Professor Emeritus

### About

Dr. Tomozawa has been a faculty member of the University of Michigan, Physics Department since 1966 and became a Professor Emeritus in 2003. Dr. Tomozawa has focused on theoretical high energy physics research his whole career and he currently continues to publish research annually in the area of general relativity, cosmic rays and astrophysics.

Dr. Tomozawa earned a B.S. in Physics in 1952 and a D.Sc. in 1961 from Tokyo University. He was an Assistant at Tokyo University from 1956 to 1957 and at the Tomonaga’s Institute of Tokyo University of Education, now known as Tsukuba University, from 1957 to 1959. He left Japan in 1959 and worked at Cambridge University, University College London, University of Pisa and the Institute for Advanced Study at Princeton. Dr. Tomozawa also spent time at SLAC National Accelerator Laboratory in Stanford University (1972) and at the Yukawa Institute of Theoretical Physics, Kyoto University (1988-89). His work is well known as the Weinberg-Tomozawa formula for pion nucleon scattering length.

In 1985, Dr. Tomozawa proposed the evidence of a new particle at 3 PeV, and named it a “Cion” particle, as the cause of the knee energy of cosmic ray energy spectrum (a bump at 2.6±0.3 PeV for neutrino cross section by ICE CUBE is a possible candidate for Cion). In 2015, he discovered the physical metric that is the exact solution for the Einstein equation which fits the time delay experiment by Shapiro for the solar system. In his metric, the size of compact objects (black holes and neutrino stars) are 2.6 times the Schwarzchild radius and the gravitational red shift on the surface is √3 = 1.732. Dr. Tomozawa’s metric serves to replace Newton’s law of gravity and will be essential to future study and understanding of black holes and neutron stars.

**Selected Publications:**

Local Commutativity and the Analytic Continuation of the Wightman Function, Journal of Mathematical Physics, 4, 1240 (1963). The author has shown that the analyticity regions of the Wightman functions, intersection of any two and the union of any of them, are simply connected. This finding makes the Hall-Wightman theorem obvious and the CTP theorem in quantum field theory is straight forward conclusion.

Axial-vector Coupling Constant Renormalization and Meson-baryon Scattering Length, Nuovo Cimento, 46A, 707 (1966). This article, along with the work of Steven Weinberg, is quoted as the Weinberg Tomozawa formula. In particular the application to pion nucleus bound states and discussion on Kaon physics are actively pursuit fields. In the web search by Weinberg Tomozawa term or interaction, one encounters more than 15,000 references.

Magnetic Monopoles, Cosmic Rays and Quantum Gravity, in the Proc. of 1985 INS International Symposium on Composite models of Quarks and Leptons (Tokyo, edit. Terazawa, H. and Yasue, M.) pp. 386 (1985).

Cosmic Rays, Quantum Effects on Gravity and Gravitational Collapse, Lectures given at the Second Workshop on Fundamental Physics, University of Puerto Rico, Humacao, March 24-28, 1986. This lecture note can be retrieved from entering https://inspirehep.net/record/230557, then choose abstract page and click on KEK scanned document.

Ankle Phenomenon in the Cosmic Ray Energy Spectrum, Journal of Modern Physics, 4, 385 (2013). These articles discuss the sudden change of spectral indexes of cosmic ray energy spectrum at 3 PeV (so called the knee energy) and at 3 EeV (so called the ankle energy). The former is due to the change of radiation-dominated expansion rate and matter-dominated expansion rate inside massive black hole such as AGN (Active Galactic Nuclei), and the latter is due to the change of inflationary expansion rate and radiation-dominated expansion rate. This mechanism requires the existence of particle of mass of 3 PeV. Tomozawa named this particle, as Cion (Cosmic Interference Particle, the knee in Chinese, Xi, pronounced as shi). The recently observed bump in neutrino cross section at 2.6 by Ice Cube may be a candidate for Cion.

Experimental Test of General Relativity and the Physical Metric, Journal of Modern Physics, 6, 335 (2015). Schwarzschild discovered the infinite number of exact solutions of Einstein equation. The best experiment that test general relativity is performed by Shapiro and Bertotti et al on time delay of the solar system, with the accuracy of 1 in 10^5. In the past, people fit the data by approximate solution of Einstein equation. The Schwarzschild metric, an exact solution of Einstein equation does not fit the Shapiro-Bertotti data. The author found the exact solution of Einstein equation that fits the Shapiro-Bertotti data. This metric is named as the physical metric. It is found that in the physical metric, the metric functions on time part and angular part should be the same. In other words, speed of light on the angular direction is unchanged from vacuum value. This is understandable, since angular direction is perpendicular to the radial direction, which is the direction of gravity. That is why the new metric is called the physical metric.

In the physical metric, the size of object is 2.60 times the Schwarzschild radius [2.60 = (3√3)/2] and gravitational redshift on the surface is √3. These rules are applied to black holes and neutron stars. The size of neutron star is consistent with this prediction. The radius of neutron star of 1.4 Msun should be 3.0*1.4*2.60 = 10.9 km, which is close to the observed value. The size of neutron stars and black holes are proportional to the value of mass. This can be tested by observation in the future. The size of black hole at the center of the Milky Way (4.2 Million Msun) was measured to be 2.6 Schwarzschild radius. Since the experimentalists try to fit the data by using the Schwarzschild metric, they interpret as they measure a black hole shadow size. They should correct their interpretation in the future.

###### Field(s) of Study

- Elementary Particle Experiment and Theory