units of measurement unimportant? not so!

Cecil's Columns/Staff Reports
21

There’s a few disconcerting statement in the E=mc2 article that really rub me the wrong way. I don’t know much physics, but I think these statements are misleading at best:

(1) “The speed of light of course is a very large number, so E=mc2 tells you mass contains an large amount of energy. The atomic bomb is testimony to that.”

Large number?? It can be a small a number as you like,
if eexpressed in the right unit. It’s really small if expressed in googol-KM per picosecond. it’s really big if
expressed in angstroms per Century. Neither figure tells you anything basic about the speed of light.

(1.5) “…The atomic bomb is testimony to that.”
An impressive blast, but it’s not a very good example
of mass to energy. Fission only converts a small
percent of the mass of the nucleus to energy.

(2) “In most of your daily, mundane interactions, mass is conserved, so when you add up all the forms of energy, you have an mc2 on each side of the equation and they cancel each other out.”

No, No, No. EVERY reaction follows the rule, even chemical
ones. So when you burn wood, the heat comes from a loss of mass. A very small loss, as chemical reactions are relatively weak mass to energy converters. But it’s still there. E = mc2 is universal, not jsut for nuclear reactions.

22

grg, I was actually going to raise some of those points myself, but I didn’t want to seem to seem too picky about it. You’re right, it’s not meaningful to refer to an amount as large or small if it has units attached. In fact, it would be more accurate to say that the speed of light is 1, and that our typical units for measuring spatial separation are much smaller than our typical units for temporal separation.
On your first and a half point, atomic bombs do, indeed, only convert a fraction of a percent of their mass to energy. This only reinforces what Karen is saying: Even a fraction of a percent of the mass of an atomic bomb still makes enough bang to flatten a city.
As for your second point, you’re technically correct, all reactions are a mass-energy conversion of a sort. What Karen was trying to get at is that such a small percentage of the mass gets converted that we can consider the mass, per se, to be constant, to a good approximation. The amount of energy (in the form of what we commonly call energy) that changes from one form to another, however, is significant. Therefore, for ordinary reactions, it’s reasonable to use two separate conservation laws for mass and energy.

23

I must admit I never learned that in physical science. I was taught that a simple chemical reaction does conserve mass, and that thermal energy produced is simply converted out of chemical potential energy.

Chronos and grg, are you saying that if you burn a piece of wood, you don’t conserve mass? Obviously the ashes weigh less than the wood, but adding in all the smoke results than less than the original hunk of wood? Does burning wood really convert mass to energy? Or does it merely convert chemical potential energy to Brownian motion?

I’m just wondering exactly how much of my science education I am supposed to forget…

24

In the context of chemical reactions, it’s easier to think of it as potetial energy being a form of mass. If you have a sealed container and a really sensitive scale, and you burn a piece of wood, say, in the sealed container, its weight will, in fact, decrease by a very slight amount-- theoretically, at least. I’m not sure that this has ever actually been tested… Anyone know?

25

The statements that grg has labeled “(1)” were inserted by the editor. Alas, they do cloud the point I was trying to make. Let’s cross out the word “number” and change it to something like “The speed of light is of course very large”. Since “large” is a relative term, the statement is hunky dorey.

Secondly, look at the particle physics interaction where a B meson (mass = 5,280 MeV) decays into two pions (mass = 140 MeV each). Lots of mass has vanished (but total energy is conserved.) My point was that most interactions are more like dropping balls from leaning towers and such. When you drop a ball you usually write your equation like this: mgh = mv^2/2, whereas you could write it like this: mgh + mc^2 = mv^2/2 + mc^2. Where mass is conserved, the mc^2 terms cancel, so you usually leave them out. But if mass is not conserved (like in particle physics) you have to include mc^2 along with kinetic and potential energy.

26

This is a nit-pick, and I apologize in advance to Chronos and everyone else who thinks “Well, duh.”, but I think this is too important a point to leave as is:

The sealed container will only weigh less if heat or light from the fire escapes. If the box is opaque and completely insulated, burning the piece of wood won’t affect the weight.

27

Actually, ZenBeam, I don’t think you’re nitpicking. I think you’re disagreeing with Chronos head on. I think he’s saying that potential energy not only has mass equivalence, but also has just plain old mass.

Correct me if I’m wrong, Chronos.

Here’s a test. Forget the burning wood. Let’s deal with four blocks. If gravitational potential energy has mass, the four blocks should weigh more stacked up than they do if they’re all sitting on the ground.

I’m not saying I believe this - I’m way too confused on the whole mass-energy conversion thing to believe anything outright. I’m just saying, that’s my reading of Chronos’ statement,

, and grg’s

That is, Chronos and grg are saying that conservation of mass is an approximation, and no more. They very idea makes my scales itch, but then I’m kind of itchy about a lot physics in the first place.

28

Right, ZenBeam, sorry I neglected that. If the energy from the burning wood stays in the box, the total mass stays the same.
Boris, excellent example with the stacked bricks. That’s actually one way of approaching General Relativity, saying that gravity is Newtonian, but including the gravitational potential energy itself as part of what’s gravitating.
As for conservation of mass being an approximation, conservation of energy is exact, and mass is one form of energy. It happens that in everyday situations, only a very small percentage of mass ever gets converted, so one can usually be pretty safe in saying that mass is conserved. If, however, you have a kilogram each of matter and antimatter, and you react them, the approximation fails big time-- You have 2 kg before, and zero kg after.

29

Sorry. I thought ZenBeam had read Chronos’ post wrong, and was talking about smoke escaping. Why Z.B. would have written “heat or light” if he meant “smoke”, well, I don’t know what I was thinking. Like I said, my brain itches. It looks like you two agree after all.

So, if I burn wood in a sealed container, and the temperature returns to normal after the fire has gone out, the container and contents will weigh slightly less afterwards. Anybody know how to get topical antihistamines into cerebral tissue?

30

Hello all brainbusters,

I’m the guy who originally posted the question “In e=mc2, what units of measurement was Einstein using?”.

Firstly, I’d like to thank Karen for taking the time to write me such a well considered and informative reply (I was very excited to have received a published reply from Straight Dope!) .

I fully understand Karen’s point that the equation exists independently of units of measurement, because it represents a fundamental relationship in nature which is true regardless of how we measure it, and units of measure are constructs of man. However, this explanation left me curiously unsatisfied and I felt that in general, my question was left unanswered.

As I thought about it, however, I realized it was the complete stupidity of the wording of my question which might have led the thing off in the wrong direction, because it was Arnold Winkelried’s first reply which came closest to giving me a satisfactory answer. He seemed to be able to intuit what I was really asking through the haze. I guess the basis of my curiosity was a much more mundane matter, and therefore my question, should have been:

“Putting theoretical physics and the actual meaning of the equation aside, in practical real world applications of the equation, what standard units of measurement are often plugged into those variables in order to get usable mass-to-energy yield figures? So for example, if I wanted to know how many joules could be released from a croquet ball (yes I know that’s dumb), what other 2 units of measurement could be used in the other variables to give a correct answer?”

Karen might argue that it doesn’t matter what units you use, because conversion factors can always be applied to jump from one unit to another. However, I can’t imagine that certain, related, standard units of measurement are not plugged into the variables in various practical applications for which the equation is useful, in order to give an answer that is intuitive and easily comprehended.

Thank you Karen! and Arnold! and all of you who contributed to this most interesting thread and took the time to try and answer my question.

NicholasD

31

For a croquet ball, you’d probably want to use kilograms, meters, seconds, and Joules (the energy unit for the mks system). I’m not sure what the mass of a croquet ball is, but let’s say .5 kg. Since c = 310[sup]8[/sup] m/s, the energy released by the annihilation of a croquet ball would then be 4.510[sup]16[/sup] J. Of course, you could, if you really wanted, measure the mass in atomic mass units, and the speed of light in cubits per U238 half-life, and you’d still get a valid energy unit, but in practice, physicists usually use either the mks (meters, kilograms, seconds) or the cgs (centimeters, grams, seconds) system.

32

The league, stone, and fortnight measurement was good enough for me grandpap, and I ain’t about to change to one of these new-fangled systems.