the 2nd Law versus Wave Function Collapse

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the 2nd Law versus Wave Function Collapse

Postby hyksos on February 28th, 2021, 2:56 am 

The 2nd Law of Thermodynamics
versus
Wave Function Collapse

Do the probabilities of the 2nd Law have some relationship to wave function collapse? Does the measurement problem have a solution in thermodynamics? These questions are addressed in this article.

Prerequisite readings strongly recommended.


(1) Brownian ratchet
Get acllimated to thinking about paddle wheels turning in warm water. Energy considerations, energy that can do work and et cetera. https://en.wikipedia.org/wiki/Brownian_ratchet

(2) WFC
freshen up on collapse. https://en.wikipedia.org/wiki/Wave_function_collapse

(3) DCQE
Get a more sophisticated, modern understanding of collapse. https://en.wikipedia.org/wiki/Delayed-c ... tum_eraser

(4) Wigner's Friend
Get to know paradoxes surrounding collapse https://en.wikipedia.org/wiki/Wigner%27s_friend

(5) 2nd Law of Thermodynamics
In you forgot what the 2nd law was. https://openstax.org/books/physics/page ... cs-entropy
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Re: the 2nd Law versus Wave Function Collapse

Postby hyksos on February 28th, 2021, 2:57 am 

The Riddle
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Re: the 2nd Law versus Wave Function Collapse

Postby hyksos on February 28th, 2021, 3:13 am 

The Riddle

So way back in the heyday of the Copenhagen Interpretation, things were more comfortable with the measurement problem and the collapse of the wave function. When a big human observes a system, the act of observation changes the system in some way resulting in WFC. This has a nice ring to it - a kind of clickyness. When the human reaches out and "Does the measurement" this pushes a button on reality that clicks it into a collapse. It is nice and mechanical and we can sleep like babies tonight wrapped in our warm blankets of certainty.

But wait... don't get so comfortable in those blankets because along comes the Big Bad Delayed Choice Quantum Eraser.

DCQE shows that the universe cares little about whether the system was physically measured.. instead it seems to be more interested in whether a human, could in principle know the state of a quantum system. The universe showed us that if you delete the information that could have alerted you to the spin state of an electron, the said electron that you measured in the past goes back into a superposition.

This is very very weird. Consider the following example. Some university lab has measured an electron's spin state, and uses a chain of tools to display spin up or spin down on a computer monitor somewhere in the lab. The universe somehow "knows" whether a cleaning lady will come by the lab at 2 in the morning and see a the monitor through the glass door that reads "spin up" and therefore the universe will collapse that wave function of the electron to that configuration. Further the universe seems to care whether in principle, the lady could come by and see it, not whether she actually does in fact come by and see it. So wave function collapse does not turn on measurement, it turns on whether you can know the state.

Now that we have a much more modern, up-to-date understanding of wave function collapse, we turn now to the next question, and this is the Wigner's Friend paradox.

We ask the question : where is it in the chain from electron to magnetometer, to voltmeteer, to circuit, to computer screen, to pixels on a spreadsheet, to a human eye, to a human mind and finally human consciousness. Where in that chain of information flow does the wave function collapse occur?

This is the Wigner's Friend gedankenexperiment. Is the knob on a computer in a superposition in the lab, but this collapses inside the viewer's head? Or does collapse occur much earlier prior to large things like knobs and such?

And furthermore, what if another human is in the chain of information flow from electron to ---> you? Can this person be in a superposition?

For brevity I will be referring to a "superposition of brain states". Wigner's Friend raises a perplexing paradox. A quantum riddle. Namely if superposition of brain states happen in a friend, why do we never experience them in our own heads?
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Re: the 2nd Law versus Wave Function Collapse

Postby hyksos on February 28th, 2021, 4:18 am 

The Solution
The laws of physics are time-reversible. You can take an 4KHD video of colliding billiard balls with stereo sound, and play that video in reverse. The physics in the reversed video are perfectly compatible with physics, and indeed all energy conservation is preserved.

You can also record a snowball smacking into a brick wall and sticking onto it. The reverse video, showing a snowball releasing heat to the bricks, re-freezing and flying off the wall are all compatible with physics. Energy considerations are all capiche and good-for-go.

Imagine now you have immersed a paddle wheel into a water tank and fixed a string around its axle. THe string goes over a pulley and connects to a 500 mg bob weight. YOu release the bob weight and it falls to the floor, turning the paddle in the water slowly. Instead of smacking into the floor with a wack, the bob gently lands. THe lack of energy in that collision with the floor is represented in an increase in the temperature of the water.

Again, the reverse video of our pulley-water-bob system is physically plausible. Some heat energy in the water smacks against the paddle, turning it in the opposite direction and raising the bop against gravity. All conservation of energy and momenta are conserved. Good and good.

But wait. Why is it that we never see billiard balls absorbing air energy, and suddenly moving away from each other? Why do we never see snowballs refreezing and flying off walls? Why will we never see warm water align just perfectly to turn a paddle wheel and raise a bob? Are we missing something?

We are not. Ludwig Boltzman himself said the 2nd law of thermodynamics is not a fundamental law of nature. Instead it is only true "in the limit" of the number of particles. Snowballs are comprised of something on the order of 1.82 x 1024 atoms. Paddle wheels in water tanks are a physical system comprised of a number of atoms some factor of 100 larger than that.

Vis-a-vis the Brownian Ratchet issue, one has to imagine that the random motion of water molecules in the water tank just all accidentally line up so that they all collide with the paddle wheel at just the right angle to start turning it the opposite direction, and hence lift the mass weight from the floor. The laws of physics perfectly permit this scenario to happen. The issue as to why this is never observed happening is because the probability of this occurring is so low that you will never see it happen in your lifetime. Nor in the lifetime of the entire universe. The probability of a bunch of warm molecules all accidentally lining up is so low that you would never see it in the lifespan of a million universes.

Always remember, the inability of ever observing this happening is not a law of nature. It is merely an observed regularity of probability and chance.

After our short jaunt into thermodynamics and reversibility, we continue back to where we began. There is obviously something extremely important about humans in particular that has some bearing on the collapse of the wave function in a quantum system. There is something about the fact that a cleaning lady could know the electron's spin state that initiates collapse, in the case of Wigner's friend, the friend seems like she would be in a superposition, while Wigner himself is not.

(One could contend that humans contain some ephemeral substance or attribute of "consciousness" that is not in regular matter and has some metaphysical casual connection to the wave function in some convoluted way. That view is certainly compatible with observation. ) However, consider an alternative in light of the above exposition. There is a connection between paddle wheels in water, snowballs against bricks, and human bodies. They all share a common underlying attribute --- they are irreversible processes.


I think we all have an intuitive notion of how improbable it would be for warm water molecules to all accidentally line up and turn the paddle wheel backwards. However, I want you to now consider an entire human brain made up of living neuron cells. Those are biological processes, containing neurotransmitter molecules in vesicles... containing the transcription of protein from DNA, and including a process called a neuronal spike, which is a chain reaction of charges racing down an axon from one neuron body to a receiver at the end. All these processes must run perfectly backwards to get reversibility. While all of these processes running reverse are permitted by physics, you will never see them happening. Imagine how improbable the reverse process is. I don't know about you, but that probability is so low it makes me want to cry. The human brain coming to "know" something is a process among millions of neuron cells. That is not just irreversible, it is wildly violently irreversible.

So we draw a little bit closer as to what it is about humans that illicits wave function collapse. Irreversibility is the first key into the door of the solution.

I declare here that W's friend is indeed in a superposition of brain states. In fact, I'm going to go ahead and say that Wigner himself is in a superposition of brain states. (howdoyalikethat). The next question you would naturally ask me is "Then why don't we ever see this?" "Why don't we see humans, or ourselves in superpositions as you have claimed?"

The answer lies in realizing that you have asked two quite different questions. You want your cake and you want to eat it to.

"Are human bodies in a superposition of states?" Yes. (your cake).

"Then why is this is not observed?" (eat it too).

The second question has moved the goalposts and is asking something very different than the first one. Superposition of brain states are permitted by the laws of physics. Ergo they are allowed to occur in nature. Done and done. But then asking to observe a body in a superposition is a different ball of wax altogether. When a human observes and then "comes to know" a fact about the world, human cells are coordinated, and when they coordinate in the millions --- the process is highly irreversible.

One intuition to remember is that human neuron cells are like millions of paddle-watertank-bob systems all connected together in mass. They perform work using ATP in mitochondria, and when that work is done the energy is an unusable state of heat. A better analogy is that a single mitochondrian in one cell is the paddle-watertank-bob system, but at molecular scale.

Systems which neither absorb energy from the surrounding environment nor give energy up to it are isolated systems. In such systems reversibility is easy to obtain probabilistically and so superpositions are naturally easier to sustain over long periods of time and easier to observe. In the case of photons passing double slits, there is explicitly no energy transfer to the environment, and superpositions abound. If you built a machine that is perfectly isolated from the energy of the surrounding environment, it would presumably also maintain a long-lived superposition. Indeed, that device would be a Quantum Computer.

Armed with this theory of wave function collapse, we start gaining useful predictions on some earlier questions lingering above. Lets go back to

Where in that chain of information flow does the wave function collapse occur?

So we have a human person observing a laptop screen, which shows a spreadsheet. In one of the cells on that spreadsheet program it displays either spin up or spin down for an electron that was measured. Can the pixels on the screen of that laptop be in a superposition?

The answer is no. Because the laptop is plugged into the wall. It takes in electrical energy and uses it to switch transistors in a circuit. This work uses up Gibbs free energy, and expels the energy as heat using a fan on the bottom side. Aha! Those are irreversible processes. HEat will never be seen collecting out of the room to go into a laptop case and start reversing transistor states in silicon. We can know that the laptop itself cannot be in a superposition as its component parts are engaging in time-irreversible thermodynamic processes. Since the laptop is not in a superposition, we rest assured that its display pixels are only showing a single result.

Thus wave function collapse occurred far earlier in the information-flow chain than the human observer. "Consciousness" played no role.

Interestingly, anywhere along the causal chain in which only reversible processes occurred, we can declare that superposition was maintained, regardless of how far away those systems are located in space. Once the chain contains a energy-using system that performs work , the superposition will be destroyed, to the extent of probabilities on their reversible-ness.

We have a coherent explanation for the appearance of wave function collapse when "measurement/observation" takes place. Superpositions do manifest even in biological systems, but the probability of ever observing them is another matter.
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