KipIngram

Ok, so I have a question that's nagging at me, but I'm not sure I know how to express it cleanly. I can picture electrons changing energy levels, quanta either going through slits or not, etc., but all of that imagery causes me to think of energy doing this. Which would mean it's energy residing (or not residing) in the modes of the fields. I can also think in terms of action when I set up an action minimization problem to find a trajectory. Thinking in terms of action is easy enough, because that integral definition of action is right there staring at me. But you talk constantly as though it's action that transfers from field to field in these interactions, and thus would be associated with the modes of the fields and so on, rather than energy. I know the definition of action, but I'm fuzzy on how it manifests in this picture I'm trying to build. I do see that when I set up and solve an action problem I'm making reference to an initial state and a final state, and the action is associated with some possible trajectory between them. And in the quantum problems we're talking in terms of an initial state and a final state, and I sort of think we're not supposed to imagine the intervening "trajectory points" as even existing in a real way. We just start here and finish there. is that the right way to look at it? We start in this state, and end in that state, and in getting from here to there we have an integral number of action quana moving from "these modes in these fields" to "those modes of those fields"? So, do we talk about action instead of energy because the possible paths from initial state to final state have action associated with them? I'm watching the first of the Harvard lectures right now, btw - you're right; 70's video quality sort of sucked.

Ok. So I think it's time again for me to try to tackle an introductory QFT book. I've tried before, but found myself "no sufficiently ready." I don't think the math was the problem; I think I was just totally missing the right way of thinking about it all. Maybe I can do better this time. Can you recommend any particular online reference?

What do you mean by "fulfill"? Are you noting that there's no concept of a wave evolving "by itself"? That in any evolution there has to be something playing the role of the operator (such as the propogator)?

The thing is, both of these expressions are in two-logic-level form. Product of sums, and sum of products. So in that sense they're already "simplified." Those are the forms that would give you the fastest operation in a logic circuit. So knowing what the "cost" criterion is would help.

You mean like the Exploratorium? Only maybe bigger?

Well, imagine the logical extreme. Imagine you counteract everything that ends lives prior to the opportunity to reproduce. In other words, you pass forward every genome your population ever produces. Just to make sure we're really at the logical extreme, let's say we do so in equal proportions. Now you've "switched off" natural selection completely. Are you arguing that the species will wind up fitter in that case than in the one where natural selection does operate?

Well, he also states in that book that people with VERY high IQs sometimes do less well; they have difficulty "fitting in." But the reason I mentioned it was mostly because of the "up to 125" point - there is a measurable correlation between IQ and success up to there, implying that it does "matter." That's a refutation to those who dismiss the whole business of IQ. It's measuring something that contributes to success in at least parts of the spectrum.

Coder: Are you familiar with Karnaugh maps? Endy0816: I may be tired or something, but I'm not seeing those simplify to just one variable.

But each interaction / measurement has to cause at least one quantum's worth of action change to the involved fields, right? And I read Hobson to imply that that each quantum of action would come from a distinct mode of the field? And that the action comprising that quantum is actually spread out over all of space? Saying the above in a different way: The fundamental "unit" of interaction is the transfer of one quantum of action from one field to another field, which affects both fields everywhere in space.

Gladwell's Outliers argues that up to about IQ 125 you can show a correlation between higher IQ and career success, but IQ in excess of 125 doesn't seem to have much measurable impact on success.

Ok, I recognize that as a valid counter-argument, but I think the real right answer would be in the middle of the two extremes. Just a guess - this is certainly not my profession. But your point is very valid - by failing to reproduce individuals because of "weakness X," we could altogether lose out on "new strength Y." So yes, very good point. And I think it's also very reasonable to say that if it's as easy to defend against a threat as giving a shot, then that's really not that important of a threat anymore, is it? I.e., if it's that easy for us to protect ourselves, it's just not as necessary that we are born with the protection in place.

HB of CJ: Your arguments imply that our goal is the strengthening of the species over evolutionary time periods. In that context "just letting natural selection work" is indeed the right strategy. But I for one am very glad we aren't pursuing such a "eugenics like" approach to operating our civilization. Instead, we've chosen to have compassion for individuals of the species. I could not be more happy that I've had the opportunity to immunize my children against diseases that previously wracked our societies. The genetic fitness of humans living hundreds of thousands of years from now just does not matter to me as much as those five girls, and for that matter not as much as any living human.

Hmmm. Maybe but I'm not sure. I just take it to be the probability that an interaction will occur. What's the other one?

Perfect - thank you.

Nice one.

So if a quantum system is confined to a potential well of the right form it can "tunnel" to the other side with some probability. I've seen examples where that's expressed as the probability curve for finding the system in various states falls off as you move into the barrier, but still has a non-zero value on the other side. But if I've interpreted what I've read correctly, there would be no tunneling with an infinite potential barrier, because the curve goes to zero at the well-side of the barrier. Does this wind up having to do with the random energy fluctuations that arise from energy and time being conjugate variables? I could also imagine the system "climbing over" the potential barrier as a result of getting the right sort of random, brief energy boost. Is this just two ways of looking at the same thing, or are then entirely different things?

One would think that, but evidently not.

So what is being referred to when I see these references to "arbitrary phase factor"? The double slit paper you linked above mentions this, when it says that "phase is arbitrary, and this can't be manifested physically" or something like that. Does that refer to the same phase, and do they mean that even though the phase matters when adding amplitudes to compute probabilities, once we have a probability the phase no longer affects the measurement outcomes? I.e., the phase doesn't affect the measured results, only the probability of obtaining them?

You're welcome. I don't really see how to take it any further without just supplying the answer, which we're not supposed to do. Good luck with it! I would imagine that with most teachers if you included some of what we've discussed in your answer you'd get most of the credit even if you don't arrive at exact numbers for the constants. It would show a conceptual understanding of the process and it's underlying mathematics. Meanwhile, you educated me a bit (Ludwig von Bertalanfft and his model), so thank you!

It was an explanation for my post. I didn't see anything you posted that should be "argued with" - it just seemed like you misinterpreted my post. As far as I can tell now we're generally in agreement. Proven valuable vaccines should be administered, independent of any sort of "moral side issues." Earlier in the thread I someone mentioned that vaccination programs were generally subjected to some sort of planning and "benefit analysis," and I concurred with that as a good idea, provided that the discourse was objective and oriented toward valid health and welfare related points. I cited the HPV episode in Texas as an example where the discourse was not driven by the right sort of thinking. That's all.

That's pretty much how I felt after I read StringJunky's remarks - very similar thinking to mine, only more well-expressed.

You missed my example above - obviously no proven vaccine should fall into that category. But one of our recent governors here in Texas opposed a proven vaccine on the grounds that administering it to teen-age girls would "encourage promiscuity." Never mind that bad stuff could happen worst case if a girl didn't have that vaccination. So he was basing his policy on personal morals. I certainly didn't mean to endorse such behavior.

Ok, so let me give you a brief overview of the pertinent bits. Say you have an equation as follows: df/dt + Af = B. First you solve the "homogenous" equation, which just replaces B with 0: df/dt + Af = 0 df/dt = -Af With somewhat less than total mathematical rigor (meaning a lot more can be said about it), you can do this: df/f = -A dt and now you can integrate both sides of that using regular calculus: ln(f) = -At + C where C is an arbitrary constant. Now exponentiate both sides: f = e^(-At+C) = e^(-At)*e^C = C' e^(-At) C' is still arbitrary; we just recognized that C' = e^C is still a constant. So the homogenous solution is f(t) = C e^(-At) where I've dropped the prime from C for convenience. Now you have to add a "particular solution that takes into account your B != 0 in the original problem. If you set df/dt to 0, then you just have f = B/A. So you can write this: f(t) = C e^(-At) + B/A If you differentiate that the B/A goes away and you verify the homogeneous solution, and it also gives you the right answer at t=infinity when the fish is fully grown and df/dt = 0. Now all that's left is to find C so that you get the hatchling length at t=0 and choose A to get the right period of growth. Does that help? Please note that A in my lesson corresponds to K in your problem, and B corresponds to K Li, so B/A is just Li.

Ok, good. I'm assuming that's dL/dt, and that you left out the slash. So now you can write this: dL/dt = K(Li - L) (sorry, don't know how to do the infinity symbol) dL/dt + KL = KLi So you have a differential equation (a simple one) and you have data that you have to match at two points in time. Have you studied differential equations?