One of the last letters written by Rutherford. This was to Raman dated 3rd Aug 1937.
Here, he is consoling Raman after he quit the Directorship of IISc. Rutherford is also discussing his possible travel plans to India.
Unfortunately, Rutherford died on 19th Oct 1937..
ref: S. Ramaseshan and C. Ramachandra Rao. C.V. Raman : A Pictorial Biography, p 108 (1988)
If you need to admire complex analysis for its elegance and visual utility, try quantum optics. Specifically, the description of quantum states. Thanks to creation and annihilation operators, the position and momentum states of a quantum optical field can be represented as quadratures. These entities can now be represented on the orthogonal axes of a complex plane. The representation of Argand diagrams starting with a classical electromagnetic field and then extrapolating them to quantum theory is a tribute to its geometrical representation. The fact that two axes can be utilized to represent real and imaginary parts of the defined state is itself an interesting thing. By certain operations within the plane, one can realize the vacuum state, the coherent state, and the squeezed state of quantum optics.
The Vacuum Spread – One of the major consequences of quantum theory, and especially the second quantization, is the realization of the vacuum states. Even when there are zero photons, there is a residual energy in the system that manifests as vacuum states. How to define the presence or absence of a photon is a different proposition because vacuum states are also associated with something called virtual photons. That needs a separate discussion. Anyway, in a complex plane of quadrature, a vacuum state is represented by a circular blob and not a point (see fig. 1). It is the spread of the blob that indicates the uncertainty. In a way, it is an elegant representation of the uncertainty principle itself because the spread in the plane indicates the error in its measurement. Importantly, it emphasizes the point that no matter how low the energy of the system is, there is an inherent uncertainty in the quadrature of the field. This also forms the fundamental difference between a classical and a quantum state. The measurement of the vacuum fluctuation is a challenging task, but one of the most prevalent consequences of vacuum fluctuation is the oblivious spontaneous emission. If one looks at the emission process in terms of stimulated and spontaneous pathways, then the logical consequence of the vacuum state becomes evident in some literature on quantum optics. Spontaneous emission is also defined as stimulated emission triggered by vacuum state fluctuations. It is an interesting viewpoint and helps us to create a picture of the emission process vis-à-vis the stimulated emission.
Figure 1. Vacuum state representation. Note that their centre is at the origin and has a finite spread across all the quadrants. Figure adapted from ref. 2.
Another manifestation of the vacuum state is the Casimir effect, where an attractive force is induced as you bring two parallel plates close to each other. The distance being of the order of the wavelength or below this triggers a fascinating phenomenon which has deep implications not only in understanding the fundamentals of quantum optics and electrodynamics, but also in the design and development of quantum nanomechanical devices.
A shift in the plane – Coherent states are also described as displaced vacuum states, and this displacement is evident in the Argand diagrams. The quadrature can now help us visualize the uncertainty in the phase and the number of photons in the optical field. One of the logical consequences of the coherent state is the number-phase uncertainty. This gets clear if one observes the spread in the angle of the vector and the radius of the blob represented (see Fig. 2). Notice that the blob still exists. The only difference is that the location of the blob has shifted. The consequence of this spread has a deeper connection to the uncertainty in the average number of photons and the phase of the optical field. The connection to the number of photons is through the mod alpha, which essentially represents the square root of the average number of photons. Taken together, the blob in the Argand diagram represents the number-phase uncertainty.
Figure 2. Coherent state representation. Note that their centre is displaced. Figure adapted from ref. 2.
Lasers are the prototypical examples of coherent states. The fact that they obey Poissonian statistics is the direct consequence of the variance in the photon number, which is equivalent to the square root of the average number of photons. This means one can use photon statistics to discriminate between sources that are sub-Poissonian, Poissonian, or super-Poissonian in nature. The super-Poissonian case is the thermal light, and the sub-Poissonian state represents photon states whose number can reach up to 1 or 0. The coherent states sit in the middle, obeying the Poissonian statistics.
Everything has a cost – Once you have a circle with a defined area, it will be interesting to ask: Can you ‘squeeze’ this circle without changing its area? The answer is yes, and that is what manifests as a squeezed state. In this special state, one can squeeze the blob along one of the axes at the cost of a spread in the orthogonal direction. This converts the circle into an ellipse (see Fig. 3).
Figure 3. Squeezed State. Note the circle has been squeezed into an ellipse. Figure adapted from ref. 2.
Note that the area must be conserved, which means that the uncertainty principle still holds good; just that the reduction in the uncertainty along one axis is compensated by the increment in another. This geometrical trick has a deep connection to the behaviour of an optical field. If one squeezes the axis along the average number of photons, it means that you are able to create an amplitude-squeezed state. This means the uncertainty in the counting of photons in that state has reduced, albeit at the cost of the uncertainty in the measurement of phase. Similarly, if one squeezes the blob along the axis of the phase, then we end up with a lowering of the uncertainty for the optical phase. Of course, this comes at the cost of counting of number of photons. I should mention that the concept of optical phase itself is not clearly defined in quantum optics. This is because an ill-defined phase can have a value of 2π, which creates the problem. An interesting application of the phase-squeezed quantum states is in interferometric measurements. By reducing the uncertainty in the phase, one can create highly accurate measurements of phase shifts. So much so that this can have direct implications on high-precision measurements, including gravitational wave detection. The anticipation is also that such tiny shifts can be helpful in observing feeble fluctuations in macroscopic quantum systems.
Pictures can lead to more than 1,000 words. And if you add them to a quantum optical description, as in the case of the states that I have defined, they create a quantum tapestry. Perhaps this is the beauty of physics, where there is a coherence between mathematical language, geometrical representation, and physical reality. Feynman semi-jokingly may have said, “Nobody understands quantum mechanics,” but he forgot to add that there is great joy in the process of understanding through mathematical pictures. After all, he knew the power of diagrams.
Here I discuss the paper that announced the Raman effect to the world…
Happy Republic Day to all my fellow Indians !
26th Jan is also an important day in the history of physics/engineering –
26th Jan 1926 – J.L. Baird “demonstrated television at his premises in Frith Street, London, to about forty people including members of the Royal Institution…..The Times was the only newspaper invited, and its reporter published the story on 28 January”. This exactly a 100 years today !
26th Jan 1939 – Niels Bohr publicly announced nuclear fission, specifically the splitting of the uranium atom.
26th Jan 1954 – Morris Tanenbaum et al. at Bell Laboratories showed a working silicon transistor.
McLean, Donald F. 2014. “The Achievement of Television: The Quality and Features of John Logie Baird’s System in 1926.” The International Journal for the History of Engineering & Technology 84 (2): 227–47. https://doi.org/10.1179/1758120614Z.00000000048.
“Niels Bohr Announces the Discovery of Fission – Nuclear Museum.” n.d. Https://Ahf.Nuclearmuseum.Org/. Accessed January 26, 2026. https://ahf.nuclearmuseum.org/niels-bohr-announces-discovery-fission/.
“The Lost History of the Transistor.” 2004. IEEE Spectrum 41 (5): 44–49. https://doi.org/10.1109/MSPEC.2004.1296014.
Wikipedia. 2025. “History of the transistor.” December 22. https://en.wikipedia.org/w/index.php?title=History_of_the_transistor&oldid=1328866801.
A small sampling of Raman’s publication. These papers are related to light scattering and form the foundation on which he made his famous discovery. Raman wrote more than 400 research papers in his lifetime (apart from monographs, lectures and public talks). Writing such a series of papers on a particular topic can be observed throughout his career.
A note to young scholars: intellectual monuments are built this way: thought after thought, day after day, paper after paper. Never underestimate what can be achieved with consistent, honest effort.
“Everybody wondered (and still wonders) why the Stockholm committee systematically ignored Sommerfeld’s pioneer work in modern physics. Such an omission is actually impossible to understand.”
Leon Brillouin, in the foreword of his book WAVE PROPAGATION AND GROUP VELOCITY (1959)
Brillouin further mentions the teachers who taught him, and rates Sommerfeld among the best:
“I had the great privilege of attending, as a student, lectures given by some prominent physicists, such as H. A. Lorentz, H. Poincaré, and P. Langevin. But I was especially impressed by Sommerfeld’s mastery as a teacher.“
In reference to a recent article on higher education in the Economic Times, a well-known tech entrepreneur and philanthropist wrote the following on X/Twitter: “75% of Indian higher education institutions still not industry-ready. Lot of work left to transform. But the 21st century requires education, research, innovation, and startups as four pillars of a university.”
This is a thought I do support, but I think there is one more important meta-pillar, perhaps a ‘foundation’ on which all these pillars are standing, and that is called ethics. Below are five aspects of ethics that I think need further attention.
There is an inherent connection between cooperation and trust, and that is founded on an ethical principle. The world requires an ethical recap, and it should be part of individuals, institutions, and governments. There is a rich history of ethics in all the cultures across the world, and it is worth revisiting them in a new light. Perhaps it is high time that we “Make Ethics Great Again.”
In physics, the general theory of relativity is one of the most remarkable achievements. It has turned out to be one of the most profound theories in the history of physics. In 1916, Albert Einstein proposed this theory, and it was confirmed in 1919.
Right after this confirmation, around 1920, two Indian gentlemen named Satyendranath Bose and Meghnad Saha translated Einstein’s German work into English. What you are seeing as an image is the remarkable book Principles of Relativity, containing the original papers by Einstein and Minkowski. This translation was done by M.N. Saha and S. N. Bose, who were then at the University College of Science, Calcutta University. It was published in 1920 by the University of Calcutta.
The book also contains a historical introduction by Mahalanobis, the celebrated statistician, although he was originally trained as a physicist himself. This historical introduction is itself quite remarkable.
If you look at the table of contents of this book, you will find the following:
The historical introduction discusses the evolution of ideas that led to the fruition of the general theory of relativity. This turned out to be one of the most important expositions of the general theory of relativity, soon after the emergence of the theory and its subsequent confirmation by Eddington through his famous solar eclipse expedition. This is a remarkable document, and it is available on the Internet Archive.
based on my blog.
VISMAYA - History & Philosophy of Physics 