New quantum probability rule offers novel perspective of wave function collapse

May 14, 2018 by Lisa Zyga, Phys.org feature
Credit: Shrapnel et al. Published in the New Journal of Physics

Quantum theory is based heavily on probabilities, since measuring a quantum system doesn't produce the same outcome every time, but instead yields one of many outcomes that each occur with a certain probability. Now in a new paper, physicists have presented a new quantum probability rule for assigning probabilities to measurement outcomes, or events, that essentially combines two of the most important quantum probability rules (the Born rule and the wave function collapse rule) into one.

The physicists, Sally Shrapnel, Fabio Costa, and Gerard Milburn, at The University of Queensland in Australia, have published a paper on the new rule in the New Journal of Physics.

One of the most important probability rules in quantum is the Born rule, which gives the probability that a measurement yields a certain event. However, things get a little bit more complicated when predicting consecutive events. Although in classical scenarios it's possible to assign joint probabilities to consecutive events using conditioning, in quantum scenarios this is not possible since each measurement necessarily disturbs the system. So in quantum mechanics, the state must be updated with this new information after every measurement.

In order to update the state, a "state update rule" or " rule" is applied. In the new paper, the physicists explain that this update is basically an "ad hoc ingredient," since it is introduced as an axiom (which cannot be proved), and is a completely separate entity from the Born rule. Although this additional rule works well for practical purposes, it poses problems for understanding the true nature of quantum theory—in particular, for interpretations of quantum theory as a statement about the knowledge of reality, rather than of reality itself.

To address these problems, the physicists propose and prove a unified probability rule, which they call the "Quantum Process Rule." They show that this rule is more fundamental than the Born rule, as both the Born rule and the state update, or collapse, rule can be derived from this new rule—that is, the update rule does not need to be independently introduced. Unlike the Born rule, the Quantum Process Rule can assign joint probabilities to consecutive events.

One of the interesting implications of showing that wave function collapse follows from the new probability rule is that it suggests that the collapse does not need to be regarded as a fundamental aspect of quantum theory. This implication offers an alternative perspective of wave function collapse, as well as a new understanding of the nature of .

"The main significance of the work is that we derive a single, unified probability rule that subsumes both the Born rule and the collapse rule," Shrapnel told Phys.org. "This means that one no longer needs to explain wave function collapse in terms of a physical process, but can instead view this part of the formalism as simply a case of classical probabilistic conditioning. It is this latter possibility that means we can consider the quantum state as being about our knowledge rather than a direct description of physical reality."

Explore further: A non-probabilistic quantum theory produces unpredictable results

More information: Sally Shrapnel, Fabio Costa, and Gerard Milburn. "Updating the Born rule." New Journal of Physics. DOI: 10.1088/1367-2630/aabe12

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8 comments

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rogerdallas
1 / 5 (2) May 14, 2018
This result makes sense on many levels. Never do we deal with "physical reality". Instead we are working with a brain model, something internalized, and that brain model can be taken as our "knowledge of physical reality". You would expect a certain degree of accuracy in our brain modeling, since we don't usually try to walk through walls. But when we venture into regions well outside of ordinary experience the models don't work very well. So we resort to mathematical formalism-- like the wave function or the Born rule.
swordsman
1 / 5 (2) May 14, 2018
The error in measurements ALWAYS occurs, mechanical or electrical, although it is sometimes negligible. One solution is to "characterize" the measurement through a series of known measurements. In three dimensional space, a single electromagnetic measurement will always produce an error. However this error can be predictable in many cases. It is very difficult to make measurements of atomic interactions,especially for mechanical models, which is a good reason to utilize electromagnetic models. Thank you, Max Planck, for your insight in developing the first electronic atom model. The mechanical model of Einstein has limitations which have resulted in errors in measurement that can be surmounted by the electromagnetic model.
Mimath224
5 / 5 (2) May 14, 2018
A new quantum probability rule eh? Like to keep an eye on this one to see who opposes it so I can understand it a little better.
NoStrings
3 / 5 (2) May 15, 2018
Wow. It will take a few days to follow and corroborate or reject with certainty, but if it is correct, I like it.
This review here can't give it justice; no fault of Lisa's this time, a good summary. But to understand the point, read the original publication.
Mimath224
4 / 5 (1) May 15, 2018
Wow. It will take a few days to follow and corroborate or reject with certainty, but if it is correct, I like it.
This review here can't give it justice; no fault of Lisa's this time, a good summary. But to understand the point, read the original publication.

Yes, downloaded the PDF (unread as yet) but as an interested layman(technician background) and not a practicing researcher, I might have questions but a learned critique is outside my scope. A personal opinion, perhaps.
torbjorn_b_g_larsson
not rated yet May 19, 2018
That working with different theories of quantum mechanics allows for different axiom sets is both natural - since the theories handles different objects - and nothing new. For example, many-world quantum theory handles many-world objects and can also combine two Copenhagen axioms into one IIRC.

However, I think this paper is a non-starter. They try to model a universe where quantum physics observations are independent of the instrument, so they can postpone - really abstract away - the collapse rule. But instrument independence is not our universe. If we observe that light goes through a slit in a double-slit experiment as photons, we lose the interference pattern from both slits.

The two organizations publishing the "New Journal of Physics" - what a trust filling name (/not) - are Institute of Physics and Deutsche Physikalische Gesellschaft, both physics amateur organisations. It looks like a humdrum predatory journal to stay away from.
torbjorn_b_g_larsson
not rated yet May 19, 2018
@rogerdallas: No, it does not make sense, see my previous comment. And physicists deal with nature, what philosophers call "reality", since that is what we observe.

Mathematics and statistics is used to quantify observations. That is their only rationale, usefulness.

I have a hard time understand if there were any actual criticism in there.

@swordsman: Einstein never published "mechanical" models, except for his mechanical (and thermodynamical) refrigerator invention. Planck's atom model has been rejected by observations.

So what were you trying to say?
mackita
not rated yet May 19, 2018
this update is basically an "ad hoc ingredient," since it is introduced as an axiom (which cannot be proved), and is a completely separate entity from the Born rule
It would mean, that classical quantum mechanics (from which the Born rule has been derived) represents incomplete description of reality, no matter how well proved it is experimentally. This "ad hoc ingredient" therefore corresponds another layer of epicycles of geocentric model.

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