Macroscopic Superposition States in Isolated Quantum Systems

Happy Thanksgiving! :-)

Macroscopic Superposition States in Isolated Quantum Systems 

https://arxiv.org/abs/2011.11661   

Roman V. Buniy and Stephen D.H. Hsu 

For any choice of initial state and weak assumptions about the Hamiltonian, large isolated quantum systems undergoing Schrodinger evolution spend most of their time in macroscopic superposition states. The result follows from von Neumann's 1929 Quantum Ergodic Theorem. As a specific example, we consider a box containing a solid ball and some gas molecules. Regardless of the initial state, the system will evolve into a quantum superposition of states with the ball in macroscopically different positions. Thus, despite their seeming fragility, macroscopic superposition states are ubiquitous consequences of quantum evolution. We discuss the connection to many worlds quantum mechanics.

It may come as a surprise to many physicists that Schrodinger evolution in large isolated quantum systems leads generically to macroscopic superposition states. For example, in the familiar Brownian motion setup of a ball interacting with a gas of particles, after sufficient time the system evolves into a superposition state with the ball in macroscopically different locations. We use von Neumann's 1929 Quantum Ergodic Theorem as a tool to deduce this dynamical result. 

The natural state of a complex quantum system is a superposition ("Schrodinger cat state"!), absent mysterious wavefunction collapse, which has yet to be fully defined either in logical terms or explicit dynamics. Indeed wavefunction collapse may not be necessary to explain the phenomenology of quantum mechanics. This is the underappreciated meaning of work on decoherence dating back to Zeh and Everett. See talk slides linked here, or the introduction of this paper.

We also derive some new (sharper) concentration of measure bounds that can be applied to small systems (e.g., fewer than 10 qubits). 

Related posts:

Classics on the arxiv: von Neumann and the foundations of quantum statistical mechanics 

Pure State Quantum Thermalization: from von Neumann to the Lab 

Entanglement and fast thermalization in heavy ion collisions 

Fun fact: Professor Buniy was a postdoc in my group at Oregon. Before coming to the US for graduate school in theoretical physics he was among the last group of young men to serve in the Soviet Army (Strategic Missile Forces IIRC!)

I suppose he has a document like this one:

Here he is in 2011, working on the null energy condition and instabilities in quantum field theories: 

 

Bruno Maçães on the election and Trump 2024

 

Post-election observations from Bruno Maçães. 

TrumpTV? Spectacle over Substance in 21st century American politics? Ivanka 2024? The Meme Industrial Complex?

If Bruno is correct the best we can hope for in the US is managed decline -- which is at least better than unmanaged decline!

More Bruno.

Polls, Election Predictions, Political Correctness, Bounded Cognition (2020 Edition!)

Some analysis of the crap polling and poor election prediction leading up to Nov 2020. See earlier post (and comments): Election 2020: quant analysis of new party registrations vs actual votes, where I wrote (Oct 14)

I think we should ascribe very high uncertainty to polling results in this election, for a number of reasons including the shy Trump voter effect as well as the sampling corrections applied which depend heavily on assumptions about likely turnout. ... 

This is an unusual election for a number of reasons so it's quite hard to call the outcome. There's also a good chance the results on election night will be heavily contested.

Eric Kaufmann is Professor of Politics at Birkbeck College, University of London.

UnHerd: ... Far from learning from the mistakes of 2016, the polling industry seemed to have got things worse. Whether conducted by private or public firms, at the national or local, presidential or senatorial, levels, polls were off by wide margins. The Five Thirty-Eight final poll of polls put Biden ahead by 8.4 points, but the actual difference in popular vote is likely to be closer to 3-4 points. In some close state races, the error was even greater. 

Why did they get it so wrong? Pollsters typically receive low response rates to calls, which leads them to undercount key demographics. To get around this, they typically weight for key categories like race, education or gender. If they get too few Latinos or whites without degrees, they adjust their numbers to match the actual electorate. But most attitudes vary far more within a group like university graduates, than between graduates and non-graduates. So even if you have the correct share of graduates and non-graduates, you might be selecting the more liberal-minded among them. 

For example, in the 2019 American National Election Study pilot survey, education level predicts less than 1% of the variation in whether a white person voted for Trump in 2016. By contrast, their feelings towards illegal immigrants on a 0-100 thermometer predicts over 30% of the variation. Moreover, immigration views pick out Trump from Clinton voters better within the university-educated white population than among high school-educated whites. Unless pollsters weight for attitudes and psychology – which is tricky because these positions can be caused by candidate support – they miss much of the action. 

Looking at this election’s errors — which seems to have been concentrated among white college graduates — I wonder if political correctness lies at the heart of the problem. 

... According to a Pew survey on October 9, Trump was leading Biden by 21 points among white non-graduates but trailing him by 26 points among white graduates. Likewise, a Politico/ABC poll on October 11 found that ‘Trump leads by 26 points among white voters without four-year college degrees, but Biden holds a 31-point lead with white college graduates.’ The exit polls, however, show that Trump ran even among white college graduates 49-49, and even had an edge among white female graduates of 50-49! This puts pre-election surveys out by a whopping 26-31 points among white graduates. By contrast, among whites without degrees, the actual tilt in the election was 64-35, a 29-point gap, which the polls basically got right.

See also this excellent podcast interview with Kaufmann: Shy Trump Voters And The Blue Wave That Wasn’t 

Bonus (if you dare): this other podcast from the Federalist: How Serious Is The 2020 Election Fraud?

Added: ‘Shy Trump Voters’ Re-Emerge as Explanation for Pollsters’ Miss

Bloomberg: ... “Shy Trump voters are only part of the equation. The other part is poll deniers,” said Neil Newhouse, a Republican pollster. “Trump spent the last four years beating the crap out of polls, telling people they were fake, and a big proportion of his supporters just said, ‘I’m not participating.’” 

In a survey conducted after Nov. 3, Newhouse found that 19% of people who voted for Trump had kept their support secret from most of their friends. And it’s not that they were on the fence: They gave Trump a 100% approval rating and most said they made up their minds before Labor Day. 

Suburbanites, moderates and college-educated voters — especially women — were more likely to report that they had been ostracized or blocked on social media for their support of Trump. ... 

... University of Arkansas economist Andy Brownback conducted experiments in 2016 that allowed respondents to hide their support for Trump in a list of statements that could be statistically reconstructed. He found people who lived in counties that voted for Clinton were less likely to explicitly state they agreed with Trump. 

“I get a little frustrated with the dismissiveness of social desirability bias among pollsters,” said “I just don’t see a reason you could say this is a total non-issue, especially when one candidate has proven so difficult to poll.”

The East Is Red, The Giant Rises

Apologies for my recent inactivity. I've been busy finishing several projects and also distracted by our recent election.

Possibly the biggest global impact of this election is on US-China relations.

It seems likely that Biden will be our next president (although I am interested to see what closer inspection of the election reveals), and based on this I think odds have shifted in favor of a continued rise of the PRC in global economic and military power. I now think that the US lacks the will to counter China's continued rise: their main potential failure mode over the next 20 years is internal, not likely a consequence of external pressure. (Although of course there is still a chance the US and China will blunder into a war, with terrible consequences for the whole world.) 

Note I am not saying the US-China cold war or supply chain decoupling are off, just that the US is unlikely to put sufficient pressure on China to significantly retard its development over the next 20 years. This will have to be re-evaluated in 2024, of course, but we may pass the tipping point.

In 2004 I made some forecasts of where China would be in 2020. These forecasts were met with skepticism then but have mostly been correct. See

Benchmarks in China development: emergence of a middle class

Sustainability of China economic growth

My main assumptions were that the differential in growth rates between China and developed countries would average about 5 percent per year -- e.g. 7% vs 2%, and that China would largely close the technology gap.

A growth differential of +2-3% between now and 2050 would lead to a PRC economy which is about twice as large as the US economy (PPP). In 2004 I expected the PPP and nominal measures of Chinese GDP to narrow (I said over the next ~30 years, so I still have about 15 years for that to happen). If that occurs by 2050 then the PRC economy would be about twice as large as the US economy in nominal terms as well. GDP per capita in China would still be only half that of the US, but a 2-1 total GDP ratio has huge implications for geopolitics, the military balance of power, etc. (Note I am not even factoring in COVID-related impacts on the two economies, which are strongly in favor of PRC.) 

Another metric which should be carefully monitored is the ratio of STEM human capital between the two countries, which will continue to move significantly in China's favor.

I displayed the IMF figures below in my 2004 post on sustainability of Chinese economic growth. I felt that +20y along the trajectories described was realistic for PRC, and I was correct.

It would be interesting to see updated 2020 versions.

 

See also 

Beijing 2019 Notes 

Beijing 2019 Notes Addendum

In my earlier post on Beijing I emphasized the issue of scale in China -- massive scale that is evident in the video above. 

I traveled in SE Asia before the 1997 currency / economic crisis. At that time there was plenty of evidence of a bubble in those countries -- unused infrastructure and real estate built on spec, few signs of real technological or productive capability, etc. China had aspects of that 10 years ago, but now it's apparent that earlier infrastructure investment is being put to good use. 

As I walked around Beijing I strained to find things around me -- buildings, solar panels, batteries, cars, high speed trains, electronics, software infrastructure, even airplanes -- that couldn't be sourced in China. Other than a few specific tech stacks that will get serious attention in coming years (e.g., CPUs) I was not able to think of many areas in which China has not caught up technologically. 

See Can the US derail China 2025?

There is a consistent Western cognitive bias concerning China: a severe underestimate of her capabilities and the capabilities of her people. This bias persists and analysts should carefully recalibrate in light of their previous predictions and the actual outcomes. Separate from this bias is an overall lack of knowledge and a willingness to accept lazy generalizations...