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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Meaning of the Planck Temperature
I don't understand what makes the Planck Temperature the "absolute hot". To my understanding Temperature is just a measure of the kinetic energy of the particles, so is the Planck ...
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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 ...
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Derivation of $G=\frac{\hbar c}{m_\rm{P}^2}$
I read that the gravitational constant can be expressed in terms of Planck length.
$$G=\frac{\hbar c}{m_\rm{P}^2}$$
What is the derivation of this relationship?
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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 ...
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Is there a link between $G$ and speed of light? [closed]
I tried to resolve $G$ from natural units (like Planck), and found that
$$ G = (K \times c / r_0)^3 $$
where
$ G = 6.67430 \times 10^{-11} $ is gravitational constant,
$ K = 1.66053906660 \times ...
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1answer
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Can fundamental quantities be “unified”?
( Probably a stupid question. But the thought crossed my mind. I'm not a physicist; I'm a mathematician)
Is there any way that the fundamental quantities (like length, time ) be "unified" in some ...
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1answer
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Derive the conversion factor from SI to Geometric units [closed]
In the geometrized system of units, $G = c = 1$. This directly gives us the definitions for second and kilogram in this system, as $1\:s = c_0\:m$ and $1\:kg = G_0c_0^{-2}\:m$, where I have used the ...
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1answer
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Converting units when $c=G=1$
In my homework assignment it is written that to convert from time to length you need to multiply by $c$, and to convert from mass to length you need to multiply by $G/c^2$, however I dont entirely ...
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Why does natural units technique only works in equations in Physics?
Example where it will not work is $(\frac{A}{B})^m = n$. Set $A=B=1$ and then solve for $m$.
And example where it will work is:
$(E/c)^2 = p^2+ (mc)^2$.
You can drop $c$ and put it back later by ...
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Are there any system of units where we get the value of all the fundamental constants to be 1?
As far as I know the magnitude of constants depends on our units of measurements, so are there any units of measurements such that all the magnitude of all the fundamental constants is 1?
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What is the advantage of natural units over SI units?
Why do physics professionals often use various different systems of units instead of SI units. Especially I ask about when constants like $c$ or $\hbar$ are put to 1....what is the advantage of this?
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System of Units Based on Energy and Time
Is it possible to have a system of units in which Time and Energy as the fundamental quantities and others as derived quantities. Also using only pi,e , avagadro number and planck's constant
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1answer
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In particle physics/SM, how to demonstrate that dimension of length is 1/energy?
In particle physics/Standard Model, using $\hbar=1, c=1$, how to demonstrate that dimension of length is 1/energy?
More generally, how to find dimension of a given operator, for example the covariant ...
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3answers
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Unit of Pressure - $\frac{N}{m^2}$ or $\frac{kg}{cm^2}$
I am came across Pressure being given with unit $\frac{kg}{m^2}$ at a lot of technical papers I am reading.
However, as far as I understand, Pressure is defined as $\frac{N}{m^2}$ which is not same ...
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1answer
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How to reintroduce $\hbar$ and $c$ into a formula written in natural units? [duplicate]
I am looking for a way to translate formulas written in natural units into either HLU units or SI units.
Seeing the Planck constant and the speed of light would help me understand what is going on.
...
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1answer
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Undoing problems caused by setting $c = 1$ { or “Undoing $c = 1$” }
In the mathematical derivation of equations for physics, and involving wave propagation in particular, the propagation speed at the start of the derivation is often set to one (c = 1).
I am working ...
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Can we get the values of $G$, $h$ and $c$ to be numerically equal if we use a convenient system of measurement?
The speed of light in vacuum is approximated to be $3×10^8\ ms^{-1}.$ But, if we change the units, we can get a different number. For example, it won't be $3×10^8$ if we used $ft\,s^{-1}$ instead of $...
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1answer
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The expression of the fine-structure constant post-May 2019 [closed]
Those of us who are engineers were never fond of the common expression from physicists that
$$ \alpha = \frac{e^2}{\hbar c} $$
implying that the units of the elementary charge are in "$\sqrt{hc}$".
...
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2answers
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Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale? [closed]
In this recent question, there was a comment 'The "zero point" of Kelvin is natural, but the scale is not'. This led me to wonder whether setting $R = 1$ in the ideal gas law would be an attractive ...
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3answers
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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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1answer
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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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2answers
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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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2answers
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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):
$$\begin{align}
\mathrm{d}\tau^2 &...
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2answers
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Could there be some system of units such that all fundamental constants are 1? [closed]
The fundamental constants in physics have extremely low values because of our scale compared to fundamental particles. Could there be such a system of units such that all fundamental constants are 1?
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What are the units of a scalar field if I only impose $c=1$?
I know that a scalar field in 4d in natural units ($\hbar = c =1$) has mass dimension 1. We can see this by requiring that the kinetic term in the action
$$ \int \text{d}x^4 \: \partial_{\mu} \phi \: \...
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1answer
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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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1answer
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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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Planck units and special relativity
The fundamental relation of special relativity linking time to position is
$$
\begin{align}
dx=cdt
\end{align}
$$
I am performing a change of variable to rewrite it in terms of energies as a Force F ...
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0answers
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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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1answer
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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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2answers
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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: $$\sqrt{s}=\...
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1answer
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How do I convert natural/Planck units to SI? [closed]
I am looking at a paper which has set:
$\beta=1/kT=1$ where k is the Boltzman constant.
It uses natural planck units ie $m=\hbar=k=1$.
Does it make sense to extract a temperature $T$ and mass $m$ ...
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1answer
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Why do people say that the string length is on the order of the Planck length?
As I understand it, string theory has only one fundamental dimensionful quantity - the string tension $T = 1/2 \pi \alpha'$, where $\alpha'$ is the Regge slope (in units where $c$ and $\hbar$ equal $1$...
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1answer
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What is the Planck scale magnetic field strength?
Using the constants $\mu_0$ (or $\varepsilon_0$), $c$, $\hbar$, $e$ and $G$, it is possible to define two quantities with units of magnetic field :
\begin{align}
B_1 &= \sqrt{\frac{\mu_0 c^7}{\...
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4answers
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How can I change our units so that Newton's gravitational constant is $G=1$?
I'm just wondering if you can change our arbitrary values for , say, the kg, meter, or newton so that G=1 instead of 6.67x10^-11
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Why is the Schwarzschild radius associated with the tiniest micro black hole formed by a Planck mass twice the Plank length?
If one calculates the Schwarzschild radius, $r_s$, of a Plank mass $m_p=2,18*10^{-8} (m)$ one gets:
$$r_s=2{\frac{G{m_p}}{c^2}}=1,48*10^{-27}*2,18*10^{-8}=3,22*10^{-35}(m)$$
Now the Planck length $...
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1answer
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Cosmological constant in a semiclassical approximation of quantum gravity
Why is it the case that, in a semiclassical description of quantum gravity, the cosmological constant is small in Planck units?
Why does this mean that
$$\ell \gg G$$
for $\Lambda = - 1/\ell^{2}$?
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4answers
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How to express an energy in natural units
If I have some angular frequency e.g. $\omega [\text{rad } \text{s}^{-1}]$, I can easily express this as an energy as $E = \hbar \omega [\text{ J}]$.
Now suppose I am working in Natural (Planck) ...
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1answer
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Dimensions of charge in natural units
The natural units
$$G = c = \hbar = k_{B} = 1$$
set fundamental constants of gravity, relativity, quantum physics, and statistical physics to simple numbers.
However, surprisingly, the natural ...
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1answer
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d'Alembertian inconsistency
I'm reading The Feynman Lectures on Physics, Volume II, Chapter 25. I'm confused as to why the d'Alembertian is defined in there as follows (Page 25-7, Eq 25.20):
$$ \Box^2 = \frac{\partial^2}{\...
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1answer
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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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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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If Higgs field is present everywhere in the universe, then why can't we use it to find the absolute motion of an object relative to it?
Why can't we describe absolute motion relative to Higgs field?
