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26

As we cannot resolve arbitrarily small time intervals, what is ''really'' the case cannot be decided. But in classical and quantum mechanics (i.e., in most of physics), time is treated as continuous. Physics would become very awkward if expressed in terms of a discrete time. Edit: If time appear discrete (or continuous) at some level, it could still be ...


17

There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here, but for some reason I am not allowed to link to it normally: http://211.144.68.84:9998/91keshi/Public/File/34/482-7386/pdf/nature10779.pdf) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump ...


12

I'm the author of the novel mentioned above and I'd like to clarify. Neither I nor my novel claim the universe is a computer. The operating principle of the novel's universe is that all things are One through balance. The protagonist, Paul, is asked if his universe is a computer. He answers that in a balanced quantum universe this would be impossible. Why? ...


11

I'll chip in here because I'm a research student and I work with a stellar evolution code (the Cambridge STARS code) more-or-less daily. Regarding some of the comments to the question, stellar evolution is actually quite fast, depending what code you use. Certainly, it isn't like hydrodynamics or N-body simulations like those used in galaxy ...


11

I'd say there's no conclusive evidence, but in quantum physics, Planck time is sometimes cited as a possible smallest unit of time. The source for my data is Quantum Gods: Creation, Chaos, and the Search for Cosmic Consciousness by Victor J. Stenger. In there, he goes into a lot of detail about this in one chapter.


11

The horizontal component of running is believed to be fairly negligible for humans. Some research suggests that the limit isn't strength related at all, but design --- in particular, based solely on power, humans could theoretically run up to almost 40 mph. The issue is two fold: first, our limbs are actually too heavy, for big strength (e.g. climbing in ...


10

I would suggest looking at the formalism of Floquet space. The basic idea is that one uses a time-independent but infinite dimensional Hamiltonian to simulate evolution under a time-dependent but finite dimensional Hamiltonian by using a new index to label terms in a Fourier series. A good, short introduction can be found in Levante et al. For more details, ...


9

It most certainly exist outside secret labs :) Like Gerben wrote, the fields are called molecular dynamics (MD) and quantum chemistry which, as computers grow faster, will be essential tools of nanotechnology and medicine. Molecular Dynamics is currently implemented by making certain approximations in that electron motion is not explicitely modelled. In ...


9

The two main free destop programs that I know about, Stellarium and Celestia, do not include the proper motion of the stars when they move forward and backward in time. At least according to documentation that I've seen. These programs claim to do it but I have no experience with them: Home Planet (free) Starry Night (commercial) The Sky (commercial) ...


9

Geant is a framework---which means that you use it to build applications that simulate the detector and physics you are interested in. The simulation can include all of physics and the complete detector including electronics and trigger (i.e. you can write your simulation so that it output a data file that looks just like the one you are going to get from ...


9

I think it's important to note that quantum or quantized time is not equal to discrete time. For instance, we have "quantized" space. By this we mean that it receives quantum treatment. But the underlying coordinates still form a continuum. So even if you live on a finite circle and only consider wavefunctions so that you get a countable set of basis ...


9

I've played the game, see my report: http://motls.blogspot.ca/2012/11/a-slower-speed-of-light-mit.html?m=1 and I join M. Buettner. I am confident that all relativistic effects are incorporated. It includes the length contraction in the direction of motion, time dilation, but those basic things are rapidly changed by the fact that it really shows what you ...


8

One has to realize that a Monte Carlo simulation is an integration tool. Suppose you have a curve in an xy plot, y=f(x). If you throw random (x,y) pairs in the square containing the f(x) and count the number where y is less than f(x) versus the number y larger than f(x) you get an estimate of the area under f(x), i.e. the integral of the function. In ...


8

First of all, I do not have any experience with this, I am an Astronomy hobbyist at best. So I am just going to present what I found with minimal comment at this time. I found this web page that links to several programs: http://nbody.sourceforge.net/ They link to the University of Washington and their n-body shop. I don't know what your status must be ...


7

The thing you are reading is NOT an article(that you should trust). Even if the universe were a simulation there is NO such proof in QM. Though physical processes can be thought of as computations it does not imply existence of "super computer". Also, even if such a "super computer" exists it must be a part of some universe. That universe must also be ...


7

Your method is known as the forward Euler method, the simplest DEQ-solver but a really bad one. I suppose it's the approximation everyone tries first, at least I did, too, when I started with such simulations... and soon was troubled by similar "numerical explosions", which can't really be avoided with this algorithm which is why it's virtually never used in ...


6

This is, no doubt, one of the biggest challenges for realistic simulations: waves crashing, hair moving under wind and whatever other movement involving turbulence will be hard to solve. Though it is true that one can solve the equations of motion for each individual particle in a 'molecular dynamics' fashion, that is just infeasible for a system that goes ...


6

There's a huge difference between the number of bits you can store in a given space and the number of bits you need to describe that space. Take a single atom of iron with its 26 electrons. For a complete description, you need the many-particle wavefunction $\psi(\vec{x}_1, \vec{x}_2, \vec{x}_3, \dots, \vec{x}_{26})$ (ignoring spin for the moment). Imagine ...


6

Monte Carlo is a particular numerical technique heavily used in Physics, mainly when one needs to "brute force" the calculation. Virtually, all areas of Physics can make use of simulations that include some sort of Monte Carlo code, from the designing of detectors in particle physics (think Fermilab and LHC: Geant4), passing by out-of-equilibrium ...


6

Monte Carlo are very important in almost any particle physics experiment and are used in a variety of ways including To prototype the experiment without spending many millions of dollars. They can be used to show that the proposed physics signal will be detectable among the many known physics effects to test variations on the proposed detector design ...


6

Is there a reason that you are interested in QED in particular? For processes within current experimental ranges, the standard perturbative treatment is incredibly accurate, and simulations are not really necessary. A sector of the standard model where simulations are incredibly important is in strong interactions (QCD) for which a perturbative treatment ...


6

Your problem is highly nontrivial. The theoretical tool to be used is the renormalization group, which extracts the relevant dynamics of the large scales of the system. But if we were able to use it "in a blind way", then we would have a technique to study the macroscopic dynamics of any microscopic system... and this would made a lot of my colleagues ...


6

What you are talking about is similar to the problem of quantum gravity. Since gravity is an effect of the curvature of spacetime, to have a quantum theory of it, you need to quantize the spacetime manifold. This is done with spin foams which are little units of volume in spacetime that have spins associated to them. They connect together like total ...


6

I think the problem could be to do with your distinction of positive and zero/neutral Wigner states. I believe that the best way to understand the statement in this paper is as follows: For simplicity consider a single qudit state $\rho$, then this state has a positive Wigner representation if $W_{\rho}(\boldsymbol{u})\ge0 ...


6

This probably isn't exactly what you're looking for, but if you're looking for the time-independent bound states of a system, the Fourier grid Hamiltonian method may be applicable. Here is an application of it to the following strange-looking potential well: Here are a few low-energy bound states: And here are some of the high-energy ...


5

Yes it is a bit like waveguide for electrodynamics. You've got absolutely the same equation. The difference is in boundary conditions -- instead of Dirichlet you've got to use Neumann boundary conditions. While of course it works only if you are able no neglect all the non-linear effects -- your waves are low enough.


5

Addressing just the physics part (go to stack overflow for the programming), and using the equation that you've been given: $$ x(t) = A \cos \left( \omega t + \delta \right) $$ Let's look at the form of the solution. It is sinusoidal The curve will have a maximum value of $A$ (because cosine has a maximum value of 1) When $\delta$ is $0, \pm 2\pi, \pm ...


5

Coordinate invariance guarantees that the phase space $M$ can be endowed with a symplectic 2-form $\omega$ which locally is given by $\omega = dq^i \wedge dp_i$. This form is closed ($d\omega = 0$) and nondegenerate, i.e. $\omega^n$ is a volume form, where $2n$ is the dimension of $M$. The other conditions say that for any Hamiltonian function $H$, the ...


5

In order to know with certainty where every particle was going to be you would need to know its mass, velocity and state very accurately - as any rounding errors or uncertainty will be magnified over the timespans involved. Unfortunately it is impossible to know to 100% precision where anything is, so we are already at strike 1. If you could somehow hold ...



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