Hot answers tagged scales
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From the Wikipedia article for Reynolds number:
In fluid mechanics, the Reynolds number (Re) is a dimensionless number that gives a measure of the ratio of inertial forces to viscous forces and consequently quantifies the relative importance of these two types of forces for given flow conditions.
In addition to measuring the ratio of inertial to ...
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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit?
In real life, the current can't jump instantaneously because there is always some finite inductance in a circuit. However, this is just a typical idealized textbook problem where the inductance is assumed identically zero, so the current can jump instantaneously according to the assumptions of the problem. Note the current also jumps in their solution for ...
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There is a phenomenon called decoherence in quantum mechanics which is largely responsible for this. Basically (the following is a simplification), all the strange behavior that occurs in QM tends to happen when the wavefunctions of different particles are in phase. Decoherence occurs when the phases are randomized, so there's no special correlation between ...
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All we can do precisely is give a probability for some physical quantity to have its observed value. For example (subject to various assumptions!) the probability of the cosmological constant having it's observed value is around 1 in $10^{120}$. Since this is absurdly low we say it's fine tuned.
But where you draw the line between fine tuned and not fined ...
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Molecules vibrate with frequencies in the range 10$^{12}$ to 10$^{14}$Hz. Although I don't know of any strict definition, I would take the view that a molecule must hold together for a few vibrations otherwise what you have is a collision not a molecule. That means the lifetime must be greater than 10$^{-14}$ to 10$^{-12}$ seconds, depending on the molecule.
...
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In physics we distinguish between the physics of "atoms and molecules" and nuclei. Atoms and molecules are described by the same theory, thus I will ignore those molecules here completely and only consider the difference between nuclei and atoms.
I suppose you recognize that an atom is a bound system, so is a nucleus a bound system. Maybe you have seen how ...
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The hierarchy problem is not only about big numbers, such as $M_{pl}/M_{EW}$, per se'. In fact in QCD there is no hierarchy problem associated to the ratio $M_{pl}/\Lambda_{QCD}$.
The problem is actually about the quantum numbers of certain operators in a Wilsonian EFT. The point is that we understand the SM as an effective low-energy description of the ...
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There are many physical intuitions often presented in various texts on fluid dynamics. I won't mention those here. I will, however, mention that mathematically the passage from a particle point of view to a continuum point of view is still a largely un-resolved problem. (With suitable interpretation, this problem was already posed by Hilbert as his 6th of 23 ...
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The theory of fluids introduces material parameters in the stress tensor, which help model the substance. "The viscosity coefficient is the proportionality constant relating a velocity gradient in a fluid to the force required to maintain that gradient. The thermal conductivity is the proportionality constant relating the temperature gradient across a fluid ...
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This is a very good question. I think there is no quantum field theory
which predicts all particle masses.
Masses (measured in Planck unit) are real numbers. The real numbers are NOT predictable,
just like the radius of the orbit of Earth moving around Sun (measured in Planck unit) is not predictable. So the real fundamental constants are NOT predictable,
...
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The classical electron radius is a length scale at which the classical self-energy of the electron completely accounts for the mass. It tells you where the classical theory of a pointlike electron breaks down.
The compton wavelength tells you where quantum mechanics takes over. The ratio of the compton wavelength to the classical electron radius is the ...
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That wiki article itself provides the answer:
In simple terms, the classical electron radius is roughly the size the electron would need to have for its mass to be completely due to its electrostatic potential energy - not taking quantum mechanics into account.
So since the the photon is massless, and uncharged (it doesn't interact with itself), its ...
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Even a physical quantity which changes by discrete amounts can often be well approximated by a continuous function of time.
The derivative is a property of a mathematical function. Any differentiable function must necessarily be continuous, and a continuous function will change by arbitrarily small values for an arbitrarily small change in inputs.
The ...
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Of the four forces in the quantum field theory framework:
the strong is mediated by the gluon and the effective potential this creates is of the order of the size of nuclei, because it is very short range at the current size of the universe . Very short range.
The Z and W bosons are mediators of the weak interaction, and are much heavier than protons or ...
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You can't do it for real in quantum field theory, there are always adjustible parameters. The reason is that quantum field theory doesn't have a fundamental length, it is defined on the continuum, so it can always be rescaled. But if you have a quantum gravity theory that reduces to quantum field theory at energies less than some large energy, you can get ...
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It's the same problem because the low scale matches in both definitions; and the high scale matches in both definitions, too. Both problems are the puzzle why the two scales are so much different.
First, the low scale. In the Higgs fine-tuning, you define the low scale as the Higgs mass. But the Higgs mass can't be parameterically greater than the Z-boson ...
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This is an extremely comprehensive review of electronic properties in two-dimensional electron systems (2DESs):
http://rmp.aps.org/abstract/RMP/v54/i2/p437_1
but, as you can imagine, it covers almost everything there is to cover in 2DESs. For areas (in transport) you're focusing on you will find only sections IV C and D useful; it involves computation of ...
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The reason the Planck mass is big is the same reason that the Planck length is small--- we are living on a scale which is enormous in Planck units. So everything around us is made from enormous atoms which have tiny, tiny masses, and you need a large number of atoms to make 1 Planck mass, just as you need a large number of Planck lengths to make 1 meter. The ...
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Why is current not 0 in a regular resistor - battery circuit immediately after you closed a circuit?
This question is working within the realm of 'circuit theory', which is an idealization useful for introductory teaching of electromagnetism. It is really a simplification of electrodynamic field theory, just a special case making useful assumptions. A lot of conceptual problems in circuit based questions come from forgetting that you are dealing with a ...
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Physics is all about making the right approximations, in the hope that we can gain some actual physical insight into our problem and make verifiable predictions.
For example, say you wanted to calculate the trajectory of a cannonball that has been fired from a cannon. It would be a Sisyphean task to account for all the possible variables that could affect ...
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Good question! When I started writing this answer I couldn't think of an example, but then I realised that Brownian motion fits the bill, as I'll explain below. So please forgive the somewhat tangential introduction:
To a reasonable degree of approximation, temperature can be thought of as energy per degree of freedom. I say approximation because in quantum ...
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Consider the neutral, Schwarzschild black holes in $d=4$. If they're large, they're solutions to Einstein's equations. However, Einstein's equations have higher-derivative correction terms that go like $(L^2 R)^k R$ where $L$ is a characteristic length and $R$ is the Riemann curvature, schematically: many possible contractions are possible.
These terms may ...
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Brandon, the simple truth is that you have just asked one of the hardest and least understood questions in all of physics. So, don't feel bad if you don't understand it very well, because, er... no one else really does either?
It's not that we can't model this stuff mathematically. Shoot, Richard Feynman's version of something called Quantum Electrodynamics ...
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Yeah, it's just an ansatz.
For most practical purposes, it doesn't matter precisely which Lagrangian you work with, because most of the physical values you're computing only depend on the large size asympotics of the correlation functions, i.e., on the universality class of the Lagrangian. You can add any reasonably small non-renormalizable perturbation ...
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