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#681
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Stuart Noble wrote:
Norman Wells wrote: John Rumm wrote: Norman Wells wrote: To test that, it's vital to have a definition of 'mass', isn't it? You see, according to the definition in Chambers Dictionary of Science and Technology, mass is defined as 'the quantity of matter in a body'. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Relating the mass simply to the number of atoms would seem to preclude any gain is mass with velocity (something intrinsically linked with time dilation), and time dilation is something that has been observed. Mass it seems is not as "fixed" as classical physics would have us believe. If you're going to talk about mass, as you have, you have to know what it means, not say in Humpty Dumpty fashion "it means just what I choose it to mean - neither more nor less". So, what is mass? What is your definition? This thread interests me, not because I understand a bloody word of it, but because people with degrees in the subject end up squabbling over what appear to be fundamentals. Is that the nature of the beast maybe? So far we seem to have graduates from Imperial College and York, but I may have missed some. Any chance of the others combatants declaring their credentials? Not as a dick waving exercise, but to give people like me an insight into the extent to which experts can disagree. Engineering, Cambridge. |
#682
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Bambleweeny57 wrote:
On Mon, 21 Sep 2009 11:58:51 +0000, Stuart Noble wrote: This thread interests me, not because I understand a bloody word of it, but because people with degrees in the subject end up squabbling over what appear to be fundamentals. Is that the nature of the beast maybe? So far we seem to have graduates from Imperial College and York, but I may have missed some. Any chance of the others combatants declaring their credentials? Not as a dick waving exercise, but to give people like me an insight into the extent to which experts can disagree. The politest description of much of this thread might be Newtonian v. Einsteinian physics. Newtonian physics is good for about 99.99% of what we observe & do as humans. Einsteinian physics starts to "kick in" at the extremes. No, it kicks in everywhere. Its just the two worldviews converge at small scale low energy events. Newton is a good approximation to Einstein, for small energies. Much of the physics in this area is still theoretical & difficult to fully grasp with a strong mathematical background and this is the reason for "discussions" amongst scientists. Significant sums of money are going into test these theories with things like the LIGO gravity wave detector and the Large Hadron Collider. This is where I duck That's not really about relativity much though. That's about fine structu Not how it behaves in a gravitational field. BW |
#683
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brightside S9 wrote:
On Sun, 20 Sep 2009 18:56:58 +0100, "Norman Wells" wrote: Look, his formula can be used to calculate the energy that could theoretically be released from a certain mass, or to calculate the mass that could be formed from a certain amount of energy. And you can do that with any mass or any amount of energy at any time. But those calculations only have any significance or relevance if what you're doing is actually converting mass into energy or vice versa. And mass is not actually converted into energy on earth in any processes except nuclear reactions and radioactive decay, whatever you may think. No you forgot chemical reactions. However because the change in mass is so small and inperceptible, chemistry has aworkable law of "Conservation of Mass", which is confusing *you*. Common example given in physics text books is the explosion of 1kg of dynamite. This results in a mass loss of about 0.6nkg and energy release of 5.4MJ. So for chemistry the mass loss is *imperceptible* but the energy release is obvious. That's circular. The writers have assumed that e=mc^2 applies, calculated a spurious result in a case where it clearly doesn't actually apply, and concluded that chemical reactions therefore obey the formula. Isn't it convenient that in all of these cases where e=mc^2 is erroneously applied, the change of mass they say occurs can't actually be demonstrated because it's always so 'imperciptibly small'? If you consulted a _chemistry_ text book it would doubtless say that there is no loss of mass at all, the energy coming not from destruction of matter, which would be required for mass loss, but from the chemical reactions in which compounds of high chemical energy combine to form compounds of lower intrinsic energy. |
#684
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Stuart Noble wrote:
Norman Wells wrote: John Rumm wrote: Norman Wells wrote: To test that, it's vital to have a definition of 'mass', isn't it? You see, according to the definition in Chambers Dictionary of Science and Technology, mass is defined as 'the quantity of matter in a body'. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Relating the mass simply to the number of atoms would seem to preclude any gain is mass with velocity (something intrinsically linked with time dilation), and time dilation is something that has been observed. Mass it seems is not as "fixed" as classical physics would have us believe. If you're going to talk about mass, as you have, you have to know what it means, not say in Humpty Dumpty fashion "it means just what I choose it to mean - neither more nor less". So, what is mass? What is your definition? This thread interests me, not because I understand a bloody word of it, but because people with degrees in the subject end up squabbling over what appear to be fundamentals. I agree. It should be so simple. But what can you do if people use words to mean whatever they want them to, and fail to define their terms even when pressed? Is that the nature of the beast maybe? No, just the standard of the participants. Some, like me, want to clarify issues. Others want to obscure them. |
#685
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dennis@home wrote:
"Stuart Noble" wrote in message om... This thread interests me, not because I understand a bloody word of it, but because people with degrees in the subject end up squabbling over what appear to be fundamentals. Is that the nature of the beast maybe? So far we seem to have graduates from Imperial College and York, but I may have missed some. Any chance of the others combatants declaring their credentials? Not as a dick waving exercise, but to give people like me an insight into the extent to which experts can disagree. There is no disagreement with the fundamental laws or the equations governing them (well not in this thread). There are a group who think the equations are universal and a group that think they are not. So far the group that don't think they are universal have posted stuff that the "universal" group can't or won't explain. other than to state they are universal so must apply. Quite the reverse. We have posted plenty of material that asserts that it is so if einsteins theory remains inviolate. Its not a question of whether it is or isn't. Einstein's theory says it HAS to be. It is not possible to take energy out of a system without decreasing its mass. THATS WHAT THE ****ing theory is all about FER CHRISSAKES. Its called the principle of energy mass equivalence. It is absolutely universal, with no exceptions, or Einstein's theory is down the toilet. I didn't postulate the theory: It's not down to me to prove or refute it. I am merely stating what the theory *says*. There are a lot of scientists and mathematicians trying to produce a universal model ATM, the latest attempt is called string theory. They wouldn't be doing this if the others were universal would they? Your inability to grasp the difference between universal applicability, and ubiquity is astonishing. Can you not grasp a statement like 'all water is wet' which has universal applicability, does not cover the sexual orientation of Goldfish? What the "universal" group are saying is that the people working on string theory aren't as clever as they are as the existing maths is universal. That is a complete lie. To see why some think they are not universal have a look at http://www.superstringtheory.com/index.html and then decide for yourself if you can apply E=mc2 everywhere and interchange mass for energy at a whim. where does that say anything about relativity? where does it refute Einstein's theory? You will notice that at least one problem they are working on is the fact that relativity tends not to work unless you ignore the effect of gravity (http://www.superstringtheory.com/basics/basic3.html). Something you can't do in the real world even if you are TNP. The reality is that this is not an argument between experts at all. Oh dear. You appear not to have understood even that rather dumb view. The point is that string theory RECONCILES relativity with the subatomic view. Not refutes it. |
#686
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Norman Wells wrote:
The Natural Philosopher wrote: Norman Wells wrote: Java Jive wrote: I've already pointed out in another post complete with a link to K&L that this definition of mass is WRONG! What you are using is a scientifically loose description of it in common parlance, NOT a definition. That's strange. I thought dictionaries were there to provide definitions. Well there you thought wrong. Yes, of course. Does Matron know you're out? And besides, there seems to be a marked reluctance on the part of some here, to give the definition on which they rely, even when asked several times over. I think that's because they'll be found out to be fiddling the facts to fit their conclusions. F=ma. Ah, Newton's second law, I believe. I thought you'd moved on from classical Newtonian mechanics. It's quite true of course, but how does it help? It defines mass in terms of force and acceleration. It is the definition. |
#687
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Java Jive wrote:
On Mon, 21 Sep 2009 12:23:41 GMT, Bambleweeny57 wrote: The politest description of much of this thread might be Newtonian v. Einsteinian physics. Newtonian physics is good for about 99.99% of what we observe & do as humans. Einsteinian physics starts to "kick in" at the extremes.[] That's being very polite indeed! It's also what I've been saying all along. Where I have a problem is with those who say it's not just at the extremes but in everything we do, including winding up the weight on a cuckoo clock. FWIW, my suspicion is that Norman is in the wrong, because otherwise, as I pointed out 4 days ago, a photon would not have mass and be bent by the sun, whereas in a famous post WWI experiment, it was proved that light *is* bent by the sun. In fact, astronomers now use the phenomenon of gravitational lensing to magnify distant objects that would otherwise be less observable. And if that's not 'at the extremes', I don't know what is. |
#688
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dennis@home wrote:
To see why some think they are not universal have a look at http://www.superstringtheory.com/index.html and then decide for yourself if you can apply E=mc2 everywhere and interchange mass for energy at a whim. If you can, I'd like to know how I can get up to London using the energy in a 50g lump of lead please. |
#689
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J G Miller wrote:
On Sun, 20 Sep 2009 19:29:10 +0100, Norman Wells wrote: Tell me, what mass has been created, not its quantity but its nature. No additional atoms or sub-atomic particles are created. The mass of each and every sub-atomic particle that has mass is increased however. Define 'mass' then. |
#690
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Norman Wells wrote:
The Natural Philosopher wrote: Norman Wells wrote: How can you MEASURE the 'quantity of mater' in anything? You count the atoms. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Whose mass varies slightly with temperature. No it doesn't. According to the only supported definition of mass that we have here, ie the one from Chambers Dictionary of Science and Technology, mass is 'the quantity of matter in a body'. Unless you increase the quantity of atoms in a body you cannot increase its mass. That's logic, see? Logic based on false premises is nit the truth. They're the only premises we've got. You see, you haven't provided any alternative viable definition, despite having been asked several times. If you maintain, contrarily, that the number of atoms increases with heating, I never said that. You can't be saying anything else if you say that mass increases with heating. you should be able to tell us the nature of the atoms created, and whether they're the same as those already there (if so why?) or different (in which case what?). The atoms are *not constant* in mass.. The number of atoms _is_ the mass, silly. It follows from the definition of mass. It follows from YOUR definition of mass, sure. But that is not the definition that science in fact uses. So you say, so you say. But since you've given no viable alternative definition, so mine is the best. I have givben youu at least one. You just persist in lying about it Get it through your thick skull: Energy has mass. Energy IS mass. No nuclear transformations are necessary. But there's a difference in fact between energy and mass Not if you use the Einstein worldview, there isn't. Its merely how they appear to you. OK, here's a 50g lump of lead, and I want to go to London. Plenty of energy there to do that, you say, so how do I do it? If it was chemical energy, I could easily release that and convert it into kinetic energy, like I do in a car. But how do I do it with a lump of lead? Should be easy enough if it's energy already surely. Dont be sillier than you have to be. You said there was no difference between energy and mass. How do I get to London using the energy of a 50g lump of lead? Serious question based on _your_ propositions. Can you support them or not? Its wholly beyond your capabilities. I am not here to solve your trivial transport problems. However given an appropriate nuclear reactor, it might be just enough to blow your arse to kingdom come, which is probably where it belongs ;-) OTOH if you attached to a string to it over a pulley and dropped it down a hiole, it might get you to lodon. Or best of all, get someone to smash your skull in with it, and call the london ambulance service. ;-) namely that mass, ie matter, has a tangible physical form. If energy is converted into mass, it must be converted into atoms or at least sub-atomic particles. What atoms? What sub-atomic particles? The confusion arises from your insistence that atoms and particles have fixed masses. They don't. But you can't even define mass. And without that, you can't possibly say that they don't. The dictionary definition, however, leads logically and inevitably to the fact that they do. Sigh. Mass has been defined for you perfectly clearly and simply. It is the 'm' term in the equation F=ma. Er, sorry, but that isn't a definition. It's a formula in which it appears. To know what a formula means, you must know first how all the symbols in it are defined. So applying that to your chambers 'definition' that's completely invalid as well! |
#691
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Norman Wells
wibbled on Monday 21 September 2009 14:34 dennis@home wrote: To see why some think they are not universal have a look at http://www.superstringtheory.com/index.html and then decide for yourself if you can apply E=mc2 everywhere and interchange mass for energy at a whim. If you can, I'd like to know how I can get up to London using the energy in a 50g lump of lead please. Easy. *You* take 50g of antimatter-lead, shove both up your behind whilst pointing your head towards London. Two problems solved. -- Tim Watts The ****artist formerly known as Tim S |
#692
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Norman Wells wrote:
The Natural Philosopher wrote: Bill Wright wrote: "Dave Liquorice" wrote in message ll.co.uk... On Sat, 19 Sep 2009 09:20:18 +0100, Norman Wells wrote: Norman, I suggest you wander off and do some in depth reading about the advancements in the scientific theories relating to Quantum Mechanics that have taken place in the last 30+ years. You appear to be stuck in the theories of 50+ years ago. Unfortunately that won't help at all with situations that don't involve quantum mechanics in the slightest. The physics of sub-atomic particles has no relevance unless you're considering sub-atomic particles. Winding a cuckoo clock doesn't. OK how does a clock spring store energy without *any* atomic/sub-atomic effects? Because it's springy, stupid. And how does it get to be that way without reference to its molecular constituents? Intra-molecular conformation for one thing. If, for example, you have two long molecules that are intertwined, it will take some force to separate them. That's nothing to do with the molecules themselves but their physical arrangement or conformation. Ah, so its not about the lumps, its about the connections. And what, pray, are the connections 'made of'? What holds the atoms in this arrangement? why don't they wander off independently? Iron and steels vary in their springiness because of their crystalline structures. What you're observing are physical, macro effects. And how come they take up crystalline forms? |
#693
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Norman Wells wrote:
The Natural Philosopher wrote: Paul Martin wrote: In article , dennis@home wrote: While you may take the view that any splitting of atoms is fission, the majority would take the view that fission is induced by the interaction of free neutrons with nuclei. The other stuff is radioactive decay. With fission, an nucleus splits into two nuclei of smaller atomic number, with the emission of gamma rays and some particles (usually neutrons). Radioactive decay *usually* results in the emission of a particle or photon, without the neucleus splitting. Radon is a decay product of radium. Radon is the most common source of radioactivity on the planet's surface. Whereas of course just a few hours ago, you were claiming it as a product of a nuclear reactor at the earth's core, saying: "Of course it has nuclear reactions going on down there..where else would all the radon come from?" What do you know? So what is a fission product except part of a nuclear reaction? |
#694
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J G Miller wrote:
On Sun, 20 Sep 2009 21:46:00 +0100, Norman Wells wrote: That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. That is not the quantity mass, but the quantity amount of substance (SI unit mole). The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). Mass is a measure of the inertia of a body, and it not a measure of the number of elementary particles. So you say, but don't support. According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. |
#695
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Java Jive wrote:
That's not the way scientific measurement works. The best that even a scientific dictionary can give is a description. Don't be absurd. Dictionaries exist to provide definitions. A Dictionary of Science and Technology exists to provide definitions of scientific and technological terms Perhaps you're not familiar with their purpose. And actually, though I'm definitely not interested in arguing the matter, I'd also dispute that normal dictionaries actually supply definitions. sigh education today. |
#696
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John Rumm wrote:
however the relativistic difference in mass (approx 1x10^-16 kg), is dwarfed by the effects of the variation in gravitational field caused by the 1m height differential, so the experiment is fatally flawed before you begin. How convenient. |
#697
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Norman Wells wrote:
J G Miller wrote: On Sun, 20 Sep 2009 19:29:10 +0100, Norman Wells wrote: Tell me, what mass has been created, not its quantity but its nature. No additional atoms or sub-atomic particles are created. The mass of each and every sub-atomic particle that has mass is increased however. Define 'mass' then. Define reality Norman. Is what you think it is? Is it what I think it is? Looks like we have moved from Poper to Godel. And beyond. http://en.wikipedia.org/wiki/M%C3%BCnchhausen_Trilemma Reality is ultimately what we agree it is. If we don't agree, then nothing more can be said. Einstein produced an internally consistent theorem, one of whose predictions was that mass and energy as classically defined, were aspects of one thing. You cant prove its correct, and so far you haven't proved its incorrect. So in your case, lacking the ability to even understand it, it becomes a matter of Faith I suppose. |
#698
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Norman Wells wrote:
J G Miller wrote: On Sun, 20 Sep 2009 21:46:00 +0100, Norman Wells wrote: That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. That is not the quantity mass, but the quantity amount of substance (SI unit mole). The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). Mass is a measure of the inertia of a body, and it not a measure of the number of elementary particles. So you say, but don't support. According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. http://math.ucr.edu/home/baez/physic...y/SR/mass.html If you can understand beyond the first word. |
#699
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John Rumm wrote:
Norman Wells wrote: You see, according to the definition in Chambers Dictionary of Science and Technology, Which is simply wrong. Well, that's nice of you just to diss a reputable and reliable source like that. Patronising even. Especially since I've asked you numerous Hardly. The dictionary is giving you a very simplistic definition of mass. Adequate for some purposes, but not if you wish to discuss matters of quantum physics or (special) relativity. times to provide the definition of mass that you use and give its source and, every time, you have been unable to do so. Now you're asking us to How about: "The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/ 9x10^2^0, the energy being measured in ergs, and the mass in grammes". [A. Einstein, 27/09/1905, http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ ] That's not a definition at all. If I say "A pound is a measure of the weight of a body" does that define what a pound is? Try again. dismiss an established definition and replace it with, well, what exactly? Something woolly and undefined with no scientific foundation which you just state supports your case when there is no justification for that at all. Erm, see above. You've confirmed that you have no understanding of what a definition is, let alone provided one that is precise. mass is defined as 'the quantity of matter in a body'. It isn't. Its defined precisely by Newtonian mechanics as the value of the inertia of the object. Is that the definition you use? Where does that come from? Anyway, I though you were dissing Newtonian mechanics as well. Newtonian mechanics is as far as it goes. However it is an approximation, that omits detail. How can you MEASURE the 'quantity of mater' in anything? You count the atoms. Which only tell you the mass if you know other things. The number of atoms _is_ the quantity of matter in a body. It is composed of nothing else. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Whose mass varies slightly with temperature. No it doesn't. According to the only supported definition of mass that we have here, ie the one from Chambers Dictionary of Science and Where does this assertion that Chambers Dictionary of Science and Technology is the only supported definition come from? Find me another. Technology, mass is 'the quantity of matter in a body'. Unless you increase the quantity of atoms in a body you cannot increase its mass. That's logic, see? Logic indeed. However if you start from a flawed baseline, any logical derivation from it can't hope to be right can it? For any typical human interaction with the world around us, the notion that mass is "the quantity of matter in a body" is adequate. However you need to also accept its only an approximation to the reality. So, what is mass, according to you? If you maintain, contrarily, that the number of atoms increases with heating, I never said that. You can't be saying anything else if you say that mass increases with heating. You can, if you accept that the mass of atoms changes and that you reject the concept that mass is defined purely as the number of atoms you have. If you start from the baseline that mass is defined by the combined effect of both their number, and their embodied energy, then it is quite easy. But you haven't started from anywhere. You haven't defined mass. you should be able to tell us the nature of the atoms created, and whether they're the same as those already there (if so why?) or different (in which case what?). The atoms are *not constant* in mass.. The number of atoms _is_ the mass, silly. It follows from the definition of mass. Only from Chambers, and it should hopefully be clear that this is an over simplistic definition. Which we should replace by what exactly? |
#700
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The Natural Philosopher wrote:
Norman Wells wrote: John Rumm wrote: Norman Wells wrote: To test that, it's vital to have a definition of 'mass', isn't it? You see, according to the definition in Chambers Dictionary of Science and Technology, mass is defined as 'the quantity of matter in a body'. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Relating the mass simply to the number of atoms would seem to preclude any gain is mass with velocity (something intrinsically linked with time dilation), and time dilation is something that has been observed. Mass it seems is not as "fixed" as classical physics would have us believe. If you're going to talk about mass, as you have, you have to know what it means, not say in Humpty Dumpty fashion "it means just what I choose it to mean - neither more nor less". The very point I made to you. I am using 'mass' to mean exactly what it says in the dictionary definition, no more and no less, and utterly consistently. So, what is mass? What is your definition? The property of an object that leads to its inertia. We know everything has it. What we want to know is what it is. _Define_ the term, and give your source. |
#701
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The Natural Philosopher wrote:
Norman Wells wrote: The Natural Philosopher wrote: And besides, there seems to be a marked reluctance on the part of some here, to give the definition on which they rely, even when asked several times over. I think that's because they'll be found out to be fiddling the facts to fit their conclusions. F=ma. Ah, Newton's second law, I believe. I thought you'd moved on from classical Newtonian mechanics. It's quite true of course, but how does it help? It defines mass in terms of force and acceleration. It is the definition. All it is is a formula, so perhaps you don't understand the concept of 'definitions'? To understand a formula, you have to know exactly what all the little letters in it mean and how they are defined. It's totally illogical to point to a formula and say that it 'defines' anything. It doesn't. It merely shows the relationship of things that are already defined. If you know two of the variables in the equation, you can _calculate_ a value for the third, but it doesn't _define_ what it is. So, yet again, we're no further forward, are we? |
#702
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On 2009-09-21, Norman Wells wrote:
J G Miller wrote: On Sun, 20 Sep 2009 21:46:00 +0100, Norman Wells wrote: That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. That is not the quantity mass, but the quantity amount of substance (SI unit mole). The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). Mass is a measure of the inertia of a body, and it not a measure of the number of elementary particles. So you say, but don't support. According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. http://science.howstuffworks.com/relativity2.htm "Mass and Energy Mass has two definitions that are equally important. One is a general definition that most high school students are taught and the other is a more technical definition that is used in physics. Generally, mass is defined as the measure of how much matter an object or body contains - the total number of sub-atomic particles (electrons, protons and neutrons) in the object. If you multiply your mass by the pull of earth's gravity, you get your weight. So if your body weight is fluctuating, by eating or exercising, it is actually your mass that is changing. It is important to understand that mass is independent of your position in space. Your body's mass on the moon is the same as its mass on the earth. The earth's gravitational pull, on the other hand, decreases as you move farther away from the earth. Therefore, you can lose weight by changing your elevation, but your mass remains the same. You can also lose weight by living on the moon, but again your mass is the same. In physics, mass is defined as the amount of force required to cause a body to accelerate. Mass is very closely related to energy in physics. Mass is dependent on the body's motion relative to the motion of an observer. If the body in motion measured its mass, it is always the same. However, if an observer that is not in motion with the body measures the body's mass, the observer would see an increase in mass when the object speeds up. This is called relativistic mass. It should be noted that physics has actually stopped using this concept of mass and now deals mostly in terms of energy (see the section on the unification of mass and energy) . At this stage, this definition of mass may be a little cloudy, but it is important to know the concept. It should become clearer in the special relativity discussion. The important thing to understand here is that there is a relationship between mass and energy. Energy Energy is the measure of a system's ability to perform "work". It exists in many formsàpotential, kinetic, etc. The law of conservation of energy tells us that energy can neither be created nor destroyed; it can only be converted from one form to another. These separate forms of energy are not conserved, but the total amount of energy is conserved. If you drop a baseball from your roof, the ball has kinetic energy the moment it starts to move. Just before you dropped the ball, it had only potential energy. As the ball moves, the potential energy is converted into kinetic energy. Likewise, when the ball hits the ground, some of its energy is converted to heat (sometimes called heat energy or heat kinetic energy). If you go through each phase of this scenario and totaled up the energy for the system, you will find that the amount of energy for the system is the same at all times. [...] Energy-Mass Unification You should readily understand how a system with very little mass has the potential to release a phenomenal amount of energy (in E=mc^2, c^2 is an enormous number). In nuclear fission, an atom splits to form two more atoms. At the same time, a neutron is released. The sum of the new atoms' masses and the neutron's mass are less than the mass of the initial atom. Where did the missing mass go? It was released in the form of heat - kinetic energy. This energy is exactly what Einstein's E=mc^2 predicts. Another nuclear event that corresponds with Einstein's equation is fusion. Fusion occurs when lightweight atoms are subjected to extremely high temperatures. The temperatures allow the atoms to fuse together to form a heavier atom. Hydrogen fusing into helium is a typical example. What is critical is the fact that the mass of the new atom is less than the sum of the lighter atoms' masses. As with fission, the "missing" mass is released in the form of heat - kinetic energy. One often-misinterpreted aspect of the energy-mass unification is that a system's mass increases as the system approaches the speed of light. This is not correct. Let's assume that a rocket ship is streaking through space. The following occurs: 1 Energy must be added to the system to increase the ship's speed. 2 More of the added energy goes towards increasing the system's resistance to acceleration. 3 Less of the added energy goes into increasing the system's speed. 4 Eventually, the amount of added energy required to reach the speed of light would become infinite. In step 2, the system's resistance to acceleration is a measurement of the system's energy and momentum. Take notice that in the above 4 steps, there is no reference to mass. Nor does there need to be." |
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Tim W wrote:
Norman Wells wibbled on Monday 21 September 2009 14:34 dennis@home wrote: To see why some think they are not universal have a look at http://www.superstringtheory.com/index.html and then decide for yourself if you can apply E=mc2 everywhere and interchange mass for energy at a whim. If you can, I'd like to know how I can get up to London using the energy in a 50g lump of lead please. Easy. *You* take 50g of antimatter-lead, shove both up your behind whilst pointing your head towards London. Two problems solved. Sadly, I don't have any anti-matter lead, so I can't escape this asylum that easily. |
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"The Natural Philosopher" wrote in message ... I didn't postulate the theory: It's not down to me to prove or refute it. I am merely stating what the theory *says*. Go on then show me how it works with the hydro electric problem I set earlier. You should find it easy. |
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The Natural Philosopher wrote:
Norman Wells wrote: The Natural Philosopher wrote: Paul Martin wrote: In article , dennis@home wrote: While you may take the view that any splitting of atoms is fission, the majority would take the view that fission is induced by the interaction of free neutrons with nuclei. The other stuff is radioactive decay. With fission, an nucleus splits into two nuclei of smaller atomic number, with the emission of gamma rays and some particles (usually neutrons). Radioactive decay *usually* results in the emission of a particle or photon, without the neucleus splitting. Radon is a decay product of radium. Radon is the most common source of radioactivity on the planet's surface. Whereas of course just a few hours ago, you were claiming it as a product of a nuclear reactor at the earth's core, saying: "Of course it has nuclear reactions going on down there..where else would all the radon come from?" What do you know? So what is a fission product except part of a nuclear reaction? It can be the product of natural radio-active decay. A nuclear reaction is usually taken as necessitating bombardment with neutrons. |
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The Natural Philosopher wrote:
Norman Wells wrote: You said there was no difference between energy and mass. How do I get to London using the energy of a 50g lump of lead? Serious question based on _your_ propositions. Can you support them or not? Its wholly beyond your capabilities. I am not here to solve your trivial transport problems. However given an appropriate nuclear reactor, it might be just enough to blow your arse to kingdom come, which is probably where it belongs OTOH if you attached to a string to it over a pulley and dropped it down a hiole, it might get you to lodon. Or best of all, get someone to smash your skull in with it, and call the london ambulance service. ;-) I'll take that as a 'no' then. |
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The Natural Philosopher wrote:
Norman Wells wrote: The Natural Philosopher wrote: Bill Wright wrote: OK how does a clock spring store energy without *any* atomic/sub-atomic effects? Because it's springy, stupid. And how does it get to be that way without reference to its molecular constituents? Intra-molecular conformation for one thing. If, for example, you have two long molecules that are intertwined, it will take some force to separate them. That's nothing to do with the molecules themselves but their physical arrangement or conformation. Ah, so its not about the lumps, its about the connections. And what, pray, are the connections 'made of'? What holds the atoms in this arrangement? why don't they wander off independently? Friction, shape, conformation, and lack of desire to be adventurous. Iron and steels vary in their springiness because of their crystalline structures. What you're observing are physical, macro effects. And how come they take up crystalline forms? Everyone should have a hobby. |
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The Natural Philosopher wrote:
Norman Wells wrote: J G Miller wrote: On Sun, 20 Sep 2009 19:29:10 +0100, Norman Wells wrote: Tell me, what mass has been created, not its quantity but its nature. No additional atoms or sub-atomic particles are created. The mass of each and every sub-atomic particle that has mass is increased however. Define 'mass' then. Einstein produced an internally consistent theorem, one of whose predictions was that mass and energy as classically defined, were aspects of one thing. You cant prove its correct, and so far you haven't proved its incorrect. I wouldn't dream of proving it incorrect. Of course mass and energy are aspects of one thing, just as pounds and dollars are aspects of money. Dollars can be changed into pounds and vice versa, but only if you follow defined steps. They don't do it magically all by themselves. And that's what we're arguing about here. Mass and energy _can_ be interchanged, as has been demonstrated conclusively in nuclear reactions. But my point is that they don't do it magically all by themselves either, and they don't do it at all unless you follow particular procedures to make it happen. Otherwise, you'd be able to tell me how to get to London on the energy in a 50g lump of lead, wouldn't you? So in your case, lacking the ability to even understand it, it becomes a matter of Faith I suppose. No. What I understand is based on scientific evidence and observation. |
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The Natural Philosopher wrote:
Norman Wells wrote: J G Miller wrote: On Sun, 20 Sep 2009 21:46:00 +0100, Norman Wells wrote: That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. That is not the quantity mass, but the quantity amount of substance (SI unit mole). The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). Mass is a measure of the inertia of a body, and it not a measure of the number of elementary particles. So you say, but don't support. According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. http://math.ucr.edu/home/baez/physic...y/SR/mass.html If you can understand beyond the first word. Oh yes. So, what definition are you using then? |
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Java Jive wrote:
Well, I've proved one thing today to my satisfaction at least: Norman just doesn't know when he's just been disproved. It's like arguing against a devout religious belief - a complete waste of time. http://dictionary.reference.com/browse/dictionary dictionary No mention anywhere of 'define', 'definition', or any variant of the word. You've never heard of the expression 'dictionary definition' then? |
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Jim Lesurf wrote:
In article , Norman Wells wrote: The Natural Philosopher wrote: However most scientists even today working outside the field of physics don't have more than a hazy understanding of relativity, so you find plenty of folks who think like Norman, that relativity doesn't apply outside of nuclear situations. Not that he is in any sense a scientist, or scientifically trained. Nevertheless, it does. No it doesn't except where mass and energy are actually interconverted, which does not happen as a matter of normal physical operations which just effect energy-energy conversions. As 'Natural Philosopher' has been trying to explain to you I know. He's been _so_ kind. According to general relativity mass and energy are simply two ways to observe the same fundamental property. That's where we differ. I say that they are related and can be interconverted under some conditions, a bit like dollars and pounds. They are not the same, however, otherwise someone would be able to tell me how I can travel to London using the energy in a 50g lump of lead . So if any system gains energy it also gains mass. if you disagree with that you are rejecting one of the axioms of general relativity. It's a bit dodgy, though, if you have to revise your definition of such a fundamental concept as 'mass' in order for it to fit your theory. Usually, when that happens, most people do the sensible thing and reject the theory instead. Been some years since I read it, but if you doubt this, go and read 'Gravitation' by Misner, Thorne and Wheeler. If you can cope with the maths it should explain it to you. IIRC The smaller book by Berry also dealt with this, but I can't recall as it was ages ago I read that as well. You say that if I raise a lump of lead against the force of gravity, it gains potential energy and therefore mass. Tell me, what mass has been created, not its quantity but its nature. Is it electrons, neutrons, protons, complete atoms or what? If it's complete atoms of lead, please tell me how the energy knows to create atoms of lead, ie each with 82 protons, 122 neutrons and 82 electrons, rather than any other atoms. If it's other atoms, is it not the case that sufficient raises and lowerings of the block will eventually change its chemical composition? Actually it is that every atom, electron, or other 'particle' in the system tends to gain intertial mass by an amount that sums to the total increase in energy of the system when you take the c-squared factor into account. You see, here we go, 'inertial mass' now. Is that the same as 'mass'. Is it the same as 'relativistic mass'. Why do all the proponents of this theory have to keep revising what they mean by 'mass' in order to make their points? It smacks of smoke and mirrors to me and in that sense is just like religion. This is linked to effects like atomic clocks based on level transitions altering their output. which are easily measured these days if you have the kit and have a clue. So yes, people have measured this via application of general relativity, and measured the effect on the atoms and molecules. Look up the papers in the journals if you want to know, rather than refuse to accept ot. I can't help it if you don't understand all this or refuse to accept it, though. Afraid that's your problem, not one for physics. So far as I know, you aren't a university academic mis-teaching poor students and confusing them about this. So it is none of my concern if you refuse to accept what 'Natural Philosopher' keeps trying - remarkably patiently - to tell you. I've said I'm grateful, haven't I? What more do you want? |
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Norman Wells
wibbled on Monday 21 September 2009 15:21 Tim W wrote: Norman Wells wibbled on Monday 21 September 2009 14:34 dennis@home wrote: To see why some think they are not universal have a look at http://www.superstringtheory.com/index.html and then decide for yourself if you can apply E=mc2 everywhere and interchange mass for energy at a whim. If you can, I'd like to know how I can get up to London using the energy in a 50g lump of lead please. Easy. *You* take 50g of antimatter-lead, shove both up your behind whilst pointing your head towards London. Two problems solved. Sadly, I don't have any anti-matter lead, Your personal inadequacies don't make it not possible. so I can't escape this asylum that easily. Nicely summed up... -- Tim Watts The ****artist formerly known as Tim S |
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Norman Wells wrote:
The Natural Philosopher wrote: Norman Wells wrote: J G Miller wrote: On Sun, 20 Sep 2009 19:29:10 +0100, Norman Wells wrote: Tell me, what mass has been created, not its quantity but its nature. No additional atoms or sub-atomic particles are created. The mass of each and every sub-atomic particle that has mass is increased however. Define 'mass' then. Einstein produced an internally consistent theorem, one of whose predictions was that mass and energy as classically defined, were aspects of one thing. You cant prove its correct, and so far you haven't proved its incorrect. I wouldn't dream of proving it incorrect. Of course mass and energy are aspects of one thing, just as pounds and dollars are aspects of money. Dollars can be changed into pounds and vice versa, but only if you follow defined steps. They don't do it magically all by themselves. And that's what we're arguing about here. Mass and energy _can_ be interchanged, as has been demonstrated conclusively in nuclear reactions. But my point is that they don't do it magically all by themselves either, and they don't do it at all unless you follow particular procedures to make it happen. Otherwise, you'd be able to tell me how to get to London on the energy in a 50g lump of lead, wouldn't you? So in your case, lacking the ability to even understand it, it becomes a matter of Faith I suppose. No. What I understand is based on scientific evidence and observation. Norman. Think of it this way. Energy has weight. ANY energy has weight. That's all it means |
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Norman Wells wrote:
The Natural Philosopher wrote: Norman Wells wrote: J G Miller wrote: On Sun, 20 Sep 2009 21:46:00 +0100, Norman Wells wrote: That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. That is not the quantity mass, but the quantity amount of substance (SI unit mole). The mole is defined as the amount of substance of a system that contains as many "elemental entities" (e.g. atoms, molecules, ions, electrons) as there are atoms in 12 g of carbon-12 (12C). Mass is a measure of the inertia of a body, and it not a measure of the number of elementary particles. So you say, but don't support. According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. http://math.ucr.edu/home/baez/physic...y/SR/mass.html If you can understand beyond the first word. Oh yes. So, what definition are you using then? I am not. I am merely telling you what the current definition is. See that paper. |
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Norman Wells wrote:
Jim Lesurf wrote: In article , Norman Wells wrote: The Natural Philosopher wrote: However most scientists even today working outside the field of physics don't have more than a hazy understanding of relativity, so you find plenty of folks who think like Norman, that relativity doesn't apply outside of nuclear situations. Not that he is in any sense a scientist, or scientifically trained. Nevertheless, it does. No it doesn't except where mass and energy are actually interconverted, which does not happen as a matter of normal physical operations which just effect energy-energy conversions. As 'Natural Philosopher' has been trying to explain to you I know. He's been _so_ kind. According to general relativity mass and energy are simply two ways to observe the same fundamental property. That's where we differ. I say that they are related and can be interconverted under some conditions, a bit like dollars and pounds. They are not the same, however, otherwise someone would be able to tell me how I can travel to London using the energy in a 50g lump of lead . So if any system gains energy it also gains mass. if you disagree with that you are rejecting one of the axioms of general relativity. It's a bit dodgy, though, if you have to revise your definition of such a fundamental concept as 'mass' in order for it to fit your theory. Usually, when that happens, most people do the sensible thing and reject the theory instead. Been some years since I read it, but if you doubt this, go and read 'Gravitation' by Misner, Thorne and Wheeler. If you can cope with the maths it should explain it to you. IIRC The smaller book by Berry also dealt with this, but I can't recall as it was ages ago I read that as well. You say that if I raise a lump of lead against the force of gravity, it gains potential energy and therefore mass. Tell me, what mass has been created, not its quantity but its nature. Is it electrons, neutrons, protons, complete atoms or what? If it's complete atoms of lead, please tell me how the energy knows to create atoms of lead, ie each with 82 protons, 122 neutrons and 82 electrons, rather than any other atoms. If it's other atoms, is it not the case that sufficient raises and lowerings of the block will eventually change its chemical composition? Actually it is that every atom, electron, or other 'particle' in the system tends to gain intertial mass by an amount that sums to the total increase in energy of the system when you take the c-squared factor into account. You see, here we go, 'inertial mass' now. Is that the same as 'mass'. Is it the same as 'relativistic mass'. Why do all the proponents of this theory have to keep revising what they mean by 'mass' in order to make their points? It smacks of smoke and mirrors to me and in that sense is just like religion. Because you are a thick ****, basically. We are trying to paint pictures that you can grasp. BUT you dont want to grasp them. |
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On Mon, 21 Sep 2009 13:03:10 +0100, Mark
wrote: Yes. And still are. Ahh, they're pulllin' your leg. IIRC most of the banks are still making a profit, albeit less than before the bubble burst. This is normal. Most businesses can relate to a heyday they once had when salaries grew freely and when Empires were built. Every few years there has to be a correction. The trouble is in the public service under the Jack - Boot of the unions there can be no such correction so it goes on and on until such time as the dire state of public services brings the government down. We had Balls on the television over the weekend saying how he could reduce educational costs at a stroke by dispensing with or merging together high up managerial jobs in schools. I can remember when my daughter went to a smallish primary school they had *More than one* Deputy Headmistress (Plus the head). When she moved on to middle / senior school / sixth form these so - called "schools" all had their own "Head of" and a deputy "Head of", and within each year in such a "school" every year had a * year leader*, each major subject also had a "Head of" and they closed the school about 3 days per year so they could all have "meetings". For all their fancy job titles and nested levels of responsibility, none of them had any authority to actually action any change at all, and a fair proportion of the kids never got to read and write. So "Old Balls" is probably right. Nowadays they're charging high interest rates on loans and giving low interest rates on investments so that they can recapitalise. Taxpayers will also be paying through the nose for the foreseeable future to cut government borrowing. Seems like we're going to be paying for this fiasco twice over. That's par for the course. We pay our NI contributions to cover the cost of medical and dental care but in extremis with toothache you have to pay again (a second time) to go private, ditto elective surgery such as arthritic joint replacement, otherwise you can wait up to 18 weeks for treatment unable to go to work or even walk at all for that matter. |
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Norman Wells wrote:
John Rumm wrote: Norman Wells wrote: You see, according to the definition in Chambers Dictionary of Science and Technology, Which is simply wrong. Well, that's nice of you just to diss a reputable and reliable source like that. Patronising even. Especially since I've asked you numerous Hardly. The dictionary is giving you a very simplistic definition of mass. Adequate for some purposes, but not if you wish to discuss matters of quantum physics or (special) relativity. times to provide the definition of mass that you use and give its source and, every time, you have been unable to do so. Now you're asking us to How about: "The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/ 9x10^2^0, the energy being measured in ergs, and the mass in grammes". [A. Einstein, 27/09/1905, http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ ] That's not a definition at all. If I say "A pound is a measure of the weight of a body" does that define what a pound is? can be, if you define body and weight. However it would be a wrong definition: A definition though. Try again. dismiss an established definition and replace it with, well, what exactly? Something woolly and undefined with no scientific foundation which you just state supports your case when there is no justification for that at all. Erm, see above. You've confirmed that you have no understanding of what a definition is, let alone provided one that is precise. mass is defined as 'the quantity of matter in a body'. It isn't. Its defined precisely by Newtonian mechanics as the value of the inertia of the object. Is that the definition you use? Where does that come from? Anyway, I though you were dissing Newtonian mechanics as well. Newtonian mechanics is as far as it goes. However it is an approximation, that omits detail. How can you MEASURE the 'quantity of mater' in anything? You count the atoms. Which only tell you the mass if you know other things. The number of atoms _is_ the quantity of matter in a body. It is composed of nothing else. Well that is a very very thin-ice statement. Many models would say that it was a lot more than that. It certainly isn't enough to shake a random bunch of atoms in a bag and say 'look, garlic sausage' That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Whose mass varies slightly with temperature. No it doesn't. According to the only supported definition of mass that we have here, ie the one from Chambers Dictionary of Science and Where does this assertion that Chambers Dictionary of Science and Technology is the only supported definition come from? Find me another. WE have. Half a dozen now. But it seems that because you are a thick ****, the only one you can understand, is the Chambers. Presumably written by thick ****s for thick ****s. Technology, mass is 'the quantity of matter in a body'. Unless you increase the quantity of atoms in a body you cannot increase its mass. That's logic, see? Logic indeed. However if you start from a flawed baseline, any logical derivation from it can't hope to be right can it? For any typical human interaction with the world around us, the notion that mass is "the quantity of matter in a body" is adequate. However you need to also accept its only an approximation to the reality. So, what is mass, according to you? Energy. Bound energy. If you maintain, contrarily, that the number of atoms increases with heating, I never said that. You can't be saying anything else if you say that mass increases with heating. You can, if you accept that the mass of atoms changes and that you reject the concept that mass is defined purely as the number of atoms you have. If you start from the baseline that mass is defined by the combined effect of both their number, and their embodied energy, then it is quite easy. But you haven't started from anywhere. You haven't defined mass. See Godel. you can split the world into related bits, and design a system, that is self consistent, but as to whether the initial splitting is meaningful..no one can say. you should be able to tell us the nature of the atoms created, and whether they're the same as those already there (if so why?) or different (in which case what?). The atoms are *not constant* in mass.. The number of atoms _is_ the mass, silly. It follows from the definition of mass. Only from Chambers, and it should hopefully be clear that this is an over simplistic definition. Which we should replace by what exactly? |
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The Natural Philosopher wrote:
Norman Wells wrote: The Natural Philosopher wrote: According to my Dictionary of Science and Technology, which is the only _definition_ that's been provided in this thread, it's 'the quantity of matter in a body'. As such, it _is_ a measure of the number of elementary particles. It cannot be otherwise. http://math.ucr.edu/home/baez/physic...y/SR/mass.html If you can understand beyond the first word. Oh yes. So, what definition are you using then? I am not. In that case, you fall at the first hurdle. You cannot base any argument on 'mass' if you don't know what it means. |
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The Natural Philosopher wrote:
Norman Wells wrote: John Rumm wrote: Norman Wells wrote: times to provide the definition of mass that you use and give its source and, every time, you have been unable to do so. Now you're asking us to How about: "The mass of a body is a measure of its energy-content; if the energy changes by L, the mass changes in the same sense by L/ 9x10^2^0, the energy being measured in ergs, and the mass in grammes". [A. Einstein, 27/09/1905, http://www.fourmilab.ch/etexts/einstein/E_mc2/www/ ] That's not a definition at all. If I say "A pound is a measure of the weight of a body" does that define what a pound is? can be, if you define body and weight. However it would be a wrong definition: A definition though. Maybe English isn't your first language then? The number of atoms _is_ the quantity of matter in a body. It is composed of nothing else. Well that is a very very thin-ice statement. Many models would say that it was a lot more than that. It certainly isn't enough to shake a random bunch of atoms in a bag and say 'look, garlic sausage' It is, however, what they consist of. Entirely. The fact that a bag of atoms does not spontaneously form a garlic sausage in fact supports my argument, not yours. That must mean that it's a direct measure of the number of atoms the body contains, since all matter is composed of atoms. From that it follows that, however hot any amount of something is, it has exactly the same mass as it always had, because it always contains the same number of atoms. Whose mass varies slightly with temperature. No it doesn't. According to the only supported definition of mass that we have here, ie the one from Chambers Dictionary of Science and Where does this assertion that Chambers Dictionary of Science and Technology is the only supported definition come from? Find me another. WE have. Half a dozen now. But it seems that because you are a thick ****, the only one you can understand, is the Chambers. Presumably written by thick ****s for thick ****s. You don't understand what a definition is, so you wouldn't recognise one if it bit you on the bum. I've been referred to book after book, article after article, but still no-one will state the definition _they_ use of something so basic and fundamental as 'mass'. And without that, they cannot sustain any valid argument. It's all waffle, shifting sand, smoke and mirrors. Technology, mass is 'the quantity of matter in a body'. Unless you increase the quantity of atoms in a body you cannot increase its mass. That's logic, see? Logic indeed. However if you start from a flawed baseline, any logical derivation from it can't hope to be right can it? For any typical human interaction with the world around us, the notion that mass is "the quantity of matter in a body" is adequate. However you need to also accept its only an approximation to the reality. So, what is mass, according to you? Energy. Bound energy. Is 'bound energy' a subset of energy? How is it related to 'energy'? What are the differences that differentiate it from other forms of energy? If you maintain, contrarily, that the number of atoms increases with heating, I never said that. You can't be saying anything else if you say that mass increases with heating. You can, if you accept that the mass of atoms changes and that you reject the concept that mass is defined purely as the number of atoms you have. If you start from the baseline that mass is defined by the combined effect of both their number, and their embodied energy, then it is quite easy. But you haven't started from anywhere. You haven't defined mass. See Godel. you can split the world into related bits, and design a system, that is self consistent, but as to whether the initial splitting is meaningful..no one can say. You're not a Jehovah's Witness are you? |
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Switch off at the socket?
Norman Wells wrote:
See Godel. you can split the world into related bits, and design a system, that is self consistent, but as to whether the initial splitting is meaningful..no one can say. You're not a Jehovah's Witness are you? A bit of a cheek, but what are your academic credentials, Norman? Just out of interest, not being sarcastic here. |
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