Originally posted by Great King Rat
Right, but there must be "something" to cause that spacetime curvature?

As I remember, there are four fundamental forces in nature. Are you saying there would be essentially only three?

I remember reading something about Gravity "leaking" into our "universe" from another dimension.

Space-time curvature is produced by mass (or rather energy). When Einstein came off the boat in New York the media asked him to sum up his theory for laymen. He said something along the lines of:

Spacetime tells matter how to move, matter tells spacetime how to curve.

If one takes the view that gravity does not exist because it is only curved spacetime then one also has to take the view that the other forces do not exist either as they are geometric in origin as well (see e.g. the chapter on connections in principle bundles in Geometry and Topology in Physics by Nakahara).

The stuff about gravity leaking into other dimensions sounds like Brane world theory. It's a way of trying to resolve the fact that gravity is far weaker than it should be. The idea is that it leaks into an extra dimension (the other forces are constrained not to) and so drops off as 1/r^3 instead of 1/r^2 until the other dimension (which is small) is saturated, so we see a much weaker force that we'd expect to.

Originally posted by DeepThought
Space-time curvature is produced by mass (or rather energy). When Einstein came off the boat in New York the media asked him to sum up his theory for laymen. He said something along the lines of:

Spacetime tells matter how to move, matter tells spacetime how to curve.

I quoted that earlier, but as far as I can tell it is a quote from John Archibald Wheeler and not Einstein.

https://en.wikiquote.org/wiki/John_Archibald_Wheeler

Originally posted by DeepThought
No, you're confusing understanding maths with understanding a collection of statements. To fully understand the whole of Newtonian mechanics one has to understand the Hamilton-Jacobi formulation. Not knowing about that is no barrier to understanding special relativity (it helps with General relativity if one is interested in calculating geodesics). A ...[text shortened]... rs do not not understand a field just because they don't have the complete professional toolkit.

I guess I just hold a personal belief that something is not understood until its is understood in the frame of mathematics. I personally don't claim to understand much, and it bothers me when others do so recklessly.

Originally posted by twhitehead
I quoted that earlier, but as far as I can tell it is a quote from John Archibald Wheeler and not Einstein.

https://en.wikiquote.org/wiki/John_Archibald_Wheeler

Yes, I replied to the post and then read yours. I got that it was from Einstein from a book I read many years ago. It's entirely plausible that the book I read got the originator of the quote wrong. The Wikiquotes page gives it as being in a book by Wheeler. It's entirely plausible that Wheeler was quoting Einstein, but didn't feel the need to attribute the quote (thinking it was famous enough not to require the attribution), or even that he did attribute it to Einstein but the Wikiquotes contributor didn't notice...

Originally posted by joe shmo
I guess I just hold a personal belief that something is not understood until its is understood in the frame of mathematics. I personally don't claim to understand much, and it bothers me when others do so recklessly.

Socrates agrees with you. Not understood or not understood completely? I agree that for a really deep understanding of most physics theories a mathematical understanding is essential. But it is also quite easy to deceive oneself into thinking one understands a problem because one can regurgitate a collection of equations. Quantum mechanics is a prime example of this. Solving Schrodinger's equation is a relatively easy problem mathematically, but they are still arguing over the interpretation of the wavefunction.

Originally posted by DeepThought
Socrates agrees with you. Not understood or not understood completely? I agree that for a really deep understanding of most physics theories a mathematical understanding is essential. But it is also quite easy to deceive oneself into thinking one understands a problem because one can regurgitate a collection of equations. Quantum mechanics is a prime ...[text shortened]... problem mathematically, but they are still arguing over the interpretation of the wavefunction.

Well... it's mostly the non-physicists who argue over the wave function, and physicists over 70 years old who have nothing better to do.

Originally posted by joe shmo

2) Newtonian Physics is a simplification of Relitivistic mechanics. ...

Very strictly speaking, Newtonian physics doesn't come from relativity nor vice versa. Newtonian physics assumes absolute time and space and implicitly implies that the speed of c should be the same for all observers. Relativity says there is no absolute time and space and the speed of c is the same for all observers. Also, relativity says mass varies with speed while Newtonian physics says it doesn't. The two clearly contradict and in several important ways. So your inference has a flawed premise. At least for motion, for 'low' velocities (say <0.1% of c) and low values for certain other variables, Newtonian physics gives a good enough approximation of what relativity predicts and is fine there for purely practical purposes and is often more convenient with simpler equations, but, nevertheless, relativity is the exactly correct (or at least that is what is generally assumed) while Newtonian physics is not entirely incorrect but 'approximately' correct for 'low' variable values.

Also, there is absolutely no way you can derive relativity equations from Newtonian physics equations and Einstein had to reject much of the basic assumption behind Newtonian physics to derive relativity! Thus knowing the Newtonian physics equations isn't absolutely essential for you to learn relativity although I think it should make that learning at least a bit easier. In fact, it is perfectly possible to directly learn relativity without learning a single one of the Newtonian physics equations not found in relativity (I say " not found in relativity" because there is some small overlap of content). I hope I have clarified that for you (assuming you are here to learn something about science else this post is wasted on you and is only for somebody else who is curious).

Originally posted by KazetNagorra
Well... it's mostly the non-physicists who argue over the wave function, and physicists over 70 years old who have nothing better to do.

Hey, I'm not that old! Do a quick search for "Copenhagen" in the abstract in quant-ph on arXiv.org and you'll find a healthy debate about the correct interpretation (with the Copenhagenists, especially, claiming that their interpretation is quantum mechanics). Although you are right in that in their research most physicists don't worry about it, as it's not their immediate problem and unlikely to affect the outcome of their research. The interpretation "used" in practice is the ensemble interpretation, which is a sort of Copenhagen™ Lite in that it says basically the same thing, but doesn't make any claims about the non-existence of the Wavefunction or anything other than measurement which is what the Copenhagen™ interpretation does (this is real pre-Popper logical positivism).

Originally posted by DeepThought
Socrates agrees with you. Not understood or not understood completely? I agree that for a really deep understanding of most physics theories a mathematical understanding is essential. But it is also quite easy to deceive oneself into thinking one understands a problem because one can regurgitate a collection of equations. Quantum mechanics is a prime ...[text shortened]... problem mathematically, but they are still arguing over the interpretation of the wavefunction.

I actually disagree. I am strongly of the opinion that knowing the mathematics or equations is not necessary for understanding.

Originally posted by DeepThought
Hey, I'm not that old! Do a quick search for "Copenhagen" in the abstract in quant-ph on arXiv.org and you'll find a healthy debate about the correct interpretation (with the Copenhagenists, especially, claiming that their interpretation is quantum mechanics). Although you are right in that in their research most physicists don't worry about it, ...[text shortened]... which is what the Copenhagen™ interpretation does (this is real pre-Popper logical positivism).

I'm of course exaggerating a bit, I'm just saying that in experimental practice, the whole interpretation issue is irrelevant (as you say).

Originally posted by twhitehead
I actually disagree. I am strongly of the opinion that knowing the mathematics or equations is not necessary for understanding.

That post has to be read in conjunction with my last post on page 2. One can have an understanding of a theory without knowing the mathematical aspects, but if one does not one cannot understand it as deeply because one is missing the mathematical aspects.

However, mathematics does not have to be understood solely in terms of strings of symbols - most of the classical geometric arguments are essentially visual, for instance Thales' theorem (a triangle circumscribed by a circle with its base along the diameter is right angled) is proved using similar triangles and the rule that the interior angles of a triangle add up to 180 degrees.

Originally posted by DeepThought
That post has to be read in conjunction with my last post on page 2. One can have an understanding of a theory without knowing the mathematical aspects, but if one does not one cannot understand it as deeply because one is missing the mathematical aspects.

However, mathematics does not have to be understood solely in terms of strings of symbol ...[text shortened]... ing similar triangles and the rule that the interior angles of a triangle add up to 180 degrees.

Well I guess a large part of our understanding of the world could be labelled 'mathematical'.
My point was that we can have a strong intuitive understanding of most of physics without ever memorising all the equations or being able to solve problems - and quite often there are people who can solve certain problems but don't have a more intuitive understanding.

I would agree however that both are better than one or the other.

Originally posted by DeepThought
Socrates agrees with you. Not understood or not understood completely? I agree that for a really deep understanding of most physics theories a mathematical understanding is essential. But it is also quite easy to deceive oneself into thinking one understands a problem because one can regurgitate a collection of equations. Quantum mechanics is a prime ...[text shortened]... problem mathematically, but they are still arguing over the interpretation of the wavefunction.

I'm meaning to imply a complete understanding. I also agree that one doesn't guarantee the other or visa-versa, I have many of my own personal experiences that I believed I understood a system because I could apply the mathematical model. Needless to say, I have been unpleasantly surprised when things don't work out quite as planned. Although in most of those cases its more that I overlooked things that had an effect... if I had thought of them I could have adjusted the model, and things would have went better. However, I almost always have better first time success in delivering a working design than some of my coworkers who only use 'understanding' as opposed to 'mathematical understanding'. Practical application can very rarely (with the exception of trivial cases) be cleanly done without math.

Originally posted by humy
Very strictly speaking, Newtonian physics doesn't come from relativity nor vice versa. Newtonian physics assumes absolute time and space and implicitly implies that the speed of c should be the same for all observers. Relativity says there is no absolute time and space and the speed of c is the same for all observers. Also, relativity says mass varies wi ...[text shortened]... ing about science else this post is wasted on you and is only for somebody else who is curious).

I never said that Relativity was derivable from Classical Mechanics. I said that Classical Mechanics was a simplification of Relativity. Under the right assumptions Relativity should break down to Newtonian mechanics, saying this is not the same as saying Relativity is derivable from Classical mechanics. So yes, I guess one could go straight to Relativity, and yet is that usually how its done? NO, because in practice if you can only gain a 'basic' grasp of Newtonian mechanics you a a snowballs chance in hell of working within the framework of Relativity to any point and purpose.

Originally posted by joe shmo
I never said that Relativity was derivable from Classical Mechanics. I said that Classical Mechanics was a simplification of Relativity. Under the right assumptions Relativity should break down to Newtonian mechanics, saying this is not the same as saying Relativity is derivable from Classical mechanics. So yes, I guess one could go straight to Relativit ...[text shortened]... snowballs chance in hell of working within the framework of Relativity to any point and purpose.

I don't know if it would be 'breaking down', it would really just lower the number of digits of accuracy, for instance, the flight time close to c would be different from Newtonian physics but close to Earthy velocities, they would read about the same out to a sufficient number of decimal places that there would be no usable difference, unless extremely accurate atomic clocks were in use and as they can now, tell the difference in time flow if the clock is raised a meter from it's previous position, now in a different gravitational strength.