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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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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QFT Resource in SI Units?

I am looking for a book on QFT with all fundamental constants left in place in SI units...without the pesky conversion to natural units. Could anyone recommend such a book or notes?
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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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What is the meaning of inferred absolute zero temperature? Why does the resistance temperature graph it is obtained from behave that way?

I asked this on the Electronics Stack Exchange and someone suggested for me to ask it here too. https://electronics.stackexchange.com/q/542983 Studying basic direct current circuits, I've come across ...
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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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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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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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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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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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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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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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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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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.