Questions tagged [physical-constants]

This tag is for questions relating to physical constants which are any of a set of fundamental invariant quantities observed in nature and appearing in the basic theoretical equations of physics. Accurate evaluation of these constants is essential in order to check the correctness of the theories and to allow useful applications to be made on the basis of those theories.

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Running of the fine structure constant: meaning of $\alpha(Q^2=0)$?

In Measurement of the Running of the Fine-Structure Constant, the L3 collaborations writes At zero momentum transfer, the QED fine structure constant $\alpha(0)$ is very accurately known from the ...
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Rydberg energy and Hubble constant

Although they are of different dimensions, the value of the Rydberg energy is very close to that of the Hubble constant. Rydberg energy (R): $2.179 \times 10^{-18}$ [Joule] = 13.6 [eV] Hubble ...
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What are the numerical values of the gauge coupling constants? [duplicate]

I mean the values of: $U(1)$ gauge coupling $SU(2)$ gauge coupling $SU(3)$ gauge coupling
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Is the Planck force a truly "Planck unit"?

The Planck force appears to be defined as the ratio of the Planck energy to the Planck distance, $ F_P = E_P/l_P $ that can be rewritten as $$ F_P = \frac{ E_P }{ l_P} = \frac{ c^4 }{ G }. $$ Isn't it ...
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Is Planck length constant in String Theory? Does it have a renormalization flow?

Is Planck length constant? Planck length $l_p$ is dependent on Newton constant $G_N$ which is related to coupling constant of interaction of gravitons, but from field theory point of view, we know ...
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Trouble with the algebra in Srednicki book chapter 28

I'm studying chapter 28 in Srednicki (the renormalization group) and I'm having troubles figuring out how he derives eq. (28.15) (last summation above) from eqs. (28.7) and (28.9). More specifically ...
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Angular momentum dimensions

In Cohen-Tannoudji's book vol.1 page 648 the following is said: $|\psi \rangle$ an arbitrary state. $\langle\psi|\vec J^2|\psi \rangle=\sum_{i=1}^3\langle\psi|J_i^2|\psi \rangle=\sum_{i=1}^3 ||J_i|\...
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Planck's Law notation

I have just picked up the book Elementary Quantum Mechanics by Peter Fong, and on the first page he writes Planck's law as $$u(\nu)d\nu=\frac{8\pi h \nu^3}{c^3}\frac{1}{e^{h\nu/kT}-1}d\nu$$ where $u(\...
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What does it mean that dimensionless physical constants cannot be calculated but only measured?

I have read a passage in Wikipedia about the List of unsolved problems in physics and dimensionless physical constants: Dimensionless physical constants: At the present time, the values of various ...
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How convert 1 Debye to atomic units

I would like to convert 1 Debye to atomic units. I have that $$ 1~\mathrm{Debye} = 10^{-18}\mathrm{StatC}\cdot \mathrm{cm}\\ = 10^{-20}\mathrm{StatC}\\ = 10^{-20} \mathrm{cm}^{3/2}\mathrm{g}^{1/2}\...
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What physics laws justify Planck's units? [duplicate]

It is usually said that Planck units have no scientific ground, yet they are useful indeed because many laws collapse, make no more sense at, say, Plancks length or time. Can you mention a couple of ...
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Relativistic Corrections to the Binding Energy of Atoms

The binding energy of atoms is the minimum energy required to remove an electron of an atom from its orbital. Using dimensional analysis, we can derive the following equation. $$E_B\propto\frac{m(ke^2)...
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Is there a "Moore's law" for humanity's ability to accurately measure fundamental physical constants?

The CODATA releases seem to represent the scientific consensus on what their values approximately are. Their accuracy improves over time. Say, for the electron mass, would it be accurate to expect a ...
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How does the constant proportionality balance an equation?

The Newtonian universal law of gravitation, Every object in the universe attracts every other object with a force that is proportional to the product of their masses and inversely proportional to the ...
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Why is the Fermi Constant sometimes listed in units of 'joule metre$^3$'? How is that related to its normal units of GeV$^{-2}$ or J$^{-2}$?

Normally, the Fermi Constant is valued as $1.1663787\times10^{-5}$ GeV$^{-2}$ or its equivalent in Joules. But on Rampfesthudson and Oxford Reference, it says, $1.435\times10^{-36}$ joule metre$^3$ I ...
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Could our universe still work if either one of $c$, $h$, $q$, $G$, permeativity, permeability or $H_o$ were slightly different? [closed]

Could our universe still work if either one of c, h, G, q, permeativity, permeability or Ho were slightly different? Also all of them are thought of as being constants for the whole history of the ...
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Is the exact definition of the Planck units important?

Wikipedia says there are other, possibly better ways to define the Planck Units based on whether we want to factor in or out a $2$ or a $\pi$ or a $4\pi$ as the case may be. Most of them represent ...
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Why are Yukawa couplings regarded as fundamental constants if their values vary with scale?

Why are Yukawa couplings regarded as fundamental constants if their values vary slowly with the energy scale (distance scale) at which they are measured? This question is the same as why are quarks ...
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Is Planck temperature really the highest temperature?

Actually I was learning about Wien's displacement law. It states that $$\lambda T=2.898×10^{-3} mK$$ This is actually a part of Planck's law where the Planck's constant originated. Now Planck's ...
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h-bar limits measurement precision. What limit arises for h-bar itself?

The question is simple. h-bar, or $\hbar$, limits the precision of every measurement, books tell us. For example, length measurements are limited by the Compton wavelength. What limit for the ...
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What are the energies (in eV) that we need to reach to create 'strings', gravitons and a 'Theory of Everything' (quantum gravity)?

Somehow, I cannot find an answer on the Web.... Possibly because nobody knows, of course, but I would still like to find a 'ballpark' answer... Creating the particles or whatever (and whatever they ...
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Relationship between electron $g$ value and fine structure constant from QED

The wiki article on the fine structure constant says that 'The theory of QED predicts a relationship between the dimensionless magnetic moment of the electron and the fine-structure constant $\alpha$' ...
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Vacuum permittivity vs 1/(36π) nF/m

Vacuum permittivity is $ϵ_0\approx8.8541878128×10^{−12}\,\mathrm{F⋅m^{−1}}$. Therefore, within 0.14%, $ϵ_0\approx\displaystyle\frac 1 {36\,π}\,\mathrm{nF⋅m^{−1}}$, thus $\displaystyle4\,π\,ϵ_0\approx \...
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Strength of strong force and electromagnetic force

In this link, it is claimed that the strength of the strong force w.r.t. the E&M force is about 137 times larger. Does this have anything to do with the fine structure constant?
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Why don't strings have a Planck mass of vibrational energy?

It is claimed that strings have a length $l_S$ within an order of magnitude of the Planck length $l_{Pl}=10^{-35}$ m. If they oscillate at the speed of light, $c=10^8$ m/s, then their natural ...
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3 votes
4 answers
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Why is there a $1/2$ in the definition of energy per degree of freedom $E=(1/2)kT$?

I was looking for an authoritative definition of Boltzmann's Constant. That led me to this discussion on NIST's site: Kelvin: Thermodynamic Temperature Thus, internal energy and temperature are ...
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17 votes
8 answers
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How can Planck's constant take different values?

I have seen books and papers mentioning "In the semiclassical limit, $\hbar$ tends to zero", "the scaled Planck's constant goes as $1/N$ where $N$ is the Hilbert space dimension" ...
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Clarification of derivation of Bohr radius according to Griffiths

I'm currently going through Griffiths QM (second ed.) and am on the section (page 150) where he derives the Bohr radius. This is the line he gives $$ \kappa=\left(\frac{me^2}{4\pi\epsilon_0\hbar^2}\...
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1 answer
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Prediction of constants with the standard model

I am trying to understand how the standard model predicts constants. Does it also predict fundamental constants such as the mass of the electron? And when looking at the result of the $g-2$ experiment,...
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Why does everyone keep using torsion balances for measuring the gravitational constant?

Most of the experiments aimed at measuring the gravitational constant use very complex setups involving suspended balls (Cavendish-like experiments). This is however not exactly the ideal setup – and ...
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Is there a explanation to why bodies with higher heat capacity transfer heat to bodies with lower heat capacity?

We know that $C$=$mc$ Where($m$ is the mass of the body and $c$ is the specific heat) , A body $M_1$ with $C_1$ and another body $M_2$ with $C_2$ where ($C_1$ $\gt$ $C_2$), What is the reason that ...
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1 vote
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What happened to the Planck charge on Wikipedia? [closed]

Wikipedia used to have a nice article about the Planck units, with contributions made directly by Don Page. I recently visited the current article and the Planck charge kind of disappeared. I also saw ...
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How do we actually build the new kilogram?

Once upon a time the kilogram was a piece of metal preserved in a vault located in a basement. If I needed to build a high precision balance all I needed to do was tuning the the value of my kilograms ...
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Is the value for the Boltzmann Constant different in 2D?

So I'm simulating some hard sphere collisions and want to determine the Boltzmann constant in two dimension, using the equation $$PA=Nk_BT$$ where $A=\pi R^2_{\text{container}}$, $P=(\text{average ...
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What is the physical meaning and origin of the gravitational constant $G$?

Is $G$ just a value to fix the units in the equation? Something like a proportionality constant or a coupling constant?: $$F=\frac{G m_{1} m_{2}}{r^{2}}$$ Does it have any physical meaning or physical ...
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What, exactly, is the Fermi Constant? What is its value? And what is the difference between $G_f$ and $G_f^0$?

There is no Wikipedia page for Fermi's Constant, and the page they DO have is confusing. From Fermi's Interaction: How can $G_f^0$ not be equal to $G_f$? What is the difference? And when they give ...
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Can the Planck length be altered by relativistic motion? [duplicate]

If a spaceship is flying by you at high speed relative to you, will the Planck length in the moving frame be smaller than the planck length in the non-moving frame. Will observers in the different ...
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3 votes
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A finer tuned universe [closed]

I was reading about the idea of the fine-tuned universe and the anthropic principle. It is stated how small changes in some of the physical constants would render life as we know it impossible. My ...
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What are $δ$ and $ε$ in the list of Dirac's five 'fundamental constants', concerning his 'Large number hypothesis'?

From Jean-Philippe Uzan's Varying Constants, Gravitation and Cosmology: Dirac formed five dimensionless ratios among which1 δ ≡ H0ħ/mpc2 ∼ 2h × 10−42 and equation M1 and asked the question of which of ...
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String length $\gg$ Planck length?

The potential energy of a string $E_{pot}$ is given by $$E_{pot}=T \times L\tag{1}$$ where $T$ is the string tension and $L$ is the length of the string. The internal kinetic energy $E_{kin}$ of a ...
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2 answers
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How does the weight to break a bar depend on the dimensions?

Imagine a horizontal bar of glass, say, 10 cm long, 1 cm large and 1 mm thick. At one end it is maintained stably, e.g. by a screw clamp, and at the other extremity, some increasing weight is added (e....
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How to write the unit of molar gas constant correctly?

Is it $8.314J{mol}^{-1}K^{-1}$ or $8.314JK^{-1}{mol}^{-1}$ or $8.314mol^{-1}K^{-1}J$ or $8.314K^{-1}mol^{-1}J$ or $8.314mol^{-1}JK^{-1}$?
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$G$ expressed as a function of $c$?

The escape velocity for a given mass $M$ and a given radius $r$ is given by: $v_e = \sqrt{ \frac{2 G M}{r} }$ With $M$ = 25 kg and $r$ = 1/$c$ we have: $v_e = 1.0001917061 \approx 1$ Can we express $G$...
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Does General Relativity provide a value for $G$? [duplicate]

It only recently was specifically pointed out to me that Einstein was right, and Newton was wrong. Newton wasn't wholly wrong. He theorized that gravity was a force that acted between bodies, and came ...
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What, exactly, is the difference between a 'gauge coupling constant' and ones like the Fine Structure Constant?

Several times in my reading I have come across mentions of gauge coupling constants, usually denoted $g_1$, $g_2$ and $g_3$, which have different values than the Gravitational Coupling Constant $G$ or ...
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2 votes
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What is the concise form of physical constants? (What is the number in the parentheses?)

According to nist : Proton mass $(m_p)$ : Numerical value $: \mathrm{1.672 \ 621 \ 923 \ 69 \ × \ 10^{-27} \ kg}$ Concise form $\ \ \ \ \ \ \ \ \ \ : \mathrm{1.672 \ 621 \ 923 \ 69(51) \ × \ 10^{-...
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Is the electromagnetic coupling constant of the muon exactly the same value with the electron $α \approx1/137$?

I am asking because I want to know If I can use the Schwinger equation: $$a_{e}=\frac{\alpha}{2 \pi} \approx 0.0011614$$ to calculate the one-loop QED contribution to the anomalous magnetic moment of ...
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Is it impossible for anything to touch anything else because of Planck lengths?

Suppose you touch a cube. There would still be a Plank length between your hand and the cube. Does this mean that it is impossible for anything to touch anything, specifically because there is always ...
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2 answers
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Why does the ladder operator contain the $\hbar ω$ part?

For homework I was deriving the ground state wavefunction for quantum harmonic oscillator using the ladder operator method. From what I've understood, the whole idea starts by factorizing the ...
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2 votes
1 answer
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Does electromagnetism have no free parameters?

In SI units, Maxwell's equations (in vacuo) seem to have two free "parameters" or "constants". The vacuum permittivity, however, can be eliminated by properly redefining the ...
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