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Post by mrsonde on Feb 27, 2015 7:50:35 GMT 1
Trying to apply them to the physical world of space and time and the movement of masses certainly does - utter confusion and logical error, at least. Zeno's paradoxes all depend on this elementary mistake, delightful though they are (as are Cantor's discoveries about the mathematical concept of infinity - some infinities are larger or smaller than others, for example.)
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Post by Progenitor A on Feb 27, 2015 10:28:57 GMT 1
delightful though they are (as are Cantor's discoveries about the mathematical concept of infinity - some infinities are larger or smaller than others, for example.) Indeed I have always found that concept, impeccable as the logic may be, very amusing
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Post by mrsonde on Mar 2, 2015 7:50:10 GMT 1
You can even do things like dividing them, and get a non-zero answer, nickrr might like to note.
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Post by nickrr on Mar 8, 2015 15:36:30 GMT 1
Getting back to the original question raised in this thread, here's a link to a class by Alan Guth (one of the originators of inflationary theory) explaining inflation: www.worldscienceu.com/courses/master_class/master-class-alan-guthHe confirms the explanation I gave earlier in the thread but of course in more detail. He spends some time explaining why the concept of negative gravitational energy is required and why it's a fundamental concept not just in inflationary theory but in the Newtonian theory of gravity. No doubt mrsonde will let us know why he's just another second rate physicist who doesn't understand the basics of physics!
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Post by Progenitor A on Mar 8, 2015 19:49:01 GMT 1
Getting back to the original question raised in this thread, here's a link to a class by Alan Guth (one of the originators of inflationary theory) explaining inflation: www.worldscienceu.com/courses/master_class/master-class-alan-guthHe confirms the explanation I gave earlier in the thread but of course in more detail. He spends some time explaining why the concept of negative gravitational energy is required and why it's a fundamental concept not just in inflationary theory but in the Newtonian theory of gravity. No doubt mrsonde will let us know why he's just another second rate physicist who doesn't understand the basics of physics! All very well I am sure But surely your assertion that gravitational energy is equal and opposite to the Kinetic + Mass energy of the universe is confuted by Mr Guth's theory that at very high densities the gravitational energy is positive or attractive. This means that initially the universal force was outward (explosive) with no counteractive negative gravitational force; yet somehow, magically the negative gravitational force becomes equal to (repulsive gravitational energy + mass energy + kinetic energy); in other words a new energy pops us to make negative gravitational energy equal these (positive gravitational energy having disappeared). In other words how does positive gravitational energy transfer its energy to negative gravitational energy? The answer to this question might answer another big puzzle As the universe is expanding it is also accelerating. This means that the kinetic energy of the universe is increasing. But, the gravitational energy of the universe is weakening (or at best remaining constant)as the increasing energy masses separate in distance. In other words the universe is gaining energy. Where does this increased energy come from? God I suppose Odd how God looks up when we become puzzled!
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Post by mrsonde on Mar 9, 2015 11:55:03 GMT 1
I can't be bothered to listen to Guth's defence of his own theory, and certainly not as evidence for a concept that he invented to make that theory possible! That's called a circular argument. It is certainly not a fundamental concept in Newtonian gravity - not mentioned once, either in the maths (where a negative result is absolutely impossible), or in any expostulation of it.
Another mathematical physicist that doesn't understand that just because you can make mathematical terms work in a formula gives no evidence whatsoever that such terms tell you anything at all about what exists in the real world, or how that universe actually works. Guth's reputation as such a mathematical physicist rests entirely on inflation being valid. The only evidence that inflation is valid is that the maths works. Just as the only evidence that Hoyle's Solid State worked was that his and Chandrasakhar's maths were sound. It is a very regrettable development in Physics generally that this confusion between empirical evidence and the mathematical content of a theory has become so thoroughly embedded in the past century that many mathematical physicists - this covers nearly every "cosmologist" these days - have completely reversed the dependency. So much so, and so little educated in logic and philosphy are they, that many of them actually believe the universe is mathematical, so are not in the least surprised when their invented mathematical concepts work!
As Russell, one of the first thinkers to notice this alarming development, said in 1927: "Physics is mathematical, not because we know so much about the physical world, but because we know so little: it is only its mathematical properties that we can discover. For the rest, our knowledge is negative." This simple point has almost comletely been forgotten, not only in Physics but in science generally.
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Post by nickrr on Mar 15, 2015 18:25:35 GMT 1
At very high densities inflationary theory says that gravity becomes repulsive not attractive.
We have been talking about negative gravitational energy, not force. With these two misunderstandings (among others) your argument collapses. If you want to understand the basics of inflationary theory I again suggest that you watch the presentation. Even if you don't agree with it (and of course not every physicist does) you might be able to argue against it more coherently.
It does if the maths agrees with, or even better predicts, measurements in the real world. Virtually every physical theory is based almost entirely on maths. Theories like relativity and quantum mechanics, two of the most successful theories formulated by humans, rely for their validation entirely on the real world agreeing with the mathematical results. For quantum mechanics for instance we have no idea what the "real" world is like - we only have the maths. When Newton formulated his theory of gravity he had no idea how gravity worked - he just had a mathematical formula with which to calculate it's effects.
The Russell quote is absolutely correct but I'm not aware of any justification for your claim that it's been forgotten - unless, of course, you can supply some evidence? In particular, have you evidence that Alan Guth doesn't understand this or are you just making things up at random for the sake of your argument?
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Post by mrsonde on Mar 16, 2015 1:29:47 GMT 1
It says it can not that it does. It says so because at such a small scale quantum fluctuations allow for such a possibility. There is no explanatory mechanism leading to a "does". Similarly, there is no explanatory mechanism leading to any sort of predictive means by which after a certain distance or density gravity should become one or the other, repulsive or attractive, or anything else one might like to dream up.
This whole introduction of Guth's wild speculation has nothing to do with your original contention, which was based on a loose metaphorical identification by Hawking of gravitation and "negative energy". A negative gravitational force would presumably be a positive gravitational force, therefore - presumably, what we have, and what anyone anywhere has any empirical evidence for.
And this means what? How does it manifest itself? How are we possibly going to confirm the existence of such an "energy" - whether it's negative, or negative negative, or positive, or anything else?
No one agrees with Guth's theory any more, including Guth - it' moved on considerably. Those elaborations, by Schwarz and others, make no use of any notion like "nagtive gravitational energy", as far as I'm aware.
No, I'm afraid not. That's the crux of the mystery. Uranus and Neptune were discovered using mathematical formulae that we know do not describe the real world - in fact, you could have predicted them using Ptolemaic epicycles, if we'd had good enough observations. Similarly, the confirmation of Bohr's model of the atom worked with hydrogen, the first orbitals anyway, and this seemed at the time a great triumph - but as it turned out was entirely accidental.
That's your opinion.
No, I'm afraid not. There was a spectacular confirmation of GR with Eddington's eclipse expedition, granted: but that's highly unusual - virtually unique, I think. I can't think of any other comparable result, until Feynman's QED (which, again, we now know is not accurately descriptive of the real world.) As for quantum mechanics - it never gave mathematical predictions agreing with the real world. It did so probabilistically, of course, within a margin of error.
That's your opinion. To my mind, it's an incomprehensible one. I doubt if even you know what you mean by it. As far as I'm concerned, all such gibberish means is that physicists do not have a firm understanding of what their maths means. I've never come across anyone who denies this, other than you.
Exactly. Just as now. The only difference is that philosophically we now understand this - or should do.
You've just given one, Nick. Your view is not at all unusual, I think. Neither is Russell - or me - the only one to point it out. After the enormous furore following the publication of Guth's theory, many empirically minded physicists pointed out exactly the same thing. I'll give you a long list of quotes from them if you doubt it. Nothing's changed since the 70s, other than those empirically-minded physicists have become more and more marginalised.
Guth doesn't understand the primacy of empricial observation? I don't know, to be honest. I think the issue, as has the whole field of Physics, has become almost impossibly blurred. I watched a Horizon the other night saying that Guth has been confirmed by such an observation, though of course nothing of the sort had happened at all - just as the discovery of Neptune wasn't a confirmation of Newton. These are very complicated matters. From what I've read of Guth he doesn't understand it, no. Maybe I'm wrong about that - he seems a very personable chap, but it would be good if he stressed the necessary humility of his position, as Einstein was always intelligent enough to do. But it seems possible to me that you can no longer progress in his field (and this wasn't his field, to begin with) if you do.
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Post by fascinating on Mar 16, 2015 8:38:32 GMT 1
I am reading the book now, so could you point where it is not accurately descriptive?
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Post by mrsonde on Mar 17, 2015 16:33:02 GMT 1
All of it, is the point. Mathematically it's remarkably accurate of course - but this is not to mean that conceptually it's descriptive: (Russell's quote needs to be expanded, so that it is not merely the real world's mathematical properties that we can discover, but actually those properties are often not in the real world at all, but are rather the properties of the overlaying grid that we have veiled it with.) QED is not as accurate as Newtonian mechanics, despite the hyperbole. If either had been descriptive of the real world, there would have been no need or room for QM or Relativity; nor would there have been any need or room for QCD, or any question whether the Higgs boson existed or not, or any other remaining puzzle in particle physics or by extension cosmology at all.
Most physicists, certainly between Newton and Faraday, understood this - it is not merely that the distinction between mathematical abstraction and the empirical reality it has been abstracted from has gradually been "forgotten", it is that a new Platonism has gained firm hold in physicist's philosophical worldview, since Solvay at least. For them the mathematical abstraction is the real world.
The mystery is how a mathematical theory can as Nick points out entail certain predictions - surprising predictions, to be Popperian about it - that are empirically confirmed, despite the theory not being descriptive (it can and usually is replaced by a different theory, with conflicting conceptual contents, that turns out to be "better" - predicts yet more surprising observations, while still accounting for the ones already made using the theories it has superceded.) If you don't find this utterly mysterious, you're either a monumental genius or you haven't quite grasped what's going on.
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Post by mrsonde on Mar 17, 2015 16:40:26 GMT 1
Feynman certainly did, by the way.
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Post by mrsonde on Mar 17, 2015 17:00:25 GMT 1
I've just rewatched the fantastic doc on the Antikythera mechanism en.wikipedia.org/wiki/Antikythera_mechanism, the astonishing multi-geared "computer" that could predict solar and lunar eclipses thousands of years into the future - it could tell the Greeks (possibly even the Babylonians, depending on how old it is) about the one this week, for example, and that it would occur at about 9 in the morning, and how much of the disc would be obscured, and even what colour the Moon would be. All done by thirty or so interlocking gearwheels, modelling the solar system to incredible accuracy. The designers were fully aware that the Moon orbited the Earth in an ellipse, that itself rotated, and so a sliding pin mechanism built into one of the gearwheels moved fractionally in and out as the wheel turned every "nine point whatever whatever years" so that it turned its reciprocal very slightly faster or slower, thus precisely modelling the variable speed of the Moon as it followed its elliptical course. This I suggest is an accurate analogy of mathematical formulations of physical theories. They require operators like sliding pins in a round cogwheel - but of course there is no sliding pin, and there are no cogwheels, however stupendously accurate the model might appear to be by dint of its predictive power. The underlying mystery is how such a model, built using principles that have no direct correlate in the real world (no pin or wheels in the sky), can be "accurate" in this sense of predicting novel and surprising observations. I can conceive of only one possible solution to this most profound of mysteries (and it's the same puzzle as how we're able to understand the world at all, conceptually or linguistically) is that the universe is geometrical, and at least some of our mathematical theories have geometrical content, and so can approximate according to how well we've captured that geometry. QED is not geometrical at all, except in the most abstruse manner, lifted from GR, which is why Feynman was under no illusion that it was "true". Inflation theory is similarly not geometrically derived, which is why it will (and has been) superceded. That's my view, at any rate - but these are very very deep waters, and I confess I'm only just waving not drowning.
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Post by fascinating on Mar 18, 2015 8:29:47 GMT 1
All of it, is the point. Mathematically it's remarkably accurate of course - but this is not to mean that conceptually it's descriptive: (Russell's quote needs to be expanded, so that it is not merely the real world's mathematical properties that we can discover, but actually those properties are often not in the real world at all, but are rather the properties of the overlaying grid that we have veiled it with.) QED is not as accurate as Newtonian mechanics, despite the hyperbole. If either had been descriptive of the real world, there would have been no need or room for QM or Relativity; nor would there have been any need or room for QCD, or any question whether the Higgs boson existed or not, or any other remaining puzzle in particle physics or by extension cosmology at all. Most physicists, certainly between Newton and Faraday, understood this - it is not merely that the distinction between mathematical abstraction and the empirical reality it has been abstracted from has gradually been "forgotten", it is that a new Platonism has gained firm hold in physicist's philosophical worldview, since Solvay at least. For them the mathematical abstraction is the real world. The mystery is how a mathematical theory can as Nick points out entail certain predictions - surprising predictions, to be Popperian about it - that are empirically confirmed, despite the theory not being descriptive (it can and usually is replaced by a different theory, with conflicting conceptual contents, that turns out to be "better" - predicts yet more surprising observations, while still accounting for the ones already made using the theories it has superceded.) If you don't find this utterly mysterious, you're either a monumental genius or you haven't quite grasped what's going on. Hmmm. For me mathematics is a language ("I have these concepts which I label by the words one, two, three etc. One means an instance of any thing. Two means there is one and another one instance of that thing. Three means two and another one of that thing etc."). But these concepts are based on the real world, which has quantities in it, doesn't it? There are quantities of space eg there are 93 million one-dimensional "lumps" of space, each a mile long, between Earth and Sun. Each lump of space is exactly the same (never mind what is occurring inside each lump), so it is an unavoidable fact that the Universe does have features which repeat so quantities are real. Unless, perhaps, it is said that, in the example, we should not label each one of those 93 million lumps with the word "space"; that could be just a human cast on the real Universe, where every single lump of what we call "space" is a different thing entirely, because the what we label lump number 1 is entirely different to lump number 2 - it's in a different position for a start, and anyway this lumping is arbitrary anyway. But I cannot get around the fact that there is a distance between the Earth and the Sun, and I think it is greater than that between the Earth and the Moon. I'd like to know what you mean by the "real world".
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Post by mrsonde on Mar 18, 2015 9:26:17 GMT 1
You can call maths a language if you want, but it's one that can be defined entirely self-referentially - there is no need for any "things" outside of it to define it ostensively. All that's required are operationally defined terms and a set of rules by which you're allowed to combine them. By such terms and rules, your axioms, you derive theorems, the implications of those rules - thus you create arithmetic, sets, and geometries.
That these arbitrarily defined terms and freely defined rules can apply (or not apply) to the physical universe is a consequence of that universe having dimensions - space-time, an affine manifold in the jargon, that can be measured, that can form enclosures, and has its own geometrical rules by dint not of arbitrary axioms but by the fact of its existence. We don't know what that geometry is - although the geometries that we can and do arbitrarily invent are able to approximate it in the match between its implications and our measurements. Then there's the stuff that enables us to measure at all, by giving the distinctions within that affine manifold - energetic forms. We don't know how to derive this stuff, and all the forms it takes, from our geometrical approximations - we're closer and closer, no doubt, but still not there. When we get there theoretical formulations like QED, QM, the Standard Model of the particle zoo, Relativity, etc will be seen as (largely arithmetical) approximations to a correct axiomatic description of that existent geometry, as Newton's gravitation is to Einstein's.
Yes? Have I answered your question?
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Post by fascinating on Mar 18, 2015 9:50:22 GMT 1
You are saying that the Universe does, in reality, have dimensions, (space-time)? So it is a real property of the Universe that there are quantities within it that can only represented for us in mathematics, yes? And that the rules that we a apply to mathematics are representations of what happens in the real world (if you have one hydrogen atom and add another hydrogen atom then you have two hydrogen atoms)?
I did ask you to tell you what you meant by the real world.
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