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New Solutions for Quantum Gravity with TensorFlow
Friday, November 15, 2019
Posted by Thomas Fischbacher, Researcher in Compression, Google Research, Zürich
Recent strides in machine learning (ML) research have led to the development of tools useful for research problems well beyond the realm for which they were designed. The value of these tools when applied to topics ranging from
teaching robots how to throw
to predicting the
olfactory properties of molecules
is now beginning to be realized. Inspired by advances such as these, we undertook the challenge of applying
TensorFlow
, a computing platform normally used for ML, to advance the understanding of fundamental physics.
Perhaps the biggest open problem in fundamental theoretical physics may be that our current understanding of
quantum mechanics
only includes three of the four fundamental forces — the
electromagnetic
,
strong
, and
weak
forces. There is currently no complete quantum theory that also includes the force of
gravitation
, while still matching experimental observations, i.e., an accurate model of
quantum gravity
.
One promising approach to a unified model that includes quantum gravity, which has survived many mathematical consistency checks, is called
M-Theory
, or "
The Theory formerly known as Strings,”
introduced in 1995 by
Edward Witten
. In the everyday world, we all experience four dimensions—three spatial dimensions (
x
,
y
, and
z
), plus time (
t
). M-Theory predicts that, at very short lengths, the Universe is described, instead, by eleven dimensions. But, as one can imagine, establishing the connection between the four-dimensional world that we observe and the 11-dimensional world predicted by M-theory is exceedingly difficult to solve analytically. In fact, it might require analytic manipulation of equations having more terms than there are electrons in the Universe.
This summer, we published an
article
in the
Journal of High Energy Physics
where we introduced novel ways to address such problems through creative use of ML technology. Using simplifications enabled by TensorFlow, we managed to bring the total number of known (stable or unstable) equilibrium solutions for one particular type of M-Theory spacetime geometries
to 194
, including a new and
tachyon-free
four-dimensional model universe. The geometries that we studied are special in that they are still (barely) accessible with exact calculations that do not require neglecting potentially important terms. We have also released a short instructive
Google colab
as well as a more powerful
Python library
for use in related research.
Applying TensorFlow to M-Theory
This work is predicated on a key observation that a mixed numerical and analytic approach can be more powerful than a purely analytical method. Instead of attempting to find analytic solutions with brute force, we use a numerical approach that leverages TensorFlow for the initial search for solutions to the model. This then yields hypotheses on which specific combinations can be tested and analyzed with stringent mathematical methods, ultimately proving the actual existence of a conjectured solution. This represents a novel methodology for making further progress in theoretical physics.
Conclusion
We hope that these results will be an important step in interpreting M-theory, and demonstrate how the research community can use new ML tools, such as TensorFlow, to approach other similarly complex problems. We are already applying the newly discovered methods in further theoretical physics research.
Acknowledgements
This research was conducted by Iulia M. Comşa, Moritz Firsching, and Thomas Fischbacher. Additional thanks go to Jyrki Alakuijala, Rahul Sukthankar, and Jay Yagnik for encouragement and support.
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