# Tag Info

125

What you're looking for is Landauer's principle. You should be able to find plenty of information about it now that you know its name, but briefly, there is a thermodynamic limit that says you have to use $k_\mathrm BT \ln 2$ joules of energy (where $k_\mathrm B$ is Boltzmann's constant and $T$ is the ambient temperature) every time you erase one bit of ...

50

I think this question makes hidden, inarticulated assumptions about reality. In physics, we make observations and then try to find models that match them. The models, though, belong only to us and exist in our heads and textbooks. We perform the calculations required to make our predictions in our models. We cannot say whether nature makes similar ...

45

I just wanted to give a more concrete idea of how we know these equations even though we have trouble proving analytical theorems about them. Stuff moving in space Consider any stuff (as in, any conserved quantity) distributed over space. We know that we can describe this with a time-dependent density field $\rho(x,y,z,t)$ such that any little volume $dV$ ...

45

Numerical analysis is used to calculate approximations to things: the value of a function at a certain point, where a root of an equation is, or the solutions to a set of differential equations. It is a huge and important topic since in practice most real problems in mathematics, science and technology will not have an explicit closed-form solution (and even ...

36

All of it can be simulated to a certain level of precision - given enough computing power AND correct experimental values for all the parameters. The tricky bit without tests is to get experimental values for eg. the thermal conductivity of Plutonium at TPa of pressure. Experimental tests can also only validate something to a certain level of precision - ...

35

As a computational physicist working in materials/condensed matter, I'm either highly biased or well-placed to comment on this. Physics, in practice, is divided into three overlapping approaches: experimental, theoretical, and computational. (The highest impact research papers usually include a combined effort from all three.) If you plan to go into ...

29

1) yes, it basically will find a non-optimal solution. At every point, the top of the ray looks for the bigger potential gradient, the charge in the surrounding volume grows, polarizing surrounding material (air, in this case) until a bigger gradient shows up and the ray continues over that direction. This is why the lightining path looks like a jigsaw; its ...

22

To some extent this answer is echoing things that @Martin said... but from my own point of view. In my experience of (Monte Carlo) simulation, the model you implement captures your knowledge of the physics of the situation; and if your knowledge is "perfect", your calculation, with sufficient compute power at your fingertips, will also be "perfect". ...

21

Lattice QCD calculations involve computing the inverse of the Dirac operator $\gamma\cdot D+m$. The difficulty of inverting an operator is controlled by its smallest eigenvalues, and computing the inverse of the Dirac operator becomes harder as $am\to 0$. The exact scaling of the computational cost depends on the algorithms. It was once feared that realistic ...

19

As @QMechanic mentioned in a comment, the Navier-Stokes equations are just $F = ma$, but they look much scarier. Assuming an incompressible fluid, you have: $$\rho \frac{D u_i}{D t} = -\frac{\partial \sigma_{ij}}{\partial x_j} + f_b$$ where $\rho$ is the density (mass per unit volume), $D u_i /D t$ is the acceleration (written in the Lagrangian form, ...

18

I think perhaps some of the other answers are taking computer science to be synonymous with computation. I guess that this is perhaps not what you mean, but rather theoretical computer science. There is obviously a huge overlap with quantum information processing of which I think you are already well aware, so I will ignore that. Much of physics (including ...

14

Yes, it is possible. Working with pure quantum mechanics means you will need to solve the many-body Schrödinger equation, which has no exact solution, so some approximation must be done numerically. Different approaches into solving this equations gave birth to different numerical methods, and some methods are more efficient for solving specific problems, ...

13

You are asking quite a few questions, so let me try to go step by step. First, an area law is a very special property among quantum states: If you pick a random state, it will have almost maximal entropy (i.e. a volume rather than an area scaling). So essentially any state would be a counterexample ;-) On the other hand, ground states appearing in nature ...

13

I can't really know why your professor used C++, but there are several reasons why you would: Performance: Scientific computations might require top-notch performance. C++ allows for very low level control over the hardware and has many possibilities for micro-optimization while still providing high-level abstraction. Of course, this is also the reason that ...

13

One way to think about it is that a particle "sniffs out" its immediate surroundings and reacts to gradient: a trend like a declining potential in one direction. Single-celled organisms do this. Plant orient toward the sun. A rock on an incline "senses" that it's center-of-mass is slight off from the point of contact with the ground. This is all loosely ...

12

this is a broad, complex, somewhat tricky question with many angles that an entire survey or book could be written on but unfortunately it seems one hasnt yet. heres a "grab bag" of some deep parallels noticed over the years that such a book might cover & "research leads" for further inquiry. Modelling and simulation. as computing capability has ...

12

I think anyone who says "there's no need to do experiments, we can simulate everything!" either: Doesn't know what they're talking about Is trying to sell snake oil Is a scientific fraud trying to push pseudoscience as actual science I have never seen a serious, honest scientist claim that simulation is sufficient substitute for empirical evidence, even ...

12

If you really want a general gravitation simulator (i.e. one that will handle more then two bodies), then there are methods for reducing the error involved in the simulation, but there aren't any methods for eliminating the error. Below are a few approaches - none of these approaches are perfect, since there's a balance between physical accuracy, programming ...

12

This usually only applies to a wall bounded flow and is normally restricted to incompressible fluids. This result usually manifests in boundary layer theory and can be obtained through order of magnitude analysis of the Navier-Stokes equations. The steady, incompressible, and constant property momentum equation in the $y$ direction takes the form,  u \frac{...

12

The Navier Stokes equations are a combination of Newton's 2nd law of motion (differential form) with the 3D version of Newton's law of viscosity (i.e., the mechanical constitutive equation for a Newtonian fluid). What you were taught in Physics at school was correct. Not many analytic solutions exist to interesting practical problems, and numerical ...

11

The entanglement of any region in a matrix product state of bond dimension $D$ is bounded by $S\le 2\log D$. Thus, in order to simulate a system with a lot of entanglement, the bond dimension (and thus the memory and time of the computation) will grow exponentially with the entropy. Conversely, we know that if for a state $\vert\psi\rangle$ the $\alpha$-...

11

Numerical relativity begin in the mid-1960s and had a major breakthrough in 2005. The LIGO gravitational wave observatory had started collecting data in 2002, so there was a strong impetus to be able to match theoretical simulations of merging black holes to observations. This paid off in 2016 when LIGO made its first detection. Einstein's equations are ten ...

11

Such a simple question, but it opens up so many cans of worms. Here's my crack at a comprehensive answer simpler than what you'd find in a textbook. I'm sure a numerical relativist would have a much more inside scoop... this is coming from more of a mathematical perspective. First I'll try to clear up some general difficulties which I think were ...

10

EDIT: This answer is specifically from the perspective of very computationally oriented fields like theoretical plasma physics. Most physicists can program, and in fact many are rather good programmers. It would be difficult to work in modern physics without being able to program. Unfortunately, many are also not terribly good programmers (I've read many a ...

10

You are asking two questions. I am only going to address one of them: Can the Church-Turing hypothesis be deduced from other fundamental law of physics? There are two fundamental theories of physics that account for nearly all experiments and observations performed to date: general relativity and the Standard Model. If we could simulate these theories by ...

10

But the most glaring is that it is quite clear that the moment you introduce anything less than zero latency (speed of gravity). The entire system falls apart, planets fly off, everything dissipates. Newton himself didn't quite like the instantaneous action at a distance as implied by his law of gravitation. The only saving grace is that it worked. Laplace ...

10

But now we have fast computers and advanced numerical methods. But not only do researchers still use PT for particular problems, much of theoretical work in quantum mechanics is still based on first-order (or second-order at best) PT. The reason perturbation theory has not been abandoned is computational complexity. This field (CC) is the study of how the ...

10

This is a supplement to Thomas's answer from March. I don't yet have enough reputation to add a comment, so let me write something not quite so brief but hopefully still clear. Although certain lattice QCD calculations with physical masses are currently feasible (and underway), many projects still need to use heavier masses. This is particularly true of ...

10

Yes, this is possible -- I used to study it in undergrad, actually. I would say that the prerequisites are probably a few semesters of quantum mechanics -- enough to learn concepts like Born-Oppenheimer approximations, perturbation theory, and angular momentum theory. A course specifically in atomic and molecular physics would also help. As you say, and as ...

9

While not strictly lattice QCD, Michael Creutz' 30 year old lattice gauge papers have very simple C implementations (!). For example, look at this paper, which gives a very readable explanation of lattice gauge simulations, with source code: http://latticeguy.net/mypubs/pub165.pdf The source code is also available here: http://thy.phy.bnl.gov/~creutz/z2/ ...

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