posted
I can never seem to get this straight, which I suppose is par for the course when quantum mechanics is involved. When a photon is measured, or interacted with vis-a-vis some classical apparatus the wave function collapses and an actual measurement does occur. Vague and simplistic, but am I basically on the right track so far? It may, however, interact with other photons without forcing a collapse, nor destroying entanglement it has already developed. Am I still all right? If so, where does the line get drawn when it comes to interactions where an object's properties force those with which it interacts to move into the classical world and take on definite definitions? And how does something made up of the quanta become itself classical?
quote:Mathematically, classical physics equations are ones in which Planck's constant does not appear. According to the correspondence principle and Ehrenfest's theorem as a system becomes larger or more massive (action >> Planck's constant) the classical dynamics tends to emerge, with some exceptions, such as superfluidity. This is why we can usually ignore quantum mechanics when dealing with everyday objects; instead the classical description will suffice.
posted
You are in effect asking about how wave-function collapse occurs; this is not understood. There is no first-principles answer. (Except many-worlds, in which case there is no classical interaction, there's just the wave-function splitting into non-interacting parts.) Experimentally speaking, somewhere around the microgram level, IIRC.
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posted
Thanks for that KoM. Out of curiosity is the cause of wave function collapse being studied directly with any kind of vigor right now, or is looked at as more of a 'we'll get there' type thing?
Microgram seems pretty big. I didn't realize you had to reach that level, though I suppose it's still a relief to a certain, boxed feline.
posted
Well, to be more accurate, quantum effects have been demonstrated (I vaguely recall) at the microgram level, which is not to say that decoherence usually occurs above that level.
I don't know if there's anyone really attacking the collapse stuff at the moment, except insofar as quantum gravity may answer the question. It seems like the sort of thing that would literally create a new paradigm; it's not a small problem of the kind you can get a three-year grant to look into.
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posted
Microgram sounds way too big too me. I'll have try looking it up. The quantum effects with which I am familiar aren't significant until you start looking a structures less than 100 nanometer. A hundred nanometer particle has a mass of attograms (10-21) not micrograms. A one centimeter particle would have a mass of around a microgram. That's a freaking boulder.
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posted
As I say, "I vaguely recall"; I won't insist on the number. I did find a recent paper suggesting that microgram-scale quantum resonators are "within reach", at least.
quote:A one centimeter particle would have a mass of around a microgram.
Only if it had a density of 2.4x10^{-4} kg/m^3, or about one-five-thousandth that of air. Assuming a spherical particle with radius one cm, we get
1 microgram / (4pi/3)(1cm)^3 = 1e-9 kg / (4pi/3)(0.01m)^3 = 1e-9 kg / 4.2e-6 m^3 = 2.38e-4 kg/m^3.
For comparison, Wiki gives the density of air at sea level and 20 Celsius as 1.2 kg/m^3.
[ January 13, 2010, 04:13 PM: Message edited by: King of Men ]
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quote:Originally posted by King of Men: As I say, "I vaguely recall"; I won't insist on the number. I did find a recent paper suggesting that microgram-scale quantum resonators are "within reach", at least.
quote:A one centimeter particle would have a mass of around a microgram.
Only if it had a density of 2.4x10^{-4} kg/m^3, or about one-five-thousandth that of air. Assuming a spherical particle with radius one cm, we get
1 microgram / (4pi/3)(1cm)^3 = 1e-9 kg / (4pi/3)(0.01m)^3 = 1e-9 kg / 4.2e-6 m^3 = 2.38e-4 kg/m^3.
For comparison, Wiki gives the density of air at sea level and 20 Celsius as 1.2 kg/m^3.
Woops, I was using length in meters and density in g/cm3. I hate it when I crash a satellite into Mars.
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posted
Right. Going the opposite way, if we take the density of air again, we find
1.2 kg/m^3 = 1e-9kg/((4pi/3)r^3) r^3 = (1e-9/(1.2*4pi/3))m^3 r = 5.8e-4m
so a scale of half a millimeter. That does actually sound very large, but on the other hand air is not dense. Perhaps iron would have been a better material, 7870kg/m^3, to give 3.1e-5 meters, about the size of a neuron.
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Out of curiosity is the cause of wave function collapse being studied directly with any kind of vigor right now, or is looked at as more of a 'we'll get there' type thing?![[Wink]](wink.gif)
