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Schrödinger’s cat – A theistic expansion

This section is based on a conversation between myself and Justin on duality and shared truth. Justin’s hypotheses is that the volume of believers of a given deity is in direct proportion to is Absolute Truth. Although I have discussed Absoluteness earlier…see Absolute Truth, the point that mass-belief makes an object of that belief true is an interesting theory (if only to find the Simple Truth).

To address this theory I will start with an interesting thought experiment: Schrödinger said: In 1935 Schrödinger published an essay describing the conceptual problems in QM1. A brief paragraph in this essay described the cat paradox.One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following diabolical device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small that perhaps in the course of one hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The Psi function for the entire system would express this by having in it the living and the dead cat (pardon the expression) mixed or smeared out in equal parts.It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a “blurred model” for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.We know that superposition of possible outcomes must exist simultaneously at a microscopic level because we can observe interference effects from these. We know (at least most of us know) that the cat in the box is dead, alive or dying and not in a smeared out state between the alternatives. When and how does the model of many microscopic possibilities resolve itself into a particular macroscopic state? When and how does the fog bank of microscopic possibilities transform itself to the blurred picture we have of a definite macroscopic state. That is the measurement problem and Schrödinger’s cat is a simple and elegant explanations of that problem.

In English I think!!! He is saying in the micro (quantum) world, the cat can quite easily exist in both states at the same time and there is no contradiction…In probability terms that is, the cat is both dead and alive at the same time. It has a 2 in 1 chance of being alive or dead!

What he was saying is that it is not unreasonable in the micro world to consider both states true at the same time. The issue is, as you traverse from the micro (immeasurable) to the Macro (observable) we find it difficult to believe that the cat can be both dead and alive at the same time. This is the quandary with quantum physics. We observe in macro and yet theorise in micro, where both possibilities are true at the same time. In theoretical terms I have no problem with this.

As to the theory that God’s existence, probability is based on the volume of current belief; this is at odds with Shrodinger’s thought experiment. Only the physical macro is true in one or other state in our physical world i.e. the cat is either dead or alive and can not be both, independent of the volume of faith by the people. What I am alluding to is even of 99.99999 % of the population were to believe in a given deity, without objective proof, its existence is still in the balance, AND, in the Macro physical world, a duality is simply not possible. 

But, the argument may be that the deity is not of the Macro world and can be a duality, the macro-macro (for want of a better term – theological super-space) can not be observed and as with the quantum micro is in both states (a superposition). In other words God is and isn’t at the same time. Ergo; 2 in 1. Is this a contradiction? Schrödinger I think would not see any contradiction here – provided it did not offend his theological belief. I doubt he would conclude that a given state is based on the percentage of belief. If 90% of the population believe that Schrödinger’s cat is alive, they would be wrong, as would the 10% who believe it is dead; they would also be right on both sides of the divide, as the truth would be: everyone is right and wrong at the same time.

Is this true in reality under test? In other words, does the Micro ascend to the Macro. I do not know in general terms, but how does this equate to deity Macro-Macro? Well according to test – per results below – Schrödinger is correct that in the micro quantum state there is duality (superposition); and that can be observed from the macro through physical experiment by associated results. But how this equates to theology is somewhat tenuous. We need to work in the realms of philosophy: If only we could build a machine and illustrate both states are true definitively at that higher level. Who knows one day!

But even if we had a machine, we would prove that there is a superposition and that would prove that God is there and God is not. Would this help us in the real world?  For Micro there is application as the mathematics that are derived from superposition understanding, and other applications to come, will be no doubt mind blowing! But to know the Macro-Macro is a superposition will not stop man killing men for their version of truth! See test results below, and what do you conclude?email me if you wish to add comments or challenge any points made. I will be happy to publish any comments made. 

Article retrieved from the web 13^th April 2004: http://www.boulder.nist.gov/timefreq/ion/qucomp/cat.htm

In 1935, Erwin Schrödinger proposed a “thought experiment” to highlight one of the ways in which quantum mechanics contradicts our experiences of reality (E. Schrödinger, Naturwissenschaften 23, 807 (1935)). His proposal involved placing a cat (a macroscopic object) inside a closed box with a vial of cyanide and a radioactive atom initially prepared in the metastable state (a microscopic object). The radioactive atom has a probability of ½ of decaying in one hour. If it decays, then the cyanide is released and the cat dies; if it does not decay, then the cyanide is not released and the cat remains unharmed.The paradox arises because the atom, being a microscopic object, must be described by quantum mechanics. After one hour, and before it is observed, the atom is in an equal superposition of being decayed and undecayed. However, if quantum mechanics is a universal and complete theory, it must describe the whole system. And, since the state of the cat is correlated with the state of the atom, the cat must also be in a superposition of being dead and alive. This clearly contradicts our everyday experience of cats!This sort of apparent contradiction arises whenever the state of macroscopic objects is correlated with that of microscopic objects. It comes about because in our experience of our macroscopic surroundings, objects are either in one state or another, but never in a superposition of several states at the same time.Our ability to create “coherent states” of motion in our trapped atom has allowed us to create a Schrödinger cat-like situation. In our case, we can put the atom in a superposition of two electronic levels, each of which is correlated with a different state of the atom’s motion. The microscopic electronic state plays the role of the radioactive atom, whereas the coherent state of motion plays the role of the cat’s livelihood.We create our “Schrödinger cat” by creating coherent states using our “walking standing light wave” technique. The key to “cat” production is to adjust the polarization of our laser beams so that only the 2S½(F=1,mF=1) state interacts with the laser, while the 2S½(F=2,mF=2) state does not. Thus, the laser only creates a coherent state out of the part of the wavefunction in the upper electronic state. The sequence of laser pulses used is as follows.

See hyperlink reference for diagram. 

We start out in the ground motional and electronic states after sideband cooling and optical pumping (a). We next use a carrier transition to split the wavefunction into an equal superposition of ground and excited electronic states, both parts of which are in the ground motional state (b). We then use our “walking standing wave” to create a coherent state of motion in the upper electronic state, while leaving the motion in the lower electronic state unaffected (c). Another pulse on the carrier swaps the wavefunctions (d). Another pulse of the “walking standing wave,” this time with a different phase, creates a different coherent state of motion in the part of the wavefunction that is now in the upper electronic state (e). At this point, we have one coherent state in the upper electronic state and a different coherent state of motion in the lower electronic state. Thus, a microscopic superposition within the atom has been transformed into a larger superposition of atomic motion.Recall that our only observable is the probability that the atom is in the ground electronic state after the experiment. We use this observable to show that we have, indeed, created a “cat” by applying a final laser pulse on the carrier transition (f). This recombines the parts of the wavefunction in the upper and lower electronic levels. If the two wavepackets overlap in position and momentum at the moment of recombination, then they can constructively or destructively interfere, changing the relative probabilities of finding the atom in the ground or excited electronic states. If the wavepackets do not overlap, or if the system is in a mixture rather than a superposition prior to recombination, then there is no interference and so the probability of finding the atom in the ground state is ½. Data from one of our experiments are shown in the following graph, showing the expected interference fringe.

See hyperlink reference for diagram. 

The x-axis represents the separation of the two coherent-state wavepackets in phase space (measured by the angle between them). The y-axis is the probability that the atom is in its ground electronic state after step (f). The x-axis is the phase angle between the two coherent state creation pulses. The above figure corresponds to a situation in which the motional wavepackets are 84 nm apart at their maximum situation, which is approximately ten times the spatial extent of either motional wavepacket. Note that the contrast of the fringes is not one. In fact, the contrast is theoretically expected to degrade exponentially with the square of the physical separation when the system is coupled to the environment. This decoherence process underlies the reason quantum superpositions are not generally seen in the macroscopic world.In the future, we hope to use our “Schrödinger cat” state as a sensitive detector of decoherence. Characterizing decoherence is important for evaluating our system for possible use in larger-scale quantum computation, and represents research at the boundary between the quantum and classical worlds.

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