C. Roth, M. Danielewski, Quaternion Quantum Mechanics: from Hamilton spacetime...

Transcript

we can okay we can start in this moment I think yeah okay yes so well it's my pleasure to present a first speakers is Professor R and professor danieleski and the title of the talk is Quon quantum mechanics from Hamilton SpaceTime the displacement for potential in plank Kleiner crystals please go on thank thank you very much for letting me speak here today thanks to the organizers and a special thanks to M it's a great honor I would like to talk about three ideas today first how can we use pterion in quantum mechanics to drive the shinger wave equation and why would anyone want to use Pion second how does this give us an antic interpretation of quantum mechanics and what is the reasoning and motivation behind this and third how can this be visualized this presentation is based on a paper by m danielowski and Luke Shan sappa that was recently published and at the end I will give you a short idea of what we are currently working on let's start with a visualization this is what I will try to explain to you today and by the end of this talk I think you'll know exactly what this is a brief overview of the presentation in the introduction I will try to convey the motivation behind this why we think it makes sense to work on such a topic next I will introduce the plank ciner Crystal then I will try to convince you that quion are actually quite practical next I will dive deep into the topic and try to explain to you the main ideas including how we can derive the short wave equation and some other equations and finally if time permits I will give you an idea of work in progress including a simulation of spin one half of one and two particles as you all know there are many interpretations of quantum physics most of you know the Copenhagen interpretation which in which case the wave function is not real it just related to probabilities and the wave function is set to collapse upon measurement immediately then there are me show you the laser pointer maybe then of course there's the Broly bone interpretation which is a pilot wave sometimes it's called pilot wave in this sense there is a real wave but there's still a particle involved there's some other interpretations and I'm sorry if your favorite interpretation is not there I think we can all agree that nobody really agrees and that's why we think it's worthwhile to investigate this topic now there's another interpretation the neoclassical and it's not much talked about in this interpretation it is a realist interpretation the wave is onti wave is real and there are no particles at all a few quot quotes from selected scientists maray Gilman he got a Nobel Prize in elementary particle physics he said Neil Spore brainwashed a whole generation of theorists into thinking that their job of finding an interpretation of quantum mechanics was done 50 years ago and maybe this is still true today even schinger the famous shinger he did not like the probability interpretation at all he always considered Ed it to be a real ATI wave he said let me say at the outset that in this discourse I'm opposing not a few special statements of quantum physics held today I'm opposing as it were a whole of it I'm opposing its basic views that have been shaped 25 years ago when Max Bourne put forward his probability interpretation which was accepted by almost everybody so he wasn't happy about this now are assistants that are well known that are classical let's look at some of these maybe you have heard of the word phonon sometimes you read in the literature it's referred to as particle of sound or particle of heat um phonons are spontaneous vibrations of atoms in a crystal lattice they are studied in condensed metaphysics it's it's classical so we are talking about a real crystal that vibrates and interestingly this vibrational mode they behave similar to particles they are also called quasi particles they behave like Bono bosons just like photons too there are a lot of similarities between photons and phonons both are bosons both are quantized and behave like particles or as wave they have the same description in terms of quantum mechanics so given the similarities doesn't make make you wonder if maybe photons are more similar to phonons than we may think and maybe this not such a crazy idea there are numerous papers on bubbl slit experiments and interference experiments with phonons plasmons and polaritons now all these are Quasi particles now all these are classical that means we can see these waves you can look at them in the microscope so it doesn't require Consciousness to collab wave function it doesn't require the universe to split in multiple other universes right this is very simple um and so the question is given that we can do the same kind of experiments with these quasi particles is it really are photons really so different maybe it's not so crazy to at least think about that maybe it's not so different the wave function collapse of phonons has been studied as well the quantum mechanical property of phonons in a one-dimensional lce are studied with the conclusion that phonon behaves in all essential respects as a normal Quantum particle so this could be an interesting system to think about how what a photon actually could be the next piece of puzzle is makovski spacetime as you all know special relativity and general relativity are usually described using A Spacetime which is an intervol and Continuum of three spatial and one time Dimension now in this model gravity is caused by time curvature and I don't have to explain this you you all know that now what many of you may not know is that there is a mathematically equivalent model initially developed by hogen Kleiner what he did he did a simple coordinate transformation where instead of space and time we use space and density and everything else is the same you can imagine this literally like an elastic solid like picture here like a grid or a crystal um whenever there's a lot of matter in this model it changes the density so gravity in this model is actually Optical refraction it's an optical mechanical analog to general relativity and you may think this is crazy but there are actually a lot of researchers using general relativity for to study Optical phenomenon they used the metric tensor to calculate Optical behavior in condensed matter and if you were in glasses you know what refraction is so here's a simple example you can even do in your kitchen you can take some bowl of glass and put water in it and a sugar you create a sugar gradient now this creates an optical uh gradient refraction and when you shine a laser light through it it would actually bend the laser light this is an example of how uh a gradient of refraction can cause a light to bend there's some more sophisticated examples and analoges in in Optics there are multiple papers on this this one is from nature so on the left side here um this is the experiment and the right side is the calculation this is an optical black hole basically what they did they have some kind of a meta material that has an increased refractive index and as the light you know in goes to the medium to The Meta material it keeps bending more and more until it's actually captured uh in the middle so it's literally behaves like a black hole and the formulas used are exactly the same there are even black holes of Sound by the way this is a picture of hog Kleiner and a painter painted his famous World Crystal of course it probably won't look just like that maybe more like this oh I have to change my mouse pointer here this is a simulation of what this Crystal might be so before we go into more detail um what are the properties of such a crystal well it's we model it as a face Centric cubic Crystal it has um Dimensions or the plank length as you can see very small plank mass is the mass of such a particle now keep in mind when I say particle this is obviously not a particle like we talk about with normal matter this is think of it more as as a grid system in an abstract sense a little bit so what can we say as a summary about this plank cliner Crystal well it is essentially the fabric of space time except here we use um space density imagine it like a 3D coordinate system and the fourth dimension is is density it has grid size uh plank length it is an elastic solid which can have deformations it can have compression and torsion deformations and there is an optical analogous model of gravity it's basically refraction even Maxwell talked about this he said the Assumption therefore that gravitation arises from the action of the surrounding medium leads to the conclusion that every part of this medium possesses undisturbed and enormous intrinsic energy and that the presence of dense bodies influences the medium so as to diminish this energy wherever there is a resultant attraction as I'm unable to understand in what way the medium can possess such properties I cannot go any further in this direction in searching for the cause of gravitation and also Einstein thought about this so in um 1920 he said more careful reflection teaches us however that the special theory of relativity does not compel us to deny ether we may assume the existence of an ether only we must give up ascribing a definite state of motion to it recapitulating we may say that according to the general theory of relativity space is endowed with physical qualities in this sense therefore there exists an ether according to the general theory of relativity space without and theer ether is Unthinkable for in such such space there Not only would be no propagation of light but also no possibility of existence for standards of space and time measuring rods and clocks nor therefore any SpaceTime intervals in a physical sense now I'm sure some of you will say well hasn't this been this Pro in Michael some moral experiment and you know what doesn't that mean there's a absolute frame of reference and what about special relativ so if there are any questions about this at the end I have a few slides if there's time left I would happy to go into this to explain a little more so now the quion why would anyone want to use quion now you all know what quion are so I don't have to explain this to you but for those who don't um I you know in airplanes use a gyroscope which uses um is a measuring device for measuring the location the orientation of an airplane for instance now what can happen is when you rotate when you flip the airplane 90 degrees you get something called a gimbal lock where the two axes actually interlock with each other and then they move together which is a problem and this actually happened in Apollo 11 they even had a special button there in Apollo and um it happened they had a gim loock in the mission and they had to steer manually now with quion this doesn't happen so cion are are used a lot actually in computer Graphics in robotics in navigation in you know um visual if a game developer for instance everywhere everywhere where we have to deal with rotation in space for instance when you want to move a camera in a scene to another place it's not just translation it's also rotation so basically laser pointer uh basically you know the first one is a Scala the third the the the other three uh determine the axis of rotation so it's it's very visual in a way and whenever you have rotations involved it really really helps use cion who actually invented them it was actually um Sir William Ron Hamilton the history goes that he was working uh with 3D operations but he was using vectors and he got stuck with it for years because he just couldn't figure out how to get this to work you know he was wondering about introducing a second complex number but it just didn't work and it was said that he was walking across this um program Bridge with his wife and suddenly had the idea oh we have to use a third complex number and he was so worried that he would di have a heart attack right there he actually carved it into into um the bridge so that if any if he would die this this knowledge would not get lost now if you think about this ik some you know some people find this weird but when you think about this as terms of rotational axis it's actually not strange so each one is just an axis of rotation so you go um I is 90 degrees and then um J and then K it's obvious that you go to minus one so when you look at this in a geometrical sense is actually quite straightforward now you all know that you know there only four division algebras the reason I mentioned this is there is no division algebra it for vectors there's no division operation for vectors right so it's kind of clumsy to use dot in cross product now unfortunately in physics a lot of things has been used derived using vectors which is a Pity because quion would actually be um better suited for that so also uh Maxwell recognized the importance of Pion he said the invention of the calculus of Pion is a step towards the knowledge of quantities Rel ated to space which can only be compared for its importance with the invention of triple coordinates by deart the idea of this calculus as distinguished from its operations and symbols are fitted to be of the greatest use in all parts of science so actually he tried to reformulate electromagnetism with curnan but he failed others tried also un failed so people gave up for a long time I guess people were just used to using vectors so on fortunately all of quantum mechanics has been built upon with vectors and matrices instead of quarion and we hope to change them so let's go back to the crystal now let's talk about the deformations what kind of deformations are there so we'll be using the symbol U for the deformation field and there is basically two parts there's compression and there's twist we'll be using the symbol Sigma for the Divergence of youu and the symbol five for the the curl of you just a simple visualization so the left side is is compression and the right side shows you twist in all these animations I'm using this red dot so basically I I have marked one grid element so we can see exactly the movement of that that's what this is just in case you wonder so we can actually see what happens and keep in mind we're actually um looking at this in three dimensional space so me just so you have to imagine it's a whole field right I'm just showing a plane to make it simpler but we're actually looking at a a field so a threedimensional again this is left side is compression and the right side you have twist using three dimensions but usually a plane is kind of easier to to see so maybe you can kind of see where this is going because um well Helm H holds Helm holds figured out that you can split up a vector field into two parts is called the hel Hol decomposition he has proven um that such a field can you can depose it into the rotational part and the diverged part now the nice thing about this purely based on definition it's clear that the twist of the compression is zero and also the opposite the Divergence of the twist must also be zero and this is comes in quite handy because you can when when you have equations you can always eliminate these terms very easily now we also need to talk bit about gaoui goui uh Baron Augustine Lis gauchi he's a French mathematician he developed the displacement mechanics there are actually 16 Concepts and theorems named after him and he wrote over 800 Research articles he developed the mechanics of how to work with displacement Fields if you imagine you have in your room a a big coordinate system with rubber bands for instance and the three directions we have to keep in mind when you have a deformation the whole uh volume has to stay the same and also uh Clos curves stay the same so basically you don't rip anything apart so you can do any kind of deformation but it has to it has to be continuous um the volume doesn't change essentially you don't break the coordinate system and you don't create any knots in it either so this is the equation of motion um let me just I think I have an animation here yeah so again this is just a simple animation of of a 3D Crystal PL plan Crystal the kind of motion you might see there and it's actually quite simple so the acceleration is related to the gradient of compression and the twist of the twist we will use this as a basis to derive the wave equations now as you will know um vectors are really not suited in this because there's no division operation it's so it's actually much simpler to use quorans for this so after many attempts to to construct an algebra in R3 Vector space Hamilton realized that it was that you needed a four-dimensional space to do this and this is where the quion now come in so there exists a deformational field deformation field Sigma such that one could represent the solenoidal the vector and scalar field as a superposition of real and imaginary Parts at each point so this is basically the scalar part and this is the vectorial part and now all we have to do is combine these two it's really quite simple and you have hom holds and you have you have G and now we just combine that so let's again look at the equation of motion and now all we do is we we apply the H mod decomposition which means we use the div and and Rod operator and then we see what happens so when we apply the div operator what happens as you as I told you before based purely on the on on the definition right all these red terms will go away because the diversions of the twist is zero so this will go all vanish now when you look at this maybe some of you can guess what comes out of this well when we do this this goes away and we substitute the Divergence of view with the sigma zero then what we end up with is simply longitudinal waves in space now most people think of this as you know look at in a plane but actually again we're looking at three dimensions and again match the whole the grid right we're looking at the whole volume the three dimensional longitudinal wave now that was quite simple now we just do this again we do the opposite we app apply the curl operator to this and again because purely based on div um definition we know that all these red terms go away because the twist of the compression is zero so when we do that we end up with this and what do you think happens now when we replace this well we get transverse waves that was kind of obvious right so all we did now we replaced the The Twist of of you the down and now we have transverse waves and again we're looking at this in three dimensions of course not not just flat so three dimensions again this is the summary what we did before we have these two uh wave equations now what happens when we combine them I mean you know we don't have just only transvers or only compression waves when we add them up we get we get all kinds of waves so here's an example and I wonder if some of you recognize this I hope you guys do I will tell you the end what kind of wave this is so as you can see you can form many many shapes of waves a hint is the red line here maybe you can see what this red line do so again this red line Marks One grid point and you can see what it's doing now we need to also talk about the energy of the deformation field so here this is the equation and both the um equation of motion and this equation they obey the oiler L relation so we can imagine this is sort of like a pendulum where the energy is either in the kinetic or a potential energy in this case this would be the U dot that's the velocity of a one grid element so when I play this you can see that red dot that again Marks One grid element you can see that the energy you know when the velocity is high there is no no strain and the opposite when there's um no strain there's High Velocity so it's like pendulum and again it is other L relation and um what's important here is also when when you look at the span of this so that the maximum kinetic energy is the same as the maximum of the strain energy um now when we start to think about shinger and all this I I'll get to back to this later and I'll I'll talk a little bit more about this image so what we can do now um so the energy equation acts as a local boundary condition and what we can do we can rewrite right the equation of motion as a multi system and now we end up with two equations the first one is the K Gordon equation which is well known it's a relistic wave equation it's Laurence invariant now I wonder if you eyes recognize what the second one is what we can do now since we're actually working with a real elastic solid we can put in the values of the plank planer Crystal you know plank Mass the length the plank time and so on and we do that and we do the substitution here then we can express this as a function of the local mass density now maybe you recognize this now what this looks like because um when you look at this part this is actually um G the gravitational constant so it's very interesting that we able to derive um the gravitational constant from this model so this is the this is the result from using this elastic solid model gaoui and this is the official nist these are nist values of course these values change uh you know because it's not super accurate you can see that the values changed from 2016 2014 but you can see how close it is this is actually very close I think that's pretty cool here is a summary of several other physical constants of this plank cliner Crystal now what I find interesting the young model is is really really high if you think about it I think a diamond it's around 10 to the 12 or something like this so this this Crystal you have to imagine it's very stiff it's much stiffer than Diamond which is pretty interesting and using the young modelist you can actually calculate the speed of light so again this was calculated using just this model which is I think it's pretty cool so let's get back to the uh energy because our goal is to calculate the Shing our wave equation so it has to do something with energy so to do this um in this model um the energy we have to look at a certain volume because what is a particle in in this model there's there are no particles so the particle really is just a volume the energy contained in a certain volume okay we obviously the energy is constant and also for the deration we assumed that it's mostly stationary so it doesn't move around at relative s speeds so what we have to do we have to calculate the integral um of in this volume of this energy to do this we'll need an operator D which acts on quion and actually it corresponds physically to the gradient in 3D space which is kind of cool so this directly connects quion to the elastic solid to physical reality so all the calculations we do have a physical meaning we also need the normalized velocity it's not a trick and of course please the details are in the paper because there are several pages and I have no time to put this on you know um yeah so we and this the normalized velocity is equal to the normalized gradient of of the mechanical potential now there's a few tricks so we take the um energy of the deformation field we calculate the integral about of a certain volume then there's a few tricks we do so we replace these terms with f and you can probably guess why then um we Ed the normalized gradient of mechanical potential now the mass here you wonder about this Mass this mass is not on this mass is basically the energy of the system divided by C squ so there's no particle again it's just the energy in in that volume and so there's a little tricky part which is explained in the paper a little bit more it's uh for you have to use the dwa Raymond Lemma to do this and maybe you recognize this already what we can do now we can replace um these constants with h bar and this Lambda is actually it's a multiplier so we might as well well use energy here energy when we do this we get the time invariance Shing equation all with cion so let's compare a little bit the Shing equation with the complex traditional Shing equation and there's only one only one major difference you know the complex Shing ER equation you have the complex I and which is kind of weird I think because you know we're operating 3D space so to me it it's much more iCal to use you know three complex numbers because you're looking at a 3D space so that's the main difference now you may wonder if this is really compatible but actually it's quite easy to see that um you can convert um a quion back to a complex number but simply by projection so here on top we have the mechanical potential the four potential of The Quon and at the bottom we have the same thing for the classical quantum mechanics and it's it should be easy to see that you know you basically can project it down to a plane so in summary in this model the wave function is real it's ontological there are no particles none there is just all waves and everything we we we we call particle is basically quasi particles or you know it looks like particles it's quantized energy and so on it's energy is pure wave energy uh the mass is related to the overall energy in the certain volume of course you may Wonder well what's next this is just the beginning okay obviously we'll have to the next step to me obviously is direct equation and spin one half now why why is spin one half important well because you know protons neutrons electrons they all have spin one half and it's the source of the poly Exclusion Principle and uh most of you probably know what spin one a half is it means you have to rotate something and it returns to the same state after 720 degrees and the direct equation describes that so we really to understand spin one half in the elastic model because if we can't do it then the model is not going to work so in case you don't know what spin one half is here I have a short simulation you can try this yourself so you take a the goal is you take a cup and you rotate it continuously you can't spill the coffee you you can't move your fingers you can't switch arms you can't get up either so I don't know if I can do this here so the trick is of course you have to um twist your arm a little it's a little bit small space here so when you do this when you do this about 100 times then in your head you can visualize oh it's getting going better now okay so this is spin one half so what I was wondering can we visualize this in in a computer simulation so to make this more understandable to people and um yeah so I wrote this it's a simulation in unity 3D C you can actually zoom into this and fly around so this this has been one half um again there's one grip point that you can see how it's moving and I added this sphere only um so that you can see the rotation better and again this is of course not and and it doesn't tear apart space so this is completely compatible with with um it doesn't tear it doesn't create knots it doesn't tear apart grit or anything and again this is threedimensional so here on the right side I added a second plane so we can see here's a a closeup so maybe you can see better what you'll notice is that the sphere appears to rotate um the sphere appears to rotate twice before it gets back to its original um situation basically so this is spin one half so this is perfectly compatible with an elastic solid model here I remov the sphere so we can you can follow the vector there a little tiny symbol it shows how this grid element is moving around we can also do this with two actually so now um what's interesting about this one is so I I have again the sphere is only for visualization purposes there is no sphere okay this is just to help you see you notice that the spin is opposite so one is spin up the other one is spin down and the reason for this is in the middle or so I will switch it um to equal Spin and you can see that it's not compatible if you have two particles the same spin that get too close to each other it will rip apart it it's not compatible so this one will create it doesn't work especially when they get closer together you can intuitively see that this it will create a mess so now they have equal Spin and you can see it creates a mess so it needs to have opposite spin it's a very simple visual intuitive understanding of why you have need spin up and spin down and of course you know with this model we can create much more complex Spinners um not not just that what I showed you but you know any any combin there's many many ways how you can create Spinners with this model but again it's all all compatible with the elastic solid model so I hope I was able to motivate you a little bit to look in this area maybe and hopefully other scientists will join and to do more research in this topic so I want to thank you very much for your attention and I also want to mention um other researches so several will follow but elash melt and Robert close were not not able to talk today and I hope if you're interested you will also consider uh looking at their research thank you very much are there any questions oh thank you very much thank you for Pres presentation of such number of physical and mathematical ideas and presentation of models of this ideas and uh well uh do we have some questions please well I ra the hand can I yeah can you okay so it's very nice talk uh as I understand your model of particles is like uh like you have some small volume and you integrate energy momentum tensor energy inside it it's like a stationary wave basically the wave energy it's like a soliton wave so we have a a stationary wave right can imine this in a certain volume now we when we integrate over this volume we know that part what we call particle it's in there so in the whole energy in there corresponds to one particle in clotes yeah yeah so that's why how I understand it so but this model is quite similar to the approach of schwinger you know he he forget about particles because for him particles were very you know nasty construction yeah and and he instead take energy momentum Tor integrate over the volume and he instead of particles considered currents and you know currents are are the the basic construct in his theory so I I think it it could be somehow connected with with his ideas at least in my understanding of of your theory yes question thanks may I speak oh no yeah I see lots of hand I need to call out or um I have a a comment yes may I speak yeah yeah yeah I I just I I want to my name is DKI as an old relativist I cannot agree with you that in generality space times is contrary it is an elastic body this geometry is dynamical my second remark is that they remember many years ago specialist on socalled continual theory of dislocation in crystals for example crer discovered very big similarity between between this continual Theory ofation and general relativity this observation led him and pres professor H from K to gener generalization of SpaceTime model from reman manifolds manifolds with metric leit connection to more General reman cartan manifold this metric manifold with torsion you you have told about yeah I can also in case you want to wonder about special relativity I have a slide too on that in case anyone has a question about that um monre yes please do you hear me yes because my microphone sometimes is sing off I have so can I speak yeah yeah I I have a first comment concerning I like them very much and but they were invented by Rodriguez in 1840 I actually had your paper yeah you're right yes yeah yeah you're right three years earlier but I saw that too late are you're right actually yeah yeah yeah okay so I I have a question and you mentioned that you can calculate the speed of light for me speed of light is something like a natural constant and it's so how do we really derve speed of light or on what does it depend oh okay well it depends on the material con so let's just pretend we're looking not at SpaceTime but just another material it's easier to talk about so maybe there's less conflict so um in any material maybe I can show this right any material we have what water whatever it is you you have a speed of a speed the wave speed let's call it the wave speed okay the wave speed is is constant in in that particular material let's just forget for a moment about SpaceTime and all that so now we have to imagine a world where everything is composed of waves in in that material let's take a phoneon world you have you have a crystal with phonons in there and there is this phonon clock so what this is is you have a um a little phonon wave okay that moves around the circle and that's one click right no problem here now this speed of light in this case speed of that wave is constant throughout that Medium okay it's it's in in an absolute sense now what happens when we watch a god like obser we watch we watch what happens now let's say we move this phon on clock right this phone on clock is now moving actually downward sorry it's moving downwards now what happens is the path is getting longer as the phon on clock moves now thing is the the speed of that wave is constant so that length is the same as that length that means it will not get all the way around that means this phone on person wearing this phone on clock will think that time is is actually slower so when they come get back later together they meet up they will count the clicks for instance how many clicks were passed on their clock they will see that you know this clock had fewer clicks than this one and it's simply uh so basically special relativity is a property of any wave system any wave system so now in our case we are composed of waves so everything electrons protons we are waves you know photons or waves or measuring sticks or waves so so if you think of that then it's actually obvious that any moving system in any Moving System any clock we have is compos of wave that has to tick slower because the path if if you move it it will be helical it will get longer it will stick slower it's actually so simple when you think about this but I know people always think oh it's got it has to be more comp compated but actually I don't think it's it doesn't have to be more complicated what do you think about that so you don't derrive the speed of light in in vacuum you say it depends on on on the medium on ones on the young mod yeah maybe Mark can also talk about this it depends on the young modelist it's the square root of uh you know better the the equation for deriving the speed of light stiffness and such things depends on stiffness and young model is really high 114 so it's very super stiff as you can imagine otherwise the speed of light wouldn't be so quick okay thank you so thank you very much Maran okay good we're being recorded again Maran kinsky wrote Shantel are you a wave also and that's actually my question now to you because you used a word in your talk you said this is ontological and you me meant the waves but in real experim well sorry in the real world there are tables and chairs and people and in your world there are no tables or chairs or people so I think you should not use the word ontological I see them waves these waves of yours are in our imagination okay and they're in our mathematics and they may give good predictions but they are not the last word in fact they're only an interface to predictions about what actually happens in the real world like the Moon being there or not being there and so on so this was my yeah remark to you and it was a beautiful talk beautiful beautiful pictures to movies well actually when you zoom into the J right the thing is the point is when you zoom if you could if we were like Godlike beings we could do that and look it all the way in detail at the end what we would see if we were Godlike beings we would not see any particle we would we would see the waves so that's we wouldn't see the waves well we cannot because we are human we are made of waves but it if L it there's a phone may be made of I don't know if we're made of waves we can imagine we're made of waves but I think this is in this model in this model we are all vibrations so imagine there's like a big Crystal with phonon worlds phon on people and phon on chairs you zoom in there with microscope you would see the wiggling of the the crystal right that's in a way that's what we it's an analog model basically yes in in the model in the model yeah well we think that it could be actually the model it could actually be you know the way so the universe could be a a big elastic solid I know it sounds strange but well maybe it could be really but I still think that actually if it is it's still only half of reality and for instance um uh you mentioned the work of um Ilia I forget his yeah um who says well okay I mean we can bring back reality and have particles and clicks as well and and have a preferred reference frame and and bring back reality bring back ontology to everything but we have to accept action at a distance then depend well we can talk about this is a whole big topic as you know sure we'll just on that yeah totally I agree there's some issu there yeah okay thanks so thank you very much who else can I make a one question sure okay so there is a model of there is famous vol book the universe in h droplet so he somehow also models the SpaceTime in so so actually um the metric is encoded by different uh order parameters uh and there is like mapping of B of equations to to to curve SpaceTime right so so so did you make attempt in this Direction with this quaternionic model and do you have extra possible predictions that were not accounted from previous models well this is work in progress so we're actually thinking about what the next steps are so maybe if you have some pointers we could try to go in that direction we are actually open for ideas and also if anyone wants to collaborate maybe and has you know can help us all right thank you one other remark okay in relativity we have no letter we need no letter we don't need it that's true we don't need it yeah that's true we can never detect it we don't need it so like just like in when you have sound waves in air you don't need the air to calculate you know the doler fact you don't need it but it doesn't mean it's not there so even Einstein said you know um it makes sense to consider it it's just you can't you can't you can never detect it you cannot it doesn't have a movement in itself but it's not this do it's not a a problem in terms of the mathematics is exactly the same relativity excluded notion of yeah just you don't need it but if even if you have it because special relativity it's basically a wave uh it's any any wave system will will will automatically have special relativity and you don't need it right to calculate anything it would because actually you know that the Lawrence um the gamma the Lawrence Factor actually came from Lawrence and he actually had this initially they were actually using The Ether to calculate things and they realized oh it's way too complicated so then they figured out a way how to do this without ether but it doesn't mean it's not there just because you don't need it may I have a word it was a question about future future is in every direction is unol the unsolved problem density functional Theory obviously using qu will be able to substitute several constants introduced over the years for accounting different interation between particip Whatever by this by the story of course what will be final results is difficult to say but surprising are accuracy of the physical constants obtained by using this model if you you can verify everything just everything is agreement next Direction already said D she didn't mention about it because paper is now under revision so it would be before another interesting clent equation again it's much more Rich quatal Quantum mechanic is much more richer and in agreement with all res there is no there are no contradictions several of you asked about general relativity I will memorize H cliner what he really did he assumed basically the same with some special constants but he introduced defects defects that were generated by mass especially high mass densities like Star whatever this def the deform space GD as you as shant was saying and this creates gravitional interactions according to this is situation what we did is is even simpler we don't have to introduce defects in fact energy itself deforms space and creates gravity but basically concept are the same what what Kleiner did is in fact he obtained general relativity equation in agreement which is in agreement with exactly exact exactly the same expression yeah exactly the same we I believe another very interesting Direction said about this by introducing deep refraction around big mass star whatever and by inversing the geometry we obtain I believe we obtain the same equ at the moment we have SIMPLE TI this you may say Newton formula for equation but next step I'm basically I'm completely sure but I'm not mathematician I cannot do this by myself some somebody has to spend some time with this but obviously for me a results will be very similar to having CL which which means general relativity so what we did in fact in this simple few papers we combine quantum mechanics with gravity at the moment in the simplest form thank you thank you thank you very much well who else last last remark if in relativity because we have no ER then we also have no absolute frame of reference all frame reference inity are equivalent and allance sure yes i' be happy to I have several papers I can send you if you like the link because this has been derived before so people have derived you know special relativity based on on a model with an elastic solid model so that's actually not new and yeah we can never detect it but you know it doesn't mean it's not there we will never know about it we never know exactly what that frame of reference is in a way you know the fabric of space is is the same right whether you use space density or space time in fact that gravity bends space time you are still actually kind of talking about an absolute frame in a way in a way it's kind of similar okay who else oh so thank you very much