Severian

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.

Presumably they aren't anymore. The are thought to be outside of our horizon because of inflation in the early universe - a period where the universe grew exponentially. There is no contradiction in this because there was no information flow - it was the fabric of space-time itself which was stretching. Einstein's postulate is only saying that information should not move faster than c.

Presumably they aren't anymore. The are thought to be outside of our horizon because of inflation in the early universe - a period where the universe grew exponentially. There is no contradiction in this because there was no information flow - it was the fabric of space-time itself which was stretching. Einstein's postulate is only saying that information should not move faster than c.

That is not what I said. GR and a theory of gravitons are not equivalent. GR is a classical theory whereas a theory of gravitons would be a quantum theory. I was pointing out that one did not need to think of GR as bending space-time - one can write down GR as a classical theory in the same manner as classical electromagnetism (as written down by Maxwell), with gravitational waves playing a similar role to light. The concept of a photon only occurs when one quantizes electromagnetism. The photon is a 'quanta' of light. Unfortunately no-one has been able to quantize gravity sucessfully, but the assumption is that its quantization will be similar to that of electromagnetism and a 'quanta' of the gravitational wave would be called a 'graviton'. PS: Reading my previous post I see how you could have picked that up wrongly. Entirely my fault. I have edited the post to make it clearer.

That is not what I said. GR and a theory of gravitons are not equivalent. GR is a classical theory whereas a theory of gravitons would be a quantum theory. I was pointing out that one did not need to think of GR as bending space-time - one can write down GR as a classical theory in the same manner as classical electromagnetism (as written down by Maxwell), with gravitational waves playing a similar role to light. The concept of a photon only occurs when one quantizes electromagnetism. The photon is a 'quanta' of light. Unfortunately no-one has been able to quantize gravity sucessfully, but the assumption is that its quantization will be similar to that of electromagnetism and a 'quanta' of the gravitational wave would be called a 'graviton'. PS: Reading my previous post I see how you could have picked that up wrongly. Entirely my fault. I have edited the post to make it clearer.

They are just different ways of trying to describe the same thing - one classical and one quantum. GR can be reformulated to look almost exactly like Maxwell's theory of classical electromagnetism (which was written down in completely covariant form before special relativity!). It is only when one tries to quantize the theory of gravity that problems arise, whereas electromagnetism nicely quantizes into QED with photons.

Its actually weirder than that because of the non-local nature of quantum field theory. The two bodies wouldn't exchange a single force carrier - they would only do it if they can excahnge 2 at once in order to 'balance the books'. Since they would br borrowing energy from the uncertainty principle, they have to give it back pretty quickly, so the exchange can only happen if there is a compensating exchange. But again, since T=0 is impossible, this is all speculation.

I personally think there should be no income tax and no sales tax - everything should be generated from corporation tax. That way salaries will become more transparent, and the companies would pass on the cost of corporation tax by reducing salaries anyway. (Of course, self-employed people should pay a tax too!)

I agree with Lucid

Why not do fusion? Tremendously exciting and interesting and vey cutting edge. If they fix the problems with it they will have solved all the world's energy problems.

Somehow 'softmore' seems more appropriate..... I do agree with that schools are taking the wrong approach. There is a tendancy for teachers to think that kids find maths hard, so they try and remove the maths and make the kids do subjects in a more qualitative nature, thinking they will be able to motivate the kids better and give them a more 'intuitive' feels for the subject. But in science, I think this is counterproductive. Once one gets beyond a certain level of understanding, maths is essential to certain subjects like physics. You need to have a good grounding in maths in order to understand and enjoy higher level physics, and in my opinion we are actually making the subject harder by teaching it in a qualitative manner. Unfortunately this is happening in first year university teaching now We really need to give the new students an entire semester of only maths to try and bring them up to speed. However, this would be so unpopular (since it is thought of as 'hard') that the students wouldn't take the course.

Yes, I agree. The impact is really how much momentum it transfers, and since the momentum/velocity relationship is non-linear the higher velocities have disproportionately more more momentum (and thus more 'impact').

Lol. Fair enough, I stand corrected. But Hooke's law is the law which governs a spring - if gravity obeyed Hooke's law it would mean that a planet at the other end of the universe would feel a stronger gravitational attraction to the sun than the Earth would. So I stand by my statement that it is lucky that we have 1/r2... Incidentally, QCD, the force which binds quarks into protons behaves very like Hooke's law. Fortunately the force is not long range because when you pull the quarks apart you put so much energy into the system that you create a quark-antiquark pair straight out of the vacuum. In essence you break the spring.

You are right - I don't agree. Mass doesn't change - it is just that momentum and velocity have a non-linear relationship: [math]p=\frac{mv}{\sqrt{1-\frac{v^2}{c^2}}}[/math] Old text books tend to define mass as p/v, but this is somewhat bogus since mass is a property of the body and should not change with reference frame.

I think our problem is that the questions don't have answers. 1. If the number you want is x, then you are inisiting that [math]x=\sqrt{a}=\sqrt{a+1}=\sqrt{a+2}=...[/math] where a is some integer. Clearly this is impossible. Unless I am misunderstanding the question. 2. the eqaution you give gives a relation between a, b, c and d, but doesn't tell you their values. So the object you want to find is not known.

I voted: outside the solar system. I suspect that creation events are actually rather rare (since all life on Earth seems to be evolved from the same creation event (or maybe 2, if you believe some of the wilder ideas), so it probably needs somewhere to have a pretty good environment not to kill off the life very quickly. I don't see that nice environment anywhere in this solar system other than Earth.

Lightsword: you didn't convince him The most important staement you made was the first one: relativity does not have objects increasing in mass as they move faster. That is just a legacy of bad high school physics teachers who don't understand what they are talking about.

As I said before, I think this is a semantic problem. Mak10: go back and reread the question again. I think you are misinterpreting it. The ball is thrown out of the train with a speed of 70mph with respect to the train, or in other words at 0mph with respect to the ground...

I am not sure if this is really what you are asking' date=' but the force is gravity and it is coming from the sun. Gravitons haven't been experimentally confirmed but the assuption is that they pass momentum between the sun and the Earth, causing the force on the Earth. the analogy which is often made is two ice skaters throwing a ball between each other. It is not a terribly good analogy since the ice skaters will move away from one another where-as the exchange of gravitons from Earth to sun is supposed to make them attract one another. They don't mean it isn't charged in that sense. They mean that there is not a positive and negative charge like there is for electromagnetism. Under gravity objects with mass always attract and by an amount proportional to their mass.

Yes and no. If you take a Newtonian viewpoint, it is not 'continuing along its currect path' - it is being pulled towards the Earth by gravity. The force is not 'balanced' so the Earth is in 'free-fall' about the Sun. If the Earth did not have any angular momentum it would simply fall in (or alternatively imagine the Sun was a 2d-plane rather than a sphere, again the Earth would just fall down to the surface). It is only because the Earth has so much momentum that by the time it 'falls' toward the sun, it it is already passed the sun, so wings round into empty space again (so to speak). In the Einstein view, you are correct that the Earth has no net force on it. It is travelling in a straight line with no deviation, and only appears to be attracted to a point because of the warped topology of space time. The bowling ball/trampoline analogy is misleading only because of the disappative effects: the tennis ball loses energy too fast and falls into the centre too quickly. Otherwise it is fine.