Three Roads to Quaternion Gravity

Transcript

[Music] I'm Doug stand a physicist sitting down to tell you about this paper I wrote what is it called three roads to quaternion and gravity it's about 13 pages long double-spaced it will be submitted to a conference I went to on space-time the ontology of space-time fifth meeting uh or so I don't know whether it's going to be accepted I know only 19 people went to the meeting not a big crowd-pleaser as it were in Bulgaria a little bit hard to get to but it was valuable to me and I am trying to as best as I can formally present my new proposal for how gravity might work so what are the three roads now the first road was the one I figured out in the spring of 2015 the hundredth year anniversary of Einstein's proposal for gravity general relativity and it was based on this very simple observation that if we take some event so D I will just use DQ and we square that sucker up there'll be a time component there'll be a space component and then there'll be three other terms over here and the observation was that this is Lorentz invariant doesn't change for inertial observers they all agree on that quantity no matter what the heck is going on and that's the basis of special relativity the other three terms I didn't have a name form I eventually called them in that spring space times time because there's space and you multiply it by time pretty sophisticated name if I say so myself not okay those are Lorentz variant so under these Lorentz changes whether the rotations are boosts those guys are going to change and we're okay with that every complete understanding of what's going on in special relativity involves knowing what doesn't change and what does change and how those things do change so then I asked the converse question I said well what sort of physics appears when you say hey two observers agree to that and that space times time but they don't agree on their interval and the only area of physics where the intervals really seems to change much at all is in fact general relativity like wow that would certainly be way simpler held in terms of the kind of algebraic manipulations you have to do if that was really true and so that's why I began exploring and I must confess I always thought about it in terms of XY and Z but in this paper I point out that this is a far more general way to think about these squares because that first term there is it is that one and this one is that one except this applies no matter what your choice of coordinates are you know you could go the spiracle coordinates or you know cylindrical coordinates doesn't matter that would be the space x time term and i'm saying that that always is the same for absolutely everybody so so that was that was Road one let's just keep that well the problem with that is that remember how I said all these are these Lorentz transformations that are you know intimately associated with that interval being constant because you do that change and lo and behold that doesn't work so you really must pair your invariance principle whatever is with the transformation and I eventually did that no I didn't this guy purple penguin did that sort of thing for me are how point it point me the right direction and so you can see that the space times time term there it doesn't change at all that's my underlying symmetry but it means that things like speed that does in fact change and it goes up by this gamma squared and then finally if you take if you do the square that I've been discussing you see where the gamma kind of goes and that's that's all well and good I think one of the nicer things that came out of this paper was it was this little graph here where I've got constant intervals that's the stuff of special relativity and then I've got the graph of constant space times time and you go well those are just kind of like a 45 degree relationship there that's like I shouldn't be a big deal that should be easy to figure out it should be I don't know why it hasn't been I don't know why haven't people haven't explored it but this picture actually has made kind of creep to mean something and that is some people I had said hey why don't you do more with your proposal and it's like because I'm not sure where to go next well I actually started to get an idea going and that is I'm gonna go back and look at my books on special relativity and say wow this is how they solved it this this kind of this kind of little riddle and what I'm going to say is well let me look at that riddle rotated by 45 degrees and see if I now can make a statement about my proposal for how gravity works and to me that might be a path to kind of flesh out this idea more than that I have so far okay great then the final leg the final road is to realize that that transformation law well although it's got these gamma and the gammas take velocities unless you have velocities indifferent that have different the last different values in space-time it's not really going to do anything so you really have to now look at space-time as having some kind of velocity everywhere you are here that would then kind of go into that expression and it's like well what Boston would be and of course it's it's the escape velocity some a velocity to get yourself free of gravity and that only came about you know in less last summer summer 2018 when I realized yeah yeah I've got my gammas that's a good thing I've got my transformation law to go along with my conservation principle but then you have to have a velocity field and that's related to gravity and so now now I had to fight flesh out that idea again I'm not super confident about my capacity to do that which is my normal way but but that's what you need to plug into there to see if if things are working out if you just use Newton's the Newtonian escape velocity you do better than Newton did just not good enough to get along with our current best test so of Wheatfield gravity and so then if you come up with kind of more an ad hoc way of having a velocity field well you can do better but then people will complain rightly so I should say that you've got this kind of have ad hoc proposal for the velocity field and they they don't like it all right but that's what it's like when you're coming up with a new proposal for how gravity works you gotta expect a lot of bumps along the way and at least at least this this paper represents my first effort at formally introducing returning gravity to the physics public thank you very much [Music]