Energy and Mass in Relativity Theory

The following sections are included:

• Preface

• Contents

The following sections are included:

• INTRODUCTION

• PHOTON MASS AND VELOCITY OF LIGHT AND OF RADIO WAVES

• PHOTON MASS AND STATIC FIELDS

• PHOTON MASS AND BLACKBODY RADIATION

• CONCLUSION

Newtonian mechanics provides a perfect description of the motion of a body when its velocity v is much less than the velocity of light: v ≪ c. But this theory is manifestly incorrect when the velocity is comparable with c, especially when v = c. To describe motion with arbitrary velocity, up to that of light, we have to turn to Einstein's special theory of relativity, i.e., relativistic mechanics. Newton's non-relativistic mechanics is but a particular (although very important) limiting case of Einstein's relativistic mechanics…

The following sections are included:

• Two fundamental equations

• E = mc² historical artifact

• Einstein's papers of 1905 and 1906

• ‘Gravitational mass’

• E = mc² as on element of mass culture

• References

I am disturbed by the harm that Lev Okun's earnest tirade (June 1989, page 31) against the use of the concept of relativistic mass (“It is our duty … to stop this process”) might do to the teaching of relativity. It might suggest to some who have not thought these matters through that there are unresolved logical difficulties in elementary relativity or that if they use the quantity m = γm₀ they commit some physical blunder, whereas in fact this entire ado is about terminology. There are perhaps 40% of us who find it useful ocassionally to write m for E/c² and 60% who don't. But why the latter should try to coerce the former beats me…

Present-day ideas concerning the relationship between mass and energy are presented. The history of the origin of archaic terms and concepts that are widely used in the literature in discussing the problem of mass and energy is related, and arguments are presented for the necessity of abandoning these archaic terms and concepts.

A natural system of fundamental physical units c, ħ, and m_P is discussed, where c is the velocity of light, ħ is Planck's constant, and m_P is the Planck mass, which is related to the Newtonian gravitational constant by the equation . In a natural system of units; such questions as: “How does the anthropic nature of the physical universe arise? Is it unique, or does an infinite set of universes exist?” and “Are the fundamentals of the physical universe knowable and what is the strategy for knowing them?” become particularly urgent.

The subject of my talk was chosen by Professor Zichichi and the title was formulated by him. I have never given such historical talks before: about four hundred years of historical development in some field. Therefore I will stick to physics. My talk will consist of ten parts:

• Introduction

• The mass of a particle

• The mass in XVI-XVII centuries

• The mass in XVIII-XIX centuries

• The mass of a system of free particles

• Interactions and binding energy

• Quarks and gluons confined in hadrcns

• The pattern of masses of elementary particles

• Scalars and the nature of mass

• Conclusions.

The origin and the early history of several ideas concerning possible properties of the vacuum are briefly sketched. The topics include the CP properties of the vacuum, the possible existence of a mirror world, phase transitions in the early universe, vacuum domain walls, and the decay of the false vacuum.

Special Relativity is a classical and simple theory. In spite of this, the pedagogical literature on it is still not free from confusion. This confusion is caused by the frequent usage of archaic notions, notations and equations, which have nothing to do with the essence of the theory, only with the history of its development. The aim of this short comment is to explain the basic notions of Special Relativity and to help the beginner to recognize and avoid the confusing notations and equations.

Please refer to full text.

A brief review is given of the state-of-the-art in elementary particle physics based on the talk of the same title given on January 22, 1998, at the seminar marking the 90th anniversary of the birth of L D Landau. (The seminar was hosted by the P L Kapitza Institute for Physical Problems in cooperation with the L D Landau Institute of Theoretical Physics).

This paper is concerned with the classical phenomenon of gravitational red shift, the decrease in the measured frequency of a photon moving away from a gravitating body (e.g., the Earth). Of the two current interpretations, one is that at higher altitudes the frequency-measuring clocks (atoms or atomic nuclei) run faster, i.e. their characteristic frequencies are higher, while the photon frequency in a static gravitational field is independent of the altitude and so the photon only reddens relative to the clocks. The other approach is that the photon reddens because it loses the energy when overcoming the attraction of the gravitational field. This view, which is especially widespread in popular science literature, ascribes such notions as a ‘gravitational mass’ and ‘potential energy’ to the photon. Unfortunately, also scientific papers and serious books on the general theory of relativity often employ the second interpretation as a ‘graphic’ illustration of mathematically immaculate results. We show here that this approach is misleading and only serves to create confusion in a simple subject.

The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in two ways: On the one hand, the phenomenon is explained through the behavior of clocks which run faster the higher they are located in the potential, whereas the energy and frequency of the propagating photon do not change with height. The light thus appears to be redshifted relative to the frequency of the clock. On the other hand, the phenomenon is alternatively discussed (even in some authoritative texts) in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body. This second approach operates with notions such as the “gravitational mass” or the “potential energy” of a photon and we assert that it is misleading. We do not claim to present any original ideas or to give a comprehensive review of the subject, our goal being essentially a pedagogical one.

The influence of static gravitational field on frequency, wavelength and velocity of photons and on the energy levels of atoms and nuclei is considered in the most elementary way. The interconnection between these phenomena is stressed.

In order to directly demonstrate that in static gravitational field the rate of clocks increases with their distance from the source, a simple thought experiment is proposed.

The famous debate between Einstein and Bohr on the (in)consistency of quantum mechanics was described in detail by Bohr in his essay of 1949. The present article comments not on the main subject of the debate but only on the terminology that is relevant to the notions of the theory of relativity and which was used by the participants. In particular, their statement on the equivalence of mass and energy should not be taken literally. In fact, the rest energy is meant here. The authority of the two great physicists should not be misused to preserve the confusing terminology.

This paper consists of three separate articles on the number of fundamental dimensionful constants in physics. We started our debate in summer 1992 on the terrace of the famous CERN cafeteria. In the summer of 2001 we returned to the subject to find that our views still diverged and decided to explain our current positions. LBO develops the traditional approach with three constants, GV argues in favor of at most two (within superstring theory), while MJD advocates zero.

The following sections are included:

• MASS IN SPECIAL RELATIVITY

• ATOMS IN STATIC GRAVITY

• PHOTONS IN STATIC GRAVITY

• MISLEADING TERMINOLOGY

• UNSOLVED PROBLEMS OF m

• ACKNOWLEDGEMENTS

• REFERENCES

The following sections are included:

• Introduction

• Pomeranchuk on vacuum

• Landau on parity, P, and combined parity, CP

• Search and discovery of

• “Mirror world”

• Zeldovich and cosmological term

• QCD vacuum condensates

• Sakharov and baryonic asymmetry of the universe, BAU

• Kirzhnits and phase transitions

• Vacuum domain walls

• Monopoles, strings, instantons, and sphalerons

• False vacuum

• Inflation

• Brane and bulk

• References

We consider a few thought experiments of radial motion of massive particles in the gravitational fields outside and inside various celestial bodies: Earth, Sun, black hole. All other interactions except gravity are disregarded. For the outside motion there exists a critical value of coordinate velocity particles with v < v_c are accelerated by the field like Newtonian apples, and particles with v > v_c are decelerated like photons. Particles moving inside a body with constant density have no critical velocity; they are always accelerated. We consider also the motion of a ball inside a tower, when it is thrown from the top (bottom) of the tower and after elastically bouncing at the bottom (top) comes back to the original point. The total time of flight is the same in these two cases if the initial proper velocity υ₀ is equal to .

The problem of fundamental units is discussed in the context of achievements of both theoretical physics and modern metrology. On one hand, due to the fascinating accuracy of atomic clocks, the traditional macroscopic standards of metrology (second, metre, kilogram) are giving way to standards based on fundamental units of nature: velocity of light c and quantum of action h. On the other hand, the poor precision of the gravitational constant G, which is widely believed to define the “cube of theories” and the units of the future “theory of everything”, does not allow to use G as a fundamental dimensional constant in metrology. The electromagnetic units in SI are actually based on concepts of prerelativistic classical electrodynamics such as ether, electric permittivity and magnetic permeability of vacuum. Concluding remarks are devoted to terminological confusion which accompanies the progress in basic physics and metrology.

The “famous formula” E = mc² and the concept of “relativistic mass” increasing with velocity, which follows from it, are historical artifacts, contradicting the basic symmetry of Einstein's Special Relativity, the symmetry of 4-dimensional spacetime. The relation discovered by Einstein is not E = mc², but E₀ = mc², where E₀ is the energy of a free body at rest introduced by Einstein in 1905. The source of the longevity of the “famous formula” is the irresponsible attitude of relativity theory experts to the task of explaining it to the non-experts.

The notion of “relativistic mass” presents a kind of pedagogical virus which very effectively infects new generations of students and professors and shows no signs of decline. Moreover in the Year of Physics it threatens to produce a real pandemia.

Various facets of the concept of mass are discussed. The masses of elementary particles and the search for higgs. The masses of hadrons. The pedagogical virus of relativistic mass.

The talk consists of three parts. “History” briefly describes the emergence and evolution of the concept of photon during the first two decades of the 20th century. “Mass” gives a short review of the literature on the upper limit of the photon's mass. “Charge” is a critical discussion of the existing interpretation of searches for photon charge. Schemes, in which all photons are charged, are grossly inconsistent. A model with three kinds of photons (positive, negative and neutral) seems at first sight to be more consistent, but turns out to have its own serious problems.

The “famous formula” E = mc² and the concept of “relativistic mass” increasing with velocity, which follows from it, are historical artifacts, contradicting the basic symmetry of Einstein's Special Relativity. The relation discovered by Einstein is not E = mc², but E₀ = mc², where E₀ is the energy of a free body at rest. The source of the longevity of the “famous formula” is irresponsible attitude of relativity theory experts to the task of explaining it to the non-experts.

This review describes the history of the discovery of the violation of the spatial parity P, the charge conjugation parity C, and the combined parity CP. The hypothesis of the existence of mirror particles was intended by its authors to restore the symmetry between left and right. The review presents the emergence and evolution of the concepts of ‘mirror particles’ and ‘mirror matter’ and can serve as a concise travel guide to ‘mirror-land.’ An important part of the review is the list of about 200 references with their titles.

The evolution of the Sakata model is described on the basis of personal recollections, proceedings of international conferences on high energy physics and some journal articles.

The talk stresses the importance of the concept of rest energy E₀ and explains how to use it in various situations.

The article traces the way Einstein formulated the relation between energy and mass in his work from 1905 to 1955. Einstein emphasized quite often that the mass m of a body is equivalent to its rest energy E₀. At the same time, he frequently resorted to the less clear-cut statement of the equivalence of energy and mass. As a result, Einstein's formula E₀ = mc² still remains much less known than its popular form, E = mc², in which E is the total energy equal to the sum of the rest energy and the kinetic energy of a freely moving body. One of the consequences of this is the widespread fallacy that the mass of a body increases when its velocity increases and even that this is an experimental fact. As wrote the playwright A N Ostrovsky “Something must exist for people, something so austere, so lofty, so sacrosanct that it would make profaning it unthinkable.”

It is shown that the most important effects of special and general theory of relativity can be understood in a simple and straightforward way. The system of units in which the speed of light c is the unit of velocity allows to cast all formulas in a very simple form.The Pythagorean theorem graphically relates energy, momentum and mass. The paper is addressed to those who teach and popularize the theory of relativity

The following sections are included:

• Name Index