I think the source of my confusion was in thinking of conservation of momentum and angular momentum as fundamental principles of reality, that must be exact regardless of any limits of our ability to measure those things; so that in principle, we could find that conservation of momentum and...
I came across this video of Leonard Susskind saying that all symmetries in physics are approximations.
Unfortunately, I don't have the links on hand, but I have come across other sources of physicists claiming that all symmetries are approximations.
My confusion though is that it was my...
I have spent a bit of time with Special Relativity and am just starting to learn General Relativity, so I still have a lot to learn but this thread was clarifying and made me aware of some false assumptions I was making. Thanks again!
Another question is, does the fact that the formation of a black hole and the collision of two black holes entail a lot of dynamical processes mean that we can't apply standard gravitational time dilation to the process? I imagine that if two black holes are colliding and creating gravitational...
I mentioned the gravitational waves observation, understanding that they are emitted outside of either black hole, since I assumed they shouldn't actually collide (in earths frame), since this would take infinite time. However, since the infinite time dilation only applies to an object falling...
My understanding from General Relativity is that if as distant observers we watch a probe or any test mass approach a black hole, time dilation goes to infinity as the probe gets closer to the event horizon. This would imply that we would never observe a black hole form, or the collision of two...
It turns out my problem was in making an embarrassingly simple mistake. I often have erroneously thought of numbers like ##a## or ##b^*## as merely real numbers or a real number with a factor of ##i## attached, and not like the complex number, ##z=x+iy##. With this in mind I was then able to...
I’m not sure what lead you to this assumption that I didn’t try. I did try, and then came here when it was clear I was missing something. The previous comments gave me some clues of what I need to review, so I will be continuing to try.
I worked out the expectation values of the components of a 1/2 spin particle. However, I'm confused about Griffiths notation for the x and y components.
For the x component I got, ## \left< S_x \right> = \frac \hbar 2 (b^*a+a^*b)## which is correct, but Griffiths equates this to ##...
Right, I wouldn't expect any book to be 100% up to date. But this book was published in 1987, so I wasn't sure if this book is so significantly outdated that there are a lot of glaring problems with it that it would be best for me to just find a new book. I also wasn't sure, being this is an...
I have a copy of Griffiths Introduction to Elementary Particles (1st Edition) and was thinking of beginning to work through it. I was curious if anyone knows if this text is sufficiently up to date or if there have been any major developments in particle physics that would make it worth getting...
Sorry for the confusion here. Yes, I understand that. When I initially asked the question about a grounded conductor dissipating all charge, I had misunderstood Delta2 in post #4, thinking that they were implying we could have net charge on a grounded conductor even in the absence of some...
OK, when you said regardless of external charge, I thought you meant that we could have nonzero potential in a grounded conductor in the absence of external charge. But again since the conductor is grounded, even in the presence of external charge, the conductor should still have a potential of...
When we ground a conductor, aren't we saying we are dissipating all charge? In that case, what is producing a nonzero potential?
Wouldn't bringing in infinite external charge be effectively the same as maintaining current in the conductor?
In that case there is current in the conductor. So even though charge on a grounded conductor has rearranged itself under the influence of an external charge, the potential must still be the same as ground (V=0) since there is no current. Therefore anywhere on the conductor, regardless of the...
If we set the potential at infinity to be zero, we find that the potential of a grounded conductor is V=0. The conductor being grounded has no net charge and produces no external field, so I understand why in that situation we would say the potential of the conductor is zero.
However, in...
Thank you very much for your thorough response! Your explanation is much clearer to me. It makes sense now that it is a natural assumption to make that ## \phi ## be independent of velocity. I can see now what Schutz was trying to get across, but I think that Schutz not stating the assumptions...
I've been going through Bernard Schutz's A First Course in General Relativity, and I'm hung up on his "proof" of the invariance of the interval. At the beginning of section 1.6, he claims that he will prove the invariance of the interval, and after a few lines shows that the universality of the...
That's right, thanks for pointing that out.
This is a helpful guideline.
I had suspected this would be the case.
Thanks for the link. I'm going to have to take some time to digest this.
In solving physics problems, I have often done some type of simplifying where I eliminated an x in the numerator and denominator, or eliminated some other terms. For example, maybe I have something like ## \frac {x} {x^2 + x} ## and I simplify this to ## \frac {1} {x+1} ##. Or I have something...