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Some physicists are known for one equation. E. C. G. Sudarshan left marks on several fields: particle physics, quantum optics, the theory of open quantum systems, and one famous speculative idea about particles faster than light. This post explains three of them in plain terms, and what a student can learn from how he worked.
Who was E. C. G. Sudarshan?
The Physics Today obituary by M. K. Balasubramanya and M. D. Srinivas gives the outline. Ennackal Chandy George Sudarshan was born on 16 September 1931 in Pallam, India. After a BSc from Madras Christian College and an MA from the University of Madras, he joined the Tata Institute of Fundamental Research in Bombay, where he worked on cosmic-ray showers with Homi Bhabha. He also served as scribe for Paul Dirac's quantum mechanics lectures. He then went to the University of Rochester as a doctoral student of Robert Marshak, finishing his PhD in 1958.
After Harvard, Rochester, Bern and Syracuse, he joined the University of Texas at Austin in 1969, and directed the Institute of Mathematical Sciences in Chennai from 1984 to 1991. He died in Austin on 13 May 2018. His honours included the Padma Vibhushan in 2007 and the ICTP Dirac Medal in 2010, which he shared with Nicola Cabibbo.
What is the V-A theory of the weak interaction?
The weak interaction causes beta decay, where a neutron turns into a proton, an electron and an antineutrino. In the mid-1950s experiments showed that it violates parity: it treats left-handed and right-handed versions of a process differently. Physicists needed a theory with that built in.
Sudarshan analysed all the weak-decay data and concluded that the interaction must have a specific mathematical form, a mix of "vector" and "axial vector" parts, written V minus A. The Physics Today obituary notes that this structure explained all but four experimental results, and when those experiments were repeated they agreed with his theory. He and Marshak published the theory in Physical Review in 1958. The ICTP citation says it "opened the way to the full description of the unified electroweak theory".
What is the optical equivalence theorem?
Light can be described classically, as waves, or quantum mechanically, as photons. For many experiments both give the same answer. The question was how to tell, from a beam's properties, whether it is genuinely quantum.
In April 1963 Sudarshan published Equivalence of semiclassical and quantum mechanical descriptions of statistical light beams in Physical Review Letters. The obituary explains the idea: any state of light can be written as a weighted mixture of "coherent states", the quantum states closest to a classical wave. The weights form a quasi-probability distribution. For ordinary light the weights behave like probabilities. For some light they take negative values, which no classical wave can produce. Negative weights are the signature of quantum light, seen in effects such as photon antibunching, where photons arrive more evenly spaced than chance allows.
What was the tachyon idea?
In 1962 Sudarshan, with Vijay Deshpande and Olexa-Myron Bilaniuk, published "Meta" relativity in the American Journal of Physics. Its abstract says it re-examines, within special relativity, the old hypothesis that a particle might move faster than light. Such particles were later named tachyons. No experiment has detected one. The paper's value was in taking the question seriously within relativity, and a short calculation shows what such a particle would have to be like.
Start from the energy formula E = mc² / √(1 − v²/c²).
For v greater than c, the quantity under the square root is negative. At v = 2c it is 1 − 4 = −3, so the square root is i√3, an imaginary number.
For the energy to be real, the mass term would have to be imaginary too, say m = iμ. Then E = iμc² / (i√3) = μc² / √3, about 0.58 μc².
In general the energy becomes E = μc² / √(v²/c² − 1). As v grows, the denominator grows, so E falls; as v comes down toward c, E grows without limit. Such a particle would speed up as it loses energy, and could never slow down to c.
So a faster-than-light particle would have to live entirely on the far side of the light barrier, never crossing it. That is the strange but consistent picture the paper explored.
What else did he predict?
With Baidyanath Misra he described what they called Zeno's paradox in quantum theory in 1977. Their abstract concludes that "an unstable particle which is continuously observed to see whether it decays will never be found to decay". In other words, frequent measurement can hold a quantum state in place, an idea now called the quantum Zeno effect.
What can a student take from his way of working?
Use all the data, not just the convenient part. His V-A conclusion came from checking every weak-decay result and trusting the theory when four experiments disagreed.
Ask what would make something genuinely different. The optical equivalence theorem gives a sharp test for "quantum" instead of a vague feeling.
Take odd questions seriously. "Can anything go faster than light?" sounds like science fiction, but asking it carefully taught people more about relativity.
To build intuition for light as waves before you reach photons, try our guide to Young's double slit problems. Interference is easier to see than to read, and the Fermi Simulation Lab has interactive simulations for ideas like this.
Take the energy formula above and compute E for v = 3c with m = iμ, then check that it is smaller than at v = 2c.
