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प्रश्न
“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.
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उत्तर १
An equation which agrees with experiment must also be simple and hence beautiful. We have some simple and beautiful equations in Physics such as
- E = mc2 (Energy of light)
- E = hv (Energy of a photon)
- KE = 1/2mv2(Kinetic energy of a moving particle)
- PE = mgh (Potential energy of a body at rest)
- W = F.d (Work done)
All have the same dimensions. One experiment shows dependency of energy on speed, the other shows dependency on frequency & displacement. That's the beauty of equations in Physics coming from different experiments.
उत्तर २
Generally it is considered that physics is a dry subject and its main aim is to give qualitative and quantitative treatment i.e., any derived relation or equation must be verified through experimentation. It is felt that truth of an equation is more important than the simplicity, wonderfulness, symmetry or beauty of the equation. But frankly, if a relation is true to experimentation and simultaneously it is simple, interesting, symmetrical, wonderful or beautiful, it will certainly add to the charm of the relation.
संबंधित प्रश्न
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The dimensions ML−1 T−2 may correspond to
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Find the dimensions of pressure.
Find the dimensions of magnetic field B.
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]
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Find the dimensions of magnetic permeability \[\mu_0\]
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Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
cos 0 + cos π/3 + cos 2π/3 + cos 3π/3 + cos 4π/3 + cos 5π/3 = 0.
Use the known cosine values to verify the result.
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The changes in a function y and the independent variable x are related as
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
