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Ah right, of course. Thank you for helping me with this!

Thank you, I think this helps clarify things for me. The way I understand it then is, since the fourth parameter is fixed by the normalization condition, and since the overall scale of ## \psi ## is irrelevant to the continuity conditions and therefore, to the fact that we get quantized energy...

On page 160 in Shankar, he discusses how we get quantized energy levels of bound states - specifically for the particle in a box. We have three regions in space; region I from ## \ - \infty, -L/2 ##, region II from ## \ -L/2, L/2 ##, and region III from ## \ L/2, \infty ##. For the...

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

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

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

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...

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

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...

Thank you for this clarification!

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 Earth's 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.

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.

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 ##...

I suspected that. Thanks for the feedback!

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...

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

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

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

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...

OK, this has helped. I think now I just want to study this whole subject in more depth. Do you have any recommendations for textbooks that go into more depth with magnetic fields/magnetic materials? I have taken E&M so I have a basic understanding of magnetic fields.

OK, this is interesting to me. I have been imagining this scenario as essentially the same as when we create a bar magnet, so this may be the crux of the issue. If we take a bar of iron, wrap it in wire and pass current through it such that we get a strong uniform magnetic field through the...

OK, thanks for helping again. I think there is a lot more lacking on my end of understanding about this than I realized. I think what would help me is if I laid out my understanding of the scenario and if you pointed out where I'm mistaking, or maybe where I am missing more that I need to...

The idea was not to try to eliminate any EM fields. I only cared to prevent current moving from the wire to the cylinder and vice versa. I want to understand only what is going on with the magnetic fields and induced magnetic fields in and outside the cylinder. I'm imagining that the wire is...

I'm imagining the current to return externally to the cylinder, but with the wire insulated from the cylinder such that current isn't moving from cylinder to wire and vice versa. How can we be sure that there would be a magnetic field external to the cylinder in this case? The induced external...

I was just in a conversation with someone regarding the magnetic field resulting outside of a solid cylinder, with a current moving down the center of the cylinder, and then the resulting magnetic field after removing the current. Now I haven't thought about magnetic fields/magnets for a while...

OK, now thinking of it from the perspective of the derivative makes it clear. I was actually already aware of that, but for some reason, I was stuck trying to see it by trying to evaluate a path integral. Thanks for flipping my brain on this

I actually have a few things I'm thinking about here. I'm curious as to whether a velocity dependent force field absolutely cannot be a conservative force field, in principle. I have at times come across statements in physics that I found out had mathematical exceptions for, but we don't...

Ok, in that case, we have $$ ma = G \frac {mM} {R^2}$$ so $$a = G \frac {M} {R^2}$$ which is independent of the mass 'm'. I guess deriving it from Newton's law of gravity, which is more general than the special case of 'f=mg', is actually bit more illuminating. Thanks

Thanks, I wonder why some explain it in this way..

I understand that gravitational acceleration is independent of mass. However, I've seen a common mathematical description of this that I can't help but find circular. I suspect that there's an error in my thinking that I'm hoping someone can point out for me. It goes like this; ##F=mg## but we...

Ah of course, thanks.

I'm going through Ray D'Iverno's "Introducing Einstein's Relativity", and there is a step he makes in deriving the Lorentz transformations that doesn't seem necessary to me. So I'm not sure what I'm missing. He derives them from Einsteins postulates of relativity. From the postulate that the...

I remember how weird it was to me when I learned that, in a vacuum, a feather and hammer would fall at the same rate. It doesn't feel weird anymore. But isn't anything that we haven't experienced and violates our intuition going to feel weird? As you learn more about it, your intuition will...

Thanks for posting this. Very clear explanation.

@maline I wasn't trying to show that the probability was merely less than one. I was attempting to show why the probability of transmission of the electron is higher than the transmission probability of electron + proton. But I think I see your concern now. In the OP it was stressed that the...

I should note, I don't think X*Y is the exact probability of electron and proton tunneling at the same time, but I expect the actually probability to have a similar form.