Probabilities of the Quantum World (Pt-4)
Summarizing the Masterpiece by Daniel Danin
[To refresh, text in such square brackets is my commentary. Rest of it is a faithful documentation of the most fascinating story ever told of the Quantum Revolution]
[At the end of Part-3, Professor Max Planck had just introduced the word “Quantum”]
Planck was born in 1858 and at the time of his greatest achievement he, like J. J. Thomson, was in his Forties. And just like Thomson he immediately felt that his scientific discovery was a burden.
In a letter to the skillful experimenter Robert Wood, Planck wrote that his proposed solution was simply ‘a mathematical technique’ and frankly, he did not expect anything exceptional from it.
At the time, he had already spent six years looking for a unified formula to account for the energy spectrum of the electromagnetic radiation of a heated body. He was unable to reach this goal until… Until he saw that he could successfully resolve this question if he assumed a very strange thing: That the light was emitted and absorbed in separate portions! That was his idea. He called this portion of radiation a “quantum”.
[Lets back up for a bit. The problem that Planck and others were confronted with is a practical one. Lets say there is a furnace which is red hot. It will radiate heat. The problem was to find out how much heat it would radiate. Sounds quite simple, right? But no! When a body emits light it gives to the surroundings a bit of its energy. If the Energy radiated is taken to be a continuous variable, then, if we do the math, an infinite amount of energy could be radiated from a hot furnace! This seemed absurd and quite frustrating to the physicists of the time.
Planck’s master stroke was to allow only a certain minimum lower limit to the division of the Energy spectrum. This was a sharp left turn in the realm of classical physics where both space and energy were continuous. Remember the derivative from basic calculus formulated by Newton? That can only happen if the variable is continuous.
Planck’s idea can be understood by the following problem of measuring the distance between two points A & B. Since length is a continuous variable, theoretically, we could keep dividing the distance between A & B by half and then again by half and so on endlessly. Then we could sum up the infinite small pieces to get the total distance but since the number of small pieces would be infinite and the length of the small pieces would be extremely small but finite, the sum would be infinite (infinite pieces x small length = infinite). This is absurd! How can the distance between two given points be infinite? The problem comes with allowing distance to keep getting smaller and smaller without a limit.
Now say we practically have a ruler with millimeter markings and we use that to measure the distance between A & B. We can only measure to the closest millimeter mark. We can’t measure any more accurately than that. Now the distance between A & B is equal to the number of millimeter marks x 1 mm. Finite.
This was Planck’s master stroke. He said that similar to the millimeter marking, Energy also has a smallest possible limit beyond which it cannot be divided any further. Doing this one thing efficiently solves the problem of infinity when summing up the energy radiated by a hot furnace. This smallest division of Energy Planck called a Quantum.]
Planck proposed that energy can be exchanged in terms of whole quanta; it was either one quantum or two, three, a hundred or a million quanta — but never a million and an eighth or a quarter. Fractions of quanta did not exist. He introduced the quanta into the formula where it was necessary but did not propose to introduce them into nature! It was a ‘working hypothesis’, nothing more, just a ‘scaffolding’.
Planck did not change his views until the end of his life; he dies after World War Two in his late eighties already fully aware of the physical reality of radiation quanta, monstrously demonstrated to a shaken mankind by the atomic explosions at Hiroshima and Nagasaki. Fifteen years after Planck died, Niels Bohr commented to the historians in an interview given shortly before his own death:
“In some sense it can be said that he used the last forty years of his life, not to say fifty, to try to get his discovery out of the world.”
[Let this sink in a bit. What started out as merely a clever mathematical formulation to get around the problem of infinity when solving radiation heat problems has today become one of the key secrets of Nature we have unraveled. The Planck Length is the scale at which classical ideas about gravity and space-time cease to be valid and mysterious quantum effects dominate.]
Fortunately for our understanding of nature, the life of remarkable ideas does not entirely depend on the intentions or lack of will of their originators. Planck in the first decade of this century warned the young Ioffe not to question the nature of light just because a few years before such questioning had been attempted by another young scientist — and successfully at that.
That young scientist was Einstein. It was his ‘first step’ which Planck later recalled in his Nobel lecture. The twenty-six-year-old expert of the third grade in the Swiss Bureau of Patents somehow desperately needed what Planck was afraid of, namely, ‘to go further’. In 1905 he published in the seventeenth volume of the German Annalen der Physik three papers which found immortal place in the history of natural sciences. The first opened the way to the final proof of the atomic structure of matter. The second consistently presented the foundations of the relativity theory. And the third paper was an introduction to the physics of quantum theory of light.
Einstein dared to proclaim the physical reality of quanta
He said that they were particles of radiation, literally, small bodies ‘localized in space’. This definition implies that in their motion in space the quanta occupy a certain localized position. That was what made Einstein’s idea so bold.
In 1900 Planck announced that bodies emitting light would deliver it to the theorists only in certain portions! But that limitation was only for theorists: in fact the quanta did not exist. In 1905 Einstein suggested a different nature for the emitted quanta: they were minute bodies that preserved their integrity in space! But, unlike Rutherford, Einstein did not say that he knew ‘what the quantum looks like’.
In five years the theory of quanta appeared to become, in the words of Max Planck, a source of continuing torment for the scientists.
As the Newtonian mechanics was being replaced by the relativity theory brought forth by a young boy from Ulm, Relativity immediately became the subject of common talk. Even thirty years later an older Einstein complained and warned at the same time:
“One cannot regard a concept as senseless only because it differs from classical physics.”
There were also a few months of despair when the twenty-one-year-old Einstein tried to find a classical explanation for the inexplicable constancy of the velocity of light, and for Planck’s quanta
“All my attempts to apply the fundamentals of physics to these results failed completely. It was as if I could not find solid land to put my feet on and build on. Gradually I began to despair… The longer and harder I tried, the more I felt that only the discovery of a general… concept could lead us to reliable results.”
Einstein arrived at his Relativity Theory after 10 years of thought.
[Wait… If he found it when he was twenty-six, that means he started his search at sixteen! Did he ever go to Prom I wonder?!!]
Time and Space are Relative
It was not without reason that Einstein wrote:
“Forgive me, Newton; you found the only way open in your time to a man of the highest scientific capability and strength of thought. The concepts created by you are still the leading ones in our physical thinking, though we now know that if we aspire to deeper understanding of the interrelationships in nature, we shall need to replace these concepts with other farther from the sphere of our immediate experience.”
Let’s jump to the Solvay Conference of 1911 in Brussels where Lorentz, the chairman of the conference opened that meeting with the following phrase:
“It is quite probable that while we are together discussing this problem, a thinker in a remote corner of the world has worked out its solution”
[In 1911, lets see where we were in our quest to understand Nature. We knew that for most normal life, Newton’s Laws were sufficient. If however, things started to move at high speeds, we needed Einstein’s Special Relativity. In normal life mass, length and time are all unchanging when things move. In Special Relativity, as things move fast, length contracts, mass increases and time dilates. So far so good.
As things get massively heavy, like for example, stars like our sun, we need Einstein’s General Relativity. Here the distortion of the fabric of space-time happens due to the massive mass of things like starts and planets.
When things get really small, like atoms for example, at the Planck length scale, Relativity breaks down and Quantum effects kick in.]
[To go to the Moon, all we need is Newton. For GPS to work, we need Einstein.]
Here we are… the Quantum has been proposed by Planck as a mathematical tool to avoid the infinity. Einstein has made quanta real. But through all this, the atom is still doomed to be unstable.
We are patiently waiting for Niels Bohr…
… To be Continued
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