algore

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.

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 It sounds like my view is out of date.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.

While you were transporting the cat, I suppose you had to feed her half as much food, and clean out her litterbox half as often, as usual? Leo32: A second step might be to influence the quantum state of the cat on one side such that the chances of it being found alive are much higher than they are in the original experiment, after the boxes have been separated. Some of the texts on entanglement make me think, and I'm not sure about this, that this increased chance of the cat being found alive is "transported" at a speed higher than that of light. In other words, the quantum state of the remote cat would be changed immediately together with the manipulated quantum state of the local cat. - Evidently that's not possible. Suppose your fellow researchers transported 100 cats as you propose, then you "manipulated" the ones left behind so their probability of living became (let's say) 99%. Then your fellow researchers (who might be very far away, such that light would take a long time to travel there) immediately open the 100 transported boxes and find a huge preponderance of dead ones - they would know, with a very high probability, what you had done. OTOH suppose you manipulated your stationary cats to be 99% dead; when they open the boxes they find 99 live ones, and again they can tell what you did. So we could represent a "1" by lots of deaders, and a "0" by lots of live ones, and thus transfer binary information faster than light (with a high probability). That's not allowed: info can't be communicated faster than light. So we know one of the steps in your proposal is not possible, without even needing to figure out which one.

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"?

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.

Swansont, I didn't say that matter doesn't have both wave and particle properties. In fact I explained exactly how it works: Schroedinger's eqn describes the probability wave, while observation collapses it so that the particle is seen. I even mentioned the 2-slit experiment. You can do this yourself at home using sunlight, exactly as Thomas Young first did it 200 years ago - it's very instructive and convincing. My point was, the way the particle-wave duality is presented to a layperson (like noz92) is often dogmatic. Simply "it's both a particle and a wave - believe it because I say so". The real, complete story is both more complicated and more interesting. I admit I could have made the point more clear; rereading my first parapgraph, it does sound like perhaps I'm denying this elementary fact of QM. However if you had read the rest of my post it's obvious that I understand the Copenhagen ontology. Unless you think there's something wrong with my explanation? If so, please tell me what it is. A couple more points: note that we actually have a full 200 years of experiments proving wave-particle duality, not just 100. And, I didn't say it hasn't been observed with atoms; in fact, you're right: it has. Woxor, at this time I neither believe nor disbelieve in dark matter. We definitely can't detect dark matter directly (ie, using any form of electromagnetic radiation). The evidence is all indirect, consisting entirely of certain gravitational anomalies. In various situations (expansion of the universe, gas leaving galaxies, etc) cosmological objects are receding more slowly than we expect. There are 3 possible reasons: 1) calculation of mass (of the universe, or of galaxies) is too low due to some error; 2) General Relativity equations are incorrect at these cosmological scales; or 3) there is some extra matter we can't detect which supplies the missing mass. The "dark matter" theory assumes #3; my personal best-guess is #2; nobody knows the right answer yet. We definitely can see (ie, via electromagnetic radiation) normal black objects, in three ways: reflected EM radiation, absorbed (or blocked) EM radiation, and black-body radiation. It's well established that "dark matter" can't be seen in any of these ways, which is why it remains such a puzzle. Have you ever heard of "zodiacal light"? Here's the story .. in 1845 Leverrier established that the perihelion of Mercury's orbit precesses 43 sec / 100 years more than Newton's equations predicted. At the time he said this apparently indicated that Newton could be wrong under these extreme conditions, which are so far from normal experience, and that "future researchers" would probably someday find tiny modifications to Newton that would explain the discrepancy. It took 70 years, but finally a guy named Einstein proved him right. In the meantime, however, other physicists, dogmatically holding to Newton, came up with a far-fetched explanation. They calculated that if there were some nebulous gasses between the Sun and Mercury, "zodiacal light", in just the right configuration, it would explain the precession anomaly without disproving Newton. True, they couldn't detect these nebulous gasses in any way .. now, we can see that they were dogmatic and wrong. I suspect today we're in an analogous situation, and "dark matter" is this generation's "zodiacal light". But of course I don't know - the resolution of this problem is left to future researchers. Swansont, I must say you've illustrated my larger point very well. A non-dogmatic scientist, after carefully reading my post, would calmly and rationally point out what he thought were my mistakes. OTOH a religious believer whose dogma is questioned would read a few sentences and dash off an impassioned reply. Which of these two do you sound like?

It's a good question noz92. A few decades ago it wouldn't have come up because back then physicists explained the whole picture .. today physics instruction has become pure dogma. "Particle is also a wave" "big bang universe was infinite in extent and also condensed into a point" "dark matter exists even though it's impossible to detect, just because we say so", etc. It's exactly like "God is a trinity, both 3 and 1" or "the Pope is infallible", or "6,301 angels can dance on the head of a pin" etc. You must have faith in your priest / physicist, who is the fount of all mystical wisdom. If you have any doubts, genuflect before a cross, or a picture of Stephen Hawking, and admit you're a miserable sinner Anyway, (now that I've gotten that off my chest) here's the answer to your question. You're right that if a baseball were literally, simply, a wave, you could tell. After a while, as you watched it, it would start to spread and get fuzzy round the edges. Obviously that's not so, and I'm sure Hawking didn't say precisely that. Instead, the position (and momentum, energy etc) of a particle is specified by two things: a <i>probability</i> wave (described by Schroedinger's equation) and the <i>collapse</i> of that wave function, which happens when the particle is observed or measured. (BTW no one knows precisely how that collapse happens). So, suppose you have an observed particle in an exact location (because it has just been observed), then you allow it to evolve without observation. Its position starts to become uncertain as the probability wave function starts to spread out according to Schroedinger. If you could see it (which you can't) it would look just like any wave you're familiar with. After a while the probability wave will spread out over an arbitrarily large area. At this point, conceptually, there is no particle per se, just a large area wherein the particle <i>might</i> be. Now, you observe or measure it (by, for instance, shining a light on it). At that instant the wave "collapses" - completely disappears (well, MWI says it continues to exist in "infinite parallel universes" but let's not go there, requires too much faith ) - and the actual particle is seen to be somewhere within its spread. According to QM there is absolutely no way to know where it will be, but it's more probable to be found where the wave function was "higher" (again, see Schroedinger's equation for the details). To clarify, consider the famous 2-slit experiment. (If you're not familiar with it look it up on the net). We fire a particle (from, for instance, an electron gun like the one in a traditional TV set) at a barrier containing two slits. On the other side is a screen (like the face of the TV's cathode-ray tube) which "observes" (records) where the particle hits. We do this again and again and see a pattern build up on the screen from the successive hits (which remain marked on the screen by a little dot). Until it hits the screen the "particle" has traveled as a spread-out wave function, so (just like a water wave) it passed through both slits, and these two paths interfered with each other on the other side. So instead of seeing the image of two slits on the screen, opposite the two slits in the barrier, as would have happened if the particle were just simply a particle, we get an interference pattern on the other side. So you see it's not as simple as "the particle is a wave". Rather, the particle's position is determined by a probability wave function, which we can never directly observe. All we can ever observe is an actual particle, solid and distinct, after the collapse of the wave. Why do you never see anything like this happen with a baseball? According to the most sensible "quantum ontology", it's continually being observed, so its wave function is continually being collapsed. That may be because you're constantly looking at it, or perhaps the wave function is spontaneously collapsed by something like gravity (according to Penrose) or whatever - but the point is that with large objects it's just about impossible to let the wave evolve long enough to detect its effects. However it's easy enough to do it with small things like photons (eg, the diffraction fringe that happens to light going around a sharp corner, which was known in Newton's time). With very careful experiments we've observed these effects with objects as large as alpha and beta rays. Hope that helps.

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?"

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?

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

Thanks swansont .. Yes, the binary pulsar data is significant, but are you sure it indicates that the "the results are consistent with the speed of propagation being c with a high degree of precision"? I had thought it only showed the likely existence of gravitational radiation, which would occur at any speed less than infinite; that's what was said in early reports, back in the late 70's. Perhaps the greater accuracy of the data obtained by continued observations has allowed the determination that it must be c. (Note that even Newton was dubious about gravity acting "instantaneously", so I've been using "instantaneous" as short-hand for "much faster than c".) But if you're right, why did Fomalont and Kopeikin say "We became the first two people to know the speed of gravity" in New Scientist? And remember the many observed gravitational anomalies leading some physicists to postulate a "fifth force", cosmological constant, or similar. Most recent is the so-called Pioneer/Voyager anomaly, which is even more interesting than previous ones in being very short-range. Don't these oddities raise a doubt in your mind about such delicate observations as the tiny anomalies in distant neutron stars? Oh well, I'm just picking at nits - seems I lose this argument Nevertheless let me briefly review the previous GR evidence to show it doesn't determine gravity speed. Gravitational redshift: these observations have nothing to do with speed of gravity propagation, only the increase in potential at the nearer point of observation which causes the frequency "clock" to run slower. Note that the redshift could be computed simply by the difference in Newtonian potential energy (hbar omega / c^2) (GM/r2 - GM/r1) where omega is the frequency (assuming like Newton it's unchanged) and r1, r2 the radial distances from the center of mass of the two observations. If Newton had guessed photons existed, and their frequencies would change according to E = hbar omega, he could have computed the GR redshift result to the first order - which I think is still accurate enough (the higher order effects would become significant only very near Schwarzschild radius). Admittedly I'm not up on recent results observing redshift coming out of very strong fields such as white dwarfs. Perihelion precession (and geodetic precession, gravitomagnetic precession): Mercury, being slow and in a weak, static gravitational field, would show virtually the same orbital precession no matter what gravity speed is. That was also true of the binary neutron star precession as of 1980, and probably is still true. Bending of light rays near massive objects: doesn't it seem obvious that given the extremely short distance between the ray and the object that the speed of gravity difference would be far too subtle to detect? That was always assumed, until recently. Yet Fomalont and Kopeikin, examining bending of distant light past Jupiter, claim they can tell the difference between different speeds of propagation. Sounds fishy .. Shapiro time delay of radio signals: measured most recently and accurately by GPS .. same considerations mentioned above apply. As far as I know, until F & K no one dreamed that such effects could be affected by gravity propagation speed, since they depend on being very near a more-or-less stationary massive object. And so on .. but to avoid constantly repeating "unless things have changed since 1980" I guess I'll stop here Thanks for the reference to questions about F&K's result - it really does sound flawed. fuhrerkeebs take note - gullibility might have its disadvantages! Finally, to JHAC, Crash and others: please check out what I said above. You can't use theoretical predictions to prove experimental observations - it's the other way around. Once the observation is made, it proves (well, "strongly supports") the theory. Your arguments go something like this: 1. GR depends on a number of assumptions or principles, one of which is "gravity acts at c". 2. All the other principles have been proven by actual experiments on nature (the ultimate arbiter) therefore we trust GR to a high level. 3. Since we trust GR, <i>all</i> its assumptions must be correct, even those not yet observed. 4. Therefore gravity acts at c. I hope you'll agree this "logic" isn't satisfactory.

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.

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!

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.

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.

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 ..

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!

Well, yes, but there had always been the little issue of experimental proof (finally resolved).

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 .. ?

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!

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!

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!

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?