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.

learn more… | top users | synonyms

2
votes
2answers
36 views

Natural unit conversion

I'm a bit confused about different notions of "natural units" that I encounter occasionally. I'm familiar with Planck units, and in particular I can understand the conversion between, say, metres and ...
6
votes
1answer
268 views

Why dimensionality of the Electric Charge varies with the spacetime dimensions?

The point is: We can find via dimensional analysis that the electric charge dimensionality varies with the dimension of space-time. $$[\text{charge}] = eV^{(3-D)/2}$$(You can see below the way I did ...
2
votes
1answer
106 views

Why are log scales so common?

I am currently reading a very nice book on scales in physics. There is a discussion on the different physical scales which are based on the effect of the corresponding phenomena, the given examples ...
2
votes
1answer
69 views

Deriving (dimensionless) physical constants from theory

The Wikipedia entry on Physical Constants says: With the development of quantum chemistry in the 20th century, however, a vast number of previously inexplicable dimensionless physical constants ...
2
votes
1answer
155 views

Drag - Dimensional Analysis / Buckingham Pi

Dimensional Analysis / Buckingham Pi Theorem I'm working on dimensional analysis and I'm having trouble. Here's a problem from my book I'm working on for practice. I'm suppose to consider a small ...
0
votes
1answer
82 views

Is the dimension “number of particles” a fundamental, or derived dimension (based on mass), or does it depend on the context, or is it dimensionless?

I consider "fundamental quantities" to be those that have dimensions that are are like length, mass, time, temperature, and so on. "Derived quantities" have dimensions that can be written in terms of ...
0
votes
1answer
53 views

Dimensionless numbers in relativistic theory

Dimensionless numbers allow physicists and engineers to extend the physical modeling landscape by reducing otherwise complex mathematics to a simple proportional relationship. For example by assuming ...
0
votes
1answer
94 views

What are the mathematical models for force, acceleration and velocity?

In mechanics, the space can be described as a Riemann manifold. Forces, then, can be defined as vector fields of this manifold. Accelerations are linear functions of forces, so they are covector ...
3
votes
0answers
160 views

Can mass dimension of a field be viewed as another 'quantum number'?

While studying SUSY in 4D, I noticed the dynamical chiral superfield has dimension [GeV], whereas the dynamical vector superfield (for gauge theories) is unitless. Because I was introduced to the ...
2
votes
0answers
19 views

Do the non-dimensionalizing equations that result from the Buckingham-$\pi$ algorithm necessarily have a unique solution?

Consider the Buckingham-$\pi$ algorithm: Let us say that we have $n+1$ relevant variables: $\{Q_0, ..., Q_n\}$. Let us say that we can define their dimensions in terms of $k$ basic dimensions. So, ...
2
votes
0answers
29 views

Quantum Efficiency Estimation

Might there be a way to do a rough estimate of the quantum efficiency of a photo-detector like a CCD or CMOS sensor based only on a picture taken with it? I've read papers and guides (like this one: ...
2
votes
0answers
355 views

What prediction led to the vacuum catastrophe?

The disagreement between predicted and measured energy density of the vacuum is one of the great unsolved problems of science. According to this book the predicted energy density was obtained as ...
2
votes
0answers
268 views

Dimensional analysis to estimate order of magnitude of quantities

In the Coursera course From the Big Bang to Dark Energy on several occasions dimensional analysis was used to estimate the scale of quantities. This almost seems like a contradiction in terms to me, ...
2
votes
0answers
46 views

Scaling in Vlasov equations

This question is in reference to the paper, http://arxiv.org/abs/1301.7182 What exactly is the argument being made on page 6 and 7? One deduces that the function $\Delta$ has to be such that, ...
1
vote
0answers
48 views

What does mathematical equivalence means here?

On Motls blog, http://motls.blogspot.com/2012/06/on-importance-of-conformal-field.html, while I was trying to understand what dimensional transmutation means, he said: I said that by omitting the ...
1
vote
0answers
37 views

Connection between the cosmological constant $\Lambda$ and the cutoff scale $\Lambda$

I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT. Cosmology: The cosmological constant enters the Einstein equations. In the special case of the ...
1
vote
0answers
44 views

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 ...
1
vote
0answers
165 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 ...
1
vote
0answers
50 views

How to determine that the renormalization constant $Z_3$ must depend only on $g$ and $\Lambda/m$

In Le Bellac's book, Quantum and Statistical Field Theory, the renormalization constant $Z_3$ is introduced with the equation $$ \Gamma^{(2)}_R(k^2, m^2, g) = Z_3 \Gamma^{(2)}(k^2, m_0^2, g_0; ...
0
votes
0answers
22 views

Exercises with solutions in dimensional analysis - reference request

I am currently trying to brush up on my skills in dimensional analysis, and computing with units. Is there a good source of worked examples, and exercises with solutions? I'd prefer to have solutions ...
0
votes
0answers
19 views

Non-dimensionalizing the “bead on a rotating hoop, with viscous damping” problem

This is not a homework question. Rather, this is an exercise I have taken up on myself. In particular, I am trying to find an algorithmic way to non-dimensionalize known equations, using the ...
0
votes
0answers
25 views

What is the “Pidebuck” generalization of Buckingham π about?

The site http://www.oasification.com/PideBuckingham_en.htm links to two articles that seem to propose a generalization of the (Vaschy?-)Buckingham Pi Theorem which looks quite interesting, but ...
0
votes
0answers
143 views

How can q=mcp(deltaT) be made dimensionless?

Specifically, how can I make $m C_p$ dimensionless? I've tried using the Reynolds number and Peclet number definitions to plug into there but the closest I've gotten to was: $q=\pi D Re Pe ...
0
votes
0answers
78 views

Choice of units when truncating Taylor series for physical quantities

It is common practice in physics to truncate Taylor series of (possibly) very complicated functions to obtain a good approximation of the relevant physical behaviour; for example, the Coulomb ...