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"Physics breaks down" is a bad way of saying what people are trying to say. It's the sort of thing that sounds cool at first, but then it starts misleading people. What scientists mean is "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there." They do ...


50

Let me give an example of a very, very mild case of 'theory breaks down'. Boyle's law is stated as follows: $$ P_1V_1 = P_2V_2 $$ Expressing that for a given quantity of gas the pressure and volume are inversely proportional to each other. At low pressures Boyle's law holds good. The reason that it holds good is that at low pressure the gas molecules take up ...


22

"Physics breaks down" sounds good, but it is confusing. A better phrasing would be "known physics breaks down." Physics attempts to model reality using mathematics. In this sense, physics has no "laws." In the famous words of Captain Barbossa, "They're more like guidelines." However, we have many of these ...


18

The phrase "in principle" means that the action being described is hypothetical, usually assuming certain ideal conditions. It contrasts to an action performed "in practice", which refers to actually carrying out the task with all the real-world complications that arise. The use of "in principle" implies that the task may be ...


10

"In principle" things are things which can easily be derived from the fundamental principles of the model. This tends to get used in situations where the real life application of this is more complicated. As an example from my computer science background, if given a matrix problem $Y=MX$, it is, in principle, possible to solve for $X$ given $Y$ by ...


4

It's important to be aware that the phrase is by no means limited to physics, and it means the same thing there that it does in other contexts. It does not mean the same thing as "hypothetically". Instead, you use it when you have a simplified model for a situation, and the thing is possible in that model, even if it isn't possible in the more ...


3

Coupling means simply that both equations involve both fields, so that you can't solve them separately. Now, both equations involve a relation between the curl of one field and the other field. So if we take the first equation and apply curl, the right hand side will contain $\nabla \times \mathbf{B}$, which we can write in terms of $\mathbf{E}$ and get an ...


3

In this context, "intrinsic" means that the Hall conductivity comes from the Berry curvature. That is, it's a contribution intrinsic to the band structure. Disorder can produce "extrinsic" contributions to the anomalous Hall effect through so-called side-jump and skew-scattering mechanisms. If you're interested, you can see this answer of ...


2

More generally, it’s often said that laws of physics ’break down’ under conditions where their underlying assumptions no longer hold. For example, Newtonian physics works very well most of the time, but at relativistic speed it becomes increasingly inaccurate. For comparison, it’s ok to assume that the Earth is flat if you’re building a house, but not if ...


2

In principle is the opposite of in practice. That is something may be easy/possible in principle, but hard/impractical to do in practice. For example, finding roots of a 4-th degree polynomial is possible in principle, but is is rarely done in practice as the expressions are cumbersome and it is often easier to resort to numerical procedures.


1

$\nabla \cdot \mathbf{G} = 0 \implies \mathbf{G} = \nabla \times \mathbf{H}$ is part of the Helmholz theorem (you also need to make some assumptions about the asymptotic behavior of $G$). $\nabla \cdot \nabla \times \mathbf{H} = 0$ is a relatively straightforward identity in vector calculus, an easy proof is just to write out the components in Cartesian ...


1

If referring to electrical (not thermal) conductivities, then yes they are the same thing. Though the term Hall usually pops up when dealing with the Hall effect (classical or quantum) meaning the transverse conductivity is dominated by the effect of an external magnetic field.


1

The words "ordered" and "disordered", in relation to entropy, are the source of a lot of confusion and are not even always an accurate description. In your coin example, a more typical use of the word "ordered" would be to say that all three coins are the same (either heads or tails). If you start in an ordered state, and each ...


1

The spring force doesn't limit the degrees of freedom of a body connected to it. For instance if you have a mass on one end of the spring and the other is fixed then the body is free to do oscillations and if you given some horizonatal displacement then it's free to move in that direction too. There is no constraint on the body and so it's not a constraint ...


1

This is the continuous spin Ising model. It has a phase transition at large $\beta$ in any dimension greater or equal to $2$; see this paper, for instance. It is also known as the infinite spin Ising model. It was first introduced by Griffiths in this paper. See also this paper for a more geometrical way of analyzing this model (through a generalization of ...


1

A very simple example of physics breaking down can be explained via Newton's law of universal gravity: $$F = G\frac{ m_1 m_2 }{r^2}$$ Here $r$ is the distance between centers of the masses $m_1$ and $m_2$, and $G$ the gravitational constant. The problems: -If you have two massive object that can be brought infinitely close together, the force value would ...


1

You are asking about a black hole's singularity, and what we mean when you see phrases like "physics breaks down" or "there is an issue with renormalizability". General relativity also works perfectly well as a low-energy effective quantum field theory. the real problem is not so much nonrenormalizability as high-energy behavior ...


1

For all we know a black hole could just be a very dense sphere ... One you reach or pass the event horizon, the force required to prevent you falling towards the singularity at the centre of the black hole becomes infinite. The future path of any object within the event horizon reaches the singularity within a finite amount of time. So we can be certain ...


1

Edit: I made a mistake in interpreting your question. Since you're only interested in knowing how to generate the full algebra this is how it is done: To get a matrix which rotates a spinor about an axis $\hat{n}$ by angle $\phi$ we just have to calculate $$\exp\Big(i(\sigma_x \hat{n}_x+\sigma_y \hat{n}_y+\sigma_z \hat{n}_z)\frac{\phi}{2}\Big)$$ All this ...


1

To cleave a crystal, one provides a little defect at the edge (a nick, for example), then applies some pressure at that point. Pressure causes the defect to propagate, cleaving the crystal along a crystalline axis. This is a common method to cut crystals because it’s easy, relatively controllable, and leaves an ideally flat and clean surface. It’s also a ...


1

I suppose it depends on the material, but when I was researching 2D semiconductors, we actually just used Scotch tape. You press a piece of tape down firmly onto the surface of your sample and then slowly peel it away. The sample ends up being cleaved as several layers from the top separate from the bottom of the sample. (This happens because these samples ...


1

No. Physicists don’t have a special term for $dt/dx$. They would just call it “inverse speed”. It doesn’t occur frequently enough to have its own name.


1

Take a globe. Spin it around its normal axis, the polar axis the way the Earth spins. Then pick the globe up and while it is still spinning the first way, flip it north to south the way you would a coin. There you have a sphere spinning over two axes at the same time and your axis of mass makes no sense. The center of mass and only the center of mass is ...


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