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# Quantum Field Theory - Science topic

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Is it finally time for mainstream physics to acknowledge that the quantum fluctuations of Quantum Field Theory, which superseded the Dirac Sea, is the medium for the propagation of light, and that it is therefore one and the same thing as the luminiferous aether of the nineteenth century?
Frederick David Tombe : Unfortunately, I have no idea which year and who first proposed the QFT notion of the bubbling fluids of the quantum vacuum.
But to my knowledge, I was the first (and still the only one!) who proposed the idea of virtual matter-antimatter particle pairs popping in and out of existence in the quantum vacuum in an article - 2001, which was sent to Professors Halton (Chip) Arp and J.V. Narlikar to contest their idea of (Narlikar-Hoyle) "variable mass" theory (infant atoms with low atomic energy levels as the initial phase of the ejected quasars with high red-shift, slowly growing to "adulthood" to low redshift in time) as the origin of the mass of the quasars. Chip Arp initially rejected my idea as absurd; but after many long e-mail exchanges, Chip (the only one) finally accepted my idea and approved my first two publication, 1. "Cosmic Gamma Ray Halo" (2003) and 2. "Ambartsumian, Arp and the Breeding Galaxies" (2005). My idea about quasars ejection energy was thoroughly discussed with Chip Arp in late 2008 in a meeting in Munich, when Chip and his astronomer wife were in the Max-Planck Institute, at Garching. Unfortunately, Chip soon fell ill with serious disability; sometimes after our meeting and passed away in December 2013; without writing a promised Foreword for my book, "The Dialectical Universe." My other publications and books on this idea soon followed. The philosophical basis of this idea was elaborated in my article "Philosophy of Space-Time - Whence Cometh Matter and Motion? A book of the same title appeared later.
In RG, I think I first discussed this issue in August 2018 in the following forum. Dr. Christian Baumgarten and many others hotly rejected my views:
The idea of the Virtual Particles of the quantum vacuum forms the basis of my dialectical view of the universe from the microcosm to the macrocosm; as is expressed in the soon to be published book, "Dialectics Not Metaphysics of Nature - From the Quantum to the Cosmic".
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Dear Sirs,
I did not find an answer to this question in Internet for both quasi-relativistic and relativistic case. I would be grateful if you give any article references.
As I think the answer may be yes due to the following simplest consideration. Suppose for simplicity we have a quasi relativistic particle, say electron or even W boson - carrier of weak interaction. Let us suppose we can approximately describe the particle state by Schrodinger equation for sufficiently low velocity of particle comparing to light velocity. A virtual particle has the following properties. An energy and momentum of virtual particle do not satisfy the well known relativistic energy-momentum relation E^2=m^2*c^4+p^2*c^2. It may be explained by that an energy and a momentum of the virtual particle can change their values according to the uncertainty relation for momentum and position and to the uncertainty relation for energy and time. Moreover because of the fact that the virtual particle energy value is limited by the uncertainty relation we can not observe the virtual particle in the experiment (experimental error will be more or equal to the virtual particle energy).
In the Everett's multi-worlds interpretation a wave function is not a probability, it is a real field existing at any time instant. Therefore wave function of wave packet of W boson really exists in the Universe. So real quasi relativistic W boson can be simultaneously located in many different space points, has simultaneously many different momentum and energy values. One sees that a difference between real W boson and virtual W boson is absent.
Is the above oversimplified consideration correct? Is it possible to make any conclusion for ultra relativistic virtual particle? I would be grateful to hear your advises.
A virtual particle is a particle, whose energy-momentum relation doesn’t correspond to that of a real particle.
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Science has many unsatisfactory explanations about dreams. Has anyone used quantum field theory to explain dreams? Is there any relation between dream mapping and neuron electric field?
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Dear Sirs,
In the below I give some very dubious speculations and recent theoretical articles about the question. Maybe they promote some discussion.
1.) One can suppose that every part of our reality should be explained by some physical laws. Particularly general relativity showed that even space and time are curved and governed by physical laws. But the physical laws themself is also a part of reality. Of course, one can say that every physical theory can only approximately describe a reality. But let me suppose that there are physical laws in nature which describe the universe with zero error. So then the question arises. Are the physical laws (as an information) some special kind of matter described by some more general laws? May the physical law as an information transform to an energy and mass?
2.) Besides of the above logical approach one can come to the same question by another way. Let us considers a transition from macroscopic world to atomic scale. It is well known that in quantum mechanics some physical information or some physical laws dissapear. For example a free paricle has a momentum but it has not a position. Magnetic moment of nucleus has a projection on the external magnetic field direction but the transverse projection does not exist. So we can not talk that nuclear magnetic moment is moving around the external magnetic field like an compass arror in the Earth magnetic field. The similar consideration can be made for a spin of elementary particle.
One can hypothesize that if an information is equivalent to some very small mass or energy (e. g. as shown in the next item) then it maybe so that some information or physical laws are lossed e.g. for an electron having extremely low mass. This conjecture agrees with the fact that objects having mass much more than proton's one are described by classical Newton's physics.
But one can express an objection to the above view that a photon has not a rest mass and, e.g. rest neutrino mass is extremely small. Despite of it they have a spin and momentum as an electron. This spin and momentum information is not lost. Moreover the photon energy for long EM waves is extremely low, much less then 1 eV, while the electron rest energy is about 0.5 MeV. These facts contradict to a conjecture that an information transforms into energy or mass.
But there is possibly a solution to the above problem. Photon moves with light speed (neutrino speed is very near to light speed) that is why the physical information cannot be detatched and go away from photon (information distribution speed is light speed).
3.) Searching the internet I have found recent articles by Melvin M. Vopson
which propose mass-energy-information equivalence principle and its experimental verification. As far as I know this experimental verification has not yet be done.
I would be grateful to hear your view on this subject.
Information isn't a special kind of matter-it's a property of any kind of matter, that describes the state matter is found in.
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An electron is usually described as being a “point particle”. Collision experiments are interpreted as indicating an electron must be smaller than about 10-18 m. However, this size is incompatible with an electron also having physical angular momentum of ħ/2. An electron would need a radius of about 2 x 10-13 m and be rotating at the speed of light to have ħ/2 physical angular momentum. This conundrum forces physicists to postulate there must be an “intrinsic” form of angular momentum that does not involve rotation. However, the Einstein-de Haas experiment proves that reversing an electron’s spin with a magnetic field imparts physical angular momentum to a ferromagnetic rod. Do you believe there really is an “intrinsic” form of angular momentum that can be converted to physical rotation of an iron rod when an electron’s spin is reversed?
The alternative explanation is that experiments that attempt to measure an electron’s size have been misinterpreted. For example, if an electron’s electric field is considered a fundamental part of the electron’s structure, then it is ridiculous to ignore the fact that an electron’s energy is distributed over a much larger volume than 10-18 m radius. In fact, an electron’s classical radius of 2.8 x 10-15 m is the size where 100% of an electron’s energy would be in its electric field. A sphere with radius of 10-18 m and charge e would have more than 2,000 times too much electric field energy. The solution I have proposed incorporates an electron model that is a rotating quantized wave with a mathematical radius of 3.86 x 10-13m. What is your solution to the electron’s spin problem?
Taking the idea of Dirac as inspiration yields the following visualization: https://www.motionmountain.net/research.html#qed
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It might be a stupid question to ask, but is it possible to change the strength of the vacuum fluctuation locally, i.e. create an area in which the local density of virtual particles is lower than in other areas? Specifically I think of QED and a certain resonator in which all the supported ground state wavefunctions have a "hole" (= vanishing wave function) in the middle of the resonator (is that even possible due to completness constraint of the wavefunctions?). As per my understanding this would imply lower vacuum fluctuations in that "hole".
My physical intuition tells me that such a device is impossible, because vacuum fluctuation are very fundamental linked with the Heisenberg uncertainty principle and because of "homogenity" of spacetime (at least in the framework of flat space time, ignoring Unruh-effect etc.). However, I do not have any good explanation yet, which rules out the resonator I described above. An inhomogeneity in the vacuum fluctuations could be measured immediately, for example via the lifetimes of elementary particles.
I really look forward to references, opinions and suggestions on this topic.
Dear Philip Rübeling,
what you adress is possible, and is described in theories of Cavity QED.
See, for example, the book "Introduction to Quantum Optics - From a Semi-classical Approach to Quantized Light" from Grynberg, Aspect, and Fabre, Complement 6B Cavity quantum electrodynamics.
Kind regards
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The following Binary Physics project challenges your knowledge about quantum mechanics, quantum field theory, gravity, astronomy, Dark Matter, Dark Energy, Elementary Particles, forces, etc:
Published version:
If you can't understand it, do you really think that you are a good thinker who can think outside the box to verify the reality of something?
Hans Gennow, thanks. However, I used a simple binary equation to calculate the origin of the first universe. And it made the smallest (Plack scale) universe that the smallest elementary particles. And it could be a large universe with the expansion of the universe.
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1) Can the existence of an aether be compatible with local Lorentz invariance?
2) Can classical rigid bodies in translation be studied in this framework?
By changing the synchronization condition of the clocks of inertial frames, the answer to 1) and 2) seems to be affirmative. This synchronization clearly violates global Lorentz symmetry but it preserves Lorenzt symmetry in the vecinity of each point of the flat spacetime.
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We may consider the time of a clock placed at an arbitrary coordinate x to be t and the time of a clock placed at an arbitrary coordinate xP to be tP. Let the offset (t – tP) between the two clocks be:
1) (t – tP) = v (x - xP)/c2
where (t-tP) is the so-called Sagnac correction. If we insert 1) into the time-like component of the Lorentz transformation T = g (t - vx/c2) we get:
2) T = g (tP - vxP/c2)
On the other hand, if we consider the space-like component of the Lorentz transformation X = g(x-vt) we know that the origin of both frames coincide x =X = 0 at t = 0. If we want x = X = 0 at tP = 0 we have to write:
3) X = g(x - vtP)
Assuming that both clocks are placed at the same point x = xP equations 2)3) become:
4) X = g (xP - vtP)
5) T = g (tP - vxP/c2)
which is the local Lorentz transformation for an event happening at point P. On the other hand , if the distance between x and xP is different from 0 and xP is placed at the origin of coordinates, we may insert xP = 0 into 2)3) to get:
6) X = g (x - vtP)
7) T = g tP
which is a change of coordinates that it:
- Is compatible with GPS simultaneity.
- Is compatible with the Sagnac effect. This effect can be explained in a very straightfordward manner without the need of using GR or the Langevin coordinates.
- Is compatible with the existence of relativistic extended rigid bodies in translation using the classical definition of rigidity instead of the Born´s definition.
- Can be applied to solve the 2 problems of the preprint below.
- Is compatible with all experimenat corroborations of SR: aberration of light, Ives -Stilwell experiment, Hafele-Keating experiment, ...
Thus, we may conclude that, considering the synchronization condition 1):
a) We get Lorentz invariance at each point of flat space-time (eqs. 4-5) when we use a unique single clock.
b) The Lorentz invariance is broken out when we use two clocks to measure time intervals for long displacements (eqs. 6-7).
c) We need to consider the frame with respect to which we must define the velocity v of the synchronization condition (eq 1). This frame has v = 0 and it plays the role of an absolute preferred frame.
a)b)c) suggest that the Thomas precession is a local effect that cannot manifest for long displacements.
Cameron Rebigsol I understand your world view and Sir Isaac Newton would have agreed with you. Newton explained gravity and made the connection between the gravity on Earth (e.g. the falling apple) and the motion of the moon. He worked out that it would all be explained by an inverse square law of distance. Even Newton was a bit puzzled about how this "action at a distance" worked.
James Clerk Maxwell pointed out that this "action at a distance" was not a good explanation and felt that there had to be some mechanism through the medium to produce electromagnetism and gravity.
I agree with the viewpoint of Maxwell and I do take as my starting assumption that General Relativity is completely correct as there is sufficient evidence for this. Then the question of "action at a distance" is resolved because it is the state of the medium (i.e. spacetime) which is the underlying cause of the gravitational and electromagnetic forces.
Richard
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Please, see the attached file RPVM.pdf. Any comment will be wellcome.
More on this subject at:
I think that an interesting point is that, using units with c = 1, the 4-velocity (dt,dx,0,0) is a 1-tensor that is the same for any offset of clocks of the inertial frame. Then we have that the 4-velocity (dt,dx,0,0) transforms the same for any synchronization, it satisfies the Einstein addition of velocities and consequently it also satisfies the principle of constancy of speed of light. On the other hand, as it behaves like a tensor under Lorentz transformations, the relativity principle holds for it an for all derived 1-tensors like velocity, acceleration and so on.
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You can find the wording in the attached file PR1-v3.pdf. Any comment will be wellcome.
More on this topic at:
I think that an interesting point is that, using units with c = 1, the 4-velocity (dt,dx,0,0) is a 1-tensor that is the same for any offset of clocks of the inertial frame. Then we have that the 4-velocity (dt,dx,0,0) transforms the same for any synchronization, it satisfies the Einstein addition of velocities and consequently it also satisfies the principle of constancy of speed of light. On the other hand, as it behaves like a tensor under Lorentz transformations, the relativity principle holds for it an for all derived 1-tensors like velocity, acceleration and so on.
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Ordering the Yukawa couplings from bigger to smaller, they follow a clear exponential relationship. Is there a reason for it?
Manuel Urueña Palomo As mentioned the Yukawa couplings are independent variables, at the classical level. Quantum fluctuations lead to a dependence on the scale. This paper might be useful: https://arxiv.org/abs/1403.3058.pdf
This dependence is expressed by differential equations. Now it's possible to impose a particular relation between the couplings at some scale-for instance exponential, in the example at hand-and then use the equations to check whether this relation holds as the scale varies. Such relations can be, in turn, deduced by studying the symmetries of the system of differential equations.
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As we know Higgs field gives mass to subatomic particles fermions like electrons, quarks etc. Even Higgs boson has mass because it interect with Higgs field. My question is like photons why do Neutrinos do not interect with Higgs field? Its mass is zero like photons if that so can Neutrinos travels like that of speed of light?
Neutrinos are the only elementary particles that don't interact with the Higgs field. The process by which they acquire mass is different.
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Could this be the wave collapse in a quantized field with a dynamic curvature of expansion and attraction? This is a mathematical simulation of a quantum superposition field through moiré patterns, but one can also find the single moiré pattern in an experiment. For this purpose, a photon field is quantized a million times, instead of photons being quantized by a two-slit experiment.
Hadi Jabbar Alagealy The first document is a mathematical simulation of a field, but one can find the single pattern also in a physical experiment. Instead of the double-slit experiment, no single photons are quantized by 2 slits, but a photon field is quantized millions of times. I have added the result of the experiment to the appendix.
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An electron exhibits wave properties in some experiments and point particle properties in other experiments. This is designated “wave-particle duality”, but these are contradictory words. A wave has a wavelength and has energy distributed over a volume. A point particle has virtually no volume and energy concentrated at a point. Therefore, these contradictory properties cannot be equal parts of a single model. The electron model often associated with the Copenhagen interpretation of quantum mechanics is a point particle that achieves an electron’s wave-like probability distribution by discontinuous jumps. This is an example of a particle dominated model that is not fundamentally a wave.
Quantum field theory describes an electron as an “excitation” of the electron field. Such an excitation is sometimes illustrated as a localized wave oscillation on a sea of harmonic oscillators. This model is more wave dominated. The particle properties are achieved by the “collapse of the wave function” to deposit an electron’s properties (spin, charge, momentum, etc.) at a point when the wave-based electron is “observed”.
These are just incomplete examples to encourage discussion. What mental picture do you have of an electron? Does your model also address an electron’s electric/magnetic field that is distributed over a relatively large volume? Is the human intellect capable of conceptually understanding an electron?
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I am familiar with elementary quantum mechanics which is a non-relativistic treatment of a single particle interacting with a given potential energy function produced by a fixed (given) environment. I don't understand quantum field theory and searched for a book with a title like "Quantum Field Theory for Dummies". The closest thing that I could find to that is 300 pages long. I have a question that maybe has a quick answer that can be given without reading 300 pages (I am trying to learn a lot of things so quick answers are appreciated if possible). My understanding from the first few chapters of that book is that what was a wave function in elementary quantum mechanics becomes an operator in quantum field theory. The operator is a function of time and space coordinates so there is a different operator for each space-time point. What I don't understand, even after reading a few chapters, is what that operator operates on. In elementary quantum mechanics, operators operate on elements (state vectors) of a vector space (a Hilbert space) and I know the mathematical significance of these elements (state vectors) that the operators operate on. I have no idea of what the entities are that the quantum field theory operators operate on. Can this be explained to a person with my level of education in a few paragraphs?
Dear Dr. L.D. Edmonds
You can try the Book by Prof. H. Hankel, many years ago I read it. Is not well-edited but it is a wonderful forgotten piece of the origin of the second quantization, that is, the quantization of the fields as really it was conceived for solidists. It is much easier to read than Prof. Bogoliubov and Shirkov's classical monography.
Attached is the refecerence in a slide.
Best Regards.
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Actually more constraints...
The discovery of the mysterious He-2-4 nucleus and its geometry enabled me to calculate its mass accurately in 2 parity ways..
Using some logic I hit He-2-4 only to know its mysterious properties known but not taught much: (0) Most Symmetric, (1) Most Abundant, (2) Most Stable, and (3) Mother Nuclei to rest except Hydrogen.
A Geometric Model Satisfying.. (1) Quark, (2) QCD, (3) Yukawa Strong Force Quanta of 200 or 204 Electrons. (4) Thompson Problem of equidistribution charges, (5) CCP Packing of Energy or Mass in the most efficient way in Nature which makes sense for Nucleus, (6) Satisfying Vector Equilibrium Model, and showing evidence of Gravity Gradient Through Density.
Enabling: Leading Through Accurate Calculations it 2 Parity Steps with 99% Accuracy
Dear Friends, I feel obliged to share this with you as some of you wanted me to share. This is a very mystical experience to me, as it is not me but some transcendental revelation. Many discoverers have experienced this. When I re-read the paper, I get shudders and goosebumps.
Please read my paper on He-2-4 to understand the Geometry of the nucleus, which is the mother nucleus for the rest of nuclei along with the father Hydrogen. The first compound to be synthesized in the Universe is HeH (Helium Hydride) as found out. It is one of the most read scientific papers on Research Gate with 1050reads ( along some more reads in another version of the paper) and with 3 Recommendations. Reads for such an esoteric subject are rare. It often stands out as the "Most-Read" status and for 2017 to 2018 it held this record.
In 2008, I hit upon a connection between Photon and Electron/Positron without violating any laws of Physics except one experiment which is the most famous failed experiment. e.g, Michelson Morely. Then in 2010, trying to fit my theory in Strong/Nuclear Force, I hit this mysterious nucleus which we are not taught about. It took me till 2017 to get the geometry and calculations for its mass right.
My theory is nothing but 3 Orthogonal Fields shown in most of the EMF and QM experiments in Physics: where Electric, Magnetic, and Space are orthogonal fields. Unfortunately, we take (Vaccum of) Space to be granted and fail to understand that it is a Field with Supra Super Fluidity (it is like the Ghost passing through you without you feeling it, like in the case of millions of Neutrinos passing through you and one not feeling them but in the Yogic path you could wake up to this field). Some of you have seen my yogic trick of temporarily increasing the size of my fingers or toes by meditation but the second part of the experiment demonstrates that Space is a dynamic Supra Super-Fluid Field.
I was only encouraged to publish the paper when I found I was using the same units as Yukawa used, who was the first Noble Prize Winner for the Strong Force. His approach was more complex modified Dirac Equations but mine was a simple argument, that Nature would reuse components previously built in its walk of the Stack of Reality. The same arguments I used that Electron and Positron are 3D-vortexes weaved using Photons (in Space-Time constraints).
Like Crystal Molecules having Geometric Structure, the nuclei have it too. Modern Physics can't give us a simple picture of the nuclei.
He-2-4 nucleus is the most Symmetric, the most Abundant, the most Stable and tries to satisfy Quark and QCD models. It uses Yukawa's unit of the strength of 200 Electrons Mass (actually 204), the Packing of Spheres Problem (for most efficiently packing mass per unit of volume, which makes sense for a nucleus) for the inner layer, and the Thompson Problem (of distributing 'n' charges in Space for minimal energy or entropy needed for stability) for the outer layer. Then gradient of Gravity is seen (which justifies using Space as Field). e.g., gravity decreases with the increase in the altitude and lighter-dense things float up, while heavy-denser things float down.
The Noble gases are not only stable because of 8 electrons in their orbit (except He, in which case it is 2), but the Noble nuclei are stable with the quanta in units of He-2-4 (which is not taught). The corollary is that a skyscraper is not stable because the top floor is stable but the ground foundation is also needed to be stable.
It also satisfies the Equal Partition Theorem and the Principle of Reuse/Recycle by Nature, which Modern Physics does not use. It uses Muon and Anti Muon as building blocks - the next higher energy/mass resonance of Electron and Positron.
It proposes uses of a Space Field which can be called Dark Energy, Higgs Field, Ether, Prana or Chi. It uses Equivalence Energy Principle to see how much Electro Static Energy will be required to hold the cluster of 12 Nodes and 6 Nodes in the next layer.
There are two parity ways in which the mass of the nucleus is calculated to the accuracy of 99% (variation will happen based on speeds of the nucleus and secondary effects). In complex calculations, we match results up to all digits in two different paths! The baffling part is that all complex vector and energy operations in two different paths lead to the same result while satisfying all constraints!!!
It also demonstrates the Gravity at works at this fundamental level (which is mentioned in another paper).
Dirac was one of the great of all time
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An electron and a muon have very different energies, but they produce the same electric field. One explanation is that the charge "e" electric field is a fundamental entity, that will never be understood as having a conceptually understandable structure. The other alternative is that the charge "e" electric field has a conceptually understandable structure, made of something more fundamental.
It is not sufficient to say the electromagnetic force is transferred by virtual photons. The structure of virtual photons is unknown. Therefore, this is just giving a different name to something that is not understood. We think of gravity as a great mystery, but at least we can see gravitational effects scale with mass (energy). With electrical charge "e", we do not even have that level of understanding. Therefore, is an electric field an fundamental distortion of spacetime?
Since this is a discussion question, I will now offer my answer. The link below models the quantum vacuum as a quantifiable field that forms all particles and forces. This article generates a wave-based model of an electron, including its electric and gravitational fields. The model predicts an electron’s electric and gravitational fields are united. Equations in this article prove an electron's electric field has structure and this structure is related to an electron's gravitational field.
If you want to see how the fundamental elementary particles can be created out of vacuum through a quantum mechanical process, you should look into my first book "Born: A universe" (can be downloaded from my profile). From this process the size of the particles are determined like their masses. They are constructed by a confined quantized constant field that is spinning. Concerning the electron the elementary charge is as well determind. It also leads to a relativistic reformulation of the Newton law where photons also are included.
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An electron’s electric-magnetic field extends far from the electron’s center of charge. When we designate the electron’s energy, we include the energy in the electron’s electric field. The energy in an electric field external to charge e is: Eext = αħc/2r , where r is radial distance and α is the fine structure constant. For example, the energy in the electric field beyond 1 nanometer from charge e is about 1 eV. NIST specifies an electron’s energy to a standard uncertainty of 1.5x10-4 eV. Therefore, the experimentally measured electron energy includes the electron’s electric field energy extending out to about 5 micrometers. We know an electron’s electric field extends far beyond this distance. Does this mean an electron’s radius also extends indefinitely?
How do you visualize the structure of an electron? Do you include an electron’s electric field as a fundamental part of an electron? If so, how big is your electron model?
Andre,
You are attempting to explain the speed of light using the properties of E and B fields. It is true that these fields are important, but a complete answer must go deeper and answer the question: What is the structure of all fields? If the quantum vacuum is modeled as a sea of Planck length vacuum fluctuations, oscillating at Planck frequency (Wheeler’s “quantum foam”), then the quantum vacuum becomes a quantifiable field. Planck length (Lp) times Planck frequency (ωp) equals the speed of light (Lpωc = c). The quantum vacuum becomes a stiff elastic medium with an enormous impedance and bulk modulus. Waves in this medium propagate at the speed of light. This is proposed to be the single “universal field” that generates all particles, all forces and all other fields.
Support for this statement comes from the fact that this model generates predictions that the gravitational and electrostatic forces between two electrons are related through a square exponent. This falsifiable prediction is proven correct by 8 equations in Section 12 of the attached preprint. This paper also proposes an answer to the question: Is an electron’s electric field part of the electron’s structure? A wave-based electron structure is proposed and tested. This wave-based electron model extends indefinitely. It creates both an electron’s electric and gravitational fields. The energy in an electron’s electric field is a fundamental part of the electron model.
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I am by no means an expert on this subject, but a few papers on this subject sparked an interest into whether instantons give rise to a non-zero vacuum expectation value or could be involved in the generation of the Higgs field.
Instantons in mathematical physics arise as solutions to a set of non-linear differential equations than minimize the Yang-Mills functional for a non-abelian gauge theory. This is part of the differential geometric way of writing classical fields in terms of a connection and the curvature of a connection. The classical electromagnetic field is a U(1) connection and the curvature form of this connection is an anti-symmetric matrix that whose entries are the electric and magnetic fields. For non-abelian groups such as SU(2) and SU(3), the connection and curvature of the connection formalism give rise to the weak force of the Z and W-, W+, and the 8 gluons of the SU(3) strong force. The instanton number can be thought of as describing the number of instantons present and is an expression of how "twisted" or topologically non-trivial the vector bundle or underlying space is.
The Higgs field is what gives spin 1/2 particles mass as well as giving mass to the Z and W-, W+ particles. The masses of spin 1/2 particles are determined by something called the Yukawa coupling. My question is how can instantons contribute to a non-zero vacuum expectation value and are there theories that say the Higgs field is built up in this way?
The short answer is No, instantons don’t do this in the Standard Model. The reason is that, in four spacetime dimensions, there is a phase transition between a phase where the expectation value of the Higgs field vanishes and a phase where it doesn’t.
Incidentally, instantons are not, just, classical solutions of the esuatiins of motion of the gauge fields, that connect different vacua of gauge fields, there can exist instantons that connect different vacua of scalar fields.The existence of distinct phases for the scalar field, in the presence if the gauge fields, too, implies that such field configurations, that could affect the expectation value of the scalar, don’t exist.
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Operator product expansion is made in the deep ultraviolet region. In thermal field theory, it is explicitly shown , that the UV divergence in the quantum corrections does not depend on temperature. Hence, temperature shouldn't play any essential role in OPE, in thermal field theory(TFT). On the other hand, TFT is not Lorentz invariant. Hence, in the mixing of scalar operators in OPE, the matrix of anomalous dimensions should vary with quantum corrections due to the non- Lorentz invariant. Hence , I cannot understand the relevance of OPE in thermal field theory.
Gravity is an action-at-a-distance force. Gravitational waves caused by the revolution of the sun affect the orbits of planets and provide some planetary precession data. The chasing effect of gravitational waves also causes the planetary orbital mechanical energy to continue to increase slowly until the planet escapes from the solar system. Gravitational waves exist; the gravitational model under the influence of gravitational waves that we constructed was a physical model. Through the calculation of planetary orbital precession, the correctness of the gravitational equation under the influence of gravitational waves is verified.
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Dear RG members:
Screenshot from:
Vonsovskii, S. V. and Svirskii, M. S. 1961. About the spin of phonons. Soviet Physics of the Solid State. 3:2160. In Russian.
Do you know any article/book which uses explicit expressions containing Anisotropic Elastic Langragians L( Cij )?
For instance: cubic, hexagonal, or tetragonal ones? Other symmetries are also welcome.
L can be written in the 4th index range - ijkl or Voig - ij notations, but the math expressions must contain explicitly the elastic stiffness components Cij or compliances Sij (if S-1 C ~ 1) according to the point symmetry group.
For example: in the isotropy case: 2, in the cubic case 3, in the hexagonal case 6 and so on.
A lagrangian is defined as L(Cij) = K( ρ v2 ) - U( Cij ), therefore the potential term U(Cij) does have to include an expression invariant to the point group symmetry considered.
I did an intensive search on the web, so far only two papers with two expressions (isotropic and cubic cases) both papers from the '60s.
Thank you all so much for the interest.
I have públished a preprint with the answer to this thread. The Lagrangian for D4 point group symmetry.
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I am looking to understand what is soliton in qft, not in optical devices because it seemed to me that solitons look very different in optical field than in qft, but I am trying to understand what this means and I am very confused about topological solitons , the solitons are like taking L = 1 2 ∂µφ∂µφ - U (φ) and after use a metric like mikosky metric, after this I could use euler lagrange for the field of motion equation and this would give me a non-relativistic lagragian , and the problem is that I cant get the static solution because I don't know how to do it, are the solitons a static solution for some potential? , Maybe solitons should exist only in the 1d + 1d field which has local symmetry u (1) or are there solitons in 3d + 1d? ,what means solitons in BRST quantazation bacuase i fell that brst dosent have any relatiship with solitons.
Thank you, I have been studying qft for my pre-university research project for my application, thanks for the comments.
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is there a deeper fundamental property of neutrino oscillations? How does it work at the field level? is there any advanced mathematical connection or is only a physical fact?
I have a more simple view on the neutrino:
IMO the neutrino is a simple particle with a very weak interaction with matter. This weak interaction gives rise to only a few possible interactions in specific circumstances giving rise to neutrinos with different mass, i.e. there is only one type of neutrino but with different masses according to the interaction which created it.
As far as I know, the neutrino doesn't travel at light speed and, it doesn't follow the mass law "m=m_o gamma".
JES
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Being a first year Master's student, I wish to pursue my research on the aforementioned, but the abundance of resources ended up confusing me as to where to start. Suggestions are appreciated.
Stam Nicolis , thank you very much!
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i want to know that going on in this topic and that could be the most important papers ,such as Scattering of two-dimensional massless Dirac electrons by a circular potential barrier and i only want to know more in this topic ,could yo give me an idea?
The cross-section is one of the topics of subjects in research in high physics energy.
The Compton scattering effect is the core of your question .
The two-dimensional Dirac electrons is one both the most problems in quantum mechanics ,this indicate to potential barrier
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I don't see this limit - I never saw a proof of it. Can somebody indicate a proof?
Typically, at high velocities the number of particles is not well defined. QM works with a defined number of quantum particles while the quantum field theory (QFT) works with undefined number of quantum particles.
At high velocities the wavelengths of the quantum particles is very short, which makes difficult experiments of interference. Applying the Ehrenfest theorems, a wave-packet can be considered a particle, if its global movement is under examination, and this is the typical situation in the QFT.
On the other hand the formalism of the QFT uses raising and lowering operators. At high velocity instead of the wave-function one has a field operator. At low velocity the wave-function is just a function, many times it is an eigenstate of an operator associated with a property of the quantum system. What become these operators at low velocities?
It seems to me that the non-relativistic QM and QFT use two different formalisms which are not the limit of one another.
You are wiser than me. So, please go slowly. Phil, I lost you here:
"When the Hamiltonian operator is constructed it is the sum over free energies E(p) where p is the three momentum and the Fock space occupation number operators N(p) = â(p)â(p). i.e. Ĥ = sump ( E(p)N̂(p))."
I don't know what you mean by free energy. This is a concept from the thermodynamics. But I think you mean something else. So, please write its formula.
Then, you say,
"The non-relativistic limit is handled via the c-number coefficient alone."
There is no such coefficient in Ĥ as you expressed it.
"The raising and lowering operators don't enter at this point."
No, no! It seems to me as abracadabra. I want to see how these operators disappear from the Hamiltonian as the velocity decreases. They disappear gradually, not suddenly "at this point".
With thanks to both of you, kind regards, and waiting for explanation,
Sofia
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According to Yangton and Yington Theory, any spinning particle with polarization shall have Wave Particle Duality such as photon and electron. Also according to Particle Radiation and Contact Interaction Theory, any traveling particle with the capability of making contact interaction with the same particles in space will form a field such as graviton and electron. However, not all particles can be a wave or to form a field.
According to Yangton and Yington Theory, gravitational force is generated between two gravitons with side by side contact. Because of this reason, for two distance objects, a graviton particle must first escape from the parent object, then travel to the target object to make a side by side contact, such that the propagation of gravitational force can be fulfilled. This is called “Particle Radiation and Contact Interaction Theory”.
Like a photon emitted from a heat source by absorbing thermal energy to overcome its energy of separation, graviton can also be emitted from an object by absorbing thermal energy to overcome its gravitational force. It is obvious that the amount of the gravitons (M) emitted from the parent object to the target object should be proportional to the total amount of gravitons in the parent object, as is proportional to the mass of the parent object (m1). Also according to the Inverse Square Law, the amount of the gravitons (M) emitted from the parent object to the target object should be inversely proportional to the square of the distance (r) between parent object and target object. Therefore,
M ∞ m1/r2
Furthermore, the total gravitational force (F) generated from side by side contact between the gravitons (M) emitted from the parent object to the target object should be proportional to both the amount of the gravitons (M) emitted from the parent object to the target object and the total amount of the gravitons on the target object which is proportional to the total mass of the target object (m2). Therefore,
F ∞ (m1/r2) m2
As a result, Newton’s Law of Universal Gravitation can thus be represented as follows:
F = G (m1m2/r2)
Where G is the gravitational constant 6.674×1011 N m2kg-2.
Gravitational field is the summation of the graviton vectors (graviton with direction) generated from all the objects in the universe onto a point in space. Therefore, the gravitational field can be represented as follows:
Fg = G (∑ m/r2 S)
Where Fg is gravitational field, G is the gravitational constant 6.674×1011 N m2 kg-2, m is the mass of an object, r is the distance between the object and the unit mass, S is the unit vector in the same direction of the graviton vector generated by the object and ∑ is the summation of m/r2 S of all objects in the universe.
Furthermore, ∑ m/r2 S represents the summation of the graviton vectors emitted from all the objects in the universe onto a point based on Particle Radiation and Contact Interaction Theory. With the linear relationship and the same directions between gravitational field and the summation of graviton vectors at any point in space, gravitational field can be considered as a “repercute” of the distribution of graviton vectors in space.
Similar to gravitational field, the electrical field is defined as the electron vectors applied from all charged particles in the universe onto a point in space. Therefore, based on Particle Radiation and Contact Interaction Theory, electrical field can also be interpreted as a “repercute” of the distribution of electron vectors in space.
As a result, both the gravitational and electrical fields can be derived from Particle Radiation and Contact Interaction Theory with a linear relationship to the distributions of graviton vectors and electron vectors respectively. Therefore, Particle Radiation and Contact Interaction Theory can be considered as the foundation of Quantum Field Theory, Quantum Gravity Theory and Unified Field Theory.
First of all, nobody said that QM or wave function are wrong. Secondly, we are talking about quantum field theory which is one level above QM.
De Broglie's Wave is only true for those particles that have wave characters such as those properties having cycling, oscillating or circulating effects on the positions. In other words, any particle which is polarized and has repeating moving process will have wave property, or more precisely, Wave Particle Duality. But not all particles are waves as De Broglie claimed.
However, in modern physics, it is claimed that all particles are fields, not a particle, nor a wave. They exist everywhere in the universe, and a single surge of the field can form a particle. Even more, theoretically, an unified field theory (one field) can be used to represent all different subatomic particles.
Edward
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Feynman's parton model (as presented by, for example, W.-Y. P. Hwang, 1992, enclosed) seems to bridge both conceptions, but they do come across as mutually exclusive theories. The S-matrix program, which goes back to Wheeler and Heisenberg (see D. Bombardelli's Lectures on S-matrices and integrability, 2016, enclosed), is promising because - unlike parton theories - it does not make use of perturbation theory or other mathematically flawed procedures (cf. Dirac's criticism of QFT in the latter half of his life).
Needless to say, we do not question the usefulness of the quark hypothesis to classify the zoo of unstable particles (Particle Data Group), nor the massive investment to arrive at the precise measurements involved in the study of high-energy reactions (as synthesized in the Annual Reviews of the Particle Data Group), but the award of the Nobel Prize of Physics to CERN researchers Carlo Rubbia and Simon Van der Meer (1984), or Englert and Higgs (2013), seems to award 'smoking gun physics' only, rather than providing any ontological proof for virtual particles.
To trigger the discussion, we attach our own opinion. For a concise original/eminent opinion on this issue, we refer to Feynman's discussion of high-energy reactions involving kaons (https://www.feynmanlectures.caltech.edu/III_11.html#Ch11-S5), in which Feynman (writing in the early 1960s and much aware of the new law of conservation of strangeness as presented by Gell-Man, Pais and Nishijima) seems to favor a mathematical concept of strangeness or, more to the point, a property of particles rather than an existential/ontological concept. Our own views on the issue are summarized in (see the Annexes for our approach of modeling reactions involving kaons).
In the first half of the 20th century some theorists (e.g. Heisenberg, Brouwer, etc.) tried to develop the concept that space itself has a metric (the minimal length scale of discrete space). The size of the metric was thought to be ≈ 1 x 10-15 m because of the size of the minimal wave length of electromagnetic waves and the diameter of particles. However, 1 x 10-15 m is too large in relation to both amplitudes of 1 electromagnetic wave so the minimal length scale must be ≈ 0,5 x 10-15 m or a bit smaller. The consequence is that we cannot detect phenomena smaller than ≈ 0,5 x 10-15 m.
We are aware of the existence of discrete space because without a spatial structure there are no observable differences in the universe. But observable reality is created by discrete space and we know it because of the spatial differentiation of force fields (the general concept of QFT). The consequence is that the nature of everything we can observe and detect are mutual relations (“proved” by the formalism of QM). Thus we don’t measure the bare existence of the spatial units of discrete space, we measure the mutual interactions between the units, the exchange of variable properties.
It is obvious that these mutual interactions of the units of discrete space cannot “split” a unit of discrete space (even the ancient Greek philosophers reasoned some 2500 years ago that there is a limitation on reductionism). The magic word in theoretical physics to solve the problem is “asymptotic freedom”. We really like it to give problems a fuzzy name so we can keep our ambiguous concepts.
Recently astronomers have observed large regions of gravitational polarization in the early universe (Cosmic Microwave Background radiation by the BICEP2 Collaboration). That is a problem because the CMB radiation is the exchange of electromagnetic waves between the Hydrogen atoms in the early universe. So how is it possible that there are already regions of huge gravitational fields if there are no stars, etc.? There are also observations of “full grown” galaxies that already existed about 0,7 billions years after the proposed “big-bang”. These galaxies have an enormous black hole in the centre so cosmologists have termed these black holes “primordial” black holes. But thanks to the BICEP2 measurements we now know that our universe created the enormous black holes first, before there was the creation of Hydrogen atoms.
Now there is your question about the existence of quarks. Are they real or are they the result of tricky theoretical constructions with the help of “asymptotic freedom”? Moreover, can QCD elucidate why vacuum space created enormous black holes before the Hydrogen atoms emerged from vacuum space around the black holes? I will read your paper about ontology and physics. ;-)
With kind regards, Sydney
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In quantum field theory the charge of an electron, and therefore of course its associated electric field, is intrinsically smeared out by quantum fluctuations in its position. Indeed, due to the uncertainty principle the picture of electrons as ideal point-particles certainly breaks down for distances r /mc, the Compton radius.
In addiction we know that the g factor of the electron is not exactly 2, so one cannot regard the electron as a point source. The renormalized (physical) electron can no longer be considered point-like.
I stand by my statement: "If the electron has a center of mass, it is because it is a composite particle." This has nothing to do with phase-space considerations.
Of course, any point-like particle has a sort of minimal phase-space extension in accord with the uncertainty principle.
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I would like to know what you think of this theory
The gravitational field is formed at the quantum mechanical level. They are connected, like a sheet of paper - tends to 0 across, and along - tends to infinity.
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Does that mean that in each trial of an experiment there is a different number of particles? Or, alternatively, does it mean that in any given trial the number of particles is undefined?
If the second variant is correct, what is its phenomenology? Do particles get into or exit from the vacuum? There are experiments with coherent states of atoms, and, as far as I know there is no vacuum of atoms, i.e. the vacuum does not contain atoms, only elementary particles.
Another question is: are we sure that a coherent state is indeed a quantum superposition of Fock states and not a mixture? A believe in the first option, and because of that I ask what is the meaning.
Dear Sofia,
Natalia did not write about "mass deviation from the m/e ratio". Rather, she wrote about "mass derivation from m/e ratio".
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Do any of you know what has happened to the International Journal of Advanced Science and Technology (IJAST), since it lost its SCOPUS indexing a few months or so ago?
At the end of April (2020), IJAST, which appears to have two publishers, NADIA and SERSC, emailed me to say that my paper on Quantum Field Theory had passed the peer-review process and was now accepted for publication. However, I responded to them, during early May, to ask them about some corrections that I wanted to make, along with questions I had about the mixed messages regarding publication fees that I received in that initial email contact, but they never responded. I then continued to email them a number of times, fully expecting some kind of response regarding the corrections and, nearly four months down the line, I have still not had one single response. Consequently, I am now worried that my article will never ever see the light of day, and neither Elsevier and SCOPUS can help me because they stopped indexing IJAST round about the time I submitted my manuscript to them (or possibly just before).
Does anyone know what is going on and what can I do? Please respond with any help or advice on this matter.
Kind regards,
Stephen Mason
The journal “International Journal of Advanced Science and Technology” is published by the 'publisher' “Science and Engineering Research Support Society” and this publisher is mentioned in Beall’s list:
This is a red flag that you are dealing with a potential predatory journal. However, the matter is more complicated than that. This ‘publisher’ named “Science and Engineering Research Support Society” (SERSC) seems to have hijacked the journal “International Journal of Advanced Science and Technology” from NADIA, a publisher located in Australia. This is the real journal with a legit Scopus journal was/is: https://nadiapub.com/journals/ijast/
they are the real owner of ISSN: 2005-4238 https://portal.issn.org/resource/ISSN/2005-4238
with location: PO Box 5075, Sandy Bay, Tasmania 7005 Australia
The other ‘publisher’ use as location: PO Box 5014, Sandy Bay TAS 7005, Australia
It seems to me that NADIA publishes the original subscription-based journal (and it seems that after two years they make the papers fully accessible). At some point the scam started with the people behind the fake society SERSC.
See for example:
Toptsis, A., Chaturvedi, R. A., & Feroze, A. (2009). Kohonen-guided Parallel Bidirectional Voronoiassisted Heuristic Search. International Journal of Advanced Science and Technology, 5, 15-34. (see attached file called original paper 2009)
And the duplicated paper by the hijackers:
Toptsis, A., Chaturvedi, R. A., & Feroze, A. (2017). Kohonen-guided Parallel Bidirectional Voronoiassisted Heuristic Search. International Journal of Advanced Science and Technology, 23, 15-34. (see attached file called Hijacked version 2017)
So definitely a sign something is seriously wrong. Apart from not paying anything I think not much can be done but hope that your paper will not be published at this ‘publisher’ and you might be able to publish your work elsewhere on the long run.
Best regards.
PS. It is even worse…the “Science and Engineering Research Support soCiety” seems to be a legit organization from South Korea:
but the “Science and Engineering Research Support Society” from ‘Australia’ corresponding to:
is not. So it looks like a double hijack operation were the scammer stole the identity of a society (with little or no internet activity) and in name of this society ‘publish’ journals that belong to subscription-based journals from another publisher and use the obtained indexing from the original owners as a decoy.
I will add this case to my list which I try to keep updated in the discussion:
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When applied to simple models, large N expansion is not very tricky, however I would like to know if it is possible to automatize this process to don't expend much time in such calculations.
The only thing that I am aware of, and I will stress is that I have never used it, is the FeynCalc package. I don't know if you can use those tools to build routines that you need. I suppose that you might you already know of this package.
Anyway, good luck.
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This is a common question that arises in the teaching of quantum-field-theory (QFT), i.e. whether the above is merely a prescription that works or are there deeper reasons behind it ? There are several related questions which may arise, e.g. is the prescription a purely relativistic effect ? What are the implication for "causality" in QFT ? What is the relation of this prescription to the symmetry of "particle-antiparticle-conjugation (C)"-symmetry and the "time-reversal symmetry(T)" ? How does one recover the purely causal-("retarded") propagator in the non-relativistic-limit ?- etc.
The i*epsilon is needed to avoid sending information backwards in time.
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I am running a geometry optimization in ADF indicating different basis sets for different atoms, and I get the error above. When the basis set is the same for all atoms, the same input runs without problems.
Does anyone know how I could fix it?
Thanks!
Dear Huiyang,
The issue was that I was indicating
U $ADFHOME/atomicdata/ZORA/QZP/U.4f where it should read U$ADFHOME/atomicdata/ZORA/QZ4P/U
I hope this helps.
Dani
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Following well-known books in quantum mechanics (QM), such as "Quantum Mechanics" by Eugen Merzbacher, once influential and authoritative on QM, is today a slippery slope in many parts.
The simultaneous appearance of classical wave and particle aspects no longer can be defended in QM. The only thing that exists in Nature, as we know from quantum field theory (QFT), is quantum waves, NOT particles and NOT waves as in Fourier analysis (classical).
The Heisenberg uncertainty principle in QM seems, thus, to have to be modified -- as it is, in contradiction with itself, based on continuity by using the Fourier transform. Can we express it in QFT terms (not based on continuity)? Can that influence LIGO and other applications?
Thus, there is only one (not two or even three) case of photon interference in the two-slit experiment, and that is the case that is often neglected -- the quantum wave case. See the two-slit experiment at low-intensity, for example at: https://www.youtube.com/watch?v=GzbKb59my3U
All: For a background on why we can suspect that the Heisenberg uncertainty principle is fundamentally wrong, one can see its supposed "justification" using the classical theory (not quantum) of Fourier transform, see:
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AI pattern recognition was instrumental in the detection of the Higgs boson:
AI pattern recognition deep learning expectation here, however, is an eventual match of LHC->FCC ever-higher energy density pressure hydrodynamic plasma flow peak widths:
Matching the Nonequilibrium Initial Stage of Heavy Ion Collisions to Hydrodynamics with QCD Kinetic Theory
with turbulence:
as anticipated to some extent by Wolfram:
Indeed, any flow can be modeled in the form of partial differential equation system. There are bundle of studies on applications of AI in chemistry, medical, earth sciences, neurosciences, bio informatics, physics ...are to name a few.
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Why and how preferential axes of atomic orbitals develop (e.g. px, py, pz) while the atom of hydrogen is inherently taken to be spherically symmetric? does the orientation axis of a given orbital can be pointing to any random direction until a spherical-symmetry destabilizing field (e.d. electromagnetic) is applied at a given direction?
Here's some addition from my side: it is correct only l=0 (resp. j=0) states are spherical symmetric. I have not seen that a linear superposition of states for l=1,2,... can lead to a spherical charge distribution. Therefore I may say that "All energy levels with j=0 of all atoms are spherically symmetric." This implies all nonrelativistic l=0 states of course.
However, due to the m degeneracy, there always exists an equal weight non-coherent superposition -- meaning not a linear superposition of states but an addition of probability densities -- such that the resulting probability density is spherically symmetric. This is due to the fact that for a given l the sum over all m of the spherical harmonics squared is a constant. This leads to the experimental fact that the atomic form factor at scattering experiments is a function of r only. But of course, this constant scattering constitutes a non-isolation of the atom and a constant perturbation due to the measurement. The outcome therefore levels all angular dependency of the individual states at the time of the individual scattering -- hence the non-coherent superposition.
Simply said: would you be able to "just look at" the atom, it would appear spherical.
And again, the statement obtains that there are no preferred axes.
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As we know, many cosmologists argue that the Universe emerged out of nothing, for example Hawking-Mlodinow (Grand Design, 2010), and Lawrence Krauss, see http://www.wall.org/~aron/blog/a-universe-from-nothing/. Most of their arguments rely on conviction that the Universe emerged out of vacuum fluctuations.
While that kind of argument may sound interesting, it is too weak argument in particular from the viewpoint of Quantum Field Theory. In QFT, the quantum vaccuum is far from the classical definition of vaccuum ("nothing"), but it is an active field which consists of virtual particles. Theoretically, under special external field (such as strong laser), those virtual particles can turn to become real particle, this effect is known as Schwinger effect. See for example a dissertation by Florian Hebenstreit at http://arxiv.org/pdf/1106.5965v1.pdf.
Of course, some cosmologists argue in favor of the so-called Cosmological Schwinger effect, which essentially says that under strong gravitational field some virtual particles can be pushed to become real particles.
Therefore, if we want to put this idea of pair production into cosmological setting, we find at least two possibilities from QFT:
a. The universe may have beginning from vacuum fluctuations, but it needs very large laser or other external field to trigger the Schwinger effect. But then one can ask: Who triggered that laser in the beginning?
b. In the beginning there could be strong gravitational field which triggered Cosmological Schwinger effect. But how could it be possible because in the beginning nothing exists including large gravitational field? So it seems like a tautology.
Based on the above two considerations, it seems that the idea of Hawking-Mlodinow-Krauss that the universe emerged from nothing is very weak. What do you think?
A universe can be created from nothing without any external laser or strong gravitational field. In QFT vacuum real particles can be created and annihilated thereafter provided their lifetime dt and energy dE satisfy the uncertainty relation, roughly dtdE~h where h is the Planck constant.
Owing to the uncertainty relation, borrowing a small amount of energy (dE~0) from vacuum is allowed for a long time. According to some estimates the total energy (including negative gravitational energy) of our Universe is precisely zero or very close to zero. Hence, if the Universe is created as a quantum fluctuation its lifetime can be almost infinite.
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There is a plenty of examples of classical solutions to low-energy effective theories that were proved to have vanishing α'-corrections to all orders and hence be also perturbatively exact string solutions in the literature, see e.g.
Since in all the literature I'm familiar with, the proof of α'-exactness of leading-order solutions relied heavily on the fact that the corresponding spacetime metric admits a covariantly constant null Killing vector, I'm currious if this is always the case.
Is anyone aware of some paper which proves α'-exactness for leading-order solutions beyond those with spacetime backgrounds admitting a covariantly constant null Killing vector?
(I'm aware of the fact there are also different approaches in finding exact string solutions that do not relly on proving α'-exactness of leading-order solutions and hence may yield exact string backgrounds with no covariantly constant null Killing vectors but the present question is focused strictly on this approach.)
Stam Nicolis So, your problem with my question lies in the terminology I used - correct? Specifically, is it the term "string solutions", by which I mean solutions of effective field equations for the background fields?
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In my opinion velocities more than that of light are imaginary only.We can not observe velocities more than that of light.
Based on this imaginary concept how a field is described and got 'Nobel' for its predicted particle.
Means, the calculation of predictions by standard model and quantum field theory may be correct. But still the most fundamental of quantum mechanics need some modifications which may modify even the standard model also.I feel that these modifications may develop new concepts in cosmology, black holes, dark matter and particle physics.
After considering all your views about 'consciousness of atom' and 'smartness of atom' I felt that it is useless to continue this discussion for me. It is deviated from the topic in the question(a topic on particle physics). So I am not interested to discuss it further.
You may have another forum for its discussion.
All the best...
Regards.
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When Dirac introduced his magnetic monopole for explaining the quantization of the electric charge he left the mass as a free parameter of such particles, but nowadays we have many different kind of models for such particle. My question is what is the value of the mass employed for trying to look for this particle scattering processes in particle detectors or cosmological measurements
Dear Stam,
I'm sorry to say that you don't know what is a magnetic monopole at all and let me to say that Maxwell equations cannot tell anything about this issue as the magnetic (or electric ) dipole. Respect to the different aspects of the magnetic monopole, although is not the best reference let me to recommend you the basic
where you have the topological interpretion.
More explicitally(just two simple references )the magnetic monopole in the Standard Model as I have told you
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What interaction(s) in quantum field theory combines two particles of spin 1/2 and - 1/2, mediated by a virtual particle, so the products have no spin? Is the virtual intermediary known to carry spin +-1 or -1? Is any virtual particle known to carry spin +1 or -1?
I am not a quantum field theorist. I would like to know what the inputs are, what the virtual intermediar(ies) are, what the reaction products, with a few literature references.
Thank you.
Intrinsic spin (not the z-component of it) of a particle is always non-negative.
However, SU(2) isospin can be either positive or negative. For example a u-quark having isospin +1/2 may couple to a d-quark of isospin -1/2. At the interaction vertex a W boson is either emitted or absorbed, depending on your Feynman diagram. W boson is a isospin one particle.
If you want to know how to change z-component of intrinsic spin of a particle (say electron) then look at the interaction of magnetic field with electron spin. Magnetic fields can be manipulated to reverse z-component of intrinsic spin. See literature on Hahn-echo, e.g, "Spin echoes", E.L. Hahn, Physical Review. 80: 580–594 (1950).
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In trying to do the twist expansion of the gluon function, I was using the operator product expansion of <P|FFFF|P> where I defined FF=O as my operator. Using this, I then said <P|OO|P>= C<P|O|P>. Is this correct, or would there be additional operators that would come into play in this expansion?
Thanks! Stam Nicolis I will take a look at that reference!
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NOTE: In consequence of some answers of users due to whom part of the issues become clarified, I do from time to time MODIFICATIONS in this question stressing the remaining questions.
Shan Gao, the author of the book
proposed a new interpretation for the QM: a substructurea of QM consisting in a moving particle. But instead of moving continuously, as in Bohm's mechanics, or as in the trajectories of all forms considered by Feynman in his path-integral theory, Gao's particle performs a random, discontinuous motion (RDM) - see section 6.3.2 and 6.3.3 in his book. In short, gao's particle jumps all the time from a position to another
"consider an electron in a superposition of two energy eigenstates in two boxes. In this case, even if the electron can move with infinite velocity, it cannot continuously move from one box to another due to the restriction of box walls. Therefore, any sort of continuous motion cannot generate the required charge distribution. . . .
I conclude that the ergodic motion of a particle cannot be continuous. . . .
. . .
a particle undergoing discontinuous motion can . . . “jump” from one region to another spatially separated region, whether there is an infinite potential wall between them or not.
. . . .
Furthermore, when the probability density that the particle appears in each position is equal to the modulus squared of its wave function there at every instant, the discontinuous motion will be ergodic and can generate the right charge distribution"
An important implication of the RDM interpretation is, as the author says, that the charge distribution of a single electron (for instance, in an atom) does not display self-interaction
"Visually speaking, the ergodic motion of a particle will form a particle “cloud” extending throughout space (during an infinitesimal time interval around a given instant), . . . . . . This picture . . . may explain . . . the non-existence of electrostatic self-interaction for the distribution.
Part of the questions regarding this picture were already clarified by the posts of some users. The questions remained non-clarified are:
1) Is Gao's picture of a particle jumping from position to position, and visiting in this way all the volume occupied by the wave-function, fit for obtaining the Feynman path integral?
Feynman considered two points in tim and space (t1, r1) and (t2, r2). He also considered all the possible paths between these two points - the majority of the paths having crazy forms, though being continuous. The particle starting at (t1, r1) and traveling to (t2, r2), was supposed by Feynman to be totally non-classical - it was supposed to follow SIMULTANEOUSLY all the paths, not one path after another. This is was permitted him to do summation over the phases of the paths, and obtain the path integral.
The movement of Gao's particle is not only discontinuous and endowed with no phase, but it os also SERIAL, one point visited after another. What you think, if one would endow these discontinuous trajectories with phases, could we obtain Feynman's path integral despite the seriality of his particle's movement?
3) Gao author also says
"discontinuous motion has no problem of infinite velocity. The reason is that no classical velocity and acceleration can be defined for discontinuous motion, and energy and momentum will require new definitions and understandings as in quantum mechanics"
This statement seems to me in conflict with the QM, because the uncertainty principle says that if at a given time a particle has a definite position, the linear momentum (therefore also the velocity) would immediately become undetermined. QM doesn't say that the linear momentum does not exist.
Can somebody offer answer(s) to my questions/doubts?
We can only catch the quantum world in a model. Most aspects of that world cannot be perceived, not even when observation is aided by sophisticated equipment. Several scholars in the early decades of the twentieth century have tried to discover which model could fit. One of them was John von Neumann. He doubted long between Hilbert spaces and projective geometries and finally he selected Hilbert spaces. Many quantum physicists followed him in that choice. Then Schrodinger came with his equation that used a wavefunction. Apart from him Heisenberg came with his matrix theory. Then Dirac showed that both theories are principally identical and could be represented in a Hilbert space. The wavefunction is a hypothetical object. It is never observed. Quantum objects behave in ways that can be explained by similarity to wave behavior. Their detection patterns shoe interference behavior. Nobody ever saw a quantum object as a wave or as a wave package. In similar sense show quantum objects behavior that is similar to the behavior of point-like particles. However, no instrument can directly observe a point-like particle. So the model that must explain the behavior of quantum objects must offer an explanation of this wave-particle dualism.
A separable Hilbert space can archive the dynamic geometric data of a point-like particle when it applies quaternions for the eigenvalues of its operators. However, the eigenspaces of the operators in a separable Hilbert space are countable. These eigenspaces can only store an ongoing hopping path. The squared modulus of the wavefunction is a detection probability distribution. As a storage medium the separate Hilbert space can only implement the wavefunction or better its squared modulus as the descriptor of a coherent hop landing location swarm. The ongoing hopping path can recurrently regenerate such hop landing location swarm when the hopping object hops around in a stochastic manner such that after each cycle the path is closed. If the object can be characterized by its wavefunction, then each cycle must generate a coherent swarm that represents a closed hopping path, while each time the location density distribution of the hop landing location swarm is practically identical. This can only happen if a stochastic mechanism generates the hop landing location in a sufficiently controlled way. This means that the mechanism must be a stochastic process that owns a characteristic function, which is the Fourier transform of the location density distribution that describes the hop landing location swarm that the mechanism recurrently reproduces. Thus the separable Hilbert space, the stochastic proces and the operator that manages the storage of the dynamic geometric data of the hopping object are all private to the quantum object. Together, they form the platform on which the object lives. The eigenspace of the operator archives the complete life story of the quantum object.
In quantum physics many of such objects exist and each of these elementary particles owns it own platform.
A Hilbert space applies a private version of a quaternionic number system to define the inner products of pairs of vectors. It uses that same version for the specification of the eigenvalues of its operators. Further it applies a vector space from which the Hilbert space retrieves its vectors. Many separable Hilbert spaces can share the same vector space. The selected version of the quaternionic number system is also used as the private parameter space of the Hilbert space. A dedicated reference operator manages this parameter space in its eigenspace. However, in a separable Hilbert space, that eigenspace only stores the rational values.
One separable Hilbert space acts as a background platform. Its reference operator manages the background parameter space of the model. All other separable Hilbert spaces float with the geometric center of their private parameter space over the background parameter space. In this way will all elementary particles float over the background parameter space.
So where Dirac used only one Hilbert space, a better suited model will apply a myriad separable Hilbert spaces that all share the same underlying vector space.
The elementary particles act as elementary modules. Together they constitute all other modules that exist in the model. Some modules are modular systems.
This sketches the main structure of an applicable model.
The main message is that the hopping paths of the particles recurrently regenerate a similar coherent hop landing location swarm that show particle behavior and wave behavior. The particle lives on a platform that moves as one unit.
The map of the swarm on the background parameter space moves smoothly, while the image of the point-like particle hops violently.
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The shell model treats the motion of nucleons within the nucleus as non-relativistic; I'm looking for models that treat the motion of nucleons as relativistic.
There are three main models for nuclear structure research at present :droplet model, shell model and collective model.They all have their own limitations.If you want to look for models that treat the motion of nucleons as relativistic.The key issue is what is the formula of strong interaction?Then using the formula to creat a dirac function to explain p-n structure.
Well,It would be very successful! if your theory could solve the problems of binding energy, abnormal magnetic moment, lifetime, isotope number and neutron/nucleon number ratio of 118 elements.
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Greetings,
Completing Bachelors in Engineering this June'19, I thought I'd start with Masters/PhD in Gravitational Physics this fall but I received rejections from almost every graduate school I applied to. To where I received an offer from, I won't be able to pay off the tuition fees.
Of course I knew that to receive an offer, one needs to have some experience with the subject. With the engineering curriculum on one hand, I tried to manage my interests in gravity. From watching lecture videos by Frederic Schuller and Leonard Susskind to reading books by Sean Carrol and to even doing a summer research internship on black hole geometries, I tried to gain experience on the subject.
I wish to understand relativity from a mathematical point of view.
" A good course in more abstract algebra dealing with vector spaces, inner products/orthogonality, and that sort of thing is a must. To my knowledge this is normally taught in a second year linear algebra course and is typically kept out of first year courses. Obviously a course in differential equations is required and probably a course in partial differential equations is required as well.
The question is more about the mathematical aspect, I'd say having a course in analysis up to topological spaces is a huge plus. That way if you're curious about the more mathematical nature of manifolds, you could pick up a book like Lee and be off to the races. If you want to study anything at a level higher, say Wald, then a course in analysis including topological spaces is a must.
I'd also say a good course in classical differential geometry (2 and 3 dimensional things) is a good pre-req to build a geometrical idea of what is going on, albeit the methods used in those types of courses do not generalise. "
- Professor X
^I am looking for an opportunity to study all of this.
I would be grateful for any opportunity/guidance given.
Thanking you
PS: I really wanted to do Part III of the Mathematical Tripos from Cambridge University, but sadly my grades won't allow me to even apply :p
There are two sides to your problem: the practical and the ambitional. You will have to look after both. Recognize the practical issues but don't let go of your ambition. You may have to get a temporary job just to live, but that does not mean you give up on your dreams.
Your problem is not unique and has been overcome by famous scientists. Faraday started working for a bookbinder and ended as a revered scientist. His personal drive got him through. Dirac got a first degree in electrical engineering and ended as a revered theorist. Einstein worked early on in a Patent office and ended as a revered theorist. Other examples can be found, such as Ramanujan. Now there's a great example of talent beating disadvantage. So you see, it's not the end of the world if there are practical difficulties in your way at this time in your life. If you keep your spirits high, focused on what really interests you, you may succeed. It may be very hard, but don't give up.
You should understand that training is not enough. You have to practice being creative. Some people on this forum will probably disagree with the following suggestion, but have a go at writing a paper on a novel topic and seeing the reaction. It may take time to find a problem that you can work on, and you may very well get rejection. But having a go will teach you more than doing a lecture course on analysis. Papers do not all have to be in quantum field theory or relativity. Go on the arXives and see what sort of topics are viable for you. Most likely, at this stage, it might be in the General Physics section. But at least you might start from there.
Good luck in your ambition. Never give up.
George Jaroszkiewicz
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If the particles inside the material collide within a very small time, we will have a very small time uncertainty Delta t (time uncertainty is the uncertainty on the instant of time, where the Event does happen) also. By Heisenberg's uncertainty relation
Delta E * Delta t >= hbar/2
the energy uncertainty Delta E becomes large also. We therefore can estimate the particle in some Energy state around the energy it would classicaly have (we have a band broadness given by Delta E). I know the Quantum Zeno effect, where extremely frequent interaction of a particle with some other will undergo (almost) no time Evolution. Because Delta E is very big in this case, collisions with classical Energy transfer epsilon will have no significant and observable effect when
epsilon < Delta E.
So only collisions with really high value of epsilon do contribute to observable effects, however, These Kind of collisions are rare. Therefore, there will be very little temporal changes observed.
Question: Let the particle be trapped in an external potential with higher Magnitude than the particle's kinetic Energy expected classical and "on-shell". If the Energy spectrum of a particle is broadening in a material with very high collision frequencies, will there be a higher probability for Quantum Tunneling out of the potential?
I think yes, for a short time. Matter-antimatter pairs can Pop out for a very short time, These pair is consisting of virtual particles. But virtual particles have effects on the Dynamics. Maybe there are also effects outside the barrier due to virtual particles Tunneling out (how would this effect look like?)?
Which other quantum effects we observe in material with high collision frequency? Maybe also vacuum polarization even if the characteristic energy scales for that effect are far lower?
I believe we do observe quantum tunneling in material with high collision frequency but they will not be observable or not at least observable with our current technology. During the collision the time gap will be extremely small and thus will affect the emission of collided substituents. As their collision will create disturbance in surrounding and thus this disturbance will create favorable condition for creation of matter antimatter pair, which will diminished as breaking virtual particles.
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Within the most general linear axions Einstein Maxwell dilation model(EMD), translational and rotational symmetry are both broken. Recovering translation invariance is not as much as simple to restore the rotational one. For the latter it is enough to set the condition Yx(φ)kx2=Yy(φ)ky2 while for the former it is not so straightforward.
Also see this Ph.D thesis, from Universidad Aut ́onoma de Madrid, by Amadeo Jim ́enez, which discusses various ways of symmetry breaking in Holographic models, Spontaneous breaking, Anomalous breaking, transport phenomenon and so on, http://inspirehep.net/record/1607633/files/fulltext.pdf
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Hello,
Suppose I have a charge at rest, my question is, since the electric field of this charge will "go" to infinity for eternity, where does the energy come from to maintain that field.
We all know that the charge value and the field "strength" are time independent, and since the field propagates at finite speed, we must be loosing energy to fill the yet unfilled space with this field.
Dear Newgato,
It is very good that one made his mind to undersatand the nature of the things. It is so the nature of the things and how they behave is predicted by experimental observations. What is observed is that when a particle is charged with an electric charge,then an electric field is always associated with this charge. The charge is the origin of the electric field. It follows that where ever the charge moves because of any cause its electric field is belonging to it. This is the issue as i understand and believe it.
Best wishes
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Suppose I have a coil placed above a conducting non magnetic plate, I run an AC current in the coil, and I want to know what is the mutual induction between the coil and the plate ?
Mutual inductance between them
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What is the physical meaning of bogoliubov transformation ? Specially on quantum field theory ?
If a pair of coupled harmonic oscillators are described by coordinates( x1,p1,x2,p2) and a canonical transformation is introduced to decouple them, then the set of transformation matrices behave as if it is a Lorentz transformation in 2+1 dimensions. This is Bogoliubov transformation. For a detailed discussion in the context of Condensed Matter Physics, see
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The Schrödinger self adjoint Hamiltonian operator H correctly predicts the stationary energies and stationary states of the bound electron in a hydrogen atom. To obtain such states and energies it suffices to calculate the eigenvalues and eigenfunctions of H. Since 1926 up to now, and for the foreseeable future of Physics, any theoretical description of the hydrogen atom has to assume this fact.
On the other hand the Schrödinger time dependent unitary evolution equation $\partial \Psi / \partial t = -iH(\Psi)$ is obviously mistaken. So much so that in order to explain transitions between stationary states the unitary law of movement has to be (momentarily?) suspended and then certain "intrinsically probabilistic quantum jumps" are supposed to rule over the process.
Transitions are physical phenomena that consist in the electron passing from an initial stationary state with an initial stationary energy, to another stationary state having a different stationary energy. Physically transitions always involve the respective emission/absorption of a photon. Whenever transitions occur the theoretical unitary evolution is violated.
It is absurd to accept as a law of nature an evolution equation that does not corresponds with the physical phenomena being considered. Electron transitions are not predicted, nor described by, nor deducible from the Schrödinger evolution equation. In fact Schrödinger evolution equation is physically useless. This is the reason for Schrödinger's "Diese verdammte quantenspringerei". Decades of belief in unitary evolution originated countless speculation, contradiction and confusion with enormous waste of human talent and time.
Assume then that physicists accept the mistaken nature of unitary evolution and proposes its replacement with a novel equation that a) is consistent with the predictive virtues of H b) deterministically describes transitions In principle a probability free, common sense, rational, deterministic, well constructed replacement of Quantism should be a welcome relief for physicists and chemists, and for philosophers of science as well. Then, among equations and theories currently accepted by mainstream Physics, which ones would be affected by the eventual replacement of unitary evolution? Here is a short list of prospective candidates that the reader can extend and refine Quantum chemistry Dirac equation Quantum field theories Quantum gravity Standard model Lists of physical theories are available at
For more on the inconsistencies of Quantism and details on a theory that could replace it see our Researchgate Contributions page
With most cordial regards, Daniel Crespin
Dear Christian,
You wrote: "There seems nothing wrong with Schrödinger's equations. Only Bohr and Heisenberg did not like it. They preferred the mystery."
And so did most in the community almost from the start.
De Broglie and Schrödinger already considered transitions as "not instantaneous" even as Schrödinger introduced the wave equation, and this was practically 100 years ago, not a few decades ago, and this is what they were attempting to address, but could interest nobody else.
At the beginning of the 1950's, Schrödinger himself very publicly and futilely protested again about the very idea of instantaneous quantum jumps. Unfortunately, nobody paid attention.
If you had even glanced at the paper I referred Daniel to in the first answer in this thread, you would have found the direct quotes from him and the actual references where you can find them.
It is to this 100 years disconnect that I have been trying to draw attention.
At long last, some research seems to be resuming in the right direction.
Best Regards
André
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In reference to the attached presentation material regarding the sum of the following infinite series 1+2+3+4+... the following comments are due
• The obvious answer is a huge positive whole number beyond our imagination
• But what if a theory wants the answer not to be so?
• Are we allowed to challenge the theory?
• Are we allowed to bend the rule or even cheat to get the desired value?
• Is this bending, of the rule, only applies for exceptional cases or can be exercised freely?
My conclusions are
• It is a well-known fact that how feeble tricks are used in mathematics to obtain some haphazard values from divergent series to baptize certain theories in physics.
• Three types of tricks are used to obtain the desired results
1. Ignoring or hiding divergent quantities
2. Ignoring or hiding conditions for formulas
3. Extending the domain of a formula
• These tricks simply erode confidence in mathematics as a sure scientific tool.
• It is a legitimate question that if these flagrant deceptions are exercised to fool ourselves, who knows what other tricks are used to obtain desired results from complicated mathematical derivations?
The main question is; why for heaven’s sake, mathematics needs cheating in dealing with new challenges in science. Either it is not competent enough to cope or it is just a subjugated slave in the hand of any popular theory
Ziaedin Shafiei Dear Ziaedin,
The problem depends on how one defines and accepts a trick. If we understand by a trick a "skillful act" that can be put in simple sequences of logical steps, then it is a mathematical act. If we understand by a trick an act intended to "deceive or mystify" others or oneself, then this clearly cannot be accepted. The problem is accepting illogical ideas put in deceptive bright capsules.
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According to common understanding the fundamental interactions of the standard model are mediated by the exchange of so-called gauge bosons (photon, gluon etc.). Now, the e.g. number of gauge bosons is related to the gauge group of the corresponding theory. But the wording "exchange particle" is apparently motivated by the graphical representation of Feynman diagrams. I wonder if we would talk and think differently if this tool of organizing your perturbative expansion would not have been invented.
By the way: the background of this question is the following: Since I believe that Feynman diagrams cannot be interpreted realistically, the notion of (virtual) exchange particles appears to me questionable (i.e. based on an artefact, like the specific solution technique of perturbation theory). But perhaps this “exchange” idea could be motivated also differently and independently.
Dear Oliver,
"...do physicists commit a fallacy in the Whitehead sense or are are we not in the arena of "logical reasoning"? "
That depends. Of course, we can argue logically with Feynman diagrams as long as we and our conversation partners know the mathematical terms symbolized by the lines and stick to the logic of the Feynman rules. Most physicists use Feynman diagrams in this way.
However, if the internal lines are "explained" as particles that are able to leave their mass shell, then this is a fallacy, because such explanations leave the logical arena of the Feynman rules.
Although well-intentioned, such pseudo-explanations are superfluous for the experts and give the laymen a false understanding of particle physics.
Walter
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(This question is not mine, I copied here an issue raised by Hans van Leunen in one of my threads. I think it is worth of a separate discussion.)
Here are some of the problems Hans van Leunen posed:
• Why does the squared modulus of the wavefunction describe a probability density distribution? Probability density of what?
• What is the relation of these distributions with fields?
• How do they interact? Do you know the mathematics that describes these interactions?
• obviously physical reality is ruled by stochastic processes and not by all kinds of strange forces and force carriers.
I would add a problem of myself
• for which particles we may speak of a quantum field, and which ones are "too much classical" to be represented by a field? For instance, for atoms we may speak of a field, or only for elementary particles?
I trust that Hans would explain his views, and I also hope that the thread won't remain only mathematical. I mean, I think that it would be interesting to discuss the meaning of the concept of field in QFT.
André,
You will have little problem in imagining a one-dimensional normal distribution. The famous bell shaped function. Now take a two-parameter normal distribution. It has an elliptic or a a round rotational symmetric bell shape. Next take a three-parametric normal distribution. It means that the parameter space is three-dimensional or with time included four-dimensional. The shape is a bell in four or five dimensions. One extra than you are used to with the usual bell. The value of the bell function is still defined in real numbers. The squared modulus of the wavefunction will not differ much from this three-parametric normal distribution.
This function specifies the probability of detecting the owner of the wave function at the location and time of the parameter value. For a point-like object it can be the location where the object actually was, is or will be. The problem is that this smooth distribution in fact describes the location density distribution of a swarm of locations that may be hop landing locations. The swarm may reflect the hop landing locations of a cycle of a stochastic hopping path of a point-like object. The mystery lies thus in the fact that the wavefunction is a smooth function, while it may represent a swarm of discrete locations. The location density distribution may have a Fourier transform. That makes the location density distribution a wave package. Usually moving wave packages disperse. However, not this one because the swarm that the location density distribution describes may be recurrently regenerated and that regenerates the location density distribution.
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An example of density of Lagrangian of a scalar field ϕ(x), is
(1) L = ½(∂ϕ/∂t)2 - ½(∇ϕ)2.
(From this density of Lagrangian, one derives the Klein-Gordon equation).
I miss the phenomenological significance of the two terms in (1):
• the Lagrangian is defined as T - V, where T is the kinetic energy and V the potential energy. In the expression (1) the quantity
(2) π(x) = ∂ϕ/∂t
is considered canonical momentum, i.e.
(3) T = ½ ∫ d3x (∂ϕ/∂t)2
is considered as density of kinetic energy. But, ∂ϕ/∂t does not suggest me a momentum, but, rather, the value of the energy.
• the other term, ½(∇ϕ)2, is defined as "gradient energy". I understand that it is not meant to play the role of a potential energy V. But, if it is not part of the kinetic energy, not of the potential energy, then, what yes it is?
(NOTE: meanwhile I got some useful explanations from Stam Nicolis and from Marcos Souza, but I would appreciate more clarifications.)
Sofia,
In my opinion, the field itself is not quantized. Instead field excitations can be quantized. Obviously, oscillations can be quantized. This is shown by the solutions of the Helmholtz equation. However, the set of solutions of the wave equation covers many other solutions and this includes solutions that cannot be represented as waves or wave packages. Two very particular solutions usually escape the attention of physicists. These are the pulse responses that only occur in odd numbers of participating dimensions. I call them shock fronts because they are not waves. During travel the front keeps its shape. The one-dimensional shock front also keeps its amplitude. This means that it can travel over huge distances without losing its integrity. The spherical shock front diminishes its amplitude as 1/r with distance r from the trigger location. It means that over time it integrates into the Green's function of the field. The (quaternionic) Green's function possesses some volume. Thus the spherical pulse response injects a bit of volume into the field. The dynamics of the spherical pulse response shows that this volume quickly spreads over the full field. Thus, the local deformation that is due to the volume injection quickly fades away. To generate a persistent deformation, a mechanism must recurrently regenerate the spherical pulse response. The effect depends on the regeneration rate and the density of the produced pulse location distribution. So the relation between deformation and the pulse response is rather complicated.
Instead photons can be represented by strings of equidistant one-dimensional shock fronts. In this case the Einstein-Planck relation E=h v defines a more direct relation between the energy of the photon and the energy of the shock fronts that constitute the photon. Planck's constant h relates the energy of the photon to the emission duration of the photon.
In any case, the shock fronts play the role of basic quanta. The one-dimensional shock fronts play the role of pure energy quanta. The spherical shock fronts play the role of a quantized mass-capability. The capability depends on the regeneration rate and on the density of the location distribution.
The mathematics of the discussed shock fronts are treated in detail in
TheStructureOfPhysicalReality.pdf ; http://dx.doi.org/10.13140/RG.2.2.10664.26885
and
I use quaternionic differential calculus to show that in principle all basic fields can produce the discussed field excitations. Each of these excitations require a correct actuator. For example, a spherical shock front requires an isotropic actuator. This is delivered by the embedding of a quaternion that breaks the symmetry or the arithmetic capabilities of the embedding field.
For me the fact that this embedding invokes a stochastic process that owns a characteristic function is still a mystery. Still, it is the reason of existence of the wavefunction of elementary particles.
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quantum field theory says:::::: the vacuum state is not truly empty but instead contains fleeting electromagnetic waves and particles that pop into and out of existence.
then sound should travel through vacuum.......do sound travel through vacuum?
The interaction with the virtual quanta of the vacuum is very weak and the sound which is an atomic phenomenon reacts very-very weakly with those virtual states. The neutrinos also go through our bodies or the entire Earth with very few or no interactions.
The vacuum polarization has been observed in specific experiments with and atoms. Another interesting case for vacuum efects is the Casimir Effect.
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I now have created a compact version of the theory of everything'' I am developing since several years, also including the biological and psychological extensions dealing with human body, human soul, and human mind, in the latter case, comprising mental disorders just like drugs applied to treat mental disorders. In particular, in the last chapter (On the Quest of the Actual Nature of Being''), I there present formal boxes which compactly elucidate the central feature of all this, namely the interrelation of forces and fields in the context of macroscopic systems and microscopic systems, naturally incorporating gravitation, electromagnetism, and self-interaction, by way of example, also presenting the way to the notions weak interaction'' and strong interaction'' as used in quantum field theory. Please consult the copies Understanding Nature Truly'', part one, two, and three presented in RG in the context of my projects
Theory of Everything'' (part one) and Human Soul as Mathematical Object ...'' (part two, three). Do these formal boxes contain enough information to show that the theory of everything'' I am developing since several years indeed works? Do these formal boxes contain enough information to show that theory of everything'' is not what people so far a looking for, but something completely different? Do these formal boxes contain enough information to show that exactly this is the problem preventing that people realize the way I am going as the right way?
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we know very well it is possible to collapse a wave-function of any fundamental particle in our laboratory..
what about nature like Earth, sun, galaxy????
does nature is the consequence of collapsed wave-function? if so, who collapsed that? or does nature is the consequence of without collapsing wave-function?
i welcome unique scholars to answer this question....
thank you......
DearStam,
You write: " The wavefunction in quantum mechanics doesn't have anything to do with any resonance phenomenon-that's, simply, wrong."
It is not wrong, quite the contrary. It is this discovery by de Broglie in 1923 that gave Schrödinger the very idea to use a wave function to describe the hydrogen orbitals.
You seem to have missed quite a bit of information on the origin of the introduction of the wave function and the historical fact that it was meant to represent a resonance state.
In 1923, De Broglie wrote:
"l'onde de fréquence ν et de vitesse c/β doit être en résonance sur la longueur de la trajectoire."
"the wave of frequency ν and velocity c/β must be in resonance on the whole length of the trajectory."
Ref: De Broglie, L. (1923) Ondes et Quanta. Comptes rendus T.177 (1923) 507-510.
The following year, de Broglie published two more notes, in one of which he mentioned that from this viewpoint, Bohr's famous "frequency condition law" could be interpreted as involving some sort of "beat" of "pulsation" ("un battement" in the original French text), that is, a resonance state associating the frequency of the emitted wave to the initial electron stationary state and to its final stationary state. Two years later Schrödinger introduced the wave function to account for this measurable condition.
Ref: Einstein, A., Schrödinger, E., Pauli, W., Rosenfeld, L., Born, M., Joliot-Curie, I. & F., Heisenberg, W., Yukawa, H., et al. (1953) Louis de Broglie, physicien et penseur. Éditions Albin Michel, Paris. Page 462.
Ref: De Broglie, L. (1924) Sur la définition générale de la correspondance entre onde et mouvement, Comptes rendus de l'Académie des Sciences. (Paris) 179, 39.
Ref: De Broglie, L. (1924) Sur un théorème de Bohr, C. R. Acad. Sci. (Paris) 179, 676, Comptes rendus de l'Académie des Sciences. (Paris) 179, 39.
Einstein initially disagreed that the wave function could represent a resonance state, but he recognized his understanding of the fact in 1952:
"Ich will dem zusammen mit Frau B. Kaufman verfassten Beitrag zu diesem Bande einige Worte vorausschicken in der einzigen Sprache, in der ich mich mit einige Leichtigkeit ausdrücken kann. Es sind Worte der Entschuldigung. Sie sollen zeigen, warum ich, trotzdem ich De Broglie visionäre Entdeckung des inneren Zusammenhanges zwischen discreten Quantenzuständen und Resonanzzuständen in relativ jungen Jahren bewundernd miterlebt habe, doch unablässig nach einem Wege gesucht habe, das Quantenrätsel auf anderem Wege zu lösen oder doch wenigstens eine Lösung vorbereiten zu helfen."
"I will begin my contribution prepared for this book in collaboration with Mrs. Kaufman with a few words in the only language in which I can express myself with any ease. They are words to express regret. They are meant to show why - although I observed admiringly in my years of relative youth the genial discovery by Louis de Broglie of the intimate relation between the discrete quantum states and resonance states - I nevertheless ceaselessly searched for some manner to resolve the enigma of quanta by some other means, or at least help in preparing such a solution."
Ref: Einstein, A., Schrödinger, E., Pauli, W., Rosenfeld, L., Born, M., Joliot-Curie, I. & F., Heisenberg, W., Yukawa, H., et al. (1953) Louis de Broglie, physicien et penseur. Éditions Albin Michel, Paris. Page 4.
In the same reference (Page 16), Schrödinger clearly expressed his frustration for the neglect of any research in this direction in the chapter that he contributed:
"For it must have given to de Broglie the same shock and disappointment as it gave to me, when we learnt that a sort of transcendental, almost psychical interpretation of the wave phenomenon had been put forward, which was very soon hailed by the majority of leading theorists as the only one reconcilable with experiment, and which has now become the orthodox creed, accepted by almost everybody, with a few notable exceptions."
Schrödinger and de Broglie were convinced that the frequency of an emitted quantum could be produced only by means of a progressive mechanical process dependent on the resonance characteristics of an electron initial stationary state, and whose emission mechanically determined in a clearly describable manner the altered resonance characteristics of the final stationary states and that solving this problem would be useful not only in spectroscopy, but also in chemistry.
He expressed the same frustration about the neglect for research in the electron resonance states in this ref:
Schrödinger, E. (1952) Are there quantum jumps? Brit. J. Philos. Sci. 3 109,233.
All of these references are still available, to be accessed by interested scientists.
Irrespective of opinions on this issue, research on resonance states needs to finally be resumed for the last hurdles to be resolved.
Best Regards
André
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"I thought about quantum mechanics a hundred times more than general relativity, but I still don't understand," Einstein said.
Perhaps the most difficult to understand is the wave-particle duality, which may be because the understanding of it is only in the form of mathematics.In fact, no one can actually verify the wave-particle duality, because the experiment can't verify a single photon.
Electrons orbiting the nucleus of the cycle and the volatility of the particles there are closely linked, we can think of chemical bonds between atoms and atomic are fluctuating, at a certain moment because electronic is only a position on the orbit, and from the time a constantly changing position, the this kind of change has the regularity.When two atoms of electrons near each other, two atoms repel each other, and when electrons in an atom near the nucleus of another atom when they will attract each other, so that can form regularity of volatility.
Inner surface cracks in the double-slit experiment of atom has been in a regular wave conditions, when the particle is trying to through the gap, when near the atom will be fluctuations in the perforated of atomic bomb, a reflection of photonic and electronic electromagnetic ejection in such a state of regular fluctuations, as the accumulation of time and the number of regular interference fringes are formed.The smaller the momentum of a particle is, the larger the Angle of the ejection is, the greater the spacing of the stripes, the longer the wavelength is.
Electronic counter near the double slit to observe, emitting a large number of photon hits the aperture inner surface of atoms, and makes the surface atomic wave interference, can be seen as inhibits such a state of regular wave, the particles will no longer through double slit by regular reflection and ejection, which in turn has emerged two bright stripe.
This is why increasing gap width will not cause interference and diffraction, because of the emitted particles and gap edge contact and collision probability becomes a matter of fact interference and diffraction and crack width, crack of fluctuations, particle momentum, launch position and the Angle of aperture.
No there isn't. All this is understood and taught in physics courses, so it would be useful to actually study quantum mechanics, instead of trying to guess.
These lectures: http://www.feynmanlectures.caltech.edu/III_toc.html might be a good place to start.
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it is possible to measure only one quantum state out of superposition states...beyond this observed state what happen to remaining super-positioned quantum states?
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