Questions tagged [units]

Units are standards of measurement used for different types of quantities.

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Black Hole Entropy Calculation

I was watching "Leonard Susskind on The World As Hologram" ( youtube ). At one point he describes the way Bekenstein calculates the entropy of a black hole. Paraphrasing: Take a minimally sized black ...
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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 $...
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Units conversion - quanta/cm$^2$/s and photons/cm$^2$/s

Can you tell me if there is any difference between these 2 units? $\log \mathrm{quanta/cm^2/s}$ vs $\log \mathrm{photons/cm^2/s}$ Thanks
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Using the boltzmann equation to find neutrino decoupling temperature

I'm an undergraduate student currently following a particle astrophysics lecture. I was reading some stuff about the neutrinos decoupling before the $e^+ e^-$ annihilations. It's possible to quickly ...
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76 views

Units and missing constants in quintessence expressions?

In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
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52 views

What is the constant appearing in the low energy action?

Usually one finds this expression for the low energy action $$S = \frac{1}{2\kappa_0^2}\int d^D X\; \sqrt{-G}\; \mathrm{e}^{-2\Phi}\,(R-\frac{1}{12}H_{\mu\nu\lambda}H^{\mu\nu\lambda}+4 \partial_{\mu}\...
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302 views

Scale-invariant differential operator

For example, the differential operator Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}.$$ My questions are: Is it scale-invariant? what is scale-...
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31 views

Empirical determination of masses and charges of a set of objects using only kinematics experiments

Suppose you have $n$ physical objects that you want to determine the mass and charge of. You do not have access to any reference object with known mass and charge (that also includes things like the ...
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67 views

Dimensionally inconsistent!

This equation doesn't seem to be correct. Dimensionally inconsistent, in fact! How then, is it established? $$s_{t}=v_{0}+\frac{1}{2}a(2t-1)$$ (In case you don't know, this is the equation used to ...
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41 views

Unit conversion in cosmology

In cosmology (Dodelson) , the natural unit is $\hbar=1, c=1, k_B=1 $. There the author writes the critical density of the universe $\rho_{cr}$ as \begin{align*} \rho_{cr}&=1.879 \ h^2\ \times 10^{-...
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How to Measure Electric-Field Probe Sensitivity?

I am doing some reading on current methods for detecting electric fields. A figure of merit for the systems is, naturally, the minimum strength of field that can be measured, in units of Volts per ...
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30 views

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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2answers
52 views

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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61 views

Geometrized units in Wald

I am trying to follow a derivation in this paper from Wald Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation $$ Q/m \leq 2 B_0 m$$ where $Q$ is the system ...
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1answer
61 views

What does pc(eV) = 300 Br(G cm) mean?

In the January 1983 issue of the American Journal of Physics, Edward Purcell published a one-page "Round-Number Handbook of Physics" (see e.g. http://lemeshko.blogspot.com/2008/06/one-page-round-...
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59 views

How do you properly derive atomic units from SI units?

I'm learning atomic units and I'm having trouble figuring out how to derive the atomic units version of energy, time, electric field, magnetic field, etc. For example the Wikipedia page has a list of ...
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97 views

How is thrust per unit power measured?

Typically, thrust efficiency is measured in specific impulse, as thrust per fuel consumption rate: $$I_\text{sp} = \frac{F_\text{thrust}}{\dot{m}_\text{fuel}} \quad \text{or} \quad I_\text{sp} = \...
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Mixed unit conversion

I have a silly question. I am not used to different unit systems and I am stuck with trivial problem. I have expression for energy of harmonic oscillator: $$ \Delta E = \frac{1}{2}\Omega^2\Delta Q^2. ...
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131 views

Minimal substitution, four-potential and units

When we make the minimal substitution \begin{equation*} p^\mu\rightarrow p^\mu+\frac{e}{c}A^\mu \end{equation*} the four-potential $A^\mu$ must be proportional to $1/e$ in order to ensure the whole ...
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228 views

Are Heaviside-Lorentz unit and Gaussian unit natural units?

I am studying electromagnetism and have encountered the Heaviside-Lorentz unit and Gaussian unit. In these unit systems, the constant $c$ keeps occurring. For example, the Maxwell equations are of ...
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47 views

Rewrite equations of physics using Planck units

I was reading this site http://astronomy.swin.edu.au/cosmos/P/Planck+Units and in it is stated that "If we use the Planck Units, we can rewrite all of the equations of physics such that: c = G =$ \...
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68 views

Units of a quantum electromagnetic field

The recalling $\mathbf p \rightarrow \mathbf p -q\mathbf A$, the vector potential has units $$ \langle \mathbf{A} \rangle \leftrightarrow\Big[\frac{\text{momentum} }{\text{charge} }\Big]$$ If we take ...
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40 views

Units of Neuron input current

My question stems from some of the equations used in a paper in Phys Rev E titled "Dynamical response of the Hodgkin-Huxley model in the high-input regime" (located here: http://journals.aps.org/pre/...
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130 views

Why is the cross section's unit Barn particularly equal to $10^{-28} m^2$?

Why is the microscopic cross-section's unit Barn particularly equal to $10^{-28} m^2$. Is there any history or reason behind that?
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187 views

Photon Propagator in QFT

Please forgive my temporary split-brain, but I'm a little thrown off by something when considering units at the moment. In QED (depending on the guage), the photon propogator is written as $<0|\...
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78 views

Is there a 3D analogue of angle?

A one-dimensional angle is a wedge, almost like a slice of pizza. A two-dimensional angle is an angle squared, like the cone of light produced by a flashlight. This is called a solid angle. Is ...
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179 views

Units of angular power spectrum

I am not sure whether this question might be better suited for crossvalidated or stackoverflow, but I will give it a try here: I have a map of the full sky in in the healpix format, units are $\rm ...
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86 views

What unit system puts a bunch of powers of ten in Maxwell's equations?

In what unit system can we get the Maxwell equation in the following form (section 1.2 from Lewin's book Advanced Theory of Waveguide) $$\nabla\times \vec E = -10^8\mu \frac{\partial \vec H} {\...
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31 views

How to understand/derive Eq 5.5 in Geiner's Quantum Mechanics - An Introduction?

Geiner's Quantum Mechanics - An Introduction has an unnumbered equation above Eq. 6 in section 2.4 discussing density -- not sure if it is energy density -- of radiation: ... $$dE/dV = E/V =a T^4$...
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115 views

Do doomsday arguments influence doomsday hypotheses?

The doomsday argument supposes that in the absence of any other knowledge, if we know the age of something now, we may assume that we are seeing it in the middle of its lifetime and then calculate our ...
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22 views

Units and measurement

I read on the characteristics of units (i) It should be easily understandable. (ii) It should be changed with change in physical factors. (iii) It should not change with place or time. I want ...
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Units after integrating a ratio metric: Point Source Transfer Mobility

I want to calculate the so called Line Source Transfer Mobility (LSTM) from 10 equispaced Point Source Transfer Mobilities (PSTM). The PSTM measures the response to an excitation, and it is defined ...
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53 views

What's does square root of number of atoms mean?

Number of atoms $N$ was counted in 3 dimension. $x,y,z$. However, when calculate it, i.e. in many cases such as refractive index , people take the square root of it, i.e. in reflective index $n=\sqrt{...
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35 views

Why is contact resistance measured in $\Omega~\mu m$?

In many papers the contact resistance of a metal in contact with a semiconductor is given in units of $\Omega~\mu m$, for example in the paper by Li et al. (Appl. Phys. Lett. 102 (2013), p. 183110): ...
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75 views

After the redefinition of the units of fundamental physical quantities in 2019, will an uncertainty incur in the Universal constants values?

I am specifically interested in the following constants because being a student these are some of the most common constants that I face: $R$ (universal gas constant) Stefan constant Permeability of ...
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87 views

Self inductance of a circular coil

I have read from my reference that the self inductance of a wire ring is derived in a non-trivial manner. I have copied an image off the result below, let me know if I should translate it to Latex. ...
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1answer
22 views

Units of forcing function in the inhomogeneous wave equation

The units of the d'Alembertian are distance$^{-2}$. It should be the case that the inhomogeneous wave equation describing $$\square u = f$$ should have matching units on both sides. My understanding ...
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188 views

How to convert J/mol-K to BTU/mol-R manually?

How to convert $\frac{J}{mol-K}$ to $\frac{BTU}{mol-R}$ manually? Sorry for such a simple question, I am new to Physics and I'm getting confused when it comes to conversions of units. Please bear ...
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What are the starting units to perform the Gauss method?

To calculate the Gauss method, we need : the respective geodetic latitude the equatorial radius of the body (here earth) the respective local sidereal time the respective declination the respective ...
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Constants of proportionality in Force Equations/ Physics in General

I was in physics class and we were talking about the gravitational constant G (6.67 x 10^-11 Nm^2/Kg^2). The question came up: "Why does $F= (GMm)/r^2$ have a constant of proportionality and not $...
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36 views

Significant figures in multiplication with units

Why does it make sense to round to the smallest significant figure instead to the largest unit? If I have one measurement made to the nearest millimetre and another to the nearest picometre then why ...
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1answer
87 views

I'm confused about electric flux?

In a previous physics class, I learned that the electric flux was $\vec{E}\cdot\vec{A}$ (dot product), and hence the unit is $Nm^2/C$. But in my electromagnetics book, it says the unit is Coulomb, and ...
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Downsampling the wavelength spacing of spectral radiance

I have spectral radiance measurements, $L_e$, that I need to downsample, and I want to make sure I do this correctly. Let's say the measurements are a constant value of $5\times 10^{-3}\: \rm W \: m^{-...
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38 views

Scaling atomic units with energy

In Hartree atomic units, $e = m_e = k_e = \hbar = 1$, and \begin{align} 1&\mbox{ a.u. of energy is }E=\frac{m_ee^4}{(4\pi\varepsilon_0 \hbar)^2}=27.21\mbox{ eV.} \\ 1&\mbox{ a.u. of time is }\...
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238 views

What are the actual electromagnetic units in the foot-pound-second (FPS) system?

So I've been reading this Wikipedia article, and I came across the cited note that someone has derived the electromagnetic units for the FPS system. However, I can't find that publication so does ...
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How to handle rational power of units when fitting experimental data

I collect urban aerosol data and I would like to post-process it for analysis purposes. Raw data are diameter cut counts $N_i$ ($\mathrm{dm^{-3}}$) that stands for particulate concentrations: number ...
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Interpreting impulse value “c kg”

I have a small question about a physics exercise concerning the relativistic relationship between energy and momentum. The exercise says: We have 2 objects with rest mass 8 kg. We shoot the objects ...
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4answers
79 views

How do I know which units to use without context?

Let's talk about $Q = m c \Delta T$. Let's say I didn't know this equation by heart, but I naturally deduce it. How do I know which units to use (if I hadn't made myself clear, I mean units like ...
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In the process of probability of two flavor neutrino, how does the factor $1.27$ comes from?

Up so far I have been working on deriving probability for two flavor neutrino and have consistent results with wikipedia or textbook. But I have some trouble with deriving some factor $1.27$. \...
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1answer
241 views

Convert units of Empirical Orthogonal Function (EOF) for sea surface temperature data

I have a dataset of daily averaged sea surface temperatures for an entire year. I wish to use an empirical orthogonal function to find the dominant patterns within the data. Consider that my ...