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to explain the Uranium atom using Schrodinger’s theory would require 276 dimensions, while including time we have only four
J.J. Thomson originally hypothesised that the mass of the positive charge was equally spread through the atom and that electrons were embedded in its surface. Hence the ‘Plum Pudding ‘ model. Then Rutherford proved through experiment that the mass of the atom was concentrated in its nucleus and that electrons spun in circular orbits around it. This was the ‘planetary’ model. The planetary model did not work because it was demonstrated that if classical physics were applied to the problem the electron would rapidly radiate away its energy and plunge into the nucleus in approximately 1 x 10^^-10 seconds. Thus it was thought that classical physics could not apply at the nuclear and atomic level. Neils Bohr then postulated that, yes the mass of the atom was concentrated in its nucleus but that electrons could orbit around the nucleus only in certain allowed orbits. While they were in any of these allowed orbits the electrons never radiated energy and hence did not lose energy and therefore did not spiral into the nucleus. This is the picture of the atom that still holds good today, although it has to be said that the theory had to be propped up first by Schrodinger’s theory of standing waves and then later by Louis De Broglie’s theory of matter waves.
So far so good the only problem is that no-one including De Broglie could ever explain what matter waves were or what was waving and that Schrodinger’s standing wave theory when applied to more complicated atoms resulted in huge numbers of dimensions being needed.
Quoteto explain the Uranium atom using Schrodinger’s theory would require 276 dimensions, while including time we have only fourDo not confuse mathematical dimensions with dimensions of space and time.
I missed where he said that. I'm assuming that McQueen is speaking of 276 nucleons? If so then he was confusing dimensions with degrees of freedom. That is incorrect. He's confusing dimensions with degrees of freedom. Each particle moves in a three dimensional space. That means it requires 3 coordinates to determine how many numbers to takes to determine where that particular particle is found. However there are 276 nucleons which means there are 276 degrees of freedom.See http://en.wikipedia.org/wiki/Degrees_of_freedom_(mechanics)
FUNDAMENTAL NOTIONS• The most basic conception of dimension is as a degree of freedom.
The concept of dimension is, in its most basic and intuitive form, the concept of measuring certain aspects of an object independently from all of its other aspects. This idea of dimension is also known as "degrees of freedom."
In physics and mathematics, the dimension of a space or object is informally defined as the minimum number of coordinates needed to specify any point within it. Thus a line has a dimension of one because only one coordinate is needed to specify a point on it (for example, the point at 5 on a number line). A surface such as a plane or the surface of a cylinder or sphere has a dimension of two because two coordinates are needed to specify a point on it (for example, to locate a point on the surface of a sphere you need both its latitude and its longitude). The inside of a cube, a cylinder or a sphere is three-dimensional because three coordinates are needed to locate a point within these spaces.
In mechanics, the degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its configuration. It is the number of parameters that determine the state of a physical system and is important to the analysis of systems of bodies in mechanical engineering, aeronautical engineering, robotics, and structural engineering.
Do you understand the difference now? In the first one it speaks of an "object" but they mean geometric object like the surface of a sphere, a sphere itself (points inside the sphere plus points on the surface), a cone, a worldline of baseball in spacetime is one dimensional because only one number is needed to parameterize it.
What you have posted is very useful, although it is reasonable to assume that the position of an electron in an atom must in some way relate to a dimension ..
and indeed according to Schrodinger’s wave equation the electron disperses until it is present everywhere, in fact to all purposes it could be said to exist in a disembodied state !
The lamb shift and the possibility of ‘virtual’ photon exchange between the nucleus and the electron obviate the need for such ‘wave packet’ solutions which lead to the disembodied view of light advocated by quantum mechanics.
Why can’t a photon be simultaneously both a wave and a particle?
Q. Why can’t a photon be simultaneously both a wave and a particle?Ans. Because it's never observed to be that way and in physics we only talk about what is observed.
With all due respect to you and the obvious amount of learning you have with regard to Quantum mechanics and its working, it seems to me that we are talking at cross purposes. Quote Q. Why can’t a photon be simultaneously both a wave and a particle?Ans. Because it's never observed to be that way and in physics we only talk about what is observed. What do you mean when you say that the photon has never been seen to be simultaneously a wave and particle ?
That's not something that can easily be explained in a few sentences. It'd be best if you read the Feynman Lectures V-III on this. You can download it at http://bookzz.org/book/850372/761029Basically the particle aspect can be seen when a single particle is localized. The wave aspect is seen when a large number of particles shows an interference patter. You can't have a large number of particles and a single particle in all but the oddest case such as an ensemble of a large number of single particle experiments which show interference. But even so that's when you compare them. A single particle can be a large number of particles simultaneously.