Newtonian universe

One of the misleading statements, used to introduce most accounts of big-bang theory, is that the theory is based on general relativity. It is, more precisely, based on the assumption that the universe expands. The only connection between expanding universe and general relativity occurs in de Sitter s 1917 solution (Section 6.3) in terms of a variable hypersphere, which is characteristic of curved four-dimensional space-time. To define this variability as an expanding universe it is necessary to separate time from space coordinates, an operation which is not allowed in relativity theory. The expansion of such a Newtonian universe is deduced from galactic redshifts, but as stated by Parish (1981) ... 

Pearson,. I.R.A., 1994. Report on University of Wales Institute of Non-Newtonian Fluid Mechanics Mini Symposium on Continuum and Microstructural Modelling in Computational Rheology. /. Non-Newtonian Fluid Mech. 55, 203 -205. 

The next day the Times ot London carried an article headlined Revolution in Science/New Theory of the Universe/Newtonian Ideas Overthrown. Einstein had triumphed over Newton (who, of course, remains a stellar figure in science). The drama of that moment was enhanced by the contrast with the recently concluded World War I, which had caused millions to die, empires to fall, and the future to be uncertain. At that time Einstein emerges, bringing newlaw and order. From that time on the world press made him into an icon, the divine man, of the twentieth centui y. 

Koyre, A. (1965). Newtonian Studies. Chicago University of Chicago Press. 

Yoo, S, S.i Ph.D. Thesis, University of Illinois, Chicago (1974). Heat transfer and friction factors for non-Newtonian fluids in circular tubes. 

The phenomenon of attraction of masses is one of the most amazing features of nature, and it plays a fundamental role in the gravitational method. Everything that we are going to derive is based on the fact that each body attracts other. Clearly this indicates that a body generates a force, and this attraction is observed for extremely small particles, as well as very large ones, like planets. It is a universal phenomenon. At the same time, the Newtonian theory of attraction does not attempt to explain the mechanism of transmission of a force from one body to another. In the 17th century Newton discovered this phenomenon, and, moreover, he was able to describe the role of masses and distance between them that allows us to calculate the force of interaction of two particles. To formulate this law of attraction we suppose that particles occupy elementary volumes AF( ) and AF(p), and their position is characterized by points q and p, respectively, see Fig. 1.1a. It is important to emphasize that dimensions of these volumes are much smaller than the distance Lgp between points q and p. This is the most essential feature of elementary volumes or particles, and it explains why the points q and p can be chosen anywhere inside these bodies. Then, in accordance with Newton s law of attraction the particle around point q acts on the particle around point p with the force d ip) equal to... 

Expanded and revised version of papers and discussion comments originally presented at a conference on Newtonian studies, held at the University of Texas at Austin, Nov. 10-12, 1966. First published Texas Q 10 (3) Autumn 1967... 

C. U. Ikoku, Transient Flow of Non-newtonian, Power Law Fluids, Ph.D. Thesis, Petroleum Engineering Department, Stanford University, (1978). 

To overcome the discrepancies between the predictions of Weber s correlations and subsequent experiments, Mahoney and Sterling 248] modified Weber s theory, and derived a universal equation for the breakup length of laminar Newtonian jets ... 

See Arnold Thackray, Atoms and Powers An Essay on Newtonian Matter Theory and the Development of Chemistry (Cambridge Harvard University Press, 1970), and Robert E. Schofield, Mechanism and Materialism British Natural Philosophy in an Age of Reason (Princeton Princeton University Press, 1970). 

Thackray, Arnold. Atoms and Powers An Essay on Newtonian Matter-Theory and the Development of Chemistry. Cambridge Harvard University Press, 1970. 

In the absence of friction, there are two forces acting on the mass m whose position vector at time t is denoted by the vector r[r] measured relative to the support point, which is the origin of a set of Cartesian axes with three-component k in the upward vertical direction. The first is the force of gravity on the mass, which acts downwards with a value —mgk. The second is the centripetal force, unknown for the moment, which is directed along the support towards the universal point. We denote this force by — Tr t, where Tis a scalar function of time to be found. The Newtonian equations of motion can then be written as... 

Barnes, A.A. (2000) A handbook of elementary rheology. University of Wales, Institute of Non Newtonian Fluid Mechanics Department, pp 199... 

P. H. T. Uhlherr, Hindered Settling in Non-Newtonian Fluids—an Appraisal, CHER 75-1, Dept, of Chemical Engineering, Monash University, Melbourne, Australia, Jan. 1975. 

Accordingly pragmatic individuals have long been interested in the evolution of a universal explanation for fluid behavior of all kinds and the establishment of quantitative relationships with which to correlate and extrapolate the flow curves of all fluids, Newtonian and non-Newtonian alike. Progress toward the former of these two objectives appears to be too limited to warrant presentation at this stage, but recently a method has been proposed (F2, Mil, W4) by means of which the flow behavior of all fluids which are not time dependent may be compared. Two indexes are necessary to accomplish this ... 

The transition from a macroscopic description to the microscopic level is always a complicated mathematical problem (the so-called many-particle problem) having no universal solution. To illustrate this point, we recommend to consider first the motion of a single particle and then the interaction of two particles, etc. The problem is well summarized in the following remark from a book by Mattuck [18] given here in a shortened form. For the Newtonian mechanics of the 18th century the three-body problem was unsolvable. The general theory of relativity and quantum electrodynamics created unsolvable two-body and single-body problems. Finally, for the modem quantum field... 

Bames, H.A. 2000. A Handbook of Elementary Rheology. The University of Wals Institute of Non-Newtonian Fluid Mechanics, Aberysthyth, U.K. 

We notice that Newtonian mechanics adds an additional aspect to the Galilean principle of universal fall the latter is true provided that the ratio mg/mi is constant... 

J.P. Hernandez-Ortiz. Boundary integral equations for viscous flows non-Newtonian behavior and solid inclusions. PhD thesis, University of Wisconsin-Madison, Madison, 2004. 

According to Newtonian physics, the universe and all of the objects in it are simply an extremely complicated collection of masses and charges. This implies that if you knew the state of the universe at any one time (exactly), you could predict (exactly) the future. Of course it is unrealistic to actually do a set of measurements which define the conditions at one time with enough accuracy, but it is in principle possible. Therefore, Newtonian mechanics predicts that the future is perfectly determined by the past. There is no such thing as free will , and you need not worry about studying for the next examination it has already been determined how much you will study, and what you will score on the test ... 

K. Figala and U. Petzold, Alchemy in the Newtonian circle personal acquaintances and the problem of the late phase of Isaac Newton s alchemy , in Renaissance and Revolution, ed. J. V. Field and F. A. J. L. James, Cambridge University Press, Cambridge, 1993, pp. 173-192. 

The last term corresponds to the constant of integration asociated to the total energy of the sphere (and varies as a2). Its value depends on the initial conditions. Furthermore, it expresses a link between the geometry and the material content of the Universe, which cannot be specified in the Newtonian approach we had and can be justified only within the framework of GR. The form of the above equation is independent of the radius a of the sphere and we shall therefore admit that the equation still holds for the quantity li(t), the constant K being then the constant k which is involved in the Robertson-Walker metric element ... 

Although these are the equations that we would right down from first principles in a Newtonian analysis, they are also the small-scale and small-velocity limit of General Relativity. To account for the expansion of the Universe, we change to comoving coordinates, r and peculiar velocity, u, defined from physical coordinates, x, and velocities, v as... 

More so than any other physicist of the twentieth century, Werner Karl Heisenberg challenged our fundamental notions of the surrounding world. It could be argued that as the author of papers on quantum mechanics and the uncertainty principle, he nailed the coffin shut on the deterministic Newtonian version of the universe. Heisenberg replaced precision and accuracy with probabilities and uncertainties, and in so doing, he opened up the world of the subatomic to our understanding. 

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