## Wednesday, September 12, 2012

### Violation of Heisenberg's uncertainty principle, or evidence for Quantum Mechanics?

A recent paper entitled  Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements  appeared (see the arXiv link to the paper).

This paper was presented to the public in some articles which gave the wrong idea that quantum uncertainty is disproved  (see for example Heisenberg uncertainty principle stressed in new test, with the subtitle "Pioneering experiments have cast doubt on a founding idea of the branch of physics called quantum mechanics.").

I will argue that the experiment presented in the paper actually supports Quantum Mechanics. This may be not quite explicit in the paper, but also there is nothing against the standard view on quantum mechanics in it.

Heisenberg originally stated his principle in terms of measurement-disturbance relationship (MDR). This is how he understood it at that time. The uncertainty principle which was proven theoretically, either in the context of wave mechanics, or from the non-commutativity of the operators, is correct, and it's correctness is acknowledged by the paper. This is called Heisenberg's uncertainty principle (HUP), and is very different from MDR.

The paper refers to previous theoretical works which disprove MDR, and present experimental evidence purported to confirm the violation of the MDR.

Why do I claim that the violation of MDR supports Quantum Mechanics? Because, if MDR would be correct, it would be enough to explain quantum uncertainty. Recall that even Heisenberg originally thought that the uncertainty is due to disturbance caused by measurement. If the states would behave as they are due to the measurement disturbance, then we could consider them classical, and extract Born's probability rule as we calculate probabilities in statistical mechanics. But we know this is not true. Quantum states exhibit properties which can't be explained by classical mechanisms. Among these, HUP plays an important role, together with entanglement. The service made by this paper is that it shows that the wrong version of the uncertainty principle can be violated. The authors seem to me to support the HUP:

"These two readings of the uncertainty principle are typically taught side-by-side, although only the modern one [HUP] is given rigorous proof."

and

"Our work conclusively shows that, although correct for uncertainties in states [HUP], the form of Heisenberg's precision limit is incorrect if naively applied to measurement [MDR]."

[1] Violation of Heisenberg’s Measurement-Disturbance Relationship by Weak Measurements

[2] arXiv link to the paper

[3] Heisenberg uncertainty principle stressed in new test

## Friday, April 20, 2012

### Analytic Reissner–Nordström singularity

This paper can be downloaded for the following 30 days from the Physica Scripta website.

Abstract:

An analytic extension of the Reissner–Nordström solution at and beyond the singularity is presented. The extension is obtained by using new coordinates in which the metric becomes degenerate at r = 0. The metric is still singular in the new coordinates, but its components become finite and smooth. Using this extension it is shown that the charged and non-rotating black hole singularities are compatible with the global hyperbolicity and with the conservation of the initial value data. Geometric models for electrically charged particles are obtained.

## Sunday, January 22, 2012

### Is semi-classical gravity wrong?

Semi-classical gravity is not considered fundamental, yet it escaped to experimental falsification. Of course, maybe we don't have yet the technology, or at least ideas of experiments we can do, to falsify it. It would be nice to be able to differentiate it experimentally from various quantum gravity approaches. But theoretically, it stands pretty well: being the most straightforward union between general relativity and quantum mechanics, it inherits their successes.

Are we sure that the theoretical reasons to reject it are so good? The regularization works promising for the semi-classical Einstein equation. The main problem seems to be that of singularities, but is there any evidence that this will not be solved?

One possibility is to rewrite Einstein's equation in a different way, which is equivalent to the original, but works in singularities. A simple type of metric singularity is when the metric becomes degenerate. The metric can be smooth (hence its components in a chart remain finite), yet the Kretschmann scalar can diverge, sure sign of a singularity. In arXiv:1105.0201, arXiv:1105.3404, arXiv:1111.0646 is developed the mathematics of such metrics, and it is consistent and without infinities, if the proper variables are used (for example, we have to use $g_{ab}$ and $R_{abcd}$, but not $g^{ab}$ and $R^a{}_{bcd}$).

Once we have this extension of the semi-Riemannian geometry developed, we need to show that we can apply it to the singularities of the Schwarzschild, Reissner-Nordstrom and Kerr-Newman singularities. In the standard expressions of these solutions, some components of the metric diverge. But there are coordinates which make the metric smooth - similar to how the Eddington-Finkelstein coordinates removed the apparent singularity on the event horizon, only that in our cases the metric becomes degenerate at the singularities. So, we can now write an equation equivalent to Einstein's, valid even at the singularities of these black holes, or at more general black holes which change in time, for example by Hawking evaporation (arXiv:1111.4837, arXiv:1111.4332, arXiv:1111.7082, arXiv:1108.5099). We can write field equations on such spacetimes, and the information can now pass through these singularities. Similarly, we can write this extend version of Einstein's equation through a FLRW singularity, without having problems with the infinities (arXiv:1112.4508).

About the problem of the wavefunction collapse. If it is discontinuous, it will lead to violations of the energy conservation. It will also imply (never observed) violation of the conservation of other quantities like spin or electric charge. So, maybe the wavefunction remains all the way unitary. How can this be possible, when the projection postulate seems to tell that it is discontinuous? A possibility is described here, here, and at arxiv:1309.2309.

I don't want by this to claim that General Relativity, and semi-classical gravity, have no problems, or that they are all solved by the solutions presented here. What I want to say is that, to justify other more radical theories, people frequently make claims about how General Relativity fails in one place or another. GR will most likely be replaced by a more complete theory, but it is important to know how much we can keep from it, and how much we should change.