A math exam question asked for the ratio of two wheels given the required information about the number of revolutions made along a certain distance by the two wheels of a penny-farthing bike.
Some students gave the ratio of the radii while others gave the ratio of the areas.
What should an...
In his article 'Quantum theory of radiation', Reviews of Modern Physics, Jan 1932, volume 4, Fermi gives the relativistic hamiltonian function ##W_a## for a point charge by equation (13),
## 0 = - \frac 1 {2m} \left( \left[ mc +\frac {W_a - ~eV} c \right ]^2 - \left[ p -\frac {eU} c...
I am a retired High School teacher trying to use tensors in getting the Euler-Lagrange equations from the em lagrangian density.
I attached a document in my post since I am not fluent in writing LaTex.
Can anyone, please check my work.
Thanks.
As the secant AE is moved downwards, the exterior angle remains equal to the same interior angle, with the result that as the secant becomes a tangent, the cyclic quadrilateral disappears and the exterior angle becomes equal to the angle in the alternate segment. pdf is attached.
It is...
The graph of y = x - 1 CUTS the x-axis at x = 1 while the graph of y = x2- 1 TOUCHES the x-axis at x = 1.
The point at which the tangent touches the curve is shown mathematically by having two solutions of x, i.e. x = 1 (twice).
Is there some deeper meaning to these two identical solutions for x?
When discussing Lorentz transformations some books use
xμ/ = Λμ/αxα
while some other books use
x'μ= Λμαxα.
Perhaps someone can help me understand which is the better notation.
Thanks.
Is there redundancy in the phrase ‘an isolated free particle’?
Do not the words ‘free’ and ‘isolated’ imply each other?
Any help is much appreciated.
Thanks
A line in 2-dimensional euclidean space can be determined by the coordinates of any two particular points on the line. Hence four "parameters" are required.
Now let’s consider a line given by the usual equation
y = mx + c.
c, being the intercept on the y-axis, is related to the point (0,c) which...
During my reading I met with,
(Λ-1)μν = Λνμ ≡ ημρΛρσησν.
Is it correct to say that η raises and lowers the indices of Λ giving Λμν, which, in turn, will give (Λ-1)μν = Λμν?
Thanks for any help.
The symbol for a Lorentz transformation is sometimes Λαβ and sometimes Λμν.
When Λαβ is shown by a matrix, the upper index denotes the entries in the rows and the lower index denotes the entries in the columns.
When Λμν is shown by a matrix, does the upper index still denotes the entries in...
Homework Statement
I was reading in a book that,
" For any function f(x) whose functional form changes from f(x) to f'(x), we can write
\bar{\delta}f(x) = f'(x) - f(x)
= {f'(x') - f(x)} - {f'(x') - f'(x)}
=...
Difficulty regarding notation for Lorentz transformation
Please can somebody explain to me the relation between Δ^{σ}_{μ} and Δ_{σ}^{μ} as symbols representing a Lorentz transformation?
Thanks.
Homework Statement
A cylindrical metal bar of lenght L hangs by two strings in a horizontal position. The metal bob of a simple pendulum hits one end of this metal bar in a direction perpendicular to the crossection of the bar. Find an expression for the time t of contact during the impact...
Can someone explain why the covariant derivative of g_{\alpha\beta} with respect to x^{\lambda} is always zero?
I am asking for a physical reason why it must be so.
Let r_{\mu} be a tensor in coordinates x^{c} and R_{b} be a tensor in coordinates X^{c}.
Then let r_{\mu} = 0.
Then {\partialX^{\nu}/\partialx^{\mu}}R_{\nu} = 0.
I read in a book that one can divide both sides of the last equation by the partial derivative to get R_{\nu} = 0.
I do not...
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Consider an experiment to prove that the acceleration in a certain direction on a given mass is directly proportional to the resultant force in that direction given that the given mass is constant. The acceleration can be measured using light gates. This resultant force can be...
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One of the postulates in SR is that the speed of light in vacuum is constant for all observers. Is there a theory in which this is derived and is not a postulate?
Thank you.
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I started to read ‘QFT in a Nutshell’ by A. Zee. In the introduction to the path integral formulation of quantum mechanics there is the story about a particle going through a series of screens with holes drilled through them. Then the number of holes in each screen is increased. This...