Remember E = mc2? It’s the one equation that you are allowed to include in your popular-physics book (unless you’re George Gamow, who couldn’t be stopped). Mark gave a nice explanation of why it is true some time back, and I babbled about it some time before that. For a famous equation, it tends to be a bit misunderstood. A profitable way to think about it is to divide both sides by the speed of light squared, giving us m = E/c2, and take this as the definition of what we mean by mass. The mass of some object is just the energy it has in its rest frame — according to special relativity, the energy (not the mass!) will be larger if the object is moving with respect to us, so the mass of an object is essentially the energy intrinsic to its state, rather than that imparted by its motion. Energy is the primary concept, and mass is derived from it. Interestingly, the dark energy that makes up 70% of the energy of the universe doesn’t really have “mass” at all, since it’s not made up of objects (such as particles) that can have a rest frame — it’s a smooth field filling space.
All of which is to say that the mainstream media have let us down again. C. Clairborne Ray, writing in the New York Times, attempts to explain whether a spinning gyroscope weighs more than a stationary one, and answers “The weight stays the same; there is no known physical reason for any change.” Actually, there is! The spinning gyroscope has more energy than the non-spinning one. As a test, we can imagine extracting work from the spinning gyroscope — for example, by hooking it up to a generator — in ways that we couldn’t extract work from the stationary gyroscope. And since it has more energy, it has more mass. And the weight is just the acceleration due to gravity times the mass — so, as long as we weigh our spinning and non-spinning gyroscopes in the same gravitational field, the spinning one will indeed weigh more.
Admittedly, it’s a very tiny difference — the energy will increase by an amount proportional to the speed of the spinning gyroscope, divided by the speed of light, that quantity squared, which is really tiny. Nothing you’re going to measure at home. (I’m guessing it’s never even been measured in any laboratory, but I don’t know for sure.) And the article is correct to emphasize that there is no difference in mass that depends on the direction of spin of the gyroscope — that would violate Lorentz invariance, which is something worth looking for in its own right, but would be a Nobel-worthy discovery for anyone who found it.
I agree that no-one has ever done that experiment, because measuring such tiny differences is impractical using something as crude as a meter rule . Equally, no-one has ever demonstrated that the Moon is not made of cheese by seeing what Moon rock tastes like. After all, that’s certainly the direct way of doing it, and using mass spectrometers, chromatographs, etc, well that just leads to an indirect inference that the Moon doesn’t have at least a slightly cheesy flavor. Fortunately, it is in the nature of science that we accept such inference when the “direct” way of doing something is impractical.
In exploring some links related to this article, I was brought by the commodious vicus of internet recirculation to a series of articles on fusion energy technology. Turns out the science and the basic engineering were solved in October 2006 by a Navy R&D project led by now deceased scientist, Dr. Robert Bussard, former Asst. Director of the Atomic Energy Commission.
Although October 2006 marked the breakthrough, it also marked cancellation of the project by the Bush Administration, which needed the insignificant amount of further engineering development money for the Iraq War.
Here’s a link to a video of a talk about the project Dr. Bussard delivered to Google employees before he died.
Here’s a link to an interview he gave about the technology.
How about it, Cosmic Variance? An article on this would be great.
Mike, the kind of physical-chemical analysis done of Moon rocks is of course “direct” – it doesn’t require human taste buds, good grief. I’ve made my case to the extent that any fair observer would concede the issue. I think we have a case here of people just wanting to keep on pounding their original line out of misguided stubbornness, vanity, or whatever even after a good argument has been made against their perspective. This is as unhealthy as it is dismayingly commonplace.
“What we’ve got here is a failure to communicate!” – the Boss from Cool Hand Luke
PS – Of course you also forgot the theoretical basis for LC being good, but me just saying “We haven’t’ measured it directly” (and I keep saying, I don’t give a damn that we haven’t, I believe in it too but just want that admitted), versus the poor theoretical basis for saying the Moon is made of green cheese. So now are you going to argue with that too, just so you don’t have to ever concede to anyone?
I congratulate you on a rare moment of insightful introspection.
Heh – I said good argument, that’s what I was waiting to hear from anyone else. I’m not sure you’d know if it was rare for me to get that general point, whether intro- or extro- spection is the best spin on it.
hey Mike, maybe you should go and check for yourself if the moon is made of cheese. that would dissuade you of many things to believe in.
It’s a shame that neither you nor Neil actually read what I wrote. If you had, you would see that I likened the requirement that one “directly” measure Lorentz contraction (a thing most people believe to be true) using a meter rule (a completely impractical way to make such a measurement) to testing the hypothesis that the Moon is not made of cheese (a thing most people believe to be true) “directly” by tasting it (a completely impractical way to make such a measurement).
Personally, I am happy to accept the measurements of spectrometers, etc, as the more appropriate way to measure the composition of the Moon and hence show directly that it doesn’t taste of cheese, just as I am prepared to accept interferometric measurements of distance as the appropriate way to measure directly the very small effects of Lorentz contraction in the laboratory.
The fact that no-one has used a meter rule to do so may well be true, but it is entirely uninteresting as using a meter rule to measure such a distance is no more “direct” a measurement than using interferometry, just as the fact that no-one has actually tasted Moon rock may well be true, but is uninteresting because tasting Moon rock is no more “direct” a measure of its cheesiness than using a mass spectrometer.
Was that spelled out explicitly enough this time?
Well Mike et al, maybe we can gracefully wrap this one as follows: First, again, I was referring simply to whether Lorentz contraction had been “directly” measured in the strictest way as a matter of historical interest, not whether it needed to be to warrant our belief, whether practical or not, etc. Claims per se shouldn’t be harried over extraneous matters; such matters should be made as side points. As for whether interferometer measurements should count as “direct”: Sure, once we are assured of the Einstein postulate about light speed constancy. But as I said, the null result of the MM experiment could of course in principle have derived from Galilean behavior of light propagation. So, accepting interferometer results depends on “auxiliary assumptions”, warranted as they may be. It could be a matter of semantics in philosophy of science whether that can be called “direct,” maybe we can just say it’s a judgment call depending on how anal retentive one is.
In any case, here’s a quote from one of the top physicists in the field. He supports my position exactly and the situation hasn’t changed since then:
“It is an amazing fact that there does not seem to exist any direct or simple experimental verification of the Lorentz-Fitzgerald contraction. There is no reason whatever to doubt that the effect exists, precisely as called for by theory. So far, nevertheless, the difficulties – (1) of securing an object of appreciable length that moves with a speed comparable to that of light and, (2) of determining two events, one at either end, which are simultaneous for the observer – have proved insuperable. This very fundamental conclusion of the theory awaits actual proof.”
Albert Shadowitz, Special Relativity, 1968, p. 168 of Dover paperback.
The only problem with asking a famous physicist is that he is unlikely to have ever traveled anywhere sufficiently relativistically to be in with a shot of whipping his ruler out to measure Lorentz contraction. Surely, more productive to seek the views of a cosmic ray muon, whom you would never have met at all if he hadn’t just “directly” measured the Lorentz contraction of the Earth’s atmosphere as it flew past him.