Schodinger Equation

There is an aspect of mathematical modelling in physics that is especially interesting in the context of this discussion, involving crucial parallels across quantum mechanics, electromagnetism and hydrodynamics. There is a powerful history of using the same mathematics for each, dating from the work of Helmholtz and Tait[i] in the mid nineteenth century and based on the quaternions of Hamilton.

Helmholtz separated out the motion of a fluid into linear motion, rotation and deformation and saw clear analogies between hydrodynamics and electromagnetism. Tait used quaternions to aid the calculations.

These parallels continue to the present day. The work of David Hestenes[ii] on ‘geometric algebra’ is a direct development of the mathematics of Hamilton. He observes that  ‘The Dirac theory has a hidden geometric structure’, and relates this to rotation. This mathematics has been found by Lasenby, Gull and Doran[iii] at Cambridge to provide ready access to problems in general relativity, and by Rowlands[iv] at Liverpool to do the same for quantum mechanics.

Rowlands derives the key equations of quantum physics with elegance and simplicity. Doran suggests that ‘geometric algebra is the natural language in which to formulate a wide range of subjects in modern mathematical physics’, and that ‘the new results obtained include a real approach to relativistic multiparticle quantum mechanics, a new classical model for quantum spin-½ and an approach to gravity based on gauge fields acting in flat spacetime.’

Next: There is no ‘next page’ on this site, but for a more detailed and more rounded picture of modern physics and evidence for a hydrodynamic aethereal background, visit my site at www.physicsroguescience.com

Thanks for reading!

Esau James…   ©2010

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[i] Helmholtz, ‘Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen’; Tait, ‘Quaternion investigations connected with electro-dynamics and magnetism.’

[ii] David Hestenes, Clifford Algebra and the Interpretation of Quantum Mechanics, in J.S.R. Chisholm & A.K. Commons (Eds.), Clifford Algebras and their Applications in Mathematical Physics. Reidel, Dordrecht/Boston (1986), 321-346.

[iii] Chris JL Doran’s Ph.D. dissertation in 1984 is entitled ‘Geometric Algebra and its Application to Mathematical Physics’. Quotes are from the introduction.

[iv] For example: P. Rowlands and J. P. Cullerne, The nilpotent representation of the Dirac algebra, in K. Bowden (ed.), Implications, (2001, Proceedings of XXII ANPA Conference, Cambridge, August 2000), 99-106.

AG Kelly, an Irish researcher, carried out experiments where he rotated parts of the electromagnetic equipment and asked the question ‘Does the field rotate with the magnet?’[i] In 1995, Pelligrini and Swift asked: ‘Maxwell’s equations in a rotating medium: Is there a problem?’[ii]

Re-examining an older result they observe that the ‘field equations for a rotating object are well known and the analysis is straightforward, but the result disagrees with the Wilson experiment’. They conclude ‘that the conventional theory applied in the current way does not describe the results of existing experiments.’ Much the same conclusion is reached by Kelly. Read the rest of this entry »

We might think that, given the well-studied parallels between electromagnetism and hydrodynamic rotation, we could use Maxwell’s equations to tell us the axes of rotation of both electricity and magnetism. Actually we can’t. All that his equations tell us on this question is that the direction of the electric field is always orthogonal to the direction of the magnetic field.

Maxwell’s key paper on vortex rotation was in 1861. In ‘On Physical Lines of Force’, he talks of the vortex axis in two ways, as being along the line of magnetic force and also along the line of the magnetic field. In the vast majority of situations these are not the same. Read the rest of this entry »

There are further theoretical precedents for the suggestion that the underlying reality for matter and hence for light, gravitation and electrodynamics is in a fluidic background.

Hydrodynamic explanations for phenomena covered by twentieth century theory date back well before 1900. Max Jammer states that ‘The earliest hydrodynamic interpretation was proposed by Erwin Madelung’, and that ‘Arthur Korn … had published in 1892 a hydrodynamic theory of gravitation and of electricity which he subsequently extended to optics and spectroscopy.’ [i]

James Clerk Maxwell derived his equations of electromagnetism from physical assumptions about an ethereal (he didn’t use the ‘a’) background, and in his early writings on this, that background was specifically fluidic. Later this became complicated, and this deserves a more detailed treatment, which I shall try to provide at some point. Read the rest of this entry »

Schrödinger’s equation looks like this:

Schrödinger did not create this in the way that Maxwell did with his equations, which were derived from physical analysis of a presumed background ether. This is a brilliant piece of pure mathematical modelling. The key element here is ψ (or psi). It is shown as varying in both space and time (x and t in brackets), and in quantum theory ψ does not have a physical interpretation, although the square of ψ is a measure of the probability of a particle being observed. Read the rest of this entry »

What sustains all the metaphysical nonsense promulgated in the name of quantum theory is its mathematical core, and that is something that is immensely accurate and hugely impressive.

Schrödinger’s formula is commonly described as a ‘wave equation’. Given what has been written about Schrödinger by Jammer and others, it is perhaps surprising to find that he never accepted this description, referring in 1952 to the ‘so-called wave picture’[i], and in 1957 to ‘so-called wave mechanics’[ii]. Read the rest of this entry »

The Schrödinger equation has successfully resisted mechanistic analysis since the time of its inception.

To quote from Max Jammer’s ‘The Philosophy of Quantum Mechanics’, Erwin Schrödinger consistently ‘interpreted quantum theory as a simple classical theory of waves.  In his view, physical reality consists of waves and waves only.  He denied categorically the existence of discrete energy levels and quantum jumps, on the grounds that in wave mechanics the discrete eigenvalues are eigenfrequencies of waves rather than energies’[i]. Read the rest of this entry »