ajb

What? But what you said makes no sense. It is just nonsense.

I am not sure what a particle is without space-time, I am not sure what gravitational collapse of a particle means - with or without space-time. The general accepted idea is as follows.... String theory, loop quantum gravity and so on all suggest that space-time at some level should be 'fuzzy' - that is described by a noncommutative geometry. Keeping time as classical , it may be possible that the dynamics of some theory involving a noncommutative geometry - our quantum space - in some macroscopic classical limit give us space as we know it. This is plausable, but no theory has really been given yet. However, this is would not be enough. If space comes as some classical limit then so should time - we like to treat space and time on equal footing. Now we are in trouble. We would like some theory on or of a noncommutative geometry to be such that the dynamics in some limit gives us space-time + general relativity (+ maybe small corrections). But we have to do this without time from the start. This is a big problem - we don't know how to do physics (so dynamics) without time!

Of course. I had in mind physical situations where these non-linear effects are too small to be detected.

Only if the non-linear effects are small. I am sure there are such examples, but I can't think of anything off the top of my head.

If the equations are non-linear then you cannot usually add solutions to get another solution. It depends what you mean - for sure there are some equations that a change of variables can make them linear. But more generally, we can always (or just about always?) linearise a differnetial equation. This gives us an approximation to the original equation, which more or may not be a reliable thing to do.

I mean you will need a mathematical theory that show that we really can think of matter (or fields) as being the source of space-time. General relativity and field theory are based on space-time already 'existing'. A theory that has space-time as something emerging is going to be different to these existing theories - or mathematical frameworks. I am not saying that it is impossible to create some theory - it is an interesting question and I think linked to some things in NCG and so on.

In general no - you cannot add or subtarct solutions to the field equations and get another solution. What is often done is add this small linear correction and in an approximate sense the sum of the background and the correction satisfy the field equations

And you disagree? Which is what I have said in this thread earlier. Nobody should be in fear for their lives when dealing with an officer of the law - but it seems that some people are and maybe for good reason. I don't understand what you are really arguing here. I understand that in principle all peoples should be treated the same - but that is not what we are seeing. ------------------------------ There is a BBC report on 'Why do US police keep killing unarmed black men'. That report presents he finding from the study that I spoke of way back in this thread. It is interesting reading. http://www.bbc.com/news/world-us-canada-32740523

Agreed... nobody has said it is all one sided or that the police do not need to look at themselves.

You are missunderstanding. Nobody has said that nothing needs to be done. Nobody had said that people should accomodate fears and biases. Nobody has has said that people should tolerate police killings and so on.

Which she knew full well would happen. She took the risk for a greater good. We all know this... but it is besides the point. All that some of us have said is that a measure that individuals can take today is to be extra careful when dealing with the police. Not that they should have to do that, but it could save their lives. If they want to risk getting shot for some higher goal then so be it. Only they can make that choice.

I guess this is another related issue to look at - it is related to gun issue in the US.

Was her life in danger? Either way she took the risk for a meaningful cause. 'Should' is the problem here. No one thinks they should - just the harsh reality right now is that some people may need to be more careful when dealing with the US police than others. That sucks, it is unfair and wrong. I don't think anyone is saying otherwise. And of course, it is not the root problem. It is much wider than just the police - it is an issue across US society. Segregation is still in force in the US, this is the biggest problem.

Okay, you can think of gravitational waves as small changes in the background geometry. These are described using the wave equation - hense gravitational wave.

Maybe off topic, but I just read about a shooting in the UK --- http://www.bbc.com/news/uk-england-norfolk-36767865

You are right, no one should have to... I think we all agree with that.

I am wondering if one can make some comparison with people who were young adults in the 60's -- thinking about the open attitudes towards sex.

The it is up to you to make sense of this. Such an understanding is outside of general relatiivty and standard field theory - both classical and quantum.

With no details ... you work with the linearised field equations. You think of a background metric plus a linear 'correction' g = g0 +h. You then take the 'correction' to satisfy the linearised Einstein field equations. Then you make a choice of gauge (do a little maths) and you can write the equation that h must satisfy as the wave equation.

We will have to wait and see - or really they will. I expect some level of disappointment, assuming there is some large deviation in peoples expectations.

Gravity must have been present in the Universe right away - it is something to do with the very nature of space-time itself. It may have been the case that supergravity was important in the early Universe. You are really getting to the limits of our knowledge now.

Of course not, and that is not really my argument here. The point is that if you really think that the people are out to shoot you then you would be wise to be extra careful. It is wrong, you should not have to think this etc. But right now every black kid in the US has to be told in school and at home to carefully comply with the instructions of a police officer. This, is by no means a fix - not even a bandaid. It is a much deeper issue that goes back a long way - for example your race can determine where you live, what school you go to, your local services and even the shops you go to. The BBC wrote a report in this http://www.bbc.com/news/world-us-canada-35255835 It seems that guns are not the prime issue, but for sure they make a bad situation worse.

Very sci-fi I would say .... stop watching The Matrix while drinking

Great, but can you give us some more details - like the actual mathematical theory, or at least some some of the aspect. By 3-torus you mean SxSxS?

I guess this should be in speculations... Anyway, generally what is a 'relativistic illusion' as opposed to a relativistic effect? How can we tell the difference? ------------------------------- Edit: I had a quick look at the paper - not much in the way of mathematics as is needed for a theory. Just loads of pretty pictures and some basic calculations done with numbers to some stupid number of decimal places. To be honest, I was not expecting much more.