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occasion of quantum mechanic s 100th birthday in 2025 i decided i submit a talk about it to the march meeting of the dpg the german physical society in göttingen and to have to show something i put it out on the arxiv today the idea is as follows the ghz experiment is a beautiful version of bell s inequality that demonstrates you get to wrong conclusions when you assume that a property of a quantum system has to have some unknown value even when you don t measure it i would say it shows quantum theory is not realistic in the sense that unmeasured properties do not have secret values different for example from classical statistical mechanics where you could imagine to actually measure the exact position of molecule number 2342 in your container of gas for details see the paper or this beautiful explanation by coleman i should mention here that there is another way out by assuming some non local forces that conspire to make the result come out right never the less on the other hand there is bohmian mechanics this is well known to be a non local theory as the time evolution of its particles depend on the positions of all other particles in the system or even universe but what i found more interesting is also realistic there it is claimed that all that matters are particles positions including the positions of pointers on your measurement devices that you might interpret as showing something different than positions for example velocities or field strengths or whatever and those have all possibly unknown values at all times even if you don t measure them so how can the two be brought together there might be an obstacle in the fact that ghz is usually presented to be a correlation of spins and in the bohmian literature spins are not really positions you will always have to make use of some stern gerlach experiments to translate those into actual positions but we can circumvent this the other way we don t really need spins we just need observables of the commutation relation of pauli matrices you might think that those cannot be realised with position measurements as they always commute but this is only true as you do the position measurements at equal times if you wait between them you can in fact have almost pauli type operators so we can set up a ghz experiment in terms of three particles in three boxes and for each particle you measure whether it is in the left or the right half of the box but for each particle you decide if you do it at time 0 or at a later moment you can look at the correlation of the three measurements as a function of time of course as you measure different particles the actual measurements you do still commute independent of time and what you find is the blue line in ghz correlations vs bohmian correlations you can also numerically solve the bohmian equation of motion and compute the expectation of the correlation of positions of the three particles at different times which gives the orange line clearly something else no surprise the realistic theory cannot predict the outcome of an experiment that demonstrates that quantum theory is not realistic and the non local character of the evolution equation does not help either to save the bohmian theory one can in fact argue that i have computed the wrong thing after measuring the position of one particle at time 0 or by letting it interact with a measuring device the future time evolution of all particles is affected and one should compute that correlation with the corrected effectively collapsed wave function that however i cannot do and i claim is impossible since it would depend on the details of how the first particle s position is actually measured whereas the orthodox prediction above is independent of those details as those interactions commute with the later observations in any case at least my interpretation is that if you don t want to predict the correlation wrong the best you can do is to say you cannot do the calculation as it depends on unknown details but the result of course shouldn t in any case the standard argument why bohmian mechanics is indistinguishable from more conventional treatments is that all that matters are position correlations and since those are given by psi squared they are the same for all approaches but i show this is not the case for these multi time correlations post script what happens when you try to discuss physics with a philosopher posted by robert at 4 29 pm 1 comments wednesday may 22 2024 what happens to particles after they have been interacting according to bohm once more i am trying to better understand the bohmian or pilot wave approach to quantum mechanics and i came across this technical question which i have not been able to successfully answer from the literature consider a particle described by a wave function psi x and a bohmian position q that both happily evolve in time according to the schrödinger equation and the bohmian equation of motion along the flow field now at some point in time the actual position of that particle gets recorded either using a photographic plate oder by flying through a bubble chamber or similar unless i am not mistaken following the having a position is the defining property of a particle mantra what is getting recorded is q after all the fact that there is exactly one place on a photographic place that gets dark was the the original motivation of introducing the particle position denoted by q so far so good i hope my question however is what happens next what value of q am i supposed to take for the further time evolution i see three possibilities i use the q that was recorded thanks to the recording the wave function collapses to an appropriate eigenstate possibly my measurement was not exact i just inferred that the particle is inside some interval then the wave function only gets projected to that interval and thanks to the interaction all i can know is that q is then randomly distributed according to p psi 2 where p is the projector new equilibrium anything can happen depending on the detailed inner workings and degrees of freedom of the recording device after all the bohmian flow equation is non local and involves all degrees of freedom in the universe something else all three sound somewhat reasonable but upon further inspection all of them have drawbacks if option 1 were the case that would have just prepared the position q for the further evolution allowing this to happen opens the door to faster than light signalling as i explained before in this paper option 2 gives up the deterministic nature of the theory and allows for random jumps of the true position of the particle this is even worse for option 3 of course you can always say this and think you are safe if there are other particles beyond the one recorded and their wave functions are entangled option 3 completely gives up on making any prediction about the future also of those other particles note that more orthodox interpretations of quantum mechanics like copenhagen whatever you understand under this name does make very precise predictions about those other particles after an entangled one has been measured so that would be a shortcoming of the bohmian approach i am honestly interested in the answer to this question so please comment if you know or have an opinion posted by robert at 3 41 pm 0 comments wednesday january 24 2024 how do magnets work i came across this excerpt from a a christian home schooling book which is of course funny in so many ways not at least as the whole process of seeing is electromagnetic at its very core and of course most people will have felt electricity at some point in their life even historically this is pretty much how it was discovered by galvani using forge legs at a time when electricity was about cat skins and amber it also brings to mind this quite famous youtube video that shows feynman being interviewed by the bbc and first getting somewhat angry about the question how magnets work and then actually goes into a quite deep explanation of what it means to explain something but how do magnets work when i look at what my kids are taught in school it basically boils down to a magnet is made up of tiny magnets that all align which if you think about it is actually a non explanation can we do better using more than layman s physics what is it exactly that makes magnets behave like magnets i would define magnetism as the force that moving charges feel in an electromagnetic field the part proportional to the velocity or said the other way round the magnetic field is the field that is caused by moving charges using this definition my interpretation of the question about magnets is then why permanent magnets feel this force for the permanent magnets i want to use the they are made of tiny magnets line of thought but remove the circularity of the argument by replacing it by they are made of tiny spins this transforms the question to why do the elementary particles that make up matter feel the same force as moving charges even if they are not moving and this question has an answer because they are dirac particles at small energies the dirac equation reduces to the pauli equation which involves the term thanks to minimal coupling vec sigma cdot vec p q vec a 2 and when you expand the square that contains in coulomb gauge vec sigma cdot vec p vec sigma cdot q vec a q vec a cdot vec p vec p times q vec a cdot vec sigma here the first term is the one responsible for the interaction of the magnetic field and moving charges while the second one couples nabla times vec a to the operator vec sigma i e the spin and since you need to have both terms this links the force on moving charges to this property we call spin if you like the fact that the g factor is not vanishing is the core of the explanation how magnets work and if you want you can add spin statistics which then implies the full stability of matter story in the end is responsible that you can from macroscopic objects out of dirac particles that can be magnets posted by robert at 4 45 pm 1 comments monday november 13 2023 how not to detect mond you might have heard about recent efforts to inspect lots of wide binaries double stars that orbit each other at very large distances which is one of the tasks the gaia mission was built for to determine if their dynamics follows newtonian gravity or rather mond the modified newtonian dynamics einstein theory plays no role at such weak fields you can learn about the latest update from this video by dr betty spoiler newton s just fine mond is an alternative theory of gravity that was originally proposed as an alternative to dark matter to explain galactic rotation curves which it does quite well some argue better than dark matter since it has been investigated in other weak gravity situations as well in short it introduces an additional scale a_0 of dimension acceleration and posits that gravitational acceleration either in newton s law of gravity or in newton s second law are weakened by a factor mu a frac a sqrt a 2 a_0 2 where a is the acceleration without the correction in the recent studies reported on in the video people measure the stars velocities and have to do statistics because they don t know about the orbital parameters and the orientation of the orbit relative to the line of sight that gave me an idea of what else one could try when the law of gravity gets modified from its 1 r 2 form for large separations and correspondingly small gravitational accelerations the orbits will no longer be keppler ellipses what happens for example if this modified dynamics would result for example in eccentricities growing or shrinking systematically then we might observe too many binaries with large small eccentricities and that would be in indication of a modified gravitational law the only question is what does the modification result in a quick internet search did not reveal anything useful combining celestial mechanics and mond so i had to figure out myself inspection shows that you can put the modification into a modification of 1 r 2 into mu 1 r 2 frac vec r r 3 and thus into a corresponding new gravitational potential thus much of the usual analysis carries over energy and angular momentum would still be conserved and one can go into the center of mass system and work with the reduced mass of the system and i will use units in which gm 1 to simplify calculations the only thing that will no longer be conserved is the runge lenz vector vec a vec p times vec l vec e_r vec a points in the direction of the major semi axis and its length equals the eccentricity of the ellipse just recall that in newton gravity this is an additional constant of motion which made the system so 4 2 rather than so 3 symmetric and is responsible for states with different ell being degenerate in energy for the hydrogen atom as one can easily check dot vec a h vec a dot vec p times vec l dot vec e_r dots 0 using the equations of motion in the first term to test this idea i started mathematica and used the numerical ode solver to solve the modified equations of motion and plot the resulting orbit i used initial data that implies a large eccentricity so one can easily see the orientation of the ellipse and an a_0 that kicks in for about the further away half of the orbit clearly the orbit is no longer elliptic but precesses around the center of the potential on the other hand it does not look like the instantaneous ellipses would get rounder or narrower so let s plot the orbit of the would be runge lenz vector orbit of would be runge lenz vector vec a what a disappointment even if it is no longer conserved it seems to move on a circle with some additional wiggles on it did anybody mention epicycles so it is only the orientation of the orbit that changes with time but there is no general trend toward smaller or larger eccentricities that one might look out for in real data on the other hand the eccentricity vec a is not exactly conserved but wiggles a bit with the orbit but comes back to its original value after one full rotation can we understand that analytically to this end we make use the fact that the equation of motion is only used in the first term when computing the time derivative of vec a dot vec a left 1 mu 1 r 2 right dot vec e_r mu differs from 1 far away from the center where the acceleration is weakest on the other hand since vec e_r is a unit vector its time derivative has to be orthogonal to it but in the far away part of the the ellipse vec e_r is almost parallel to the major semi axis and thus vec a and thus dot vec a is almost orthogonal to vec a furthermore due to the reflection symmetry of the ellipse the parts of dot vec e_r that are not orthogonal to vec a will cancel each other on both sides and thus the wiggling around the average vec a is periodic with the period of the orbit q e d there is only a tiny net effect since the ellipse is not exactly symmetric but precesses a little bi...