We numerically solve the functional differential equations (FDEs) of 2-particle electrodynamics, using the full electrodynamic force obtained from the retarded Lienard–Wiechert potentials and the Lorentz force law. In contrast, the usual formulation uses only the Coulomb force (scalar potential), reducing the electrodynamic 2-body problem to a system of ordinary differential equations (ODEs). The ODE formulation is mathematically suspect since FDEs and ODEs are known to be incompatible; however, the Coulomb approximation to the full electrodynamic force has been believed to be (...) adequate for physics. We can now test this long-standing belief by comparing the FDE solution with the ODE solution, in the historically interesting case of the classical hydrogen atom. The solutions differ. A key qualitative difference is that the full force involves a ‘delay’ torque. Our existing code is inadequate to calculate the detailed interaction of the delay torque with radiative damping. However, a symbolic calculation provides conditions under which the delay torque approximately balances (3rd order) radiative damping. Thus, further investigations are required, and it was prematurely concluded that radiative damping makes the classical hydrogen atom unstable. Solutions of FDEs naturally exhibit an infinite spectrum of discrete frequencies. The conclusion is that (a) the Coulomb force is not a valid approximation to the full electrodynamic force, so that (b) the n-body interaction needs to be reformulated in various current contexts such as molecular dynamics. (shrink)

Visit the author's Web site at www.11PicsOfTime.com Time is a mystery that has perplexed humankind since time immemorial. Resolving this mystery is of significance not only to philosophers and physicists but is also a very practical concern. Our perception of time shapes our values and way of life; it also mediates the interaction between science and religion both of which rest fundamentally on assumptions about the nature of time. C K Raju begins with a critical exposition of various time-beliefs, ranging (...) from the earliest times through Augustine, Newton and Einstein to Stephen Hawking and current notions of chaos and time travel. He traces the role of organised religion in subverting time beliefs for its political ends. The book points out how this resulted in a facile dichotomy between 'linear' and 'cyclic' time, thereby inaugurating a confusion which, according to the author, has handicapped Western thought ever since, eventually influencing the content of science itself. Thus, this book daringly asserts that physical theory, traditionally regarded as amoral and objective, has depended on cultural beliefs about time. The author points out that time beliefs are again being manipulated today as the credibility of science is being exploited to promote a picture of time and, hence, a pattern of human behaviour which is convenient to the agenda of globalisation of culture. The linkages between modern theology and this 'brave new physics' are traced against the wider context of the so-called 'clash of civilisations', and the attempts to remake the world order. The conclusions point to the need to de-theologise time. The author challenges Einstein's understanding of relativity theory and suggests that a 'tilt in the arrow of time', or a small tendency towards cyclicity, will help repair the prevalent confusion about time. A 'tilt' also enables a physics that permits both memory and creativity, so that purpose and spontaneous growth of order are returned to human life. The book ends with a vision of Man as Creator, surprising God. Extensive research in physics, the history of science, comparative religions, and sociology lend weight to the important and challenging conclusions reached by the author. Written as a rejoinder to Stephen Hawking's A Brief History of Time, this book goes much further and, unlike any previous book, it gives a critical exposition of various world religions-Buddhism, Christianity, Hinduism, Islam, and Jainism-while exploring their intricate links, through time beliefs, to current physics on the one hand, and to global political and economic trends, on the other. This book will appeal to scholars and laypersons equally. It will fascinate anyone who reads it and will teach its readers to question the unquestionable. (shrink)

Current formal mathematics, being divorced from the empirical, is entirely a social construct, so that mathematical theorems are no more secure than the cultural belief in two-valued logic, incorrectly regarded as universal. Computer technology, by enhancing the ability to calculate, has put pressure on this social construct, since proof-oriented formal mathematics is awkward for computation, while computational mathematics is regarded as epistemo-logically insecure. Historically, a similar epistemological fissure between computational/practical Indian mathematics and formal/spiritual Western mathematics persisted for centuries, during a (...) dialogue of civilizations, when texts on "algorismus" and "infinitesimal" calculus were imported into Europe, enhancing the ability to calculate. It is argued here that this epistemological tension should be resolved by accepting mathematics as empirically based and fallible, and by revising accordingly the mathematics syllabus outlined by Plato. (shrink)

Contrary to the informed consensus, time travel implies spontaneity (as distinct from chance) so that time travel can only be of the second kind.

To eliminate racist prejudices, it is necessary to identify the root cause of racism. American slavery preceded racism, and it was closely associated with genocide. Accordingly, we seek the unique cause of the unique event of genocide + slavery. This was initially justified by religious prejudice, rather than colour prejudice. This religious justification was weakened when many Blacks converted to Christianity, after the trans-Atlantic slave trade. The curse of Kam, using quick visual cues to characterize Blacks as inferior Christians, was (...) inadequate. Hence, the church fell back on an ancient trick of using false history as secular justification for Christian superiority. This trick had resulted in a false history of science during the Crusades when scientific knowledge in translated Arabic texts was indiscriminately attributed to the early Greeks, without evidence. This false history enabled belief in religious superiority to mutate into a secular belief in White superiority. After colonialism, and the Aryan race conjecture, the belief in White superiority further mutated into a belief in Western civilizational superiority, openly propagated today by colonial education. Hence, to eliminate racist prejudice, it is necessary to engage simultaneously with the allied prejudices about Christian/White/Western superiority, based on the same false history of science. (shrink)

Current formal mathematics, being divorced from the empirical, is entirely a social construct, so that mathematical theorems are no more secure than the cultural belief in two-valued logic, incorrectly regarded as universal. Computer technology, by enhancing the ability to calculate, has put pressure on this social construct, since proof-oriented formal mathematics is awkward for computation, while computational mathematics is regarded as epistemo-logically insecure. Historically, a similar epistemological fissure between computational/practical Indian mathematics and formal/spiritual Western mathematics persisted for centuries, during a (...) dialogue of civilizations, when texts on "algorismus" and "infinitesimal" calculus were imported into Europe, enhancing the ability to calculate. It is argued here that this epistemological tension should be resolved by accepting mathematics as empirically based and fallible, and by revising accordingly the mathematics syllabus outlined by Plato. (shrink)

I once wrote to Daya ji about what seemed to me a paradox in contemporary Indian philosophy. It is one thing that Indian philosophers in academia do not engage with science, or even with its history and philosophy. It is quite another thing that they do not engage with ethics. Ethics, after all, is at the core of philosophy. Without an ethical principle one often does not know how to respond to something fundamentally new, such as the bewildering variety of (...) new developments in science and technology that impinge on our daily life. I was disappointed that Indian philosophers remain engaged in the study of Spinoza, Kant, Hegel, and the like, or are immersed in Sanskrit texts—neither of which provide much guidance .. (shrink)

Previously we saw that racist prejudice is supported by false history. The false history of the Greek origins of mathematics is reinforced by a bad philosophy of mathematics. There is no evidence for the existence of Euclid. The “Euclid” book does not contain a single axiomatic proof, as was exposed over a century ago. Such was never the intention of the actual author. The book was brazenly reinterpreted, since axiomatic proof was a church political requirement, and used in church rational (...) theology adopted during the Crusades, as a counter to Islamic rational theology. Deductive proofs are MORE fallible than inductive or empirical proofs. Even a validly proved mathematical theorem, such as the “Pythagorean” theorem, is invalid knowledge in the real world. There is no concept of approximate truth in formal mathematics. Nevertheless, the myth of “superior” axiomatic proofs in the “Euclid” book continues to be reiterated by Western historians, and colonial education teaches axiomatic mathematics. Actually, superior practical value comes from the two “Pythagorean” calculations well known toIndian/Egyptian tradition, but unknown to Greeks. The advantage of related decolonized courses in mathematics has been pedagogically demonstrated. But understanding and political will are needed to change colonial/church education. (shrink)

Experiments with the simple pendulum are easy, but its motion is nevertheless confounded with simple harmonic motion. However, refined theoretical models of the pendulum can, today, be easily taught using software like CALCODE. Similarly, the cycloidal pendulum is isochronous only in simplified theory. But what are theoretically equal intervals of time? Newton accepted Barrow’s even tenor hypothesis, but conceded that ‘equal motions’ did not exist – the refutability of Newtonian physics is independent of time measurement. However, time measurement was the (...) key difficulty in reconciling Newtonian physics with electrodynamics. On Poincaré’s criterion of convenience, equal intervals of time ought be so defined as to make the enunciation of physics simple. Hence he postulated constancy of the speed of light. (The Michelson–Morley experiment was not critical.) The theory of relativity followed. But does there exist a proper clock? (shrink)