Questions tagged [dimensional-analysis]
Dimensional analysis means to obtain results by analyzing the units in question, etc. DO NOT USE THIS TAG if your question is about degrees of freedom or spatial dimensions.
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Which dimensionless number would be appropriate for the given system?
I'm designing an experiment for a multiphase system. The real system as shown has 2 fluids, liquid 1 and liquid 2 where liquid 1 is moving upwards due to momentum imparted on it by upward rising ...
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2answers
30 views
Dimensional Analysis on Rotational Motion Laws
So I was solving some rotational motion problems when I decided to include the units in solving (just realized the necessity of doing this). Then I ran into some problem regarding the units in the ...
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1answer
55 views
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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38 views
Regarding the units of a proportionality constant
I got a general query regarding variation of two physical quantities.
If we have two physical quantities say $A$ & $B$ such that $A$ is directly proportional to $B$. There exists a proportionally ...
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1answer
72 views
How should units be treated?
First sorry I don't know how to properly use this page yet. Secondly, in a electricity problem I've found the following expression:
$$(q_1*q_2)/r_1 +(q_1*q_3)/(r_1+r_2)+(q_2*q_3)/r_2=0\tag{1},$$
and ...
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121 views
Could gravitons be dimensionless?
If the metric $g_{\mu\nu}$ is dimensionless (i.e. does not have associated dimensional units) and gravitons are quantum excitations of the metric does that mean that gravitons themselves are ...
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79 views
Why do all Feynman diagrams with same number of external legs have the same mass dimension?
In the Ch.18, book of QFT by Mark Srednicki (p.118), it says the diagram have the same mass dimension with tree diagram with the same external lines, because both of them contribute to the same ...
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1answer
41 views
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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49 views
How do we know that the universe is really fine-tuned? [duplicate]
How physicists come to the conclusion that the cosmological constant and the other constants are really fine-tuned in a way that if they are changed just a bit, then stars and life won't exist?
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28 views
What happens to radians in this calculation? [duplicate]
I rewrite N as kg m s^-2 and try to get Pmax, which is in Watts to kg m^2 s^-3 but when I do so I am left with an rad^2.
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39 views
Why does the electric displacement vector $D$ have the same unit of charge density?
I was in doubt about electric displacement, after some time I tried to find the unit of $D$ which is $Cm^{-2}$. Why?
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2answers
116 views
Why we write the constant in front of the Einstein-Hilbert Action?
Why we write the constant?
$$S_{EH}=\frac{c^4}{16\pi G}\int \sqrt{-g}R d^4x$$
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59 views
Why don't electric current and volumetric flow rate express units/dimensions of area in their denominators?
The definition of current is $I = \frac{dq}{dt}$ and the definition of volumetric flow rate is $Q = \frac{dV}{dt}$.
In written, non-mathematic language, I have seen current described as: "Electric ...
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1answer
26 views
Dimensional analysis with space-distributed variables
I read several books about Dimensional Analysis and the "Pi theorem".
It frequently happens that both the "governed" variable and some of the "governing" variables are entities which are "...
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1answer
21 views
What evidence exists to show that hyperdimensions are spacially perpindicular to the dimensions before it?
I've heard of a tesseract which is supposedly spacially perpendicular to the other 3 dimensions. Is there evidence this is possible in our universe or another?
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1answer
78 views
How do you explain the unit of this formula?
I have trouble trying to interpret the following formula:
$$G_{SCI} = \mu N^{span} G^3 \mathrm{arcsinh}\,(\rho \Delta f^2)$$
$$G_{SCI} = \frac{P_{SCI}}{B},$$ where $P_{SCI}$ is the self-channel ...
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2answers
62 views
SI Units and the Coriolis Parameter
I am trying to solve the following equation numerically $$|u_\text{max}|=\frac{\Delta p}{|f|\rho}\frac{\sqrt{2}}{R}\mathrm e^{-1/2} \tag{1}.$$
Here, $\Delta p=20\ \mathrm{hPa}$, $R=500\ \mathrm{km}$ ...
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76 views
How to find the age of the universe from fundamental constants? [closed]
PAM Dirac had found a number with dimension time using fundamental constants like mass of electron, universal gravitational constant, speed of light and so on.
This number that he had found coincided ...
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69 views
Why $k$ is chosen to be unitless? [duplicate]
In $F = kma$, why $k$ is taken to be unitless?
If $k$ is unitless and 1, then we have $F=ma$. This means (I guess) the physical quantity Force is product of different (from Force) physical quantities ...
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1answer
87 views
Is $\hbar, c, e$ truly independent? [closed]
Considering the constants: $\hbar, c, e$. Basically people considering them as very independent constant. However, if you think about it, $\hbar$ was initially introduced during $E=\hbar \nu$, thus ...
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3answers
78 views
Understanding importance of Planck energy
Planck length is considered to be smallest length possible in the universe. Planck time is smallest time interval possible.
Similarly what is importance of Planck energy because it is neither ...
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37 views
In addition to $K_e/K_m = c^2$ (due to James Clerk Maxwell), are the constants that arise from $G/K_m$ and $G/K_e$ also limits?
Prior to James Clerk Maxwell we understood there to be three laws:
$$\text{Gravity: }\;\;\; F_g= G \frac{m_1m_2}{r^2}\hat{r}$$
$$\text{Electricity: } F_e= K_e \frac{q_1q_2}{r^2}\hat{r}$$
$$\text{...
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3answers
73 views
Finding the difference of two temperatures of $^\circ \rm C$ in Kelvin
Denote by $a$ and $b$ temperatures measured in $^\circ \rm C$. My aim is to find their difference in Kelvin ($\rm K$). I thought of this question for fun after noticing that I can approach this ...
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1answer
74 views
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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1answer
87 views
Spurion analysis: pedagogical example
I wanna to understand how Spurion analysis works. Physicist widely use this (From statistical field theory to quantum mechanics problems, as I understand from Google), but I don't know foundations ...
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1answer
24 views
Balance the units of the following hamiltonian
The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure ...
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20 views
Hall conductance units and physical intuition
In the quantum hall effect state, electrons in the bulk are doing cyclotronic orbits, and electrons on the edge are going around the sample's edge.
The cyclotronic electrons are all in the same ...
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1answer
47 views
Is the dimensionality of space considered a universal constant? [duplicate]
What if the dimensionality was something like 3.0001 or 2.999? Would we be able to tell the difference? I heard about fractional dimensionality in 3b1b and was wondering about its implications for ...
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4answers
320 views
Normalization of the action in Special Relativity
The action for a massive point particle in Special Relativity is given as
$$A =-mc^2\int d\tau,$$
Where $\tau$ represents the proper time, and $m$ represents the (rest) mass. From what I could ...
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1answer
57 views
When is a parameter considered small for perturbation and how does physical units affect that?
In perturbation theory procedures (not specific to any particular topic) we tend to have (or delibrately insert) some small variable $\epsilon$ in an equation that is otherwise difficult to solve if ...
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Assume the equation $x = At^3 + Bt$ [closed]
I would greatly appreciate some help with this. :)
Assume the equation $x = At^3 + Bt$ describes the motion of a particular object, with x having the dimension of length and t having the dimension of ...
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1answer
68 views
Is the coefficient of drag the same on two similar objects?
if I had two objects, scaled perfectly to each other so that one is $5$ times the size of another while keeping the shape the same, would their coefficients of drag, $C_d$, be the same in the formula $...
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53 views
Most general renormalizable Lagrangian with 2 Weyl spinors and a complex scalar field
I am asked to write down the most general Lorentz-invariant Lagrangian in 4d-spacetime which contains a left-handed Weyl spinor $\psi_{L}$ and a right-handed Weyl-spinor $\psi_{R}$ as well as a ...
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3answers
105 views
What is definition of physical quantities? [closed]
What is definition of physical quantities? What is mass, force, length, time? If you ask it to any physics student then I am sure he won't be able to answer it. In fact nobody can (no?). Textbooks ...
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Where does $\ell_{g} = \frac{\hbar^{2}}{2GMm^{2}}$ come from?
$$\ell_{g} = \frac{\hbar^{2}}{2GMm^{2}}$$
This is an equation for the characteristic length scale that contains the constants $\hbar$ and $G$.
My question is where does this equation come from and ...
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38 views
Question regarding the frequency approximation of a pendulum
I have a problem with the formula for the frequency of a pendulum oscillation for small angles.
If I use torque and angular momentum, approximating $\sin\theta$ to $\theta$ with a 2nd order Taylor ...
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2answers
2k views
Is this textbook answer incorrect? [closed]
In my physics textbook (Tipler et al.), the following equations were given as a solution to a problem. I am slightly in doubt of their equations. I think the answer should be $\frac{m_2}{m_1+m_2+(I/R^...
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1answer
50 views
Mass dimension of Klein Jordan field [closed]
I like to know about dimension of KG fields,
Wikipedia searches don't give me a satisfied answer
Can any one please help me?
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14 views
How do the similarity transformation connects between characteristic length and time scales?
I'm currently taking a course in analytical mechanics, and we we're studying about similarity transformation. when I read the lecturer's notes, he gave as an example the harmonic oscillator $$ L = (1/...
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59 views
Dimensionless Schrodinger equation
I have a question about the dimensionless Schrodinger equation. When solving a problem of quantum tunneling of electrons through potential barrier, for example we can use units $\hbar=m_e=1$. After ...
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1answer
89 views
Gaussian (CGS) unit of temperature: is there a statkelvin?
In the Gaussian (CGS) system of
units, the unit of electric charge
(statcoulomb) is derived from the
units of length, mass and time. Using Coulomb's law, we find that the dimension
of electric charge ...
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1answer
98 views
Why does Dimensional Analysis “work”? [duplicate]
We started the first day of our semester today by having a review of dimensional analysis. Viewing it afresh, I began wondering how it all “works”, i.e. what is the physics behind it all?
Nature sure ...
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50 views
On the connection coefficients for a dimensionless metric tensor
If $g_{\mu \nu}$ is dimensionless, it follows that
$$\Gamma ^\lambda _{\alpha \beta} = \frac{1}{2} \sum_\sigma {g^{\lambda \sigma} \left(\frac{\partial g_{\sigma \beta}}{\partial x^\alpha} + \frac{\...
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2answers
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Dimensionless expression for differential equation
I am working through Nonlinear Dynamics and Chaos by Steven H Strogatz. In chapter 3.5 (overdampened beads on a rotating hoop), a differential equation is converted into a dimensionless form. I am ...
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Why transcendental terms in the laws of nature are dimensionless?
Through my years in nuclear engineering, it has always been the case that in physical relations, the arguments of transcendental functions, e.g., the exponential in the law of radioactive decay, $N=...
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Dimensional analysis: physical meaning of Pi groups
Given a physical problem, I know how to use Buckingham theorem in order to obtain the required number of indipendent non-dimensional Pi groups. However, I am not sure about how to interpret physically ...
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1answer
76 views
Power counting and divergences
Often, in many books such as Peskin and Schroeder, a Feynman diagram or the effective potential is expanded as a function of the external momenta or the classical fields respectively. Consider the ...
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24 views
Rules on combining dimensionless (Buckingham) $\pi$ terms?
The best way I know how to ask my question is to provide two examples described in two textbooks, and ask why the first example was able to perform a particular operation and if the same operation ...
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1answer
60 views
Metric elements of the Schwarzchild metric
I am learning about the Schwarzchild metric $g_{\mu\nu}(x)$ for the spacetime geometry outside a spherically symmetric source with mass $M$.
In the book by Cheng, a spherical coordinate system $(t,...
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3answers
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Is the unit for spacetime intervals time or space distance?
This is no question on sign convention, and it is no question if ds or $ds^2$ shall be considered as the spacetime interval: I have taken my personal decision to opt for the signature (+,-,-,-) ...
