Severian

Well, I would say it is stronger than that. Irrespective of what the final quantum theory of gravity is, it will have a particle which at low(ish) energies transmits the force - we may as well call that a 'graviton' (although recognising it may not be fundamental in that form). In other words we must have an effective theory containing a particle which mediates gravity (even if the effective theory is non-renormalisable like Fermi's theory). OK, then this particle must be massless, since gravity is long range - if the graviton had a mass, gravity would become short range, just like the weak nuclear force. Of course, this is really only a limit on the mass since we only have to have gravity having a range of > 16 billion light years, but the mass must be very very small if it is there. (This would be stronger than the bounds on the photon mass for example.) Now if a particle is massless, then it travels at c, and thus gravity propagates at c. In other words it is more certain that the graviton travels at c than that the photon does!

Yes, gravity 'travels' at the speed of light (as your first option).

Not from where I am sitting. There is so much crap flying around here that if you dodge it on the fly past it will still get you on the rebound. I have special government funding which is supposed to reduce my admin and teaching (so I am one of your scientifically orientated guys), but the crap is still flying my way...

This is unfortunately very true. The government and universities are really piling all the admin jobs onto academics these days so they have very little time to do research. Considering the pay is often 1/3 or less what a similarly qualified person can earn there seems little point in staying. If you are not going to get to do any science anyway, why not do a better paid 'normal' job?

If you have any questions about particle accelerators, just ask. This is what I do for a living. My most recent paper was with ATLAS (one of the detectors for the LHC).

Well, if we want the acceleration to be one standard gravity (9.81ms-2), and have one revolution per day (just like the Earth has): The acceleration is [math]a=\omega^2 r[/math] where [math] \omega = \frac{2 \pi}{60 \times 60 \times 24 s} = 0.727 \times 10^{4} s^{-1}[/math], then we need a radius of: [math]r=\frac{a}{\omega^2}=\frac{9.81 \times 60^2 \times 60^2 \times 24^2}{4 \pi^2} m = 1.17 \times 10^{10} m[/math] which for reference is about 1821 times the radius of the Earth.... If you want it to be the same radius as the Earth, [math]r=6.4 \times 10^6m[/math] then we need an angular velocity of: [math]\omega = \sqrt{\frac{a}{r}} = \sqrt{\frac{9.81 ms^{-2}}{6.4 \times 10^6m}} = 0.001238 s^{-1}[/math] which corresponds to a speed on the surface of [math]v = \omega r = 7923.2 ms^{-1}[/math] which is roughly 24 times the speed of sound!

Thank you for pointing this out.

It sounds like you have been watching those conspiracy theory shows on TV. I am fairly sure that the moon landings did happen, but I do think that some of the pictures were faked for propoganda reasons.

That is true, but it usually worked the other way around. The physics theories force the need for mathematics. Indeed, this is true for most of your examples: It was clear that the ability to factor large numbers was useful in the real world long before the RSA theorem came about. This was only 30(ish?) years ago. The RZ function is just an integral. The fact that it was calculated before it found use in physics is neither here nor there. If it had not been, the physicist doing the problem would have calculated it. There are plenty of examples of (much harder) integrals which were not known when physics encountered them. This depends on your definition of symplectic geometry. If you regard Hamilton's work as symplectic geometry, I must ask you if you regard Hamilton as a mathematicain or as a physicist? QFT is based on the Hamlton principle. Modern symplectic geometry postdates QFT. No - string theory is in principle testable, so I have no objection. But once again, the motivaton of string theory is physical. I have no objection to you studying it. Who knows, you might do something which physicists find useful. What I do object to is the prejudice that anything which is not mathematically rigourous, in the pure mathematician sense, is wrong and not useful. You demonstrate this attitude yourself in your post: Ironically, this "treating divergent series by approximating by the first few terms" was the subject of my PhD. But the fact of the matter is that it works! My calculation is being used successfully by high energy physics experiments and correctly predicts the physics that they see. To suggest that this should not be done is the real prejudice. And my calculation involved the cancellation of lots of 'infinities'. You would presumably criticise Feyman's path integral formalism in this light? But again this has been tremendously successful in modern physics. Or how about the theory of Renormalization of QFTs? That won the Nobel prize a few years ago. I agree that it is undefined on its own. As I also pointed out, one has to make a clarification as to what one means by 0/0 before coming to a conclusion. I notice that you cut off the rest of the sentence, which is pointing out that if one defined the '0's on the left hand side in the same way then the answer is 1. In this light, your response seems a little disingenuous.

That is true, but it usually worked the other way around. The physics theories force the need for mathematics. Indeed, this is true for most of your examples: It was clear that the ability to factor large numbers was useful in the real world long before the RSA theorem came about. This was only 30(ish?) years ago. The RZ function is just an integral. The fact that it was calculated before it found use in physics is neither here nor there. If it had not been, the physicist doing the problem would have calculated it. There are plenty of examples of (much harder) integrals which were not known when physics encountered them. This depends on your definition of symplectic geometry. If you regard Hamilton's work as symplectic geometry, I must ask you if you regard Hamilton as a mathematicain or as a physicist? QFT is based on the Hamlton principle. Modern symplectic geometry postdates QFT. No - string theory is in principle testable, so I have no objection. But once again, the motivaton of string theory is physical. I have no objection to you studying it. Who knows, you might do something which physicists find useful. What I do object to is the prejudice that anything which is not mathematically rigourous, in the pure mathematician sense, is wrong and not useful. You demonstrate this attitude yourself in your post: Ironically, this "treating divergent series by approximating by the first few terms" was the subject of my PhD. But the fact of the matter is that it works! My calculation is being used successfully by high energy physics experiments and correctly predicts the physics that they see. To suggest that this should not be done is the real prejudice. And my calculation involved the cancellation of lots of 'infinities'. You would presumably criticise Feyman's path integral formalism in this light? But again this has been tremendously successful in modern physics. Or how about the theory of Renormalization of QFTs? That won the Nobel prize a few years ago. I agree that it is undefined on its own. As I also pointed out, one has to make a clarification as to what one means by 0/0 before coming to a conclusion. I notice that you cut off the rest of the sentence, which is pointing out that if one defined the '0's on the left hand side in the same way then the answer is 1. In this light, your response seems a little disingenuous.

This is exactly the point I made in my later comment, that on need not take the limits in the same way (or even use limits for both). I never suggested that 0/0=1 was the only result, only that it could occur, and is reasonable, for some definitions. Did you read my post? I am a physicist, not a mathematician. While I am no expert on the details of the mathematical definitions, I am certainly an expert on how maths is applied in the real world (no pun intended). I personally don't have much time for things which one cannot apply in the 'real world'. Perhaps you could enlighten me as to what abstract maths which have no application is actually good for? This is actually a good example of the difference between a (pure)mathematician and a physicist. In physics, infinities like this arise all the time in our theories and we have to deal with them. This means that we have to regulate them in some way and come up with an answer that we can apply. We do this in various ways (such as extending space-time to non integer dimensions) and use these 'mathematically undefined' theories to predict the outcome of experiments. The fact that this proceedure works amazingly well makes a mockery of your prejudices. We cannot afford to stick our heads in the sand and say that the physical laws of the universe are not defined.... Lol. The word 'asshole' isn't mathematical enough for you? I normally don't post in this forum because, as I pointed out before, I think it is pointless. I only posted because I felt that Homunculus' attacks on the teacher were unjustified. (As are your attacks on me, but I suppose that just means that you are a little Homunculus...) He is defined to be an asshole by his attacks on the teacher, not by his mathematical opinions. PS: These are Science fora. If you are not interested in science, why do you post here? In fact, if your definition of pure mathematics is that it should not be applicable to the real world, maybe we should remove all discussions of it from this site?

This is exactly the point I made in my later comment, that on need not take the limits in the same way (or even use limits for both). I never suggested that 0/0=1 was the only result, only that it could occur, and is reasonable, for some definitions. Did you read my post? I am a physicist, not a mathematician. While I am no expert on the details of the mathematical definitions, I am certainly an expert on how maths is applied in the real world (no pun intended). I personally don't have much time for things which one cannot apply in the 'real world'. Perhaps you could enlighten me as to what abstract maths which have no application is actually good for? This is actually a good example of the difference between a (pure)mathematician and a physicist. In physics, infinities like this arise all the time in our theories and we have to deal with them. This means that we have to regulate them in some way and come up with an answer that we can apply. We do this in various ways (such as extending space-time to non integer dimensions) and use these 'mathematically undefined' theories to predict the outcome of experiments. The fact that this proceedure works amazingly well makes a mockery of your prejudices. We cannot afford to stick our heads in the sand and say that the physical laws of the universe are not defined.... Lol. The word 'asshole' isn't mathematical enough for you? I normally don't post in this forum because, as I pointed out before, I think it is pointless. I only posted because I felt that Homunculus' attacks on the teacher were unjustified. (As are your attacks on me, but I suppose that just means that you are a little Homunculus...) He is defined to be an asshole by his attacks on the teacher, not by his mathematical opinions. PS: These are Science fora. If you are not interested in science, why do you post here? In fact, if your definition of pure mathematics is that it should not be applicable to the real world, maybe we should remove all discussions of it from this site?

It is possible and reasonable to define 0/0=1. 1/0 isn't really a well defined concept, because it involves an infinity. We can regulated the infinity by saying that it is the limit of a normal number. So [math]\frac{1}{0} \equiv lim_{x \to 0} \frac{1}{x}[/math]. In that case, using our definition of 1/0, [math]\frac{0}{0} = \frac{1}{0} \frac{0}{1} \equiv \frac{\lim_{x \to 0} \frac{1}{x}}{\lim_{x \to 0} \frac{1}{x}}=1[/math] The difficulty (or ambiguity) arises when we realise that we needn't have used the definition of 1/0 to say what 0/1 is. We could have just done [math]\frac{0}{0} = \frac{1}{0} \times 0 \equiv \lim_{x \to 0} \frac{1}{x} \times 0 =0[/math]. But in the opinion of a physicist 0/0=1 is the most sensible choice since we use the same symbol for numerator and denominator, implying that they are the same thing. In a physical situation (which let's face it is all maths is good for) we only really get close to zero, so a limiting case approach is fine. Professor Homunculus does seem to be a bit of an asshole.

It is possible and reasonable to define 0/0=1. 1/0 isn't really a well defined concept, because it involves an infinity. We can regulated the infinity by saying that it is the limit of a normal number. So [math]\frac{1}{0} \equiv lim_{x \to 0} \frac{1}{x}[/math]. In that case, using our definition of 1/0, [math]\frac{0}{0} = \frac{1}{0} \frac{0}{1} \equiv \frac{\lim_{x \to 0} \frac{1}{x}}{\lim_{x \to 0} \frac{1}{x}}=1[/math] The difficulty (or ambiguity) arises when we realise that we needn't have used the definition of 1/0 to say what 0/1 is. We could have just done [math]\frac{0}{0} = \frac{1}{0} \times 0 \equiv \lim_{x \to 0} \frac{1}{x} \times 0 =0[/math]. But in the opinion of a physicist 0/0=1 is the most sensible choice since we use the same symbol for numerator and denominator, implying that they are the same thing. In a physical situation (which let's face it is all maths is good for) we only really get close to zero, so a limiting case approach is fine. Professor Homunculus does seem to be a bit of an asshole.

Either you have been taught nonsense or you misunderstood. One does not need to have atmospheric effects to have colours. White light (from the sun) hits the flag and and the red stripe absorbs all the (visible) wavelengths of light except for the red ones. The red wavelengths are reflected and so the stripes appear red. The flag stands proud because it has an extra wire in it.

Either you have been taught nonsense or you misunderstood. One does not need to have atmospheric effects to have colours. White light (from the sun) hits the flag and and the red stripe absorbs all the (visible) wavelengths of light except for the red ones. The red wavelengths are reflected and so the stripes appear red. The flag stands proud because it has an extra wire in it.

They are not mutually exclusive.

They are not mutually exclusive.

Even in Newtonian mechanics, space isn't 'empty'. Implicitly, there is always a 'rule' telling you how to measure distance (the metric). Now, in non-GR mechanics this rule never changes, and is very simple, so there is a tendancy to not think of it as a property of space. But it is! In GR, the presence of mass/energy changes this rule, so that it is not the same everywhere and it then becomes more apparent that it is a property of space. But in principle nothing has changed.