# Tag Info

## Hot answers tagged scales

8

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 ...

7

Instead of assuming the earth is made of metallic hydrogen, let's just compare Earth's density of $5.52 \times 10^3 kg/m^3$ to that of neutrons' $2.3 \times 10^{17} kg/m^3$ because degenerate matter consisting of neutrons is what you get when electrons are forced into nuclei. That's a density increase of about $4.17 \times 10^{13}$ (at least 3 orders of ...

6

When you look at crystalline substances, there is really not that much space between the atoms. What people mean when they say that an atom is mostly empty space, is that the INSIDE of the atom is very sparsely populated with stuff. This is because the stuff in question, the nucleus and the electrons, are tiny in comparison to the actual size of the atom. ...

5

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 ...

5

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 ...

4

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 ...

4

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 ...

4

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 ...

4

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. ...

3

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 ...

3

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 ...

3

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 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 ...

3

According to the same Wikipedia article you cite, ...the zero point is determined by placing the thermometer in brine: he used a mixture of ice, water, and ammonium chloride, a salt, at a 1:1:1 ratio. This is a frigorific mixture which stabilizes its temperature automatically: that stable temperature was defined as 0 °F (−17.78 °C). The second point, at ...

3

Actually, the Higgs scale is not the TeV scale. The Higgs scale is the scale of electroweak symmetry breaking, i.e. $\mathcal O(100 \mathrm{GeV})$. The Terascale comes into play along with the Higgs, as supersymetry - the most popular extensions of the Standard Model - would actually like a small Higgs mass, much smaller than its measured value ($< M_Z$ ...

3

Reynold's number is defined to be: $$\text{Re} = \frac{ v D }{ \nu }$$ where $v$ is the characteristic velocity for the flow, $D$ is a characteristic size and $\nu$ is the kinematic viscosity. Now, why should we care? Why is Reynold's number important? Well, the first thing to realize is that the Reynolds number is a dimensionless number. This means ...

2

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 ...

2

Theories don't predict units unless you put units in. A theory which predicts the masses of the fundamental particles would actually only predict the mass ratios $a_\phi$. Presumably they would emerge as eigenvalues of some operator, or perhaps as the zeros of some complicated function.

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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 ...

2

For EM, macroscopic bodies are generally electrically neutral so there is no net electric force between them. For gravity, macroscopic bodies are gravitationally "charged"; I can't think of any that are gravitationally neutral.

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Let me note that the cross-section of Thomson scattering of low-frequency electromagnetic radiation on a free electron is of the same order of magnitude as the classical radius of electron squared (loosely speaking).

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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 ...

2

There is a popular physics book (similar to The Elegant Universe, but different) (EDIT: a comment suggested this is The Black Hole War, and that sounds right, although I can't reference the exact figure) that I remember addressing the significance of the Planck Mass relative to the idea of elementary particles versus black holes. For now, Wikipedia will ...

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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 ...

2

The story is this, as much as I remember. Fahrenheit chose the zero point on his scale as the temperature of a bath of ice melting in a solution of common table salt (a routine 18th century way of getting a low temperature). He set $32^{\circ}$ as the temperature of ice melting in water. For a reproducible high point on the scale he chose the temperature of ...

2

If you want the new physics to solve the hierarchy problem, it's best if it is close to the weak scale, or else you will be left with a residual little hierarchy. You are describing the "big desert" between the weak and GUT scales. I think it was motivated by the idea that SUSY lived at the weak scale, solving the hierarchy problem and insuring gauge ...

1

As already said size of elementary particles is not so simple. Orderer from high mass to lower (add 125GeV to the Higgs): (From Matt Strassler's blog) Anyway, why don't you create an image yourself?

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