# Tagged Questions

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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### Arguing on dimensions of logarithms and exponentials [duplicate]

Suppose you have some physical quantity $x$ of dimension $l$. We all know that the dimension of $x^2$, for example, will be $l^2$, and that of $\dfrac{1}{x}$ is $l^{-1}$. However, what will be the ...
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### Are units of angle really dimensionless?

I know mathematically the answer to this question is yes, and it's very obvious to see that the dimensions of a ratio cancel out, leaving behind a mathematically dimensionless quantity. However, I've ...
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### Do all equations have identical units on the left- and right-hand sides?

Do all equations have $$\text{left hand side unit} = \text{right hand side unit}$$ for example, $$\text{velocity (m/s)} = \text{distance (m) / time (s)},$$ or is there an equation that has different ...
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### Difference between theoretical equations and empirical equations

Some equations are theoretical in the sense that they are derived from an underlying theory. Other equations are empirical in the sense that they were selected only because they fit experimental data ...
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### Why do constants have dimensions?

I am just a beginner in dimensional analysis, and I see that $G$, the universal gravitational constant, is independent of everything. Speed, for example, depends on distance and time, but $G$ does not ...
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### A simple explanation of Kepler's Third Law

Is there a simple way to explain how Kepler's third law follows from the inverse square law that of gravity (and laws of motion) For example for Kepler's second law we can say it's because Gravity ...
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### Dependence on UV cut off of some $\phi^4$ diagrams

Consider the one loop corrections to the propagator and the vertex in $\phi^4$-theory:                 ...
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### Functions and Length Scales

Regretfully I have to start with an apology as I fear I might be unable to express the question rigorously. Often reading physics papers the concept of "length scale" is used, in statements such as ...
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### Visualizing Physical Units in Phyiscs

I do best in physics when I can make sense of the units that accompany values, and I do this by visualizing in my mind what is happening. Take for instance, $v=\frac{s}{t}$. When I think of velocity I ...
### Dimensions of $\phi$ in scalar field theory
On Srednicki page 90-91 (in printed edition) he derives that $$[\phi] = \frac{1}{2}(d-2) \tag{12.10}$$ from {\cal L}=-\frac{1}{2}\partial^{\mu}\phi\partial_{\mu}\phi -\frac{1}{2}m^{2}\phi^{2} - ...