24
votes
Accepted
Isn’t natural units prone to mistakes?
You are quite correct that the use of natural units removes a useful method for detecting errors.
This is an example of a more general concept in information theory. If you use the minimum number of ...
- 61.8k
21
votes
Is the Bohr radius deprecated?
In a word: No. The Bohr radius is a key concept and it is not deprecated.
In the modern outlook, the Bohr radius is the length unit of the atomic system of units, i.e., it is the natural length scale ...
- 135k
16
votes
Accepted
Dimensions of momentum?
Actually, you are correct in that energy and momentum have different dimensions. What is actually happening is that
in the book you are reading, the author is using units (called "natural units&...
- 30.2k
11
votes
Accepted
Is the Bohr radius deprecated?
Perhaps a more recent theory regarding the atomic radius that you might be interested in is Schrödinger's quantum mechanical model. The wave function, represented by $\psi$, is pretty useful in ...
- 265
10
votes
Accepted
When we set $c=1$ and $\hbar=1$, why is energy still measured in $eV$?
You appear to have misunderstood the natural system of units. Most HEP courses cover it on the very first lecture on the subject (at least Feynman's did).
The system reorients [L], [M], [T] to [V],[S],...
- 66.3k
10
votes
What is the logic behind Planck units?
The numeric values for dimensionful quantities are actually their ratio with some arbitrary standard that has same dimension. So when you say your length $L=10$ meters it means $L$ is ten times longer ...
- 4,193
9
votes
Dimensions of momentum?
It is common in QFT (and relativity in general) to use natural units in which $c=1$. In SI units, the 4-momentum takes the form $\mathbf p = (E/c, \vec p)$ where $\vec p = \gamma m \vec v$ is the 3-...
- 71.4k
9
votes
Where does Planck's constant come from in non-renormalizability of quantum gravity?
One way to think about it is in terms of the path integral. For perturbative quantum gravity around flat space, we expand the metric as
$$
g_{\mu\nu} = \eta_{\mu\nu} + h_{\mu\nu}
$$
where $h_{\mu\nu}$ ...
- 55.3k
8
votes
What's the matter with Planck mass $M_P$ in Einstein-Hilbert action?
You are comparing apples with oranges.
Let's first agree on the dimensions of the relevant quantities, basically Freshman physics:
$$[G] = L^3 M^{-1} T^{-2} \\
[S]=
M L^2 T^{-1}\\
[\kappa]=\left [\...
- 66.3k
8
votes
Accepted
Is my friend right about omitting $c^2$ in world famous tiny equation?
This is basically a philosophical question, but I'm going to take what will probably be an unpopular position that your friend's reason is basically wrong in the context of an introduction to special ...
- 49.4k
8
votes
Accepted
Why can we set $c$ and $\hbar$ to 1 when it changes the result?
It's easiest to think about this as a matter of units. What is the value of $c$? $3 \times 10^8 \mathrm{m/s}$? $6.7 \times 10^8$ miles/hour? Suppose I invented two new units, the florp (for space) and ...
- 10.1k
8
votes
Is the exact definition of the Planck units important?
I think it's all just order-of-magnitude stuff and factors of $\pi$ etc. are unimportant, but would be happy to be corrected.
Having said that, if someone defined a Planck time $t_p$ and then defined ...
- 61.8k
8
votes
What physics laws justify Planck's units?
We have, at yet, no specific evidence that any of our current laws of physics collapse at the Planck scale. However, we do expect that at or near the Planck scale quantum gravitational effects will ...
- 109k
8
votes
Accepted
What does the qualifier NOMINAL exactly refer to?
"Nominal" value in these sorts of engineering contexts means the following. In engineering contexts, we often label things by their values. A great example is a 2x4 piece of lumber. 2 refers ...
- 15.2k
7
votes
Accepted
How to express an energy in natural units
If you set $\hbar = c = G = 1$ then any physical quantity can be declared equivalent to any other physical quantity and you can transform an expression that says that this is so in any other unit ...
- 10.3k
7
votes
Accepted
Undoing problems caused by setting $c = 1$ { or "Undoing $c = 1$" }
Redimensionalization, as you were probably taught when introduced to nondimensionalization. You must know the dimensions of everything involved, however, otherwise you cannot do much.
If your ...
- 66.3k
7
votes
Natural units without unwelcomed $\pi$
The constant $\pi$ is a number which "falls" quite naturally out of all sort of abstract mathematical calculations. The claim that it is "unnatural" to see it in physical formula ...
- 9,970
6
votes
What is the significance of Planck charge?
My understanding of the Planck charge is that it is the unit charge necessary to normalize
the speed of light (and other "instantaneous" interactions e.g. strong force and gravity), $c=1$
reduced ...
- 1,731
6
votes
How to put $c$ back into relativistic equations?
Putting the factors of $c$ and $G$ back can be a tedious business. Many of us do it by (educated) guesswork, followed by checking that the guesses give sensible results.
The rigorous way to do this ...
- 363k
6
votes
Accepted
Why did my professor write down the Einstein field equations like this?
The extra term in the field equations, $\lambda g_{\mu\nu}$ is often written with a capital lambda, i.e. $\Lambda g_{\mu\nu}$. $\Lambda$ is the cosmological constant.
The second part of your questions ...
- 7,008
6
votes
Accepted
In natural units, where $\hbar = c = 1$, what is $G$?
If $\hbar = c = 1$ then length is time, and mass is inverse length or inverse time.
This is correct. In this way, since $[G]=[M^{-1}L^3T^{-2}]$ in SI units, its dimensionality reduces to
$$
[G]
=[M^{-...
- 135k
6
votes
Einstein's Field Equations differ by a factor of $\frac{1}{c^4}$. Why is that?
It's very common in GR to work in natural units where $c=1$. Some people take it a step further and set $G=1$ as well. With a bit of practice, it's easy to use dimensional analysis to re-insert ...
- 71.4k
6
votes
How total mass of universe is calculated?
This is a cute observation, but is essentially just dimensional analysis. It follows from doing a rough order of magnitude estimate where you only keep track of the Hubble constant plus fundamental ...
- 55.3k
5
votes
How can I change our units so that Newton's gravitational constant is $G=1$?
This is commonly done in general relativity to avoid cluttering up already complicated equations with factors of $G$ and $c$. The system of units is called geometrised units. The table here gives the ...
- 363k
5
votes
Accepted
Do the Planck voltage and the Planck current have a natural physical interpretation in classical general relativity?
To avoid the issues raised in Andrew's answer, let us work in SI units. Then the Planck voltage is
$$\frac{c^2}{\sqrt{4\pi \varepsilon_0 G}} \approx 1.04 \times 10^{27} \text{ V}$$
and the Planck ...
- 4,110
5
votes
A question about natural/geometrized units
For reference, here is table 2 from page 4 in reference [$1$]:
When we reconvert an SI unit back into an SI unit, shouldn't we get back 1 kg?
Yes. The source of confusion here seems to be a ...
- 55k
5
votes
Accepted
Would setting the ideal gas constant to $1$ yield an attractive natural temperature scale?
In natural units Boltzmann's constant, $k$, is normally set to one, rather than $R$. They differ by a factor of Avogadro's number; a mole is an arbitrarily defined unit based on the kilogram and is ...
- 3,265
5
votes
Accepted
What is the significance of Planck units?
All Planck units are constructed from $c$, $\hbar$, and $G$. The speed of light $c$ is the defining constant of Special Relativity. Planck’s constant is the defining constant of quantum mechanics. ...
- 52.2k
5
votes
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 fact, in the Planck system of units G is taken to be 1. The trouble is that Newton was working with units of mass, distance, and time, that had already been chosen (feet, pounds, seconds), and they ...
- 737
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