> After some time, most of the particles in the coffee are correlated with air particles; the coffee has reached thermal equilibrium.
No doubt this is some way oversimplified explanation, but it still makes no sense.
Say I have hot coffee and lukewarm coffee. The lukewarm coffee will equilibrate faster. Does it interact with the air faster? What if I bring in coffee that's the same temperature as the air, so that it's instantly at equilibrium. Does it interact with the air instantly?
I'm having a difficult time following his explanation. Here are a few of my stumbling points. Maybe you can help me out. 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1? 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do you take a log of a matrix? 3) Why does the interpretation rely on the density matrix? I've always thought…
Without reading the paper or watching the video. > 1) What does it mean that entangled particles are supercorrelated? How can S(A|B) = 2 or -1? The density matrix does not have the same properties of a joint probability distribution, so quantum entropy doesn't really have the same properties of classical entropy. [1] > 2) The formula for Von Neumann entropy is S = -Tr(p log(p)), where p is the density matrix. How do…
Good answers. Just a small comment: quantum entropy is a generalization of classical entropy. In particular, if A and B are classically correlated, then S(A|B) has all the properties of a classical entropy (Shannon's, in this case), for instance, it is non-negative.
At or very near the Big Bang, the Universe was in a state of minimum Entropy i.e. minimum entanglement i.e. maximum order (in some sense).
Post Big bang the cosmological arrow of time is in the direction of increasing disorder i.e. increasing Entanglement i.e. decreasing order
On a smaller closed system, Before is when the system is more pure, less entangled, more ordered After is when it has become less ordered, more entangled.
I have a question. I just went to a source of physical (quantum) randomness http://www.randomnumbers.info/ and I'm giving you a random number between 0 and 10,000 which I've just generated there. Here it goes: 6296. Ok. Now that light cone had finally reached you. And you (neurons in your brain to be precise) are thoughtfully entangled with that random event (outcome), now in your past. Now imagine the following. A f…
> There are no entanglements any more which link you to that event. Not directly, but the information has spread out from your neurons into the surrounding matter ad nauseum. It's just we can't interpret the information anymore. The event still happened in your past, you just can't see it through your limited human view of reality.
And what if you would move away from that surrounding matter? Or, say launch it away with near light speed, so it would get behind the horizon at some point. How is that situation different from the one in which I've just generated the number and the light cone haven't reached you yet?
The reasoning sounds a bit iffy as in: “Finally, we can understand why a cup of coffee equilibrates in a room,” said Tony Short, a quantum physicist at Bristol. “Entanglement builds up between the state of the coffee cup and the state of the room.” I think you can understand coffee cooling quite well without any quantum stuff - the atoms in the coffee are moving faster than those in the room. There will be a tendency…
I don't know why tim333 is being downvoted. The particular quote does sound iffy - Boltzmann did explain the cooling of coffee via purely classical processes.
The basic idea - the particle system moves throughout phase space. The vast majority of phase space consists of areas where thermal equilibrium is reached. If you compute the time it would take for the system to return to a non-equilibrium state, it's way larger than the age of the universe.
(Note: I'm not an amateur, though I did leave the field a few years back.)
> There are no entanglements any more which link you to that event. Not directly, but the information has spread out from your neurons into the surrounding matter ad nauseum. It's just we can't interpret the information anymore. The event still happened in your past, you just can't see it through your limited human view of reality.
And what if you would move away from that surrounding matter? Or, say launch it away with near light speed, so it would get behind the horizon at some point. How is that situation different from the one in which I've just generated the number and the light cone haven't reached you yet?
> And what if you would move away from that surrounding matter?
You can't :)
By surrounding matter I meant the rest of your body that isn't neurons, as well as the environment outside your body.
I have a question. I just went to a source of physical (quantum) randomness http://www.randomnumbers.info/ and I'm giving you a random number between 0 and 10,000 which I've just generated there. Here it goes: 6296. Ok. Now that light cone had finally reached you. And you (neurons in your brain to be precise) are thoughtfully entangled with that random event (outcome), now in your past. Now imagine the following. A f…
1. When you tell me the result 6296, my brain becomes only classically correlated with it, not entangled. The source of randomness (whether you got it through a quantum experiment or not) does not matter here, as I am only receiving the classical information.
2. After I forget it completely, all I can say is that I (my current body) am not correlated with the event --- but there is no reason to think of the event as being in my future. It's simply not correlated to me any longer. The process of forgetting means dumping all correlations with an event in the environment. For instance, neurons interact with blood stream that interacts with lungs, passing along those correlations to some air particles. So for my current body, the event never happened, although you might have written the number down and will always remember it. In other words, the past is relative.
I've always wanted to study quantum mechanics because of this very "entanglement". Can people please post recommendations on good resources/books on the topic for a person like me having no solid experience with physics(except college level courses)?
The bible is Nielsen and Chuang's Quantum Computation and Quantum Information: http://www.amazon.com/Quantum-Computation-Information-Cambri... See also these resources in Nielsen's blog: http://michaelnielsen.org/blog/writing/
That looks interesting. Does one need to have a background in QM before reading this? If yes, what would you suggest as a good read on basics of QM?
Is this really new? IANAP, but I clearly remember being taught about the Arrow of Time as a probabilistic/thermodynamical phenomenon even in high school and I also read similar explanations that involved causality and probability theory without refering to quantum entanglement . Is the "quantum" bit even needed there for anything?
Probability theory is how we model the arrow of time, but it's not a physical mechanism by which the arrow of time occurs. The article covers this distinction.
I have a question. I just went to a source of physical (quantum) randomness http://www.randomnumbers.info/ and I'm giving you a random number between 0 and 10,000 which I've just generated there. Here it goes: 6296. Ok. Now that light cone had finally reached you. And you (neurons in your brain to be precise) are thoughtfully entangled with that random event (outcome), now in your past. Now imagine the following. A f…
1. When you tell me the result 6296, my brain becomes only classically correlated with it, not entangled. The source of randomness (whether you got it through a quantum experiment or not) does not matter here, as I am only receiving the classical information. 2. After I forget it completely, all I can say is that I (my current body) am not correlated with the event --- but there is no reason to think of the event as…
> So for my current body, the event never happened, although you might have written the number down and will always remember it. In other words, the past is relative.
So where this event would be for you? In the future? Again?
Yes. Past is definitely relative. Special relativity is very specific about that ;)