# Randomness - Quantum Mechanics

If there is pure probabilistic randomness for quantum particles, why isn't this randomness seen in macroscopic objects too, after all they are made up of quantum particles? Why and How does this randomness end as we move towards macroscopic particles from quantum particles?

• I am not talking about Brownian motion. I am talking about the probabilistic randomness at 'quantum level' – user197045 May 29 '18 at 13:54
• The short version of this is that quantum mechanics predicts probability distributions for measurable quantities. Classical mechanics correctly predicts the evolution of the expectation of these quantities, but not the overall distribution. Classical mechanics therefore gives correct answers when these distributions are sharply peaked. – jacob1729 May 29 '18 at 13:55
• As an example of what @jacob1729 (nice number by the way) is saying, take a look at the Galton board. Just because individual elements in a system have a probabilistic behavior does not mean the overall system will behave in the same way. Order can still arise from randomness. – Aaron Stevens May 29 '18 at 14:09

## 1 Answer

If there is pure probabilistic randomness for quantum particles,

Quantum mechanics is very deterministic,, it determines the non randomness of the probability distributions for particles and radiation in the underlying microcosm.

What is a probability distribution?

The likelihood of a particular outcome among the set of possible outcomes is expressed by a number from 0 to 1,

If it is random, there exist mathematical distributions that describe the statistical accumulation of the random variables.

Quantum mechanics gives mathematical distribution for specific variables which are not random but depend on potentials and interactions , they are compared with data , and are validated.

why isn't this randomness seen in macroscopic objects too, after all they are made up of quantum particles? Why and How does this randomness end as we move towards macroscopic particles from quantum particles?

It usually ends because the quantum mechanical solutions depend on the Planck constant $h=6.6.10^{-34}joulesec$, a tiny number, considering that the flight of a mosquito is of order $0.00000025$ joules, orders of magnitude larger than $h$. The quantum mechanical probabilistic determination gives rise to the classical solids liquids and gases as one goes from small distances to large, and small energies compatible with $h$, to larger ones, usually after the nanometer level.

The "usually" is to qualify for long range quantum effects, as superfluidity, superconductivity,. lasers, and even diamonds/crystals.

The quantum mechanical probabilistic equations are such, that special macroscopic states emerge and are another validation of the theory.

• You can't directly compare the value of the Planck constant with the energy of a mosquito in flight. They're not dimensionally equivalent. I'm not clear what the relevant length scale to convert is as it depends on the more specific example but I suppose the flight time is roughly what you want (which show $h$ to indeed be small). – jacob1729 May 29 '18 at 17:11
• @jacob1729 to compare you would have to multiply the energy with time in seconds, and the argument still holds. – anna v May 29 '18 at 17:12