pdf here), a 24-page overview of the topic, very helpful for beginning study. It all got me over the hump ...
15k views

### How can a photon have no mass and still travel at the speed of light?

I've read a number of the helpful Q&As on photons that mention the mass/mass-less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make ...
2k views

### What is the fallacy in this infinite motion machine?

I realize this isn't possible, but I can't see why not, especially if you change the model a little bit so that the balls simply travel through a tube of water on the way up, rather than exactly ...
2k views

### Do two beams of light attract each other in general theory of relativity?

In general relativity, light is subject to gravitational pull. Does light generate gravitational pull, and do two beams of light attract each other?
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### Telescopes to avoid as a beginner? [closed]

I've heard people talk about "department store scopes" or "trash scopes". How do I know what to avoid in a beginner scope? How can I know that I'm not getting something we will be more frustrated with ...
1k views

### Are these two quantum systems distinguishable?

Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground ...
8k views

### Why don't electrons crash into the nuclei they “orbit”?

I'm having trouble understanding the simple "planetary" model of the atom that I'm being taught in my basic chemistry course. In particular, I can't see how a negatively charged electron can stay ...
2k views

### Is a “third quantization” possible?

Classical mechanics: $t\mapsto \vec x(t)$, the world is described by particle trajectories $\vec x(t)$ or $x^\mu(\lambda)$, i.e. the Hilbert vector is the particle coordinate function $\vec x$ (or ...
1k views

### If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons?

If photon energies are continuous and atomic energy levels are discrete, how can atoms absorb photons? The probability of a photon having just the right amount of energy for an atomic transition is ...
4k views

### Getting started general relativity

What are some good books, videos, websites for getting started with general relativity? Mathematically rigorous preferred!
886 views

### Examples of number theory showing up in physics

My question is very simple: Are there any interesting examples of number theory showing up unexpectedly in physics? This probably sounds like rather strange question, or rather like one of the ...
2k views

### Is a proton collision (collisions like in the LHC) visible to the human eye?

I was curious if a proton collision is visible to the human eye. (This might sound like a really basic question and forgive me if it is. I am very inexperienced in Physics and just wanted an answer ...
2k views

### What's the real fundamental definition of energy?

Some physical quantities like position, velocity, momentum and force, have precise definition even on basic textbooks, however energy is a little confusing for me. My point here is: using our ...
921 views

### Are quantum effects significant in lens design?

Over on Photography, a question was asked as to why (camera) lenses are always cylindrical. Paraphrasing slightly, one of the answers and follow-up comments asserted that quantum effects are ...
9k 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 ...
936 views

### The Pioneer anomaly finally explained?

Pioneer 10 & 11 are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an unusual deceleration of both spacecrafts has been measured to be approximately ...
652 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 ...
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 ...
12k views

### Maximum theoretical data density

Our ability to store data on or in physical media continues to grow, with the maximum amount a data you can store in a given volume increasing exponentially from year to year. Storage devices continue ...
4k views

### Why doesn't the bike fall if going with a high speed?

Why does the bike fall when its speed is very low or close to zero and is balanced when going with a high speed?
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 ...
1k views

### How to write a paper in physics

I really like to do research in physics and like to calculate to see what happen. However, I really find it hard to write a paper, to explain the results I obtained and to put them in order. One of ...
2k views

### Why quantum mechanics?

Imagine you're teaching a first course on quantum mechanics in which your students are well-versed in classical mechanics, but have never seen any quantum before. How would you motivate the subject ...
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 ...
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 ...
353 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 ...
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?
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 ...
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 ...
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 ...
800 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 ...