Volume 22: Pages 559-563, 2009

Basic assumptions and black holes

Sanford Aranoff ¹

¹Department of Mathematics and Department of Science, Rider University, Lawrenceville, New Jersey 08648, USA

Science develops by initially proposing hypotheses to explain phenomena, then creating a formal consistent mathematical framework, verified by experiment and observation, called a scientific theory. This theory must exclude solutions that violate basic physical principles or yield inconsistent mathematics. New observations may challenge the theory, but do not necessarily invalidate it as a basic mathematical inconsistency would. Science continues by developing hypotheses to explain what the current theory cannot. The paper discusses objects falling into black holes using general relativity as examples of both valid theory and developing hypotheses. The existence (according to most physicists) of a black hole is part of a valid theory. The crossing of the event horizon of the black hole is an extension of the theory, but is not part of the theory, for the mathematics is not consistent, and the results violate basic principles. Another example of an invalid extension of a theory is given from special relativity. Since this theory is easier to understand, it helps clarify the point. One needs to be clear what is part of the theory, and what is not part of the theory. The statement “an observer crossing the event horizon and losing all contact with the rest of the universe is part of physics” is a counterexample to the proper understanding of theories. Statements incorrectly based on theories may be obstacles to the advance of science. One needs to understand the philosophical underpinnings of science, and how one can tease out the hidden assumptions of a theory.

Keywords: Mathematical Assumptions and Scientific Theories, Special and General Relativity, Black Holes, Quantum Mechanics

Received: June 13, 2009; Accepted: September 10, 2009; Published Online: November 10, 2009