Posted on 10/25/2004 1:46:25 AM PDT by accipter
CONSIDER a verbal description of the effect of gravity: drop a ball, and it will fall.
That is a true enough fact, but fuzzy in the way that frustrates scientists. How fast does the ball fall? Does it fall at constant rate, or accelerate? Would a heavier ball fall faster? More words, more sentences could provide details, swelling into an unwieldy yet still incomplete paragraph.
The wonder of mathematics is that it captures precisely in a few symbols what can only be described clumsily with many words. Those symbols, strung together in meaningful order, make equations - which in turn constitute the world's most concise and reliable body of knowledge. And so it is that physics offers a very simple equation for calculating the speed of a falling ball.
Readers of Physics World magazine recently were asked an interesting question: Which equations are the greatest?
Dr. Robert P. Crease, a professor of philosophy at the State University of New York at Stony Brook and a historian at Brookhaven National Laboratory, posed the question in his Critical Point column and received 120 responses, nominating 50 different equations. Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance. In general, Dr. Crease said, a great equation "reshapes perception of the universe."
(Excerpt) Read more at nytimes.com ...
No -- that one was more along the lines of relativity. Sorry for my sloppiness.
For example, let us let "A" be "the simultaneous occurence of two events." For observer 1, they may indeed be simultaneous; however, for observer 2, they may not be simultaneous.
Another measurement may be different but one ought not call that other measurement "A."
Actually, I think the Copenhagen interpretation says something along the lines of "Measurement A is what it is, partly because of the fact that I measured it." Essentially, what A is is in some sense dependent on the fact of my observing it. (See Schroedinger's Cat.)
Ah, yes -- but this is precisely what I'm talking about: here is a case where apparently "Beauty = Skank".
Physicists at that Copenhagen meeting simply agreed that by using waves to represent particles, or objects, that the wave function describing them exists in a superposition of states prior to some interaction. That's all. When you are using waves to represent objects, probabilities ensue, not certainties. The probabilities are still certainties and the fact that your representations fall short of what the objects actually are does not change, or effect what they are. THis pen is still what it is, regardless of what you know about it. If I give it to you to examine and you come back claiming it's a horse, it's still a pen.
The laws of nature are constant and existed before the big bang. The universe you see today does not directly manifest all the laws of nature. What can easily be seen of this universe is a subpart. "current theories speculate that the laws as we know them may have been "formed" as part of the Big Bang"
No one said that. WHat they do hold is that what you see is a result of the big bang. There is no generalization, or claim, that these laws were created. They are simply a manifestation of what is possible with the laws of nature.
" you're making all sorts of metaphysical assumptions about the nature of reality."
Nope, they're scientific and logical. No assumptions were made, except a = a.
Simultaneity is not a property of an event. It is a relationship of an observer to an event. What observer1 and observer2 measure is mutually computable to both.
..what A is is in some sense dependent on the fact of my observing it...
It would be more accurate to say that what is measured in some respects depend on what A is. The measurement isn't the object; it may be all you are entitled to know, however.
The Compton wavelength is a wavelength. that's why they call it a wavelength. It represents the wavelength of the energy contained in the rest mass.
lCompton = h*c/E.
Where E=moc2.
Or, lCompton = h/moc.
h is momentum/dim(length), or E/dim(time).
pearls placemarker.
Agreed, but note that in so-saying, you've placed a constraint on what constitutes a permissible "A".
The measurement isn't the object; it may be all you are entitled to know, however.
Perhaps -- but then again, in the Practical Applications section of the Schroedinger's Cat link, we see that light that is in a superposition of states can be "collapsed" to a definite state by an observer. In that case, "A is A" because the observer made it so.
Anyway.... I've had fun with this, but it's interfering with work, so I've gotta knock off now....
Is it the same pen now, as it was just a moment ago? No, it's not -- so what, precisely do you mean by "this pen?"
Particles do scatter off diffraction gratings exactly as though they were waves with the Compton wavelength.
Any particular pen, it doesn't matter.
" Is it the same pen now, as it was just a moment ago? No, it's not "
Pens are stable objects on the time scale of months.
Oh? Is that true at the quantum level? Are you saying that there is no change between now and 10 minutes ago, even at the macro level? Is it the "same" pen you bought months ago?
The point here is that you're stuck having to a priori define "this pen?" before you can understand what "A is A" means with respect to it.
No. The pen is what it is regardless of whether, or not you even exist. The pen exists and is what is is regarless.
Yes.
That would be the DeBroglie wavelength, I believe.
A = A
Right, that's the DeBroglie wavelength, which depends on the particle's kinetic E. The Compton wavelength depends on the particles rest mass only there can be no scattering of that wave, because it means the particle "came apart" and no longer exists with the same ID. It became other objects.
No. See, e.g., Quantum foam.
I think you're right. Consider my comment so changed. (And thus irrelevant to your point.)
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