# 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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### Is the Planck mass the "lower limit" for gravity?

The Planck units are often treated as being the "lower limits" to things: the Planck length for length, the Planck time for time, etc. But the Planck mass, which is about $2.2\times10^{-5}$ ...
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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: \...
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### What are natural units?

I need to make a presentation on natural units. My professor asked me to visualize a world where $c$ and $\hbar$ are actually equal to unity. Like, what are the consequences? I also want to know the ...
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### How to convert quantities between SI units and a natural unit system?

Let's say I'm working in a natural unit system defined by a set of physical constants set to dimensionless numbers. How can I convert quantities between that natural unit system and a more ...
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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 ...