Posts tagged ‘wave function’

June 9th, 2013

The Philosophy of Science Directory

by Max Andrews

This is a compilation of posts, which focus on the philosophy of science. These posts will cover a broad spectrum within the philosophy of science ranging from multiverse scenarios, scientific theory, epistemology, and metaphysics.

  1. MA Philosophy Thesis: “The Fine-Tuning of Nomic Behavior in Multiverse Scenarios”
  2. Natural Law and Scientific Explanation
  3. Science and Efficient Causation
  4. Which Comes First, Philosophy or Science?
  5. The Postulates of Special Relativity
  6. There’s No Such Thing as Creation Science–There’s Just Science
  7. Time Travel and Bilking Arguments
  8. “It’s Just a Theory”–What’s a Scientific Theory?
  9. Exceptions to a Finite Universe
  10. Teleology in Science
  11. Duhemian Science
  12. The Relationship Between Philosophy and Science
  13. The History of the Multiverse and the Philosophy of Science
  14. Where’s the Line of Demarcation Between Science and Pseudoscience?
  15. Miracles and the Modern Worldview
  16. Mass-Density Link Simpliciter
  17. Scientific Nihilism
  18. Q&A 10: The Problem of Defining Science
  19. Q&A 6: Scientism and Inference to the Best Explanation
  20. The Quantum Universe and the Universal Wave Function
  21. The History and Macro-Ontology of the Many Worlds Interpretation of Quantum Physics
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October 24th, 2012

Hugh Everett and the Many Worlds Interpretation

by Max Andrews

In 1956 Hugh Everett III published his Ph.D. dissertation titled “The Theory of the Universal Wave Function.”  In this paper Everett argued for the relative state formulation of quantum theory and a quantum philosophy, which denied wave collapse.  Initially, this interpretation was highly criticized by the physics community, and when Everett visited Niels Bohr in Copenhagen in 1959 Bohr was unimpressed with Everett’s most recent development [1].  In 1957 Everett coined his theory as the Many Worlds Interpretation (MWI) of quantum mechanics.  In an attempt to circumvent the problem of defining the mechanism for the state of collapse Everett suggested that all orthogonal relative states are equally valid ontologically. An orthogonal state is one that is mutually exclusive.  A system cannot be in two orthogonal states at the same time.  As a result of the measurement interaction, the states of the observer have evolved into exclusive states precisely linked to the results of the measurement.  At the end of the measurement process the state of the observer is the sum of eigenstate—or a combination of the sums of eigenstates, one sum for each possible value of the eigenvalue.  Each sum is the relative state of the observer given the value of the eigenvalue [2].  What this means is that all-possible states are true and exist simultaneously.

October 23rd, 2012

Karl Popper on the Many Worlds Interpretation

by Max Andrews

In a brief section of Karl Popper’s Quantum Theory and the Schism in Physics[1] he discusses his attraction to the Many Worlds Interpretation of quantum physics as well as the reason for his rejection of it. Popper is actually quite pleased with Everett’s three-fold contribution to the field of quantum physics. Despite his attraction to the interpretation he rejects it based on the falsifiability of the symmetry behind the Schrödinger equation.

Popper’s model allows for a theory to be scientific prior to supported evidence.  There is no positive case for purporting a theory under his model. There can only be a negative case to falsify it and as long as it may be potentially falsified it is scientific.  Thus, a scientific theory could have no evidence or substantiated facts to provide good reasons for why it may be true. What makes this discussion of MWI interesting is that despite Popper’s attraction to MWI it’s not the attraction that makes it scientific, it’s his criterion of falsification.

In favor of MWI:

  1. The MWI is completely objective in its discussion of quantum mechanics.
  2. Everett removes the need and occasion to distinguish between ‘classical’ physical systems, like the measurement apparatus, and quantum mechanical systems, like elementary particles.  All systems are quantum (including the universe as a whole).
  3. Everett shows that the collapse of the state vector, something originally thought to be outside of Schrödinger’s theory, can be shown to arise within the universal [Schrödinger] wave function.
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July 11th, 2012

Word of the Week Wednesday: Decoherence

by Max Andrews

Word of the Week: Decoherence

Definition: A loss of coherence between the angles of components in a superposition and a loss of information due to environment, which gives the appearance of a wave function collapse.

More about the term: A wave function collapse occurs when the outcome of a quantum state is determined by an observer. An observer can be a concious observer or even the interaction of particles.  Instead of a determinate state, decoherence is akin to pulling one string out from an entire knot of strings. Decoherence is a major talking point and factor in multiverse scenarios.

In 1956 Hugh Everett III published his Ph.D. dissertation titled “The Theory of the Universal Wave Function.”  In this paper Everett argued for the relative state formulation of quantum theory and a quantum philosophy, which denied wave collapse.  Initially, this interpretation was highly criticized by the physics community and when Everett visited Niels Bohr in Copenhagen in 1959 Bohr was unimpressed with Everett’s most recent development.[1]

May 16th, 2012

Word of the Week Wednesday: Mass Density Link Simpliciter

by Max Andrews

Word of the Week: Mass Density Link Simpliciter (I know this is four words but it’s one term)

Definition: Referring to the understanding and interpretation of the ontology of the wave function in quantum mechanics. This involves what link one should use to go from wave function talk to talk of ordinary macroscopic objects.

More about the term:  Because of Einstein’s relativity the Newtonian and Laplacian models have been abandoned.  The present discussion of how God interacts with the world has shifted to quantum mechanics. There are over a dozen interpretations, which mathematically describe the quantum world. 

April 24th, 2012

The de Broglie-Bohm Interpretation of Quantum Mechanics

by Max Andrews

I’ll be the first to admit that settling on an interpretation of quantum mechanics can be very difficult.  I’ve always preferred my science to be deterministic.  This appears in many interpretations such as Many-Minds and Many-Worlds.  A less controversial interpretation is the de Broglie-Bohm interpretation.  Below is an introduction to the theory taken from a paper by Ward Struyve.

In de Broglie’s pilot-wave theory the description of a quantum system by means of the wavefunction is extended by considering point particles which follow definite trajectories. The velocity field of these particles is fully determined by the wavefunction. Given the initial positions of the particles, their trajectories are fully determined by this velocity field. In this sense the particles are ‘piloted’ by the wavefunction, hence the name pilotwave theory.

February 8th, 2012

Word of the Week Wednesday: Multiverse

by Max Andrews

The Word of the Week is: Multiverse

Definition: The term to designate the existence of many worlds or universes.  Contrary to just one world, a uni-verse, there are many worlds, a multi-verse.

More about the term: The multiverse is not monolithic but it is modeled after the contemporary understanding of an inflationary model of the beginning of this universe suggesting a plurality of worlds.  Max Tegmark has championed the most prominent versions of the multiverse.[1]  There are four levels of the multiverse.

  1.  Level One:  The level one is, for the most part, more space beyond the observable universe.  So, theoretically, if we were to go to the “edge” of the universe there would be more space.  Having this model as a version of the multiverse may be misleading because there is still only one volume, landscape, or system involved.  A generic prediction of cosmological inflation is an infinite space, which contains Hubble volumes (what we see in our universe) realizing in all conditions—including an identical copy of each of us about 10^10^29 meters away.[2]
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