Cheers,

-cvj

(#3 skirts very close to the usual misunderstanding of Heisenberg, but I guess it’s still legit.)

The answer to #1 could be “all or several of the above”, right? I mean, sure, most of the radiation is infrared but it’s probably some sort of continuous spectrum. If it’s an ideal blackbody, then all frequencies are emitted to some degree.

For #3, the most obvious answer is (b) but you could probably come up with situations under which (c) and (d) are correct as well if you squint hard enough. I suppose it depends on how you define, say, the velocity operator in the theory you’re considering (which is a tricky issue in itself), and what definition of mass you use. They just have to be noncommuting. (…unless *Heisenberg’s* uncertainty principle is specifically the p/x one, I suppose.)

And, yes, I had the same objection several other posters did to #6, specifically because I’ve participated in a million frustrating Usenet arguments with Tom van Flandern about the speed of gravity in which the role of conservation conditions in general relativity turned out to be very important to the question. If it had only asked “if the sun stopped shining…” it would be much easier to answer. Though, come to think of it, you could still have lots of fun arguing about what “right now” means in this context.

To find the answer, use google to search for images of rainbows. If the background sky is bright you can’t see the effect, but if the rainbow is bright and the background is dark, the effect is quite striking, I think. I’ve also seen this first hand, which is why started thinking about it. What is going on? (I think I know, but I haven’t seen it described anywhere.)

Fermat’s principle assures that the angles given by Snell’s law always reflect light’s quickest path between P and Q.

????

You might enjoy watching MIT professor Walter Lewin lecture on the rainbow. He explains what’s going on.

Tom

When you look at a rainbow you see the arcs of color, often against a dark backdrop of clouds. You also see the grayish mist of the falling rain. Where does the mist appear brighter?

a) inside the rainbow
b) outside the rainbow
c) the brightness is the same inside and outside
d) it varies

To find the answer, use google to search for images of rainbows. If the background sky is bright you can’t see the effect, but if the rainbow is bright and the background is dark, the effect is quite striking, I think. I’ve also seen this first hand, which is why started thinking about it. What is going on? (I think I know, but I haven’t seen it described anywhere.)

Gavin

But there are different answers one could plausibly defend, and that’s okay. It’s not about getting a grade, it’s about understanding the unity of disparate natural phenomena.

Which of these is not an example of the same underlying physical phenomenon?

a) heat from a radiator
b) music from a violin
c) radio waves from a broadcast tower
d) light from an incandescent bulb

my answer is b) music.

the others are all examples of electomagnetic waves: radio waves, visible light, infra red (radiators really heat rooms by convection, but the radiator will lose some heat in the form of infra red radiation, no?).

–Q

I’m hoping it’s fairly obvious that the primary difference between (b) “music from a violin” and the other choices is that the medium of propagation for sound (compression of the atmosphere, to put it simply) is different than for the other choices (wave propagation of electromagnetic). In space, no one can hear you play Vivaldi.

There is no physical principle that I know of, categorizing certain kinds of SOUNDS as music and others as mere noise.

I’ll make a stab at answering your quiz: my choice is (b) music from a violin. The key word as I see it, is *music*. Now if you had used the word “noise” instead, I would not have selected it. There is no physical principle that I know of, categorizing certain kinds of noise as music.

Even if you take the string theorists viewpoint that the energy may “leak” away into a brane instead of actually disappearing I think I’m correct in saying that you still need to ensure that energy is conserved regardless.

While some might of thought it “dreamy,” there is a direct physics correlation to that leaking in the collider. Although it is encompassed, like you said.

So where did it go, and how is “it” encompassed?

I don’t know. GR is my area of quasi-expertise so I’d feel nervous about commenting on theories outside that. There are two important points to note however. Firstly, regardless of how many dimensions a theory requires one would assume that it must still obey the usual sanity requirements associated with “ordinary” theories. The most important of these is that the energy of a system must be conserved in some sense. I’m unable to see how going to extra dimensions would allow one to dispense with energy conservation. Even if you take the string theorists viewpoint that the energy may “leak” away into a brane instead of actually disappearing I think I’m correct in saying that you still need to ensure that energy is conserved regardless. Presumably, (n->oo)-dimensional models should still contain some conservation laws that prohibit such things occurring.

Secondly, show me a working theory of gravity coupled to matter fields in infinite dimensions.

Couldn’t the Sun theoretically vanish in a theory with infinite extra dimensions?