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  1. kmm

    I Are all symmetries in physics just approximations?

    Sounds interesting! Putting that on my 'to read' list.
  2. kmm

    I Are all symmetries in physics just approximations?

    Yes, perhaps I have overly romanticized the "laws of physics" as absolute things, fully capturing the nature of what they describe.
  3. kmm

    I Are all symmetries in physics just approximations?

    Interesting. Thanks for that, I will take a look at that paper.
  4. kmm

    I Are all symmetries in physics just approximations?

    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...
  5. kmm

    I Are all symmetries in physics just approximations?

    This is opening a new door for me to explore! I will be looking further into this. Thanks for the clarification!
  6. kmm

    I Are all symmetries in physics just approximations?

    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...
  7. kmm

    I Observing black holes in a finite time (in Earth's frame)

    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!
  8. kmm

    I Observing black holes in a finite time (in Earth's frame)

    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...
  9. kmm

    I Observing black holes in a finite time (in Earth's frame)

    Thank you for this clarification!
  10. kmm

    I Observing black holes in a finite time (in Earth's frame)

    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...
  11. kmm

    I Observing black holes in a finite time (in Earth's frame)

    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...
  12. kmm

    I Confused about some notation used by Griffiths

    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...
  13. kmm

    I Confused about some notation used by Griffiths

    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.
  14. kmm

    I Confused about some notation used by Griffiths

    OK thanks. Well it looks like I need to just review complex numbers, because the factor of 2 and these relations aren't obvious to me.
  15. kmm

    I Confused about some notation used by Griffiths

    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 ##...
  16. kmm

    Particle Is Griffiths Introduction to Elementary Particles up to date?

    I suspected that. Thanks for the feedback!
  17. kmm

    Particle Is Griffiths Introduction to Elementary Particles up to date?

    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...
  18. kmm

    Particle Is Griffiths Introduction to Elementary Particles up to date?

    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...
  19. kmm

    Potential of a grounded conductor in the presence of an external charge

    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...
  20. kmm

    Potential of a grounded conductor in the presence of an external charge

    No it doesn't, and at this point my initial confusion has been cleared up.
  21. kmm

    Potential of a grounded conductor in the presence of an external charge

    Right, I meant net charge. Yes, I was considering the condition where our reference point was at infinity that we set to zero.
  22. kmm

    Potential of a grounded conductor in the presence of an external charge

    Definitely. In this case, I was assuming an ideal situation.
  23. kmm

    Potential of a grounded conductor in the presence of an external charge

    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...
  24. kmm

    Potential of a grounded conductor in the presence of an external charge

    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?
  25. kmm

    Potential of a grounded conductor in the presence of an external charge

    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...
  26. kmm

    Potential of a grounded conductor in the presence of an external charge

    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...
  27. kmm

    I Bernard Schutz proof of the invariance of the interval

    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...
  28. kmm

    I Bernard Schutz proof of the invariance of the interval

    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...
  29. kmm

    I How to think about x/x, or (x-1)/(x-1) etc.

    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.
  30. kmm

    I How to think about x/x, or (x-1)/(x-1) etc.

    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...
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