DCP Foundation #2: How to Replace Continuum Physics with a Discontinuum Physics Based on Einstein's 1954-55 Beliefs

DCP Foundation #2: How to Replace Continuum Physics with a Discontinuum Physics Based on Einstein's 1954-55 Beliefs © 2026 by Emory Taylor and Rajan Iyer is licensed under Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-nd/4.0/.

Einstein's 1954-55 beliefs were expressed by Einstein (1) in his three 1954 letters, and (2) his 1955 addition of section "D" to "Appendix II" of his posthumously published 1956 fifth edition of his book "The Meaning of Relativity" [1,2]. These were reprinted in "DCP Foundation #1: Einstein Said Relativity Theory is Not Fundamental" [3].

From Einstein's first 1954 letter, the situation is that relativity theory and what Einstein was referring to as "contemporary physics" are not fundamental and must be replaced [1,3].

From the first paragraph of Einstein's second 1954 letter, (1) the physics that describes reality must be either a continuum based theory or a discontinuum based physics ("there is here no compromise"), and (2) the discontinuum theory does not include differential math and space and time, at least not in a fundamental way, and (3) what occurs are only "numbers and number-fields and rules for the formation of such on the basis of algebraic rules with exclusion of limiting processes" [1,3]. It must be pointed out that, in the previous sentence, (3) is only a speculation by Einstein; It is possible a discontinuum physics can be developed using (2) and excluding (3).

From the second paragraph of Einstein's second 1954 letter, Einstein states what he believes to be the problem with continuum physics (meaning with relativity theory and "contemporary physics"): The material point is the problem because it is a discontinuous element and should never have been used in a continuum physics [1,3]. Knowing the problem is the material point, (1) it logically follows that the material point must falsify relativity theory from being a fundamental theory, and (2) it is necessary to find the falsification within relativity theory. This means the remainder of Einstein's second 1954 letter can be ignored because (1) it addresses aspects of the material point, but a decision to investigate the material point as a problem causing the falsification of relativity theory has already been determined to be necessary, and (2) it addresses the algebraic theory Einstein was considering, but it has already been pointed out in the previous paragraph that the algebraic theory is a speculation and it is possible to develop a discontinuum physics that does not include differential math and space and time, at least not in a fundamental way.

From the first sentence of Einstein's third 1954 letter, it is logical to consider the "atomistic character of nature" to be the problem that the use of the material point in a continuum physics cannot resolve [1,3]. This means that, while investigating how the material point falsifies relativity theory from within relativity theory, the "atomistic character of nature" must play a role, which means the falsification of relativity theory from being fundamental will involve the material point and the atomistic character of nature. Knowing this should make it easier to locate the flaw within relativity theory that falsifies relativity theory from being a fundamental theory. The second sentence (of Einstein's third 1954 letter ) is just a restatement of discarding (not using) the continuum concept and space and time [1,3]. In the third and final sentence, Einstein states that he does not know what concepts to use as elementary (aka fundamental) concepts for the theory to replace the continuum-based physics [1,3]. Logically, he means other than the discontinuum concept, which essentially means Einstein did not know what to us as the replacements for space and time, which, because Einstein used spacetime in relativity theory, means Einstein does not know what to use as the replacement for spacetime [1,3].

From Einstein's 1955 addition of section "D" to “Appendix II” in the posthumously published 1956 fifth edition of Einstein's book "The Meaning of Relativity", Einstein states:
"... From the quantum phenomena it appears to follow with certainty that a finite system of finite energy can be completely described by a finite set of numbers (quantum number). This does not seem to be in accord with a continuum theory, and must lead to an attempt to find a purely algebraic theory for the description of reality. But nobody knows how to obtain the basis of such a theory" [2].

The decision has already been made not to use an algebraic theory but to instead develop a discontinuum theory that does not include differential math and space and time, at least not in a fundamental way. But in Einstein's 1955 addition of section "D" to “Appendix II” in the posthumously published 1956 fifth edition of Einstein's book "The Meaning of Relativity", Einstein spoke of "finite energy", meaning Einstein was thinking of the replacement for relativity theory in terms of energy [2]. This means the development of a discontinuum theory that does not include differential math and space and time, at least not in a fundamental way, will involve a replacement for spacetime that is thought of in terms of energy.

In the above information, two conclusions have been reached: (1) it is necessary to search through relativity theory to find in it a flaw that used the material point and the atomistic character of nature to falsify relativity theory, which means falsifying relativity theory from being fundamental from within relativity theory, and (2) developing a discontinuum theory that does not include differential math and space and time, at least not in a fundamental way, will involve a replacement for spacetime that is thought of in terms of energy.

It is important to understand what Einstein believed prior to his three 1954 letters and his 1955 addition of section "D" to “Appendix II” in the posthumously published 1956 fifth edition of his book "The Meaning of Relativity." He believed:
(1) the observer independent, external physical reality (also called ONX physical reality) exists (aka is real) and is fundamental [4,5,6];
(2) time dilation and length contraction are real, not apparent [4,5];
(3) spacetime exists (aka is real) [4,5];
(4) gravity is a curvature of spacetime [4,6].
Special relativity (SR) and general relativity (GR) describe physical reality (aka ONX physical reality) [4-6]. This means from the above list (1) - (3) are from SR and (1) and (4) are from GR.

It is important to understand what Einstein believed after his three 1954 letters and his 1955 addition of section "D" to “Appendix II” in the posthumously published 1956 fifth edition of his book "The Meaning of Relativity." He believed:
(1) physical reality (aka ONX physical reality) is not fundamental and must be replaced [7,8];
(2) SR is not fundamental and must be replaced [1,7];
(3) time dilation are and length are apparent, not real [1,7];
(4) something is wrong with the system of measure in SR and it must be fixed [1,7];
(5) spacetime does not exist and must be replaced [1,7];
(6) GR is not fundamental and must be replaced [1,8];
(7) replacing gravity as a curvature of spacetime with gravity as a curvature of the energy form of the replacement for spacetime [1,8].
SR and GR describe physical reality (aka ONX physical reality) [4-6]. This means from the above list (1) - (5) are from SR and (1) and (6-7) are from GR.

For the discontinuum physics that replaces continuum physics, the following must be accomplished:
(1) falsifying relativity theory from being fundamental from within relativity theory, which means searching through relativity theory to find in it a flaw that used the material point and the atomistic character of nature to falsify relativity theory;
(2) developing a discontinuum theory that does not include differential math and space and time, at least not in a fundamental way, which means spacetime is not included and its replacement should be thought of in terms of energy;
(3) replacing ONX physical reality;
(4) replacing SR;
(5) making time dilation are and length apparent, not real;
(6) fixing the system of measure used in SR;
(7) replacing spacetime, with the replacement thought of in terms of energy;
(8) replacing GR;
(9) replacing gravity as a curvature of spacetime with gravity as a curvature of the energy form of the replacement for spacetime.

References
[1] J. Stachel, Einstein from ‘B’ to ‘Z’ (Birkhauser Boston, c/o Springer-Verlag New York, Inc., NY, 2002), pp. 141-154.
[2] A. Einstein, “The Meaning of Relativity” (Princeton University Press, Princeton, NJ, USA, 2005), pp. 165-166.
Free copy at https://lectures.princeton.edu/sites/g/files/toruqf296/files/2020- 08/_Albert_Einstein__Brian_Greene__The_meaning_of_rel_BookZZ.org_.pdf. Accessed 21 Oct. 2026.
[3] Taylor, Emory, and Rajan Iyer. "DCP Foundation #1: Einstein Said Relativity Theory is Not Fundamental." Discontinuum Physics, 2026, https://discontinuumphysics.com/sp/dcp-foundation-1/.
[4] A. Einstein, Ann. Phys. 17, 891 (1905).
[5] A. Einstein, Relativity: The Special and General Theory (Crown Publishers, Inc., New York, 1961), pp. 1-57, 59-104, and 113-114.
[6] Einstein, Albert. "The Field Equations of Gravitation." Translated from "Die Feldgleichungen der Gravitation," Prussian Academy of Sciences Proceedings, 1915, pp. 844–47. Free English translation at: https://en.wikisource.org/wiki/Translation:The_Field_Equations_of_Gravitation.
http://reprints.gravitywaves.com/Gravitation/Einstein-1915_TheFieldEquationsOfGravitation_EFEs_Wikisource.pdf.
[7] E. Taylor, "Falsification of Einstein’s relativity" Physics Essays 34, 4 (2021). http://dx.doi.org/10.4006/0836-1398-34.4.578. Read it for free at: https://discontinuumphysics.com/sp/published-paper-1/.
[8] E. Taylor and R. Iyer, "Rethinking special relativity, spacetime, and proposing a discontinuum" Physics Essays 35, 1 (2022). Pages 55-60. http://dx.doi.org/10.4006/0836-1398-35.1.55. Read it for free at: https://discontinuumphysics.com/sp/published-papers-clone-2/.