Demystifier said:
As a first step, look at Ref. [49] in the paper.
Thanks for the direction on this Demystifier. Firstly, apologies if the questions that follow are of the sort that you don't even know where to begin to try and explain. I have been in discussions before where someone poses a question that just doesn't seem to make sense and you can be left scratching your head as to how to even begin addressing it. So, no offence taken if this post falls into that category.
I read the paper but didn't understand most of it. I've started studying some maths again, so far refreshing what I've learned in high-school, so it'll be a long time before I can understand the maths in the paper. Is it possible to get a very rough, general idea of what the paper says, do you think, without the mathematics? In my mind I'm trying to get a rough understanding of the consequences of what the paper says, as opposed to being able to determine the accuracy of what is being said, if that makes sense?
In truth, I probably didn't understand too much after the introduction even (or possibly even in the introduction).
To allow for gravitational Lorentz violation without abandoning the framework of general relativity (GR), the background tensor field(s) breaking the symmetry must be dynamical. Einsteinæther theory is of this type. In addition to the spacetime metric tensor field gab it involves a dynamical, unit timelike vector field u a .
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I have a very limited understanding of fields, but I tend to think of them as analogous to a sheet of some sort stretched out through space, with a vector field having some sort of directionality to it at a given location - perhaps another analogy here might be like a putting green, the kind you see in golf video games, where arrows show the direction the ball is likely to break.
My understanding of the above would be that there some form of fundamental, deeper lying field - the background tensor field - which might break Lorentz invariance, which appears to be a necessity for Bohmian mechanics.
To say that the Earth and everything else is made of Ether, I am picturing some sort of fundamental field which gives rise to all matter. My intuitive thinking would be that this would be a single universal field, but I think you suggested that this might not be the case.
A separate, but related question: under the Bohmian interpretation, is the Universe continuous?