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I think we both agree that when both particles have returned to their starting points energy has been conserved.
Yes the antimatter particle has velocity and has gained kinetic energy but the kinetic energy gain is at the cost of loosing the equivalent amount of potential energy.
Ah yes! The dreaded PE/KE debate []
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Ah yes! The dreaded PE/KE debate []At this risk of introducing a gigantic poisson rouge, or at least providing a common target that you might both agree to aim at, a body does not actually have any potential energy because of its position.The "energy" is not in the body at all. It's in the gravitational field.It's not really very different from the situation of a bow and arrow. (I'm sure the clever reference back to the previously mentioned target has not gone unnoticed.) When the archer pulls back the string, the potential energy is stored in the bow, not the arrow.Admittedly it is a bit more complicated than that because the energy stored in the gravitational field is also a consequence of the position of the mass within it, but the energy that is converted into kinetic energy was not stored within the object, so it had to be stored in the field.Exactly what this has to do with antimatter, I do not know, but perhaps it might help.
Hi, I found this discussion really facsinating, thanks. imatfaal, I'm trying to understand your explanation. Please could you help? Firstly, are you suggesting the following, and please could you clarify where I may have mis-understood?
(1) Take a positron and an electron, which are 'stationary'(2) They may combine, and would turn into light(3) The light may move through a gravity field, and then its frequency would change: blue shift if moving towards a (positive?) mass(4) The light can then turn back into a positron and electron, which are now both moving faster than before because the frequency of the light increased. (5) Under the original assumption, the particles may easily be returned to their starting positions without changing the system's kinetic energy
Next, are you saying the following (is this right)? (a) At stage 5 the total gravitational potential energy of the system is the same as at stage 1(b) The particles are moving faster, so Total kinetic energy has increased(c) No other forms of energy would have been changed(d) a b and c would only imply that the total energy of the system has increased, which violates the principle of conservation of energy.
Lastly, may I ask a few questions? These will demonstrate my complete lack of knowledge, sorry! (i) If the pair were to be re-combined and moved back to where they started in the form of light, then would the light start at the higher frequency again (higher because of the additional kinetic energy)? And would the frequency drop this time (as it moved in the opposite direction to before through the field; red shift on the way out instead of blue shift on the way in)? And therefore if they re-appear at the original position by this method would they be 'stationary' again?
(ii) How can we move the pair back to their starting positions, without changing the total kinetic energy of the system? [Edit: I re-read the description by Supercryptid, but I'm still struggling with this bit: "The net result is that you can change their height above the Earth's surface with no net change in the energy of the system."(Should it be re-worded "..kinetic energy of the system."?) How can this be achieved? Does this mean that the energy to move them back out through the field is zero? So they pull against each other in the field, and a small tap sends them off and an equal and opposite one to stop them when they get there? ]
(iii) So to get to (5), have we assumed that both the inertial mass and gravitational mass of the positron are negative? If so, would negative mass affect how the kinetic energy of the system is measured at stages (4) and (5)? May a positron in motion have negative kinetic energy under our assumption, and would this resolve the apparent violation in conservation of energy? Or did we get there without needing negative inertial mass? But then confirming they are still to be treated as the same once again resolves that situation.
(iv) Is it OK to ignore the magnetic potential energy between the positron and the electron? (I think it is, because the electron and positron start and finish the same distance apart - is that right?)
(v) Couldn't half the light go in the wrong direction, and need to be reflected back by a mirror or something? If so, would that move the mirror a bit, or heat it, or change the frequency of the light, and is that relevant when adding up all the energy in the system? Or can all the light go where we want it, without adding components to the system? Can it still do so on a macro scale?
Good luck with ignoring your phd research, perhaps my questions will help with that! I'm busy ignoring a piece of coursework for my accountancy exams right now []
This is a bit beyond the discussion here, but I thought it was interesting:http://iopscience.iop.org/0295-5075/94/2/20001/Under CPT symmetry (http://en.wikipedia.org/wiki/CPT_symmetry), general relativity apparently predicts that matter and antimatter gravitationally repel. I suspect this is highly theoretical at this point, since it's arbitrarily applying a conservation law from quantum mechanics to general relativity, but it's definitely interesting.
imatfaalSorry about the delay in replying.In thinking about this problem I have come to realize that the situation is considerably more complicated than I initially believed. The original gedanken, you and I all assumed that both matter and antimatter particles individually have to conserve energy, surely they don’t. Energy only has to be conserved within the system.
To demonstrate what I mean:-If a fixed quantity of photons are available to produce matter and antimatter particles then the same quantity are produced regardless of the gravitational field. However, the higher in the gravitational field this happens then the more photons are required to produce the matter particles (cost of production plus higher PE) and the fewer to produce antimatter particles (cost of production plus lower PE). The lower in the field this happens then the less photons are required to produce the matter particles and more required to produce antimatter particles. Although energy is not conserved particle to particle, it is conserved within the system.Do you agree?
Quote from: MikeS on 26/06/2011 06:25:23imatfaalSorry about the delay in replying.In thinking about this problem I have come to realize that the situation is considerably more complicated than I initially believed. The original gedanken, you and I all assumed that both matter and antimatter particles individually have to conserve energy, surely they don’t. Energy only has to be conserved within the system.It's the system that in a book-keeping exercise conserves energy. I never thought an other way and sorry if I gave that impression.QuoteTo demonstrate what I mean:-If a fixed quantity of photons are available to produce matter and antimatter particles then the same quantity are produced regardless of the gravitational field. However, the higher in the gravitational field this happens then the more photons are required to produce the matter particles (cost of production plus higher PE) and the fewer to produce antimatter particles (cost of production plus lower PE). The lower in the field this happens then the less photons are required to produce the matter particles and more required to produce antimatter particles. Although energy is not conserved particle to particle, it is conserved within the system.Do you agree?Not really - it's a clunky way of thinking of a very simple thought experiment. the xs ke that inital experiment theorised is the neatest way of visualizing it. You do not need extra energy to create a particle pair at a higher potential! Please try to work through with the two pairs of invariant potentials and it will become clear