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Questions tagged [absolute-units]

Absolute units, or natural units, are a system of units where certain universal dimensionful constants are set to 1. This often simplifies various formulae. Planck units, Atomic units, Stoney units, and Particle/Atomic natural units are examples of absolute unit systems.

Absolute units, or natural units, are a system of units where certain dimensionful constants are set to 1. This often simplifies various formulae.

For example, in non-natural units, the Benkenstein–Hawking black hole entropy formula is $$\frac{S}{k_B}=\frac{1}{4}\frac{A}{l_P^2},$$ where $l_P$ is the Planck length and $k_B$ is the Boltzmann constant. If one uses natural units where the Boltzmann constant and the Planck length are set to 1, this reduces to $$S=\frac{A}{4}.$$

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What is the decay width and why is it given in energy units?

I'm reading Thomson, Modern Particle Physics, and in chapter 16 author says that the decay width of the Z boson is $\Gamma_Z =2.452 \pm 0.0023 \,\mathrm{GeV}$. He also says the total width of the decay is the sum of the partial widths,…
Patrick
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How to get Planck length

I know that what Planck length equals to. The first question is, how do you get the formula $$\ell_P~=~\sqrt\frac{\hbar G}{c^3}$$ that describes the Planck length? The second question is, will any length shorter than the Planck length be…
user2346
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Why do universal constants have the values they do?

This is meant to be a generic question of the type that we get repeatedly on this site, in different versions: The origin of the value of speed of light The gravitational constant G theoretically? What if Planck's constant were smaller or bigger…
user4552
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Do the Planck voltage and the Planck current have a natural physical interpretation in classical general relativity?

Most Planck units are a product of powers of all three of $\hbar$, $c$, and $G$, so we will not be able to fully understand their physical significance until we have a full theory of quantum gravity. But some of them are only powers of one or two of…
tparker
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Isn’t natural units prone to mistakes?

Suppose I am deriving a length contraction formula using natural units. If I arrive at $L = L_0 \sqrt{1 - v^2}$, I know that I should divide $v^2$ by $c^2$ to get the correct answer in SI units. But what if I mistakenly forgot to square the velocity…
Atom
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What exactly are we doing when we set $c=1$?

I understand the idea of swapping from unit systems, say from $\mathrm{m\ s^{-1}}$ to $\mathrm{km\ s^{-1}}$, but why can we just delete the units altogether? My question is: what exactly are we doing when we say that $c=1$?
user12345
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How can Planck units be consistent with conflicting dimensions of mass?

I suspect I'm missing something obvious, but I'm coming up blank. I've gotten pretty comfortable with so-called natural units over the years: in doing quantum mechanics/QFT, it's common to set $c = \hbar = 1$ and in GR, it's common to set $c = G =…
user27578
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Can entropy be equal to zero?

I've searched for it but I only found contradicting answers from "scientists": Dr. David Balson, Ph.D. states: "entropy in a system can never be equal to zero". Sam Bowen does not refutes the following affirmation: "It is know[n] that entropy is…
Nikki Vidanicus
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Can a half-life be given in electron-volts?

I'm using this link to search for particular energies in which gammas may be emitted (for nuclide identification on a gamma spectrum). If on the above link you go down to the "γ condition #1" line, and put the energy between 2241 an 2243, and click…
Matt
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Why is the action dimensionless in natural units?

As I understand it, a natural system of units is one in which the numerical values of $c$ and $\hbar$ are unity, i.e. $c=\hbar =1$. What I find confusing is that they are still dimensionful, i.e. $[c]=LT^{-1}$ and $[\hbar]=ML^{2}T^{-1}$. So, how…
Will
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Is the Bohr radius deprecated?

The Bohr radius ($a_0$ or $r_{\text{Bohr}}$) is a physical constant, equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of…
Derek Seabrooke
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How to recover units?

Theorists frequently use convenient units like $\hbar=1$ or $m=2$ or whatever is useful to simplify the notation in the problem. And after all the calculations are done the units are recovered based on what the unit of the answer needs to be. I can…
ftiaronsem
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Dimensions of momentum?

I am learning realitivity in college and in our class our lecturer explained four-momentum. When I was reading a book in QFT. it writes the momentum as $p^{\mu} = (E,p^i)$. Why is one of the components energy? Energy and momentum have different…
user276350
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Is my friend right about omitting $c^2$ in world famous tiny equation?

I know $E = mc^2$ says that inertial mass of a system is equal to the total energy content of a system in its rest frame. My friend told me the $c^2$ can be omitted from this equation because that's just an `artifact' when measuring inertia and…
RK James
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Where does Planck's constant come from in non-renormalizability of quantum gravity?

I am trying to understand the idea that gravity breaks down at the Planck scale, but I am confused by the use of natural units ($c = \hbar = 1$). The Einstein-Hilbert action in natural units is: \begin{equation} S_{EH} = \frac{1}{16 \pi G}\int d^4 x…
Caspar201
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