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Here's my understanding of the Maccone paper. Edit: I only skimmed it. Super-condensed QM intro: In the formalism of quantum mechanics, the dynamics of physica
by Maro 17y ago
Here's my understanding of the Maccone paper. Edit: I only skimmed it.
Super-condensed QM intro:
In the formalism of quantum mechanics, the dynamics of physical processes are represented by unitary operators. If Y(0) is the state of the system at t=0, then the dynamics (change, movement) of the system is represented by a unitary operator U(t), such that the state of the system at time t is Y(t)=U(t)Y(0). The technical term unitary roughly means that it is time-reversible: there exists the inverse of U(t) meaning that the inverse physical process can also occur (the hidden assumption is that there is a 1-1 correspondence between operators in the formalism and actual physical processes). The problem is, if everything is time-reversible, why don't we see glasses unbreaking or gas that came in to fill the room through a little hole finding its way out again?
Measurements in QM are not unitary. If you measure something, you can't undo it. Measurements are in this sense an "add-on" to QM.
The following argument probably pre-dates the Maccone paper:
Take a room which contains a quantum system Q and an observer O. The observer makes measurements on Q, which are not unitary, so he sees time irreversible processes. Now take a superobserver O', who is outside the room. To him, the room (Q and O together) make up a quantum mechanical system Q', which may be described in a unitary way. This means that the superobserver O' can argue that even though the observer O only sees time irreversible processes, the inverse process can in fact occur (glass unbreaking), but they reverse the observer O itself (who is part of Q'), meaning that he "forgets" what he measured, his ink "disappears" from his notebook, and so on.
Maccone's contribution seems to be that he identifies O measuring Q with O and Q becoming quantum entangled and provides some formalism.
Substitute "time-irreversible" for "entropy increasing" for trendiness (eg. to pick up girls in a bar =)).
- hughprime 17y agoI skimmed the paper the other day, but still didn't quite understand what he was on about. In particular, I didn't understand why he feels the need to invoke quantum mechanics at all. Thermodynamic systems don't flow backwards from high-entropy to low-entropy states simply because there are far more high-entopy states than there are low-entropy states. Or to put it another way, what does Maccone think would happen in a purely classical universe? Would not entropy still increase there? I find that discussing thermodynamics works terribly for picking up girls in bars, but maybe I just go to the wrong bars.
- Maro 17y agoSusskind answered a similar question during his stat. phys. lectures which you can watch on iTunes. Somebody asked the following question: given that entropy is the volume of the system in phase space and Liouville's Theorem (of classical physics) tells us that the volume in phase space is conserved, how come entropy increases? His answer: Liouville's Theorem holds, the volume stays the same, but the blob representing the system (the system's microstates) spreads out in a fractal way in phase space, increasing the "coarse-grained" phase volume / entropy. Then, a "you can't set the initial conditions infinitely precisely" / "you can't measure inifinitally presicely" type argument is invoked to say that in terms of real-life reversibility the course-grained volume is what matters, so entropy has increased despite Liouville. Explained here: http://www.google.com/url?sa=t&source=web&ct=res&cd=21&url=http%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DR-jQ4I0VkdoC%26pg%3DPA70%26lpg%3DPA70%26dq%3Dliouville%2Btheorem%2Bentropy%26source%3Dbl%26ots%3DRKI8zXfw-0%26sig%3DtZOa77uJCTs8-XibeaJWf3qhPKk%26hl%3Den%26ei%3DrquWSvulI47Y-QatkeTQCQ%26sa%3DX%26oi%3Dbook_result%26ct%3Dresult%26resnum%3D1&ei=rquWSvulI47Y-QatkeTQCQ&usg=AFQjCNGLutp18ilwZw-_ZISvOG_oxCbISw&sig2=mk0O2_FIpPZ3etOpTas28g http://www.google.com/url?sa=t&source=web&ct=res&...