I looked at the first paper, but didn't quite spot the Aha! moment where the equation was derived. As I understood it, the derivation was left outside the paper for being too complex. Is my understanding correct ?
Just that point particles were modeled as singularities
I understand that the derivation in the paper is entirely classical, my question is in regards to the use of singularities generally to substitute for point particles following geodesics. Is that something that we expect to carry through to a theory of quantum gravity ?
Since I am reading the papers and trying to make sense of them, I will meanwhile ask a question:
Do we expect that particles are related in any way to singularities in quantum gravity ?
How can you say that there is no analytic solutions when you allow approximation as part of the definition of analytical solution ? There is, in the approximation that one of them has zero mass!
Anyway, my question is more that is there a general argument that one can make for why such a result...
Perhaps I am using the word analytically incorrectly. What I meant is symbolically or mathematically, through algebra and calculus, and by taking approximations where necessary.
Do you need an analytical solution to check such a property of trajectories? Surely the question is simpler than to require the full GR simulation of two black holes.
Perhaps a better question is : if you solve EFEs numerically for far away black holes, will the black holes approximately satisfy the geodesic equation in their approach ?
What I have in mind is you take the equations obeyed by two far away black holes and approximate them to get some notion of trajectory and coordinates of these two objects, and then derive that they will approach each other following a particular trajectory using EFEs, then that would...
Rather than plugging the metric into the geodesic equation, can you derive for example that two black holes far away from each other will obey an equation with a second order derivative in proper distance and 2 first order derivatives contracted with the connection in terms of the metric?
Since the EFE describes the shape of spacetime, it describes the way black holes, for example, evolve. Can one derive the geodesic equation from it in some limit ?
Hey, why was this changed to B level ?? I'll have you know that I am the graduatest of the graduates. I deserve the A level just as much as the next guy, even if my question betrays it!
I'm happy with the answer for any of them.
Why is such a question difficult to answer ? Why is it not just listing possibilities and trying models for them ?
If singularities don't exist in QG then what prevents particles from just collapsing falling further until they collapse into a singularity? Is there a repulsive force in QG ? Is time infinitely stretched near a singularities? What else could be happening?
As an elaboration, the phase space path integral can be cut into pieces made up of an endpoint having a specific position and momentum, and even though the cut pieces wouldn't inherently have a physical meaning. Wigner function is also a function which assigns numbers to specific position and...
I have heard of phase space path integrals, but couldn't find anything in Wikipedia about it, so I am wondering, what does it compute ? In particular, are the endpoints points of definite position and momentum? If so, how does one convert them to quantum states ? Also, how is it related to...
Does anyone know of any resources studying these spacetimes and how physics looks like in them ? Writing 2+2 never gets you any good results on google.
:oldsurprised: What is this sorcery ?
When I put up one finger and five fingers I get six fingers, where did all of these hands come from?
We should get Costello to teach them some maths
This person will not be able to appreciate the next course in Spanish literature because he did not build his vocabulary enough. Had he learned his vocabulary well, he would have been able to read about the Spanish history through its own historians, and he would have been able to go to Spain to...
This is why I was very tempted to make the butcher die, no one will dare to take his knives!
Or something like this :smile:
But that is not the problem, the problem is what will happen to the Co-op owner?? Now he can never get his money from the pig farmer! And he is still indebted to the...
I should have used variance instead of distortion, sorry. I mean by "distortion in the ratio" the variance in the ratio between different countries. I, too, didn't mean deviation from 50% ratio.
How large can we expect the distortion in the ratio to be to still be able to say that the intrinsic traits are the main factor in deciding the ratio ?
If the actual distortion is large enough, doesn't this imply that indeed the main factors in deciding the ratio are external conditions ...
@jeffery_winkle
If your claim is true that the male to female ratio in physics is due to something inherent in men and women, then I suppose approximately the same ratio should hold in the different countries worldwide?
It is very easy to disprove the pythagorean theorem! First, bring a ball ...
Not going to finish the proof to avoid spoilers :biggrin:
Edit:
Although I suppose that an assumption of the theorem is that you are not allowed to bring a ball
It is sometimes difficult to consciously see that one has a certain bias or belief when asked about it directly, but it would reveal itself through a clever question.
This is exactly what @epenguin was talking about.
A very nice feature for readers and helpers alike :smile:
When subscribing to a forum, is it possible to subscribe only to one (or two) of those levels ?
Are you talking about physics calculations or maths calculations ? Are you carrying the algebra all the way to the last step or are you plugging numbers into the equations at the first possible step ?
Can you show us an example of a question with these needless calculations or symbolic...
Then these books will have what you want, you will love them if you like challenging yourself :smile: The Feynman lectures are very insightful, I think they would make the most impact by reading the corresponding chapter in them after finishing the problems of that chapter in your main...
Morin is a problem book, you can use it concurrently with Kleppner as a source of extra problems if you want. Alternatively, you can jump into Purcell right after Kleppner.
However, these books are very physical so do not count on seeing a lot of mathematical proofs there. For a mechanics book...
Along with Boas, the beginning mathematical methods textbook in the UK is:
http://www.amazon.com/dp/0521679710/?tag=pfamazon01-20
See if it has what you want.
That is definitely the case. What I meant was more like, do you have to unlearn things from this book if you want to do mathematics for mathematics later ? Is this book better than other methods books in that aspect ?
I do not understand this statement. K&K problems are never highly computational, and if you understand the answer, it usually does not take too much space to write it.
@Cosmophile: If you are finding the problems difficult, then that is all the more reason to do them. You will never get better...
A very good student might also notice that n and n -1 must swap values when going from n = 10 to 9, and that is only possible if 9 is actually -9. That makes n = 10 the only possible solution. But is this not a bit too much to expect from a high school student ? I think @collinsmark was looking...