Quantum Physics: How Small? How Fast? How Long?

Length

Atomic nuclei range from about 10^-4 to 10^-5 of the size of an atom.  If the atom were about the size of a medium-sized airport (say, 3 km) then the nucleus would be about 30 cm, about the size of a basketball.  Now imagine the airport, 3 km, having a sphere encompassing it.  If you change the basketball to a golf ball you have a rough scale of the hydrogen atom with its central proton.  Inside the golf ball are the quarks.  Change the scale from the proton being the size of a golf ball to the size of a marble, about 1 cm.  The sphere is now the size of the earth’s orbit.  The actual size of a proton is about 10^-15m.  This is equivalent to one femtometer, or one Fermi (1 fm).  The smallest distance probed is 10^-18m, which is one thousandth of a fermi.  The fundamental particles such as quarks are smaller than this.

The radius of the Hubble volume, or known universe, is about fourteen billion light years, which is about 10²⁶m away.  The size of your desk is about 10²⁶ times smaller than the universe and only 10¹⁸ times larger than the smallest probed distance.  The mean distance between the large distance of the universe and the smallest distance probed is 10⁴m, or 10 km.  This means that the mean distance of the universe is about six miles.

Word of the Week Wednesday 1/11/12

The Word of the Week is: Quantum-Logic

Definition:  An interpretation of quantum mechanics developed by John von Neumann in the late 1930’s.  Quantum logic says that everyday logic cannot be applied to the quantum world.  Contrary to Boolean logic, quantum logic says that and and either do not have the same meaning in the quantum world.

More about the term:  This interpretation isn’t known to be deterministic or indeterministic.  That is still up for debate.  However, there is no collapse of the wave function.  Also, local causation is uncertain as well.  There is little debate on the issue but the majority understanding of this is that it has a unique history (contrary to other non-collapse interpretations like Many Worlds).  When using Boolean logic to assess quantum logic it may seem that quantum logic is self-contradictory; however, if quantum logic is assessed internally it is indeed consistent.  The major problem for this system is extrapolating applied logic.  Boolean logic is certainly valid in everyday life but is invalid in the quantum world.  One way or another it seems that contradictions may arise somewhere along the way.  For more information see John Gribbin’s Q is for Quantum.

Example of use:  Consider the double slit experiment where a photon is shot at a wall with two slits and the photon goes through either one (or both).  So, because there is no wave collapse the photon actually goes through both slits.  There’s a different logical significance in this experiment.

The Delayed Choice Experiment in Quantum Physics

Source: SUNY

If photons are fired through the experiment one at a time (firing photons at a wall with two holes and a photon detector on the other side of the holes), they will build up an interference patter on the other side, as if they had gone through both holes at once and interfered with themselves.  If the experiment is set up so that detectors monitor which hole the photo goes through, the photon is indeed observed to be going through only one hole, and there is no interference pattern.  If a detector is set up not at the holes but intermediate between the two holes and the back wall detector screen then it may be possible to see which route a particular photon took after it had passed the two holes before it arrived at the screen. 

Neutrinos Faster Than Light or Extra Dimensions?

Source: CERN Press

By now we’ve all heard of the news coming out of CERN and OPERA on 23 September that the Italian accelerator, OPERA, measured neutrinos traveling faster than the speed of light.  I didn’t comment on the finding right away because I wanted to do some research on the claims and on what exactly happened.  So here are my two-cents.

So, what exactly is a neutrino?  A neutrino is a fundamental particle and crucial for the standard model of particle physics.  The neutrino comes tin three types: [associated with] the electron, muon, and tauon, which are fermions and part of leptons.  The have no electric charge and interact only via the weak nuclear force (see the Oxford Companion to Cosmology for more on this).  These particle are incredibly difficult to detect and pass through our bodies all the time (this is a nice little Italian cartoon that has an excellent depiction of neutrinos).

So, what happened?  CERN sent the neutrinos 730lm to the Italian accelerator OPERA.  The journey only took 2.43 milliseconds and the scientists timed it to within 10 nanoseconds. (A millisecond is a thousandth of a second, 1/1,000s and a nanosecond is a billionth of a second, 1/1,000,000,000s).  The neutrinos arrived 60 nanoseconds earlier than they would have if they were traveling at the speed of light (c = 299,792,458 m/s). There are three options of what could have happened.

1. Option One.  The experiment was in error and the calculations are simply incorrect.
2. Option Two.  The speed of light is not the cosmic speed limit and there must be slight adjustments for relativity theory.
3. Option Three.  The neutrinos took a shortcut through extra dimensions.

Option One: Experimental Error.  The OPERA team spent three years trying to calculate and find every error they could possibly find.  The neutrinos are produced by colliding protons into a graphite target to produce pions and travel a 1km tunnel and decay to produce neutrinos.  Electronic delays in the timing system that records when protons arrive at the graphite target introduce uncertainty.  However, this margin of error is 5 nanoseconds. Where the pions decay is also unknown, which produces an error of 0.2 ns.  Measuring the distance is also difficult because the OPERA lab in Gran Sasso is inside of a mountain, which is undetectable to GPS.  However, the distance can still be calculated to within 20 cm.  The error is 0.67 ns.  With the other errors taken into consideration, the total error bar is 7.4 ns.  Remember, if experimental error is going to be the prevalent option the errors have to account for 60 nanoseconds.

Option Two: Adjusting Relativity.  If it really is the case that the neutrinos did travel faster than the speed of light then Einstein isn’t completely thrown to the curb.  There must be a theory that will account for this that will be closer to the truth.  This has historical precedence.  Newtonian physics were thought to explain the universe until Einstein came around with the concept of relativity.  Newton wasn’t necessarily wrong, Einstein just provided a more accurate theory.  If neutrinos can travel faster than c then we need another Einsteinian discovery.  Not that big of deal.

Option Three: Extra Dimensions.  It may be the case that the neutrinos, when travel with an incredible amount of energy, travel through the smaller curled up dimensions.  Consider the neutrinos traveling into the fourth dimension, this would actually make the distance much shorter.  Hopefully this illustration will help.  Take a piece of paper and draw a straight line across the paper.  Label one end of the line A and the other B.  This line is one-dimensional.  Take the paper and fold it so it creates an upward arch.  Now, if you were to travel from A to B by going through the paper instead of curving around the outside of the paper then the distance would be shorter.  This may, perhaps, be what happened to the neutrinos. (For more information on the discovery see New Scientist No. 2832, October 1-7 2011).

I tend to lean more towards option three, that the neutrinos passed through the smaller extra dimensions.  This would be an incredible development that would contribute to and, possibly, confirm a prediction of string theory.  Part of this may be wishful thinking on my part but this may potentially be an incredible empirical find that would confirm the mathematics.  Now, what about further philosophical or theological implications?  I don’t think this has too much of an impact on philosophy or theology that hasn’t already been addressed concerning the philosophy of science or of scientific theology.  For more on these implications see “The Relationship Between Science and Philosophy,” “Einstein, the Big Bang, and Natural Theology,” “Einstein on Free Will,” and “Einstein’s Impact on the Epistemic Method.”

The Philosophy Behind ‘Source Code’

Ben Ripley and Duncan Jones’ recent film Source Code is loaded with philosophical underpinnings and pushes the edge of current science.  Jake Gyllenhaal plays the role of an Army helicopter pilot (Colter Stevens) who faced a near-death injury in battle but wakes up to find himself in the body of another person, Sean Fentress, on a Chicago bound train.  Colter, while embodied in Sean’s body, needs to gather vital intelligence on the terrorist attack that is going to happen on the train in eight minutes to help prevent a future attack soon to come.  Though at times I got tired of monotonous scenes after Colter’s failed attempts the plot and philosophical and scientific edge makes a great film for those deep thinkers out there.

Inside the Source Code

This is how it works.  The Source Code is a computer program that takes the electromagnetic field from one person’s brain and allows that person to assume the role of another individual bearing the same likeness.  The personal duplication only lasts for eight minutes because that’s how much memory can be accessed by the electromagnetic field of the brain (per the movie).  The first important metaphysical question to be asked is how does this work with personal identity? For clarification I will refer to Colter’s embodiment of Sean on the train as code-world and Colter’s consciousness reflected in his personal self as real-world.  If real-world Colter assumes the identity of code-world Sean then what happens to code-world Sean at the moment Colter assumes his identity?  Now remember, code-world Sean was once real-world Sean during those real-world eight minutes Colter embodies Sean.  Also, code-world Colter was once real-world Colter at the same moment of code-world Colter going “back” as code-world Sean.  This begs the question, to whom do we predicate personal identity to Colter when he is in the code-world?  This isn’t so much of a time travel issue rather it’s related to parallel realities.  This may seem like Hollywood’s inability to be philosophically trained in consistent metaphysics but perhaps Ripley’s writing isn’t inept, perhaps it’s pushing the edge of contemporary philosophy and science!

Now let’s look at the issue of the parallel realities.  Max Tegmark is a leading proponent of the multiverse.  His is a little more extreme than many other proponents since he advocates a fourth-level multiverse, which is to say that mathematics is equivalent to physical reality.  The Source Code would be equivalent to the third-level multiverse.  The third level multiverse assumes unitary physics and that every possible physical particle interaction actually does occur.  Consider the illustration of a man and a woman who meet up for drinks.  It could go a number of ways, she could say, “Sure, let’s have a drink” or she could say, “No, I’d rather not.”  In this scenario both outcomes actually occur and reality splits and each story continues its course.  Now this model assumes that consciousness may be explained on the quantum level.  Source Code is consistent here.

The issue now is getting from one reality to the other.  Columbia University physicist Brian Greene is one of the leading string theorists and he believes there is a way to verify whether or not this can me done.  At the Large Hadron Collider in CERN hundreds of physicists from around the globe gather together and construct high energy particle experiments.  What happens is that they accelerate particle beams near the speed of light with the potential of producing 14 TeV.  These particle beams collide and reveal smaller sub-particles.  It works in a way similar to building a block made of legos and when you throw one block of legos at another block it was come apart and the smaller components will be left.  That’s how sub-particles are discovered.  Greene’s prediction is that when collision events occur and the data reveals that less energy is present than there should be then it may be that some particles, or energy, have been transferred into another brane (or another reality).  It’s not as though this idea is so far fetched or that it is unfalsifiable, branes may actually exist.  In regards to the modesty of the position this interpretation is known as the Many Worlds Interpretation (though it still faces its physical challenges and dissenters).  The MWI was developed my Hugh Everett and Tegmark is the contemporary who has carried the torch at this point.

In order for Source Code to be achieved there would have to be a tremendous amount of concentrated energy, that would be the consciousness of Colter, and specify that on the consciousness of Sean (or the electromagnetic field).  The precision and energy are almost certainly impossible to harness that energy in such a specified way to be able to determine the specified outcome of each particle interaction from one brane to another.  It’s the concepts of merely transferring energy from one brane to another that is possible.  Source Code takes the advances of modern high energy physics and fictionalizes it to be able to traverse realities.  It certainly raises metaphysical questions of identity, which are quite worth entertaining.  We shouldn’t always shape our metaphysics to what knowledge of the physical world we do have.  Our physics may not confirm or suggest certain ideas like this but these hypothetical thought experiments are great mental exercises and thought experiments.  I really enjoyed this film simply because it made me think about how this could actually work.  The physics are next to impossible but the philosophy behind it is what makes the movie worth it’s praise.  The plot and character development isn’t horrible but, hey, there has to be some milieu in order to portray the idea.

Quantum Mechanics and Libertarianism

One of the most important premises behind quantum physics is to understand its indeterminacy.  My question is whether or not a theist can use this as an argument for libertarianism.  Subatomic particles behave in indeterminate ways (i.e. if you know the location of a particle you do not know it’s velocity and vise versa).  It should be noted that this doesn’t negate the laws of causality.  Without the laws of causality science absolutely breaks down.  It’s really an issue of probability with quantum physics.  The case a libertarian may make is that because quantum mechanics function in an indeterminate way, only with a probability, then nothing can be determined, everything is random.  Atheist Daniel Dennett and agnostic Stephen Hawking hold to this view of soft-libertarianism (as naturalists).

I certainly think this may be a good argument for a naturalist.  The best case that can be made for the naturalist is that neurological functions of the brain are random and what we do as agents is merely random.  However, for a theist, particularly a Christian who holds to the doctrine of creatio originans, this is problematic.  That is, God acts on an existing subject to preserve its existence an maintains the existence of the things he has created.  This begs the question, to what extent does God sustain the universe?  I think an obvious answer would be everything (i.e. atoms, particles, strings).  This isn’t to say that God causes every article or moves every particle, but he acts on them in a sustaining manner so that it may continue to exist.  What it does say is that despite the randomness there is still purpose because it is controlled and sustained by an agency (God).  For the Christian [entailing this doctrine], can the argument from quantum mechanics serve as an argument for libertarianism?  I would advocate that libertarians abandon this argument, it doesn’t work.  If anything, for a Christian, this could be used as an argument against free agency by the naturalist (an argument for naturalism).  There are better arguments for free agency to use.  I’ve heard this one before and libertarians need to abandon this.