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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What's the link between Planck Mass squared and $1/8πG$?
Good morning,
In an equation of an article, we said that 1/8πG = Mass of Planck^2. But 1/8πG = 596175243.8, is much larger than the Planck Mass^2 = 1.383*10-16 kg. Is there a conversion to do? If not, ...
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Understanding the units of cosmic string number density
I am reading this old paper: https://arxiv.org/pdf/1309.6637.pdf and trying to work out the units in equation 63. It gives the number density of cosmic strings in the radiation era as
$$
\frac{n(\ell,...
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What does the qualifier NOMINAL exactly refer to?
This question may not specifically belong to the physics domain, and rather perhaps to some engineering one, yet I couldn't find a better place to ask it either, trying my chance here...
From time to ...
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What is the logic behind Planck units?
I was curious to know the logic behind “Planck Units”, I read this question but did not understand it. Do you have a better (simpler) explanation for setting $c = G = \hbar = 1$?
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How to rigorously put back dimensions in equations involving natural units?
I was watching the first lecture of Special Relativity by Leonerd Susskind (link:Youtube) whereby setting the speed of light to 1, i.e. $c = 1 \dfrac{[l]}{[s]}$, where $[l] = 3 \cdot 10^8 \dfrac{[m]}{[...
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Physically, how are constants like $c$ or $\hbar$ allowed to be unitless in natural units?
This seems like a rather elementary question but it has been causing me some troubles.
Suppose I want to construct a unit system were $c = 1$ and $\hbar = 1$.
The constraint $c = 3 \times 10^ 8 m/s= 1$...
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When working with natural units, how do my other variables change? [closed]
I'm trying to plot energy splitting
as a function of $a$ (where $g=1$). When I set $\hbar=1$ such that $a=[t^{-1}]$, how does the value of this variable change to keep the equation consistent?
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Confusion on Absolute Temperature Scales used in solving Carnot Cycle problems
I have a Carnot Cycle problem where the temperatures of the hot and cold reservoirs are given in Celsius and I'm asked to solve for the cycle efficiency. Of course, My first step is to convert Celsius ...
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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 ...
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How do I determine what physical constants can be combined to derive a set of natural units?
I am looking into natural units (units of measurement based only on universal physical constants). Different systems of natural units use different physical constants as their defining constants. If I ...
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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 }. $$
Isn't it ...
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What physics laws justify Planck's units? [duplicate]
It is usually said that Planck units have no scientific ground, yet they are useful indeed because many laws collapse, make no more sense at, say, Plancks length or time.
Can you mention a couple of ...
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Is the exact definition of the Planck units important?
Wikipedia says there are other, possibly better ways to define the Planck Units based on whether we want to factor in or out a $2$ or a $\pi$ or a $4\pi$ as the case may be. Most of them represent ...
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Is there an absolute zero for internal energy?
Of course we can arbitrarily define a reference point to call zero. However, I was under the impression that internal energy and enthalpy were relative and had no absolute zero, and only changes or ...
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When we set $c=1$ and $\hbar=1$, why is energy still measured in $eV$?
When we set $c=1$ and $\hbar=1$, we often see in particle physics that mass and energy are expressed in terms of $eV$.
This doesn't make sense to me. If we are choosing a new unit system where for ...
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Why are there just 3 main units ($L$,$T$,$M$) in physics?
Most physics books define physical units in terms of length, time and mass. Some books add temperature. And yes, the SI unit system has 7 base units, but some are clearly redundant.
Why are exactly ...
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Solution to Klein-Gordon equation in terms of $\vec{p}$ and $\vec{k}$
A general solution to the Klein-Gordon equation can be written as:
$$\phi = \int d^3k \frac{1}{(2 \pi)^3 \sqrt{2\omega_k}} \left(a(\vec{k})e^{-i(\omega_kx_o-\vec{k}\cdot \vec{x})}+a^{\dagger}(\vec{k})...
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A question regarding dimensional analysis and a "Planck matrix"?
Let:
the speed of light in a vacuum, $c$,
the gravitational constant, $G$,
the reduced Planck constant, $\hat{h}$,
the Boltzmann constant, $k_B$
the electric constant, $\epsilon_0$
with dimensions $...
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How to convert $\rm cm^{-1}$ to $\rm eV/Å^2$? [closed]
As in the title, how to convert $\rm cm^{-1}$ to $\rm eV/Å^2$? Å stands for angstrom.
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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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Units of a scalar field
Consider the Lagrangian density
$$\mathscr{L} = \frac{1}{2} \partial_\mu a \partial^\mu a + \frac{m^2}{2} a^2.$$
I understand why $[a]=m$, i.e. $a$ has mass dimension one. What and why are the units ...
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What happens to the $2\pi$ factor in natural units?
In natural units when we define $c=\hbar=1$ and we have that energy and mass have the same units because of $E=mc^2$. The same happens for time and space due to $x=ct$. Now, when we want to relate ...
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Is temperature of 1 Kelvin equivalent to 1 eV in natural unit?
We know that the Boltzmann's constant, $k_B$=8.617 $\times$ $10^{-5}$ eV/K. Now in the natural unit, $k_B=1$.
So can I say, in the natural unit, 1 K temperature is equivalent to 1 eV in energy? 300 K ...
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Using $ct$ axis instead of $t$ axis in special relativity
I've recently started studying the concept of space-time diagrams in special relativity, and I came across the concept of representing the time axis using $ct$, with units being that of length. Now I'...
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Subatomic natural units
In High Energy Physics it seems to be common use to measure everything in terms of eV powers, by assuming $\hbar = c = 1$ (dimensionless). Often times this system of units is referred as Planck units, ...
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What does it mean for $2\pi = 1$ in a "private system of units"?
I saw the following image of an excerpt from Robert Mill's Tutorial on Infinities in QED, floating about the internet:
The book is available here, however I don't think I have access to it, unless ...
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Why don't we take the universal gravitational constant $G$ to be equal to 1 in $F= \frac{Gm_{1}m_{2}}{r^2}$?
In the derivation of Newton's Second Law, we get to an equation $F=kma$. Since this equation is essentially defining force, Newton could have taken the value of $k$ to be anything. For the sake of ...
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Units in the geodesic equation / Schwarzschild metric
Most textbooks define the geodesic equation for a particle with unit mass, such that it looks like:
$$ \ddot{x}^{\mu} + \Gamma^{\mu}_{\alpha \beta} \dot{x}^\alpha\dot{x}^\beta = 0$$
Where "dot&...
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Einstein's Field Equations differ by a factor of $\frac{1}{c^4}$. Why is that?
I am trying to familiarize myself with General Theory of Relativity. I am by no means an expert in the field, and I am doing this as my own hobby. At any rate, I have come across Einstein's Field ...
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Why do we treat the action as dimensionless in QFT?
When determining whether the couplings in a QFT Lagrangian are relevant/irrelevant/marginal, we set $\hbar = c = 1$ and use the fact that the action is dimensionless to find the dimensions of the ...
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Why is the speed of light ignored in this formula?
I'm trying to follow this worked example from my lecturer.
Here's the question:
and here's the answer to part 1:
When I was attempting this without looking at the answer, I did correctly identify ...
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What is the significance of Planck units?
There are many questions asked about different Planck units.
This question is just a generalization of all of those questions.
Planck units are considered to be natural units. The thing I don't ...
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Exponential function and natural units
The argument of the exponential function has to be dimensionless. By switching to natural units, velocity (for example) becomes dimensionless. Surely, I cannot take the exponential of a velocity now ...
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Planck constant in geometrized units? [closed]
How do I calculate the value of the Planck constant in geometrized units?
I cannot find its value anywhere.
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How do I calculate ¨Newtonian constant of gravitation over $\hbar c$¨ to get to the value in NIST? [closed]
I know this is a silly question, the definition of the value is the formula for the value itself but I have tried putting the constants in and I am not getting the same answer. What am I doing wrong?
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Why can we set $c$ and $\hbar$ to 1 when it changes the result? [duplicate]
So in my QFT course, my professor said that you can set $c$ and $\hbar$ to 1. And he gave us an example:
$$E = mc^{2}$$
And then set $c = 1$:
$$E = m$$
This seems completely ludicrous to me to do. ...
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In natural units, where $\hbar = c = 1$, what is $G$?
This seems like a simple question, but I cannot wrap my head around it. If $\hbar = c = 1$ then length is time, and mass is inverse length or inverse time. Hence $G$ should have dimensions of length ...
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Bremermann's limit vs Planck frequency
Bremermann's limit, as maximum possible computation power or CPU total computing frequency, is known to be on the order $10^{50}~\text{Hz}/\text{kg}$.
Why max computation frequency for unit mass can ...
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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 ...
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Doubt about the constant $\kappa$ of Einstein's field equations
I'm trying to understand each of the terms in this equation intuitively
but I'm having a little trouble. I know that we can represent the equation in the following way:
$G_{\mu\nu}= \kappa T_{\mu\nu}$
...
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Why did my professor write down the Einstein field equations like this?
Ok, so I was taking an online course where the professor wrote down the Einstein field equations like this
$$R_{\mu \nu }-\frac{1}{2}g_{\mu \nu }R = 8\pi G\: T_{\mu \nu }.$$
But I saw it most commonly ...
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Confusion regarding the appearance of $\hbar$ in the eigenfunctions of momentum operator
The two images below are from different books. One has the $\hbar$ in the root below which seems right to me as that gets the dimensions correct but other does not have a $\hbar$. I am confused as to ...
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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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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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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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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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