So, John Horgan, the

*End of Science*guy, interviewed Scott Aaronson, a theoretical computer scientist interested in quantum computing and computational complexity theory.

In the following, some random quotes.

### On Quantum Mechanics

*[Q]uantum mechanics is astonishingly simple—once you take the physics out of it! In fact, QM isn’t even “physics” in the usual sense: it’s more like an operating system that the rest of physics runs on as application software.*

[A]ccepting quantum mechanics didn’t mean giving up on the computational worldview: it meant upgrading it, making it richer than before. There was a programming language fundamentally stronger than BASIC, or Pascal, or C—at least with regard to what it let you compute in reasonable amounts of time. And yet this quantum language had clear rules of its own; there were things that not even it let you do (and one could prove that); it still wasn’t anything-goes.

[A]ccepting quantum mechanics didn’t mean giving up on the computational worldview: it meant upgrading it, making it richer than before. There was a programming language fundamentally stronger than BASIC, or Pascal, or C—at least with regard to what it let you compute in reasonable amounts of time. And yet this quantum language had clear rules of its own; there were things that not even it let you do (and one could prove that); it still wasn’t anything-goes.

### The Computational Universe

*If it’s worthwhile to build the LHC or LIGO—wonderful machines that so far, have mostly triumphantly confirmed our existing theories—then it seems at least as worthwhile to build a scalable quantum computer, and thereby prove that our universe really does have this immense computational power beneath the surface.*

*Firstly, quantum computing has supplied probably the clearest language ever invented—namely, the language of qubits, quantum circuits, and so on—for talking about quantum mechanics itself.*

[...]

Secondly, one of the most important things we’ve learned about quantum gravity—which emerged from the work of Stephen Hawking and the late Jacob Bekenstein in the 1970s—is that in quantum gravity, unlike in any previous physical theory, the total number of bits (or actually qubits) that can be stored in a bounded region of space is finite rather than infinite. In fact, a black hole is the densest hard disk allowed by the laws of physics, and it stores a “mere” 1069 qubits per square meter of its event horizon! And because of the dark energy (the thing, discovered in 1998, that’s pushing the galaxies apart at an exponential rate), the number of qubits that can be stored in our entire observable universe appears to be at most about 10122.

[...]

So, that immediately suggests a picture of the universe, at the Planck scale of 10^-33 meters or 10^-43 seconds, as this huge but finite collection of qubits being acted upon by quantum logic gates—in other words, as a giant quantum computation.

[...]

Secondly, one of the most important things we’ve learned about quantum gravity—which emerged from the work of Stephen Hawking and the late Jacob Bekenstein in the 1970s—is that in quantum gravity, unlike in any previous physical theory, the total number of bits (or actually qubits) that can be stored in a bounded region of space is finite rather than infinite. In fact, a black hole is the densest hard disk allowed by the laws of physics, and it stores a “mere” 1069 qubits per square meter of its event horizon! And because of the dark energy (the thing, discovered in 1998, that’s pushing the galaxies apart at an exponential rate), the number of qubits that can be stored in our entire observable universe appears to be at most about 10122.

[...]

So, that immediately suggests a picture of the universe, at the Planck scale of 10^-33 meters or 10^-43 seconds, as this huge but finite collection of qubits being acted upon by quantum logic gates—in other words, as a giant quantum computation.

### The Big Picture

*Ideas from quantum computing and quantum information have recently entered the study of the black hole information problem—i.e., the question of how information can come out of a black hole, as it needs to for the ultimate laws of physics to be time-reversible. Related to that, quantum computing ideas have been showing up in the study of the so-called AdS/CFT (anti de Sitter / conformal field theory) correspondence, which relates completely different-looking theories in different numbers of dimensions, and which some people consider the most important thing to have come out of string theory.*

*[S]ome of the conceptual problems of quantum gravity turn out to involve my own field of computational complexity in a surprisingly nontrivial way. The connection was first made in 2013, in a remarkable paper by Daniel Harlow and Patrick Hayden. Harlow and Hayden were addressing the so-called “firewall paradox,” which had lit the theoretical physics world on fire (har, har) over the previous year.*

In summary, I predict that ideas from quantum information and computation will be helpful—and possibly even essential—for continued progress on the conceptual puzzles of quantum gravity.

In summary, I predict that ideas from quantum information and computation will be helpful—and possibly even essential—for continued progress on the conceptual puzzles of quantum gravity.

*If civilization lasts long enough, then there’s absolutely no reason why there couldn’t be further discoveries about the natural world as fundamental as relativity or evolution. One possible example would be an experimentally-confirmed theory of a discrete structure underlying space and time, which the black-hole entropy gives us some reason to suspect is there.*

### P/NP

*[T]he ocean of mathematical understanding just keeps monotonically rising, and we’ve seen it reach peaks like Fermat’s Last Theorem that had once been synonyms for hopelessness. I see absolutely no reason why the same ocean can’t someday swallow P vs. NP, provided our civilization lasts long enough. In fact, whether our civilization will last long enough is by far my biggest uncertainty.*

*More seriously, it was realized in the 1970s that techniques borrowed from mathematical logic—the ones that Gödel and Turing wielded to such great effect in the 1930s—can’t possibly work, by themselves, to resolve P vs. NP. Then, in the 1980s, there were some spectacular successes, using techniques from combinatorics, to prove limitations on restricted types of algorithms. Some experts felt that a proof of P≠NP was right around the corner. But in the 1990s, Alexander Razborov and Steven Rudich discovered something mind-blowing: that the combinatorial techniques from the 1980s, if pushed just slightly further, would start “biting themselves in the rear end,” and would prove NP problems to be easier at the same time they were proving them to be harder! Since it’s no good to have a proof that also proves the opposite of what it set out to prove, new ideas were again needed to break the impasse.*

###

Musings

*This characteristic of quantum mechanics—the way it stakes out an “intermediate zone,” where (for example) n qubits are stronger than n classical bits, but weaker than 2n classical bits, and where entanglement is stronger than classical correlation, but weaker than classical communication—is so weird and subtle that no science-fiction writer would have had the imagination to invent it. But to me, that’s what makes quantum information interesting: that this isn’t a resource that fits our pre-existing categories, that we need to approach it as a genuinely new thing.*

[I]f scanning my brain state, duplicating it like computer software, etc. were somehow shown to be fundamentally impossible, then I don’t know what more science could possibly say in favor of “free will being real”!

[I]f scanning my brain state, duplicating it like computer software, etc. were somehow shown to be fundamentally impossible, then I don’t know what more science could possibly say in favor of “free will being real”!

*I hate when the people in power are ones who just go with their gut, or their faith, or their tribe, or their dialectical materialism, and who don’t even feel self-conscious about the lack of error-correcting machinery in their methods for learning about the world.*

*Just in the fields that I know something about, NP-completeness, public-key cryptography, Shor’s algorithm, the dark energy, the Hawking-Bekenstein entropy of black holes, and holographic dualities are six examples of fundamental discoveries from the 1970s to the 1990s that seem able to hold their heads high against almost anything discovered earlier (if not quite relativity or evolution).*

March 13th, 2008 at 6:03 pm

July 1st, 2008 at 4:32 pm

## fundamental

## Ideas

In a nutshell:

## Paradigm

Mathematical models of reality are independent of their formal representationsymmetryandinvariance. Basically, this requirement gives rise to nearly all of physics.## Classical Mechanics

## Mathematics of Symmetry

group theory.## Physics of Non-Gravitational Forces

quantum field theories. These in turn can be expressed asgauge theories, where the parameters of the gauge transformations are local, i.e., differ from point to point in space-time.Standard Modelof elementary particle physics unites the quantum field theories describing the fundamental interactions of particles in terms of their (gauge) symmetries.## Physics of Gravity

covariance, meaning that in the geometric language of the theory describing gravity (general relativity) the physical content of the equations is unchanged by the choice of the coordinate system used to represent the geometrical entities.vector, lets call ita. If I want to compute the length of this arrow, I need to choose a coordinate system, which gives me the x-, y- and z-axes components of the vector, e.g.,a= (3, 5, 1). So starting from the origin of my coordinate system (0, 0, 0), if I move 3 units in the x direction (left-right), 5 units in the y-direction (forwards-backwards) and 1 unit in the z direction (up-down), I reach the end of my arrow. The problem is now, that depending on the choice of coordinate system - meaning the orientation and the size of the units - the same arrow can look very different:a= (3, 5, 1) = (0, 23.34, -17). However, everytime I compute the length of the arrow in meters, I get the same number independent of the chosen representation.tensorsand the commonsense requirement, that the calculations involving tensor do not depend on how I represent the tensors in space-time, is covariance.equivalence principleand states that the gravitational force is equivalent to the forces experienced during acceleration. This may sound trivial, has however very deep implications.## Physics of Condensed Matter

solid-state physics, deals with the macroscopic physical properties of matter. It is one of physics first ventures into many-body problems inquantum theory. Although the employed notions of symmetry do not act at such a fundamental level as in the above mentioned theories, they are a cornerstone of the theory. Namely the complexity of the problems can be reduced using symmetry in order for analytical solutions to be found. Technically, the symmetry groups are boundary conditions of theSchrödinger equation. This leads to the theoretical framework describing, for example, semiconductors and quasi-crystals (interestingly, they have fractal properties!). In the superconducting phase, thewave functionbecomes symmetric.## Conclusion

## The Success

electromagnetismwith theweak force(two of the three non-gravitational forces), the theory postulated two new elementary particles: the W and Z bosons. Needless to say, these particles where hitherto unknown and it took 10 years for technology to advance sufficiently in order to allow their discovery.special relativitylead to theDirac equationwhich demands the existence of an, up to then, unknown flavor of matter:antimatter. Four years after the formulation of the theory, antimatter was experimentally discovered.## The Future…

Maxwell equations; as mentioned above, electromagnetism and the weak force were merged into theelectroweak force; and finally, the electroweak andstrongforce were united in the framework of the standard model of particle physics. These four forces are all expressed as quantum (field) theories. There is only one observable force left: gravity.The efforts to quantize gravity and devise a unified theory, have taken a strange turn in the last 20 years. The problem is still unsolved, however, the mathematical formalisms engineered for this quest - namely

string/M-theoryandloop quantum gravity- have had a twofold impact:topology).per sebecome quantizedsupersymmetricmatterFrom: http://j-node.homeip.net/knowledgebase/overview/tags: science, fundamental, analytical, reality, mathematical models## 4 Responses to “fundamental”

May 31st, 2008 at 4:21 pm

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