Context is 1D Ising model. Metropolis algorithm is used for simulate that model. Among all possible spins configurations (states) that algorithm generates only states with the desired Boltzmann probability.

Algorithm chooses spin at random and makes a trial flip. If trial satisfies certain conditions related to Boltzmann probability, flip is accepted. Otherwise flip is rejected and system is unchanged.

Define "acceptance ratio" as a percentage of accepted trials. Simulation shows that acceptance ratio is higher on higher temperature (behave as increasing function of temperature).

Questions:

Why Metropolis algorithm is not efficient at low temperatures?

Is efficiency of algorithm related to acceptance ratio?

Well, it does according to this preprint for certain scales.

What would be a simple way to explain MOND to a layman?

Does it ignore mainstream physics? How much?

It is well known in racing that driving the car on the ideal "slip angle" of the tire where it is crabbing slightly from the pointed direction produces more cornering speed than a lower slip angle or a higher one.

(More explanation as requested) I'm considering two main effects on the tire when in a turn:

The tread of the tire is twisted from the angle of the wheel it is mounted to. There is more force as speed increases, and generally, more twisting.

The tire slides somewhat at an angle on the road surface rather than rolling.

At low speeds, the angle between the pointed direction of the wheel (90 degrees to the axis of rotation) and the direction of travel is nearly 0. When the speed increases to the point the angle reaches about 10 degrees, the tire generate more grip and the car goes faster around the turn. (Higher angles produce lower grip)

So the grip is higher at 10 degrees of slip than at 0 or 20 degrees.

What is the physical effect that causes this increase in grip?

Fermilab seems to have ruled out monopoles with mass less than 850 GeV, but I have seen some estimates of the mass thought to be in the order of up to 1018 GeV, which, of course, would make them undetectable in any accelerators. By 2013, the LHC is scheduled to reach up to 14 TeV. The only disputed sighting of a cosmic ray produced magnetic monopole was in 1982 when Blas Cabrera reported discovering one (Valentine event monopole). This has never been duplicated. CERN has set up the Monopole and Exotics Detector MOEDAL. Other experiments set up to detect them are the Antarctic Impulsive Transient Antenna--ANITA, and the Antarctic Muon And Neutrino Detection Array, aka AMANDA. While both of these detected neutrinos, neither detected magnetic monopoles (looking for Cerenkov radiation produced by products of monopole interaction). Another method of detection is to look for induced current in a superconducting ring when a monopole passes through. Joseph Polchinski called the existence of monopoles

How does one build up an intuitive gut feeling for physics that some people naturally have? Physics seems to be a hodgepodge of random facts.

Is that a sign to quit physics and take up something easier?

Thanks for all the answers. On a related note, how many years does it take to master physics? 1-2 years for each level multiplied by many levels gives?

In a lot of laymen explanations of general relativity it is implied that the four dimensions of the space-time are equivalent, and we perceive time as different only because it is embedded in our human perception to do so.

My question is: is that really how general relativity treats the 4 dimensions?

If so - what are the implications (if any) this has on causality?

If no - can the theory support more than one time dimension?

"stability" is invoked as the justification for the axiomatic requirement that the spectrum of the generators of the translation group must be confined to the forward light-cone. The spectrum condition has pervasive, significant effects in axiomatic QFT. There seems to be no proof, however, that the spectrum condition actually ensures that a quantum field will be stable, partly because there is, AFAIK, no mathematical specification of what stability consists of in QFT. IF there were, I suppose the stability axiom would be central to axiomatic QFT instead of the positive spectrum condition.

Stability is intimately related with positive energy in classical physics, of course, but the concept of energy is rather different in classical relativistic field physics than in quantum mechanics, being the 00 component of the stress-energy tensor instead of being the 0 component of the 4-vector of generators of translations. The relationship between positive energy and stability in classical physics does not seem enough to justify an uncritical adoption of the spectrum condition in quantum theory as an axiom, which is supposed to be obvious enough that it is almost beyond question. Negative frequencies are certainly not ruled out for classical field theories, because the energy is not a linear functional of the frequency of the Fourier components of the field.

An axiomatic definition of stability would presumably have to specify what deformations would or should not affect the stability of a given construction. A building is only stable, for example, provided a strong enough earthquake does not occur, it is not stable sine die. Given that the deformations that are possible in quantum field theory are more varied than the deformations that are possible in classical field theory, the spectrum condition seems to require a more substantial justification.

Less axiomatically, Feynman integrals include negative frequency/energy components in intermediate calculations, though not in observables, which seems to bring the spectrum condition into at least some question.

Haag discusses the relationship of stability with the spectrum condition only extremely perfunctorily (p.29 of the 2nd edition of Local Quantum Physics), and I am not aware of an elaborate discussion by other authors. Is there one?

EDIT: Streater & Wightman, in PCT, Spin & Statistics, and all that, discuss collision states. Their discussion is entirely in terms of perturbation theory, which seems not adequate enough for an axiomatic discussion. However, because of asking this question I'm starting to see slightly more clearly why a conventional Physicist might be entirely satisfied with what there is on this.

EDIT(after acceptance of Tim van Beek's Answer): The other aspect of this is that the restriction to positive frequency is apparently not enough to ensure

I would like to expand on what I mean by the title of this question to focus the answers.

Normally whenever a theory (e.g. General Relativity) replaces another (e.g. Newtonian Gravity) there is a correspondence requirement in some limit. However there is also normally some experimental area where the new larger theory makes predictions which are different from the older theory which made predictions of the same phenomena. This is ultimately because the newer theory has a deeper view of physics with its own structures which come into play in certain situations that the old theory didn't cover well. Additionally the newer theory will make predictions based on its novel aspects which the older theory did not consider. I know that String Theory is quite rich in this regard, but am not interested in that here. Nor am I concerned as to whether experiment has caught up, as I know that ST (and Quantum Gravity in general) is not easy to test.

So for the GR to Newtonian example an answer to this question would be: bending of light rays; Mercury perihelion movement - GR had a different results to Newton. What would not count as an answer would be new structures which GR introduces like Black Holes or even gravitational curvature per se.

So does ST have anything like Mercury perihelion movement waiting to be experimentally verified, and thus "improving" on GR within GR's own back yard?

a ball is thrown up onto a roof, landing 3.60 s later at height h = 25.0 m above the release level. The ball's path just before landing is angled at ? = 64.0?with the roof. (a) Find the horizontal distance d it travels. (Hint: One way is to reverse the motion, as if it is on a video.) What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball's initial velocity?

A light modifier that is commonly used in studio photography is a honeycomb grid.

It narrows the beam of light to a circle with soft edges, as it can be seen here:

My question is: how is this happening?

A small reporter flash has a rectangular shape, if you place a rectangular shaped grid on it, it produces a "soft" circle of light. How is the light travel modified by the structure of the grid?

A uniform electric field exists in the region between two oppositely charged parallel plates 1.70cmapart. A proton is released from rest at the surface of the positively charged plate and strikes the surface of the opposite plate in a time interval 1.45

Consider the well known demonstration of diffraction by a narrowing slit. (See for example the demonstration at the 30 minute mark of this lecture at MIT by Walter Lewin)

It is my (possibly mistaken) understanding that the light emerging after the slit becomes substantially slimmer than one wavelength is polarized.
This would seem to imply that light of perpendicular polarization would not be transmitted, thus implying a fairly substantial and dramatic difference in the results of the experiment with parallel and perpendicularly polarized light. That is, instead of spreading out, the light polarized in the wrong direction would essentially just shut down as the slit narrows below one wavelength. Is this true?

According to the first law of thermodynamics, sourced from wikipedia "In any process in an isolated system, the total energy remains the same."

So when lasers are used for cooling in traps, similar to the description here: http://optics.colorado.edu/~kelvin/classes/opticslab/LaserCooling3.doc.pdf where is the heat transferred?

From what I gather of a cursory reading on traps, whether laser, magnetic, etc the general idea is to isolate the target, then transfer heat from it, thereby cooling it.

I don't understand how sending photons at a(n) atom(s) can cause that structure to shed energy, and this mechanism seems to be the key to these systems.

What are three possible locations at which the electrostatic potential of a point can be defined as having a value of zero?

Two 53.0 x 10^-9 C point charges are located on the x axis. One is at x = 0.35 m, and the other at x = - 0.35 m.

a) A third identical charge is placed on the y axis at y = 0.35 m. Find the magnitude of the force acting on this third charge? Answer in Newtons.

b) Now the third identical charge is placed on the y axis at y = 2 x 0.35 m. Find the magnitude of the force acting on this third charge? Answer in Newtons.

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Four charges are placed at the corners of a square. The side of the square is a = 0.30 m.

a) If the charge are identical and positive q = 21.0 x 10^-9 C what would be the magnitude of the force acting on each of the charges? Answer in Newtons.

b) We change the charges by q₁ = 21.0 x 10^-9 C, q₂ = 11.0 x 10^-9 C, q₃ = -12.0 x 10^-9 C, q₄ = -31.0 x 10^-9 C. What would be the magnitude of the force acting on charge q₃? Answer in Newtons.

c) We place the same charges at the corners of a rectangle of sides a and b (instead of a square). If b=2a/3 what would be the magnitude of the force acting on charge q₃? Answer in units of Newtons.

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Two 2.20-?C point charges are located on the x axis. One is at x = 1.57 m, and the other at x = -1.57 m. Determine the magnitude of the electric field on the y axis at y = 0.530 m. Answer in units of N/C.