Copenhagen Interpretation And Quantum Multiverses

  • wave-particle duality is a manifestation of quantum entities
Wave-particle duality does not mean that a photon or subatomic particle is both a wave and particle simultaneously, but that it could manifest either a wave or a particle aspect depending on circumstances. Complementarity, uncertainty, and the statistical interpretation of Schroedinger’s wave function were all related. Together they formed a logical interpretation of the physical meaning of quantum mechanics known as the “Copenhagen interpretation.

  • The Copenhagen Interpretation has three primary parts:
    • The wave function is a complete description of a wave/particle. Any information that cannot be derived from the wave function does not exist. For example, a wave is spread over a broad region, therefore does not have a specific location.
    • When a measurement of the wave/particle is made, its wave function collapses. In the case of momentum, a wave packet is made of many waves each with its own momentum value. Measurement reduced the wave packet to a single wave and a single momentum.
    • If two properties are related by an uncertainty relation, no measurement can simultaneously determine both properties to a precision greater than the uncertainty relation allows. So, if we measure a wave/particles position, its momentum becomes uncertain.
Central to the Copenhagen Interpretation is the principle known as complementarity. That the wave and particle nature of objects can be regarded as complementary aspects of a single reality, like the two sides of a coin. An electron, for example, can behave sometimes as a wave and sometimes as a particle, but never both together, just as a tossed coin may fall either heads or tails up, but not both at once.One must resist the temptation to regard matter or photon waves as waves of some material substance like sound or water waves. The correct interpretation, proposed by Born in the 1920’s, is that the waves are measures of probability. Waves of probability relate to the uncertainty principle in that it cannot be certain what any given particle will do. Only betting odds can be given. This fundamental limitation represents a breakdown of determinism in nature. It means that identical electrons in identical experiments may do different things. But, statistically, the outcome of the experiment is predictable.

Bohr, the leader of the Copenhagen Interpretation, admonished those who would ask what an electron really is, a wave or a particle. He denounced the question as meaningless or without context (such as `what is north of the north pole?’). To observe the properties of an electron is to conduct some sort of measurement. Experiments designed to measure waves will see the wave aspect of electrons. Those experiments designed to measure particle properties will see electrons as particles. No experiment can ever measure both aspects simultaneously and so we never see a mixture of wave and particle.

  • probabilities in the macroscopic world reflect a lack of knowledge
  • the quantum world is pure probability
The adoption of the Copenhagen Interpretation for quantum phenomenon poses a sharp divide between classical or macroscopic physics and quantum or microscopic physics. In the macroscopic world events appear to be deterministic. Every event has a cause. Often, the cause is difficult to directly determine, for example an apple falls from a tree because its stem weakens. We cannot tell exactly when it will fall, but we know some direct mechanical action is the cause and if we had precise knowledge of the state of its fibers we would know when and why. Thus, we resort to probabilities as a substitute for exact knowledge of the acting causes.However, the conceptual abyss seems to separate classical from quantum physics. In the quantum world, probabilities are not a substitute for detailed knowledge of hidden, relevant details; there are no relevant details, just pure chance. The classical world is determinism, the quantum world is pure probabilist. And, the probabilism nature to quantum physics has been confirmed by numerous experiments.

Hidden Variables Hypothesis:

  • macroscopic physics states that all variables are there, just hard to measure
  • Copenhagen Interpretation states that variables are not there, randomness is fundamental
In general, quantum theory predicts only the probability of a certain result. Consider the case of radioactivity. Imagine a box of atoms with identical nuclei that can undergo decay with the emission of an alpha particle. In a given time interval, a certain fraction will decay. The theory may tell precisely what that fraction will be, but it cannot predict which particular nuclei will decay. The theory asserts that, at the beginning of the time interval, all the nuclei are in an identical state and that the decay is a completely random process.Even in classical physics, many processes appear random. For example, one says that, when a roulette wheel is spun, the ball will drop at random into one of the numbered compartments in the wheel. Based on this belief, the casino owner and the players give and accept identical odds against each number for each throw. However, the fact is that the winning number could be predicted if one noted the exact location of the wheel when the croupier released the ball, the initial speed of the wheel, and various other physical parameters. It is only ignorance of the initial conditions and the difficulty of doing the calculations that makes the outcome appear to be random. In quantum mechanics, on the other hand, the randomness is asserted to be absolutely fundamental. The theory says that, though one nucleus decayed and the other did not, they were previously in the identical state.

  • indeterminacy was unpopular (not platonic)
  • Bell hypothesis is that quantum variables exist, but are hidden, special forces required
  • hidden variables are not testable, poor science
Many eminent physicists, including Einstein, could not accept this indeterminacy. They have rejected the notion that the nuclei were initially in the identical state. Instead, they postulated that there must be some other property–presently unknown, but existing nonetheless–that is different for the two nuclei. This type of unknown property is termed a hidden variable; if it existed, it would restore determinacy to physics.If the initial values of the hidden variables were known, it would be possible to predict which nuclei would decay. Such a theory would, of course, also have to account for the wealth of experimental data which conventional quantum mechanics explains from a few simple assumptions. For example, the electron would definitely have to go through only one slit in the two-slit experiment. To explain that interference occurs only when the other slit is open, it is necessary to postulate a special force on the electron which exists only when that slit is open. Such artificial additions make hidden variable theories unattractive, and there is little support for them among physicists.

The Copenhagen view of understanding the physical world stresses the importance of basing theory on what can be observed and measured experimentally. It therefore rejects the idea of hidden variables as quantities that cannot be measured. The Copenhagen view is that the indeterminacy observed in nature is fundamental and does not reflect an inadequacy in present scientific knowledge. One should therefore accept the indeterminacy without trying to “explain” it and see what consequences come from it.

Many-Worlds Hypothesis :

  • collapse of the wave function still presents a problem for deterministic physics
  • solution is to not collapse the wave function, rather split reality
  • many worlds hypothesis is allows for the existence of all quantum states, observation splits the worlds containing the states
The many possibilities carried by quantum superpositions are spread out over space and time. However, Newtonian physics is an accurate description of ordinary experience. What is the relationship between the strange quantum world and the classical world of common sense? Clearly the difference occurs when we measure or observe a quantum system. Whatever the process, it occurs at that time. The “how and why” of this process is unsolved and many believe modern physics will be incomplete until it is resolved.By the 1950’s, the ongoing parade of successes had made it abundantly clear that quantum theory was far more than a short-lived temporary fix. And so, in the mid 1950’s, a Princeton graduate student named Hugh Everett III decided to revisit the collapse postulate in his Ph.D. thesis. Everett’s idea is known as the relative-state, many-histories or many-universes interpretation or metatheory of quantum theory. Dr Hugh Everett, III, its originator, called it the “relative-state metatheory” or the “theory of the universal wavefunction”, but it is generally called “many-worlds”.

Many-worlds is a re-formulation of quantum theory which treats the process of observation or measurement entirely within the wave-mechanics of quantum theory, rather than an input as additional assumption, as in the Copenhagen interpretation. Everett considered the wavefunction a real object. Many-worlds is a return to the classical, pre-quantum view of the universe in which all the mathematical entities of a physical theory are real. For example the electromagnetic fields of James Clark Maxwell or the atoms of Dalton were considered as real objects in classical physics. Everett treats the wavefunction in a similar fashion. Everett also assumed that the wavefunction obeyed the same wave equation during observation or measurement as at all other times. This is the central assumption of many-worlds: that the wave equation is obeyed universally and at all times.

Quantum systems, like particles, that interact become entangled. If one of the systems is an observer and the interaction an observation then the effect of the observation is to split the observer into a number of copies, each copy observing just one of the possible results of a measurement and unaware of the other results and all its observer copies. Interactions between systems and their environments, including communication between different observers in the same world, transmits the correlations that induce local splitting or decoherence into non-interfering branches of the universal wavefunction. Thus the entire world is split, quite rapidly, into a host of mutually unobservable but equally real worlds.

According to many-worlds all the possible outcomes of a quantum interaction are realised. The wavefunction, instead of collapsing at the moment of observation, carries on evolving in a deterministic fashion, embracing all possibilities embedded within it. All outcomes exist simultaneously but do not interfere further with each other, each single prior world having split into mutually unobservable but equally real worlds.

  • macroscopic systems exhibit irreversible behavior (entropy) that prevents the reconnection of past worlds and present the observed world as real to individuals
  • many worlds does not allow communication between the worlds, but their existence can be tested in two slit experiments (the other worlds are doing the interfering) and with reversible mind experiments (nano-AI’s)
Worlds, or branches of the universal wavefunction, split when different components of a quantum superposition “decohere” from each other. Decoherence refers to the loss of coherency or absence of interference effects between the elements of the superposition. For two branches or worlds to interfere with each other all the atoms, subatomic particles, photons and other degrees of freedom in each world have to be in the same state, which usually means they all must be in the same place or significantly overlap in both worlds, simultaneously.For small microscopic systems it is quite possible for all their atomic components to overlap at some future point. In the double slit experiment, for instance, it only requires that the divergent paths of the diffracted particle overlap again at some space-time point for an interference pattern to form, because only the single particle has been split.

Such future coincidence of positions in all the components is virtually impossible in more complex, macroscopic systems because all the constituent particles have to overlap with their counterparts simultaneously. Any system complex enough to be described by thermodynamics and exhibit irreversible behaviour is a system complex enough to exclude, for all practical purposes, any possibility of future interference between its decoherent branches. An irreversible process is one in, or linked to, a system with a large number of internal, unconstrained degrees of freedom. Once the irreversible process has started then alterations of the values of the many degrees of freedom leaves an imprint which can’t be removed. If we try to intervene to restore the original status quo the intervention causes more disruption elsewhere.

Ms Kitty exampleThere is no “where” for cat, not even both true, wave funtcion is the description of the cat. The worlds already exist, there is no spliting.


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