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I'm reading an article that talks about general misconceptions in QM. It says in its abstract:

Two deep-seated misconceptions are responsible for the interpretation difficulties associated with quantum mechanics: the notion that the spatial and temporal aspects of the world are adequately represented by sets with the cardinality of the real numbers, and the notion of an instantaneous state that evolves in time. The latter is an unwarranted (in fact, incoherent) projection of our apparent “motion in time” into the world of physics. Equally unwarranted, at bottom, is the use of causal concepts.

Would you help me in other words what is trying to tell ?

The article is

What Quantum Mechanics Is Trying To Tell Us. U Mohrhoff. Am. J. Phys. 68 no. 8, pp. 728-745 (2000), arXiv:quant-ph/9903051.

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1 Answer 1

Sometimes, we call "misconceptions" the opinions others have, that prevent them to understand our ideas, or to agree with us. These are not necessarily wrong conceptions, but they tell a different story, which is not compatible with our story.

Quantum mechanics works perfectly fine with continuous space and time, and each point can be identified by real numbers. It works fine by evolving a state vector in time, and everything we know about quantum phenomena, was predicted by thinking about that state vector from a Hilbert vector space (over a continuous field), and that this vector evolves in a continuous time, driven by a unitary evolution operator.

But, the author of the paper wants indeed to say something. The point is that we don't know about the continuum of positions and moments from experience. According to the author of the paper, experiments can only inform us about a finite number of events, which taker place in a finite number of positions, at a finite number of moments in time. At least, this is what I understand from this quote:

the spatial properties of things and the times at which they are possessed exist to the extent that they can be inferred from facts, and facts do not warrant the inference of an infinitely differentiated space or time. Between the factually warranted times that make up the history of a system, there are gaps; there are “periods of time” that do not exist for the system (Sec. VI). Everything that can be said about those periods is counterfactual.

In my opinion, this is a healthy skepticism. We should doubt anything we can't experience*.


*On the other hand, we can't deny the success of the standard quantum mechanics, based on continuous space and time. Also, theory of relativity supports the continuity of spacetime, and breaking this continuity, means breaking the Lorentz invariance. But I just wanted to explain author's claim, not to enter in a debate.

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+1 loved the pithy "healthy skepticism - We should doubt anything we can't experience". The set $\mathbb{R}$ is a monster that bends my brain daily. –  WetSavannaAnimal aka Rod Vance Sep 21 '13 at 5:18

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