The Physics of Quantum Leaps
Created | Updated May 10, 2005
In quantum mechanics every quantity of energy and matter is quantized into units of energy, which cannot be divided - they are called "quanta". A good example of a quanta is the photon, the particle that is associated with a wave of light. Every frequency of light (electromagnetic radiation) is made up of millions of photons and these photons will have energy that increases with the wavelegnth of the light*.
In 1915 Niels Bohr proposed a new model of the atom. This is the model we know of today - where a atom consists of a central nucleus with orbiting electrons. One of the crucial characteristics of Bohr's model is that every electron exists in a certain 'energy level'. The energy of each electron is restricted to certain discrete levels, it is quantized, so we can only find electrons at certain specific places round the nucleus. The higher the energy level of an electron, the further away it is from the nucleus**. The lowest energy of an electron is called the 'ground state'. From the ground state, there is a limited number of energy levels in predictable places, untill an electron has enough energy to escape from the atom itself and become an ion.
An electron gains more energy by absorbing a photon - at the same time, it can loose energy by emmitting a photon. Every atom has a characteristic set of energy levels, so there is a 'spectrum' for each element. Colour is when light of a specific wavelegnth (energy) is emmitted from an electron in a atom; also, electrons will only accept specific wavelegnths of light because of the energy levels they are in. This underlines the spectrum for each element and allows scientists to predict what a star is made up of solely through looking at its spectral colour.
Things start to become strange when we look at what happens to the electron, when it emits or absorbs light. Every time a electron moves from one energy level to another it happens *instantaneously* - it takes no time whatsoever. It makes a "Quantum Leap". This is allowed because the energy levels are quantized - there is no 'inbetween state' from one energy level to another. Part of the strangeness of quantum mechanics is the way all units of matter and energy are quantized - even time. When the implications of this were contemplated by physicists after Bohr, they found it hard to accept. The 'quantum leap' goes against all our notions of causality and locality - it implies that an action can occur 'instantaneously'. Moreover, in Bohr's model there is no explanation to why the ground state of an element is what it is - it is simply there. When an electron emits a photon, it does so according to the laws of probability - in other words, randomly. The nature of a quantum leap is a bit like Einsteins 'action at a distance', only it does not violate special relativity because of the small distances and energies which are involved.
The physicist Ernst Schroedinger (1887 - 1961) reformed Bohrs model and developed wave mechanics. The basic underlying concept of this is that every quantum entity can be represented as a wavefunction; with certain calculable properties corresponding to the properties of the 'particle'. An electron should not be regarded as a seperated, independent particle, but rather as a wavefunction - a wave of energy existing in the atoms field. Schroedinger did not approve of what his theory had been turned into - he wanted to get a deterministic model that would remove the idea of randomness and quantum leaps. Nevertheless, wave mechanics became the foundation for all of quantum mechanics - to this day - and it incorporates the idea of probability values and the 'collapse of the wavefunction' when it is observed.
Some readers may be familiar with the way quantum mechanics has one single mathematical base, but with a whole host of interpretations to this base. For example, there is the contemporary Copenhagen Interpretation (of Niels Bohr) where particles are waves of probability, collapsing when they are observed; in this interpretation the quantum world is random and not deterministic. There is also the 'Many Worlds' interpretation of Richard Feynman
along with many other interpretations.*** The problem with quantum leaps is purely conceptual - the mathematics behind them is complete and totally accurate. Some physicists have speculated that the quantum world really is deterministic, it only appears random because we have not accounted for the existence of 'hidden variables'. A hidden variable is something that interacts with a particle, crucially determining the particles behavoir. It is like looking at a leaf blown in the wind. The leaf itself will look as if it is completely random - leaping up and down and turning round randomly. We could even derive a probability graph of its behavoir and infer what it will do next. But if an observer could know the force and direction of the winds which move the leaf, they could predict with absolute certainly what the leaf will do next. Just so if physicists could know the properties of the 'hidden variables' behind each particles behavoir.
When an electron emits a photon, it does so randomly - according to what probability options are available to its quantum state. But with hidden variable's theories, the electron has to emit the photon - from its interaction with a background of quantum waves (the hidden variables). You cannot seperate an electron from the atoms field - it becomes entangled with the state of the nucleus. A change in the nucleus, like the ejection of a neutron, causes an automatic change in the field. Thus an electron emits a photon when the nucleus (or the atoms field) interacts with an external 'hidden variable'. In the hidden variables theory of David Bohm - it is impossible to seperate a particle(wavefunction) from its field, and all quantum fields are connected.
An article published by Hal Puthoff gave an explanation of what determines the ground state of hydrogen****. In previous models, the ground state is arbitary. Puthoff used the existence of the Zero Point Field (ZPF)- a field of background energy in the Universe - to explain how the ground state of an atom arises. It is worth discussing the ZPF in further detail. In quantum mechanics, the vacuum of space is not void of energy - rather, it is seething with energetic virtual particles*(5). We can observe the effects of this energy in the Casimir Effect, where two metal plates experience a very slight pressure when they are close enough together. We also see the effects of virtual particles on the electron, in the 'Lamb Shift'. Because of the existence of virtual particles in the vacuum, an electron in an energy level will feel the effects of the virtual particles electric fields. Consequently, the electron will be perturbed and show an additional, variable energy. The effect of this perturbation was shown in 1947 by W.E Lamb, who noticed a tiny shift on the spectrum of light from the hydrogen atom.
The ZPF comes in when we consider a charge, or 'harmonic oscillator', something with a measured kinetic energy. Even when we stop the charge from moving around, there will always be a constant 'jiggle' that acts on the charge. We see this in the Lamb Shift. This is the Zero Point Energy - which comes from a background field of virtual photons, the Zero Point Field. Every particle that exists experiences this field, but only in Stochastic Electrodynamics is it recognised as like any other field - i.e like the electromagnetic field. An important aspect of the ZPF is it is only visible to accelerating charges. When a charge accelerates, it will scatter some of the ZPF energy and it will have a 'radiation resistance'. Some physicists have speculated that the ZPF is the origin of mass.
It was shown by Hal Puthoff that the ground state of Hydrogen arises from the atoms interaction with the ZPF. An electron existing in this lowest energy level will constantly absorb and emit photons from the ZPF, in a dynamic equilibrium, so the electron will get its energy maintained by the ZPF. It will be kept in the ground state in accordance with how much energy is absorbed/emmitted. When a 'quantum leap' occurs the interaction with the ZPF changes and re-establishes the electron in a higher energy level. Once the electron is free (ionised), it is not part of the atom - the only energy level will be its own. The important point of the ZPF is it provides a 'hidden variable' field that explains some of the things quantum theory puts down to probabilistic values.
One of the most interesting and controversial interpretations of quantum mechanics is the Transactional Interpretation of John Kramer. The reason it is so controversial? Because it proposes that throughout the Universe there are interactions that go backwards in time! A charged particle that accelerates will emit radiation into the future - but it will also emit radiation into the past too. The great virtue of this interpretation is it removes the indeterminism of the 'conventional' quantum mechanics (i.e the Copenhagen interpretation). It also connects one object in the Universe to any other object, without violating special relativity - it is non-local. Reversed-time interactions do not conflict with the laws of physics; in fact, they are essential! Maxwell showed in his equations that every wave of light emmitted, that goes forward in time, there must be another wave that goes backwards in time. Every physical interaction is time-symmetric; there is no discrimination between which direction in time the interaction can happen.*(6)
It has long-since been theorised and confirmed that the Universe is non-local. Something that occurs at A, can automatically effect something which occurs at B - even if the distance between both events are seperated by immense distances. Not only does 'instantaneous action' occur in quantum leaps - it occurs right across the Universe. In the famous EPR Experiment*(7) and Bells Inequality - it was shown that quantum mechanics has an inherent non-locality. If we accept this non-locality, we can reject the other side of quantum mechanics; that the world of the very small is indeterminate and random. By using the transactional interpretation, we can infer that the ZPF has a 'mirror field' of virtual photons that go into the past. These profoundly effect ordinary matter and connect every region of quantum energy to another region. We may postulate that a quantum leap is when the electron dissapears into this time-symmetric sea of photon-energy, appearing instantaneously at a different energy level. The electron is 're-organised' by interactions of the ZPF - it does not 'move' from one energy level to another; instead, it becomes a chain of time-symmetric energy, dissapearing and appearing in the same unit of 'quantized time'.
Such instantaneous 'teleportation' can only occur at the quantum level, for entities such as electrons. However, it is possible to reorganise whole atoms into single quantum states. They become 'Bose-Einstein condensates' - a whole mixture of atoms behaving as one quantum state. Every particle of matter is a wave of complex energy, ultimately sustained by the ZPF. If electrons can use time-symmetric interactions to 'teleport' from A to B, what about other quantum states? The sci-fi dream of teleportation has a kind of basis in this theory. But there are problems. Firstly, the Zero Point Field would need to be 'manipulated' to reorganise a Bose-Einstein condensate. Secondly, such a 'reorganisation' could only be accomplished in an extremely small distance. The only way to increase the distance of 'teleportation' is to reduce the mass/energy of the quantum state or change Plancks Constant. Such possibilities remain outside of todays science, but with further research into the ZPF and the wave nature of all matter, the way one part of the Universe can be instantaneously connected to another, who knows what might come next?
Notes:
*E = hf
** difference between one energy level E1 and another E2 is given by: E2 - E1 = hf . This can be translated into the photon energy required to move an electron from a lower energy to a higher, and also the wavelegnth of a photon emmitted when the photon moves from a higher energy level to a lower one.
*** Other interpretations include the 'pilot wave' like that of Louis De Broglie and Heisenbergs 'duplex' universe.
**** This article is published in the American Physical Society and is shown in the references (the prola link).
*(5) Because of the uncertainty principle. These virtual particles can only exist if they annihilate after a short time span. The uncertainity in energy*time = 2/(2pi/h).
*(6) There is one exception; and this is when the Kaon particle decays into a Pion. This does not cohere to the principle of CPT symmetry.
*(7) For an indepth explanation of the EPR experiment see http://plato.stanford.edu/entries/qt-epr/
http://prola.aps.org/abstract/PRD/v35/i10/p3266_1
http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html#c4
http://physicsweb.org/articles/news/7/9/2/1
http://users.powernet.co.uk/bearsoft/PCh2.html
http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html (official site of transactional interpretation)
In 1915 Niels Bohr proposed a new model of the atom. This is the model we know of today - where a atom consists of a central nucleus with orbiting electrons. One of the crucial characteristics of Bohr's model is that every electron exists in a certain 'energy level'. The energy of each electron is restricted to certain discrete levels, it is quantized, so we can only find electrons at certain specific places round the nucleus. The higher the energy level of an electron, the further away it is from the nucleus**. The lowest energy of an electron is called the 'ground state'. From the ground state, there is a limited number of energy levels in predictable places, untill an electron has enough energy to escape from the atom itself and become an ion.
An electron gains more energy by absorbing a photon - at the same time, it can loose energy by emmitting a photon. Every atom has a characteristic set of energy levels, so there is a 'spectrum' for each element. Colour is when light of a specific wavelegnth (energy) is emmitted from an electron in a atom; also, electrons will only accept specific wavelegnths of light because of the energy levels they are in. This underlines the spectrum for each element and allows scientists to predict what a star is made up of solely through looking at its spectral colour.
Things start to become strange when we look at what happens to the electron, when it emits or absorbs light. Every time a electron moves from one energy level to another it happens *instantaneously* - it takes no time whatsoever. It makes a "Quantum Leap". This is allowed because the energy levels are quantized - there is no 'inbetween state' from one energy level to another. Part of the strangeness of quantum mechanics is the way all units of matter and energy are quantized - even time. When the implications of this were contemplated by physicists after Bohr, they found it hard to accept. The 'quantum leap' goes against all our notions of causality and locality - it implies that an action can occur 'instantaneously'. Moreover, in Bohr's model there is no explanation to why the ground state of an element is what it is - it is simply there. When an electron emits a photon, it does so according to the laws of probability - in other words, randomly. The nature of a quantum leap is a bit like Einsteins 'action at a distance', only it does not violate special relativity because of the small distances and energies which are involved.
The physicist Ernst Schroedinger (1887 - 1961) reformed Bohrs model and developed wave mechanics. The basic underlying concept of this is that every quantum entity can be represented as a wavefunction; with certain calculable properties corresponding to the properties of the 'particle'. An electron should not be regarded as a seperated, independent particle, but rather as a wavefunction - a wave of energy existing in the atoms field. Schroedinger did not approve of what his theory had been turned into - he wanted to get a deterministic model that would remove the idea of randomness and quantum leaps. Nevertheless, wave mechanics became the foundation for all of quantum mechanics - to this day - and it incorporates the idea of probability values and the 'collapse of the wavefunction' when it is observed.
Some readers may be familiar with the way quantum mechanics has one single mathematical base, but with a whole host of interpretations to this base. For example, there is the contemporary Copenhagen Interpretation (of Niels Bohr) where particles are waves of probability, collapsing when they are observed; in this interpretation the quantum world is random and not deterministic. There is also the 'Many Worlds' interpretation of Richard Feynman
along with many other interpretations.*** The problem with quantum leaps is purely conceptual - the mathematics behind them is complete and totally accurate. Some physicists have speculated that the quantum world really is deterministic, it only appears random because we have not accounted for the existence of 'hidden variables'. A hidden variable is something that interacts with a particle, crucially determining the particles behavoir. It is like looking at a leaf blown in the wind. The leaf itself will look as if it is completely random - leaping up and down and turning round randomly. We could even derive a probability graph of its behavoir and infer what it will do next. But if an observer could know the force and direction of the winds which move the leaf, they could predict with absolute certainly what the leaf will do next. Just so if physicists could know the properties of the 'hidden variables' behind each particles behavoir.
When an electron emits a photon, it does so randomly - according to what probability options are available to its quantum state. But with hidden variable's theories, the electron has to emit the photon - from its interaction with a background of quantum waves (the hidden variables). You cannot seperate an electron from the atoms field - it becomes entangled with the state of the nucleus. A change in the nucleus, like the ejection of a neutron, causes an automatic change in the field. Thus an electron emits a photon when the nucleus (or the atoms field) interacts with an external 'hidden variable'. In the hidden variables theory of David Bohm - it is impossible to seperate a particle(wavefunction) from its field, and all quantum fields are connected.
An article published by Hal Puthoff gave an explanation of what determines the ground state of hydrogen****. In previous models, the ground state is arbitary. Puthoff used the existence of the Zero Point Field (ZPF)- a field of background energy in the Universe - to explain how the ground state of an atom arises. It is worth discussing the ZPF in further detail. In quantum mechanics, the vacuum of space is not void of energy - rather, it is seething with energetic virtual particles*(5). We can observe the effects of this energy in the Casimir Effect, where two metal plates experience a very slight pressure when they are close enough together. We also see the effects of virtual particles on the electron, in the 'Lamb Shift'. Because of the existence of virtual particles in the vacuum, an electron in an energy level will feel the effects of the virtual particles electric fields. Consequently, the electron will be perturbed and show an additional, variable energy. The effect of this perturbation was shown in 1947 by W.E Lamb, who noticed a tiny shift on the spectrum of light from the hydrogen atom.
The ZPF comes in when we consider a charge, or 'harmonic oscillator', something with a measured kinetic energy. Even when we stop the charge from moving around, there will always be a constant 'jiggle' that acts on the charge. We see this in the Lamb Shift. This is the Zero Point Energy - which comes from a background field of virtual photons, the Zero Point Field. Every particle that exists experiences this field, but only in Stochastic Electrodynamics is it recognised as like any other field - i.e like the electromagnetic field. An important aspect of the ZPF is it is only visible to accelerating charges. When a charge accelerates, it will scatter some of the ZPF energy and it will have a 'radiation resistance'. Some physicists have speculated that the ZPF is the origin of mass.
It was shown by Hal Puthoff that the ground state of Hydrogen arises from the atoms interaction with the ZPF. An electron existing in this lowest energy level will constantly absorb and emit photons from the ZPF, in a dynamic equilibrium, so the electron will get its energy maintained by the ZPF. It will be kept in the ground state in accordance with how much energy is absorbed/emmitted. When a 'quantum leap' occurs the interaction with the ZPF changes and re-establishes the electron in a higher energy level. Once the electron is free (ionised), it is not part of the atom - the only energy level will be its own. The important point of the ZPF is it provides a 'hidden variable' field that explains some of the things quantum theory puts down to probabilistic values.
One of the most interesting and controversial interpretations of quantum mechanics is the Transactional Interpretation of John Kramer. The reason it is so controversial? Because it proposes that throughout the Universe there are interactions that go backwards in time! A charged particle that accelerates will emit radiation into the future - but it will also emit radiation into the past too. The great virtue of this interpretation is it removes the indeterminism of the 'conventional' quantum mechanics (i.e the Copenhagen interpretation). It also connects one object in the Universe to any other object, without violating special relativity - it is non-local. Reversed-time interactions do not conflict with the laws of physics; in fact, they are essential! Maxwell showed in his equations that every wave of light emmitted, that goes forward in time, there must be another wave that goes backwards in time. Every physical interaction is time-symmetric; there is no discrimination between which direction in time the interaction can happen.*(6)
It has long-since been theorised and confirmed that the Universe is non-local. Something that occurs at A, can automatically effect something which occurs at B - even if the distance between both events are seperated by immense distances. Not only does 'instantaneous action' occur in quantum leaps - it occurs right across the Universe. In the famous EPR Experiment*(7) and Bells Inequality - it was shown that quantum mechanics has an inherent non-locality. If we accept this non-locality, we can reject the other side of quantum mechanics; that the world of the very small is indeterminate and random. By using the transactional interpretation, we can infer that the ZPF has a 'mirror field' of virtual photons that go into the past. These profoundly effect ordinary matter and connect every region of quantum energy to another region. We may postulate that a quantum leap is when the electron dissapears into this time-symmetric sea of photon-energy, appearing instantaneously at a different energy level. The electron is 're-organised' by interactions of the ZPF - it does not 'move' from one energy level to another; instead, it becomes a chain of time-symmetric energy, dissapearing and appearing in the same unit of 'quantized time'.
Such instantaneous 'teleportation' can only occur at the quantum level, for entities such as electrons. However, it is possible to reorganise whole atoms into single quantum states. They become 'Bose-Einstein condensates' - a whole mixture of atoms behaving as one quantum state. Every particle of matter is a wave of complex energy, ultimately sustained by the ZPF. If electrons can use time-symmetric interactions to 'teleport' from A to B, what about other quantum states? The sci-fi dream of teleportation has a kind of basis in this theory. But there are problems. Firstly, the Zero Point Field would need to be 'manipulated' to reorganise a Bose-Einstein condensate. Secondly, such a 'reorganisation' could only be accomplished in an extremely small distance. The only way to increase the distance of 'teleportation' is to reduce the mass/energy of the quantum state or change Plancks Constant. Such possibilities remain outside of todays science, but with further research into the ZPF and the wave nature of all matter, the way one part of the Universe can be instantaneously connected to another, who knows what might come next?
Notes:
*E = hf
** difference between one energy level E1 and another E2 is given by: E2 - E1 = hf . This can be translated into the photon energy required to move an electron from a lower energy to a higher, and also the wavelegnth of a photon emmitted when the photon moves from a higher energy level to a lower one.
*** Other interpretations include the 'pilot wave' like that of Louis De Broglie and Heisenbergs 'duplex' universe.
**** This article is published in the American Physical Society and is shown in the references (the prola link).
*(5) Because of the uncertainty principle. These virtual particles can only exist if they annihilate after a short time span. The uncertainity in energy*time = 2/(2pi/h).
*(6) There is one exception; and this is when the Kaon particle decays into a Pion. This does not cohere to the principle of CPT symmetry.
*(7) For an indepth explanation of the EPR experiment see http://plato.stanford.edu/entries/qt-epr/
http://prola.aps.org/abstract/PRD/v35/i10/p3266_1
http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html#c4
http://physicsweb.org/articles/news/7/9/2/1
http://users.powernet.co.uk/bearsoft/PCh2.html
http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html (official site of transactional interpretation)
