I need help calculating the impact speed of a positron and electron starting at 5 cm apart
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From: franklinhu on 12 May 2010 16:12 On May 12, 2:21 am, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > On May 12, 3:44 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > > > On May 10, 1:12 pm, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > > > On May 10, 2:38 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > Let's say we have a positron and electron at rest with respect to each > > > > other. Since they are oppositely charged, they are immediately > > > > attracted to each other and begin to accelerate toward each other. At > > > > any point in the path, you can calculate the force between them using > > > > Columbs law, based on that, you could calculate the acceleration, but > > > > how do you calculate what would be the velocity of the positron and > > > > electron as they approach each other and then collide from some > > > > starting distance like 5cm? As distance approaches zero, the force > > > > approaches infinity. Does this mean that the velocity may approach > > > > infinity due to the infinite force acting on a mass or is there some > > > > limiting mechanism? Please help? > > > > (1) The classical physics of charged point particles is broken. > > > What do you mean by 'broken'. Do you mean that they don't apply due to > > unknown reasons or because they simply don't apply for a specific > > reason. Or do you mean that the physics in this area is generally > > broken and you cannot solve this problem at all using all that modern > > physics has avaliable. I would find that hard to believe since the > > positron / electron collision must have been studied to death. > > Basically, point (3) below. A classical point charge has infinite > energy in its field, and infinite inertia as a consequence. That isn't > quite the whole problem, but it's a central problem. See M. Frisch, > "Inconsistency, asymmetry, and non-locality: A philosophical > investigation of classical electrodynamics", OUP 2005. (For a good > look at what you can do in practice despite this - if you're happy > with renormalisation, see F. Rohrlich, "Classical charged particles", > 3E, World Scientific 2007.) > > > > > > > > (2) If they were charged point particles of mass m_e (i.e., the > > > electron mass), then the velocity would approach infinity. PE -> KE > > > and all that. > > > Really???? You are saying that theoretically, the velocity would > > indeed approach infinity if there are no other limits? I tried doing a > > calculation, and as you get closer, the amount you can acclerate > > decreases. It seemed accleration was limited by the initial starting > > distance, but that didn't make any sense either, so I think I got the > > calculation wrong. > > > However, I think that we could safely put a cap on the speed at being > > the speed of light. Nothing should go faster than that. So if what you > > are saying is correct, we could presume that at some point, the > > electron and positron will attain the speed of light at some point and > > then go no faster. > > With classical mechanics, you get speed -> infinity. With relativistic > mechanics, you have speed -> c. Either way, infinite kinetic energy. > > Sounds like your attempted calculation was wrong. For an inverse- > square force, the KE goes to infinity. For other force laws, you can > get infinity, or some finite amount (which will depend on the starting > distance). > > > > (3) A classical charged point particle, in the absence of > > > renormalisation, has infinite inertia so they'd never move towards > > > each; they'd just sit there with their infinite masses. (Yes, a > > > theoretical result, but surely this is OK since classical point > > > particles are purely theoretical entities.) > > > Yes, this is the point made by other posters in that if there is no > > limit to how small an increment you could consider, then the positron/ > > electron would never reach eachother. > > No, this isn't that same point at all. If they have infinite inertia, > they never accelerate towards each other at all, if the force is short > of infinite. This isn't what we see. Worse, the observed upper limit > to the size of the electron means a classical mass much greater than > what we observe. Thus, point (1). > > > But, we know that they do > > eventually reach each other to annihillate, so this is not a > > reasonable conclusion. > > > > (4) What do you get for a classical electron, of the classical > > > electron radius, colliding with a classical positron, also of the > > > classical electron radius? Don't start at 5cm away; start an infinite > > > distance away and use PE -> KE. Ignore radiative reaction. > > > Well if you plug into the PE formula KQq/r where r= 2.8E-15, you get > > 8.22E-14 Joules > > > Curiously, this is nearly identical to the E=mc^2 formula which works > > out to 8.19E-14 Joules > > Not a coincidence. The classical electron radius is the radius that > gives you the energy that gives you the observed inertia. > > We know the electron is smaller than this. Again, see point (1) above. > When you get to near this point, you need to be very careful when > trying to use any classical result for point electrons. The safe > approach is to not trust classical results. > > (As a technical nitpick, note that if you do this calculation for an > electron-positron pair, they can only approach to within 2 r_e before > they hit.) > > > > (5) When theory fails, resort to the real world. What happens to the > > > kinetic energy of an electron and positron when they annihilate? > > > Compare the energy of the emitted gammas to the initial rest energy. > > > The difference is what the KE was. How does this compare with the > > > result from (4). It's certainly much less than the result from (2). > > > OK, we know that in the real world, the energy of the emitted gammas > > is 8.19E-14 Joules. > > > We know that the calculated kinetic energy of collsion should be > > around 8.22E-14 Joules. > > No, we know that at this point, our classical calculations are wrong. > Don't depend on calculations that we _know_ are wrong. Use > measurements. Observed energy of annihilation gammas - rest energy of > electron and positron = KE. Want higher energy photons? Just use > higher speed (therefore higher KE) electrons and positrons. > I think your point was that classical calculations must fail because of the infinities you get as you get arbitrarily close together. But, I am not talking about getting arbitrarily close together, I am talking about only getting as close as the classical electron radius of 2.18E-15 which is a relatively 'large' distance. It is larger than the sizes of most atomic nucleus and is really a surprisingly far distance on the atomic scale. So, since there are no infinites at a fixed distance, I don't see why we wouldn't be able to depend on those calculations, especially when using such comparitively large distances for the calculations. If I do the calculations you suggest, we have the observed energy 8E-14 joules - rest energy = 8E-14 which leaves us with a resultant KE of ZERO. Isn't this saying that the kinetic energy of the impact is zero???? How can that be? We know that the positron / electron are strongly attracted to each other. There has got to be some non-zero kinetic energy from just the impact. If KE is zero, then somehow the positron/electron would have to slow down and then stop before annihillation. I would find that hard to believe. The KE of the impact should be closer to what we calculated which is 8E-14 I would still find it easier to believe that the positron and electron are acclerated to light speed and they reach this speed when they are 2.8E-15m apart. When they finally collide, they release their kinetic energy of 8E-14 joules into the environment in the form of gamma rays. If you find this harder to believe, then please explain how matter is 'converted' to energy in a positron/electron annhililation event. Isn't it a gigantic (drive a truck through this one) hole that this cannot be explained? > [cut] > > > So what is the answer to this mystery.... I'll give you a moment to > > think about it... > > > I don't know about you, but I would think the logical conclusion would > > be that what we think is the energy released in the annihillation > > event, is really just the release of the kinetic energy from the > > collision of the positron and the electron. > > > Before you go nahhhhh, can't be ... think about it. We just made a > > legitimate calculation of the kinetic energy of a positron/electron > > collision. > > No, we know it isn't legitimate. We know it's wrong. > > > It just happens to be by pure coincidence, the same as the > > E=mc^2 formula eventhough the format and numbers of the PE formula and > > E=mc^2 forumulas look nothing alike and you'd think there would be no > > relationship. I just made that calculation while writing this post, > > and there can be no better 'AH-HA!!' moment than that to see both > > numbers line up. > > No pure coincidence at all, the classical radius is chosen to achieve > this. (Seehttp://en.wikipedia.org/wiki/Classical_electron_radiusfor some > details.) > > Don't get too carried away by this "coincidence". Remember (a) > measurements work, so use them to find the KE before collision, and > (b) the electron is not a billiard ball with a radius equal to the > classical electron radius.- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -
From: PD on 12 May 2010 16:18 On May 12, 3:12 pm, franklinhu <frankli...(a)yahoo.com> wrote: > On May 12, 2:21 am, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > > > On May 12, 3:44 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > On May 10, 1:12 pm, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > > > > On May 10, 2:38 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > > Let's say we have a positron and electron at rest with respect to each > > > > > other. Since they are oppositely charged, they are immediately > > > > > attracted to each other and begin to accelerate toward each other.. At > > > > > any point in the path, you can calculate the force between them using > > > > > Columbs law, based on that, you could calculate the acceleration, but > > > > > how do you calculate what would be the velocity of the positron and > > > > > electron as they approach each other and then collide from some > > > > > starting distance like 5cm? As distance approaches zero, the force > > > > > approaches infinity. Does this mean that the velocity may approach > > > > > infinity due to the infinite force acting on a mass or is there some > > > > > limiting mechanism? Please help? > > > > > (1) The classical physics of charged point particles is broken. > > > > What do you mean by 'broken'. Do you mean that they don't apply due to > > > unknown reasons or because they simply don't apply for a specific > > > reason. Or do you mean that the physics in this area is generally > > > broken and you cannot solve this problem at all using all that modern > > > physics has avaliable. I would find that hard to believe since the > > > positron / electron collision must have been studied to death. > > > Basically, point (3) below. A classical point charge has infinite > > energy in its field, and infinite inertia as a consequence. That isn't > > quite the whole problem, but it's a central problem. See M. Frisch, > > "Inconsistency, asymmetry, and non-locality: A philosophical > > investigation of classical electrodynamics", OUP 2005. (For a good > > look at what you can do in practice despite this - if you're happy > > with renormalisation, see F. Rohrlich, "Classical charged particles", > > 3E, World Scientific 2007.) > > > > > (2) If they were charged point particles of mass m_e (i.e., the > > > > electron mass), then the velocity would approach infinity. PE -> KE > > > > and all that. > > > > Really???? You are saying that theoretically, the velocity would > > > indeed approach infinity if there are no other limits? I tried doing a > > > calculation, and as you get closer, the amount you can acclerate > > > decreases. It seemed accleration was limited by the initial starting > > > distance, but that didn't make any sense either, so I think I got the > > > calculation wrong. > > > > However, I think that we could safely put a cap on the speed at being > > > the speed of light. Nothing should go faster than that. So if what you > > > are saying is correct, we could presume that at some point, the > > > electron and positron will attain the speed of light at some point and > > > then go no faster. > > > With classical mechanics, you get speed -> infinity. With relativistic > > mechanics, you have speed -> c. Either way, infinite kinetic energy. > > > Sounds like your attempted calculation was wrong. For an inverse- > > square force, the KE goes to infinity. For other force laws, you can > > get infinity, or some finite amount (which will depend on the starting > > distance). > > > > > (3) A classical charged point particle, in the absence of > > > > renormalisation, has infinite inertia so they'd never move towards > > > > each; they'd just sit there with their infinite masses. (Yes, a > > > > theoretical result, but surely this is OK since classical point > > > > particles are purely theoretical entities.) > > > > Yes, this is the point made by other posters in that if there is no > > > limit to how small an increment you could consider, then the positron/ > > > electron would never reach eachother. > > > No, this isn't that same point at all. If they have infinite inertia, > > they never accelerate towards each other at all, if the force is short > > of infinite. This isn't what we see. Worse, the observed upper limit > > to the size of the electron means a classical mass much greater than > > what we observe. Thus, point (1). > > > > But, we know that they do > > > eventually reach each other to annihillate, so this is not a > > > reasonable conclusion. > > > > > (4) What do you get for a classical electron, of the classical > > > > electron radius, colliding with a classical positron, also of the > > > > classical electron radius? Don't start at 5cm away; start an infinite > > > > distance away and use PE -> KE. Ignore radiative reaction. > > > > Well if you plug into the PE formula KQq/r where r= 2.8E-15, you get > > > 8.22E-14 Joules > > > > Curiously, this is nearly identical to the E=mc^2 formula which works > > > out to 8.19E-14 Joules > > > Not a coincidence. The classical electron radius is the radius that > > gives you the energy that gives you the observed inertia. > > > We know the electron is smaller than this. Again, see point (1) above. > > When you get to near this point, you need to be very careful when > > trying to use any classical result for point electrons. The safe > > approach is to not trust classical results. > > > (As a technical nitpick, note that if you do this calculation for an > > electron-positron pair, they can only approach to within 2 r_e before > > they hit.) > > > > > (5) When theory fails, resort to the real world. What happens to the > > > > kinetic energy of an electron and positron when they annihilate? > > > > Compare the energy of the emitted gammas to the initial rest energy.. > > > > The difference is what the KE was. How does this compare with the > > > > result from (4). It's certainly much less than the result from (2). > > > > OK, we know that in the real world, the energy of the emitted gammas > > > is 8.19E-14 Joules. > > > > We know that the calculated kinetic energy of collsion should be > > > around 8.22E-14 Joules. > > > No, we know that at this point, our classical calculations are wrong. > > Don't depend on calculations that we _know_ are wrong. Use > > measurements. Observed energy of annihilation gammas - rest energy of > > electron and positron = KE. Want higher energy photons? Just use > > higher speed (therefore higher KE) electrons and positrons. > > I think your point was that classical calculations must fail because > of the infinities you get as you get arbitrarily close together. Actually, Franklin, they fail not so much because of the infinities, but because quantum effects kick in sooner than that. That starts to become important at around 1E-10m, a hundred thousand times larger than what you're talking about. > But, > I am not talking about getting arbitrarily close together, I am > talking about only getting as close as the classical electron radius > of 2.18E-15 which is a relatively 'large' distance. It is larger than > the sizes of most atomic nucleus and is really a surprisingly far > distance on the atomic scale. > > So, since there are no infinites at a fixed distance, I don't see why > we wouldn't be able to depend on those calculations, especially when > using such comparitively large distances for the calculations. > > If I do the calculations you suggest, we have the observed energy > 8E-14 joules - rest energy = 8E-14 which leaves us with a resultant KE > of ZERO. What are you using for electrostatic potential energy, Franklin? What is the change in electric potential energy going from infinity to the distance you're talking about? This should be algebraically no harder than calculating the speed of a rock that falls to the surface of the earth from the edge of the solar system, due to the gravitational force. Can you do that calculation? What's the difference in gravitational potential energy between the edge of the solar system and the surface of the earth? A high school student should know how to do this calculation. (Just keep in mind that this classical calculation is wrong, for the reason I mentioned.) > Isn't this saying that the kinetic energy of the impact is > zero???? How can that be? We know that the positron / electron are > strongly attracted to each other. There has got to be some non-zero > kinetic energy from just the impact. If KE is zero, then somehow the > positron/electron would have to slow down and then stop before > annihillation. I would find that hard to believe. > > The KE of the impact should be closer to what we calculated which is > 8E-14 > > I would still find it easier to believe that the positron and electron > are acclerated to light speed and they reach this speed when they are > 2.8E-15m apart. When they finally collide, they release their kinetic > energy of 8E-14 joules into the environment in the form of gamma rays. > > If you find this harder to believe, then please explain how matter is > 'converted' to energy in a positron/electron annhililation event. > Isn't it a gigantic (drive a truck through this one) hole that this > cannot be explained? > > > [cut] > > > > So what is the answer to this mystery.... I'll give you a moment to > > > think about it... > > > > I don't know about you, but I would think the logical conclusion would > > > be that what we think is the energy released in the annihillation > > > event, is really just the release of the kinetic energy from the > > > collision of the positron and the electron. > > > > Before you go nahhhhh, can't be ... think about it. We just made a > > > legitimate calculation of the kinetic energy of a positron/electron > > > collision. > > > No, we know it isn't legitimate. We know it's wrong. > > > > It just happens to be by pure coincidence, the same as the > > > E=mc^2 formula eventhough the format and numbers of the PE formula and > > > E=mc^2 forumulas look nothing alike and you'd think there would be no > > > relationship. I just made that calculation while writing this post, > > > and there can be no better 'AH-HA!!' moment than that to see both > > > numbers line up. > > > No pure coincidence at all, the classical radius is chosen to achieve > > this. (Seehttp://en.wikipedia.org/wiki/Classical_electron_radiusforsome > > details.) > > > Don't get too carried away by this "coincidence". Remember (a) > > measurements work, so use them to find the KE before collision, and > > (b) the electron is not a billiard ball with a radius equal to the > > classical electron radius.- Hide quoted text - > > > - Show quoted text -- Hide quoted text - > > > - Show quoted text - > >
From: Timo Nieminen on 12 May 2010 18:58 On Wed, 12 May 2010, franklinhu wrote: > > > I think your point was that classical calculations must fail because > of the infinities you get as you get arbitrarily close together. No, that wasn't my point. Classical calculations fail for a single point charge. Classical calculations fail for a single point charge in a uniform field. Classical calculations fail for two point charges a long way apart. > But, > I am not talking about getting arbitrarily close together, I am > talking about only getting as close as the classical electron radius > of 2.18E-15 which is a relatively 'large' distance. It is larger than > the sizes of most atomic nucleus and is really a surprisingly far > distance on the atomic scale. > > So, since there are no infinites at a fixed distance, I don't see why > we wouldn't be able to depend on those calculations, especially when > using such comparitively large distances for the calculations. You don't see a problem with the classical calculations when a classical point charge has infinite inertia? When a classical sphere of charge with inertia equal to the electron mass has a radius of the classical electron radius, which is far, far larger than the size of an electron (if an electron has "size")? This is where the classical theory of a _single_ point charge is broken. If it doesn't work for 1 charge, why do you expect it to work for 2? Go read Frisch and/or Rohrlich. There's also a respectable amount in Jackson, Classical electrodynamics, which is much easier to find a copy of. > If I do the calculations you suggest, we have the observed energy > 8E-14 joules - rest energy = 8E-14 which leaves us with a resultant KE > of ZERO. Isn't this saying that the kinetic energy of the impact is > zero???? How can that be? Look up some real observed energies. Of course if you look up the theoretical gamma energies for low-energy collisions, you find that the KE was low. Not necessarily zero, but small enough compared to the total energy that you lose it in the round-off. > We know that the positron / electron are > strongly attracted to each other. There has got to be some non-zero > kinetic energy from just the impact. If KE is zero, then somehow the > positron/electron would have to slow down and then stop before > annihillation. I would find that hard to believe. > > The KE of the impact should be closer to what we calculated which is > 8E-14 > > I would still find it easier to believe that the positron and electron > are acclerated to light speed and they reach this speed when they are > 2.8E-15m apart. When they finally collide, they release their kinetic > energy of 8E-14 joules into the environment in the form of gamma rays. So you might try to deduce from the classical calculation. But the classical calculation is wrong, so why try to deduce such things from it? What should the energy be? The ground state of positronium (i.e., electron + positron system) is only -6.8eV, as compared with over 1MeV rest energy of the electron + positron. Do you expect to see this much KE when doing calculations to 3 significant figures? (If you really want to learn what is known, learn what is known about positronium. If you're happy to just know that the classical calculation doesn't even go close to working, then you don't need to go into that stuff. If you want to know _why_ the classical calculation doesn't work, Frisch/Rohrlich/Jackson.) > If you find this harder to believe, then please explain how matter is > 'converted' to energy in a positron/electron annhililation event. > Isn't it a gigantic (drive a truck through this one) hole that this > cannot be explained? It isn't a gigantic hole. We observe the reverse process. If we can, given sufficient energy, create electron-positron pairs, what's wrong with the reverse? We observe creation, we observe annihilation, no problem, no gigantic hole. It might well be a mystery, and we might not be able to explain "how" in a manner that satisfies you, or "why" in a manner that satisfies you, but that's a different thing. -- Timo
From: franklinhu on 14 May 2010 16:48 On May 12, 1:18 pm, PD <thedraperfam...(a)gmail.com> wrote: > On May 12, 3:12 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > > > On May 12, 2:21 am, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > > > > On May 12, 3:44 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > On May 10, 1:12 pm, Timo Nieminen <t...(a)physics.uq.edu.au> wrote: > > > > > On May 10, 2:38 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > > > > > > Let's say we have a positron and electron at rest with respect to each > > > > > > other. Since they are oppositely charged, they are immediately > > > > > > attracted to each other and begin to accelerate toward each other. At > > > > > > any point in the path, you can calculate the force between them using > > > > > > Columbs law, based on that, you could calculate the acceleration, but > > > > > > how do you calculate what would be the velocity of the positron and > > > > > > electron as they approach each other and then collide from some > > > > > > starting distance like 5cm? As distance approaches zero, the force > > > > > > approaches infinity. Does this mean that the velocity may approach > > > > > > infinity due to the infinite force acting on a mass or is there some > > > > > > limiting mechanism? Please help? > > > > > > (1) The classical physics of charged point particles is broken. > > > > > What do you mean by 'broken'. Do you mean that they don't apply due to > > > > unknown reasons or because they simply don't apply for a specific > > > > reason. Or do you mean that the physics in this area is generally > > > > broken and you cannot solve this problem at all using all that modern > > > > physics has avaliable. I would find that hard to believe since the > > > > positron / electron collision must have been studied to death. > > > > Basically, point (3) below. A classical point charge has infinite > > > energy in its field, and infinite inertia as a consequence. That isn't > > > quite the whole problem, but it's a central problem. See M. Frisch, > > > "Inconsistency, asymmetry, and non-locality: A philosophical > > > investigation of classical electrodynamics", OUP 2005. (For a good > > > look at what you can do in practice despite this - if you're happy > > > with renormalisation, see F. Rohrlich, "Classical charged particles", > > > 3E, World Scientific 2007.) > > > > > > (2) If they were charged point particles of mass m_e (i.e., the > > > > > electron mass), then the velocity would approach infinity. PE -> KE > > > > > and all that. > > > > > Really???? You are saying that theoretically, the velocity would > > > > indeed approach infinity if there are no other limits? I tried doing a > > > > calculation, and as you get closer, the amount you can acclerate > > > > decreases. It seemed accleration was limited by the initial starting > > > > distance, but that didn't make any sense either, so I think I got the > > > > calculation wrong. > > > > > However, I think that we could safely put a cap on the speed at being > > > > the speed of light. Nothing should go faster than that. So if what you > > > > are saying is correct, we could presume that at some point, the > > > > electron and positron will attain the speed of light at some point and > > > > then go no faster. > > > > With classical mechanics, you get speed -> infinity. With relativistic > > > mechanics, you have speed -> c. Either way, infinite kinetic energy. > > > > Sounds like your attempted calculation was wrong. For an inverse- > > > square force, the KE goes to infinity. For other force laws, you can > > > get infinity, or some finite amount (which will depend on the starting > > > distance). > > > > > > (3) A classical charged point particle, in the absence of > > > > > renormalisation, has infinite inertia so they'd never move towards > > > > > each; they'd just sit there with their infinite masses. (Yes, a > > > > > theoretical result, but surely this is OK since classical point > > > > > particles are purely theoretical entities.) > > > > > Yes, this is the point made by other posters in that if there is no > > > > limit to how small an increment you could consider, then the positron/ > > > > electron would never reach eachother. > > > > No, this isn't that same point at all. If they have infinite inertia, > > > they never accelerate towards each other at all, if the force is short > > > of infinite. This isn't what we see. Worse, the observed upper limit > > > to the size of the electron means a classical mass much greater than > > > what we observe. Thus, point (1). > > > > > But, we know that they do > > > > eventually reach each other to annihillate, so this is not a > > > > reasonable conclusion. > > > > > > (4) What do you get for a classical electron, of the classical > > > > > electron radius, colliding with a classical positron, also of the > > > > > classical electron radius? Don't start at 5cm away; start an infinite > > > > > distance away and use PE -> KE. Ignore radiative reaction. > > > > > Well if you plug into the PE formula KQq/r where r= 2.8E-15, you get > > > > 8.22E-14 Joules > > > > > Curiously, this is nearly identical to the E=mc^2 formula which works > > > > out to 8.19E-14 Joules > > > > Not a coincidence. The classical electron radius is the radius that > > > gives you the energy that gives you the observed inertia. > > > > We know the electron is smaller than this. Again, see point (1) above.. > > > When you get to near this point, you need to be very careful when > > > trying to use any classical result for point electrons. The safe > > > approach is to not trust classical results. > > > > (As a technical nitpick, note that if you do this calculation for an > > > electron-positron pair, they can only approach to within 2 r_e before > > > they hit.) > > > > > > (5) When theory fails, resort to the real world. What happens to the > > > > > kinetic energy of an electron and positron when they annihilate? > > > > > Compare the energy of the emitted gammas to the initial rest energy. > > > > > The difference is what the KE was. How does this compare with the > > > > > result from (4). It's certainly much less than the result from (2). > > > > > OK, we know that in the real world, the energy of the emitted gammas > > > > is 8.19E-14 Joules. > > > > > We know that the calculated kinetic energy of collsion should be > > > > around 8.22E-14 Joules. > > > > No, we know that at this point, our classical calculations are wrong. > > > Don't depend on calculations that we _know_ are wrong. Use > > > measurements. Observed energy of annihilation gammas - rest energy of > > > electron and positron = KE. Want higher energy photons? Just use > > > higher speed (therefore higher KE) electrons and positrons. > > > I think your point was that classical calculations must fail because > > of the infinities you get as you get arbitrarily close together. > > Actually, Franklin, they fail not so much because of the infinities, > but because quantum effects kick in sooner than that. That starts to > become important at around 1E-10m, a hundred thousand times larger > than what you're talking about. OK, certainly if the distance is is 1E-10m, then the kinetic energy is about a thousanths of what it would be at 1E-15, which would probably be unmeasurable. But, just what are these quantum effects you are talking about, and why should they completely negate the attractive force between a positron and electron? I'm not just going to take your word for it, as I've never heard of any such thing. > > > But, > > I am not talking about getting arbitrarily close together, I am > > talking about only getting as close as the classical electron radius > > of 2.18E-15 which is a relatively 'large' distance. It is larger than > > the sizes of most atomic nucleus and is really a surprisingly far > > distance on the atomic scale. > > > So, since there are no infinites at a fixed distance, I don't see why > > we wouldn't be able to depend on those calculations, especially when > > using such comparitively large distances for the calculations. > > > If I do the calculations you suggest, we have the observed energy > > 8E-14 joules - rest energy = 8E-14 which leaves us with a resultant KE > > of ZERO. > > What are you using for electrostatic potential energy, Franklin? > What is the change in electric potential energy going from infinity to > the distance you're talking about? > Huh? Haven't you seen me make the calculation in the other posts? Its 8E-14 to a distance from infinity to 2E-15m. This is equivalent to the rest energy mass of the positon/electron. > This should be algebraically no harder than calculating the speed of a > rock that falls to the surface of the earth from the edge of the solar > system, due to the gravitational force. Can you do that calculation? > What's the difference in gravitational potential energy between the > edge of the solar system and the surface of the earth? A high school > student should know how to do this calculation. > > (Just keep in mind that this classical calculation is wrong, for the > reason I mentioned.) > > > > > Isn't this saying that the kinetic energy of the impact is > > zero???? How can that be? We know that the positron / electron are > > strongly attracted to each other. There has got to be some non-zero > > kinetic energy from just the impact. If KE is zero, then somehow the > > positron/electron would have to slow down and then stop before > > annihillation. I would find that hard to believe. > > > The KE of the impact should be closer to what we calculated which is > > 8E-14 > > > I would still find it easier to believe that the positron and electron > > are acclerated to light speed and they reach this speed when they are > > 2.8E-15m apart. When they finally collide, they release their kinetic > > energy of 8E-14 joules into the environment in the form of gamma rays. > > > If you find this harder to believe, then please explain how matter is > > 'converted' to energy in a positron/electron annhililation event. > > Isn't it a gigantic (drive a truck through this one) hole that this > > cannot be explained? > > > > [cut] > > > > > So what is the answer to this mystery.... I'll give you a moment to > > > > think about it... > > > > > I don't know about you, but I would think the logical conclusion would > > > > be that what we think is the energy released in the annihillation > > > > event, is really just the release of the kinetic energy from the > > > > collision of the positron and the electron. > > > > > Before you go nahhhhh, can't be ... think about it. We just made a > > > > legitimate calculation of the kinetic energy of a positron/electron > > > > collision. > > > > No, we know it isn't legitimate. We know it's wrong. > > > > > It just happens to be by pure coincidence, the same as the > > > > E=mc^2 formula eventhough the format and numbers of the PE formula and > > > > E=mc^2 forumulas look nothing alike > > ... > > read more »- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -
From: PD on 14 May 2010 17:46
On May 14, 3:48 pm, franklinhu <frankli...(a)yahoo.com> wrote: > > But, just what are these quantum effects you are talking about, and > why should they completely negate the attractive force between a > positron and electron? I'm not just going to take your word for it, as > I've never heard of any such thing. > Then you should probably read something about it. There are a number of things going on. First of all, the more transversely confined the electron, the less confined its transverse momentum will be. This means you will no longer be able to track its path along a radius to the proton. To see why, you need to explore the Heisenberg Uncertainty Principle and what that means for electrons in atoms. Secondly, the attractive force is not negated. It is in fact *responsible* for the nature of the allowed states of the electron. Nevertheless, at that size, everything is quantized, which means many of its physical properties can only take certain values -- and those are indexed by integers. No values in between occur in nature of those properties, and no value lower than the one corresponding to the integer 1. This introduces the idea of a ground state, where certain properties have a minimum, nonzero value but can go no lower. The idea of a ground state is absolutely key in quantum mechanics. It is essential that you understand how this happens. Third, electrons have a property that is (poorly named) spin that defines how it behaves around other electrons like it. Spin is another quantum property -- it has nothing to do with rotation of anything, despite the name. If it is proportional to a whole integer, then it behaves one way -- called Bose-Einstein statistics. If it is proportional to a half-integer, then it behaves another way -- called Fermi-Dirac statistics. This has enormous implications for the allowed states of electrons when there is more than one of them around. If any of this is new information to you, then you have about a century worth of catching up to do. Fortunately, this not so difficult if you are willing to dive into a few good books. |