Robert McNees
Physicist Freeman Dyson was born #OTD in 1923.
He was known for his work in quantum electrodynamics and – among many other things – his eschatological musings about physics and the prospects for life in the far-flung future.
To the best of my knowledge, Dyson was the most prominent physicist of the modern era who never completed a PhD.
Photo: Heka Davis / AIP
Robert McNees
Before I begin, let me note that Dyson took an unfortunate position on climate change.
He allowed that humans have an impact, but insisted that existing computer models were too unreliable to justify what he saw as potentially serious consequences of climate action. He was wrong about that.
In my opinion, this always felt like a manifestation of his contrarian streak. But maybe I am wrong. In any case, I want to talk about physics. So I will leave the climate stuff to others.
Robert McNees
Dyson was one of the first physicists to really understand the meaning and power of Feynman's diagrammatic approach to QED.
He published a paper in 1949 showing that this method was equivalent to the operator approach of Schwinger & Tomonaga.
Ref: Dyson, Phys. Rev. 75, 486–502
Robert McNees
It turns out, the Japanese physicists Koba and Takeda had submitted similar work just two days before.
When Dyson learned of this he amended his paper to recognize their work. He lamented the effect of the war on the dissemination of important ideas: "The isolation of these Japanese workers has undoubtedly constituted a serious loss to theoretical physics."
Robert McNees
But my favorite bit of field theory work by Dyson is a short, beautiful paper – just two pages! – showing that perturbation theory in quantum electrodynamics produces a divergent series.
It is a fantastically simple and elegant piece of reasoning. A real classic.
Ref: Dyson, Phys. Rev. 85, 631
https://journals.aps.org/pr/abstract/10.1103/PhysRev.85.631
Robert McNees
Let me summarize the result.
In quantum electrodynamics (QED) we calculate physical quantities perturbatively, as a series in a small number α known as the "fine structure constant." Its numerical value is about 1/137.
For example, if we want to know the anomalous magnetic moment of the electron (classically it should be g=2) we get a series:
g = 2 + (1/π) α + (0.656/π²) α² + …
Increasingly complex quantum mechanical "corrections" to the classical value involve more and more powers of α.
Robert McNees
The problem is that if these series expansions for physical quantities converged for some small value of α (like 1/137), then they must be analytic functions of α around α=0.
But if this were true, the series would also have to converge for small *negative* values of α.
A theory with negative α would be pathological. Like charges would attract and all sorts of weird, unphysical things would happen. Dyson describes "an explosive disintegration of the vacuum by spontaneous polarization."
Robert McNees
Therefore, Dyson concludes, the radius of convergence for perturbative series in QED must be zero.
As long as α is non-zero, we are calculating a divergent series.
The first several terms in these series appear to converge towards results that agree with experiment to amazing precision: 12 or 13 decimal places, in state-of-the-art calculations.
Robert McNees
But eventually, a divergent series goes off the rails and veers away from convergence.
In a perturbative QED calculation, the coefficients in front of subsequent powers of α will start to grow. Slowly at first, but then fast enough to overwhelm even very large powers of (1/137).
Past that point the series runs away toward infinity.
Robert McNees
Luckily, this isn't a practical concern. Dyson's own crude estimate is that it happens somewhere around the α^{137} term in the series. That's miles away from anything we can calculate.
Why does it happen? In Feynman's approach to perturbative QED calculations, the number of diagrams needed to calculate the αⁿ term in the series grows rapidly with n. Collectively, they eventually overwhelm even large powers of α.
Diagrams: K.K. Gan, 3rd order contributions to electron anomalous magnetic moment
Robert McNees
Anyway, Dyson gracefully pulls off the argument with minimal mathematics and a lovely bit of physical intuition. It's a gem of paper and a QED classic. How marvelous that you can sum it up so succinctly:
If perturbation theory for QED had non-zero radius of convergence then it would converge for small negative values of α. But such a theory would be pathological and not give analytic functions of α for physical quantities, therefore the perturbation expansion is divergent.
Robert McNees
But what I really want to talk about is a series of four lectures Dyson gave at NYU in 1978, not long after Steven Weinberg's popular cosmology book "The First Three Minutes" was published.
Dyson turns his attention away from the early Universe and instead considers the deep future. Specifically, what are the long term prospects for life on cosmological time scales?
Robert McNees
"Time without end: Physics and biology in an open universe" was published in Reviews of Modern Physics in 1979.
Dyson notes that cosmology was beginning to achieve respectability, but speculation about the end of the universe still seemed disreputable.
"I hope with these lectures to hasten the arrival of the day when eschatology, the study of the end of the universe, will be a respectable scientific discipline and not merely a branch of theology."
https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.51.447
Robert McNees
Reader, he succeeded. Go pick up a copy of @AstroKatie's wonderful "The End of Everything."
Available wherever Universes end and books are sold.
Robert McNees
In Dyson's lectures he comes up with quantitative estimates (based on what was known at the time) for phenomena with very long time scales, and then ponders whether there are notions of "life" that might operate in perpetuity in a cold, expanding universe.
Robert McNees
First Dyson considers phenomena relevant over time scales associated with the deep future, like the dissolution of galaxies, or the liquefaction of "stable" matter due to quantum tunneling at near-zero K. Here are some estimates:
Ref: Dyson, Rev. Mod. Phys. Vol. 51, No. 3 (1979)
Robert McNees
This part is tremendous fun. You get sentences like "The cold expanding universe will be illuminated by occasional fireworks for a very long time" and "...ordinary low-mass stars that have settled down into white dwarf configurations and become cold spheres of pure iron."
It's the theoretical physics equivalent of a late-night dorm room conversation.
Robert McNees
In the next lecture he turns to biology. Assuming that the basis of consciousness is associated with structure rather than matter, he proposes a biological scaling hypothesis and argues (with a few more assumptions) that "life" might exist forever in an open universe.
The sort of life he envisions in this deep future is something like Fred Hoyle's "Black Cloud." Here's a relevant blog post by
@drskyskull:
https://skullsinthestars.com/2014/08/03/fred-hoyles-the-black-cloud/
Robert McNees
In the final lecture, Dyson argues that communication might also be possible over deep cosmological scales.
Near the end he acknowledges a problem for far-future societies communicating across deep time that sounds an awful lot like something we deal with today.
Skulls in the Stars
@mcnees thank you for the shoutout!
Robert McNees
Dyson admits that his calculations may be wrong, but argues that they are at least *plausible*. Perhaps, he suggests, "life and intelligence can succeed in molding this universe of ours to their own purposes."
He closes by quoting Haldane quoting Chesterton:
Robert McNees
Of course, a lot has changed since 1979.
We now know that the universe seems to be dominated by vacuum energy that drives an accelerated Hubble expansion. This is nothing like the sort of universe Dyson envisioned.
Dyson addresses this in a revised edition of his book "Infinite in All Directions." He points out that cosmological acceleration might one day end, landing us in a Universe more like the one he considered. If not, then his ideas about the long term prospects for life are wrong.
Robert McNees
@edwiebe See the next post!
Ed Wiebe
@mcnees He ended up with a climate denial phase too. Like so many old nobel winners he thought he knew everything.
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