A definition of time by relation of energy and mass

Goldmann et al, Graphical Abstract

The determination of an exact status that time occupies within the framework of basic physical parameters is a key-challenge of natural science. Here we describe an approach of defining time by the relation of energy and mass on the basis of Einstein’s principle of equivalence E=mc². The equation contains the term time as a basic parameter in the natural constant c. A transposition of the formula leads to the fact, that time can be considered as a factor dependent on the relation of energy and mass. Here we conclude that time is only existent at a certain place, if energy and mass have a relation of neither zero nor infinite. Therefore time is con-tinuously generated in every place due to the relation of energy and mass. The exposed introduction of a physical concept of time in the framework of fundamental parameters correlates with phenomena observable in nature.

The development of a valid basic definition of time has been the subject of various disciplines of research throughout the whole history of science. As a part of these investigations philosophers from Aristotle to St. Augustine, Kant, Husserl and Heidegger have argued the difficult question of its true nature and origin thereby revealing the significance and profound complexity inherent in this problem (Sklar 1998, 413–417). Nevertheless, time still remains mysterious to a high degree in all fields of science. yet is not explained in its proper origination, although it is considered to be endowed with properties of fundamental nature. Up to now the open and continuing interdisciplinary debate (Fraser 2001) undoubtedly reflects the delicate task to understanding its enigmatic structure.

Time indeed is influencing a large number of natural laws and the scientific pursuit of a physical definition has found its pioneers in the aim of setting it into a context of elemental principles in the persons of Newton and Einstein. Newton´s absolute and universal concept of time, criticised by Poincaré (1898) and Mach (1901) was superseded by Einstein´s theory of relativity, revealing, that every place possesses its specific natural time scale due to the influence of motion and gravity.

To date the missing of a suitable definition marked a priori by the laws of nature, in the sense of explaining a possible physical essence of time. focuses the physical interest instead upon its measurement (Feynman 1963, 5–2). An approximation towards an expounding universal definition however has to include the fact that time cannot be conceived and fixed exclusively as a measurable physical quantity and take into consideration the exact status time occupies within the framework of fundamental physical laws. The development of a coherent and comprehensive explanation might in consequence also involve the necessity to conclusively prescribe causality between time and other physical parameters in the sense of detecting their exact sequence of formation. Such a refined concept would serve for a more profound understanding of even such physical phenomena, which are as yet not entirely explained by consulting current interpretations.

The definition of time as a fundamental unit has significant historical roots and the adjustment as a SI base unit has been performed with a high degree of reflection.

Since 1967, a valid definition is achieved by the microwave–frequency resonance (9.2 gigahertz) of the caesium 133 atom. For improved accuracy, in 1997 it has been added that this definition refers to a caesium atom in its ground state at a temperature of 0 K (Bureau International des Poids et Mesures 1998). This current adjustment, valid under the preconditions of comparatively constant relations of energy and mass as present on earth is of conventional nature. Based upon local experiments, it does not take into account the relativistic effects time is liable to. An extended definition, presup-posing the claim of general applicability should take into account the need to keep its validity when applied to extreme relativi-stic situations.

A definition of time, marked by a relation of energy and mass
With respect to attaining such a significant approach, we find with energy and mass two physical constants that are, following Einstein´s principle of equivalence, directly related to the parameter time in the equation E=mc². According to the theory of general relativity time can be influenced by the relation of energy and mass (Einstein 1916, 769–822), which to a large degree is constant on earth, but can differ to the utmost under cosmic conditions.

The exposure of the following model, developed in order to determine time, depends on the basic assumption of energy and mass to be the fundamental physical parameters, which, in the sense of a further distancing from the Newtonian concept of energy and time, has to be placed in front. Yet the term time, by convention, is physically considered to be a fundamental unit. As the relation of energy and time is naturally given and experimentally proven, energy in consequence has to be defined as a dependent term. However, it has been reported, that time must not necessarily be adopted as a fundamental unit; with its finiteness in the context of basic physical parameters, as becomes apparent within cosmic phenomena (Wheeler 1979, 395–497, 1980, 341–375) at places with extreme relations of energy and mass (Oppenheimer 1939, 455–459; Hawking 1973) reveal the question, which of the para-meters used in Einstein’s equation are fundamental and which of them have to be considered to be dependent.

Einstein´s equation of equivalence (1905, 639–641) describing the relation of energy and mass (Fig. 1) contains the parameter time as clearly expressed in the definition of the speed of light (c) with the term 1s. A conversion of the formula leads to the math ematical definition of time (Fig. 1), which is then defined by the relation of a constant distance and a relation of energy and mass. Starting out from the assumption, that time is a dependent term and energy the fun-damental unit, time, as described in the formula (Fig. 1) is completely dependent on the relation of energy and mass and, only existent if energy and mass have a re-lation which is not zero or infinite. In consequence time has to be regarded as a secondary phenomenon, only emerging in a situation where energy and mass have a relation that is neither zero nor infinite. Therefore it can be considered as the outcome of a formative process, which, only in the presence of both — energy and mass as its essential ‘creators’ — is set in motion. The respective underlying formative process is the big bang (Fig. 2).

Figure 1: Conversion of Einstein’s equation of equivalence.

The theoretical approach appears to correlate with events observable, supposed or predicted in nature (Fig. 2): a black hole and the big crunch, all composed of infinite mass and a minimum amount of energy as well as a light beam in free space, consisting of a maximum share of energy and nearly no mass, are phenomena, where time reaches the boundary of existence (Wheeler 1980, 341–375; Einstein 1905, 891–921). Only under constant relations of energy and mass, like on earth, do we get the impression that time is a primary and constant term which led to the imagination of a time–beam or a time–bar.

Figure 2: Illustration of different situations which influence time, all of which depend on and start with the big bang (1°). A: light beam in free space — nearly no mass but nearly pure energy → nearly no time. B: black whole — pure mass, nearly no energy → nearly no time. C, D, E: different planets with different relations of energy and mass which is not infinite or zero which all display their own time. Only under constant conditions of the relation of free energy and mass, like on earth, time is perceived like a beam or an independent physical term.

The general influence of energy and mass upon time also has been experimentally demonstrated e.g. with atom chronometers on a plane and on ground (Hafele 1972, 166–170). Significantly and according to this model the valid standard of a time interval is based on the transition between two energy–levels of a caesium atom. The dependence of the accuracy of measurement upon the temperature (0 K) of the atom clearly expresses the dependence of time on energy; for im-proved accuracy, the state of the atom is kept at a more or less constant energetic level.

Time, as a central hypothesis of this approach is continuously generated in every place due to the relation of energy and mass. If it is constantly generated as assumed, the big bang is a further necessity in order to initiate this continuous generation by giving birth to the essential relation of energy and mass as well as to distance as the primary phenomena. Space in this context as displayed in the formula (299 792 458 m) is an essential prerequisite for the existence of time. From this angle of view, it appears to be composed of one–dimensional linearities, endowed with a direction, thus giving the impression of space. The ability of these linearities to ‘interact’ thereby lets time happen.

If energy, as we suppose, has to be regarded as a primary element, the aspect of its quantization might be brought more efficiently into concordance with relativistic predictions — a challenge that still turns out to be difficult to accept with the aid of current interpretations.

Our theoretical attempt, permitting the idea of a possible quantized space–time might, from this point of view throw new light on the way of unifying general relativity and quantum theory (Amelino–Camelina 2000, 661–664). The expositions presented here do not cover all aspects and possible consequences of this model. Although it appears to be logically consistent, it will have to be discussed and further verified by experimental studies.

Torsten Goldmann studied biology in Münster and received his PhD from the Faculty of Natural Sciences in 1995. He absolved a two–year post–doc fellowship at the Max Planck Institute of Biochemistry in Martinsried. Since 1997 he is working at the Research Center Borstel, Leibniz Center for Medicine and Biosciences. He received his venia legendi for Experimental Medicine and Molecular Biology from the University Lübeck in 2006. Horst Neitemeier studied humanities in Münster and is working at the Fachklinik Hornheide in Münster.


1. Amelino–Camelia, Giovanni (2000), “Quantum Theory’s last Challenge”, Nature 408: 661– 664.

2. Bureau International des Poids et Mesures (1998), Le Système International d’Unités (SI), The International System of Units (SI), 7th edition. Sèvre, France: Bureau International des Poids et Mesures. http://www.bipm.fr/enus/6_ Publications/si/si–brochure.html

3. Einstein, Albert (1905), “Zur Elektrodynamik bewegter Körper”, Annalen der Physik 17: 891– 921.

4. Einstein, Albert (1905), “Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?”, Annalen der Physik 18: 639–641.

5. Einstein, Albert (1916), “Die Grundlage der allgemeinen Relativitätstheorie”. Annalen der Physik 49: 769–822.

6. Feynman, Richard P.(1963), “Time”, in Richard P. Feynman, Robert B. Leighton and Matthew Sands (eds.), The Feynman Lectures on Physics, Vol. I. Reading, MA: Addison Wesley, Sect. 5–2.

7. Fraser, Julius T., and Marlene P. Soulsby (eds.) (2001), The Study of Time. Time: Perspectives at the Millennium, Vol. 10. Westport: Bergin & Garvey.

8. Hafele, Joe C., and Richard E. Keating (1972), “Around–the–World Atomic Clocks: Predicted Relativistic Time gains”, Science 177: 166–167.

9. Hafele, Joe C., and Richard E. Keating (1972), “Around–the–World Atomic Clocks: Observed Relativistic Time gains”, Science 177: 168–170.

10. Hawking, Stephen W., and George F.S. Ellis (1973), The Large Scale Structure of Space– Time. Cambridge: Cambridge University Press.

11. Mach, Ernst (1901), Die Mechanik in ihrer Entwicklung, 4th edition. Leipzig: F.A. Brockhaus.

12. Oppenheimer, Julius R., and Hartland S. Snyder (1939), “On continued gravitational contraction”, Physical Review 56: 455–459.

13. Poincaré, Henri (1898), “La mésure du temps”, Revue de Métaphysique et de Morale 6: 1–13.

14. Sklar, Lawrence (1998), “Time”, in Edward Craig (ed.), Routledge Encyclopedia of Philosophy, Vol. 9. London: Routledge 413–417.

15. Wheeler, John A. (1979), “Frontiers of time”, in Guiliano Toraldo di Francia (ed.), Problems in the Foundations of Physics. Proceedings of the International School of Physics ‘Enrico Fermi’, Course LXXII. Amsterdam: North–Holland, 395–497.

16. Wheeler, John A. (1980), “Beyond the black hole”, in Harry Woolf (ed.), Some Strangeness in the Proportion: A Centennial Symposium to Celebrate the Achievements of Albert Einstein. Reading: Addison Wesley, 341–375.

Share your thoughts

Leave a Reply

You must be logged in to post a comment.