Classical physicists thought they had physics pretty much sussed out by the late 1800s. Dynamics of classical systems – even including electromagnetism – was well understood in a wide range of contexts, but for just a few “tiny” niggling details. However, these were details which turned out, upon deeper investigation, to be huge gaping holes in our understanding which would necessitate entire new branches of physics and mathematics to be developed! Many practicing research scientists will recognize this situation – phenomena in nature that are interesting enough to study nowadays are likely to be subtler than we tend to guess at first glance.

Colour, as we see it, is related to the wavelength(s) of light that are reflected from objects in our field of view. Only red light is reflected from a red apple, for instance – not green or blue. One interesting question physicists from a century ago asked was: at a given temperature, how does electromagnetic radiation behave when interacting with a thermal system? A useful prototype of such a system is called a Blackbody, which is defined as something that is a perfect absorber (/emitter) of EM radiation and sits at a particular temperature T.

Physicists studying thermodynamics (which we introduced in Ep.6) discovered a very useful fact: that thermal systems have an average energy – per available independent mode of motion – that depends only on the temperature. This is quite a neat result and was dubbed the Equipartition Theorem. Today we recognize that polyatomic molecules have 3 types of independent modes of possible motions: translational (3 directions of linear motion), rotational (3)  and vibrational (the rest). What about photons? Those are different kinds of animals in principle, because (unlike atoms) photons have no rest mass. This makes their physics unique.

Photons behaving according to Maxwell’s equations of classical EM can have any energy that you can imagine in your mind. Putting together that Maxwellian knowledge with classic thermodynamics leads, unfortunately, to a very deeply puzzling conclusion. The puzzle can be appreciated even without math by focusing on the nub of the problem: photons in a box can exist in either the fundamental mode or any one of an infinite possible number of overtones! This is a lot like the multitude of different possible notes a musician can play on a stringed or wind instrument.

There is indeed an entire infinity’s worth of possible independent modes of motion for photons – their only constraint is that they behave like standing waves, because the EM waves aren’t allowed to leak outside the box into which we said we put this system in the first place. All we have to do to satisfy the constraint is ensure that an integer number of half-wavelengths fits into the box! And, because there is an infinite number of possible EM modes in a box, the average energy of blackbody radiation is, classically, infinite. This is called the Ultraviolet Catastrophe and is obviously in direct conflict with experiment. Our Sun, for instance, an approximate blackbody at a temperature of about 6000 Kelvin,  does not vaporize us into a puff of smoke!

So how does quantum physics address this problem? By recognizing that energy isn’t actually continuously variable, but in Nature it occurs in lumps known as quanta. A quantum or lump of EM radiation is known as a photon. Realizing that energy comes in quantized, discrete units, is enough to render the effective number of modes finite and make the sum in the average total energy well behaved. What’s even more impressive is that this single change in assumptions explains both blackbody radiation and much more besides. Along the way, we mention how hotter blackbodies radiate at shorter wavelengths. In other words, the hotter, the bluer.

To wrap up this first part of a two-part introduction to Quantum Mechanics, we talk about the Photoelectric Effect. This is a phenomenon that puzzled classical physicists of the day but was understood with an immense flash of clarity by Einstein. He recognized the reason why a UV light shone on a metal would produce an electric current, whereas longer-wavelength EM radiation would not produce any measurable current – regardless of the intensity with which it was aimed at the metal! That seemed very counterintuitive for a classical physicist.

Again, the only piece of physics really needed to explain this is the quantization idea. Not only do atomic energy levels for electrons come only in very specific energies, dictated by the Pauli Exclusion Principle for fermions and by quantum physics, but so do photon energies! Energy comes only in quantized packets or lumps. If your incoming photon doesn’t have a high enough frequency, it can’t clear the energetic hurdle required to kick an electron out to a higher energy level or even jump ship from the atom entirely (get ionized).

That’s why a current didn’t get generated when longer wavelength EM fields were used, as compared to the case with the UV light. Clearing only 90% of the height of the energy hurdle (for instance) just doesn’t cut the mustard. You don’t win an Olympic medal by beating your competitor 90% wholeheartedly. You either clear the bar for recognition, or you don’t. Same for photons kicking electrons out of metals. 

Here is the narrated slideshow (or just the audio) of my slides for Episode 7.

We kick off Episode 4 by describing how knowledge of Newton’s three laws of motion and Newton’s law of universal inverse-square gravitation aids astronomers in discovering planets orbiting other stars. The most important physics points in this story are (1) stellar recoil (like with a gun firing a bullet) and (2) blueshift/redshift, which is similar in some ways to the Doppler effect for sound, wherein frequencies are upshifted for sources approaching us but downshifted for sources moving away. This blue/redshift effect for light gets contributions from time dilation and from the motion of the source, and does not depend on any medium (EM waves travel just fine in vacuum). By focusing on spectral lines for emissions/absorption from gases like hydrogen, we show how astronomers deduce the planet/star mass ratio from observations of stellar radial velocity wobbles.

We then segue into a discussion of fundamental properties of photons. Photons are quanta of the EM field, i.e., indivisible packets of electromagnetic energy. We discuss how photon frequency f is related to photon energy E by the formula E=hf, where h is Planck’s constant. We display the entire EM spectrum of frequencies (or equivalently, wavelengths) – from gamma rays through X-rays and ultraviolet to the visible, infrared, microwave and radio bands.  We also explain the true relativistic relationship between energy, momentum, mass and the speed of light as we build up a conceptual outline of the ideas and thought processes that led Einstein to his famous theory of General Relativity. We emphasize how important Special Relativity was to the development of GR.

We also highlight the importance of Maxwell’s Equations, a beautiful synthesis of electromagnetic phenomena involving charges, currents, and electric and magnetic fields. We describe how Maxwell unified electricity and magnetism into one theoretical whole – an umbrella set of concepts that covers all electromagnetic phenomena. For art’s sake, we show off the equations.   We next emphasize the importance also of the Equivalence Principle, an idea that acceleration due to gravity is indistinguishable from acceleration from an on-board rocket. We finish our lead-up to GR with a description of Einstein’s new concept of spacetime, as a fabric warped by energy/momentum in a causal way, with gravitational disturbances moving at the speed of light. Particles just move the most natural way they can in this context, leading to curved paths like planetary orbits.

This sets the stage for our next episode (#5) developing the physics of black holes.  I hope you enjoy, and stay tuned!

Here is a PDF file of all my slides from Episode 4.