It had been known for decades that matter, like light, had both wave and particle properties, but there was no quantitative description relating the two. Schrödinger derived it. His equation begins with a wave description and leads to clusters of waves that behave like particles. His first success was to predict the average radii of the orbits of electrons in atoms. These matched the values postulated by Bohr. But there is a hitch, embedded in the word “average.” Different measurements of the same property of an object, such as position, give a variety of answers and not due to experimental error. There is at best a probability associated with each property. The Schrödinger equation has been interpreted to argue that every object actually has a mix of the values of a property until you measure it; hence, it “chooses” one. Schrödinger himself was not happy with this and hence the cat. Is it both alive and dead until you look and force it to choose one? Interpretations still raise controversy. The equation itself ranks as one of the most important in all of physics.
It had been known for decades that matter, like light, had both wave and particle properties, but there was no quantitative description relating the two. Schrödinger derived it. His equation begins with a wave description and leads to clusters of waves that behave like particles. His first success was to predict the average radii of the orbits of electrons in atoms. These matched the values postulated by Bohr. But there is a hitch, embedded in the word “average.” Different measurements of the same property of an object, such as position, give a variety of answers and not due to experimental error. There is at best a probability associated with each property. The Schrödinger equation has been interpreted to argue that every object actually has a mix of the values of a property until you measure it; hence, it “chooses” one. Schrödinger himself was not happy with this and hence the cat. Is it both alive and dead until you look and force it to choose one? Interpretations still raise controversy. The equation itself ranks as one of the most important in all of physics.
Till 1925 the idea of what the quantum theory would be was unknown. During 1925 three different but equivalent versions of quantum theory were proposed – Schrödinger-proposed wave mechanics; Heisenberg-developed matrix mechanics and Dirac-introduced operator theory. Considering the de Broglie’s matter waves Erwin Schrödinger, an Austrian physicist, argued that if a particle like an electron behaves as a wave then the equation of wave motion could be successfully applied to it. He postulated a function varying in both space and time in a wave-like manner (hence called wave function and denoted it as ψ). This function is generally complex and assumed to contain information about a system. Schrödinger set up a linear and time-dependent wave-like equation, called Schrödinger wave equation, to describe the wave aspect of a particle taking account of de Broglie’s relation for wavelength. Physically, |ψ(X, t)|2, where ψ(X, t) is the solution of the Schrödinger equation, is interpreted as position probability density. That is, |ψ(X, t)|2 is the probability density of observing a particle at position X at time t. ψ does not give exact outcomes of observations but helps us to know all possible events and their probabilities . Further, the probability interpretation allows us to find the average or expected result of a set of measurements on a quantum system.
Quantum mechanics is our most successful physical theory. It predicts the behavior of atoms, molecules, and light to ten decimal places. No experiment has ever contradicted it. It also contains a crack at its foundation. The theory’s central equation—the Schrodinger equation—describes a smooth, continuous, perfectly predictable evolution of the quantum state. But whenever anyone performs a measurement, they get a single, definite result. Which result they get appears to be random. The transition from smooth evolution to random outcome is called the “collapse of the wavefunction,” and after nearly a century of analysis, there is no agreed-upon explanation for what causes it, when it occurs, or whether it occurs at all. This is the measurement problem. The measurement problem is not a minor puzzle at the margins of the theory. It is a failure to explain the most basic operation in science: looking at the result of an experiment. Around it cluster other puzzles. Light behaves like a wave in some experiments and like a particle in others—two contradictory descriptions. Two particles that have interacted remain correlated across arbitrary distances, as though communicating faster than light. The probabilities that govern measurement outcomes appear as a postulate—the Born rule—inserted by hand with no deeper justification. And the theory offers no unified picture of reality: quantum mechanics, general relativity, and the standard model of particle physics speak incompatible mathematical languages. A century of effort has produced many interpretations of quantum mechanics. Copenhagen. Many-worlds. De Broglie-Bohm. Objective collapse. Quantum Bayesianism. None has achieved consensus. The measurement problem remains. This document proposes that the source of these puzzles is not quantum mechanics itself. It is a single, invisible assumption made at the very beginning of the theory in 1900—an assumption so deeply embedded that nobody noticed they were making it. Change that assumption, and the puzzles do not get solved. They dissolve. They stop being puzzles. They become predictable consequences of geometry.
The physicist Erwin Schrödinger described, back in 1935, one aspect of this strange phenomenon. He placed his cat in a sealed box with a piece of radioactive material which might or might not send out a sub-atomic particle. If it did, the Geiger counter was designed to trigger a release of poisonous gas in the box, and thereby kill his cat. The counter was set up to be triggered just enough to give a 50-50 chance of a particle being detected, and therefore the cat an even chance of being poisoned or not. (In those days, this sort of experiment was acceptable, particularly as it was only a thought experiment.) Radioactive behaviour is unpredictable (except in a general, statistical probability kind of way). There is no rule for working out whether or not the Geiger counter will be triggered. If the sub-atomic event does not occur, the cat lives. Otherwise, it dies. Just as a photon (in that famous experiment from ‘real-life’ physics) will quite happily go through both of two parallel slits in a screen – until someone tries to measure or detect it, at which point what the physicists call ‘the collapse of the wave function’ takes place – the particle can both trigger the poison gas and not trigger the poison gas. That is, until someone looks, Schrödinger’s idea is that his cat, for a while, is both alive and dead!
The uncertainty principle comes into force because of the wave like properties of “particles” like electrons and protons. The waves tell the dynamics of the particle – its momentum, its energy and even its angular momentum. Wave packets are made by adding together many simple waves that run forever. If electrons have the wave properties then there must be a wave equation and a wave function to describe the electron waves just as the waves of light, sound and strings are described. The success of wave mechanics was well demonstrated by Erwin Schrödinger before an acceptable interpretation of the wave function was known. Max Born utilized the probability concepts of the uncertainty principle to give us the presently accepted ideas of the wave function.
The physicist Erwin Schrödinger described, back in 1935, one aspect of this strange phenomenon. He placed his cat in a sealed box with a piece of radioactive material which might or might not send out a sub-atomic particle. If it did, the Geiger counter was designed to trigger a release of poisonous gas in the box, and thereby kill his cat. The Geiger counter was set up to be triggered just enough to give a 50-50 chance of a particle being detected, and therefore the cat an even chance of being poisoned or not. (In those days, this sort of experiment was acceptable, particularly as it was only a thought experiment.) Radioactive behaviour is unpredictable (except in a general, statistical probability way). There is no way of working out whether or not the Geiger counter will be triggered off. If the sub-atomic event does not occur-the cat lives. Otherwise, it dies. Just as the photon (in Problem 93) will quite happily go through both slits until someone tries to measure or detect it, at which point what the physicists call ‘the collapse of the wave function’ takes place, the particle can both trigger the poison gas and not trigger the poison gas. Until someone looks, Schrödinger’s idea is that his cat, for a while, is both alive and dead!
Einstein: God does not play dice and nothing travels faster than the speed of light. Schrödinger: My cat cannot be both dead and alive. Dirac: The existing quantum theory should not be considered to be the final solution. Feynman: How does it work? de Broglie: My matter wave has an imaginary part. Me: Great! This could be the missing piece the others have been looking for. In this report, I present an innovative modification to the Schrödinger equation, which yields wavefunctions capable of accurately describing quantum phenomena. Concurrently, this modification introduces an alternative interpretation to the widely recognized Copenhagen interpretation within the realm of quantum theory.