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Questions tagged [absolute-units]

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

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Planck units and other constants

Why is it that only $G$, $\hbar$ and $c$ are used as the three fundamental constants. What about the ratio of the mass of a proton to an electron, or the quantity of dark energy, and so on?
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How to find the corrsponding expression after working with natural units $\hbar=c=1$?

If one does long calculations in natural units how does one find the right expression in let's say SI units in the end? I know that natural units make the calculations easier and also help to show ...
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Grasping systems of units

Perhaps it's that I've grown up with the SI system of units, but there's something about other unit systems that doesn't sit well with me. For example, Coulomb's law in Gaussian units can be written ...
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A question about natural/geometrized units

I had a question about the following document- Natural units I understand the conversion factors. But if you look at the tables, they take an SI unit, say 1 kg, convert it into geometrized units, say ...
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Factors of $c$ when giving masses in natural units?

I am starting a course on particle physics, and have been introduced to natural units. I am slightly confused, because we are using 'natural units', and yet masses are stated as, for instance, $139....
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Conversion from Planck unit to SI [closed]

Good evening, I'm reading the paper Prehawking radiation by William G. Unruh where it says: ...a time scale of order of $m^{3}$ in Planck units, or $10^{53}$ ages of the current universe for a ...
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What are the units of time when planck's constant is equal to 1?

If I express a Hamiltonian $H$ in units of Hz by dividing the energy terms in the Hamiltonian by hbar $\tilde{H}=\dfrac{H}{\hbar}$ which means you set $\hbar =1$. Then what are the units of time? Also ...
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How to put $c$ back into relativistic equations?

Many books set the speed of light $c=1$ for convenience. For example, Weinberg in his textbook "Gravitation and Cosmology" (though $G$ is still left as a constant): $$\begin{align} \mathrm{d}\tau^2 &...
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Could there be some system of units such that all fundamental constants are 1? [closed]

The fundamental constants in physics have extremely low values because of our scale compared to fundamental particles. Could there be such a system of units such that all fundamental constants are 1?
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What are the units of a scalar field if I only impose $c=1$?

I know that a scalar field in 4d in natural units ($\hbar = c =1$) has mass dimension 1. We can see this by requiring that the kinetic term in the action $$ \int \text{d}x^4 \: \partial_{\mu} \phi \: \...
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Units of the metric tensor or how to get the unit right for the line element

In this answer it is stated that the metric tensor elements have no physical unit, i.e. $[g_{\mu\nu}] = 1$. What is the convention to get the physical unit of the line element $ds = g_{\mu\nu}dx^\mu ...
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What's the matter with Planck mass $M_P$ in Einstein-Hilbert action?

The Einstein-Hilbert (EH) action is often written as $$S_{EH}=\frac{c^4}{16\pi G}\int d^4x \sqrt{-g}R\tag{1}$$ and often as $$S_{EH}=\int d^4x \sqrt{-g}M_P^2 R\tag{2}.$$ Comparing (1) and (2), one ...
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Are ‘fundamental measures’ a thing?

The question I want to ask is: What measures are needed to describe the physical world and what are the fundamental ones of those, in the proper sense of the word fundamental? But that might be too ...
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Why is the mass dimension of the covariant derivative 1?

I'm reviewing an exam, and I can't figure this one out. I know the covariant derivative, but I'm not seeing how it necessarily has a mass dimension.
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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. ...
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What is the Planck Pressure?

What exactly is the Planck Pressure? According to wikipedia the Planck pressure "is not found except for shortly after the big bang or in a black hole". But wouldn't the pressure inside a black hole ...
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Could light be frozen?

If a beam of light in a vacuum was instantaneously changed in temperature (along with the surrounding area) to absolute zero, would the beam freeze in place or just be snuffed out? If it froze in ...
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What does it mean to say that linear momentum has dimension of inverse of length?

Hello i was reading a book written by a physicist about Fourier Transform, and there he says that the momentum space in discrete Fourier transform has it's name because of the value $ p=\frac{2\pi}{...
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1answer
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Confusion over the standard units used in special relativity and particle physics? [duplicate]

I am new to relativity and particle physics and I am struggling to understand the conventions for the dimensions that are used in particle physics. I have read this and as I understand it: $$\sqrt{s}=\...
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1answer
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How do I convert natural/Planck units to SI? [closed]

I am looking at a paper which has set: $\beta=1/kT=1$ where k is the Boltzman constant. It uses natural planck units ie $m=\hbar=k=1$. Does it make sense to extract a temperature $T$ and mass $m$ ...
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Why do people say that the string length is on the order of the Planck length?

As I understand it, string theory has only one fundamental dimensionful quantity - the string tension $T = 1/2 \pi \alpha'$, where $\alpha'$ is the Regge slope (in units where $c$ and $\hbar$ equal $1$...
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What is the Planck scale magnetic field strength?

Using the constants $\mu_0$ (or $\varepsilon_0$), $c$, $\hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field : \begin{align} B_1 &= \sqrt{\frac{\mu_0 c^7}{\...
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How can I change our units so that Newton's gravitational constant is $G=1$?

I'm just wondering if you can change our arbitrary values for , say, the kg, meter, or newton so that G=1 instead of 6.67x10^-11
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Why is the Schwarzschild radius associated with the tiniest micro black hole formed by a Planck mass twice the Plank length?

If one calculates the Schwarzschild radius, $r_s$, of a Plank mass $m_p=2,18*10^{-8} (m)$ one gets: $$r_s=2{\frac{G{m_p}}{c^2}}=1,48*10^{-27}*2,18*10^{-8}=3,22*10^{-35}(m)$$ Now the Planck length $...
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Cosmological constant in a semiclassical approximation of quantum gravity

Why is it the case that, in a semiclassical description of quantum gravity, the cosmological constant is small in Planck units? Why does this mean that $$\ell \gg G$$ for $\Lambda = - 1/\ell^{2}$?
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How to express an energy in natural units

If I have some angular frequency e.g. $\omega [\text{rad } \text{s}^{-1}]$, I can easily express this as an energy as $E = \hbar \omega [\text{ J}]$. Now suppose I am working in Natural (Planck) ...
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1answer
272 views

Dimensions of charge in natural units

The natural units $$G = c = \hbar = k_{B} = 1$$ set fundamental constants of gravity, relativity, quantum physics, and statistical physics to simple numbers. However, surprisingly, the natural ...
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1answer
40 views

d'Alembertian inconsistency

I'm reading The Feynman Lectures on Physics, Volume II, Chapter 25. I'm confused as to why the d'Alembertian is defined in there as follows (Page 25-7, Eq 25.20): $$ \Box^2 = \frac{\partial^2}{\...
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1answer
206 views

Prove gravitational constant $G=1$ in geometric units

I've seen that often geometric units are defined by setting $G=c=1$, however, I have been working with a different definition, namely, to multiply time in seconds by $c$ so that it's measured in ...
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1answer
374 views

Value of gravitational constant $G$ and speed of light $c$

In an Tolman Oppenheimer and Volkoff (TOV) equation of state for static equilibrium stars, if any one want to calculate pressure and density in $\mathrm{MeV/fm^3}$, then what is the appropriate choice ...
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Why set the mass equal to 1 in Hamiltonian for a single particle?

Why can we set the mass in the Hamiltonian for a single particle equal to 1, as in Zee p.61 and Peskin & Schroder p.20? Is it just a choice of units, $\hbar=c=m=1$?
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What is the meaning for the unit kilogram-mole?

Recently, I came across the unit J/(kg-mole * K). What is the meaning of kg-mole? Please explain me the meaning behind it. Thanks in advance, Rram
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Homework: Feynman diagram loops, confusion about natural units

I've got another homework problem that I have trouble with: 4.3 Exercise 3 Use the Feynman rules to show that the expansion in number of loops is an expansion in powers of $\hbar$. Hint: ...
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What does the symbol $M$ mean in black hole relativity calculations?

I've seen a lot of places where the ISCO of a black hole is given as $R_{ISCO} = 6M$, but it never goes into any particular detail (one source said "as you all know from your relativity courses", haha)...
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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 ...
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1answer
367 views

Why does $k^z/E$ have dimensions of inverse velocity rather than velocity?

I'm studying quantum field theory and I want to prove the cross section. In Peskin's book, equation 4.77 says that: $$ \frac{1}{\left | \frac{k_{A}^{z}}{E_{A}}-\frac{k_{B}^{z}}{E_{B}}\right |}=\frac{...
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2answers
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Proper units for physical quantities when $\hbar$=$1$

How to deal with the units of quantities if $\hbar=\tfrac{h}{2\pi}=1$? For example, the energy $E=\hbar\omega$: If I have chosen $\hbar=1$, how do I use the units to properly differentiate between ...
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1answer
241 views

About Planck tension in strings theory as stated in “The Elegant Universe”

In the book "The Elegant Universe" by Brian B. Greene, on chapter 6 it is stated that there's the so called "Planck tension" in string theory, and it is given a value of $10^{39}$ tons. This value is ...
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Acceleration Absolute from all Non-Accelerating Frame of references

Is Acceleration Absolute from all Non-Accelerating Frame of references? Though experiment: Imagine cars on a two-way highway travelling at different velocities. A motorbike is accelerating at A'. From ...
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How can geometrized units have more than one constant equal to 1?

I can understand how you could manipulate units to make a certain constant equal to $1$, like $c$ or $G$, et cetera. But how can you make it so two constants (in this case $c$ and $G$) are equal to $1$...
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Can this Temperature Scale be Considered an absolute temperature scale?

Me and My friend are having a discussion about Absolute Temperature Scales. I think Absolute Temperature Scales are those who have their zero on Absolute zero. So Can we define a new Scale (say "Namu")...
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Is there an equivalent of the Planck length for time?

Is there an equivalent of the Planck length for time? I'd just like a term I may use (high-level) for a similar "unit of time"? I am not looking for a debate on how discrete time might be, but if ...
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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, ...
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Dimension of an angle [closed]

Usually angles are described as dimensionless, justifying this by saying that they can be viewed as length divided by length. As a student of mathematics I'm asking myself wether this is a convention ...
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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. $[...
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Books or other sources for natural units, Planck units, dimensional analysis etc. for someone with only high-school physics knowledge

I'd like to know more about natural units, Planck units, dimensional analysis, etc., and things like how units are "created" by man or by the universe, universal constants and where they come from. ...
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Given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$, construct an energy of the system [closed]

How do I use dimensional analysis to construct an energy for the system given the Newton constant $G$, the speed of light $c$ and the Planck constant $h$? I don't know of any energy formulas ...
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Units in Plasma Physics

What are the units people use in plasma physics? I am having hard time converting an equation from an old paper to SI units. I saw temperature being defined in $eV$. I assume this is $eV/k_B$ with $...
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Unification: what does it mean for the forces to become equal?

The Coulomb force constant $k_c$ has si-units of $Nm^2C^{-2}$. The gravitational force constant $G$ has si-units of $Nm^2kg^{-2}$. What does it mean that at very high energies these forces become ...