Compared with other sections, this part of the essay gives a more personal take on the Planck quantities.
For people who like thinking in pictures I've included mental images of ways the Planck quantities arise (and participate in our experience.) For people who prefer the spoken word to symbolic notation I've tried to translate any formulas into plain English, or at least to favor the vocal version.
In this part I've used some intuitive nicknames for the Planck quantities. People differ in their tolerance for repetition, and when working with Planck quantities one reads and hears the name "Planck" a lot. Some people probably appreciate the repetition but I think it's relaxing to have the option of introducing variety. In this essay, which is a personal view of the subject, I refer for instance to the intrinsic frequency of the universe, the Planck frequency, as "core" frequency. The Planck temperature, the temperature of the universe at the beginning, I call "Primal" temperature, and the tiny Planck length, which is nature's length unit, I call a "stitch" because I think of it as a tiny stitch in the fabric of space-time. If you find that the nicknames put you off, there are other essays at this site using conventional vocabulary.
It will make speaking easier if we use suffixes like "-th" in a consistent way to keep biggish numbers like ten-to-seven (one followed by seven zeros) distinct from small fractions like the ten-to-seventh part (the reciprocal--one over the large number.) What I'm calling a ten-to-seventh is the small number which is reciprocal to ten-to-seven.
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Twelve powers of ten, on the frequency scale, separate the human voice from sunlight. The light in the street and the sound of a voice are local features, special to us and our star—I want to connect them to a pervasive and universal frequency: intrinsic to this space-time we live in, its voice, or if you think of frequency that way, its inner color.
The universe has a core frequency which is ten-to-forty times that of middle D on the piano. Even though my pitch sense is far from perfect I can usually produce a note near middle D, and the note is at the mid-point of the piano keyboard so it is really easy to find. It's also the note sounded by a violin's D string. The reason I can usually sing a note near middle D is that it is around the top of the bass vocal range. The same note is near the bottom of a soprano's range—it's one of the few notes which she and I can sing in unison. Middle D gives us a handle on the universe's core frequency.
One morning last fall, when the sunlight was especially beautiful, I happened to meet a retired physics professor buying lettuce at the produce store. The fact that the man invariably reminds me of a large rabbit only made our encounter there seem more appropriate. I asked him to compare the average frequency of the light in the street with the natural universal standard. He understood what I meant, his name for the standard is "Planck frequency", and he came up with an estimate — the sunlight average as a small fraction (which he guessed at) of the universal frequency.
His estimate was off by a few factors of ten — he was a particle theorist — but this didn't seem to concern either of us. The light in the street was actually a ten-to-twentyeighth part, on average. What mattered more, in my view at least, was his readiness to relate something here at the lettuce store which was special to our star—essentially the color of its light—to something universal: a frequency that creatures living around some other star might know, whatever the color of the light in their streets.
In case you are interested in what reference frequency I'm using for middle D, it's 1855 radians a second. A radian is 1/2pi of a full cycle. I'm use angular (radian) format in discussing frequency.
The Planck, or core, frequency is what gives us our natural time scale. The Planck unit time, which I'll call an instant, is the reciprocal of core frequency: the time for one even to occur at core rate. An instant is a tick of the core clock.
A question you might ask at this point is where does the natural frequency standard come from? How does it arise from light and gravity—universal things in everyday experience that we know about—and what makes core the frequency it is (ten-to-forty times the middle D on the piano) instead of something else? That question is addressed three section further down the page under the heading "How the Scales Are Interconnected."
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In the prevailing picture of the world's beginning — an explosive flash — core was the typical frequency for a quantum of light. At that first instant of time, in the prevailing model, the intitial temperature of the flash was a temperature I'm going to call Primal.
Nothing has been that hot since then. Primal (another name for the Planck temperature) is a kind of melting point for geometry and nature as we know them. No model exists for what conditions at a higher temperature could be like, so Primal serves as a de facto temperature maximum as well as the initial temperature of the universe.
The temperature scale closely parallels that of frequency. Every temperature has a specific keynote frequency one can think of as giving a handle on the color things glow when they're at that temperature. (In college physics courses, the expression for the keynote frequency is "kay-Tee over haitch-bar".) The word "color" is a bit misleading since a temperature's characteristic radiance isn't always some visible color. Nevertheless I think of that keynote frequency as a characteristic of the temperature analogous to the temperature's color. And so do other people: astronomers and physicists talk about finding the "color temperature" of something when they mean analyzing the (possibly invisible) light from it, in effect to determine the keynote frequency in the light.
Primal is the temperature which has core frequency as its keynote — and the scales are proportional: Any fraction of Primal has that same fraction of core as its characteristic keynote frequency. Take the temperature at the center of the sun for instance. Sun central is a ten-to-twentyfifth of Primal and accordingly the characteristic frequency of the light deep in the sun's midst is a ten-to-twentyfifth of core.
You could say that the Primal temperature arises from core and that they provide natural scales of temperature and frequency which are in accord. This illustrates a central theme in this essay. I'm describing natural quantities providing scales of every physical type, which arise from and are compatible with each other. Ultimately all link back to the speed of light. But Primal also provides the basis for a practical temperature scale. If we divide Primal up into ten-to-thirtytwo little steps (we can call them degrees) then our degrees turn out to be roughly the same size as the metric system's kelvins. Ours are some forty percent larger than kelvins so where a metric-speaker would say that ice melts a "273 kelvin" we would say it melts at 193 degrees. Both scales are absolute in the sense that they begin at the real zero.
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In this essay I won't use a nickname for the Planck energy. Planck unit energy was a typical energy for an archaic photon with core frequency in the original flash. Light energy, which in the Big Bang typically came in Planck-energy-sized bundles, has subsequently been divided up into smaller and smaller bundles. This dividing up of radiant energy into smaller packages accompanies cooling.
The primordial unit of energy fits comfortably with other universal amounts. A photon of light with any fraction of core as its frequency delivers that same fraction of Planck energy. To continue with the earlier example, in the energy-producing midst of the sun, where the temperature is a ten-to-twentyfifth part of Primal, a typical photon of light has a ten-to-twentyfifth of core as its frequency and therefore the energy it carries is a ten-to-twentyfifth of Planck. Like the other natural scales, those of frequency and energy are parallel and proportional.
There is more to this comfortable fit: full power, the natural reference quantity of power, simply consists of Planck units of energy arriving at core rate: in other words with oftenness equal to core frequency. Full power is Planck units dished out one per instant. In the informal language of this essay an instant is what the Planck unit time is called: the tiny duration which is reciprocal to core frequency — time it takes one event to occur when they are happening at core rate. In the case of a core vibration, an instant is the time of passage through one radian of phase.
The square of core frequency is an interesting quantity because it describes the rate vibration is delivered by a lightbeam with full power. Imagine Planck energy photons (typical of the Big Bang's primordial light, each one vibrating with core frequency) arriving at core rate. That beam of light would be delivering full power, namely Planck units of energy arriving at core rate. On the other hand it would also be a rush of vibration described by the square of core frequency — quanta of unit frequency arriving at unit rate. Planck's constant is among other things the universal ratio of power to square frequency which tells the power of any lightbeam having a given square frequency product of vibration and arrival rates. Core squared is the square frequency in this fixed relationship with full power.
Planck unit energy is just under two billion joules, if you like thinking in joules, and is enough energy to heave something weighing a ton 100 miles straight up. Quanta were very energetic back at the beginning. A ten-to-fifth part of Planck energy, enough to lift a ton one five-foot pace into the air, is equivalent to 4.7 food Calories.
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It's hardly an esoteric notion that the speed of light in emptiness serves as a universal top speed and affords a natural scale. The other scales, like the frequency-scale provided by core and the temperature-scale provided by Primal, can be seen as roughly analogous. Core and primal can be developed and introduced starting from top speed, in a sequence which goes by way of the units of force and power. The main force quantity is the one most immediately connected to topspeed. There was a discussion at the beginning of the Intuitive Planck Quantities essay of how the Planck force appears in gravity. Having units of speed and force immediately gives us the idea of full power — the power delivered by main force pushing at top speed. Full power then determines core frequency, or rather the square of core, in the way just suggested, which involved picturing a lightbeam with full power. This is how the chain from top to core goes. Once the speed of light and the force unit intrinsic in gravity are adopted as standards the rest of the units arise inevitably — they have to be what they are.
Once you have core as a scale of frequency you get the instant (Planck unit time) as its reciprocal, as was discussed earlier. Planck length is just the distance traveled at unit speed in unit time — the rest is routine. Time and length define unit acceleration and the mite-sized Planck mass is just that quantity of inertia requiring main force for it to achieve unit acceleration. In fact the Planck units are related among themselves pretty much as are the units in other systems.
Planck units for electrical quantities come about when the fundamental constant called the elementary charge is adjoined to the set, in effect making the electron (or its positive counterpart) the unit charge.
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Many of the natural reference quantities are so extreme that the scales they determine seem impractical for everyday use. However the natural speed scale is used continually in our daily lives because it is an intrinsic part of the way many instruments detect speed. These instruments, Doppler devices, actually measure fractional changes in the frequency of some signal. The fractional part (or "percentage") by which a frequency has shifted during passage is then interpreted as telling how fast something is moving as a fraction of the signal's speed. Fractional change has the nice feature of being a plain, unit-free number. It is dimensionless and absolute—a one percent increase in anything is always a change of one part per hundred regardless of which units might be used to measure the quantity and/or the change. If you get a speeding ticket the chances are someone has, in effect, measured your speed in Planck units. Practically speaking, since the speed of light is nearly the same in air as in vacuum, any time you land or take off in a passenger aircraft (and in many other ordinary circumstances) speed is measured on the Planck scale.
Besides being basic to much speed measurement on earth, the natural scale of speed pervades our fundamental perception of the universe. When astronomers look out into the night and measure the big picture's expansion, they use Doppler instruments to reckon the speeds of distant objects as fractions of the top speed, and base their inference about the beginning of time on these measurements of expansion.
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To recapitulate, besides the speed of light there are other universal natural reference quantities that anchor other physical scales. Besides top speed there is core frequency, full power, main force, Primal temperature, the elementary grain of charge, the mite-sized natural mass, the primordial Planck energy unit.
The others are linked to top speed and are in some way analogous to it—they arise from light and gravity, and they provide natural scales of their own. In particular top speed and main force are linked in a quartic force law that tells how the attractive force between two bodies is manifest in their orbital speed. The word that comes to mind is enmeshed: interwoven in the fabric of the world. Gravity's pull and the curves of things in orbit are a part of the geometry of the world, making the relation of speed and force especially intriguing.
If I were asked to speculate philosophically about the reasons for the intrinsic, ubiquitous character of natural units, what would I say? I might say that the units are rooted in four fundamental general observations about nature:
1. the boundedness of speed (c)
2. the bundledness of light (h-bar)
3. the granularity of electric charge (e)
4. the unvarying presence in gravity of the main force (c4/G)
The idea of a granular material is of one which comes in (at least approximately) equal-sized grains--sand, table salt, rice, granulated sugar. Electric charge is inherently granular. Light, on the other hand, would be better described as bundled. It comes packaged in variously sized bundles and, within each bundle, its energy, frequency and momentum are in accord. Any of the three quantities could serve as an index of the bundle's size. If a quantum of light in empty space carries 10-28 stem energy, then it must vibrate at 10-28 core frequency and it must have 10-28 of unit momentum.
It would be hard to appreciate the importance of top speed without recognizing the pervasive role played by the dimensionless or plain-number speed. This is the unit-free number v/c that measures speed by comparison with light — the fraction of top speed which an object travels. Relativity ordinarily treats speed in this fashion (the usual notation for the dimensionless speed is beta and almost every formula one encounters seems to contain a beta.) Plain-number speeds of approach and recession are what Doppler devices measure. In the case of speed, a number of practical and theoretical applications seem to compel the use of the Planck scale.
I don't want to speculate too much as to causes. For whatever reason the Planck quantities are increasingly recognized by the physics community as playing an essential role--far more so than when Planck himself introduced them before the Prussian Academy of Sciences in 1899.
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