Here i would like to post the biggest mistake ever made in physics....unfortunately even greatest and most intelligent men make mistakes or simply don,t tak into account things that could have changed the world of physics or advance the science even 50 or 100 years... this was the case of Sir Willian R. Hamilton...(adsbygoogle = window.adsbygoogle || []).push({});

Hamilton an Irish mathematician and Physicist famous by inventing the "Quaternions" and several works in math of physics, could have become a legend among all scientist and mankind, if only he had considered its own hypothesis and formulae beyond consideration...he and not Einstein Dirac and others..could have been the inventor of Relativity and Quantum mechanics...Still surprised?..let,s take a simple review..

RE-DISCOVERING QM AND RELATIVITY:

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One of the interest of Hamilton as a Mathematician..was to prove the relationship between optics (geometric) and Mechanics..(does this not sound familiar to you?..let,s go on) in fact he "proposed" invented the relationship (here,s come the hotstepper)..

[tex] \Psi=e^{iS/a} [/tex] with a------->0 very small quantity (1)

Maxwell and other had discovered the wave equation for electromagnetism...

[tex] \frac{d^{2}\Psi}{dt^{2}}=\nabla^{2}\Psi [/tex]

now if we substitute (1) into Maxwell Wave equation we get..

[tex] E^{2}=H^{2}=p^{2}c^{2} [/tex] (2)

the equation of motion for a photon¡¡¡¡¡¡....for the case V=0 E=H (classical mechanics) of course for low momentum p this does not resemble the typical Hamiltonian of free particle..

[tex] E=p^{2}/2m [/tex] so you must add a term [tex] \alpha [/tex] to this so it satisfy the equation of motion... then (2) becomes..

[tex][tex] E^{2}=H^{2}=p^{2}c^{2}+\alpha [/tex]

¡¡¡the equation of the Hamiltonian for relativity¡¡¡¡....from this you can obtain the Lagrangian the momenta, and so on

The same reasoning can be obtained for the Schroedinguer equation beggining from the Hamilton equation and using (1)

[tex] \frac{dS}{dt}+(1/2m)(\frac{dS}{dx})^{2} [/tex] [tex] (\hbar/i)ln\Psi=S [/tex]

from this two equation above and ignoring terms proportional to a------>0 you can obtain the equation of Quantum mechanics and almost the base to all quantum theory..

this is why i said the BIGGEST mistake on physics..Hamilton could have discovered the most important theories of 20-th century 100 years before..by the way i don,t think you need to be Einstein or planck to realize that a solution to Specific-Heat equation and so on is by setting [tex] E_{n}=n\hbar\omega [/tex]

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# The BIGGEST Mistake of all the times...

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