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It's official: Physics is hard

May 8, 2012
Scientists have conducted scientific research on the difficulty –- from a computational complexity theory perspective -- of addressing some of the challenges of physics.

Toby Cubitt, researcher at Universidad Complutense de Madrid, and member of the QUITEMAD Scientific Consortium (R&D Technologies Program, funded by the Madrid Government) together with other colleagues, have conducted scientific research on the difficulty -- from a computational complexity theory perspective -- of addressing some of the challenges of physics.

The work has been published in the journal Physical Review Letters , and Science magazine has also published an article, commenting on this work. Toby Cubitt and his colleagues, Jens Eisert and Michael Wolf, of the Universities of Berlin and Munich respectively, show in this article the difficulty of obtaining the equations that govern the temporal evolution of a physical system, from observations of the system at different times, thereby showing the mathematical certainty of the difficulty of physics.

The journal Science reported on February 21, 2012, in its Science Now section, the recent discovery of quantum physicist Toby Cubitt, from the Mathematical Analysis Dept. at the Universidad Complutense de Madrid, and his colleagues: it's possible to mathematically prove that physics is hard.

As we are taught in school, physics tries to provide mathematical equations that explain the evolution of a system over time, starting from observations of that system. With the current advances in supercomputers, one might expect that this process could be automated, replacing the creativity of scientists by the calculation power of computers.

Fortunately for scientists, Toby Cubitt and colleagues have shown mathematically that this is not possible, in an article recently published in Physical Review Letters.

But how can you prove that a problem is hard? The mathematical theory of computational complexity allows problems to be classified according to their difficulty. There are easy problems to solve, such adding or multiplying two numbers, which therefore can be automated, allowing a computer to solve them. But there are others, such as optimization problems of logistics in freight transport, which are very hard. So much so that, if there was a way to automate the solution, then it would be possible to automate the solution of ALL these problems (this is believed to be impossible, and is known as the "P different from NP" conjecture). It is precisely this latter class of very hard problems to which the problem of obtaining the equations governing the evolution of physical systems belongs.

Therefore, the work of Toby Cubitt and his colleagues will allow everyone to sleep soundly at night. Physicists, because supercomputers are not going to take over their jobs. And non-physicists, because although they always suspected that physics is hard and therefore difficult to understand, now there is no doubt: it is a mathematical certainty.

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Journal Reference:

  1. Toby Cubitt, Jens Eisert, Michael Wolf. Extracting Dynamical Equations from Experimental Data is NP Hard. Physical Review Letters, 2012; 108 (12) DOI: 10.1103/PhysRevLett.108.120503

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