Questions tagged [units]
Units are standards of measurement used for different types of quantities.
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When we apply these concepts to physics, where do we put the UNITS in vector spaces and manifolds? Do units have a clear mathematical meaning?
We know that the space of all displacements is a vector space.
The vector space is defined as a mathematical object $(V,k,+,\cdot)$ such that it satisfies the 8 properties, where $k$ is a field.
We ...
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How to convert Richter magnitude scale to approximate TNT?
I know the Richter magnitude scale is often used for measuring the strength of earthquakes. At the same time, explosive/destructive releases of energy are often quoted in equivalent amounts of TNT. Is ...
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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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Conversion of compound temperature units
In general one can convert from one unit to another (of the same dimension) by using (($U$,$A$) and ($V$,$B$) being compatible unit pairs in the following)
$xU=(x\ast f_{U\rightarrow A}+o_{U\...
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Are there any non-SI base units?
Are there any base units that are not in the SI system? If so why aren't they?
Edit: By this I don’t mean other systems that you can convert to (ie. Feet, Ounces, Hours, etc) I mean new base units ...
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Are there Imperial or United States Customary units of electromagnetism, luminous intensity, or moles?
In the UK, Boris Johnson's somewhat beleaguered government has recently announced a consultation on using Brexit to ensure that "more choice can be given to businesses and consumers over the ...
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Second functional derivative and its units
Say I have a functional $I[\phi,g]$ with $\phi(p)$ and $g(p)$ functions from $\mathbb{R} \to \mathbb{R}$. Also say that this functional obeys the property:
$$\frac{\delta I}{\delta g(p)} = -(g(p))^{-1}...
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What does it mean for $2\pi = 1$ in a "private system of units"?
I saw the following image of an excerpt from Robert Mill's Tutorial on Infinities in QED, floating about the internet:
The book is available here, however I don't think I have access to it, unless ...
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Going from 4d Planck mass to 3d Planck mass
I have an expression where I have converted all units such that the answer is expressed in 4d Planck mass, $m_p^{(4d)}$.
In David Tong's lecture notes, Newtons gravitational constant in 4d is given by ...
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Can we get the values of $G$, $h$ and $c$ to be numerically equal if we use a convenient system of measurement?
The speed of light in vacuum is approximated to be $3×10^8\ ms^{-1}.$ But, if we change the units, we can get a different number. For example, it won't be $3×10^8$ if we used $ft\,s^{-1}$ instead of $...
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Unit vector in displacement
When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
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Geometrized units in Wald
I am trying to follow a derivation in this paper from Wald
Specifically, at the end of the paper, just under Eq. 4.7 there is given the equation
$$ Q/m \leq 2 B_0 m$$
where $Q$ is the system ...
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Using the boltzmann equation to find neutrino decoupling temperature
I'm an undergraduate student currently following a particle astrophysics lecture. I was reading some stuff about the neutrinos decoupling before the $e^+ e^-$ annihilations. It's possible to quickly ...
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Units and missing constants in quintessence expressions?
In cosmology, quintessence is an alternative to the cosmological constant. In this approach (described here), we consider a scalar field $\phi$ and its self-interacting potential $V\left(\phi\right)$ ...
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What is the constant appearing in the low energy action?
Usually one finds this expression for the low energy action
$$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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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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Galaxies and projected radius vs arcmins
I have two sets of data (globular clusters), one for the Andromeda Galaxy and one for the Milky Way.
I want to compare the distribution of globular clusters between the two galaxies according to ...
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Converting $\rm W/m2/sr/nm$ to $\rm kR/nm$ for any wavelength
I have atmospheric spectra given in W/m2/sr/nm units and wavelength in nm. I want to convert W/m2/sr/nm to kilo Rayleigh/nm (kR/nm) for any wavelength.
I tried the following method from this paper: ...
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How do I interpret the unit of [1/dex]?
I am trying to reproduce the mass function graph from a paper. I have calculated the mass function $\frac{\rm{d}f}{\rm{d}\log M}$, where $f$ is the mass fraction with respect to the total mass in the ...
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Value of Inverse of Thermal Voltage
I am trying to solve the Poisson-Boltzmann Equations and have come about the constant
$$
\beta = \frac{e}{K_BT}
$$
which Wikipedia denotes as the inverse of Thermal voltage. Now this constant is ...
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Why aren't the interatomic Heisenberg exchange coupling parameters reported in units of energy/units of spin squared?
The Heisenberg Hamiltonian is $H_{Heis}=-\sum_{ij} J_{ij} \langle \vec{S}_i \cdot \vec{S}_j \rangle$ (generally, save different constants depending on convention). This seems to suggest that the ...
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Transduction coefficient of an electromechanical system
I have been recently doing a physics experiment which requires me to determine the transduction coefficient of a speaker system, undergoing electromechanical resonance, in an AC circuit. The quantity ...
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Is there a difference between a 'pure number' and dimensionless quantity
I see dimensionless quantities described as 'pure numbers' I mostly understand this in terms of ratios (angles, a lot of dimensionless constants) as we are not really counting or measuring anything ...
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How come $X^2$ is a physical function?
This might be a very dumb question.
When we use values that are lower then one in lets say, the expression for kinetic energy - $\frac{1}{2}MV^2$, (for example $V=0.9\frac{m}{s}$ or $V=0.8\frac{m}{s}$...
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Is 25 $\rm kGy$ measured in Kerma or dose absorbed in material?
I have been reading Trends in Radiation Sterilization of Health Care Products form the IAEA.
They keep mentioning 25 [kGy] as the dose needed for sterilization (if you ctrl + f 25 kG you will get the ...
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Problem calculating the ground state radius of Toponium using strong force potential for short ranges
If it were true that the top quark were stable we could, in theory, have a hydrogen-like bound state consisting of toponium $T \bar{T}$. Looking at the strong force, for small ranges it takes the form ...
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Why did the scientific community stop using hydrogen as the main measure for the atomic mass unit?
The only thing I could find is that the community switched form one hydrogen atom to 1/16 of Oxygen-16 (which they thought to be the only isotope that exists at time because they had no concept of ...
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Potential energy and atomic units in the Bohr model
I have a question regarding the final sentence written in the solution to part iii) (found below) for the question given below.
In the Bohr model of the hydrogen atom, the radius of the electron ...
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What is a $n_\text{eq} / \text{cm}^{-2}$?
What is "one neutron equivalent per centimeter squared"? I know it is a measure of accumulated radiation, or similar, but could not find precise definitions in Google.
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Units of energy and frequency
I read a paper about using femtosecond laser to process an atom. The units used in the paper bothered me. I have four questions.
(1) Why the unit of energy is cm$^{-1}$?
(2) It seems that the author ...
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Is there a use of the SI units gray, sievert and katal in pure physics
Since the gray and the sievert are associated with relative biological effectiveness of the radiation and the katal is associated with catalytic activity, do the gray (Gy), sievert (Sv) and katal (kat)...
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Working with CGS units when calculating magnetic moment
I am attempting to calculate the total magnetic moment of a spherical object with known volume magnetic susceptibility $\chi$ in an $\mathbf{H}$ field of 1000 Oe. I need to do this in CGS units.
Let'...
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How to find average uncertainty for a set of results?
I have determined multiple values for the refractive index of a material, each with their own uncertainty.
If I find the average refractive index, how do I find its uncertainty? Would I find the ...
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Conversion formula between attenuation coefficient (cm^-1) and (dBcm^-1MHz^-1)
So, I was presented in class the fact that (at least in Ultrasound), attenuation coefficients $\mu$ can be expressed in units $\text{dBcm}^{-1}\text{MHz}^{-1}$ as opposed to the form I was used to; ...
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Rescaling the Uehling potential formula
I found that the Uehling potential equation is written in natural units in many books and research papers. But because I’ve to make some calculations with the Uehling correction, the formula must be ...
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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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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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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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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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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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Dimension scaling of a model hamiltonian system?
I have a model 2dof double well potential Hamiltonian given as $$H = P1*P1/2 + P2*P2/2 + V(Q1,Q2) ,$$ where $$V(Q1,Q2) = -2*Q1^2 + Q1^4 - Q2^2 +Q2^4 +0.4*Q1*Q1*Q2*Q2 ,$$ there is no units are ...
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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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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 ...