Enforcing the Unity of Space and Time Using Quaternions

Transcript

[Music] hello I'm Doug Switzer and this talk is entitled enforcing the unity of space and time using quaternions it was given at the fifth international meeting on the ontology of space-time all the way in Albina bulgaria very close to the Black Sea and I traveled all that way because I thought if there were going to be a group of people who thought that time and space had to be forced together at all times and all places this would probably be the group so I decided to travel all that way and and talk to them and it really was a productive time for me ok so most of those folks don't actually use quaternions like it's a little curiosity and that's it but of course that's kind of common in physics and so instead of just presenting my abstract as such as it was I decided to actually focus on 0 and 1 and how my work might be able to relate to what they do which as I say never uses quaternions but certainly uses 0 and 1 so the first part was going to be on 0 1 the real numbers the complex numbers and the quaternions and the Part B was going to actually be simple applications of quaternions to physics and that would be like squaring a quaternion and saying hey the real part looks like it's what the underlying symmetry of special relativity and the imaginary part is what I'm speculating has to do with gravity and then if you just take a quaternion and its conjugate and form a product of that that that might actually be a road to quantum mechanics that most people don't seem to think they do they travel on ok so this big target graphic here is all the zeros and ones that I'm going to talk about and one thing I noticed as I was making up this talk was that zeros are straight lines on this graph and that most of the unities are nice curved lines except those that are Newtonian the straight lines actually come from Newtonian physics where time and space don't have anything to do with it with one another and the other important thing to notice is that there are a lot of eyes in this thing like eyes ear oh oh that's like not having an eye at all and then I 1 2 3 and I 4 is just like eyes ear o modulo 4 something like that all right so first of all we got to start with 0 and 1 I mean because that's how piano was able to build up all the real numbers and the complex numbers and all the different sort of odd numbers that are out there but I think if you think about them they're a little bit richer then they actually get credited for that their relationship is kind of deeper and it's deeper through the trivial group sounds kind of ironic says it's trevor grew up sounds unimportant alright so the first some simple math that 0 plus 0 equals 0 and 0 times 0 is 0 and 1 times 1 is 1 now the trivial group only has one element in it and these are three different ways of representing that group and I think some math sophisticated people will say yeah and they're there they're basically there's an equivalence relationship to them and so it really doesn't matter that there are these three and it's like yeah but we're doing mathematical physics we want to think about this and what its implications might be ok so when we add some thing when we add zero we end up with zero so a big riddle we have is like how does time keep on going on and if you're with this group you're not supposed to ask the question that way how does space-time keep going on and I think of zero as being here now boom yeah we'll set here now with a finger snap okay now here now is gone oh except it's somehow continued right I mean it feels like I'm here now I'm just here now it'll later and later now how do I pull that sort of stunt off and my thinking is that it's that the here now is zero at location zero zero zero and so I add that together and I get to another moment okay so and and and there's this little math thing about mathematical fields a mathematical field is is a kind of prerequisite to doing calculus the study of change and you had to be able to add and to multiply as group operations in order to say something's a mathematical field and so I was kind of excited when I realized oh wow than zero here this trivial group is a mathematical field and then I went and I looked in the definition of it and they said except there was a special clause except if the identity for addition is equal to the identity of multiplication and they K that case it's not a mathematical field and I was wondering why did they put in this special you know exception because you always have to be particularly wary when you find mathematicians doing special exceptions okay and the reason is is because it doesn't change you know zero never changes it's got that kind of quality to it and if you're going to study change which is what mathematical analysis is using mathematical fields to me you have to contrast that with something that cannot change no matter what you do and that would be this that would be zero zero has that quality so I think it's important to well it's not a mathematical field it's a it's a mathematical constant and take that into account don't forget about it I think it's important and yet one is actually kind of different in the sense that you can construct a continuous group out of one times one equals one because what you do is to say oh now I'll hit it up with all the real numbers and so that means that like if you have a quarter times four well that equals one and no matter what real number you choose there's going to be an inverse to it such that it equals one and so you can you can manufacture a continuous group starting from there we the same does not occur for 0 because 0 times 1/4 is 0 it's it's this black hole of numbers okay so in the graph on the on the side there you see I've got a node and that's it it's just about zero and then I've got some some loops there because that's for multiplication and so you started a vertex you go along the edge and you get back to a vertex and so it's just these little self loops all right so what's the implication to physics well I treat the universe the entire universe as the trivial and then we can only really do three things we can take care now of the universe adhere now and get to here now ah that's how we keep on going forward quote unquote and yet the important thing to me is that it doesn't add information you know you're adding zeros okay and so the amount of information of the universe doesn't change and if we want to think about well how does this happen in a continuous kind of way well you can take zero times zero and you end up with zero but even more importantly of course is the signal that one unity times one equals one so that can that can evolve but again the amount of information in the universe doesn't really change and so I think that's also kind of very very key and yeah so I think it does have implications for how we understand this whole thing about living in one universe how people could say but there's the multi-universe people yes they are and I don't buy their story like at all okay so now we graduate to real numbers okay so we've got zero and I think of zero now as this bridge between the positive numbers and the negative numbers and I want to think of the positive and numbers and negative numbers as being very very similar it's just that we choose different labels for them and instead of putting zero dead in the center and then the two sets looking like they march off in different directions as I was taught I actually put them side-by-side and the reason is because of course I care very much about the difference operation and in the zero in the center kind of view when you say hey what's the difference between a billion and a billion five and you go whoa I gotta go a billion this way I got to go billion five that way and then I've got to take the difference between those and notice the difference is five can you go wow that's a lot of work okay I gotta go Chuck a billion well if you got them side by side then you could say well I'm out here a billion and this much B difference between the two sets is five and that's like well that's that's super easy in fact you can go over a trillion and you could go over 10 to the 24th and the difference of 5 is still you know gonna be kind of the same sort of thing so I really think about them that way because it's so much more efficient to think about what is the difference between two sets of numbers it's not not so hard to know it's not so hard to do you don't have to carry exactly where the heck is is the zero is and so that's why I think about it that way but I also thinking about multiplication and the graph theory for that and now it's kind of interesting in the sense that like zero is just has all these these these pipe cleaners coming into it all these edges from vertices the zero has of course three sorts of self loops 0 times 0 0 x plus 1 0 times minus 1 but it also has directional arrows and maybe it's not clear that those are directional but that the ones that come over go like 1 times 0 is 0 but I can't go the other way I can't go 0 times 0 is 1 that's very very wrong and so it's this is is it's a profound sinkhole because it not only has under action Alero x' but it has directional arrows and if I didn't have those those black pipe cleaners making this big the big journey over then that's the group Z 2 and it's just this little 2 by 2 sort of that gives us the rules for Oh a plus number times a plus number is a plus number that would be that that little loop on there and that a minus number times a minus number is a plus number that's actually the gray thing with the gray pipe cleaner getting to one and then of course we have a positive number times a negative number actually stays a negative number so we have all those groups represent all those operations kind of represented in that graph so and which I had never seen before I mean I've seen Z two before and then people don't care about zero but the complete picture is more complicated than I'd kind of seen represented before all right so now we go on to complex numbers okay and again we've got to one more pair pair in there and it's a and the multiplication is represented by Z four and actually it's this number that got me thinking it's like holy complex numbers I always thought about those as two numbers the real numbers the imaginary numbers and now there's a Z for where's the Faunus and the foreignness is in oh the positive reals two negative reals the positive imaginary the negative imaginary there's my set of four and then I realized that you know I could use I to various powers and represent them all in other words I to zero that would be the positive reals I squared oh I squared this - that would be the negative reals and I to the unity would be I and I to the third would be the negative imaginaries and it also generalizes really nicely because now you say I to the N where n can be anything any positive sort of number modulo four just means oh I got this mix of real and imagined so it makes real and imaginary numbers seem kind of conceptually far kind of closer and we got this group z4 well what does that look like well it's actually got z2 in it but it's just gotten bigger and nothing nothing more than that zero of course so it's looking a little scarier it's got more loops there and a z4 is actually kind of elegant it's very nice flat plain with all kinds of loops and crosses and and directional arrows and its really kind of nice nice little boxy thing that sits in the plane but but then the guy who organizes is this guy Petkov and he says you know you should be able to to put your ideas to experiment and so I said well well let's do an experiment here and and and the experiment is to show that complex numbers should not be represented by the complex plane which they've been done for like hundreds of years I mean the 1800s where this idea came up and people have loved it I've loved it but I'm no longer happy and I'll tell you why do this this following experiment okay because the real numbers don't are not the imaginary numbers there are different animals okay and so now I'm going to do a reflection and it's going to be around the real or the imaginary axis but I'm not going to tell you whether it was the real or imaginary axis I'm just gonna hide that one piece of information from you and which one was it and there is no answer and that's that to me that's a problem it should be like technically obvious which one I did at which one I did not okay and it's not and then people have known that like since the sister was born it's like yeah rotated by 90 degrees looks exactly the same and I mean exactly the same and being exactly the same means there is no difference and being no difference is about a problem because these two are different all right so can we do anything different can we improve on on on count the complex plane and so what I did was because we're thinking about space-time is to take to the time part as a real number and a space part as an imaginary number okay and so that now complex numbers are therefore a one dimensional space-time number okay so let's look at this first one where this okay so here's a guy he hits the ball it flies out to right field and then it goes backwards backwards in what backwards in time okay that's all that is that is a reflection around the real axis because I said the real numbers are time and I'm doing that okay now in the bottom little animations that wallet how's that guy hidden two balls he's not hitting two balls he's got a huge ass mirror there and I'm just seeing these spatial reflections I'm seeing a reflection in space and so now you go oh so there are no labels here about which one I did but visually you now know you know that a reflection of real numbers requires that you remember hmm oh yeah how you can see that's going in reverse from how it was before and if it's a reflection of imaginary well that's a mirror going on so you better see like two things two things kind of moving in a mirror reflection kind of way and so now it's should be visually obvious and as a matter of fact I say whatever complex number graph you that you have now think of it as a line scan you do a line scan of it and that will give you this representation that I think is more faithful - what complex numbers really are because because they're different alright so okay so now we go on to what I'm calling space-time numbers this has got four four sets of pairs so positive and negative real numbers positive and negative imaginary I positive and negative J positive negative K the rules for addition are all going to be the same as before there's just more rules the product table now gets crazy large it doesn't go four times three to 12 it goes four times three to twelve minus two because there's a degree of redundancy because high squared play is the same as J squared is same as K squared the minus one I totally love the zero there because it really looks like a tarantula it's got like sixteen pipe cleaners going into it eight of them bi-directional and eight of them unidirectional because they all come from these this various parts of the cube over on down okay so they're the quaternions basically our space-time numbers but that except that quaternions are done over the four real numbers which again i don't think that's the deepest way to do it but it's certainly the way that hamilton did it back in the day Rodriguez did it back in the day Gauss even before them did it but I think we're going to eventually have to deal with all eight of these guys when we do relativistic quantum field theory if we ever do but we'll try but the important thing is even though it's crazy complicated looking don't get too scared because it's basically a complex number oh except that it's got instead of I it as ijk okay and well we're used to dealing with three dimensions in space so that shouldn't be that scary oh and we've got the cross product in the cross product rocks the because it means you can deal with a bicycle you know an angular momentum which shows up everywhere I mean I want tools that could deal with bicycle wheels out of the box without adding anything to it so the rules are just like for complex numbers actually it's the first the reals - the last - the combination of imaginaries and then we go out e ne and you add in this cross product and that's gonna be the product all right and these do play a role quaternions and physics they're kind of minor as things go they they they're used to do rotations in space and they're also used in the standard model it's the group su 2 is known as the unit quaternions so quaternions with a norm of 1 remember you've got to add that with the normal one it's not just its quaternions no no it's normal one and then you get su 2 all right great so and to me this kind of thing is this graph is comparing complex numbers to the quaternions or space-time numbers and I think if we were to show this to somebody who is not a professional physicist and ask them the following question like which one of these numbers that somehow it's about numbers addition and multiplication of numbers which one of these do you think would be the right one to handle three-dimensional physics and along with time and I think the answer would be universal it'd be the really complicated one all right and yet if you do professional physics you use complex numbers for quantum mechanics and you don't use quaternions for quantum mechanics I mean we go up to complex numbers and we say that's enough and then we'll add all this other stuff so we can actually do a bicycle wheel but it's like why just start with something that can handle it out of the box and you know you know to be honest this is what hangs up in my basement like literally I can I can I can reach I just reached out and touched it so it's part of my home without that animation okay I wasn't able to figure out how to make that in a wall hanging but when I think about numbers you know I literally start from thinking about 0 and 1 and how they have a relationship to each other via group theory and how it continues on to greater and greater complexity until you get to the the space times numbers which look complicated enough to actually deal with are the world that we live in all right and and you know yeah I can't put the my wall hanging up on the preprint server it's not too bad about that all right so so that's my story of numbers that are used in physics and I got some feedback and it was like man I you went on and on about these numbers and I wasn't sure you were ever going to do physics well so so now in this part I'm gonna try and do well again math all right and the math I'm going to do is I'm just going to square a quaternion and think about the real part and I'm gonna square a quaternion and think about the imaginary part and I'm gonna take a conjugate of attorney times another quaternion so those are math operations and yet I'm going to say those very simple math operations can be mapped directly to physics that in the first case it's going to be about special relativity in the second case is going to be about my proposal for quaternion gravity which is not general relativity and then finally it's going to be about quantum mechanics and you know we had some philosophers at the meeting and it's kind of like you know math is physics stop you don't have to think about other issues very direct kind of approach all right so so quaternion times of quaternion is a quaternion and i can take what ever pair of events i want to and i usually think about the change in events so i don't have to worry about like where's the origin that I'm dealing with I'm dealing with the Delta that Delta is supposed to look like it's a differential like those points could be arbitrarily close to one another in space-time and I think of them that way and when I go ahead and calculate the square that part in blue that is well we got DX d dy squared plus DZ squared that's something the Egyptians knew about that different surveyors on the on the plane of the Nile could agree upon those values that that Square even if they don't agree on the X's and Y's and disease but the square they're going to say same and Einstein's great advancement was to say well time and space have a relationship to each other and it was actually yeah that any thing was it was in his paper and it certainly was much more an emphasis of Minkowski that was that was an invariant interval of space-time and then in night 2015 I started wondering well what the heck is going to what sort of physics is going to result if people agree on the light green box and I actually think it's got to be just as important because I mean special relativity is is absolutely core that in fact when when two observers agree about the Lorentz invariant interval they disagree about those other three terms space times and well why is that of use it's of use because it now will provide you with the information about how they are moving relative to each other you know if all the two observers reported was WOW we agreed about the interval and you ask the follow-up question well what was your speed relative that other person they they don't have an answer that's a problem because they should have the answer they have the information you know and if you keep this space times time terms sitting right next to it then you'll be able to say oh they were just moving along this y direction and that's it that's the that's a complete story all right so oh and I do own quaternions comm I should say uh and the reason I bought it it was because of that light blue box I saw that and said that's that's the key to special relativity and that's not an accident that that that works out and so I bought it in like 1997 I believe alright so is that interesting or is that just funny and and there was one source on the internet this Lobos mutal who thought it was just funny he's got quite a number of experience points that's increased even since then and I do not happen to like this person to be honest although he has greater credibility on the Internet in the sense that my reputation score was and on the order of twenty nine and he went off on under this math thing and said oh this is the most important symmetry the most important value and he didn't say what symmetries were involved because you can't talk about these things without saying what was what under what group does that value not change and was you know it's is is it's just really sad that it was what I calls sophisticated garbage but that's what I expect from Louis okay so and this is a dangerous question for me to ask because because I am a fringe physicist in the sense that I am NOT a professional and therefore fringe physicists have contributed so far just about nothing and they always bring in a cowhide Stein okay but I'll tell you why I am let me read the quote okay and it's not from Einstein okay it's from Abraham Hayes who did a scientific biography of Einstein and it was right in the in the prefix he said had I to compose a one-sentence scientific biography of him Einstein I would write better than anyone before or after he him he knew how to invent invariance principles and make use of statistical fluctuations okay so this was back in 2015 and I was thinking about that very quote and I've written down on a piece of paper the square of a quaternion for like the 17 hundredths time and then I said okay I just had a proposal for how gravity works crash and burn for perfectly valid technical reasons the proposal not only used quaternions but it used a different type of number and somebody said hey how does that behave under rotations and I said well it changes then it doesn't conserve angular momentum and there firts run it took me like five days to once that critique came up of course it anyway without going too far into it I had nothing and so I wrote down the square thought about this quote and said jeez what happens if people agree to that those two other three terms which I had asked about like like literally in 1997 and as hey what are these calls people and you know got crickets and nobody said anything and it doesn't have a name that's what's weird about it see if you think about what is space over time you go well that's velocity what is space time space and you go all that's area well what's space over space and you go space over space angles those are angles okay and so what is space times time no we really shouldn't have silence there it's just a different permutation okay this has got to play a role in physics it can't just say well no I dozen of them I'm never going to be used by in any kind of physics ever I mean it's too simple and and so we are going to explore what I'm calling space times time since there isn't already a really common name for it alright alright so we're using equivalence classes here for both special relativity and my proposal for quantum gravity so in special relativity they two observers are gonna say hey we're both inertial observers but you're moving at a different speed if when we calculate in one reference frame one an interval is and we do it in the other one and the real part is exactly the thing all right and here is the Minkowski space-time diagram if the number is that at squared number is if it's positive it's going to be in the time like part of the light cone oh I should say if you calculate it and the real part is like zero then you're dealing with the black lines there you're dealing with the light cone itself and if it's negative that's the world of space like separated pairs of events and it's all very nice and simple to do and while all I'm saying that is that for quaternion gravity proposal is that the imaginary parts of the square are what we agree upon okay and so now we see the zeroes are actually the DT axis and the dr axis and it's only relatively recently that somebody said you mean there if if something is simultaneous for one observer you know the DT is zero between two events all observers are gonna agree about that well that's kind of strange this is one thing we've learned is like Oh simultaneous simultaneity is relative well we're we're exploring a different branch of physics and in this one actually you do agree on being simultaneous so this is a little scary to do but that's what the graph is and you say hold it that graph is basically the light-cone rotated by 45 degrees it's like yeah that's all it is okay and nature must be using this sort of graph somehow all right so what I found was that if I just say look here's a symmetry principle let's all be happy physicists in general that we're not engaged and I think a reason for that is that physicists usually think in terms of transformation laws you know the Lorentz transformation and other kinds of transformation laws gauge transformations and those are all of course connected to deep symmetries the the symmetry gauge symmetries and and that sort of thing but a complete picture necessarily involves both okay and I only provided one there was that very satisfy so a fellow on the internet purple penguin is the only way I know of of him the only handle I have on him he actually came up with his derivation I had a separate video on it but I did this one for the group where I here's here's the thing I wrote out and I'm gonna break it up into four parts first of all we go into the assumptions and that we're going to measure time with clocks that are in our possession you know wristwatch time as it were distance is going to be measured by a pair of events released at the same time and then transport it to some observer but what we're not going to do alright is that we're not going to say and we all agree about the light-cone because if we do that then we're just in the world of special relativity and what we're trying to do is relax things so that we might kind of get into a different space different different sort of physics different sorts of transformation laws different sorts of insights into how nature works okay and we're not going to set the origin I'm not going to worry about that we're going to take it you know Delta between two events and so once you do that you don't have to worry about yet where the origin is okay so what should we start with well if you've got this whole restriction on on how clocks work and how you're going to be measuring distance well we actually know a coordinate transformation that's that works we've got this T prime equals gamma t plus gamma beta X and you have X prime equals gamma X plus gamma beta T all right so those are totally standard where beta and gamma are exactly kind of what you expect them to be we know that works fine all right but now what we're gonna do is we're gonna choose a function like a constant function such that we get a kind of a simpler expression for for time in in the new new reference frame so T double prime okay and we're gonna add in this constant function a minus beta X Prime and when you do that you go ho you chose that just to wipe out the X X Prime's in there didn't you and it's like yeah that's exactly why I did it and when you do that sort of transformation you end up with d t double prime equals 1 over gamma DT and you go well that is strange ok cuz the relationship we're used to is it equals gamma DT not 1 over gamma DT but that's just a consequence it's just it's just algebra ok so we can't say it's wrong we can say it's strange because it is strange and one of the ways of it is strange is that if the change in this double prime frame is 0 in other words if two events were simultaneous then in the unprimed frame they're also simultaneous ok so we are not doing special relativity ok there's a clearest sign possible that we've chosen strange coordinates and change strange functions such that we've got this strange result but it's ok we're being logically consistent so let's proceed see how far we get all right so now if we think about lengths and we we don't have to worry about being simultaneous ok dad that part's easy and we fire our little photons back and they land there and we go oh so this is gonna land at 2 T and for T and you go oh so so this is back to normal we've got a DX double prime equals gamma D X so that's that's nice so now if we think about D X double prime times DT double prime but we think about them in the in the unprimed coordinates that means oh we've got a gamma and we've got 1 over gamma that means that's invariant okay that was kind of our our little goal and we've achieved it but but that's for space-time sign but let's think about speeds okay cuz speeds is what people normally think about and you go okay put one over the other and you go oh that's they're not agree good agree about speeds like at all there's gonna be a gamma squared factor involved it's like whoa so things really zip in between relative between these two frames that's that's definitely strange seems almost illegal all right all right so then what I did was I said okay let's think about intervals okay where we just have these the difference of x squared minus the difference of in-space squared and we've got both both in the primed and unprimed frame but and they're they're just they're just that they just end up being kind of boring but it becomes interesting when we take our little where we think about what the double prime frame looks like given the unprimed kind of relationships that we have and we just do this little substitution we'll get the squared and we get 1 minus beta squared and a 1 plus beta squared and then if we toss in the escape velocity of Newton from Newton's time you know when he was firing a cannon off of a mountaintop and it eventually made made an orbit and then he was like no let's let's see what it takes to get out to infinity and stop that's the value when you do that you go hold it that looks like the Schwarzschild solution of general relativity and so that will pass weak field tests I was like that's kind of cool okay now why did I put this warning thing in here I did because I actually stepped through this proof our derivation with two people at the conference and they both were like man I don't know for you you're just doing that because you end up like with a result that's connected to physics and it's like I'm totally guilty of that as a matter of fact that's one of the reasons I think I'm people don't take me too seriously is that I've been focusing on that for like of why don't we just say a really really long time that you know I know you have to do this and I got there and people like well you looked in the back of book you cheated I don't know how to really reply to that other than that's that is that what I do because I want to connect to experimental tests of gravity and it's not like you have a choice I mean what hey you haven't you know paid enough attention to what quote Clifford will has written about experimental tests you got to end up here okay and I am there and that is to me a good thing but I'm just saying you know take it with a nice big block of salt but I actually something else happened that was uh that just recently and that and that was a realization that you know of course this relativistic velocity where does it come from well it actually comes from solving Newton's scalar field theory so it's kind of like what am i doing Newton's scalar field theory along with space times time invariants to make sure that things work out well with the equivalence principle because that's what I mean that's what I'm really trying to do I'm trying to say that everything about gravity can be expressed in this type of expression for the interval squared that and that would be that would be Newton scalar Newton with space-time Simon variants and that may be the combination that's needed to come up with a new proposal that's consistent with the experimental test hmm all right but hmm I don't have a Lagrangian s'ti right there do I and well Matt now I'm kind of up in the field I mean was certainly when I wrote this I I hadn't thought about the you know escape velocity coming out at Newton's scalar theory but um you know it it's still true that it doesn't have a metric tensor that that this really is kind of being number theory number theory not geometry theory in other words there's no metrics no connections all that kind of stuff and that you know special relativity is a constraint on all physical theories that you can write and there isn't like relativistic there isn't a row there isn't a particle associated with special relativity and the space-time Simon variance well as a proposal it's kind of putting a different kind of constraint on every single physical theory you can write but because it's not based on very the metric tensor there's not going to be a rank zero sorry a rank a spin-2 particle expressing the field theory so hmm so so now as I say since I gave this talk now that I realize oh really I'm kind of relying on Newton's scalar proposal for gravity that hopefully respects the strong equivalence principle that might be worthy of further study and believe me people have studied quantizing Newton's gravity field theory because it's easier and they always the first thing they're gonna point out is it doesn't respect the equivalence principle and so therefore we know it's this is just a toy and it's a broken toy and if it's less broken well it might be kind of curious all right and and then of course the the follow-up question is what is this is this proposal going to be different in any sort of way and I think it will be in the sense of I'm always going to change terms that involve changes in time and change terms and change terms in in space and you know actually I wrote this and I I'm now starting to get worried about it that's the that's a problem of doing physics this is you know you always end up going maybe I am NOT thinking about this quite straight because I always said oh there's a time thing and there's a space thing and so the e fields won't change and the B fields are totally going to change because they both got spaced parts and spaced parts but the time part that now that I'm looking at this and you know you write it down in a concrete way I go hold it that's not a time part that's a 1-over time part so shouldn't that be not one over gamma but gamma and in other words shouldn't that be gamma squared E and gamma squared beta and this like wow that's so as somebody of limited skillset as I am I'm always doubting myself which I should I should I teach take myself with a block of salt and other people take me with a mountain of salt and so now I'm looking at that and thinking well maybe that should really be gamma squared e one thing one thing I feel confident about though is that it's not gonna be the same oh there's no way that can work out the same whereas sorry whereas in general relativity I think that the E and the B fields are actually invariance in order to transform like a tensor and they had to go through specific hoops so I really just think if we measured the pointing vector or you know measured the e field and the B field and compared them at different heights believe me that that's probably technically incredibly demanding that I think they're going to be different and I like this sort of test in the sense that it's it's it's cleaner then then anything else because it's just well if it's supposed to be the same and it's the same then general relativity is correct and if the E and B fields are actually different at different points in a gravitational field then that makes it much more likely that my proposal has is is more closer to the truth all right okay so now we're going to move on to quantum mechanics and I certainly been thinking about this for a long time and one of the first things I did as a matter of fact was to think about Hilbert spaces because Hilbert spaces have a whole bunch of properties that you absolutely must have you know inequalities and I had a few back in the day it was easy enough to show but through actual calculations with quaternions mm in a quantum mechanic context I hadn't done that I had done gee I gotta get the triangle inequality I can do that with Q star Q sort of situation so that was good but if I I go on with some of these diagrams here I was like oh so I've got all these lines that what if what if zero was just a dot right dead center and then unity would be the circle around here and that's great remember I'm treating space-time as a complex plane because it's complex plane and I've got a unit circle that is the u 1 symmetry u 1 symmetry is the symmetry underlying the conservation of electric charge I was like wow that was not hard but it should also strike you as deeply strange why do you believe strange well because points most of the points in there are going to have absolutely no way to communicate with other points in there because they're going to be space like separated I mean half of them are time like separated so that's fine but have other are gonna be kind of like space like separated so I like how the heck can they do that in a certain sense at this point I don't know but I'm only using a pencil okay which seems kind of low-tech and Wow bang I got to the symmetry underlying electromagnetism of the gauge symmetry of that and it's like that sounds like a really great thing I mean this this is probably a thing right as but now if I don't think about the space part that like as a social unit but I think of each one of them independently then I've got the symmetry su - oh and by the way this is a thing that Lobos noticed and you didn't think about the symmetry this DS T squared plus DX squared plus dy squared plus DZ squared just said well that's that's what we should focus on but if you don't think about the symmetry then you miss like everything I mean to me it's fascinating that I can just by drawing circles a sphere drawing a sphere or drawing a circle I can get to symmetries underlying the gauge symmetries of the weak field and and an electromagnetism and it's like I didn't do anything I don't know is this yes another happy accident uh anyway I actually don't know how to do a single calculation with the week field so I don't know what to do with this observation other than to say hmm I'm glad it's there I didn't say one and are you gonna get out to su3 and I think the answer is no but I do have the quaternion group q8 which has 8 things in it all that are of size one all with a normal one and I don't know that you need much more than that to do the work quote-unquote of su3 in other words the thing about su3 is it's 3 squared 9 minus 1 it has 8 things for ADA eight gluons and each one of those has a normal one and again I'm not sure how much more you need than that from your group so cooter knees are never going to be su3 they're going to be q8 and maybe q8 is enough I mean it's a provocative pretend again I can't do anything with a weak force ok I could do nothing with a strong force either but I'm kind of out of symmetries after I get up to 8 which is kind of cool because one of the deep mysteries of the standard model is why these three and why not other things and why not more things why did why does the stories appear to stop beside other people saying hey let's invent something even bigger that says there are all kinds of more particles and they're not well I got stopped here and I think that's a good thing all right but as I say quantum mechanics huge subject ok so how can you really be way way way more connected to what's going on so I came up with this testable hypothesis and there's this wonderful book quantum mechanics the theoretical minimum by Siskin and Freeman and I'm just going to go through this entire book and say can I do absolutely everything they do using quaternions hmm and people just typos returnees got poor you're done okay well you can follow my progress slow as it may be on github I've done two of the lectures so far and this is a companion book and so let me answer is that first question here because we've got your space-time dimensions and yes those will always be four there will never ever be anything different from four I cover all right but then there's going to be something I call state dimensions and what's every quaternion can be represented as a quaternion series and this is this goes back to newton's day right like yeah I can give you the sign or I could give you the the series that converges to exactly the same value and so we're gonna have one to n states where n can be an infinite that's okay and so you see in blue there's my space-time dimensions so I'm always going to try and be really clear what I'm dealing with space-time dimensions or state dimensions in fact and when dealing with quantum mechanics you're almost always talking about state dimensions but you're always working with space-time dimensions because you always see those four in blue they're always there and then it's just a question of how many states you have and a lot of the work happens with just two states and so there they are boom boom and now I just have to go and prove everything can be expressed using quaternion series to do quantum janek's and this is another I think very deep idea that again gets that graph that was up in the front and that is that you know you look around in any room and you say hey do we all the particles here know how to do gravity do they know how to do electromagnetism do they know how to do the weak force to know how to do the strong force and do they know how to do all of these at the same time and the answer of course is yes you know there's not like this particle said well I got the Maxwell equations I just got a like chill on that one for a moment it's like no you don't even know you had no moment to chill and it's like how do you do all these things all at once and and to me that that graph is is kind of the way because it's just a superposition of all of these types of symmetry all in the same space and so that's why it's so important to me to just be mister of automorphism in the sense of I'm always stay doing different operations but always ending up in exactly where I was because that's where I'm going to be in the next moment I'm gonna be the same place in space lab okay so so in summary I'm saying you can deal with special relativity and a new approach to gravity and we're working on you know doing all problems in quantum mechanics using quantum as' series and boy do I have a lot more to do I'd certainly do but if you want to join me or contribute or whatever certainly feel free to contact me all right thank you very much [Music]