Anyone who ever studied General Relativity have probably seen how to get Newtonian Gravity in the limit of slowly moving particles and weak gravity. This is exactly how it should be, as we know from our everyday experience of kicking balls around, that Newtonian physics works quite well in this case. On the other hand, it is amazing how little we know about physics if we abandon the assumption of weak gravity. Many effects are falsely attributed to the general principle of relativity*.
In this new paper my collaborators and I study what happens with General Relativity if particles move slowly with respect to the speed of light, but gravity is not assumed to be weak. It turns out that one gets a novel manifestly non-relativistic theory of gravity (i.e. with a preferred direction of time) much richer than Newtonian Gravity and formulated in a geometric language similar to Einstein’s theory.
It is most surprising that this theory - called Non-Relativistic Gravity - can encompass gravitational time dilation and many of the famous solutions of General Relativity are also exact solutions of Non-Relativistic Gravity. A welcome philosophical consequence is that this theory teaches you a lot about the general principle of relativity. Our study shows that many remarkable and celebrated effects in General Relativity are merely strong gravity effects.
Having a manifestly non-relativistic theory opens up numerous further studies one can do in cosmology, holography, string theory etc. Here the existence of a preferred direction of time is a huge simplification that makes life as a theoretical physicist a lot less miserable.
I apologise that we don’t have a more sexy title for our theory… Hopefully some will find interest in our work and perhaps even benefit from it in their own work. For those non-researchers reading along, I hope you love science in its working and enjoy looking at cool equations - feel free to comment and ask questions!
Best regards,
Dennis.
Abstract:
We study the non-relativistic expansion of general relativity coupled to matter. This is done by expanding the metric and matter fields analytically in powers of 1/c^2 where c is the speed of light. In order to perform this expansion it is shown to be very convenient to rewrite general relativity in terms of a timelike vielbein and a spatial metric. This expansion can be performed covariantly and off shell. We study the expansion of the Einstei
... keep reading on reddit ➡By 'paradigm shift' I mean a fundamentally different approach/conception of mathematics. Of course the analogy with physics is not perfect since old theories in physics are falsified but theorems in mathematics are eternal; Pythagoras' theorem remains as true today as it was thousands of years ago.
I'm coming off from the movie Interstellar, where Cooper transmits some 'inside Black Hole' data, and then they solve the problem of gravity (combine QM and GR). But, what kind of data? Do we need to know what the inside of a Black Hole looks like? Do we want to know the magnetic field strength or the electric permittivity there lol?
I mean.. while attempting to solve the problem of combining QM and GR, do we run into some unknown constants we need to plug in, constants whose values are data inside a Black Hole?
If so, does that mean that there are no more mysteries except in the realm of the extremely small?
Really interesting DVD. I haven't quite grasped how I will incorporate it into my game, yet and will probably re-watch it.
Who it's for: All levels but it's entirely defensive focused. Wim himself states that he believes in a defense first approach.
Main Points: If you like a more conceptual style of teaching as opposed to "When he does this, I do this" style. The first 15 or so minutes is spent just talking about the principal itself and how it applies to self defense. The really interesting thing I took away from his DVD is that he advocates a reactive style of grappling - that is, the person making the first move is actually at a disadvantage and he shows some examples of why. I can see how in some scenarios that is the case but I've always been a bit more aggressive in how I approach my grappling, it's quite a departure from what I'm used to. He also dedicates an entire chapter to escaping kesa gatame which is not too common in BJJ. One thing I do agree with him is that he believes that reversals - say a "sweep" from bottom side control, should be learned as they are a skill wrestlers and MMA fighters have that BJJ lacks.
The way you should be approaching this set is study how he applies his principle to positions and then find ways you can incorporate it everywhere.
Verdict: I enjoyed it, will definitely be re-watching it. I'm curious to see offensive applications of this principle and incidentally he just released two new DVD sets exploring the offensive side of his philosophy.
I'm currently self-teaching myself math and I'm on pre-calculus at the moment.
I'm trying to build myself up to learn general relativity, but I'm not sure how I would go about doing this.
Is this just an impossible task or is it possible?
General relativity is on my bucket list and I really want to learn about it properly before I die.
I'm dead serious about this.
So, what are prerequisite math topics?
I'm also not able to go to any math classes.
Thank you all and sorry if this sounds like a stupid and overambitious question.
It's a waste of time.
