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Well, it is a amazing fact that Quantum world deals with indeterminism, one can't tell about the system without directly "seeing" it. (Many novels, short stories are also formed on the same) My question is that if there is indeterminism at the very basic level - Quantum level, then how is determinism possible at the macroscopic level?

If our world is one of the possible outcome of one state then where are others?

If we assume many hyperstates in Quantum system, how is that possible if we have perfect determined state at macro scopic level.?

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  • $\begingroup$ Are you asking about the Correspondence principle? $\endgroup$ – Alfred Centauri Sep 1 '17 at 2:04
  • $\begingroup$ @AlfredCentauri it is a density matrix question , the "how" $\endgroup$ – anna v Sep 1 '17 at 3:13
  • $\begingroup$ @PranjalRana you may be interested in this essay from Nicholas Wheeler which assesses the aforementioned correspondence principle in light of the 'puzzle', 'I look about me, in this allegedly “quantum mechanical world,” and see objects moving classically along well-defined trajectories. How does this come to be so?' $\endgroup$ – CR Drost Sep 1 '17 at 3:47
  • $\begingroup$ Wow, three answers and each has a -1 score (at this time) and no comments. Tough crowd (or OP?) $\endgroup$ – Alfred Centauri Sep 1 '17 at 12:00
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Quantum mechanics and in-determinism comes when the De Broglie wavelength of the particle is of the order of the particles dimension, such that when you try to see the particle(to see means to interact with it say using photons, you disturb the particle and it is no longer on the position) you introduce indeterminacy. Whereas on the macroscopic level where the wavelength of the collection of the particle(object) is much smaller than the dimension of the object and when you try to observe the macroscopic object the position here is no longer disturbed by the photons and therefore no question of indeterminacy.

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As mentioned in the comments, the correspondence principle enters, and how it does mathematically is shown using the density matrix formalism on the quantum mechanical solutions.

Physics is about mathematically modeling data and observations so that new phenomena can be predicted.

Probability functions do predict new phenomena, with a probability attached to them. There is determinism in probability except "what" is determined is the probability distribution its self. If you throw a true dice 1.000.000 times and plot the frequency of the six numbers appearing, the plot is predicted (by probability theory) to be flat. To the accuracy of the eye looking at it, it is flat.

It is the same with quantum mechanical probabilities,except due to the complicated mathematical modeling, a complicated mathematical "summation " explains it rigorously. The classical mathematics describing the macroscopic world , ie Newtonian mechanics, classical electrodynamics etc, emerge by the use of the density matrix formalism. These lecture notes may help in the mathematical path, from simple systems to many body systems.

In a hand waving manner: the density matrix has the quantum mechanical states in rows and columns, so that the off diagonal elements show the quantum mechanical phases which determine the quantum mechanical probabilistic behavior due to a coherence of the quantum mechanical phases. When the number of entries becomes large, and by avogadro's number macroscopic states are composed of order 10^23 molecules, because of the large distances involved between atoms, most of the off diagonal elements tend to zero, except for the ones in the proximity of individual atoms, which are not seen macroscopically. Macroscopically the quantum mechanical density matrix ends up with only diagonal elements reflecting the classical system of no extra probabilistic interference between particles ( except in special cases, like superconductivity). It is part of what is called "decoherence"

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If our world is one of the possible outcome of one state then where are others?

The other possible outcomes are not in a place. Rather, there are alternative versions of each system you see around you. Different versions of a system can interact as a result of interference and entanglement under the right conditions, but such conditions don't arise in everyday life since copying information out of a system suppresses interference. As a result, the world around you looks approximately like the world as described by classical physics.

For more explanation on the other possibilities, see:

https://arxiv.org/abs/quant-ph/0104033

For more explanation of how information copying suppresses interference see:

https://arxiv.org/abs/1212.3245

If we assume many hyperstates in Quantum system, how is that possible if we have perfect determined state at macro scopic level.?

You don't have a perfectly determined state. That is an approximation that can be broken by suitable experiments.

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