Since many members requested for a simple tool to create wave functions and wanted to run simulations on those wave functions without having to learn about all those programming languages and their implementation details which is a common issue with physics students who lack programming knowledge I wanted to introduce to everyone a simple QMTools Applet Editor where you can easily write your wave equations and simulate them and embed that applet code in any of your web pages.
QMTools editor is an additional supplement which you get when you buy the Physics Text book, Modern Physics, 3rd edition by Serway, Moses and Moyer in which they have used it as a tutorial for their exercise problems. It was developed by Dr Curt Moyer and Mr Philip Brady and you can download this applet editor and other example files from this website QMTools Home.
It requires a Java Run Time environment to be installed in your computer for the application to run and you can download the JRE tool form that website itself, the help documentation section in the QMTools editor is a must read in order to understand how to interpret, create and edit the wave-functions and also to understand on how to use the editor.
The source files should be stored as .xml files to import and use with in the editor and also to transfer or to send your simulations to others so that they can import your files to their editors running in their base machines and to render it as an html file or to embed it in your web pages save your file as .html
The below applet application shows a simple example of how the equations are plotted as a function and simulated over time. You don’t need to learn any programming languages to do this just follow the instructions in the help section and start creating your own wave-functions.
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Science is a branch of philosophy that deals with developing models of the physical world that can be testified. The pioneers of science like Galileo Galilee, Newton and others were realists and they developed science in the hope of understanding the working of this universe through reason and empirical evidences.
The current Modern Science has deviated from this central dogma of science and most scientists are satisfied to just predict the possible outcomes of the system rather than to understand its exact nature and the philosophical implications that are underpinned. A more perfect analogy describing the current state of affairs is that physicists are just looking at a clock with hands from outside which ticks for every seconds but they have no idea of how this clock is working at the most fundamental level and the exact nature of its components. Most positivists are quite satisfied to predict the possible outcomes of the system and then to apply the results to develop technological applications and to account for the phenomena which is observed. The technological applications like Scanning Tunneling Microscope, Charged Coupled Devices, Magnetic Resonance imaging, Medicine through high energy particle physics .. etc and models which accurately account for the phenomena like Superconductivity, Super fluidity and Bose-Einstein condensates at absolute zero temperatures demonstrate the great success that Modern Science has had over the years.
The physicists of the 20th century are the one who contributed to this vast amount of knowledge and to exploit the strange properties and behaviour of these high energy particles to develop advanced technological applications. In the beginning of the 20th century great focus and attention was given to atomic phenomena and it was during this time that the two pillars of Modern Science namely Special theory of Relativity and Quantum Physics was developed. These theories not only changed our common intuitions and notions of our universe but also left a lot of paradoxes and problems along with the huge success they had.
In the Newtonian world both space and time were considered to be absolute and they were independent and Newton’s laws were sufficient enough to account for a wide variety of classical phenomena and Law of Gravitation described how large mass of bodies orbited around one another due to a force of attraction called gravity. The light was assumed to be propagating with speed C in a medium called the ether and the speed of light was not known to be a constant. Light which was travelling downwind along the ether wind had a speed of c+v and the light propagating upwind had a speed of c-v where ‘v’ is the speed of the ether relative to earth. There was no upper-limit for the speed of particles in Newtonian Mechanics.
All these notions of space,time and light which could be transformed using Galilean transformations for other inertial frames failed to account for the phenomena and the observations at speeds near C. The speed of light remained the same for an observer who measured its speed at rest and for an observer who was travelling at 0.5c, the speed was c and not c+0.5c. The speed of light was same in all inertial frames for all observers and also electrons which were accelerated using millions of potential voltage in particle accelerators failed to cross the light barrier of C.
These contradictions in the old theory paved way for the young Albert Einstein to postulate through his thought experiments one of the significant scientific breakthrough of the 20th century i.e. Special theory of Relativity and he postulated that the speed of light remained constant in all inertial frames for all observers and it propagated in empty space with out requiring a medium for its propagation and the laws and mathematical forms were same in all inertial frames relative to each other for all observers and the observers in different inertial frames should record observations that were consistent with the physical laws. The failure of Michelson-Morley experiment to detect ether relative to earth and Lorentz transformation gave support to his theory. Counter intuitive to our common beliefs it was space and time which changed or transformed to account for the constant speed of light. Time dilation events in which moving clocks run slower and length contraction are well testified events and space-time were considered to be relative and entangled to each other and the only quantity which was absolute was the space-time interval derived from Minkowski’s space-time diagrams.
Albert Einstein didn’t end here he went on to postulate that the laws of physics was same even for accelerating frames relative to each other and developed the theory of General Relativity and it completely over threw our notion of gravitational attraction. Today physicists don’t see gravity has a force instead they comprehend that a freely falling object takes a particular path due to the geometry of the space-time curvature rather than a force of attraction between those bodies. There is no force of attraction an object falls to the ground due to the geometry or the curvature of space-time created by the large mass of Earth and in more heavy bodies like Black Hole the curvature is so sharp that no light or no matter can escape from this strong gravitational field.
General relativity changed the way we saw how our solar system works. All the planets don’t orbit the sun using circular orbits instead the orbits are elliptical. The Sun at the center creates a large depression in the fabric of space and time and all planets are caught up in its curvature. The planet Earth would travel in a straight line and escape from the solar system if there was no enough gravitational pull from the sun to provide the necessary centripetal force to revolve around it and the most strange thing is that all planets are spiraling down towards the Sun due to the space-time curvature but the loss of orbital energy is negligible compared to the distances separated between the planet and the sun and it would take billions of years to reach the Sun and as they spiral down their orbital velocity will increase and their orbital period will shorten and all these predictions of the theory are testified with great precision up to decimal places.
Edwin Hubble showed that distant galaxies are accelerating away from us with great speeds using the Doppler effect of light of redshifts which is an another prediction of General Relativity that gravity would bend light and alters its frequency. It is also predicted that time runs slower in the presence of a strong gravitational field. All these testified predictions shows the strength of the theory and the simple, elegant and consistent postulates of Einstein which made him a universal celebrity for his ground breaking thought experiments.
Along the same lines there was an another field of science which was growing and physicists were working on it with great interest, it was statistical mechanics of ensembles applied to Thermodynamics. The physicists were working on black body radiation and its effects when subjected to higher temperatures. They found sharp deviations between the experimental observations and theoretical predictions. Classical physics couldn’t account for the phenomena of ‘Ultraviolet catastrophe’ this paved the way for the Plank’s packets of energy called quanta whose energy states where quantized and where allowed to make a quantum jump with only a limited allowed values for the system. Later Einstein used this concept of quanta and called them as photons in the interaction of electrons for the phenomena of photoelectric effect.
Louis de Broglie confirmed beyond doubt that even matter exhibit wave like properties and this started the wave-particle duality in modern physics and Heisenberg with his matrix approach to QM developed the Heisenberg’s uncertainty principle which states that it is impossible to simultaneously know the position and momentum of a particle with an uncertainty smaller than h/2. So if we know the position of a particle with great position then we have to lose all the information about its momentum. It is not possible to simultaneously know through which slit the electron has passed through and also to observe an interference pattern i.e. if we know more about the particle property of the particle then we lose any information we have about its wave nature. So both wave nature and particle nature are complementary to each other.
Neil Bohr one of the pioneer of QM who developed the atomic model was aware of the strange state of affairs that was developing during his time so he developed an interpretation of QM called the Copenhagen interpretation of QM and most physicists stick to this orthodox interpretation of QM. Bohr postulated that the equations of QM can only be applied to determine the probable outcomes of the system but it doesn’t give any element of physical reality to the nature of quantum system itself i.e. when we can’t see the superposition states of particles for example an electron passing through both the slit simultaneously and a 45* photon which is in a superposition of H or V state the Copenhagen interpretation asserts that no greater reality should be attributed to these superposition states since it can not be observed. What we know or what we can observe is the specific state the photon or the electron takes after a measurement is made by the observer. The properties like position, momentum, polarisation etc.. do not pre-exist having a definite state before the measurement. The possible outcomes crystallizes into a single result when a measurement is made. The act of measurement causes the interference pattern to be destroyed.
This state of affairs disturbed Einstein as he believed in a deterministic and an objective world where particles had definite states of position and momentum irrespective of anyone observing them. But the story which was told by QM was something different as it is very much true that the photons passed through a HV polarizer appear out randomly as horizontally or vertically polarized. The path that individual photons take and the outcome of its polarization can not be determined and it is inherently random and not due to any lack of knowledge about the photons from our part and So Einstein was proved wrong when he said that “God does not play dice”. Quantum Randomness rules which was later transformed by Stephen Hawking as “God not only plays dice but he throws them where we can not see”.
John Bell with his inequality theorem proved that the particles do not always have definite properties of position and momentum and they exist in a superposition of states. As we have understood from the Copenhagen interpretation it means that we shouldn’t assume that particles will have an attribute like position or momentum when it is not being observed. We will know that the particle has a specific position only after we have made a measurement not before that. The quantum mechanical view of the world doesn’t allow us to make a model of the physical world more over if we have to accept the positivists approach then there is no absolute reality for these particles which is independent of an observer. Does it bring an end to the objective account of the physical world of the realists? Do we have to abandon our hope of finding an objective model for the origin and working of the universe which exists irrespective of the observer observing it or not? Do humans don’t have the epistemological ability to fully comprehend the universe? All these problems will be addressed later.
A new look at measurement problem of QM
The philosophical implications of Quantum Physics has baffled physicists over the years. The theory of Quantum Physics is the highest intellectual achievement made by mankind to describe reality.
The reality that is described by QM is weird and it doesn’t fit into our common notions of classical world. The equations of QM accurately predict the possible outcomes of a system by the act of measurement and develop a probability distribution for the entities of the system in hand at a particular point in space and time. In quantum world randomness rules and this randomness is not the kind of randomness that we normally see in the classical world say of tossing a coin where if the forces acting on the coin can be accurately measured through out its journey then we can say whether it will fall as head or tail. But there is no way of telling whether a photon passing through a HV -polarizer will appear as horizontally or vertically polarised. Bohr and others previously thought that the interference pattern is destroyed due to the increase in the uncertainty in the momentum of the electron when a detector is placed behind the slits to know through which slit the electron has passed but recent findings have shown that the interference pattern is destroyed irrespective of whether the detector induces a momentum to the electron or not. One can find more information Here in which the uncertainty principle couldn’t account for the results produced.
The interference pattern is destroyed by the very act of observation this implies that the observer, the measuring device and the quantum system are entangled in some way and this entanglement which can be non-local is disturbed resulting in a specific state for the quantum system during the process of measurement. This is the reason why many physicists like Roger Penrose argue that an unified theory of everything must include consciousness at its most fundamental level. Roger penrose’s non-computability may be one of the ways the physical world might operate. John Wheeler uses the word participator for the observer in a quantum regime as the observer can not be isolated and thought as a different system. We must also describe the states of the observer along with the quantum system to fully understand the evolution of the wave and its further collapse. Both the choice of the observer as well as the observed system are responsible for the results that are observed. The measurement problem is at the heart of quantum physics and it is one of the cornerstone of QM even though it has with stood the test of times, accurately predicting the possible outcomes of the system but science is more than just finding probabilities physicists like John Bell, Einstein, Penrose will not be satisfied by the positivist approach and one has to make deep in routes into its philosophical implications and look for an alternative world view and move forward.
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