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10th November 2012, 06:12 AM | #441 |
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Thinking about this Mister Earl, I think it might be more revealing to ask the question "Why do we expect every other particle to be massless and need something to stop them being so?"
The answer to that boils down to wanting to keep gauge invariance, which it's going to be more useful to google yourself or have someone else explain than me. http://profmattstrassler.com/article...eld-were-zero/ is also a useful and well written article I think. |
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10th November 2012, 06:14 AM | #442 |
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Thanks!
True. We're discussing Farsight's posts rationally instead of just accepting what he tells us. Which is why we'd have been surprised if anyone but Farsight had reponded to the robust case being made against his ideas by trying to shut down his challengers: Farsight's beliefs must be religious, because he regards the Catholic church as his main competitor: And then there's this: We've been straight with Farsight. When he's made mistakes that a physicist would spot immediately, everybody points it out. Everybody says sorry Farsight, you're wrong. If Farsight's knowledge of physics were to improve, he might start to notice this kind of thing, and come to appreciate it. |
10th November 2012, 06:22 AM | #443 |
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They're two different measurements of the same thing. Think of the cannonball example. It's travelling at 1000m/s and you apply a constant braking force. Kinetic energy is a distance-based measure of how difficult it is to stop the cannonball. Momentum is a time-based measure of how difficult it is to stop the cannonball. Momentum is directional too, and is a vector rather than a scalar like displacement is a vector whilst distance is a scalar. Note though that the cannonball didn't actually have negative momentum.
The quantities aren't, but they're just different aspects of energy-momentum, see wikipedia. |
10th November 2012, 06:33 AM | #444 |
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I would like to say thanks to all those who educate and clarify in this thread!
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10th November 2012, 06:43 AM | #445 |
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10th November 2012, 07:22 AM | #446 |
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My highlighting:
Okay. I take two different measurements of the cannonball. One measurement tells me its mass is about 19 kilograms. The other measurement tells me its diameter is about 17 centimeters. Those measurements are related (by the density of iron), but they don't imply that mass is exactly the same thing as diameter. That Wikipedia article supports my point to the detriment of yours. It takes momentum as a scalar quantity (the magnitude of vector momentum), but it doesn't say energy and momentum are exactly the same thing. In fact, the article includes several equations from which it is trivial to prove that energy and momentum aren't exactly the same thing. Here's the first of those equations: E2 = m2c4 + p2c2If the energy E were exactly the same thing as the scalar momentum p, then we could substitute one for the other in that equation: E2 = m2c4 + E2c2from which it would follow that the energy E is always the square root of m2c4/(1-c2), which would mean the cannonball's energy depends only upon its mass. Unless you want to argue that the cannonball's energy is independent of its velocity, its energy can't be exactly the same as its scalar momentum. Maybe you were trying to argue that energy is the same as scalar momentum multiplied by the speed of light. If so, we can repeat the above calculation to get this: E2 = m2c4 + E2Unless you want to argue that every cannonball has zero mass, that interpretation doesn't work either. When citing Wikipedia articles that refute your argument is the best you can do, your argument is laughable. As everyone who knows anything about physics has been trying to tell you: Energy and momentum are related, but they aren't the same thing. |
10th November 2012, 07:36 AM | #447 |
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This is what is said, see for example this CERN webpage. But note that it isn't part of Big Bang cosmology, so much as part of the Higgs hypothesis. See for example this NASA page re the big bang.
No. The Higgs mechanism is only though to be responsible for 1% of the mass of matter, so if you take some body such as a bowling ball, then 99% of its mass is due to its energy content. If instead you took a body that consisted of a box, and you filled it with radiation, then 100% of the added mass is due to the added energy content. I'm afraid it is incompatible. The box doesn't diminish the kinetic energy of the radiation within it. The radiation bounces around inside, and the box hides the kinetic energy. When you learn about pair production and electrons and atomic orbitals where "exist as standing waves" and the Febry-Perot cavity, you realise that the electron is just another "body". |
10th November 2012, 07:42 AM | #448 |
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10th November 2012, 08:14 AM | #449 |
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It does Robo. When you drop the book, its kinetic energy doesn't appear because of some kind of spring mechanism. Have a look around at "potential energy is kinetic energy". Or work it through with a photon in a gedanken box. The massless photon adds mass to the system, and like Susskind, we say the box itself has negligible mass which we can safely ignore. When you raise the box up to the shelf, you add more energy to that system. Take two identical boxes, one on the floor and one on the shelf, and open them. Each is a radiating body losing mass, and you find that more kinetic energy is delivered by the upper photon. When it was in the box you couldn't see this extra kinetic energy, and called it potential energy. But all you ever had in the box was photon kinetic energy. Use the wave nature of matter to step up from a photon-in-a-box to a book.
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10th November 2012, 08:18 AM | #450 |
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10th November 2012, 08:27 AM | #451 |
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In an attempt to justify your claims you invent another thought experiment. When it is pointed out to you that your interpretation of your thought experiment is wrong you invent another thought experiment (and pretend it is the same one). This is not the sign of someone with a cogent argument.
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10th November 2012, 08:47 AM | #452 |
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Thanks edd.
Maybe your post had the quotes around the wrong thing? E=hf contains the h term, which is the constant of action, and action has the same dimensionality as angular momentum. I know plenty, edd. Electromagnetic waves exhibit spin angular moment which is quantized ±ħ, and can also exhibit orbital angular momentum which isn't quantized. |
10th November 2012, 08:52 AM | #453 |
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No. It is said that particles acquire mass by interacting with the Higgs field. The Higgs boson is said to be an excitation of that field.
All the way down. What they don't say is how the Higgs boson has a mass of 125GeV, they gloss over the fact that the Higgs mechanism is said to be responsible for only 1% of the mass of matter, that the LHC ingredients were protons and kinetic energy, and that the inertia of a body depends upon its energy content. |
10th November 2012, 08:54 AM | #454 |
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In order to understand and gain a deep appreciation of the necessary difference between energy and momentum, a study of Hamiltonian mechanics would be very enlightening.
But then -- that's real physics. |
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10th November 2012, 09:04 AM | #455 |
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I don't have a problem with it, I just recognise that the negative sign is merely a convention of measure. Think about it this way: if a 1kg cannonball is motionless with respect to you, you'd say it has zero momentum. If it's moving at 100m/s in some direction relative to you, coming right at you, it doesn't. But you don't say "That's OK, I'll just stand here. That cannonball has got less than zero momentum. It can't do me any harm".
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10th November 2012, 09:21 AM | #456 |
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That's a straw-man, Clinger, and you know it. We were talking about a cannonball in space with a given mass and a given motion relative to you. You apply a constant braking force to bring it to a halt, and you say its momentum is defined in terms of force x time whilst its kinetic energy is defined in terms of force x distance. But the cannonball does not have two two totally different properties called momentum and kinetic energy. You cannot remove one without removing the other. That's why in physics we talk of energy-momentum.
Of course not. I didn't either. I said they're two different measures of energy-momentum. See my response to edd above re negative momentum. Don't put words in my mouth. It doesn't refute what I said. It only refutes what you tried to pretend I said. Come on Clinger, you're going to have to do better than that. |
10th November 2012, 09:21 AM | #457 |
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I might prefer to think of it in a more appropriate manner then, Farsight.
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10th November 2012, 09:26 AM | #458 |
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With the exception of RC's posts from a few days back, I've caught up. But right now, I've got to go. Do let me know if there's anything I've missed.
ETA: noted edd. Negative signs can be misleading at times. I think binding energy is a case in point. |
10th November 2012, 09:30 AM | #459 |
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10th November 2012, 10:59 AM | #460 |
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I don't know why Farsight thinks he can get away with denying his own words, but I guess that's the best argument he has left.
Ho ho ho. Here's exactly what you said: Now you're claiming to have said they're "two different measures of energy-momentum." Make up your mind, Farsight. Are they two different things, or are they not two different things? It may not refute what you're now trying to pretend you said, but it refutes exactly what you did say. |
10th November 2012, 11:11 AM | #461 |
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10th November 2012, 11:18 AM | #462 |
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Tis seems a bit more like a counter example than a straw man.
He did not say they were "totally different" in fact he noted that they were related by the density of iron. But to clarify, lets take your claim that you cannot remove one without the removing the other, all we need do is find a case where energy is more than kinetic energy: Fire the cannon straight up on the moon (to remove air resistance) When it leaves the mussel mv and 1/2 mv^2 are related. At the top of its trajectory, it has the same energy, but zero momentum. Does this not count as changing one without changing the other? |
11th November 2012, 03:52 AM | #463 |
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I'm not denying my own words. And please, if you're going to link to my words, do link to my post instead of yours.
Yep. Shall we have a look at what I did say in post 417? Here we go: "Energy and momentum aren't two different things. They're just two different aspects of the same thing. Think of a cannonball in space travelling at 1000m/s. Try stopping it in a second. You exert a constant opposing force. In the first tenth of a second it pushes you back a long way. In the next tenth it pushes you back a lesser distance, and so on. After 0.5 seconds the distance you've gone is less than the distance you're going to go. That's where the KE=½mv² comes from. There's an integral in it, and it's a way of describing the stopping distance for a given force applied to a given "mass" moving at a given speed. Momentum however is a force x time measure. After 0.5 seconds you're halfway through the stopping time, so it's a linear p=mv. They're two different measures of something very real, not two different abstract quantities conserved by the invariant laws of physics. And like I said, it's called energy-momentum for a reason." Neither. I made it clear enough. They're two different aspects of the same thing. They're two different measures of energy-momentum. No it doesn't. What I said refutes what you're saying. Now do please try to make a sensible contribution to the discussion Clinger. |
11th November 2012, 04:18 AM | #464 |
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Noted, lenny.
No. When we fire the cannonball straight up, it's slowing down due to gravity. When it reaches its maximum height it's momentarily motionless. At that moment it isn't moving. So it has zero kinetic energy and zero momentum. Conservation of energy means that the kinetic energy hasn't mysteriously vanished, it's now potential energy, which is in the cannonball. In previous posts I've referred to this as "hidden kinetic energy", but it's hidden momentum too. The thing that's hiding is energy-momentum, and it makes the cannonball's mass increase a little. In similar vein its mass increases a little when you heat it up. |
11th November 2012, 04:49 AM | #465 |
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Conservation of energy does mean the kinetic energy has vanished (at least in that reference frame). In fact that is exactly what the first law of thermodynamics has told us.
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11th November 2012, 05:09 AM | #466 |
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Sorry, Farsight, but when I'm addressing only one of your mistakes, clarity is served by linking to my own post in which I quote you committing that one specific mistake instead of linking to the multitude of mistakes to be found within your entire rambling post.
ETA: Readers who want to slog through your entire post can do so by clicking on the link provided by my quotation of your post. So your argument is based upon equivocation: When you find it convenient to say energy and momentum are not different things, you conflate them. When called on it, you deny having said they are not different things. The readers of this thread can and will decide for themselves whose contributions have been sensible. When the core of your argument is equivocation, as when you say energy and momentum are "neither" different things nor not different things, your argument is not sensible. |
11th November 2012, 05:11 AM | #467 |
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11th November 2012, 05:32 AM | #468 |
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Am I losing my mind or did a bunch of posts disappear? I distinctly remember responding to Farsight's last response to me, and reading his response to that.
Originally Posted by Farsight
For example: An electron has, due to the Higgs mechanism, a rest-mass of 0.511MeV/c^2. That means that even when it is not moving its inertial-mass is 0.511MeV/c^2. But when it's not moving its total energy is 0.511MeV. So its inertia is proportional to its energy content. As it speeds up it gains energy. An electron moving at 0.8c would have a total energy of about 0.851MeV. That's about 0.340MeV of kinetic energy on top of its rest-mass energy equivalence of 0.511MeV. In this case the electron's total inertial-mass is 0.851MeV/c^2. So its inertia is still proportional to its energy content. So where is the principle of inertia depending on energy content being violated? The Higgs mechanism just puts a non-zero value on the minimum energy that a particle can have (which obtains when the particle is not moving). It doesn't change the relationship between inertia and total energy at all. It does change the relationship between inertia and kinetic energy. But as I explained before, that in no way violates E=mc^2.
Originally Posted by Farsight
E_t = m_ic^2: Here E_t is the total energy, and m_i is the inertial mass. E_r = m_rc^2: Here E_r is total energy of the particle when it is at rest (the energy equivalent of its rest-mass), and m_r is its rest-mass. And this is the critical point: If you solve for E=mc^2 with m=rest_mass then what you get for E is not the the total energy of the particle. It is just the rest_energy. And if you solve for E=mc^2 with E=total_energy of the particle then what you get for m is not the rest_mass of the particle. It is the total inertial_mass of the particle.
Originally Posted by Farsight
Likewise, annihilation is always into two photons. Again, going to the inertial frame where the combined momentum of the electron and positron is zero, the combined momentum of the two photons will also be zero. And of course their total energy as measured from that frame will be equal to 1.022MeV plus the combined kinetic energy of the electron and positron. So no, there is no flip-flop between mass and momentum. Momentum is always conserved. There is a flip-flop between rest-energy and kinetic-energy.
Originally Posted by Farsight
Inertial mass is proportional to total energy. Rest mass of some particles is affected by the Higgs mechanism. If a particle has nonzero rest mass due to interaction with the Higgs field, that does not contradict the fact that its inertial mass is proportional to its total energy. I suppose you might think it would if you did not understand that a particle's rest energy is proportional to its rest mass. But then it would be you contradicting E=mc^2. Or at least misunderstanding it. |
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11th November 2012, 05:46 AM | #469 |
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This seems to be Farsight's basic confusion. Inertia indeed depends on energy content, as Einstein taught us. But energy content depends on all sorts of things, including interactions with fields that pervade the universe.... and therefore inertia depends on interactions with fields that pervade the universe.
Pretty simple, really. |
11th November 2012, 06:00 AM | #470 |
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11th November 2012, 06:16 AM | #471 |
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He means mass, I think.
In the Higgs mechanism, an electron at rest has energy E that comes from its interaction with the Higgs field. Since m=E/c^2 the electron therefore has a non-zero mass, and hence inertia (when you act on it with a force F, its acceleration is F/m). |
11th November 2012, 06:38 AM | #472 |
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11th November 2012, 10:23 AM | #473 |
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Read Einstein's 1905 paper. Note "the mass of a body is a measure of its energy-content". No way is that in any way compatible with "the mass of a body is a measure of its interaction with a space-pervading field".
Not proportional to its energy content. Is a measure of its energy content. Is still a measure of its energy content. Where it's replaced by something else. It doesn't actually do that. I mentioned binding energy yesterday. When an electron binds with a proton, in the 1s orbital there's a 13.6ev mass deficit. The system has less mass/energy than the individual components at rest. It casts it aside Stimpson. Imagine you have a photon in a gedanken mirror-box. The mass of the box is so negligible that we can ignore it, like Susskind said in the lecture Robo linked to. The photon adds mass to that system, and like Susskind said about his box of radiation, it's got nothing to do with the Higgs mechanism. The box is a body, its inertia depends upon its energy content, its mass is a measure of its energy content. When it radiates, its mass is reduced. The electron is a body too. When it radiates in annihilation, its mass is reduced to nothing and it no longer exists. It would violate what Einstein said to assert that the mass of some bodies is a measure of the energy content, and the mass of some other bodies isn't. See this bit of wiki and note the quote at the bottom: "It is better to introduce no other mass concept than the ’rest mass’ m". I know about rest mass and inertial mass. I know this too. Check around and you'll see that I'm forever saying +1022keV. And that. I assume you meant two or more photons, see this. Yes there is. You aren't paying enough attention to energy-momentum and you're being led astray by the vector-quantity aspect of momentum. Take a look at energy-momentum relation on wikipedia. See where it says the equation simplifies to E=mc² for a body in its rest frame. Then a bit lower down it says if the object is massless then the energy momentum relation reduces to E=pc as is the case for a photon. Two photons each have momentum p=hf/c. When you insist that one has negative momentum, countering the positive momentum of the other, E=pc or E=hf and p=hf/c then forces you to claim that E is negative. It isn't. It's like what I was saying to edd about the cannonball. It's got no momentum if its sitting there in front of you, but if it's coming at you, it has. It doesn't matter if you say it's got positive momentum when it's coming at you this way → and negative momentum coming at you this way ←. It only has negative momentum in a book-keeping sense. You know you can't stop that cannonball in -5 seconds. You know you're going to have to duck. It isn't nonsense Stimpson. That's where the buck stops. When you say the inertia of a body doesn't depend upon its energy content but instead depends on that body's interaction with the Higgs field, you've contradicted Einstein. Einstein said the mass of a body is a measure of its energy-content. Not something else. So when you assert that the mass of a body is a measure of its interaction with the Higgs field, you're contradicting Einstein. I'm not misunderstanding it. I've bought the T-shirt. And it says E=mc² not E∝m. |
11th November 2012, 10:42 AM | #475 |
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Poor old Einstein. I'm sure he wouldn't have the sort of problem with the Higgs mechanism that you suggest - this sort of interaction with a field was surely not something he was thinking about when he wrote what you quote so often above. That he apparently omitted something does not mean that he intentionally excluded it.
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11th November 2012, 10:45 AM | #476 |
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I'm not confused at all sol.
At last! Somebody else has paid attention to what Einstein actually said. Energy content depends on how much energy you put in. Sounds like you've got a basic confusion there sol. |
11th November 2012, 10:58 AM | #477 |
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You may well not be confused. In that case you are just plain wrong.
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I start with a million dollars. I buy a house worth 511,000 dollars. I'm left with a house and 489,000 dollars. The cost of the house was set by the realtor and determined by the size location and so on of the property. I start with a million electron volts. From that million electron volts I create an electron (using some magical process). I'm left with an electron and 489,000 electron volts. The energy "cost" of the electron was determined by it's rest mass which is determined by how the particle interacts with the Higgs field. |
11th November 2012, 11:09 AM | #478 |
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That's a handy way to try and dismiss Einstein. Assert that he wouldn't have a problem with something that totally contradicts him.
I'm sure Einstein would have a big problem with it. He would reiterate that mass is a measure of energy-content, not something else. He'd point out that the LHC ingredients were protons and kinetic energy. He'd remind you how a massless photon in a box adds mass to that system. Then he'd point out that when a wave is propagating linearly at c we call its resistance to change-in-motion momentum. But when it's a standing wave in a box we call its resistance to change-in-motion inertia. Then he'd be pointing out that an electron is a body, and likening electron-positron annihilation to a radiating body losing mass, and showing you atomic orbitals where electrons exist as standing waves. And when you dismissed all that too, he would push his chair back, say ho ho ho in his rich deep voice, and show you the door. |
11th November 2012, 11:12 AM | #479 |
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If I have a photon with momentum p2 (a vector) it will have energy E=|p2|c - a positive number times a positive number. The combined energy of the system is then |p1|c + |p2|c (a positive scalar) while the combined momentum is p1 + p2 (a vector). If the two momentum vectors are of equal magnitude and antiparallel then p2 = - p1 and the combined momentum is p1 - p1 = 0. However, the total energy is |p1|c + |p1|c = 2|p1|c (a positive scalar). |
11th November 2012, 11:25 AM | #480 |
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It doesn't totally contradict him. That is your assertion based on not understanding Einstein and particle physics.
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