# algore

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1. ## About the discovery of v^2 = u^2+2as...

Galileo was the first person to solve those equations. Look up his "Discourses Concerning Two New Sciences", written in 1636. First he finds the average speed ((v+u)/2) then finds v^2 = 2as (supposing u=0, starting from rest). It's all done geometrically; this was before they invented modern algebraic methods. You may find the geometric reasoning helps make the physics behind the equations more intuitive. One reason for eliminating t from the equation was that his method of measuring time was very crude (water clock) so he could get more accurate answers using distance (rulers are much more accurate and convenient than water clocks). The main reason for these investigations was simple curiosity, but more specifically, they wanted to know how hard weights would hit, when dropped from a height, to help design weapons like catapults. I hope this answers your question.
2. ## Waves as Particles

What you say is very encouraging. It sounds like my view is out of date. I could defend the position that 2-3 decades ago (when I was still a theoretical mathematician, with a strong interest in physics) experimenters were looked down upon, but who cares? Apparently today they're finally getting the attention, respect and funding they deserve. I'll have to read up on LHC, about which I know nothing .. As for how much one person can or can't understand, if a young John von Neumann (or Leonardo da Vinci, or etc) comes along, he might be able to shed new light on the subject. Witten is brilliant, but he's no von Neumann, as I'm sure he'd agree. Certainly around 1970 we would have laughed at the suggestion (although not every great mind is a prodigy). Anyway, it's definitely not worth arguing about.

4. ## Waves as Particles

Hi Severian, note that the divergence you describe between theorists and experimenters is a recipe for disaster. There's a crying need for more "generalists" who take an overall approach rather than specializing in narrow areas. I don't think it's impossible for "one person to follow it all". If a person of ordinary intelligence can master one branch of physics (ordinary in this context might be IQ around 140) then a real genius will be able to master the whole ball of wax (since an IQ like 200 is dozens of times more capable). The problem is that such people are steered into the most advanced theoretical maths, where they publish incredibly brilliant, elaborate and dense papers on incredibly picayune and physically meaningless topics. BTW this is just my opinion - no offense is meant to anyone - perhaps I'm wrong. I know what you mean about Hawking but I consider him less offensive than many other popularizers. His best characteristic is that he often throws in a caveat like "if GR is right, then" as in "assuming GR is correct, I was able to show there had to be a big bang", etc. Nobody else (like Davies, Weinberg etc) ever does this. Actually I've given up recommending any of these books to friends who want to understand what's going on - they're too misleading. From now on I'm going to tell them "why don't you just post your dumb question on SFN"?
5. ## Waves as Particles

swansont: "Sounds dogmatic" and "is dogmatic" aren't the same thing. - Agree. Similarly, "accidentally sounds rabidly iconoclastic when sounding off a bit" and "is rabidly iconoclastic" aren't the same thing either! swansont: As far as actual physics instruction, in which colleges or universities is the duality being presented without supporting evidence? - No one, I'm sure, instructs actual physics students about this duality without presenting the evidence. However laypersons are, I think, often instructed dogmatically. I took the trouble to look up the reference to Hawking's book originally mentioned by noz92. To my amazement, Hawking devotes 3 pages to it (pp 58-61 of the "Updated and Expanded 10th Anniversary Edition") without ever mentioning wave collapse! He even goes through the 2-slit experiment, but the whole presentation is just pure magic without this crucial information. No wonder noz92 was confused .. shows he's reading carefully. Meanwhile, on a subject like non-baryonic dark matter, I suspect that a dogmatic presentation is given even to advanced physics students, although it's been so long since I was in school I can't say. Can any physics students out there tell me: when your professors go through such topics as that, or wormholes or black hole photon orbits or etc, do they ever throw in this caveat: "BTW this depends on the accuracy of GR. If GR doesn't hold exactly at cosmological scales (where of course we have no experimental evidence) then all of this could be pure fantasy"? If not, I would say they're being dogmatic, just like the old proponents of "zodiacal light", ether, phlogiston, divine creation, the 4 humors, alchemy, and countless other failed theories which were dogma in their day.

8. ## How fast is gravity?

Maybe you're right philbo1965uk, but having examined van Flandern's arguments, I'm figuring that he's wrong (and every other physicist since Einstein is right): gravity propagates at light speed. Admittedly, it remains an open question .. so, what do you say is the most interesting thing about gravity? Is it, perhaps, the question "<i>why</i> does everything attract everything else?"
9. ## Where Does Space End? It Must End Somewhere!

Edisonian: "I have never really understood how space is supposed to never end." There are a lot of ways to approach this question; here's one which is compatible with both modern physics and common sense. First, suppose the universe has some definite age, say 15 billion years. (I'm not claiming that's the case, but it's plausible). Then the farthest we can possibly see is 15 billion light years. Hubble telescope is actually theoretically capable of seeing a very bright light source even farther out, for instance 30 billion LYs. Unfortunately there hasn't been enough time for that light to reach us; it will only have travelled half the necessary distance (ignoring, if you don't mind, universe expansion). So there could very well be something out that far, but we'll have to wait 15 billion years to see it. Personally I imagine space, complete with galaxies, goes even farther: 100 billion LY, a trillion LY, who knows? Perhaps after 100 billion LY (in some direction) our normal space stops and heaven begins, with God presiding over a choir of angels playing harps; or perhaps it's just a vacuum; or perhaps we're contained in something like a fish-bowl on a coffee table in the living room of incredibly huge lizard-like aliens; or perhaps space folds back on itself via some 4th dimension - there is absolutely no way of knowing, if you accept the speed of light and the age of the universe as limiting the scope of our knowledge to 15 billion LYs. Now, if the question of what exists 100 billion LY out is unknowable and essentially meaningless, from the current scientific point of view, then the question whether it goes on to infinity is even more so. ... Does that help?
10. ## How fast is gravity?

Thanks JHAQ, yes I see now how the binary pulsar example works. Turns out my old textbook (1980) mentions it also .. back then the data was more ambiguous but now it looks like it's been firmed up and is fairly definite. I found a reference from a "professional physics kook", Tom van Flandern, which does a great job of presenting some of the misgivings that have been rattling around in my head; he claims speed of gravity is >= 2*10^10 c. Makes a distinction between gravity radiation (which he admits the pulsar data confirms) and gravity waves, which he claims are unsubstantiated. Check it out, makes interesting reading: http://www.ldolphin.org/vanFlandern/gravityspeed.html Although I can understand his arguments I'm not in a position to evaluate them, much less defend them; give me a few months! Another interesting reference seems to really debunk the Fomalont-Kopeikin result. Looks like they're the <i>only</i> guys who defend it, with a bunch of reputable physicists against them. It's another "cold fusion" episode. See http://wugrav.wustl.edu/people/CMW/SpeedofGravity.html It's interesting that this same question was addressed 2 years ago right here on this forum! It's one of these "bad pennies" that keep turning up. I must say we've taken a much more thorough look at it this time. See http://www.scienceforums.net/forums/showthread.php?t=104

12. ## How fast is gravity?

Yes, swansont, GR <i>predicts</i> that that gravity acts at c but the underlying point of my question was that prediction is not proof. Proof must ultimately come from experiment (according to Sir Francis Bacon, who invented the scientific method, and also according to common sense). If you review the actual experiments which ratify GR, none of them depends on the speed of gravity - that is, until the recent one 2 years ago that you cite (which I stupidly had overlooked; I should have googled before posting). I'm pretty sure one could formulate an "alternate GR", allowing instantaneous gravity, which is compatible with all those experiments (but don't ask me to do it). Perhaps I should have made my underlying point explicit but I "cleverly" intended to let someone answer something like "GR predicts gravity acts at c" and then make the above argument. Now the focus shifts to the Formalont-Kopeikin experiment. Could you please give a link to the "criticism that the results weren't interpreted properly"? Perhaps this is still an open question after all. Just to clarify, I don't doubt that gravity really does act at light-speed; that's been pretty obvious for many years. I was just playing devil's advocate - legitimately, I think. Accepting "obvious", but experimentally unconfirmed "truths" has been the bane of science many times in the past few centuries.
13. ## How fast is gravity?

yourdadonapagos, there are two problems that I can see with your "proof" (I put the word in quotes out of respect for Kant . First, the restriction on speed of information is only a principle, or theory. You can't use a theory to prove an experimental fact; instead, it's the other way around. When I first asked this question, years ago, I argued (correctly) that gravity speed was still an open issue. Of course, as mentioned above, it turns out we now have experimental proof that it's limited to c (1.06 c, to be exact). This constitutes more (real) proof that the theory of limited informational speed is correct. However, suppose some new "fifth force" were discovered - then we can't just assume it's limited by c because an existing theory says it ought to be; instead we'll have to verify it experimentally, thus making the theory even more certain. I'm sure Kant would agree! Second, you have to show that even if gravity were instantaneous, we could use it to actually convey information. I won't go into that issue since it's become a moot point; if we ever get to a "fifth force" I'll be happy to revisit some of the complications involved. A related issue is quantum non-locality - at first glance it seems to violate the restriction on speed of information but detailed analysis shows that it doesn't. The point is that you have to do that detailed analysis to finish your attempted proof. Thanks again for your input .. and thanks also for yours, fuhrerkeebs. I can see you're a valuiable resource and will return in the future with some more dumb questions!
14. ## How fast is gravity?

Edward Duffy, thanks for your input .. I'd never heard of tensegrity and am not too inclined to study it, since it appears to contradict some pretty well-established facts. There are a lot of alternate theories out there which, if true, would turn modern physics upside down; some are much better supported than this one, and perhaps I'll discuss them on this forum another time. As I mentioned above modern physicists have gotten far ahead of actual experimental verification, leaving the field wide open to far-out speculations .. one of which might actually be correct. Many of the brightest physicists today have (in my opinion) "fallen in love" with their theories and therefore have closed their minds to these alternatives; that's unfortunate. Still, (if you want my advice) make sure you are familiar with the accepted facts before speculating; otherwise you invite ridicule.
15. ## How fast is gravity?

Agree. But remember what Mr. Holmes said: ""It is a capital mistake to theorize in advance of the facts." If you're sure the butler did it you might not notice that the wife had a blood-stained knife in her dresser drawer .. Admittedly the last century of physics wouldn't have happened if they'd taken his advice literally. But I think his underlying point is still valid: go ahead and explore theories, but don't fall in love with them.
16. ## How fast is gravity?

The math is so elegant, how could it be wrong? And since any proof (or disproof) will probably come long after we're dead, what's the harm in believing? If you want to publish these days, skepticism will only slow you down ..
17. ## How fast is gravity?

I'm sort of old fashioned - I don't believe the theory until the experiment backs it up. Makes it hard to take stuff like alternate worlds, multiple universes etc seriously!
18. ## How fast is gravity?

Well, yes, but there had always been the little issue of experimental proof (finally resolved).
19. ## How fast is gravity?

You're posting too fast for me, fuhrerkeebs! Above response was written without seeing your recent posts. Perhaps you see what I mean now. You can't set up GR equations for a vanishing sun because that's physically impossible (mass can't disappear without release of energy). That was the point of my "tricky" question. Unless I'm wrong about that .. ?
20. ## How fast is gravity?

Thanks fuhrerkeebs, loos like you're right. I have to admit the last time I posed this question was a few years ago and I had a lot of fun with it then .. because it's impossible to even set up the relevant equations since GR doesn't allow initial conditions which specify disappearance of mass without any release of energy. I forgot to check if there were any recent results. When you confidently said it was less than 1.06 c I googled it. I see there's been a new experiment involving the light of a quasar passing Jupiter .. very similar to what I was dreaming of back then. I should have checked before asking, sorry to have bothered you!
21. ## How fast is gravity?

Thanks for your response, Callipygous, and I'm sure you're right, but please indulge .. The second part of my question is not just an afterthought - can the relevant GR equations be solved? (Full disclosure - this is a slightly tricky question). Perhaps you have some other way to show that it would be instant (not using GR tensor equations). Can you please mention what it is? Thanks very much, Callipygous!
22. ## How fast is gravity?

Thanks for your response, yourdadonapogos, and I'm sure you're right, but please indulge .. First, I'm not thinking of an explosion. If the sun exploded, all the mass would still be there, presumably expanding at some rate far below c. The earth would continue to orbit the expanding mass with little change for quite a while, until it dispersed beyond our orbit (actually the explosion would blow the earth away by that time, but that's getting far off our topic). My question postulates that the sun literally vanishes - there's no mass at all left to orbit around. Obviously that's impossible; this is just a gedanken. Second, the second part of my question is not just an afterthought - can the relevant GR equations be solved? (Full disclosure - this is a slightly tricky question). Third, perhaps you have some other way to show that it would be 8 minutes (not using GR tensor equations). Can you please mention what it is? Thanks very much, yourdadonapogos!
23. ## How fast is gravity?

Suppose the sun were to suddenly vanish. The earth would of course go flying off on a (more-or-less) straight line, tangent to its orbit. My question is, would this happen instantly, or 8 minutes later (the time it takes for light to travel from sun to earth)? Can you justify your answer by solving GR equations?
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