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Luke_A_Somers comments on Decoherence is Simple - Less Wrong
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How do you explain this with many worlds, while avoiding non-locality? http://arxiv.org/pdf/1209.4191v1.pdf If results such as these are easy to explain/predict, can the many worlds theory gain credibility by predicting such things?
Glib: start with the initial states. Propagate time as specified. Observe the result come out. That's how. MWI is quantum mechanics with no modifications, so its predictions match what quantum mechanics predicts, and quantum mechanics happens to be local.
Fulller: The first moment of decoherence is when photon 1 is measured. At this point, we've split the world according to its polarization.
Then we have photons 2 and 3 interfere. They are then shortly measured, so we've split the world again in several parts. This allows post-selection for when the two photons coming out go to different detectors. When that criterion is met, then we're in the subspace with photon 2 being a match for photon 3, which is the same subspace as 4 being a match for photon 1.
When they measure photon 4, it proceeds to match photon 1.
Under MWI, this is so unsurprising that I'm having a hard time justifying performing the experiment except as a way of showing off cool things we can do with coherence.
Now, as for whether this was local, note that the procedure involved ignoring the events we don't want. That sort of thing is allowed to be non-local since it's an artifact of data analysis. It's not like photon 1 made photon 4 do anything. THAT would be non-local. But the force was applied by post-selection.
Of COURSE... you don't NEED to look at it through the lens of MWI to get that. Even Copenhagen would come up with the right answer to that, I think. Actually, I'm not sure why it would be a surprising result even under Copenhagen. Post-selection creates correlations! News at 11.
Then the justification is simple; it either provides evidence in favour of MWI (and Copenhagen and any other theory that predicts the expected result) or it shatters all of them.
Scientists have to do experiments to which the answer is obvious - failing to do so leads to the situation where everybody knows that heavier objects fall faster than lighter objects because nobody actually checked that.
Because this happens to be mostly true. Air resistance is a thing.
Actually, if I remember the high school physics anecdote correctly, the trouble for the idea that heavy objects fall faster than light ones began when a certain scientist asked a hypothetical question: what would happen if you drop a light and a heavy object at the same time, but connect them with a string?
Wikipedia has a longer version of the thought experiment.
Got nothing to do with weight, though. An acre of tissue paper, spread out flat, will still fall more slowly than a ten cent coin dropped edge-first.
Well, yes. (Galileo, wasn't it?) Doesn't affect my point, though - the basics do need to be checked occasionally.
Nothing? Are you quite sure about that? :-)
Hmmm... let me consider it.
In an airless void, the answer is no - the mass terms of the force-due-to-gravity and the acceleration-due-to-force equations cancel out, and weight has nothing to do with the speed of the falling object.
In the presence of air resistance, however... the force from air resistance depends on how much air the object hits (which in turn depends on the shape of the object), and how fast relative to the object the air is moving. The force applied by air resistance is independent of the mass (but dependent on the shape and speed of the object) - but the acceleration caused by that force is dependant on the mass (f=ma). Therefore, the acceleration due to air resistance does depend partially on the mass of the object.
Okay, so not quite "nothing", but mass is not the most important factor to consider in these equations...
I don't know how you decide what's more and what's less important in physics equations :-/
If I tell you I dropped a sphere two inches in diameter from 200 feet up, can you calculate its speed at the moment it hits the ground? Without knowing its weight, I don't think you can.
Predictive power. The more accurate a prediction I can make without knowing the value of a given variable, the less important that variable is.
Ugh, imperial measures. Do you mind if I work with a five-centimetre sphere dropped from 60 metres?
A sphere is quite an aerodynamic shape; so I expect, for most masses, that air friction will have a small to negligible impact on the sphere's final velocity. I know that the acceleration due to gravity is 9.8m/s^2, and so I turn to the equations of motion; v^2 = v_0^2+2*a*s (where v_0 is the starting velocity). Starting velocity v_0 is 0, a is 9.8, s is 60m; thus v^2 = (0*0)+(2*9.8*60) = 1176, therefore v = about 34.3m/s. Little slower than that because of air resistance, but probably not too much slower. (You'll also notice that I'm not using the radius of the sphere anywhere in this calculation). It's an approximation, yes, but it's probably fairly accurate... good enough for many, though not all purposes.
Now, if I know the mass but not the shape, it's a lot harder to justify the "ignore air resistance" step...
You're doing the middle-school physics "an object dropped in vacuum" calculation :-) If you want to get a number that takes air resistance into account you need college-level physics.
So, since you've mentioned accuracy, how accurate your 34.3 m/s value is? Can you give me some kind of confidence intervals?
(Engineer with a background in fluid dynamics here.)
A sphere is quite unaerodynamic. Its drag coefficient is about 10 times higher than that of a streamlined body (at a relevant Reynolds number). You have boundary layer separation off the back of the sphere, which results in a large wake and consequently high drag.
The speed as a function of time for an object with a constant drag coefficient dropping vertically is known and it is a direct function of mass. If I learned anything from making potato guns, it's that in general, dragless calculations are pretty inaccurate. You'll get the trend right in many cases with a dragless calculation, but in general it's best to not assume drag is negligible unless you've done the math or experiment to show that it is in a particular case.
The problem is, we've done much, MUCH more stringent tests than this. It's like, after checking the behavior of pendulums and falling objects of varying weights and lengths and areas, over vast spans of time and all regions of the globe, and in centrifuges, and on pulleys... we went on to then check if two identical objects would fall at the same speed if we dropped one when the other landed.
Anyway, I didn't say it shouldn't be done. I support basic experiments on QM, but I'd like them to push the envelope in interesting ways rather than, well, this.