energy

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Reality, calories, and joules, oh my!

I had a moment of idle curiosity this morning just before starting to write this.  I recalled the bit of trivia that the average human power output/consumption is something around 80 or 100 Watts.  I wasn’t sure which was more typical, but it doesn’t really matter; the numbers are well within the same order of magnitude, despite having nominally different numbers of digits.

Anyway, I decided to convert that into kilocalories* per day, just to confirm that the typically described numbers match up, because if they don’t, then something very strange is going on.

A Watt is a joule per second**, so to figure out how much energy output (in joules) there is in or from a human per day, you just multiply the watts times the number of seconds in a day (24 hours per day x 60 minutes per hour x 60 seconds per minute, or 86,400 seconds per day).  Multiply that by the above-noted wattage and you get between about 6 and 8 million joules per day.

Now, there are 4,184 joules per kilocalorie, so dividing that into the number of joules yields:  roughly between 1600 and 2000 kilocalories a day, which matches the data on basal metabolic rates.  Neat.

Of course, they must match up, otherwise there would clearly be some major logical inconsistencies in our understanding of such thermodynamicalish matters.  I don’t suspect that such a mismatch would have survived the scrutiny of scientists much longer than a snowball would last in a blast furnace; in other words, I consider textbook level physics to be pretty darn reliable.  Nevertheless, it is good occasionally to check even such basic things, just to confirm for yourself that your understanding of reality is internally consistent and consistent with that which is measured and described by other people.

This is not to say that I worry about whether my “reality” is significantly different than that of other people.  I don’t.  While I have no doubt that the specific details of my personal experience are unique, this is so only in rather trivial ways.

I’ve not encountered any occurrence or argument that made me doubt whether everyone around me is subject to the same laws of physics as those to which I am subject.  Of course, if tasked or merely bored, I can conceive of ways in which all that I think I know is illusory and/or delusional, as in the argument that precedes the cogito in Descartes’s most famous (non-mathematical) work.

With a bit of effort, one can almost always imagine ways in which the world could be deeply different than it seems.  I’ve been known to do that at length‒indeed, at book length‒myself.  But the fact that a thing can be imagined is not a reason, by itself, to promote a concept into “might actually be true” space.  Presumably, there are limitless such things that could be imagined, but almost by definition (at least as I am using the word) there is only one reality.

Reality, as far as I can see, cannot contradict itself; actual paradoxes cannot be instantiated.  I’d probably be prepared to bet my life on those propositions.  But even if reality could contradict itself, that would also be a fact about reality.  Whatever reality is, it is.

That’s trivial, of course, but sometimes it’s good to be reminded of the trivial things that one carries in one’s background knowledge but rarely considers or reconsiders‒things like the interchangeability of measures of energy and power and heat between different units.

With that full circle moment, I’m going to finish for today.  I’m still very tired, and I’m rather discouraged and despondent and probably other d-words as well.  This blog is all I really do, anymore, but my energy is lagging even for this.  At least I don’t need to do payroll today, since I had to get it done early yesterday…which fact I found out yesterday.

Oh, well.  Please do what you can to have a good day.  And remember, there is no do or do not.  There is only try.

*This is what we call “calories” when speaking of human energy intake and output, but a single “true” calorie is the amount of energy (heat) required to raise the temperature of 1 gram of water 1 degree centigrade (or, well, Kelvin if you want to be pedantish).  A kilocalorie, or what we commonly call a calorie, is enough to raise a kilogram of water 1 degree Kelvin.

**A joule being the unit of energy in “SI” units.  A joule (energy) is the integral of force with respect to distance, or a Newton-meter.  A Newton is the measure of force, and is a kilgram-meter/ second-squared.  So joules have the units kilogram-(meter squared)/second squared.  Watts (a measure of power, or energy per unit time) are joules per second, which fact gives us the fun, lovely phenomenon of having cubic seconds in the denominator of the equation!

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So What Is All This GeV Stuff, Anyway?

[This is a reprint of an article I wrote for my hubpage…but I want to focus here on my own page, now, so hopefully no one will be too upset by the re-use.]

Recent news about events at the Large Hadron Collider in Switzerland has brought particle physics more into the mainstream, as scientists have discussed hints that they’re getting closer to finding and defining the Higgs particle…the messenger particle of the Higgs field.

I’m not going to try to rehash the meaning and nature of the Higgs field here. Most of the articles I’ve looked at do at least a decent job with that subject. If you want an even better treatment–as well as a fantastic summary of the state of modern physics that is thorough but extremely understandable–I recommend getting a copy of “The Fabric of the Cosmos” by Brian Greene. He does a better job of explaining difficult subjects in easy-to-understand terms (that nevertheless don’t dumb down the material) than just about anyone else I’ve ever read.

No, what I’m going to talk about is a term that’s thrown around an awful lot in articles about particles: The GeV (and more generally, the eV). The term eV is shorthand for “electron volt,” and “GeV” is the notation for “giga-electron volt”…a billion electron volts, in other words (MeV, mega-electron volt would be a million electron volts).

But wait…the articles about the Higgs (and other writings about atom smashers) refer to measures such as 125GeV as being a measure of a particle’s mass! What does that have to do with volts!? Don’t volts have something to do with electricity? Isn’t household current measured in volts? Does that mean that it takes a Billion times as much voltage as in household current to find a Higgs particle?

Well…not exactly. In physics, the electron-volt is actually a measure of energy, not the voltage in a circuit. Specifically, it’s the amount of kinetic energy (the energy of motion) a free electron would accumulate after being accelerated through a potential difference of one volt. You see, voltage is to electrical fields a lot like what pressure is to water. Voltage differences push things that respond to electric fields…and electrons are one of the most well-known of things that respond to electrical fields, and have been since at least Benjamin Franklin’s time. In other words, falling through a “pressure” difference of one volt will accelerate an electron until it has a kinetic energy that is defined as one electron-volt.

So what the heck does the kinetic energy of an electron have to do with the mass of a Higgs particle? Well, as you probably know, energy can change its form, but it doesn’t disappear, and if need be can always be measured in the same units. At every day energy levels, physicists are more likely to use joules as a measure of energy…a joule is the amount of energy put out by something that has one watt of power in one second. So a one hundred watt bulb puts out 100 joules of energy every second.

Now, when you’re dealing with smaller scale things–like electrons and protons and Higgs particles (Oh my!)–it’s better to use a smaller unit of measure. The eV is a VERY small amount of energy, and can be excellent currency when describing what goes on in interactions between subatomic particles. Just as you wouldn’t use a brick of gold to try to buy a gumball out of the grocery store gum machine, but would instead use your pocket change, you don’t usually use joules in particle physics. You COULD, of course…but you’d be using REALLY small fractions of joules and it’s just easier to use the particle physics version of pocket-change, the electron-volt.

But still, what does this have to do with the mass of a particle? I’ve been talking about energy here!

Well, now we come to probably the most famous equation in all of physics, at least as far as the general public is concerned: E=mc2 (the two here means “squared”, or a number multiplied by itself). This equation explains that matter and energy are interchangeable. Matter and energy are just two forms of the same thing. So you can describe how much Stuff something is made of by describing it in ordinary terms of Mass (such as grams and kilograms), or, if you’re feeling like it and if it’s useful, you can describe it in terms of energy. Now, the “c” in that famous equation is the speed of light, which is mighty fast: about 300,000 kilometers a second (about 186,000 miles per second). It’s already a big number, but when you multiply it by itself, it’s MUCH BIGGER. So even a little mass converts into an awful lot of energy. That’s why nuclear reactions are so powerful: they convert a fraction of a percent of the matter involved in the reaction into energy, and you get all the glory of our sun and all the horror of nuclear weapons.

So finally we arrive at the reason for using eV’s and MeV’s and GeV’s in particle physics. It turns out that, like joules, working with ordinary mass units like grams gets very cumbersome when talking about really tiny things like subatomic particles. You have to use extremely small numbers with a lot of zeroes after the decimal point. If you’d rather not deal with all those zeroes, well, since matter and energy are interchangeable, you can instead describe very small masses in terms of a pretty fair number of a similarly small unit of energy. An electron-volt is just such a useful small unit.

In other words, when they say that the Higgs particle doesn’t look like it can be more than 125 GeV in mass, they mean that, if you took its mass and turned it into free energy, the amount of energy you’d get would not be more than 125 billion electron volts. That may sound like a lot, and on the scale of subatomic particles, it IS. However, it really is a very small amount of energy, and thus an exquisitely small amount of matter.

Of course, the Higgs fields is thought to permeate literally the ENTIRE universe, and the Higgs fields effects are all carried out by Higgs particles, so the mass equivalent of the field would add up to a pretty big amount in total. In fact, ALL the ordinary things with which we are familiar are made up of particles whose masses can be described in terms of electron volts, and most of those “weigh” a lot less than the Higgs appears to. So big things are made up of small things, just lots and lots of them. Like, lots and lots of electron volts of energy can equal the mass of one small but very important particle.