Word Gems: Quantum Mechanics: Max Planck

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Quantum Mechanics

Max Planck inadvertently sets off the quantum revolution

Professor Jim Al-Khalili, The Mind-Bending Story Of Quantum Physics

In the latter 1800s, Germany was eager to enter the modern industrial age. It spent millions to acquire the patents for Edison’s light bulb.

While it was known that a bulb’s filament, charged with electricity, would glow, the underlying physics of how this actually worked was still a big question.

In 1887 the German government spent more millions to build a large technical research facility. Political power and international prestige were at stake.

Then in 1900, to superintend the research, Max Planck, a 42 year-old scientist, was hired.

why do hot objects glow

Planck set himself to discover why the color of the filament changes with the temperature. To put it more generally, why do hot objects glow in the predictable way that they do?

We take note that “visible light” is but a small fraction of the entire electromagnetic spectrum. From radio waves, on up to gamma-rays, these are all forms of light, all of these emit photons. However, the human eye is calibrated to perceive only the very narrow band called “visible light.” This means that homo sapiens, feeble as we are right now, are totally unaware of 99%+ of what is going on out there.

Featured here is the tiny sliver of the vast electromagnetic spectrum, what we call “visible light.” The changing colors of light represent ascending light frequencies: red light vibrates least vigorously and is relatively cool, on up the scale to violet which vibrates much faster and is much hotter. Note the colors of the four arrows: the red arrow, labeled “warm,” extends into the red and orange frequencies; the next arrow, marked as “hot,” is perceived by the human eye as orange because this light is a blending of red through yellow; the following arrow, “very hot,” comes to the eye as yellow light, as it combines red to green light; and the fourth arrow, seen to us as white light, which is why we speak of “white hot,” is really a union of all the colors.

the changing colors of a heated iron poker

For many years prior to 1900, German scientists had studied this issue. It had been determined that, as kilowatts increase, a charged object not only gets brighter but the color varies. Think of a hot iron poker. It begins to glow red but then changes to yellow and even white-hot.

light bulbs also exhibit this same sequence of color

It was observed that a charged light bulb also begins to glow with shades of red, then to orange, and on to yellow; and, with more charge, the bulb will get hotter and brighter - however, the change in color stops and remains in the yellow-white region.

the blackbody emission problem

As we study this area, we come across the term “blackbody” or “Planck’s blackbody” problem.

what is a “blackbody”

It is not a body colored black, as such, although it could be black. The concept of "blackness" in the term suggests an ability to absorb light; e.g., a dark shirt on a hot summer day will make you feel even warmer because it absorbs more light than it reflects.

The term "blackbody" was used in an 1860 scientific paper by German physicist Gustav Kirchhoff...

a perfect blackbody is a theoretical construct and does not exist in nature

In the article, Kirchhoff says that a perfect blackbody is a theoretical tool, something that he has "imagined." The perfect blackbody would completely capture all rays of light impinging upon it...

Such bodies are called “black” because none of the incident light would escape…

Any light emitted from the perfectly absorbing blackbody would come from the heating of the blackbody itself. In this case, the amount of light emitted, Kirchhoff said, would depend on the light-frequency that you see and the temperature of the blackbody.

As stated, there is no perfect blackbody, one that completely absorbs all light coming to it. The Sun might come closest to the ideal. Most blackbodies in physics absorb light, more or less, such as a red-hot poker or a glowing light bulb.

the bulb gets hotter and brighter, but why does the color stop changing

As the intensity of heat and brightness builds, why don’t we see blue and violet light? - each of which is “hotter” than yellow. There might be a tinge of these, but essentially they're absent. The changing color sequence abruptly halts in the yellow-white range. Why does the trend-line crash when it gets near ultra-violet?

This didn’t make sense to the scientists of the day, and it so perplexed them that, in exasperation, they gave it a dramatic name:

"the ultra-violet catastrophe"

This graph represents blackbody emission from the Sun. The “5880” is the Sun’s surface temperature in Celsius degrees. The bottom horizontal line is the wavelength of the light emitted, and the vertical graph-line to the far left signifies intensity. The bottom horizontal scale, from left to right, is 0 to 3. This means that the wavelengths on the far right are longest, and least potent: these would be radio waves, microwaves, and infrared. We see the sloping line, from right to left, trending upward, but beginning to rise precipitously at the horizontal “1” marker: notice all the space under the sloping line at this point. This means that much of what the Sun is sending us is the “infrared” wavelength, which we perceive as heat. The intensity of all this blackbody emission spikes and peaks near the middle of the “visible light” spectrum, all of which we perceive as “white light,” a combination of the various “visible light” frequencies. The peak also means, "the hotter an object, the more light it emits, the brighter it becomes." However, just before the trend-line might continue on, robustly, into the realm of ultra-violet, the entire system crashes: it’s “the ultra-violet catastrophe.”

This very similar graph represents blackbody emission from the old-style incandescent light bulb. The “2910” is the light bulb’s temperature in Celsius degrees. Notice all the space under the sloping line before it reaches “visible light.” This means that most of the blackbody emission from the old-style light bulbs constitutes lost energy. The old bulbs were very inefficient with close to 95% of the energy coming to us not in the form of visible light but only as heat – “more heat than light,” as the saying goes. The intensity, unlike with the Sun, peaks well before it reaches “visible light,” then free-falls through it, on its way, once again, to meet the “ultra-violet catastrophe.”

scientists expected to see a steadily rising slope

Max Planck, and a generation of German scientists before him, expected to see a blackbody emission graph-line progressively sloping upward; if not infinitely, then, at least, with a gradual leveling off. But why should the graph-line suddenly plunge into the “ultra-violet catastrophe”?

Max Planck is called the “father of modern physics,” or the “father of quantum mechanics” - but it was a reluctant paternity, and when the child was born, for more than ten years, he tried to give it back.

Planck was not able to solve this conundrum with conventional concepts. Light was a wave, and that was that - everybody “knew” this. It was holy doctrine of physics.

However, the concept of “light as wave” did not fit the blackbody-emission research data. What could Planck do? He thought he saw a possible solution, but this answer was heresy. Best not to go there. However, in utter frustration, he allowed himself to posit the unthinkable.

What if light were a particle? - Planck's "act of desperation"

When Planck says that “I knew” that this would be of “fundamental significance,” he means “this will be a real game-changer.”

When he says “I knew the formula,” he means “I’ve worked out the math, I can see what the answer is, but I don’t like it at all.”

And when he says “a theoretical interpretation” must be quickly sought, “no matter how high” the cost, he’s really saying, “If I’m right in all this, then we’re all in trouble, because physics as we’ve known it is done, and so we have to find a grace-saving interpretation to rescue classical Newtonianism from what, sadly, I’ve discovered.”

the genie wouldn’t return to the bottle

When Planck redid the math – now armed with a new formula that he invented – suddenly all the numbers magically lined up with the sloping line that crashed into the “ultra-violet catastrophe.” No more upward trendline smoothly going to the Moon: "That's not reality," said the math.

the literary moment of Quantum Mechanic's birth

An excerpt from Planck’s 1900 scientific paper:

This "most essential point" is that "E," or energy, light energy, is not smoothly continuous like a wave - at least not with these blackbody emissions - but, in fact, is "continuously divisible ... composed of ... equal parts," that is - light is quantized, light is made up of extremely tiny particles. These are "very definite" in nature, meaning, each is exactly like the next one, each carries the very same energy.

This unit-likeness, which Planck worked out mathematically, would later be named after him, the "Planck Constant."

However, such fanfare could not cloak his own misgivings that, truly, this was all scientific heresy: "This cannot be! Light is a wave, not a particle!" Unfortunately, for the Newtonian science community, the math could not be strong-armed into proclaiming what convention desired.

"the most revolutionary idea which ever has shaken physics"

Max Born (Nobel Prize for Quantum Mechanics in 1954) wrote about Planck:

"He was, by nature, a conservative mind; he had nothing of the revolutionary and was thoroughly skeptical about speculations. Yet his belief in the compelling force of logical reasoning from facts was so strong that he did not flinch from announcing the most revolutionary idea which ever has shaken physics."

a very brief look at the math

the famous Planck equation and constant

Planck's constant, an incredibly small number: 6.626 x 10^-34given to us in "joules per second."

A joule is a measure of energy. If given “per second,” it becomes a rate, energy transmitted per unit of time.

What does this mean? It means many things, but, essentially, though light, or energy, appears to issue as something smooth and unbroken, if we could see the inner structure, we would find a discrete, pixilated version of reality - a latticework of ultra-tiny packets of energy.

These individual energy-entities are so small, and so close together, that, to the human eye, it all seems of one piece, and therefore these tiny units must be incredibly small, indeed – but, just how small?

Planck’s Constant tells us how small - as small as a photon. That's really small, much smaller than the smallest atom.

Editor's note: However, a photon does not have "size" in the ordinary sense of the term. It has neither diameter nor "rest mass" but, as some say, is a conceptual means of energy transference. But let's save this discussion for another time.

Understanding that light is a particle began to solve some of the mystery of blackbody emission - but questions remained.

What was the cause of the “ultra-violet catastrophe”? Why did that trend-line crash? Planck and colleagues had no answer for this.

Four years later, a junior Swiss patent clerk, third class, would accomplish what the German empire, with its burgeoning coffers and a small army of white labcoats, failed to put right.

Studying physics in his spare time and even during breaks at his job, this young office-helper, quietly laboring alone in the laboratory of his own mind, would perceive the missing factor in the decades-old blackbody problem.

His name was Albert Einstein.

Editor's last word:

The historical documents featured herein are from the youtube series “Kathy Loves Physics And History.” Her articles are very informative and worth checking out.