]> Quantum Mechanics - Double Slit Experiment

Quantum Mechanics states unambiguously

That

Particles can not exist in two places at once

Kevin Aylward B.Sc.


Contents

Overview

I felt somewhat compelled to write this little ditty due to my somewhat irritating frustration of the prevalence of so much misunderstanding and nonsense associated with Quantum Mechanics.

It is quite clear that, although there are innumerable higher/better qualified Quantum Mechanics than yours truly, many of them simply fail to understand that their waffles, which are actually classical descriptions, are trivially contradictory to Quantum Mechanics.

I am by no means the only one to notice this somewhat stunning state of affairs. For example, Lubo š MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcLbyaqaaaaG+aaaWdbiaa=fwaaaa@388B@ Motl presents extremely clear technical explanations as to why/how Quantum Mechanics is systematically misunderstood. Although one might argue that that his particular presentation style is problematic.  

The fundamental issue is the failure to understand that a quantum state vector such as |X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwaaGaay5bSlaawQYiaaaa@3917@  does not refer to a measurement of position X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwaaaa@3681@ ,  but only to the probability of measuring a position,  P(X) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacIcacaWGybGaaiykaaaa@38AF@ .

Explanations invariably confuse the two, and make arguments about the state vector as if it was identically equivalent to discussing the actual position of an object, instead of what it actually is, to wit, only a description of  the probability of  obtaining a position of an object.   


The Problem

A BBC2 episode of Horizon “What Universe Are We In” 2015, illustrates the problem. Professor Seth Lloyd PhD., in explaining the double slit experiment produces the usual standard twaddle “the electron went through both slits at once”. The notable Professor Lawrence Krauss PhD also advocates this view in more than one YouTube posted debate.

Unfortunately, such a statement is indisputable false, according to standard Quantum Mechanics. The fundamental issue is that there is a general refusal to accept that the universe is subject to Quantum Mechanics, not Classical Mechanics. It is a “new” result or axiom that stands on its own and can not, in principle, be “explained” by any type of classical reasoning. For example, …well if the particle did this, to account for that… it must do this…  

If this classical type of argument is applied to the double slit experiment, the result is a result that contradicts the axioms of Quantum Mechanics. The basic mathematics of Quantum Mechanics is settled, irrespective of any ad-hoc metaphysical interpretations to the mathematics. Quantum Mechanics states that the result of any measurement, i.e. a true physical fact, is that a measurement can only result in a single eigenvalue. Applying the rules of Quantum Mechanics, unequivocally states that the probability of a particle being measured, i.e. a true physical fact, to have, say, both spin up and spin down simultaneously is zero (see appendix). This means, absolutely, that if Quantum Mechanics is correct, a particle can not be in two locations at the same time. Period.  

This is so simple and obvious, that I would guess that most would be going, wow…if it is so trivial under the standard rules of Quantum Mechanics, that two at once is a no no, why do so many “experts” tout all this metaphysical claptrap? One can only conjecture…

So, rather than the typical waffle of  “…this physical explanation of the two slit experiment proves that a particle can be in two places at once” the argument, essentially, is an argument that proves that  classical mechanics is false. Quantum Mechanics gives the correct answers, Classical Mechanics does not. It’s that simple.

I would refer the reader to Lubo š MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcLbyaqaaaaG+aaaWdbiaa=fwaaaa@388B@ Motl for the detailed mathematics, a summary of which is in the appendix of this paper.


The Roots To Confusion

One of the most common sources of misunderstandings is the widespread inability to understand what the symbols of Quantum Mechanics equations actually mean, and how to manipulate those symbols. For example, consider Boolean algebra.

The Boolean equation:

y=A+B where A=1 and B=1 results in y=1 not y=2 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWG5bGaeyypa0JaamyqaiabgUcaRiaadkeaaeaacaqG3bGaaeiAaiaabwgacaqGYbGaaeyzaiaabccacaWGbbGaeyypa0JaaGymaiaabccacaqGHbGaaeOBaiaabsgacaqGGaGaamOqaiabg2da9iaaigdacaqGGaGaaeOCaiaabwgacaqGZbGaaeyDaiaabYgacaqG0bGaae4CaiaabccacaqGPbGaaeOBaaqaaiaadMhacqGH9aqpcaaIXaaabaGaaeOBaiaab+gacaqG0bGaaeiiaiaadMhacqGH9aqpcaaIYaaaaaa@5B44@

Because the “+” operator in the context of Boolean algebra has a different definition and meaning, than that in ordinary arithmetic. Similarly, the “+” sign in Quantum Mechanics is also not an arithmetic operator; it is a probabilistic Boolean OR operator.

The equation:

|φ=a| X 1 +b| X 2 allows the calculation of the probability that the vector |φ will be either the vector| X 1  OR the vector| X 2   MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaadaGhcaqabeaacqaHgpGAaiaawEa7caGLQmcacqGH9aqpcaWGHbWaa4HaaeqabaGaamiwamaaBaaaleaacaaIXaaabeaaaOGaay5bSlaawQYiaiabgUcaRiaadkgadaGhcaqabeaacaWGybWaaSbaaSqaaiaaikdaaeqaaaGccaGLhWUaayPkJaaabaGaaeyyaiaabYgacaqGSbGaae4BaiaabEhacaqGZbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGJbGaaeyyaiaabYgacaqGJbGaaeyDaiaabYgacaqGHbGaaeiDaiaabMgacaqGVbGaaeOBaiaabccacaqGVbGaaeOzaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeiCaiaabkhacaqGVbGaaeOyaiaabggacaqGIbGaaeyAaiaabYgacaqGPbGaaeiDaiaabMhacaqGGaGaaeiDaiaabIgacaqGHbGaaeiDaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeODaiaabwgacaqGJbGaaeiDaiaab+gacaqGYbGaaeiiamaaEiaabeqaaiabeA8aQbGaay5bSlaawQYiaiaabccacaqG3bGaaeyAaiaabYgacaqGSbGaaeiiaiaabkgacaqGLbGaaeiiaiaabwgacaqGPbGaaeiDaiaabIgacaqGLbGaaeOCaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeODaiaabwgacaqGJbGaaeiDaiaab+gacaqGYbWaa4HaaeqabaGaamiwamaaBaaaleaacaaIXaaabeaaaOGaay5bSlaawQYiaiaabccacaqGpbGaaeOuaiaabccacaqG0bGaaeiAaiaabwgacaqGGaGaaeODaiaabwgacaqGJbGaaeiDaiaab+gacaqGYbWaa4HaaeqabaGaamiwamaaBaaaleaacaaIYaaabeaaaOGaay5bSlaawQYiaiaabccaaaaa@AA68@

It does not mean that there is a physical sum, where both vectors are argued to exist simultaneously in the physical world. In fact, a “sum” wouldn’t even cut it, it would need to be a logical, probabilistic AND function!

Furthermore, it is stressed that the vector | X 1 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwamaaBaaaleaacaaIXaaabeaaaOGaay5bSlaawQYiaaaa@3A08@  is not X 1 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaacaaIXaaabeaaaaa@3768@ .

This last point, whilst pretty much trivially obvious in the context of the rules of Quantum Mechanics, seems to have completely escaped the vast majority. The quantum state represented by | X 1 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwamaaBaaaleaacaaIXaaabeaaaOGaay5bSlaawQYiaaaa@3A08@  is not the same classical state represented by X 1 MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaacaaIXaaabeaaaaa@3768@ . Confusion as to what a state means in Quantum Mechanics is usually at the heart of most waffle descriptions as to what QM means.

In classical mechanics, equations refer to, for example, the actual physical positions given by X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@ . That is, the classical state is represented by X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@ .

In Quantum Mechanics, state equations only represent the probability P, for example, of obtaining X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@ . That is:

|XP(X) not |XX MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwaaGaay5bSlaawQYiaiabgkziUkaadcfacaGGOaGaamiwaiaacMcacaqGGaGaaeOBaiaab+gacaqG0bGaaeiiamaaEiaabeqaaiaadIfaaiaawEa7caGLQmcacqGHsgIRcaWGybaaaa@486C@

That is, a quantum state is represented by |X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwaaGaay5bSlaawQYiaaaa@3917@  and its associated probability, P(X) MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuaiaacIcacaWGybGaaiykaaaa@38AF@  of X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@  is not X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@  itself.

The vector |X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa4HaaeqabaGaamiwaaGaay5bSlaawQYiaaaa@3917@  itself has no direct or “instantaneous” meaning in an equation. It only has a meaning with respect to, what values of X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@  are allowed, and what is the probability that such X MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBaaaleaaaeqaaaaa@36AD@  ’s are obtained in a final calculation.

Understanding these points is key to understanding why a statement such as “the state vector is in a superposition of states” does not mean that, for example, a particle is actually in two X positions at once. It simply means that there is a probability that the particle may be at one X position or another X position.


It’s Quantum Mechanics, Not Classical Mechanics, Dah…!

The reader should refer to the standard accounts of the two slit experiment for a general overview, for example, https://en.wikipedia.org/wiki/Double-slit_experiment.

A key feature of the experiment is that single particles are fired through the slits and the appearance of a diffraction pattern appears over time as many electrons build up a pattern. In an effort to explain this result classically, it is assumed that there are two wavicles at different positions on the imaging screen side of the two slit barrier. The maximum and minimum of the wave functions of these wavicles are then argued to interfere with each, other hence accounting for the variations in density of the electrons on the screen. It is thus argued that, as this is the only way to “explain” that there is a wave pattern on the screen, it “proves” that a single electron gets split up into two as it passed through the slits, and magically combines to one on hitting the screen… Bollocks!

The mathematical rules of Quantum Mechanics, independent of any physical interpretation, are absolute in that the probability of an observable having two simultaneous eigenvalues of position, is zero. Period. So, if Quantum Mechanics is true, any argument that leads to declaring that “a particle is in two places” must be false. In this case, it means that the assumption that a particle splits up is false. There is no realistic way of escaping this conclusion.

The correct explanation for this dilemma, is that physical reality cannot be explained by classical reasoning. End of story. The universe is Quantum, not Classical. Dah… There is simply no explanation from Classical axioms that explains why there is a diffraction pattern.

So, it is astounding that many experts, and sometimes major TV personalities, spout of the laws of Quantum Mechanics in the same sentence as claiming to the masses that particles are at many places at once. They are completely confused on the point that Quantum Mechanics and their waffle Classical descriptions are contradictory. They simply have not learnt to think Quantumly and are hopelessly trying to cling to their Classical baggage.

Quantum Reality

The reality of Quantum Mechanics, is that pretty much 99% of all professional practitioners of Quantum Mechanics simply don’t concern themselves with waffle interpretations as to what is alleged to be actually happening. For the most part, it is irrelevant to the 90% of Physicists engaged in real world work designing new semiconductor processes, and the remainder engaged in designing the new legal high by simulations of the Shrödinger equation.


Many Worlds - Ho…humm…

Might as well put in my 1 cents worth on this topic…

Quantum Mechanics states that particles do not split up by the notion that all measurements must result in single eigenvectors and eigenvalues. Sure, it is possible to postulate that a particle split ups and vanishes into another universe, such that it can not be measured in our universe, in order to avoid the inherent contradiction of the postulates of Quantum Mechanics and charge and energy conservation laws. However, if it can not be measured, ever, it is simply irrelevant to our universe. We can never know, as any interaction that could “prove” alternate universes would constitute a measurement of charge or mass-energy violation in our universe, which would destroy the Quantum Mechanical argument that led to many worlds theory in the first place.

The root cause of the pathological desire for interpretations such as The Many Worlds, Bohmian Interpretation and so forth, is the complete failure to understand the fundamental point proven by Kurt Godel. That is the notion that any complete system description, must contain statements that are true, but not provable (derivable/explainable) within the system.

All interpretations, apart from the Copenhagen and Ensemble interpretations, essentially and futilely, attempt to give a classical, touchy-feely description to the experimental facts of Quantum Mechanics. The proponents of such interpretations are quite unable to remove the straightjacket clothed on them since childhood. They produce never ending classical pictures that try to “explain” how rational, common sense ideas can account for the strange results of QM. Listen up mate. Quantum Mechanics is simply one of the additional Godel axioms that need added to the cooking pot. Live with it.


Appendix

Derivation of the probability for the occurrence of two simultaneous observables.

For simplicity, consider the case of an electron having spin up or down.

Quantum Mechanics states that:

Prob=φ|P|φ Where P is the projection operator MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVv0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaajqgaG9VaaeiuaiaabkhacaqGVbGaaeOyaiabg2da9OWaa4raaKazaa2=baGaeqOXdOgabeGaayzkJiaawEa7aiaadcfakmaaEiaajqgaG9FabeaacqaHgpGAaiaawEa7caGLQmcaaOqaaKazaa4=caqGxbGaaeiAaiaabwgacaqGYbGaaeyzaiaabccacaWGqbGaaeiiaiaabMgacaqGZbGaaeiiaiaabshacaqGObGaaeyzaiaabccacaqGWbGaaeOCaiaab+gacaqGQbGaaeyzaiaabogacaqG0bGaaeyAaiaab+gacaqGUbGaaeiiaiaab+gacaqGWbGaaeyzaiaabkhacaqGHbGaaeiDaiaab+gacaqGYbaaaaa@6990@

The projection operator for the probability of two simultaneous observables A and B is given by P= P A . P B MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@8FBB@

The projection operators for spin operators A and B are given by: P A =| up up | and  P B =| dn dn | MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=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@8A26@

Hence: P= P A . P B =| up up | dn dn |=0 as  up | dn =0 because | up  and | dn  are necessarily orthogonal to each other as they are eigenvectors of a Hermitian operator. MathType@MTEF@5@5@+=feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaqGibGaaeyzaiaab6gacaqGJbGaaeyzaiaabQdaaeaacaWGqbGaeyypa0JaamiuamaaBaaaleaacaWGbbaabeaakiaac6cacaWGqbWaaSbaaSqaaiaadkeaaeqaaOGaeyypa0Zaa4HaaeqabaGaamyDaiaadchaaiaawEa7caGLQmcadaaabaqaaiaadwhacaWGWbaacaGLPmcadaGhcaqabeaacaWGKbGaamOBaaGaay5bSlaawQYiamaaEeaabaGaamizaiaad6gaaeqacaGLPmIaay5bSdGaeyypa0JaaGimaaqaaiaabggacaqGZbGaaeiiamaaaeaabaGaamyDaiaadchaaiaawMYiamaaEiaabeqaaiaadsgacaWGUbaacaGLhWUaayPkJaGaeyypa0JaaGimaaqaaiaabkgacaqGLbGaae4yaiaabggacaqG1bGaae4CaiaabwgacaqGGaWaa4HaaeqabaGaamyDaiaadchaaiaawEa7caGLQmcacaqGGaGaaeyyaiaab6gacaqGKbGaaeiiamaaEiaabeqaaiaadsgacaWGUbaacaGLhWUaayPkJaGaaeiiaiaabggacaqGYbGaaeyzaiaabccacaqGUbGaaeyzaiaabogacaqGLbGaae4CaiaabohacaqGHbGaaeOCaiaabMgacaqGSbGaaeyEaiaabccacaqGVbGaaeOCaiaabshacaqGObGaae4BaiaabEgacaqGVbGaaeOBaiaabggacaqGSbGaaeiiaiaabshacaqGVbGaaeiiaiaabwgacaqGHbGaae4yaiaabIgacaqGGaGaae4BaiaabshacaqGObGaaeyzaiaabkhacaqGGaGaaeyyaiaabohacaqGGaGaaeiDaiaabIgacaqGLbGaaeyEaiaabccacaqGHbGaaeOCaiaabwgacaqGGaGaaeyzaiaabMgacaqGNbGaaeyzaiaab6gacaqG2bGaaeyzaiaabogacaqG0bGaae4BaiaabkhacaqGZbGaaeiiaiaab+gacaqGMbGaaeiiaiaabggacaqGGaGaaeisaiaabwgacaqGYbGaaeyBaiaabMgacaqG0bGaaeyAaiaabggacaqGUbGaaeiiaiaab+gacaqGWbGaaeyzaiaabkhacaqGHbGaaeiDaiaab+gacaqGYbGaaeOlaaaaaa@C3E4@

Hence, there is zero probability, according to standard Quantum Mechanics, of two simultaneous observables.


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© Kevin Aylward 2014 MathType@MTEF@5@5@+=feaagCart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLnhiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqaqFfpeea0xe9Lq=Jc9vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=xfr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaacbaqcLbyaqaaaaaaaaaWdbiaa=nbiaaa@3771@  2016 all rights reserved

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