Reflections on the Future of Physics: From Particle Colliders to Applied Mathematics

1. Reflections and the Future of PhysicsJuly 28, 2009 Hong-Yee Chiu Former Astrophysicist, NASA Goddard Space Flight Center

2. Physics in 1959 (my Ph. D. Year) • Main thesis work: 200 MeV π-p scattering • Status: First satellite launched, laser just invented, QED was just developed, parity violation just discovered, General Relativity (GR) considered a weird science, more particle discovered as accelerators became larger. • Astrophysics was in infancy, stellar evolution was in development, no supernova theory; neutron stars, black holes were speculative objects. • No comprehensive particle theory, • ……

3. In 2009 ۩Particle physics – experiments move from laboratory to center of mass systems (collider) ۩A semi complete standard model ۩Satellites and lasers everywhere, GR in vogue, particle species almost complete but … ۩Astrophysics among the most pursued ۩Neutron stars, black holes confirmed, dark matter and dark energy discovered ۩Planetary system in other stars …..

4. Where do we go from here? • The last collider was just built (United States already quitted) Tough luck if it fails to achieve its objective • Particle model and theory still incomplete – need quantum gravity • Steve Weinberg: not possible before 2050 (in time to welcome the retirement of current generation of physicists) • Too optimistic. The approach taken so far is “not even wrong!”

5. String Theory dominates • Lee Smolin: in The Trouble with Physics he wrote: The Rise of String Theory, The Fall of Science, and What comes next? • Key point. GR requires generalized coordinates, and in Quantum GR (QGR) even generalized coordinates are not allowed, only relationships • There are at least 105 string theories, all require coordinates • At best, a transitional theory

6. Why the fall of science? • 21st century physics is tied to grants • Grants and tenure are judged by peers. • The peer group consists of special interest groups, so the trend propagates (look at the U. S. democracy, dominance of lobbyists and special interest groups). • There is virtually no possibility for another Einstein. He could never get a grant and a tenure position. (Not even a job in patent office – cutbacks, over committed.) • So special interests win, science loses.

7. Look back at 19th century science • In 1846 Uranus was discovered based on Newtonian mechanics and mathematics • By early 20th century, confidence was so high, Lord Kelvin claimed that physics was almost complete, except two dark clouds – Roentgen’s X-ray, Becquerel’s natural radioactivity … the rest is history • The great Titanic was built and the faith on engineering reached pinnacle – a lesson we never forget ever since.

8. A sister science - mathematics • Early20th century, mathematics was at pinnacle • Basic concepts were formed – Dedekind cut, Peano theorem, … • David Hilbert posted 23 most important mathematic problems to be solved • Now, around 5 problems remain unsolved • The 6th problem: To axiomatize all of physics, probably was an illusion. Even mathematics itself could not do it (Gődel, Cohen): There are limits in the power of mathematics. To axiomatize was the dream of the so-called rational mechanics.

9. Early 21st century • Clay Institute (Cambridge, Mass) posted 7 problems with million dollar prizes. Only two from Hilbert’s list made it (Riemann Hypothesis) and Poincaré’s conjecture, which has since been resolved (prize declined) • Two are of vital interest to physicists • 5 Yang–Mills existence and mass gap • 6 Navier–Stokes existence and smoothness

10. Center of gravity moved to applied mathematics • Game theory takes preponderance, because it deals with human behavior and social problems. Examples: • Prisoner’s dilemma (solution known, no analytical proof) – commercial application • Arrow’s impossibility theorem (no fair election if there are more than two parties) (received Nobel prize in economics) • Cocktail party problem

11. Prisoner’s dilemma • Two prisoners A and B were caught, no hard evidence of crime • If A and B both keep silent, they will be released because of lack of evidence. • If A confesses that B is the leader, A receives less sentence. Same is for B. • If both A and B confess and accuse each other, they both receive hefty sentences. • What should A and B do? • No analytical solution – only practical solution

12. Applications • A and B want to exchange merchandise X and Y. • A and B are honest, they get rewarded X and Y. • A is dishonest, A gains and B loses and vice versa. • Both A and B dishonest, both lose. • Let A be supermarket B is customer, the game becomes a model for business • Almost all MBA schools requires the exercise of prisoner’s dilemma.

13. Practical solution • Computer simulations: Supermarket A is honest, but keeps an eye on customer B. Occasionally A will issue coupons and discounts. If B is honest, he/she will have a good place to shop with frequent discounts. If B is dishonest, A seeks maximum punishment. (A dishonest, folds) • Conclusion: Golden rule “Give your left cheek” does not work. • Silver rule works: Confucius: Repay kindness with kindness, use justice to punish the offender.以德報德,以直報怨

14. Cocktail Party Problem • You passed by a cocktail party, and was invited to step in. you need to decide. • A passerby said, sure, you know A, B … and you should join. • Another said, wait, you do not know A, B … too well maybe you should not. • You need to make a decision: You might have a good time in joining but you might end up wasting a whole evening. • Application: Risk analysis. (Should you buy a certain stock? Get married?).

15. There are many other applications of game theory. Many patents have been filed to deal with practical matters, even in divorce cases. Sociologists try to understand the so-called tipping point theory – New York City used to be crime ridden, suddenly the crime rate dropped from 1st to 163rd. Why and how? Something caused the tipping of the scale. This is a yet unsolved problem.

16. Examples of Unresolved Physics • Defense of Quantum physics and GR • Their conclusions are absolutely (well, almost) correct; we know about quantum physics. How about GR? • Global Positioning System GPS is an example of how GR works. To get within 1 meter, one needs perhaps 10-14 accuracy, to get within 1 cm, one needs maybe 10-17 accuracy (this could be the limit). GR effect creeps in at 10-10.

17. Difficulties • For quantum physics, it is the well known Einstein–Podolsky–Rosen (EPR) paradox. • If not fixed, the theory does not have the final say – it lacks self consistency. • For GR, it is less well known that GR has solutions that violates causality. • In Gődel’s rotational universe, the light cone tilts toward past after the velocity of light circle: v>c. This makes it possible to time travel to the past.

18. Frank Tipler Cylinder • Frank Tipler showed in 1974 that it is possible to tilt the light cone towards the past around an infinite cylinder of dense matter. Several fictions have been written. • Problems with time travel to the past and future: Violation of causality. • Uncertainty principle no longer valid. • GR thus contains solutions that violate causality and uncertainty principle. • This and other difficulties must be resolved.

19. Unsolved simpler problems • Two examples. • Properties of soliton waves: a soliton wave acts like a particle and is resistant to dispersion. • Ordinary photon can travel in optical fiber for about 20 km. • High powered source which bundles many photons together to become a soliton can travel over 200 km, making transoceanic fiber optic communication possible. (This is an empirical discovery.)

20. Boiling point calculation • There is no theory to accurately calculate the boiling point. • Even the simplest case, the boiling point of liquid helium has not been accurately calculated. (Helium is almost perfect gas.) • The soliton problem and the boiling point problem are possibly related to the understanding of the Navier Stokes equation (one of the Clay Institute problems.) • One never gets a grant for these problems.

21. The future direction? • Probably no higher energy colliders in the future. • It is impossible to compete against industry on specific applications. • Lesson: By rejecting applied mathematics early in the game, most mathematics departments have been reduced to service departments, teaching undergraduate math. • Future? One should search for new frontiers within the realm of old physics.