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What is Quantum Vacuum ?
Friday 16 December 2016, by
What is Quantum Vacuum ?
An article of Albert Einstein, “On the Ether” (1924) :
If we are here going to talk about the ether, we are not, of course, talking about the physical or material ether of the mechanical theory of undulations, which is subject to the laws of Newtonian mechanics, to the points of which are attributed a certain velocity. This theoretical edifice has, I am convinced, finally played out its role since the setting up of the special theory of relativity. It is rather more generally a question of those kinds of things that are considered as physically real, which play a role in the causal nexus of physics, apart from the ponderable matter that consists of electrical elementary particles. Therefore, instead of speaking of an ether, one could equally well speak of physical qualities of space. Now one could take the position that all physical objects fall under this category, because in the final analysis in a theory of fields the ponderable matter, or the elementary particles that constitute this matter, also have to be considered as “fields” of a particular kind, or as particular “states” of the space But one would have to agree that, at the present state of physics, such a point of view would be premature, because up to now all efforts directed to this aim in theoretical physics have led to failure. In the present situation we are de facto forced to make a distinction between matter and fields, while we hope that later generations will be able to overcome this dualistic concept, and replace it with a unitary one, such as the field theory of today has sought in vain.
It is generally assumed that Newtonian physics does not recognize an ether, and that is the undulatory theory of light that first introduced this ubiquitous medium able to influence physical phenomena. But this is not the case. Newtonian mechanics has its “ether” in the suggested sense, which, however, is called “absolute space”. In order to understand this clearly, and at the same time to render the ether concept more precise, we have to go back a little further.
We consider first of all branch of physics that manages without an ether, namely Euclidean geometry, which is conceived as the science of the possible ways of bringing bodies that are effectively rigid into contact with one another. (We will disregard the light rays which might other wise be involved in the origin of the concepts and laws of geometry.) The laws for the positioning of rigid bodies, exluding relative motion, temperature, and deforming influences, such as they are laid down in idealized form in Euclidean geometry, can make do with the concept of rigid body. Environmental influences of any kind, which are present independent of the bodies, which act upon the positioning, are unkown to Euclidean geometry. The same is true of non-Euclidean geometries of constant curvature, if these are conceived as (possible) laws of nature for the positioning of bodies. It would be another matter if one considered it necessary to assume a geometry with variable curvature. This would mean that the possible contiguous positions of effectively rigid bodies in various different cases would be determined by the environmental influences. In the sense considered here, in the case one would have to say that such a theory employs an ether hypothesis. This ether would be a physical reality, as good as matter. If the laws of positioning could not be influenced by physical factors, such as the clustering or state of motion of bodies in the environment and so on, and were given once and for all, such an ether would have to be described as absolute (i.e. independent of the influence of any other object).
Just as the (physically interpreted) Euclidean geometry has no need of an ether, in the same way the kinematics or phoronomics of classical mechanics does not require one either. These laws have a clear sense in physics as long as one supposes that the influences assumed in special relativity regarding rulers and clocks do not exist.
It is otherwise in the mechanics of Galileo and Newton. The law of motion, “mass x acceleration = force”, contains not only a statement regarding material systems, but something more – even when, as in Newton’s fundamental law of astronomy, the force is expressed through distances, i.e. through magnitudes, the real definitions of which can be based upon measurements with rigid bodies. For the real definition of acceleration cannot be based entirely on observations with rigid bodies and clocks. Ii cannot be referred back to the measurable distances of the points that constitute the mechanical system. For its definition one needs in addition a system of coordinates, respectively a reference body, in a suitable state of motion. If the state of motion of the system of coordinates is chosen differently, then with respect to these the Newtonian equations of motion will not be valid. In these equations, the environment in which the bodies move appears somehow implicitly as a real factor in the law of motion, alongside the actual bodies themselves and their distances from one another, which ar definable in terms of measuring bodies. In Newton’s science of motion, space has a physical reality, and this is in strict contrast to geometry and kinematics. We are going to call this physical reality, which enters into Newton’s laws of motion alongside the observable ponderable bodies, the “ether of mechanics”. The fact that centrifugal effects arise in a (rotating) body, the material points of which do not change their distances from one another, shows that this ether is not to be supposed a phantasy of the Newtonian theory, but that there corresponds to the concept a certain reality in nature.
We can see that, for Newton, space was a physical reality, in spite of the peculiarly indirect manner in which this reality enters our understanding. Ernst Mach, who was the first person after Newton to subject Newtonian mechanics to a deep and searching analysis, understood this quite clearly. He sought to escape the hypothesis of the “ether of mechanics” by explaining inertia in terms of the immediate interaction between the piece of matter under investigation and all other matter in the universe. This idea is logically possible, but, as a theory involving action-at-a-distance, it does not today merit serious consideration. We therefore have to consider the mechanical ether which Newton called “Absolute Space” as some kind of physical reality. The term “ether”, on the other hand, must not lead us to understand something similar to ponderable matter, as in the physics of the nineteenth century.
If Newton called the space of physics “absolute”, he was thinking of yet another property of that which we call “ether”. Each physical object influences and in general is influenced in turn by others. The latter, however, is not true of the ether of Newtonian mechanics. The inertia-producing property of this ether, in accordance with classical mechanics, is precisely not to be influenced, either by the configuration of matter, or by anything else. For this reason, one may call it “absolute”.
That something real has to be conceived as the cause for the preference of an inertial system over a non-inertial system is a fact that physicists have only come to understand in recent years. Historically, the ether hypothesis, in the present-day form, arose out the mechanical ether hypothesis of optics by way of sublimation. After long and fruitless efforts, one came to the conviction that light could not be explained as the motion of an elastic medium with inertia, that the electromagnetic fields of the Maxwellian theory cannot in general be explained in a mechanical way. Under this burden of failure, the electromagnetic fields were gradually considered as final, irreductible physical realities, which are not to be further explained as states of the ether. The only thing that remained to the ether of the mechanical theory was its definite state of motion. It represented, so to speak, an “absolute rest”. If all inertial systems are on a par in the Newtonian mechanics, therefore also in the Maxwell-Lorentz theory, the state of motion of the preferred frame of coordinates (at rest with respect to the ether) appeared to be fully determined. One tacitly assumed that this preferred system would, at the same time, be an inertial system, i.e. that the principle of inertia would hold in relation to the electromagnetic ether.
There is a second way in which the rising tide of the Maxwell-Lorentz theory shifted further the fundamental concepts of physicists. Once the electromagnetic fields had been conceived of as fundamental, irreductible entities, it seemed they were entitled to rob ponderable inertial mass of its fundamental significance in mechanics. It was concluded from the Maxwell equations that an electrically charged body in motion would be surrounded by a magnetic field the energy of which would, to a first approximation, depend on the square of the velocity. What could be more obvious than to conceive of all kinetic energy as electromagnetic energy? In this wayone could hope to reduce mechanics to electromagnetism, having failed to refer electromagnetic processes back to mechanical ones. This appeared to be all the more promising as it became more and more likely that all ponderable matter was constituted of electrical elementary particles. At the same time, there were two difficulties which one could not master. First, the Maxwell-Lorentz equations could not explain how the electrical charge that constitutes an electrical elementary particle could exist in equilibrium in spite of the electromagnetic forces of repulsion. Second, the electromagnetic theory could not explain gravitation in a reasonably natural and satisfactory manner. In spite of all this, the consequences of the electromagnetic theory were so important that it was considered an utterly secure possession of physics – indeed, as one of its best founded acquisitions.
In this way the Maxwell-Lorentz theory finally influenced our understanding of the theoretical foundations of physics to such an extent that it led to the founding of the special theory of relativity. It was realized that the electromagnetic equations do not in truth determine a particular state of motion, but that, in accordance with these equations – just as in classical mechanics – there is an infinite manifold of coordinate systems, moving uniformly with respect to each other, and all on a par, so long as one applies suitable transformation formulae for the space coordinates and the time. It is well known that this realization brought about a deep modification of kinematics and dynamics as a result. The ether of electrodynamics now no longer had any special or particular state of motion. It had the effect, like the ether of classical mechanics, of giving preference not to a particular state of motion, but only to a particular state of acceleration. Because it was no longer possible to speak of simultaneaous states in different places in the ether in any absolute sense, the ether became, so to speak, four-dimensional, because there was no objective arrangement of its space in accordance with time alone. Also, following the special theory of relativity, the ether was absolute, because its influence on inertia and light propagation was thought to be independent of physical influences of any kind. While in classical physics the geometry of bodies is presumed to be independent of the state of motion, in accordance with the special theory of relativity, the laws of Euclidian geometry for the positioning of these bodies at rest in relationship to one another are applicable only if these bodies are in a state of rest relative to an inertial system. For example, in accordance with the special theory of relativity, the Euclidian geometry does not apply to a system of bodies that are at rest relative to one another, but which in their totality rotate in relation to an inertial system. This can easily be concluded from the so-called Lorentz contraction. Therefore the geometry of bodies is influenced by the ether as well as the dynamics.
The general theory of relativity removes a defect of classical dynamics; in the latter, inertia and weight appear as totally different manifestations, quite independent of one another, in spite of the fact that they are determined by the same body-constant, i.e. the mass. The theory of relativity overcomes this deficiency by determining the dynamical behavior of the electrically neutral mass-point by means of the law of the geodesic line, in which the inertia and weight effects can no longer be distinguished. Thereby it attributes to the ether varying from point to point, the metric and the dynamical properties of the points of matter, which in their turn are determined by physical factors, to wit the distribution of mass or energy respectively. The ether of the general theory of relativity therefore differs from that of classical mechanics or the special theory of relativity respectively, in so far as it is not “absolute”, but is determined in its locally variable properties by ponderable matter. This determination is complete if the universe is closed and spatially finite. The fact that the general theory of relativity has no preferred space-time coordinates which stand in a determinate relation to the metric is more a characteristic of the mathematical form of the theory than of its physical content.
Even the application of the formal apparatus of the general theory of relativity was not able to reduce all mass-inertia to electromagnetic fiels ou fields in general. Furthermore, in my opinion, we have note as yet succeeded in going beyond a superficial integration of the electromagnetic forces into the general scheme of relativity. The metric tensor which determines both gravitational and inertial phenomena on the one hand and the tensor of the electromagnetic field on the other, still appear as fundamentally different expressions of the state of the ether; but their logical independence is probably more to be attributed to the imperfection of our theorical edifice than to a complex structure of reality itself.
I admit that Weyl and Eddington have, by means of a generalization of Riemann geometry, found a mathematical system that allows both types of field to appear as though united under one single point of view. But the simplest field equations that are yielded by that theory do not appear to me to lead to any progress in the understanding of physics. Altogether it would today appear that we are much further away from an understanding of the fundamental laws of electromagnetism than it appeared at the beginning of the century. To support his opinion, I would here like briefly to point out the problem of light quanta, which problem concern, so to speak, the large-scale structure and the fine structure of the electromagnetic field.
Ther earth and the sun have magnetic fields, the orientation and sense of which stand in approximate relationship to the axes of rotation of these heavenly bodies. In accordance with the Maxwell theory these fields could be produced by electrical currents which flow in the opposite direction to the rotational movement around the axes of the heavenly bodies. The sunspots too, which for good reasons are looked upon as vortices, possess analogous and very strong magnetic fields. But it is hard to imagine that, in all these cases, electrical conduction or convection currents of sufficient magnitude are really present. It rather looks as if cyclic movements of neutral masses are producing magnetic fields. The Maxwell theory, neither in its original form, nor as extended by the general theory of relativity, does not allow us to anticipate field generation of this kind. It would appear here that nature is pointing to a fundamental process which is not yet theorically understood.
If we have just dealt with a case where the field theory in its present shape does not appear to be adequate, the facts and ideas that together make up the quantum theory threaten to blow up the edifice of field theory altogether. Indeed, the arguments are growing that the light quantum should be considered a physical reality, and that the electromagnetic field may not be looked upon as an ultimate reality by means of which other physical objects can be explained. The theory of Planck formula has already shown that the transmission of energy and impulse by means of radiation takes place in such a manner as if the latter consisted of atoms moving with the velocity of light c and with the energy h x fréquence nu, and with an impulse h x frequence nu divided by c; by means of experiments on the scattering of X-rays by matter. Compton now shows that scattering events occur in which light quanta collide with electrons and transmit part of their energy to the latter, whereby the light quanta change their energy and direction. So much is factually certain: the X-rays undergo such changes of frequency in their scattering as are required by the quantum hypothesis, as predicted by Debye and Compton.
Furthermore, a paper has recently appeared by the Indian scientist Bose, regarding the derivation of the Planck formula, which is particularly important for our theoretical understanding for the following reason. Hitherto, all derivations of Planck’s formula have somewhere made use of the hypothesis of the undulatory structure of radiation; for example, the factor 8 pi nu²/c3 of this formula, in the well-known derivation of Ehrenfest and Debye, was obtained by counting the number of eigenvibrations of the cavity that occur in the frequency range d (nu). This counting, which ws based on the concepts of the wave theory, is replaced by Bose by a gas-theorical calculation, which he applies to a light quantum situated in the cavity in the manner of a molecule. The question now arises whether it would not one day be possible to connect the diffraction and interference phenomena to quantum theory in such a way that the field-like concepts of the theory would represent only the expressions of the interactions between quanta, whereby no longer would an independent physical reality be ascribed to the field.
The important fact that, according to the theory of Bohr, the frequency of the radiation is not determined by electrical masses that undergo periodical processes of the same frequency can only increase our doubts as to the independent reality of the undulatory field.
But even if these possibilities should mature into genuine theories, we will not be able to do without the ether in theoretical physics, i.e. a continuum which is equipped with physical properties; for the general theory of relativity, whose basic points of view physicists surely will always maintain, excludes direct distant action. But every contiguous action theory presumes continuous fields, and therefore also the existence of an “ether”.
Simon Saunders, Introduction of « The Philosophy of Vacuum » (1991) :
« According to Aristotle, « vacuum » is « the empty »; il is « space breft of body ». What then is “space” and “body”? At once we have two of the central themes of metaphysics : the concept of vacuum is parasitic on the concept of space and the concept of substance. Most important of all, it rests on the distinction between the two… The atomists were surely correct in their basic tenet: in some sense the world is atomistic. Surely, then, in some sense it is possible to distinguish matter from void. What appears undeniable, however, is that in the present state of theorical physics there are many levels to this notion of existence. Certain entities – particles – categorically exist. Others – virtual particles, energy, fluctuations – exist in some sense, perhaps in a relative sense (differences in energy, etc.). Others – negative-energy particles, Rindler quanta, wave-functions – perhaps do not exist. Equally, there are levels to the concept of space : there is the manifold; there is a topology and a differentiable structure; as we add an affine structure and a metric there is a geometry. If the vacuum is the least that exists, where in our catalogue of realities is the least and most simple object ? (…) Empty space, whatever it is, now controls the dynamics of material bodies. It has a dynamic role in the organization of matter, because when we consider electromagnetism, it seems that matter, and functional relationships between particles of matter, are not able to do the job on their own. Of course space, too, may be thought of as an organization principle applied to matter. The vacuum is to causation what space is to geometric relationships. (…) What of the concept of vacuum today ? Relativity and quantum theory respectively define what is to count as space that is “empty”… The vacuum of non-relativistic quantum field theory does not exhibit zero-point fluctuations, in the sense that, there, no linear combinations of the field (or its canonical conjugate) can be considered observables (on pain of violating mass superselection) ; the uncertainety relationships between the fields may be considered purely mathematical and of no physical significance… In relativistic theory the situation is so difficult that on sympathizes with the radical approach, by Basil Hiley and David Finfelstein in particular, to abandon the traditional starting-point of the continuous space-time manifold. Not only have these authors come to a similar conclusion as to what must be abandoned in the conventional theory, but they adopt similar strategies : there must exist an object prior to space – the “pre-space” in the langage of Hiley, “causal networks” according to Finkelstein – and in both cases this object is an algebraic structure. Further, the ideas of Grassman have an important influence… In fact, Hiley and Finkelstein start from diametrically opposed positions; Hiley is concerned with hidden variable theory, Finkelstein with the extension of quantum principles to the most elementary mathematical categories. However, in this enterprise it is Finkelstein who maintains the principle of locality at the fundamental level, for it is built into the concept of a “causal network”… What drives the Finkelstein programme is above of all the demand for locally “finite” theory. (…) It seems that the vacuum need not carry spatial and temporal relationships. Must it be defined in space-time terms at all, even a space-time devoid of metrical structure? Atiyah and Braam make of the vacuum something superficially more simple, because independent of the metric; but the physical structure of space-time is made more complex, because the topology is also subject to quantum law. But is it necessary that the vacuum be associated ar all with the space-time manifold? There is the temptation of a logical retreat, that the concept of “nothingness”, “the empty”, should describe that which is empty of space and time, along with all other physical objects. Indeed, this is just the possibility offered by a closed universe; “absolute nothingness” is what is not in the universe, it is what has no physical properties whatsoever. (…) The sources of the fields of forces may perhaps be topological structures, but to date no such theory can claim a shred of empirical success (written in 1991). Ian Aitchinson, in contrast begins from the phenomenogical theory, that is the standard model, and with the fundamental distinction between force and matter. In the article “The Vacuum and Unification”, we see the vacuum in all its splendor. The coherence and variety of phenomena and concepts presently exploited in the standard model are deeplay impressive. The vacuum that emerges is rich; by turns a ferromagnet, a dielectric, a superconductor, and a thermodynamic phase. Increasingly, this vacuum is reminiscent of ether. Indeed, Aitchinsons is happy to draw parallels between the ether of the nineteenth century and the grand unified vacuum. (…) The analysis of the zero-point fluctuation due to Sciama in the article “The Physical Significance of the Vacuum Field” also demonstrates a methodology. These fluctuations provide a powerful heuristic, and even if many of the phenomena described by Sciama can be interpreted in other ways, they are seldom more simply or intuitively described. Further, the zero-point fluctuations, unlike the non-zero vacuum expectation values of the Higgs and Goldstone fields considered by Aitchinson, seem to follow from basic principles of quantum theory. But as Sciama makes clear, the cosmological implications are all the more pressing ; if the fluctuations are a reality, then so too is their associated energy density. But this energy density is infinite. It does not seem possible to eliminate this difficulty by appeal to the conventional philosophy of renormalization, where the discarded infinities are considered a symptom of the incompleteness of the theory. I have emphasized a difficulty of Sciama’s approach, let me also mention an important success. The existence of a non-zero particle distribution in the Minkowski vacuum, as described by an accelerating observer in an “appropriate” coordinate system, is a remarkable and disturbing feature of relativistic quantum theory. Must we conclude that the concept of particle is observer-dependent ? What of the energy associated whith such a particle distribution ? Unruh’s idealized model of an accelerating particle detector shows further that such particles (the so-called Rindler quanta) should be experimentally detectable. (…)”
“The Negative-Energy Sea”», Simon Saunders :
“In elementary quantum mechanics the vacuum is very simple; it is the quantum analogue of the Newtonian vacuum. In the vacuum not only are there no particles, but there is no theory. There is no Hilbert space, there is no time evolution, one cannot write dowen equations for this vacuum. The vacuum concept (as distinct from the concepts of space and time) can be described only informally. We have the same situation in classical particle mechanics. But in quantum field theory (also in continuum mechanics and classical field theory), the vacuum is modelled in the mathematics.) The idea of “vacuum” is relativized to the observable content of the theory, be it states of a medium, excitations of a field, or particle number. In quantum electrodynamics, despite the field aspect, the vacuum is defined not as the zero-valued fields (there is no state in which all the fields have eigenvalue zero), still less as a zero-valued wave function (which is not even a state), but rather in terms of the absence of any particles. The canonical vacuum is the state of emptiness. It might seem that this concept of vacuum is essentially unique, and almost as simple as in the elementary theory. Every particle observable has the value zero with probability one. Nevertheless, there are self-adjoint operators for which this is not the case, for example certain combinations of the quantum fields. From the point of view of these operators, the vacuum is not at all trivial. Properties of the vacuum picked out in this way may still be interpreted in particulate terms (almost entirely, in perturbation theory), and there is a direct connection with the picture of the quantum field as collection of harmonic oscillators (zero-point energy); but it seems to me that a more immediate problem is to understand why such operators arise in particle mechanics in the first place. In particular, one wants to understand how in the Dirac theory even well defined particle observables are required to have vacuum expectation values that are non-zero (and in fact infinite). There is a more general problem. As I have indicated, the Dirac vacuum brings in its wake the concepts of antimatter and pair creation and annihilation processes. These transform the quantum theory into an edifice of remarkable phenomenogical expressiveness and real mathematical complexity.”
“The Physical Significance of the Vacuum State of a Quantum Field”, D.W. Sciama :
“ Even in its ground state, a quantum system possesses fluctuations and an associated zero-point energy, since otherwise the uncertainty principle would be violated. In particular, the vacuum state of a quantum field has these properties. For example, the electric and magnetic fields of the electromagnetic vacuum are fluctuating quantities. This leads to a kind of reintroduction of the ether, since some physical systems interacting with the vacuum can detect the existence of its fluctuations. However, this ether is Lorentz-invariant, so there is no contradiction with special relativity… Since then, zero-point effects have become commonplace in quantum physics, for example in spectroscopy, in chemical reactions, and in solid-state physics. Perhaps the most dramatic example is their role in maintaining helium in the liquid state under its own vapour pressure at absolute zero. The zero-point motion of the atoms keep them sufficiently far apart on average so that the attractive forces between them are tooweak to cause solidification… Usually the boundary conditions associated with a physical system limit the range of normal modes that contribute to the ground state of the system and so to the zero-point energy. A trivial example is a harmonic oscillator, with corresponds to a single normal mode of frequency ν and so to a zero point energy 1/2hν. In more complicated cases the range of normal modes may depend on the configuration of the system. This would lead to a dependence of the ground-state energy on the variables defining the configuration and so, by the principle of virtual work, to the presence of an associated set of forces. One important example of such a force is the homopolar binding between two hydrogen atoms when their electron spins are antiparallel (Hellman 1927). When the protons are close together, each electron can occupy the volume around either proton. The resulting increase in the uncertainty of the electron’s position leads leads to a decrease in its zero-point energy. Thus, there is a binding energy associated with this diatomic configuration, and the resulting attractive force is responsible for the formation of the hydrogen molecule. By contrast, when the electron spins are parallel, the Pauli exclusion principle operates to limit the volume accessible to each electron. In this case the effective force is repulsive. More relevant to the present paper is the force that arises when some of the normal modes of a zero rest-mass field such as the electromagnetic field are excluded by boundary conditions on the conductors ensure that normal modes whose wavelength exceeds the spacing of the conductors are excluded. If now the conductors are moved slightly apart, new normal modes are permitted and the zero-point energy is increased. Work must be done to achieve this energy increase, and so there must be an attractive force between the plates. This force has been measured, and the zero-point calculation verified… The Casimir effect show that finite differences between configurations of infinite energy do have physical reality. Another example of this principle for zero-point effects is the Lamb shift… An electron, wether bound or free, is always subject to the stochastic forces produced by the zero-point fluctuations of the electromagnetic field, and as result executes a Brownian motion. The kinetic energy associated with this motion is infinite, because of the infinite energy in the high-frequency components of the zero-point fluctuations. This infinity in the kinetic energy can be removed by renormalizing the mass of the electron (Weisskopf 1949). As with the Casimir effect, physical significance can be given to this process in situations where one is dealing with different states of the system for which the difference in the total renormalized Brownian energy (kinetic plus potential) is finite. An example of this situation is the famous Lamb shift between the energies of s and p electrons in the hydrogen atom; according to Dirac theory, the energy levels should be degenerate. Welton (1948) pointed out that a large part of this shift can be attributed to the effects of the induced Brownian motion of the electron, which alters the mean Coulomb potential energy. This change in electron energy is itself different for an s and p electron, and so the Dirac degeneracy is split. This theoretical effect has been well verified by the observations. One can also regard the Lamb shift as the change in zero-point energy arising from the dielectric effect of introducing a dilute distribution of hydrogen atoms into the vacuum. The frequency of each mode is simply modified by a refractive index factor (Feynman, 1961).”
“Theory of Vacuum”, David Finkelstein :
“Today the vacuum is recognized as a rich physical medium, subject to phase transitions, its symmetry broken by non-vanishing vacuum values for several important fields akin to the permanent magnetization of a ferromagnet, and supporting the emission, propagation, and absorption of particles. A general theory of the vacuum is thus a theory of everything, a universal theory… The most workable theories of the vacuum today are quantum field theories. In these the vacuum serves as the law of nature, as reviewed below. The structure of the vacuum is the central problem of physics today; the fusion of the theories of gravity and the quatum is a subproblem… The next bridgehead is a dynamical topology, in which even the local topological structure is not constant but variable… The chasm between h and c is the key problem of physics today. There may be no further need to unify quantum theory and gravity if gravity and inertia are already macroscopic quantum effects. This suggestion evolves from a growing list of parallels between the stories of relativity and quantum theory which I have used in teaching them in recent decades : - each of these two theories has its own new fundamental constant (h and c) and a correspondence principle recovering the old physics in the transition to a singular limit (h->0, c->∞), each is fundamentally epistemological, in that it sets a universal limitation upon the i/o processes that link us with our experimental systems (h limiting the derterminacy of these processes, c the signal speed). In each singular limit, basically non-commutative processes becom commutative (p and x determinations for h->0, boosts for c->∞). The novel non-commutativity is expressed by a pair paradox (the two slits, the two twins). Each constant links time t to another fundamental physical variable (energy E for h, space x for c), so that the new theory is conceptually more unified than the old in an unanticipated way (clocks then defining energies and distances respectively). Each theory extends the principle of relativity to a wider class of transformation and a richer class of experimenters (Dirac’s quantum transformation theory, Einstein’s special relativity). Each is expressible completely as the theory of a transfer relation for i/o experiments (the allowed transition of quantum theory, the causal relation of special relativity). The signals that one uses operationally to define the space-time points and causal relations of relativity are actually ensembles of quanta.It is not difficult to extend this parallel from h to c to Biltzmann’s constant k, with quantum theory, space-time theory, and thermodynamics appearing as successively courser statistical descriptions of the same processes. This suggests that space-time vectors and ψ. We may call the respective inverse processes (going fron macroscopic theory to quantum) coherent and incoherent quantization, according as they start from experiences with or without quantum phase data.”
Topology of the Vacuum”, Michael Atiyah :
“ Quantum theory requires us to modify our physical ideas in profound ways, and we must inevitably start by re-examining the classical vacuum. Quantum field theory attempts to deal with the classical force-fields in a quantum-mechanical way, and the “quantum vacuum” that emerges from this theory is a complex and mysterious structure which stretches mathematics to its utmost limits. Quantum fields fluctuate and convert themselves into particles in a bewildering manner, indicating in particular the fact that the conventional separation between force and matter cannot be maintained. A genuine quatum vacuum should therefore be devoid of both matter and fields of force. There should be no particles and no geometric distortion of space-time. This ultimate vacuum might appear so empty of features as to be mathematically trivial and misleading conclusion. This quantum vacuum does indeed have interesting geometrical features, but these relate not to the traditional geometry of Euclid, Riemann, etc., involving measurement, but to that modern branch of the subject known as topology, which is concerned with qualitative properties of space. Unlike measurement, which can be conducted on a small local scale, topolical features are visible only on a “global” scale. This relation between topology and the quantum vacuum has been recognized only quite recently, and its full implications are just now being explored. It is still too early to predict how this will alter our understanding of the universe, but it is clear that we have reached a deeper level in the dialogue between mathematics and physics… A fundamental experiment, first suggested by Bohm and Aharonov, consists in sending a beam of electrons round a solenoid carrying a magnetic flux (Aharonov, 1986). The experiment shows that the electrons exhibit interference patterns, depending on the strength of the magnetic flux. Thus, the electrons are physically affected by the magnetic field even though the field lies entirely inside the solenoid and the electrons travel in the exterior region. This Bohm-Aharonov effect therefore shows that, even in a force-free region, there are physical effects. These effects are quantum-mechanical, since they are physical effects. These effects are quantum-mechanical, since they correspond to phase shifts in the wave function of the electron, and they have a topological origin since the force-free region has a cylindrical hole in it. This exhibits clearly the basic relation between quantum theory and topology, particularly in relation to notions of the vacuum. Topology may be roughly defined as the study of “holes” and related phenomena. The size of a hole and its exact location is irrelevant in topology… Going beyond the single cylindral hole or flux tube of the Bohm-Aharonov experiment, we can consider a complicated knotted configuration of tubes. The study and classification of such knots is a typical and difficult problem in topology. The more elaborate the knot, the more intricate is the structure of the external vacuum… These developpements strongly suggest that topological aspects of 3-dimensional space, as manifested by knots, should play some fundamental role in quantum physics.”
“The Vacuum and Unification”, I.J.R. Aitchison (1991) :
« It is common observationthat fundamental physics seems to have progressed, over the last hundred years or more, in the direction of ever greater unification. It is fait to describe this movement as progress, because it does appear that the drive towards unification has, in many diverse ways, acted as a powerful heuristic device in constructing phenomenologically successful theories. Less widely noted, perhaps, is the crucial role that the “vacuum” (as currently understood) has played, and still plays, in many aspects of the unification programme. This is what I want to examine, very briefly, in the present contribution. (…) Although the vacuum state is (normally) one in which the average value of all quantum fields is zero, the mean square values of the field are in general not zero: that is, there are fluctuations – and this is true even at absolute zero. These fluctuations are observable: those in the electromagnetic field account for most of the Lamb shift, in hydrogen, while those in charged-particle (matter) fields give rise to the phenomenon of “vacuum polarization” which accounts for a further contribution (small in hydrogen, but large in muonic helium) to the Lamb shift. In quantum electrodynamics, the effect of the vacuum is partially to sreen a test charge at distances of h/mc, where m is the mass of electron. In other words, at distances smaller than the size (4x10-13 m) the effective electric charge on a test body will appeare to increase. This is the usual effect of polarization in all normal dipolar media (including, in this respect, the vacuum of quantum electrodynamics (QED)). A major surprise was the discovery by Gross and Wilczek (1973) and Politzer (1973) that in non-Abelian gauge theories (such as those now believed to describe the strong and weak interactions of quarks and leptons) vacuum polarization produces a net “anti-screening” effect: the effective strong and weak “charges” decrease at small interparticle separation. It is conventional to discuss this phenomenon in terms of “fine-structure constants” α, α3, and αn, for the electromagnetic, strong, and weak interactions, respectively. (…) The field (or fields) that have a non-zero vacuum value are called generically Higgs fields, after P.W. Higgs, one of the originators of this mechanism (Higgs 1964) whereby normally massless quanta acquire mass. (…) There is actually nothing inherently unreasonable in the idea that the state of minimum energy (the vacuum) may be one in which some field quantity has non-zero average value. Plenty of condensed matter physics examples exist which display this feature – for example, the ferromagnet below its transition temperature, where there is a net alignment of the atomic spins. However, it remains a conjecture that something like this actually happens in the weak interaction case; at present, no dynamical basis for the Higgs mechanism exists, and it is purely phenomenological.”
“Vacuum or Holomovement”, B.J. Hiley (1991) :
“ Quantizing the gravitational field presents some formidable problems. The deep link between gravity and space-time implies that, if quantization is to be successfully carried out, then radical changes in our understanding of space-time will be needed. In this paper I will explore some new ideas about space-time that can be motivated through a purely algebraic approach to quantum mechanics and which call into question the notion of absolute locality. In order to bring out these ideas, a brief review of the classical and quantum notions of the vacuum, particularly in their relation to our understanding of space-time structure, is first presented. (…) The history of the vacuum has had, in my view, a rather curious evolution. Throughout history, opinions as to its nature seem to swing from one extreme to the other. It has been considered at times to be “full” or substantive, while at other times it has been treated as “empty” or void. Even from the earliest days, there has been little agreement. For instance, Parmenides argued that “emptiness is nothingness, ans that which is nothing cannot be”. To him the vacuum had to be compact plenum which he regarded as being constituted as one continuous unchanging whole. And its logic alone that forced him to the conclusion that movement is mere illusion. But surely, movement is more than just illusion. Material substance is perceived as constantly changing, some changes being rapid, others being extremely slow. Is this not more naturally explained by the Democritian atoms moving from one region of space to another not already occupied by other atoms, i.e. into empty regions? Therefore, to conceive of movement of substantive entities, must we not surely have an empry vacuum? This notion of a void, of the empty vacuum, provided the backcloth for the development of Newtonian physics. Strenghthened by the differential calculus, particle mechanics grew from the primitive concepts supplied by Democritus and extended qualitatively by Lucrecius. Particle-in-motion would provide a mechanical explanation of all physical process. Even light, in Newton’s view, was particulate in nature, with “corpuscules” moving through the vacuum, sometimes being reflected and sometimes being transmitted when they reached a transparent boundary. However, their predicted behaviour once they entered the medium was not supported by experiment, and it was wave theory that ultimately triumphed with its simpler explanations of interference and diffraction. The corpuscular theory was abandoned until the event of the quantum theory. But how could a wave be sustained in “empty space”? Surely, all our experience of wave phenomena was mechanical in origin and required a medium in which the vibrations could be sustained. The mechanical ethos had become so deeply ingrained that an explanation of electromagnetic fields in terms of vibrations in some kind of substantive ether was strongly advocated. Thus a plenum-like vacuum was reintroduced, and by the end of the nineteenth century it became fashionable to take this ether very seriously, and to seek an explanation of the ultimate source of all physical phenomena, including the atoms themselves, in terms of structures or invariant features of the plenum itself (such as vortices). It was the failure to detect any movement of the earth relative to this Maxwellian plenum that began to raise serious doubts about the existence of such a “substance”. Not only had experiments like those of Michelson and Morley failed to detect any such movement through the ether, but the very structure of the special theory of relativity made it appear that any attempt to look for such an ether was doomed to failure. The seemingly inevitable conclusion appeared to be that the vacuum is “really empty”, a notion that has dominated the more recent developments in physics. The reaction against the reintroduction of such an ether or plenum has been so strong that any theory that dared to call on such a notion was for a time deemed to be unacceptable and preposterous. In the 1960s and 1970s I often came across such a reaction when I tried to discuss de Broglie’s use of a “sub-quantum medium” as a means of providing a possible explanation of the quantum formalism. The objection was not so much against the attempt to find a more physically intuitive explanation of quantum phenomenon, but rather against the introduction of the “sub-quantum medium”. The retort, “Surely Einstein has shown us that the vacuum is “empty” and the reintroduction of such an outmoded way of thought will not provide a satisfactory understanding of phenomena”, was not uncommon. Yet in relativistic quantum field teory the notion of “vacuum polarization” had already emerged and was being used quite freely, albeit in a very formal way. But it is necessary to evoke quantum field theory, Einstein (1924) himself did not react so strongly against the notion of an ether. What he questioned was the need to interpret Maxwell’s equations “mechanically”, i.e. in terms of vibrations of a plenum-like substance. Was it necessary to regard the notion of field as an attribute of substance, or could it be regarded as something in its own right? Einstein (1969) argued that Maxwell’s equations successfully accounted for a large number of phenomena and that was not necessary to interpret the field quantities in terms of any deeper structure. Nothing was to be gained by trying to interpret these fields in terms of an underlying substance, as demanded by the mechanical approacha; Newtonian mechanics was clearly limited, so why continue to use an outmoded conceptual form? Let the continuous field be regarded as an entity in its own right. Of course, it would now be possible to take the electromagnetic field as an ether and attempt to account for all the properties of field as an ether and attempt to account for all the properties of matter in terms of his field alone. Indeed, many efforts were made in this direction. However, there were processes that were clearly not electromagnetic in origin. Gravity was one of the more obvious examples, and it soon became evident that something more was needed. Einstein was the first to realize that the electromagnetic field contained a further limitation, namely, that Maxwell’s equations are invariant only in special frames of reference, the inertial frames. (…) To Einstein (1924), terms like “the gravitational field”, “the structure of space-time”, and “the ether” were all synonymous. (…) Now returning to general relativity, it should be rembered that Einstein (1969) himself did not regard the theory as expressed through the field equations to be complete. (…) Einstein wanted to regard the particle itself as a concentration of field energy or, perhaps, even a singularity in the gravitational field so that gravity, particles, and, of course, electromagnetism could be described by one single field, the “unified field”.”
“Theory of Vacuum”, David Finkelstein (1991) :
“Today the vacuum is recognized as a rich physical medium, subject to phase transitions, its symmetry broken by non-vanishing vacuum values for several important fields akin to the permanent magnetization of a ferromagnet, and supporting the emission, propagation, and absorption of particles. A general theory of the vacuum is thus a theory of everything, a universal theory. It would be appropriate to call the vacuum “ether” once again, as long as we remember its local Lorentz invariance. The most workable theories of the vacuum today are quantum field theories. In these the vacuum serves as the law of nature, as reviewed below. The structure of the vacuum is the central problem of physics today; the fusion of the theories of gravity and the quantum is a subproblem. Here I develop a quantum-space-time description of the vacuum. Einstein considered such a programme in the 1930s:
“To be sure, it has been pointed out that the introduction of a space-time continuum may be considered as contrary to nature in view of the molecular structure of everything which happens on a small scale. It is maintained that perhaps the success of the Heisenberg method points to a purely algebraic method of description of nature, that is to the elimination of continuous functions from physics. Then, however, we must also give up, by principle, the space-time continuum. It is not unimaginable that human ingenuity will some day find methods which will make it possible to proceed along such a path. At the present time, however, such a program looks like an attempt to breathe in empty space.” (Einstein, 1936)