The Scale Of The Universe and And It's "Best Theory".

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Many of you have heard the phrase "use the right tool for the right job", and when it comes to physical theories the story is no different.  For example, I often hear that quantum mechanics is more fundamental and thus a better theory than Newtonian physics.  But is it always the better theory?  For example, does quantum mechanics describe the solar system better than Newtonian physics?  For all practical purposes the answer is a big "No Way!".

And, further, can Newtonian physics describe the large scale properties of the universe as well and general relativity?  Again the answer is no.

Look at the flash game above.  As you move the cursor back and forth, you see the universe at different scales.  And for each separate scale, a different physical theory becomes the best theory to use to describe that scale.  It really is the case that scientists are well advised, when describing the universe, to use "the right tool for the right job."

Question: But aren't the more fundamental theories are telling more about what is really going on?

Actually, it's hard to say!  For example, I've already posted on how some of the theoretical machinery going into our most fundamental theories of nature could just be clever mathematical models that just so happen to fit nature.  Not necessarily what is actually going on.   Furthermore: I'll give another example: is spacetime really curved, like general relativity says, or is something else going on like the interaction of a spin-2 graviton?  (Or something else entirely and yet the math just happens to work out making them clever models as opposed to the true reality!)

So, my advice to those who want to classify (and many do!) which physical theory is most superior or "most correct": I advise you to first ask what scale of the universe you are trying to describe.  Because, it turns out that each scale of the universe has it's own best theory.

A best theory for describing the cosmos at large... a different best theory for describing how a planes and rockets fly through the air or how bridges stand... a different best theory for describing how elementary particles interact... a different best theory etc...

Finally: It is this observation that allows cosmologists to think there may be a better theory than general relativity for describing scales larger then have been examined thus far.   Or: one reason why string theorists have good case for why there might be a better theory than standard quantum theories for describing the smallest of scales.

In short: the idea of a best theory is really scale dependent!

Click on the image to the right from XKCD.

Why Pigs Don't Diffract Through Doorways

Some of you may remember Dr. Mason at BYU, and some of you may have had him for a class or two (I had him for three classes...). There was one problem in particular that I remember solving in his quantum mechanics class. It went something like this:

Q: Figure out how slow a 75 kg pig needs to be going in order for it to diffract by a minimum of 1 meter through a door way 1 meter wide into a 10 meter wide room.

I will now solve this problem and demonstrate why pigs do not diffract through doorways.

First we have to find the de Broglie wavelength (Note: de Broglie is pronounced "duh Broy" not "Dee Brog-lee-ay" as I learned from a certain Belgian professor). Knowing the width of the slit (the door) and the distance the pig travels (10 m) before it is observed (hits the opposite wall), we can solve for the wavelength of the pig as it diffracts into the room. First we use simple trigonometry to find the angle of diffraction:

Using the fact that the room is 10 m wide and we expect a maximum in the diffraction pattern 1 m from directly opposite the door we set the opposite side of the triangle to 1 m and the adjacent side to 10 m. This gives us an angle α = 5.71°. Using this angle we then go to the equation for diffraction through a single slit:

Given the angle and the width of the slit (1 m) and the fact that we are finding the first maximum (n = 1) we can then find the wavelength of the particle necessary to do this. A simple calculation gives us a wavelength of 0.0995 meters. Assuming this wavelength represents the de Broglie wavelength of the pig we can then use de Broglie's equation,

to find the velocity needed in order for the pig to diffract through the door way. Using the fact that the pig has a mass of 75 kg and Planck's constant we can find the velocity needed. With this we find that the pig needs to be going slower than 8.88 e -35 m/s in order for the pig to diffract significantly through the doorway. But at this speed the pig will take a phenomenal 1.13 e 35 seconds or 3.57 e 27 years or 2.6 e 17 times the age of the universe, to cross the room. And that my friends, is why pigs do not diffract through doorways.

Quantum Mechanics and Free Will, By Dr. John Conway

If you want a series of philosophical discussions on quantum mechanics and free will I would suggest this series of lectures (sorry I can't embed the videos. I could figure it out but it is easier to just link to the videos). These were a series of lectures by Dr. John Conway at Princeton in 2009.

Lecture 1, March 23: “Free Will and Determinism in Science and Philosophy”
Lecture 2, March 30: “The Paradox of Kochen and Specker”
Lecture 3, April 6: “The Paradoxes of Relativity”
Lecture 4, April 13: “Quantum Mechanics and the Paradoxes of Entanglement”
Lecture 5, April 20: “Proof of the Free Will Theorem”
Lecture 6, April 27: “The Theorem’s Implications for Science and Philosophy”

The lectures are about an hour long each, so don't expect a quick fix. But just to give you a sample, "If we, human beings, do in deed have free will...then so do elementary particles....Free will means that our behavior is not a function of the past. If our behavior is a function of the past then what ever we do was written down, so to speak, in the great book before the world got started."

Applications of Schrödinger's Cat

Here is an interesting application of Schrödinger's Cat From The Big Bang Theory. (We've discussed this show before.) Enjoy.

(Unfortunately, you will have to click on the link to watch as embedding is disabled.)




Schrödinger's Cat: Giving men guts since 1935.

Quantum Darwinism. (Darwin Solves Schrödinger's Cat?)

We've discussed in this post and in its comments section that Schrödinger's Cat seems to be a paradox but only if you treat the system classically.  If you throw in quantum interactions, the paradox goes away.

I would like to discuss the (probably) best supportive case for how this happens. (Has experimental evidence as well.)  It is a recently proposed idea called Quantum Darwinism.  (See peer reviewed papers in Nature and PRL.)  This is how it works:

1. A system begins "quantumly" in a superposition of states. (Like Schrödinger's Cat)
2. After the system begins to interact with its environment, only certain states in the superposition remain stable. (Don't become destroyed.)  This is called decoherence.
3. A measurement by an intelligent observer also is an interaction (Example, if you look at it you hit it with a photon).
4. Of the initial stable states that survive, further interactions continue to destroy "unfit" states.
5. As this process continues, the surviving states actually become parent states to even more states who sometimes resemble the parent.
6. This is a form of replication.
7. Thus you have a bona fide survival of the fittest situation with certain states (and their offspring) becoming favored over others.
8. These different stable states become "orthogonal" to each other so there is no more superposition-like quantum interactions that happen anymore.
9. What emerges is a classical system.  Ie.. one where it appears the wave function has collapsed. 

This is a lot like ideas expressed in Dawkins' The Selfish Gene. (For those who have read it.)  In that book he describes how some molecule configurations are stable and some furthermore have the added ability that they can replicate. (Make copies of itself.)  Over many many years, those with the best ability to "survive" (in both the stable and able-to-replicate sense) evolve into the complex structures we see today.

This is identically the same story with Quantum Darwinism.  After interactions with the environment are taken into account, only certain states are stable.  Furthermore, some of these states can influence what states are created and destroyed as we run the clock forward. (They are parent states.)  Those states that are best equipped for "survival" contribute to the collapsed classical structure we see today.

The PRL mentioned above cites experimental evidence for the idea.  They created systems where there would be preferred stable states (after taking decoherence into account) and showed that as time when on the stable states began to replicate and a classical state emerged.  See the picture.

So, Darwinian ideas may be solution to the measurement problem in quantum mechanics and therefore explain Schrödinger's Cat.  Stable quantum states after interactions and "survival of the fittest" is factored in determine if the cat dies or stays alive.

Forget Global Warming: We Just Killed the Universe

There is a paper that has been posted on arXiv that has been causing quite a stir lately. It has even made it to the normal internet news services. Dr. Lawrence M. Krauss and Dr. James Dent, from Case Western Reserve University and Vanderbilt University respectively, have made the claim that by our observing dark energy we are affecting the life of the universe. Some news articles state it as "shortening" the life of the universe.

I tried to read through the article, but I'm not a particle physicist, nor a quantum mechanic, nor a cosmologist, but I'll give a crack at explaining it. So the idea is that in the early universe space was just as likely to decay into an unstable or metastable state that does not allow for matter, as we know it, to form or even for space as we know it to exist. But at some point the exponential expansion of the universe overcame the decay rate which is determined by a power law. Thus the universe began to grow faster than space will randomly decay, allowing for normal matter to form and for us to exist. But here comes the catch. If we observe the universe in some primordial state (i.e. observe dark energy) then the "quantum clock" of the universe gets reset and the universe reverts back to a state where the exponential growth and power law decay were roughly equal. Thus the universe reverts to a state where it is just as likely to decay as it is to expand. It follows that by our observing the universe in its most fundamental form we could conceivably cause it to decay into a state that does not allow for matter.

The problems with this are: What constitutes an observation? Do we have to observe the universe or does there have to be some interaction? in which case the observations are taking place all the time and our additional observing of the universe will not affect it any. From this point of reasoning we should assume that the universe is fairly stable (at least stable enough for us to be here, I think that is a very safe assumption) so I don't think there is anything that we can do that will significantly change the universe. The paper also mentions that it is difficult to make these assertions because they are based on quantum mechanics which doesn't really fit perfectly with gravity (GR) and when GR is taken into consideration things get sticky. Basically the only thing this idea can do is discount some versions of string theory and other unification theories.

So I hope that was a good interpretation of the paper. Let me know what you make of this paper.

Quantum suicide and Many Worlds Experiment

Max Tegmark of MIT has proposed an experiment to test the many worlds interpretation of quantum mechanics. It is called quantum suicide. From the Wikipedia:

n quantum mechanics, quantum suicide is a thought experiment which was independently proposed in 1987 by Hans Moravec and in 1988 by Bruno Marchal, and further developed by Max Tegmark in 1998^[1], that attempts to distinguish between the Copenhagen interpretation of quantum mechanics and the Everett many-worlds interpretation by means of a variation of the Schrödinger's cat experiment. The experiment essentially involves looking at the Schrödinger's cat experiment from the point of view of the cat.

Quantum immortality is a metaphysical speculation derived from the quantum suicide thought experiment. It states that the many-worlds interpretation of quantum mechanics implies that conscious beings are immortal.

A physicist sits in front of a gun which is triggered or not triggered depending on the decay of some radioactive atom. With each run of the experiment there is a 50-50 chance that the gun will be triggered and the physicist will die. If the Copenhagen interpretation is correct, then the gun will eventually be triggered and the physicist will die. If the many-worlds interpretation is correct then at each run of the experiment the physicist will be split into one world in which he lives and another world in which he dies. After many runs of the experiment, there will be many worlds. In the worlds where the physicist dies, he will cease to exist. However, from the point of view of the non-dead copies of the physicist, the experiment will continue running without his ceasing to exist, because at each branch, he will only be able to observe the result in the world in which he survives, and if many-worlds is correct, the surviving copies of the physicist will notice that he never seems to die, therefore "proving" himself to be immortal, at least from his own point of view.

Another example is where a physicist detonates a nuclear bomb beside himself. In almost all parallel universes, the nuclear explosion will vaporize the physicist. However, there should be a small set of alternative universes in which the physicist somehow survives (i.e. the set of universes which support a "miraculous" survival scenario). The idea behind quantum immortality is that the physicist will remain alive in, and thus remain able to experience, at least one of the universes in this set, even though these universes form a tiny subset of all possible universes. Over time the physicist would therefore never perceive his or her own death.

Quantum Physics and the Vice President

Many of you may be puzzled by the statements made by Dick Cheney's office several weeks ago that he is a member of both the legislative and executive branches of government, which conveniently gives him the ability to be shielded by executive privilege from Congress and from the Justice Department under the separation of powers. Under the classical laws of politics, this assertion makes no sense, but a hilarious cartoon found here (one panel is on the left) points out that Cheney's actions are simply evidence of quantum politics. Cheney's political wave function is a linear combination of the executive and legislative branches!

Seriously, though, anyone who has taken quantum mechanics needs to check out the full cartoon.