If radiation pressure is indeed a genuine electromagnetic phenomenon, then why don’t we observe it in our everyday lives?
The reason is that the magnitude of the radiation pressure from the natural light source on Earth (the Sun) is feeble.
from electromagnetic theory, this tiny amount of pressure can be calculated by the formula \(\frac{E}{c}\), where ‘E’ is the energy of sunlight on earth and ‘c’ is the speed of light in vaccum (which is \(3 \times 10^8 \text{ ms}^{-1}\) [\(9.83 \times 10^8 \text{ ft s}^{-1}\)]).
Maxwell himself recognized the low value of this energy, which he assumed to be \(83.4 \frac{\text{ft} \cdot \text{pound}}{\text{sec} \cdot (\text{ft})^2}\)
Taking this value and dividing it by ‘c’ gives us a radiation pressure of \(10^{-7} \frac{\text{pound}}{(\text{ft})^2}\).
Poynting, who extensively worked on radiation pressure from an electromagnetic theory viewpoint, compared this tiny pressure to the size of a grain in an area of \(200,0000 \text{ (ft)}^2\)!
This highlights why radiation pressure is hard to measure experimentally, and it took some trial and error to ascertain the value and the method. More on this later…
Reference :
Loudon, R., and C. Baxter. ‘Contributions of John Henry Poynting to the Understanding of Radiation Pressure’. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2143 (2012): 1825–38. https://doi.org/10.1098/rspa.2011.0573.
Sometimes, referee reports can be frustrating, especially if your paper gets rejected and criticized without justification. This is not a new thing in scientific discourse, and even accomplished researchers like S. Chandrasekhar had to face such rejections. As Chandra notes in the winter of 1956:
“The frustration of these months was due also to the fact that the Royal Society rejected my second paper on turbulence with a most discourteous referee’s report. I withdrew the paper, but continued the correspondence with the referee. The referee withdrew some of his more blatant remarks; but the whole incident was an unhappy interlude. I went specially to Washington to talk to von Neumann; and corresponded also with Heisenberg.” (Chandrasekhar, 2010, p. 38)
When a paper gets rejected, what is important is to seek feedback from people who are knowledgeable and courteous. Chandra had friends such as von Neumann and Heisenberg to seek input. One cannot get better than this.
Source: Chandrasekhar, S. 2010. A Scientific Autobiography: S. Chandrasekhar: With Selected Correspondence. (posthumously published)
The well-known astrophysicist, S. Chandrasekhar, liked the writings of Virgina Woolf. In her words, he found a unique channel to philosophize his own work, as he did in 1957:
‘By accident, I found the following quotation from Virginia Wolff (Woolf) which expressed very accurately my attitude to my work of the past years. This quotation ends my Rumford Lecture.
“There is a square. There is an oblong. The players take the square and place it upon the oblong. They place it very accurately. They make a perfect dwelling place. The structure is now visible. What was inchoate is here stated. We are not so various or so mean. We have made oblongs and stood them upon squares. This is our triumph. This is our consolation.”’ (Chandrasekhar, 2010, p. 41)
Source: Chandrasekhar, S. 2010. A Scientific Autobiography: S. Chandrasekhar: With Selected Correspondence. (posthumously published)
My previous blog discussed some historical papers related to the intensity interferometer and its connection to quantum optics. Here, I explain the basic physics of an intensity interferometer.
In the context of spatial coherence, the coherence theory expresses the degree of spatial coherence as,
with \( U_i(t) \) representing the fields of sources \( i = 1 \) and \( 2 \).
An intensity interferometer measures the intensity correlation function between such sources. If \( I_1(t) \) is the intensity of source 1 and \( I_2(t) \) is the intensity of source 2, then the intensity correlation function is given by:
If one ignores the background (the first term in the sum of the above equation) and considers only the fluctuations in the signal (the second term), then the term of relevance will be:
The signal in the intensity interferometer is thus proportional to \( \left| \gamma_{12} \right|^2 \).
A conventional interferometer measures a signal that is proportional to \( \left| \gamma_{12} \right| \), which includes the amplitude and phase, whereas an intensity interferometer measures a signal proportional to \( \left| \gamma_{12} \right|^2 \), which is not sensitive to the phase.
Intensity interferometers have certain advantages compared to conventional interferometers (such as the Michelson interferometer). Below is a partial list:
Intensity measurements (unlike amplitude or phase) can be done directly using optoelectronic instruments.
They do not require precise, sub-wavelength optical alignment, unlike amplitude- or wavefront-dividing interferometers.
They can be used with two detectors that are placed far apart, thereby improving the spatial resolution of the measurement (relevant in astronomy).
A constraint of an intensity interferometer is that the intensity of the participating source should be bright.
There is an important connection between quantum optics and radio astronomy. Hanbury Brown and Twiss in the 1950s devised the intensity interferometer.
Particularly, they were interested in measuring the ‘diameter of discrete radio sources’. The title of their seminal paper reads “A new type of interferometer for use in radio astronomy”. As the authors claimed in their paper: “The principle of the instrument is based upon the correlation between the rectified outputs of two independent receivers at each end of a baseline, and it is shown that the cross-correlation coefficient between these outputs is proportional to the square of the amplitude of the Fourier transform of the intensity distribution across the source.”(Brown and Twiss, 1954)
First, they tested their technique in a laboratory situation and followed it up with a measurement of the diameter of Sirius. Their technique was a game-changer in measuring the diameter of bright stars.
As the intensity interferometers were being developed, the laser was realized in the early 1960s. Unlike conventional light sources, laser light is coherent, and this brings in unique features that can be used to understand the nature of light. In the context of laser optics, intensity interferometers had immediate utility in studying coherence through correlation measurement. It was logical to combine lasers with intensity interferometers and study the correlation. This combination is what led to the discovery of some fascinating aspects of quantum properties of light, including anti-bunching.
If the book by Born and Wolf is considered a classic on the electromagnetic theory of light, the quantum extrapolation is the book by Leonard Mandel and Emil Wolf titled Optical Coherence and Quantum Optics.
This book discusses the interface of statistical optics, optical coherence, and quantum optics. The core argument of the book starts with probability theory and its connection to fluctuations of light and builds optical coherence, polarization, and eventually quantum optical effects of light. It is a well-written treatise on light with a flavor of experiments (Mandel did some pioneering experiments in quantum optics) and theoretical explanation (a hallmark of Wolf).
In the preface of the book, they bring together the importance of intensity interferometers and the discovery of lasers and explain how and why it led to a deeper understanding of quantum optics:
“Prior to the development of the first lasers in the 1960s, optical coherence was not a subject with which many scientists had much acquaintance, even though early contributions to the field were made by several distinguished physicists, including Max von Laue, Erwin Schrodinger and Frits Zernike. However, the situation changed once it was realized that the remarkable properties of laser light depended on its coherence. An earlier development that also triggered interest in optical coherence was a series of important experiments by Hanbury Brown and Twiss in the 1950s, showing that correlations between the fluctuations of mutually coherent beams of thermal light could be measured by photoelectric correlation and two-photon coincidence counting experiments. The interpretation of these experiments was, however, surrounded by controversy, which emphasized the need for understanding the coherence properties of light and their effect on the interaction between light and matter.” (Mandel and Wolf, 1995, p. 1)
This further led to a series of studies on light-matter interaction from a coherence perspective, and included analysis of the fluctuation of light by understanding the randomness and the associated statistics of the fluctuations. Mandel, Wolf, Glauber, E.C.G. Surdarshan and many others across the world laid the foundation and connection between optical coherence and quantum optics. What started as a technical development in radio astronomy turned out to be a vital tool in quantum optics.
Brown, R. Hanbury, and R. Q. Twiss. ‘LXXIV. A New Type of Interferometer for Use in Radio Astronomy’. Philosophical Magazine 45, no. 366 (1954): 663–82. https://doi.org/10.1080/14786440708520475.
Brown, R. Hanbury, and R. Q. Twiss. ‘Correlation between Photons in Two Coherent Beams of Light’. Nature 177, no. 4497 (1956): 27–29. https://doi.org/10.1038/177027a0.
Hanbury Brown, R., and R. Q. Twiss. ‘A Test of a New Type of Stellar Interferometer on Sirius’. Nature 178, no. 4541 (1956): 1046–48. https://doi.org/10.1038/1781046a0.
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