# What are the borders of determinism?

I, a newbie in physics, often read about "near determinism", which is most probably the actual state of physics, meaning: the "big world" is deterministic, but very small things (atoms and smaller) are indeterministic (e.g. quantum physics).

If this is true, where is the border?

At which size do objects in our universe stop to be indeterministic and start to be deterministic?

• I think this term is not used in physics, but rather in philosophy, in particular by Honderich. If I am right, you might consider having this question migrated to Philosophy SE. – Keep these mind Dec 1 '13 at 19:48
• It really depends on which quantum mechanics interpretation you use. Superdeterminism: everything is deterministic; Copenhagen interpretation: almost nothing is deterministic, the probabilities differ though. – Ali Dec 1 '13 at 19:50

There is a relationship that determines indeterminism :). It is called the Heisenberg Uncertainty Principle.

Size can be described by the variable $x$ for the position of a particle/atom/molecule. The principle says that we can only know the value of $x+\Delta x$ and the momentum of the particle $p+\Delta p$ (where $\Delta x,\Delta p$ denote small intervals) within a relationship bound by

$$\Delta x\cdot\Delta p \gt \hbar/2$$

where $\hbar$ is the reduced Planck constant

This means that if we want great accuracy in position the momentum will be indeterminate.

Equally if we want great accuracy in Energy, Time will be indeterminate.

the uncertainty principle actually states a fundamental property of quantum systems, and is not a statement about the observational success of current technology.It must be emphasized that measurement does not mean only a process in which a physicist-observer takes part, but rather any interaction between classical and quantum objects regardless of any observer.

There is no unique border, it depends on the variables under observation, but ħ is a very small number, which can be approximated with 0 in the macroscopic world. The Heisenberg uncertainty is relevant for the mircoscopic world of atoms and molecules and smaller.

• Why no $\LaTeX$? – jinawee Dec 1 '13 at 20:44
• @jinawee: I went ahead and 'fixed' it; as far as stackexchange goes, I'd say it's better to ask forgiveness than wait for permission - after all, it's easy to roll back my changes if anna disagrees... – Christoph Dec 1 '13 at 22:03
• @Christoph Sure, but editing on a mobile is a pain. – jinawee Dec 1 '13 at 22:50
• @Christoph and Jinawee why don't you both look up my age? 73 . I started with machine language in 1967 and ended with C++ by retirement. I may be permitted to stop learning new computer tools at retirement, I hope? I am grateful to anybody replacing with nice symbols . Thanks. – anna v Dec 2 '13 at 4:17
• @jinawee the comment above is also for you :) – anna v Dec 2 '13 at 5:28

The border is fuzzy.

The border is roughly determined by the value of Plank constant. If the values of the task is close to it, then quantum mechanics guides the scene.

More explicitly, atom parts (like electron orbitals) are mostly in-deterministic, while molecules, including DNA molecules, are mostly deterministic.

I'd agree with Ali that the answer depends on the interpretation. For example, the Bohm interpretation (http://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory ) is a striking example of a deterministic interpretation.

• Bohmian mechanics cannot be carried out to agree with special relativity so it is out of the game: special relativity is crucial for any interpretation of particle experiments. Generally deterministic theories are toy models and fall down when special relativity needs to be imposed, as far as I know plato.stanford.edu/entries/qm-bohm. – anna v Dec 2 '13 at 4:28
• @anna v: Actually, I am not a big fan of the Bohm interpretation, but I value it as a useful medicine against some no-go theorems. Your comment puzzles me somewhat, as it links to an entry by Goldstein, a prominent protagonist of Bohmian mechanics. You conclude based on his entry that Bohmian mechanics "is out of the game", whereas he does not:-) He writes, e.g.: "It should be possible, it seems, to construct a fully Lorentz invariant theory that provides a detailed description of microscopic quantum processes." – akhmeteli Dec 3 '13 at 4:06
• Well, nobody has shown it can be done, up to now. I believe that is where all deterministic models fall flat, and also models of discrete space and time though it is just my impression from discussions on the web. – anna v Dec 3 '13 at 5:55
• @anna v: Nobody has shown it cannot be done either, as far as I know. Again, I am not a big fan of the Bohm interpretation, but I guess it is a major achievement to show that a deterministic theory can emulate at least nonrelativistic quantum theory. So you believe the Bohm interpretation is dead, some people, e.g., Goldstein, strongly disagree... As Bell also spoke highly about the Bohm interpretation, maybe neither your opinion nor Goldstein's opinion is the last word on this issue. That's all I'm trying to say. – akhmeteli Dec 3 '13 at 8:30