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RECENT POSTS IN THIS TOPIC

Jonathan Dickau: on 4/17/15 at 18:03pm UTC, wrote I want to thank you Daniel.. I had not seen the Lloyd and Dreyer paper...

Jonathan Dickau: on 4/17/15 at 3:39am UTC, wrote Thanks for the thoughtful reply Daniel.. Sorry someone else pushed your...

Daniel Braun: on 4/16/15 at 8:39am UTC, wrote Hello Jonathan, thank you very much for your kind words and pushing my...

Jonathan Dickau: on 4/15/15 at 23:53pm UTC, wrote Hello Daniel, I greatly enjoyed your excellent essay. As luck would have...

Joe Fisher: on 4/8/15 at 15:45pm UTC, wrote Dear Daniel, I think Newton was wrong about abstract gravity; Einstein was...

Daniel Braun: on 4/7/15 at 12:07pm UTC, wrote Dear Marc, no, that equation is supposed to be exact (incidentally, I just...

Marc Séguin: on 4/6/15 at 19:17pm UTC, wrote Dear Daniel, That's quite an equation in your paper! If I understand...

Daniel Braun: on 4/6/15 at 13:54pm UTC, wrote Dear Marc, thank you very much for your kind remarks, and bumping up the...


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FQXi FORUM
October 19, 2019

CATEGORY: Trick or Truth Essay Contest (2015) [back]
TOPIC: Thoughts on a Theory of Theories by Daniel Braun [refresh]
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Author Daniel Braun wrote on Mar. 10, 2015 @ 14:02 GMT
Essay Abstract

I analyze the set of possible physical theories using the mathematical tool of set theory. The analysis starts from simple classical theories and extends all the way to quantum field theories. Guided by the analysis of existing theories of Nature, we explore how these theories could be generalized while still qualifying as a physical theory. This allows us to calculate the cardinality of the set of possible physical theories, and therefore to quantify how special our mathematical descriptions of Nature are.

Author Bio

I studied physics in Stuttgart, and, with a Fulbright grant, in Stony Brook. Then I moved to Paris and got a Ph.D. in physics at the University Paris Sud (Orsay) with work in mesoscopic solid state physics. Quantum chaos was center stage during my post-doc time in Essen, at the end of which I moved into quantum information theory. After four years in semi-conductor industry developing MRAM, I went back to academia as professor for theoretical physics in Toulouse, France. Since 2013 I am professor for theoretical physics in Tuebingen with a focus on quantum optics and quantum information.

Download Essay PDF File

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Member Tejinder Pal Singh wrote on Mar. 11, 2015 @ 07:48 GMT
Dear Professor Braun,

We read your essay with lot of interest, and enjoyed it, especially for the novelty of the idea.

We have a question in the context of non relativistic quantum mechanics and the process of quantum measurement. Do you adhere to the Copenhagen interpretation (this is the impression we get from reading your essay)? Many physicists including us regard this interpretation as problematic, because of the artificially assumed quantum - classical divide between system and apparatus. Let us consider the following three popular alternatives to Copenhagen:

Many worlds interpretation: no collapse of the wave-function, branching of alternatives [origin of Born probability rule obscure]

Bohmian mechanics as an equivalent mathematical reformulation of quantum mechanics - probabilities arise because of the so-called typicality assumption of initial condirions [We could not understand your remark "The lack of a consistent hidden variable description of the microscopic world entails a jump in cardinality of the set of possible physical theories from א2 to א3! "....to our understanding non-local hidden variable theories (generally referred to as Bohmian mechanics nowadays) are consistent at the non-relativistic level].

Phenomenologically Modified QM : GRW / Continuos spontaneous Localisation (CSL): Born rule arises from the stochastic nature of the modification.

While all these three variants have their own limitations and may turn out to be wrong eventually, it is our impression they do better than the Copenhagen interpretation.

We were wondering if the cardinality issue gets modified (looking more like classical) f you consider many-worlds / Bohemian / CSL, or is there no change compared to standard QM? We would be very interested to know what the answer is.

Thanks and regards,

Anshu, Tejinder

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Author Daniel Braun wrote on Mar. 11, 2015 @ 14:56 GMT
Dear Tejinder,

Thank you very much for your kind remarks and interest.

I did not make an assumption about the interpretation of quantum mechanics, and I don't think it enters into the cardinality calculation. The reason is that I consider possible QM theories as mappings from Hamiltonians to time evolution laws (plus possibly representations of operators for relevant physical...

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Member Tejinder Pal Singh replied on Mar. 12, 2015 @ 07:16 GMT
Dear Daniel,

Many thanks for your answer. I tend to agree with you. Many worlds is likely to be different, because no collapse takes place, and probabilities are likely only an apparent effect.

Best regards,

Tejinder

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Member Marc Séguin wrote on Apr. 6, 2015 @ 01:28 GMT
Dear Daniel,

Thank you for an interesting and ambitious essay. You raise original questions about calculating the cardinality of the ensemble of all physical quantities and physical theories. I found the following sentence particularly interesting:

"We can safely claim that no useful physical quantity is known that involves powers larger than say one hundred."

Indeed, of all the SI derived units (newton, joule, watt, etc.), only 4 involve a third (or minus third) power, and only one, the farad, involves a fourth power : F = 1 kg^−1 x m^−2 x s^4 x A^2. I had never really given a second thought about the issue... very interesting! NASA engineers that worked on the Hubble space telescope found it useful to define the jounce as the fourth derivative of the position, so its units are m/s^-4, but once again, we don't get higher than fourth power!

Later on in your essay, I think you made an interesting distinction between physical laws of "fundamental type" and of "secondary type" (that involve weird and arbitrary functions of dimensionless ratios).

Your essay deals in an original and interesting way with the question of the cardinality of possible physical laws compared to the cardinality of all possible mathematical laws, and it makes a worthwhile contribution to the ideas that have been put forward in this contest. Strangely enough, it has been a bit forgotten so far in the competition, and I hope bumping it higher will make it more noticeable. Good luck!

Marc

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Author Daniel Braun replied on Apr. 6, 2015 @ 13:54 GMT
Dear Marc,

thank you very much for your kind remarks, and bumping up the rating of my essay. Given the small number of ratings so far, this had an immediate positive effect :-) [as an aside, initially the essay was in the top 5 for several days, till a community member shot it down by apparently giving it only 1 point, whereupon it ended up in the middle range and slipped into oblivion. I...

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Member Marc Séguin replied on Apr. 6, 2015 @ 19:17 GMT
Dear Daniel,

That's quite an equation in your paper! If I understand correctly, it has been obtained by expanding some parameters to the tenth order, so it could be even "worse" if it was expanded further?

I agree with your that FQXi should organize a mock contest on the subject of the most ugly fundamental physical equation! Maybe next April 1st? :)

Marc

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Author Daniel Braun replied on Apr. 7, 2015 @ 12:07 GMT
Dear Marc,

no, that equation is supposed to be exact (incidentally, I just learned that it might contain some sign error, so I have to recheck it and possible write an Erratum. But other than that it should be exact). It results from an exact Gaussian integration of a high-order polynomial.

And yes, such a mock contest on April 1st (with the ugly equation to be found still required to be non-trivial and correct) might change a little bit the perspective of us beauty-hungry physicists :-)

Best regards,

Daniel

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Joe Fisher wrote on Apr. 8, 2015 @ 15:45 GMT
Dear Daniel,

I think Newton was wrong about abstract gravity; Einstein was wrong about abstract space/time, and Hawking was wrong about the explosive capability of NOTHING.

All I ask is that you give my essay WHY THE REAL UNIVERSE IS NOT MATHEMATICAL a fair reading and that you allow me to answer any objections you may leave in my comment box about it.

Joe Fisher

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Jonathan J. Dickau wrote on Apr. 15, 2015 @ 23:53 GMT
Hello Daniel,

I greatly enjoyed your excellent essay. As luck would have it; I use the term 'theory of theories' in my own essay, but in a rather different way. Phil Gibbs put forward a theory of theories in his 'Cyclotron Notebooks' referring to the idea that the reality we observe may not be the product of a singular mathematical pattern or model (a GUT or TOE), but rather that the universe results from a kind of path integral whose output is shaped by the full range of applicable theories - as a weighted average. In this way; we would not have to choose between loops and strings, for example, because the laws of nature employ the regularity of the Maths in both cases at once.

This notion has shaped my thinking for quite some time, but I had not thought before now that one might be able to determine the cardinality of the full array of possible theories. So you give me a lot to think about! I have boosted your score a bit, but I hope others push it higher, because you deserve a higher standing than you presently enjoy.

All the Best,

Jonathan

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Author Daniel Braun wrote on Apr. 16, 2015 @ 08:39 GMT
Hello Jonathan,

thank you very much for your kind words and pushing my score. I read the paper by Lloyd and Dreyer on the universal path integral but frankly couldn't make much sense out of it. So now I am curious to read your article, and the paper by Phil Gibbs that you mention.

I think it is an intriguing idea that laws of physics themselves might be the result of some interference, but is there even in principle a way to test this?

All the best,

Daniel

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Jonathan J. Dickau replied on Apr. 17, 2015 @ 03:39 GMT
Thanks for the thoughtful reply Daniel..

Sorry someone else pushed your ranking back down. As regards to my essay's thesis in relation to an idea in your essay; exact determinations of various quantities may have a built-in difficulty, and this can present problems with mathematization. Iterating the squaring function on the complex plane yield a bounding surface at r = 1 - any value smaller converges to (0,0i) and seed values further from the origin all diverge or are repelling points, while a value whose distance is 1 from the origin stays on the boundary forever.

But this requires infinite precision, or the preservation of unitarity as a fundamental value. If there is any noise on our calculation, or a truncation due to limited precision, this imprecision will drive the successive iterands to 0 or infinity. This is sort of like what Hawking has lately said about the fluctuation of an event horizon for a black hole being like weather forecasting. A built-in uncertainty, indeterminacy, or measurement imprecision, can all have the same effect - to drive a system to a particular result.

If we use z^2 + z instead of just z^2, things become much more interesting, but perhaps a little jitter is part of the equation. This gives me much food for thought.

Regards,

Jonathan

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Jonathan J. Dickau replied on Apr. 17, 2015 @ 18:03 GMT
I want to thank you Daniel..

I had not seen the Lloyd and Dreyer paper before your mention above (or had filed it away and forgot), but now I have downloaded it and it looks very interesting.

All the Best,

Jonathan

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