I am confident that if you ASSUME the Bohr model and adjust for the higher masses etc. then yes, you will get hydrogen like energy level structure. I prefer my approach, which first derives the force law for a symmetric version of Maxwell's equations. If it turns out to be simple inverse square (and I expect it may) then yes, the assumption of Bohr model and hydrogen like is justified; however, if it does not, because they are moving thru each other’s time-retarded, radial magnetic fields, (velocity dependent forces, etc., or any other reason) then the defect of your approach will be exposed. I suspect monopoles also have a half unit of intrinsic spin, i.e. are Fermions, etc, but do not know if magnetic monopoles have intrinsic spin. I agree that if they do, then there will be a direct analogue of "hyperfine structure." If they do have spin, then I think it will be a gross splitting of the normal two fold degeneracy (up & down spins that, for example, permits He atom to have both its electrons in the n = 1, l = 0 state and still keep Pauli happy.) I will call this splitting the "hypergross structure" as I would be very surprised if it not very large compared to "hyperfine structure" because rather than the weak interaction between the electron spin and the weak magnetic field of the nuclear spin, the monopole spin will be interacting with the strong magnetic field from the other monopole in the case of the postulated monopole atom. We will just need to disagree on which is the superior approach to evaluation of these concerns (Your "assume Bohr like" or my "start with symmetric Maxwell's eq.") I am much to rusty in these calculations and now too lazy to do more than talk about it, but confident I am correct in principle. So we can drop this subject as far as I am concerned. (If you want the last word, be my guest.) Thanks, but not now. About 25 years ago, when trying to struggle thru a paper (in Phys. Rev. Section D, as I recall) some more simple version would have been very welcome. (I lost interest in physics about 20 years ago, and now my intellectual efforts, such as they are, are related to how the mind functions etc.; but, I have become too lazy even in that, ever since I finally worked out, at least to my own satisfaction, how genuine free will could exist and yet be consistent with physics.) I have avoided stating that they have an EH. (Used expressions like "near the monopole atom, the gradient may be large" etc.) I think it posssible that an EH exists , because of their extreme mass, but we would need to find the separation of the momopoles in the ground state of the magnetic monopole atom to make an intelligent guess as to the existence or not of an EH. Not every respectable physicist accepts that even real BHs are the singularities that the mathematical BHs are. Certainly, it is conceivable that a N/S monople atom, if in a quantized, extremely small, ground state, could have an EH. I.e. look like a standard BH outside some distance from the CoM and (1) not be a true singularity and (2) not be able to radiate magnetic waves because it is in a quantized ground state. (Same reason the accelerating electon in the ground state of the hydrogen atom does not radiatively spiral into the nucleus in less than a nanosecond (I did that calculation years ago. - I forget the duration of the decay to a separation equal to the sum of their classical radii, but it is very very short.) I am not confusing HR with spectral line radiation and when you think about the fact that quantization also prevents the hydrogen's ground-state bound and accelerating electron from radiating you make understand why I think the same will happen in the ground state of the monopole atom (as well as effects I have also discussed on the conditions when HR is, or is not, possible from it. I.e. my equation M = Eg + En + En - E etc.) You should have stopped when you were "even." Please Register or Log in to view the hidden image! - You are in error here. Of course there are some practical strength and materials type problems with a big box that may or may not have a BH inside, especially as I wish that BH to have a surface temperature of 5000K, so it is a rather large box if the EH is far from the walls, as I also assume, but lets ignore all that, as it is a conceptual error you are making: When there is equilibrium at 5000K, it is impossible to tell if there is or is not a BH inside the box from the radiation emerging from a tiny hole. - It will have Planck’s black body spectrum in either case. However, take some advise from one who is probably several decades your senior. By posting here now, you are making a much more serious error. - Turn off your computer and turn on that woman you said you went to visit.Please Register or Log in to view the hidden image!
No, I am quite confident that the two will (or should) give the same answers because of the duality between electricity and magnetism that occurs when one allows magnetic monopoles to exist. Maxwell tells us that the force cannot be anything BUT an inverse square. Sure. Yours will give the correct answer but will take longerPlease Register or Log in to view the hidden image! I am still not 100% sure why we are talking about black holes here. I will go and reread your previous posts. Indeed. She is in the shower now so I could sneak away and think about physicsPlease Register or Log in to view the hidden image!
Billy T, The naive force law is just the magnetic analog of Coulomb's law. I'll derive it for you, if you like. In the presence of magnetic monopoles, the Maxwell equations take the form: \( \nabla \cdot E = 4 \pi \rho_e \) \( \nabla \times E = -\frac{\partial B}{\partial t} - 4\pi J_m \) \( \nabla \cdot B = 4 \pi \rho_m \) \( \nabla \times B = \frac{\partial E}{\partial t} + 4 \pi J_e \) Now what is the magnetic field produced by a monopole of strength g at rest at the origin? The only relevant Maxwell equation is \( \nabla \cdot B = 4 \pi \rho_m \), where for monopoles we have that \( \rho_m = g \delta^3(x) \). This leads to a magnetic field given by \( B = \frac{g}{r^2} \hat{r} \), which is just Coulomb's law. To proceed further one should solve the quantum (Bohr) problem and determine the characteristic speeds involved. If these speeds are small compared to speed of light (=1 in these units) then we expect that Coulomb's law is a good approximation. I haven't done the calculation; however, my guess is that the static approximation fails. This is because in the characteristic speed in the Bohr model is something like \( e^2 \) (e is dimensionless in these units with hbar = c = 1). For the magnetic atom one need only replace \( e^2 \) with \( g^2 \), but according to Dirac and Schwinger, we have something like \( e \sim 1/g \) (strong coupling dual to weak coupling). Thus since \( e^2 \sim 10^{-2} \) we expect \( g^2 \sim 10^2 \) and hence the orbital speed will be much greater than 1 indicating a totally failed approximation. Even allowing for \( 4 \pi \)s I missed, I think one will be in trouble with the static approximation.
I have firmly believed all along that, in the static case it would be inverse square fall off function of separation alone. (I was not entirely clear. - I was planing to start in a rotational coordinate system with the inverse square radial law assumed and then see if the transform of the magnetic forces into the lab frame could drag in something like the Coriolis force, if I recognized that the field lines did not come from where the monopole is, but from where it was. - Something like that, not well thought out, - just a fear that it might be more complex than a Bohr atom.) I do not completely understand your second paragraph, but it seems to strengthen the concern I expressed in post 41 with the following words: "If it turns out to be simple inverse square (and I expect it may) then yes, the assumption of Bohr model and hydrogen like is justified; however, if it does not, because they are moving thru each other’s time-retarded, radial magnetic fields, (velocity dependent forces, etc., or any other reason) then the defect of your approach will be exposed.'' We have sort of been waiting for you or Trilian to appear. Did you see the six points in post 1? If interested, please order your interest. E.g. say “I vote we do in order 2, 1, 4” or something like that. My intention is to try to convince you (and others) that it is at least plausible that dark matter is simply a somewhat "clumpy" distribution of small black holes. (~1 to 5 stellar mass range causing most of dark matter's observed gravitational effects.) or be convinced by the discussion here that this is not a plausible POV. For you (and other "late comers") the six points for discussion are: (1) Why there may be many stellar-size BHs, (despite the conventional view there are few, if any). (2) Why they are not individually detectable. Except if one passes near our solar system, and then only by their gravitational perturbation of planet orbits. (Not detectable, even when close, by "gravitational lensing" of more distant stars). (3) Why they are not detected by a “micro-quasar” effect (radiative interaction with in-falling “cosmic gas”) when passing near solar system. (4) More about the misunderstood, but possible prior detection of one passing by the solar system in the late 1920s. (Neptune’s unexplained perturbation that lead to the discovery of Pluto.) (5) Why any objections you may raise against these stellar-size BHs being very abundant are not fatal to that possibility. (6) Why other alternatives are less likely. ..." BenTheMan wants to start with 1, then 2, and I think I will do so later today (or on Wensday -as I will be out of town for two days, working on a house I am building all by my self. - Crazy at may age, but gets me out of Sao Paulo and into clean air at the lake for two days of manual labor a few times each month.)
I would love to know your thoughts on how genuine free will could exist and yet be consistent with physics. I think I started a thread a long time ago on why I think free will cannot exist but can u perhaps start a different thread on the above?
Hi Billy--- I found a thread pertaining to dark matter in the discussoin board alt.astro.research that you may be interested. In post 40(ish), someone (from amherst college) suggests that dark matter may be due to stellar mass black holes. See here http://groups.google.ca/group/sci.a...read/f4ae39c5463b26ab/866e76ecc9d5b7f9?hl=en& The problem that has been pointed out is that the gravitational lensing experiments seem to have ruled this proposal out. I didn't read the whole thread, as I just got back to Columbus and am on my way to bed. Hope it's useful.
Clearly this guys are ignoring the combined effects of gravity. Take a magnet see how far it can pull a needle towards it, place the needle just far way from this point, now do the same experiment by sticking a metal piece to the magnet smaller than this distance. Guess what, the needle will get pulled this time as the metal(iron) extends the reach of the magnetic pull.
I must be missing your point... This experiment certainly depends on the size of the magnet/metal piece you are using. Are you drawing an analogy between gravity and electromagnetism?
I have posted them several times during the last 3 or so years - following is not the best link, but the first I could relocate: http://www.sciforums.com/showpost.php?p=1031482&postcount=17 It is a reply to someone. If only interested in my essay, start at the bold text "Genuine Free Will is Possible" I will read BTM's link and then begin on discussion point 1 soon.
I was asking u to draw anology between workings of magnetism, and gravity with respect to extension of extent the fields pulling power.
But EandM isn't necessarily a "pulling power". It can also push. Gravity can only pull. There is a deep and beautiful reason that this is true---gravity is propogated by a spin 2 graviton, which can only give an attractive potential. Light is a spin one boson, and can be either repulsive or attractive.
This will be incomprehensible to ironically named (for black hole related thread) Singularity. Thus I will note that gravity strength for a source decreases only with distance from the source, by the square of the distance, whereas magnetic forces depend upon both distance (falling off as the cube, for large distances, not as the square) and angles. The comparison is worse than "apples to oranges."
I had to think about this for a second, but yes I agree. I was thinking that this was only true for electric dipoles, but then remembered that magnets were basically dipoles. To be fair to singularity, both forces are conservative, and they are both long range forces (unlike the strong and weak nuclear forces, which are short range). And if there are magnetic monopoles, then the force will also fall off like r^2. If singularity would clarify his/her question, or start a new thread, I'm sure it could be discussed.
This is the right thread to discuss it, since the problem is the missing matter which is just not there. So do u think the apple pulls the earth or the earth pulls the apple ?
For about a week when I was 10 or 12, I would drop a brick from my window in the morning, before going to school and bring it back to my room in the evening. I understood that my feet pushing more against the Earth as I did so would also push the Earth away (very slightly) from the brick (as well as move the brick away from the center of the Earth). I erroneously thought that I could move the Earth, because the fall of brick and restoration of it to my room (~12 hours later) both do move the Earth in the same direction. Do you understand why I could not move the Earth in its orbit by this proceedure?
Both. They both come to rest in a position somewhere between where the Earth and apple used to be. Closer to where the earth was though Please Register or Log in to view the hidden image!
Ok then, Now create a planet completely made of apples such that it generates Gravity of 1G. Now forget it, we did this just to select 1G of apples. Now use the apples to create small spheres of size S such that they generate just enough G to attract and revolve each other at max distance D. (I know this is too complicated) Now place them in a line of length L such that each of them are at interval of distance D to the adjacent ones. Phew, now the real question. Will the 1G planet attract one S sphere at distance L more than two S spheres attracting each other at distance D ?
Billy T, I am happy to hear about the topics in whatever order is most convenient and interesting for the others participating in the discussion. Also, I am pretty sure that the magnetic monopole atom is highly relativistic and therefore not amenable to easy analysis.
