lab –> www

A lab is a place where questions are asked, experiments are conducted, and theories are tested…& sometimes.. in this pursuit, the world is changed.

A case in point is the connection between CERN and the origins of www :

https://home.cern/science/computing/the-birth-of-the-web

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Everything..

This is a reverse-chronological list of all the blogs posted on this site.

Tiny value of the radiation pressure of sunlight on Earth

 

  • 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 :

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When Chandra’s paper got rejected

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)

Chandra quotes Virginia Woolf

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)

Note: The source spells Woolf as Wolff

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Intensity Interferometer – connection to coherence

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,

$$ \gamma_{12} = \frac{\left\langle U_1(t) U_2^\ast(t) \right\rangle}{\sqrt{\left\langle |U_1|^2 \right\rangle \left\langle |U_2|^2 \right\rangle}} $$

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:

$$ \left\langle I_1(t) \cdot I_2(t) \right\rangle $$

where the enclosing brackets denote a time average.

This correlation, measured in the intensity interferometer, is related to the degree of spatial coherence in the following way:

$$ \left\langle I_1 I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left(1 + \left| \gamma_{12} \right|^2 \right) $$

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:

$$ \left\langle \Delta I_1 \Delta I_2 \right\rangle = \left\langle I_1 \right\rangle \left\langle I_2 \right\rangle \left| \gamma_{12} \right|^2 $$

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.

Reference:

Dravins, Dainis. ‘Intensity Interferometry: Optical Imaging with Kilometer Baselines’. arXiv.Org, 12 July 2016. https://arxiv.org/abs/1607.03490

Pavan’s lectures on Quantum Optics

Many students outside IISER Pune have been following my course blog on Quantum Optics, so I thought I would share some lectures too. I have recorded some discussion related to statistical optics, and will eventually connect them to quantum optics in a few lectures.


Lecture 1 – Quantum Optics via Statistical Optics

topics discussed:
Temporal coherence function
Degree of temporal coherence function
Coherence time
Coherence length
Power spectral density
Spectral width


Lecture 2:

Spatial Coherence
Mutual Intensity
Coherence Area
Cross-Spectra Density
Partially Coherent Waves
Interference Equation
Visibility
Interference & Temporal Coherence
Interference & Spatial Coherence


Lecture 3 – Intensity Interferometer: Physics & History

Lecture 4: What is quantum about photons? How to measure it?