On Friday, April 27, 1900, the British physicist Lord Kelvin gave a speech entitled "Nineteenth-Century Clouds over the Dynamical Theory of Heat and Light," which began:
The beauty and clearness of the dynamical theory, which asserts heat and light to be modes of motion, is at present obscured by two clouds.
Kelvin went on to explain that the "clouds" were two unexplained phenomena, which he portrayed as the final couple of holes that needed to be filled in before having a complete understanding of the thermodynamic and energy properties of the universe, explained in classical terms of the motion of particles.
This speech, together with other comments attributed to Kelvin (such as by physicist Albert Michelson in a 1894 speech) indicate that he strongly believed the main role of physics in that day was to just measure known quantities to a great degree of precision, out to many decimal places of accuracy.
What are the Clouds?:
The "clouds" to which Kelvin was referring were:
Why This Matters:
References to this speech have become somewhat popular for one very simple reason: Lord Kelvin was about as wrong as he could possibly have been. Instead of minor details that had to be worked out, Kelvin's two "clouds" instead represented fundamental limits to a classical approach to understanding the universe. Their resolution introduced whole new (and clearly unanticipated) realms of physics, known collectively as "modern physics."
The Cloud of Quantum Physics:
In fact, Max Planck solved the black body radiation problem in 1900. (Presumably after Kelvin gave his speech.) In doing so, he had to invoke the concept of limitations on the allowed energy of emitted light. This concept of a "light quanta" was seen as a simple mathematical trick at the time, necessary to resolve the problem, but it worked. Planck's approach precisely explained the experimental evidence resulting from heated objects in the black-body radiation problem.
However, in 1905, Einstein took the idea further and used the concept to also explain the photoelectric effect. Between these two solutions, it became clear that light seemed to exist as little packets (or quanta) of energy (or photons, as they would later come to be called).
Once it became clear that light existed in packets, physicists began to discover that all kinds of matter and energy existed in these packets, and the age of quantum physics began.
The Cloud of Relativity:
The other "cloud" that Kelvin mentioned was the failure of the Michelson-Morley experiments to discuss the luminous ether. This was the theoretical substance that physicists of the day believed permeated the universe, so that light could move as a wave. The Michelson-Morley experiments had been a rather ingenious set of experiments, based on the idea that light would move at different speeds through the ether depending on how the Earth was moving through it. They constructed a method to measure this difference ... but it hadn't worked. It appeared that the direction of light's motion had no bearing on the speed, which didn't fit with the idea of it moving through a substance like the ether.
Again, though, in 1905 Einstein came along and set the ball rolling on this one. He laid out the premise of special relativity, invoking a postulate that light always moved at a constant speed. As he developed the theory of relativity, it became clear that the concept of the luminous ether was no longer particularly helpful, so scientists discarded it.
References by Other Physicists:
In his book The Trouble with Physics, theoretical physicist Lee Smolin says the following about the speech:
William Thomson (Lord Kelvin), an influential British physicist, famously proclaimed that physics was over, except for two small clouds on the horizon. These "clouds" turned out to be the clues that led us to quantum theory and relativity theory.
Physicist Brian Greene also references the Kelvin speech in The Fabric of the Cosmos:
In 1900, Kelvin himself did note that "two clouds" were hovering on the horizon, one to do with properties of light's motion and the other with aspects of the radiation objects emit when heated, but there was a general feeling that these were mere details, which, no doubt, would soon be addressed.
Within a decade, everything changed. As anticipated, the two problems Kelvin had raised were promptly addressed, but they proved anything but minor. Each ignited a revolution, and each requires a fundamental rewriting of nature's laws.