user1247

I don't think assuming the CI is a very helpful framework for responding to a question about how to interpret the wave function, especially given the philosophically fraught nature of the CI.

Eugene, the inductance of the coils are about what I expect from the simple N2 mu A / l induction formula, around 20 micro H. I guess the question is about an air-core transformer with 2 inductors in the ten micro H range.

1) The diameter is about 2 or 3 cm. 2) I've tried frequencies between 1 Hz and 100000 Hz. 3) The wires are insulated.

But if they aren't separated by any gap at all I don't see how that is going to be too problematic?

Meaning that the oscilloscope doesn't pick up a signal if the two coils are far apart, but it does (just like expected), when the two coils are situated right next to each other so that the magnetic flux from one goes through the other.

I can later, but it's really just a primary with 5 loops (diameter of a few cm) right on top of a secondary with 25 loops (also a few cm) with magnet wire.

I've measured the signal using the oscilloscope on both the primary and secondary sides

I agree Transistor and Brhans that it may be capacitive coupling, but I find it really weird that the transformer is really THAT hopeless that an oscilloscope with microvolt precision can't pick anything up

100 ohm resistor on the primary

If I put a 5V sinusoid into the primary, I can get up to a 10V sinusoid out (with a 1:5 turns ratio, and upping the frequency), again with the proviso that I DON'T ground the secondary

Adding a core doesn't seem to change things much, so I've mostly just tested with an air core. The windings are magnet wire, insulated. I've tried various ratios, but generally something like 1:5 step-up.

Yeah, I'm not so confused about what I'm seeing with no grounding on the primary. What I'm much more worried about is why I can't see a signal if I DO ground the other side of the primary!!!

I have a resistor on the primary side to make sure it's not shorted, and I can drive up the inductive reactance of the primary by increasing the frequency on the signal generator. If I hook up the scope to the primary, things look perfect.

The secondary winding is not connected to anything else. It is a very simple setup, with just the secondary winding, and one lead from it going to the scope.

No, it's pretty clearly the actual signal, with a perfect sinusoid exactly matching the frequency of the signal generator (which can be varied), with about the expected frequency-dependent voltage as well.

@Ron, I should add that, just to be clear, I completely agree that without CTCs it is ridiculous to try to get QM from GR. It's just that with CTCs things are so complicated that unless I am missing something, I don't see how the idea is obviously wrong (for example, you cannot make the computational argument you tried at the beginning to rule it out).

@Ron, fair enough. But this is why I'm trying to understand what is and what is not understood about CTCs in GR: having absolutely no constraints can make a problem more difficult, so knowing what is constrained within GR can at least help me to think about this problem for myself, and (hopefully) come to the same conclusion that such classical models are impossible. As I described in my response to you in Lubos' answer's comments, off the top of my head I can think of some ways in which CTCs could reproduce QM-like behavior... I'll think some more and get back to you...

@Ron, now you are repeating yourself. I know GR is a different kind of theory. I know QM has amplitudes and superpositions. That in and of itself is a surprisingly moronic argument, coming from you, against the idea of QM behavior being an emergent property from CTCs. Your argument that CTCs do not exist in the classical theory is, on the other hand, a perfectly strong argument against this idea. I'm just trying to make sure I understand your statements, since if you mention QM preventing something, it makes it sound like you are forgetting about the premise here.

@Ron, then what is a wormhole (you didn't answer my question)? Also, again, it's not fair to talk about the "proper quantum definition" in this context, since the hypothetical is that QM is emergent from a classical picture + CTCs.

@Ron Maimon, aren't black holes allowing CTCs the same thing as wormholes?

OK, Ron, thanks a lot, I accepted your answer. It seems to me you are basically saying that all this hype from people like Michio Kaku about wormholes are lies... this I will have to simply accept, but it is a bit surprising.

@Ron, I didn't understand your example of a paradox. You are saying that the classical GR solution doesn't allow things to enter and leave in the same universe, so how is there any paradox? But even if they could enter and leave in the same universe, your specific example would not be a paradox. But there is surely room for many paradoxes, but that's where all of the fun comes in, requiring that CTC's be consistent. This is the "game" of CTC's, no? You go back, kill your mother, then discover that you slept with some woman who turns out to actually be your mother, etc...

@Ron, I thought that was what we were discussing, the classical GR solution. It is unfair to invoke QM when the hypothetical was that all there are are classical GR solutions...

@Ron, then what did you mean in that other answer that "The reason is that the classical solution allows matter to escape."? In any case, I urge you to put what you just wrote into your answer, and I'll accept it. Thanks.

@Ron, if you add to the end of your answer something like "The CTC's cannot reproduce Bell's inequality violations," then I will accept it, and also open a new question trying to better understand why.

@Ron, maybe you are using "exterior" differently, but the Wikipedia article says there are CTCs in the "exterior" in the Kerr vacuum, and also your own first line of your answer linked to in my OP is "The reason is that the classical solution allows matter to escape." I don't know how to reconcile these different kinds of statements.

What do you mean "where you can't trust the classical theory completely"? Are you referring to quantum effects, because here I am working under the hypothetical that quantum effects ARE just GR. Or do you mean that the classical solutions are ill-understood? Finally, if you don't know what happens near the singularity, how can you be sure that nothing crazy happens? I'm curious because this seems like just a naively compelling idea to me that it would be surprising if these questions had not been nailed down completely.

By "gold star" I was being silly, meaning to accept your answer. Discovered by 't Hooft? I'm reading Wikipedia now about the Kerr metric slightly before 't Hooft chronologically (it says "all rotating black holes will eventually approach a Kerr metric"). It seems to state fairly clearly that there are CTCs and "it is possible for observers in this region to return to their past". Are you and wikipedia in disagreement, or is wikipedia simply dramatizing the "artifact" you describe?

I think this question about CTCs really gets to the heart of the question I am asking, so perhaps if you have an answer I or you could add it to your answer so I can give you a gold star.

But aren't CTCs not obviously ruled out in GR? I mean, Godel's solution is contrived, but at least it shows CTCs are not fundamentally inconsistent with GR... is it really so trivially obvious that such funny business isn't possible when extremal black holes eat each other (I'm asking seriously, not rhetorically)?

Thanks Ron, I find this answer much less condescending and more helpful than Lubos' answer. What I still don't understand is that you say this is a local hidden variables theory ruled out by Bell, and yet both from my linked papers and your own comments about the test particle and extremal black hole, it sounds like GR is not necessarily globally causal (only locally, away from too extreme metric curvature). Wouldn't this acausality imply that it is a non-local theory, and therefore not constrained by Bell?

I think a simpler way of putting the answer to the OP is that decoherence explains loss of interference effects. It does not alone explain the mechanism by the which random outcomes are chosen. The "measurement problem" has two separate components that are often conflated: 1) "why do we not see interference effects in macroscopic systems" and 2) what determines the outcome of a measurement. Decoherence addresses #1 & and not #2. For example decoherence explains why Schrodingers cat is not both alive and dead once the box is opened. But it does not explain why we end up with a given outcome.

Interference (well linear superposition in general) is perfectly compatible by itself with MWI; it is taken as an axiom with the total superposed amplitude describing "world density" (BTW this isn't necessarily an unmotivated ontology, it is simply taken as isomorphic to a mathematical description of many classical trajectories). The question is, given this amplitude, interference contributing to it or not, do the amplitudes imply Born probabilities given a uniform measure?

That would be fine if it were the only possibility, but I don't think it is, in that in principle it seems clear that such an example should exist, hence my original SE question: what is an example where you evolve a wave function into unequal probabilities that directly demonstrates this difficulty.

The canon is that the feature I am describing is indeed hopeless -- that indeed the Born rule is inconsistent with a uniform counting measure. This I accept more or less as fact. But my question is about demonstrating this directly, but simply evolving a wave packing, counting the "worlds" and showing that the principle of indifference leads to a different probability than Born. What you are showing is distinct from this, and much more obscure.

It's a fine way of avoiding amplitudes, if that floats your boat, but it just doesn't get at the question I'm asking. As you say, you have to accept the way the branches combine, which is no longer linear, and isn't derived from amplitude branch counting.

So I think a better example than the one you gave would accept the wave picture as a starting point, take a wave packet and evolve it into 2 or 3 wave packets with unequal amplitude, and show that if you treat ratios of amplitudes as ratios of "worlds" then you get the Born rule. The issue I'm getting at is that detractors say this can't work. If it did, then a 1:2 amplitude would correspond to a 1:2 probability, but it doesn't.

, because you are not at all using Schrodinger evolution, in which case, indeed, you can describe everything using probabilities. This gets at the central philosophical ontology of the MWI, which is that there is this thing called the wave function that evolves in time via Schrodinger, that underlies all of the probabilities. This wave function has an amplitude that you would like to associate with branch density.

So let me step back for a second to explain what I mean. It turns out that we can describe the time evolution of QM states using a wave equation (for simplicity we can just use the x-basis, especially considering the basis issue you raised above). Now the basic problem regarding the Born rule is that in order for this wave equation to work, the amplitudes do not correspond to probabilities. For that you have to use the Born rule. In your above example you are not confronting this central issue,

My immediate reaction is that you are not doing any time evolution that would require you to connect amplitudes to the probabilities. I agree that in principle you could have an S-matrix like program that tried to avoid the wave function entirely, in which case, yes, you would just assign this probabilities to what you are calling "branches." But these aren't the same "branches" I'm talking about, which are superposed wave functions.

As for your interpretation of MWI, I think you are potentially underestimating MWI, at least that is the worry. The fact that in principle a QM-like theory (ie subjective pure randomness from a simple first order classical wave equation) is possible with the probabilities derived from branch counting, just seems to compelling to ignore without a stronger argument (than I've been exposed to at least).

Well that's the preferred basis problem which probably ranks as the #2 objection to the MWI. A common response is that local interactions select out the position basis as preferred in the decoherence process. I think it's true that any measurement ever done in QM ultimately uses a pointer state in the position basis (the needle on an instrument for example). In any case I think my question is well-defined if you accept for arguments sake that we only work in the position basis.

OK sorry that was long...

...be too much of a coincidence. The same goes for me, and it all hinges on this question of whether the Born rule is really derived from unitary evolution alone, or that you need to add in a totally arbitrary axiomatic measure on the branches into order to get the Born rule. At the end of the day most people like Sean "derive" Born but still manage to make an assumption the ruins the above philosophical payoff, which is why no one exclaims that Sean et all have "solved the measure problem"

This is important philosophically, because I think one of the most compelling aspects of MWI derives from the fact that if you just assume unitary evolution (ie a classical theory), all of the great mysteries and paradoxes of QM, the non-intuitive stuff that lead Feynman to say no one understands QM, it is all solved by just counting up branches. This is so compelling that I think philosophically a lot of people are completely convinced it cannot possibly be a wrong ontology, it would just...

In any case I hope that explains why your proposed question wouldn't actually be answering what I want answered. It's not whether the MWI has a problem assigning probabilities (that can be axiomatized), it is whether the naive intuitive branch counting is really in conflict with Born.

...just split up the wave function in some non-50-50 proportion, in which case you can no longer trust that that proportion corresponds to some ratio of worlds, because for all you know the "measure" is built into how the amplitude is divided in the first place. This is why starting with a 50-50 branching and the re-combining I think is crucial. The above is difficult to explain, sorry if it comes across as muddled.

The problem is that I just can't find an example of this happening in reality, so it slowly started to dawn on me that maybe this criticism, which seems to be agreed on by everyone, actually might not hold up in a subtle way, ie that whenever you come up with these 1:2 vs 1:4 examples, they are contrived and if you were to actually follow backwards how you ended up with those amplitudes, they would only come from situations where you couldn't do naive branch counting because the apparatus...

But supposedly (and as best as I can tell this is pretty much agreed on by everyone, including Sean etc) this doesn't actually work, at least not naively. The reason is basically the one I described far above, that you run into trouble when you superpose wave function so that, for example, it looks like the number of worlds are in a 2:1 ratio, but the actual probability is 1:4 because of the square in the Born rule.

But what I'm trying to get at is the specific point that is even not always understood by MWI proponents, which is just that one of the superficially beautiful and compelling features of the MWI is that the probabilities are just what you get from "counting up the number of worlds." Ie if you have a wave function with two delta functions with equal coefficients then you have the same number of "worlds" in each one, so the probability is going to be 50-50 based on the principle of indifference.