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# Quantum Mechanics - Science topic

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In energy conservation situations where the transient probability is additive, irrational numbers such as 2^1/2 have no place.
However, especially in QM as I understood it, the probability amplitude is multiplicative rather than additive.
The question is why in particular is 2^1/2 so important in QM?
An irrational such as you give has no known direct relevance to QM. Its math not physics. However, enough confusion have I heard recently as to ask how you reach this idea?
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Quantum mechanical calculations of infrared spectra return the absorption coefficient times the refractive index, which is effectively the dielectric function. But this result is compared with absorbance spectra. The higher the oscillator strength, the greater become the differences (see, e.g. ). Accordingly, e.g., for the water HO stretching vibrations, it makes no sense to alter the calculations to better fit the absorbance bandshape, because those of absorbance bands and the dielectric function are different. Why is this not taken into account?
The dielectric function is a dependence of the complex relative permittivity (dielectric constant) on radiation frequency. Proceeding the complex dielectric constant one could calculate absorption and refraction.
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The standard model has 17 named fundamental particles and each of these particles are derived from a corresponding field. Do you visualize these fields as additions to the properties of the vacuum or part of a single quantum vacuum? For example, virtual electron/positron pairs are continuously forming and annihilating. Are the virtual electrons/positrons distinct additions to the vacuum or is the electron/positron field and these virtual particles a fundamental part of the quantum vacuum?
If an expanded model of the quantum vacuum incorporates all fields, this implies that a grand unification of all particles and forces is possible. However, if all these fields are independent, then unification does not appear to be possible.
John A. Macken I agree with Stellan on this one. The problem goes right back to a change in understanding after James Clerk Maxwell. Maxwell thought of a field as a classical field and attributed the forces of electricity and magnetism to an effect of the medium. Not only did he unify electricity and magnetism, he also conceptually unified with gravity by showing it to be an effect delivered by the medium. He noted that the inverse square law applies to gravity and electromagnetism.
Then Albert Einstein showed that gravity is caused by the medium of space in the form of Spacetime curvature. This was General Relativity. Unfortunately, Special Relativity creates a big problem for the unification of physics. Einstein said in his talk to the university of Leiden in 1920 that an ether is required for general relativity and this ether is space itself. He then goes on to claim (because of SR) that we cannot consider motion relative to this ether.
Deny the existence of a medium of space was a missed opportunity at unification. Now we have the standard model of particle physics and of course it is possible to replicate experimental results by defining multiple (21) physical fields with parameters in the field equations taken from experimental data. The problem is that fundamental physics is not to be understood through particles or fields but through waves in Spacetime.
Richard
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The quantum mechanical nature of atomic objects can be difficult to explain to an audience of non-experts. I was wondering whether the following analogy might be suitable: most people are familiar with the game that already very small children play, namely to stack wooden blocks on top of one another, building a higher and higher tower ... until it topples and comes crashing down. :-) My idea was to state that it is fairly easy to stack two blocks on top of another; even three or four, and so on. But as the number of blocks becomes larger, the tower becomes more and more unstable, and will crash down at the slightest disturbance. - The analogy to quantum mechanics would be that one of the essential features is that of superposition: atomic systems or even small molecular systems can be easily put into a state of superposition and stay there. However, for objects built of many atoms (hundreds, thousands, millions, ... 10 to the power of 23!), this becomes quickly impossible. The slightest disturbance from the environment will cause the superposition to be destroyed and the system "crashes down" (collapses) into a single state.
What do you think about this analogy? Is it a good one, or is it lacking in certain ways? Would you modify it? I am curious to hear your thoughts!
/ralph
I use in my lectures hydrodynamic quantum analogs based on walking silicone oil droplets:
There are great videos on YouTube, and most of quantum phenomena are covered by theses systems, as for example:
Recently, even Bell's theorem is covered in numerical models:
although with non-dynamic settings yet. Therefore, these systems can explain most of the quantum phenomenology, if not all. Interestingly, the wave-particle duality has been derived from classical electrodynamics recently, inspired by these models:
with unexpected consequences concerning the electrodynamic origin of mass, of classical mechanics and also of quantum phenomena. Sincerely yours,
Álvaro
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how can fermi energy explain the conductivity of Cu and Nickle
By the property that the fraction of the conduction band of copper that contains available states is larger than for nickel. The calculation can be quite involved in practice, but one shouldn't conflate principle with practice.
What quantum mechanics allows to understand is that the energy spectrum for electrons in any crystal is described by bands and the electrons that contribute to the conductivity, i.e. to the electric current, that an external electric field can give rise to, have energies that belong in the conduction band. So the greater this filling factor is, the better the conductor the material is.
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Consider the quantum field theory (QFT) operator (an operator for each space-time point) that the field amplitude becomes when making the transition from classical field quantities to QFT operators. We will call this the field-amplitude operator. The type of field considered is one in which the classical field amplitude evaluated at a given space-time point is a complex number instead of a real number. In the QFT description, the field amplitude is not an observable and the field-amplitude operator is not Hermitian. Can we still say that an eigenstate of this operator has a definite value of field amplitude (equal to the eigenvalue) even when the field amplitude is not an observable and the eigenvalue is not real number?
Thus, we agree that a real field amplitude is an observable, presumably. I think this can be extended to a complex field, which just consists of a couple of real fields, assembled in a complex number to better represent the O(2) symmetry.
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In the elementary quantum mechanics (QM) of a single particle responding to a given environment, the state of the particle can be specified by specifying a set of commuting (i.e., simultaneously knowable) observables. Examples of observables include energy and angular momentum. Although not simultaneously knowable, other examples include the three rectangular spatial coordinates and the three components of linear momentum. Each observable in QM is a real number and is an eigenvalue of some Hermitian operator. Now consider quantum field theory (QFT) which considers a field instead of a particle. First consider the classical (before introducing QFT operators) description of the state of the field at a selected point in time. This is the field amplitude at every spatial location at the selected time point. For at least some kinds of fields, the field amplitude at a given space-time point is a complex number. Now consider the QFT corresponding to the selected classical example of a field. Is the field amplitude an observable even when it is not a real number? It is not an eigenvalue of any Hermitian operator when not real. So if the field amplitude is an observable, there is no Hermitian operator associated with this observable. My guess (and my question is whether this guess is correct) is that the real and imaginary parts of the field amplitude are simultaneously knowable observables, with a Hermitian operator (assigned to each space-time point) for each. This would at least explain how the field amplitude can be an observable but not real and not have any associated Hermitian operator. Is my guess correct?
The same as in quantum mechanics, only now they're probabilities per unit time and unit volume.
The field amplitude isn't observable, any more than the wavefunction is; it's the modulus squared of the field amplitude that describes the probability density at each point in space and time.
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If there were the quantum mechanical equivalents of individual neurons and of larger networks of neurons, and if quantum mechanisms of error correction worked on those level, you could get something like consciousness. This is because information could (in principle) flow between neurons - that means you have a mechanism of some sort of distributed computing inside the brain. What's your view?
An alternate (rather elaborate) discussion about the two can be found below. However this particular idea just emerged once I started rethinking about information in general.
Olivier denis Yes. Your statement is right=the universe does not need me to exist.
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Can someone please help how to write Klein-Gordan equation for massless particles and also its action or Euler–Lagrange equation for massless particles?
The simple form of the Klein-Gordon equation for massless particles can be
(∂2/∂x2+∂2/∂y2+∂2/∂z2)u=0. The solution of this equation involves the result, physically verifiable, massless particles travel with constant physical velocity, with respect to a frame, assumed like a reference.
The Euler-Lagrange equation for massless particles has the simplest form: £=0. In an equivalent model in which a massless particle has an equivalent mass m, the potential energy of the particle, in a gravitational field, is mgz and, the kinetic energy is m(∂2x/∂t2+∂2y/∂t2+∂2z/∂t2)/2. The solution of the equation proves an elementary massless particle, in the equivalent model, moves with a parabolic trend with respect to the axis z of fall.
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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.
With respect to human societies and production methods, dear Anatoly A Khripov , we are witnessing the informatization of the economy. In this sense, this informatization changes the material conditions of the production process itself.
However, it is difficult to assess, if information is a new production factor or if the traditional production factors become more information-intense.
Consequently, my viewpoint from the physics of social systems (natural science of human society and mind) discerns that information converts (reorganizes) matter, energy and mass, in terms of economic production.
———-
Thermodynamic entropy involves matter and energy, Shannon entropy is entirely mathematical, on one level purely immaterial information, though information cannot exist without "negative" thermodynamic entropy.
It is true that information is neither matter nor energy, which are conserved constants of nature (the first law of thermodynamics). But information needs matter to be embodied in an "information structure." And it needs ("free") energy to be communicated over Shannon's information channels.
Boltzmann entropy is intrinsically related to "negative entropy." Without pockets of negative entropy in the universe (and out-of-equilibrium free-energy flows), there would no "information structures" anywhere.
Pockets of negative entropy are involved in the creation of everything interesting in the universe. It is a cosmic creation process without a creator.
—————
Without the physical world, Ideas will not exist. ― Joey Lawsin
Even when money seemed to be material treasure, heavy in pockets and ships' holds and bank vaults, it always was information. Coins and notes, shekels and cowries were all just short-lived technologies for tokenizing information about who owns what. ― James Gleick, The Information: A History, a Theory, a Flood
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Have these particles been observed in predicted places?
For example, have scientists ever noticed the creation of energy and
pair particles from nothing in the Large Electron–Positron Collider,
Large Hadron Collider at CERN, Tevatron at Fermilab or other
particle accelerators since late 1930? The answer is no. In fact, no
report of observing such particles by highly sensitive sensors used in
all accelerators has been mentioned.
Moreover, according to one interpretation of uncertainty
principle, abundant charged and uncharged virtual particles should
continuously whiz inside the storage rings of all particle accelerators.
Scientists and engineers make sure that they maintain ultra-high
vacuum at close to absolute zero temperature, in the travelling path
of the accelerating particles otherwise even residual gas molecules
deflect, attach to, or ionize any particle they encounter but there has
not been any concern or any report of undesirable collisions with so
called virtual particles in any accelerator.
It would have been absolutely useless to create ultrahigh vacuum,
pressure of about 10-14 bar, throughout the travel path of the particles
if vacuum chambers were seething with particle/antiparticle or
matter/antimatter. If there was such a phenomenon there would have
been significant background effects as a result of the collision and
scattering of the beam of accelerating particles from the supposed
bubbling of virtual particles created in vacuum. This process is
readily available for examination in comparison to totally out of
reach Hawking’s radiation which is considered to be a real
phenomenon that will be eating away supposed black holes of the
universe in a very long future.
for related issues/argument see
It pleases me to see this discussion, realising there are more critical thinkers out there. Let me try to add a simply phrased contribution.
In my opinion, Physics has gone down the rabbit hole of sub-atomic particles and that part of physics has become what some call “phantasy physics”. Complex maths is used as smoke and mirrors to silence critical physicists who are convinced that theory must be founded in reality and that empirical evidence is necessary.
Concepts such as ”Big bang”, black holes, dark matter etc are actually hypotheses that try to explain why the outcomes of measurements are not in accordance with the calculations made on the basis of Einsteins theories of relativity. Unfortunately, and perhaps through the journalistic popularisation of science, these concepts have been taken as reality, such as “scientists have discovered dark matter, or anti-matter”. No, they have not. What they discovered was that the measured light or matter in the universe or a part of the universe was not as much as had been predicted by calculations based on a theory. Usually in science, that would lead to a refining of the theory. Here it did not, perhaps because Einstein has been placed on such a high pedestal that his theories are seen as the alpha and omega of physics that may not be questioned or touched, as that is considered sacrilege.
The solution was the hypothesis of Cookie Monsters, things out there that ate light or matter = black holes and dark matter. Anyone who dares questions these methodological steps is intimidated and attacked with complicated terminology and complex mathematics. Most physicists are afraid of looking stupid and therefore shut up. Decades ago the physics professor who was my head supervisor (experimental physics) said to his students that if you could not explain your work in ordinary household language, then you did not really understand it yourself. He considered complicated language and naming theories and authors as a cover up for not grasping the essentials.
A reason for looking at yet another species of virtual particles is that research proposals in this field receive funding because physicists all over the world are doing it. It is the reigning paradigm and it will take a ground swell of opposition to move on to the next phase in science after the 50-odd years of the present, now stagnant, paradigm.
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I am trying to run a QM/MM in Amber on a protein-ligand system. I have looked for tutorials but they don't explain a few things such as how to heat your system and equilibrate it before MD.
Then there are errors in output files. I have run the questions in the list and applied the changes, but the errors still remain. I would appreciate if someone could share their experience on running these for protein-ligand systems.
Thank you.
Hi,
I am trying to run QM/MM with the oniom package. My system consists of  protein and DNA. During gaussian run, i am  getting  error like-
Bondstretch undefined between atoms   5618   5619 HO5'-O5' [L,L]
Bondstretch undefined between atoms   5618   5620 HO5'-C5' [L,L]
-------------------------------------------------------------------------------------------------
-------------------------------------------------------------------------------------------------
Angle bend  undefined between atoms   6536   6537   6539 N1-C6-C5 [L,L,L]  Angle bend  undefined between atoms   7471   5618   7472 OW-HO5'-HW [L,L,L]  * These undefined terms cancel in the ONIOM expression. MM function not complete
These atoms are mainly from DNA. Can you  please tell me where we have to  incorporate these parameters in gaussian?
Thank you
Vipin
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A physics experiment [1], driven on an expanding spin-orbit coupled Bose-Einstein condensate, suggested that a self-trapping effect band (explained in terms of the Peierls-Nabarro energy barrier) separates two dispersion domains characterized by a positive mass but a spin reversal. The self-trapping phenomenon was naturally explained by a negative effective mass related to a negative curvature of the underlying dispersion relation (as opposed to parabolic curvatures).
To better contextualise my question from a practical point of view, I will quote Wikipedia ( follow https://en.wikipedia.org/wiki/Spin_(physics) ): “Mathematically, quantum-mechanical spin states are described by ‘vector-like objects’ known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-1/2 particle by 360° does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720° rotation (The Plate trick and Möbius strip give non-quantum analogies).
I appeal here to physicists in a spirit of free and friendly discussion.
1. Khamehchi et al., “Negative-Mass Hydrodynamics in a Spin-Orbit–Coupled Bose-Einstein Condensate”, 2017 - https://www.researchgate.net/profile/Thomas-Busch/publication/311612111_Negative-Mass_Hydrodynamics_in_a_Spin-Orbit-Coupled_Bose-Einstein_Condensate/links/5a97b63845851535bcdee6fd/Negative-Mass-Hydrodynamics-in-a-Spin-Orbit-Coupled-Bose-Einstein-Condensate.pdf
Excerpt from Bouyle et al., "The Big Bang as a Mirror: a Solution of the Strong CP Problem", 2022 -
"In the LRSM (minimal left-right symmetric extension of the Standard Model),
requiring the two sheets of spacetime [...] to be related by a mirror symmetry
[...] also solves the strong CP problem."
+ Boyle et al., "Two-Sheeted Universe, Analyticity and the Arrow of Time", 2021 -
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In Atomic and molecular Physics, there are two notable selection rules 1) ∆l=±1and 2) ∆ml=0,±1 for a spherically symmetric potential. What is the logic behind these two rules?How do they come/derived?
The hamiltonian of such a system, usually, has the form H=H_S+H_{SR}+H_R, H_S is the hamiltonian of an isolated molecule, H_R is the hamiltonian of the radiation field, H_{SR}=\Sum_k (S^{+}+S)(a^{+}_k+a_k), here S operators refers to the system and a_k operators refers to the k-th mode of the radiation field. To see if there is enegry transition between eigenstates |x> and |y> of H_S, you should compute <y|H_{SR}|x>. If it is zero, there is no transition of such a type between |x> and |y>.
But you should take into account that there are more ways of an molecule to interract with the environment, for example dephasing H_{SR}=\Sum_k S^{+}S(a^{+}_k+a_k)
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I am following the model explained in this paper:
which could give a good estimate of the QE regardless of wavelength.
However when it comes to this equation 6, I don't see how they get the transmission amplitude (Tn) out since it is inside a summation.
I am also having difficulties seeing the restriction for the fourier components l.
On the left side of the equation is dirac-delta(l), what kind of restrictions does this lead to the value of l?
I agree that taking the integral on both sides will eliminate the delta function.
If I am not mistaken, when I have the integral on the right side, I can change it into a summation over l.
But, I should be looking for a kroneker delta and I haven't found it yet (something that enables me to look at one n at a time)
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If ever confirmed, the applicative potential would be tremendous...
I refer here to Grinwald's publication:
from which I quote below:
"Ultimate dependence on truths of pure numbers, rather than pre-existing physical law, would seem a desirable step towards a more reasoned description of quantum mechanics, which is empirically correct but appears deeply mysterious."
"A standard teaching is that the wavefunction evolves deterministically under Schrödinger’s equation, until the moment of measurement when it undergoes “collapse” according to the Born probabilities. However the central limit theorem implies a random process underlying the Schrödinger equation itself, counter to the essentially deterministic view of the wavefunction."
"More precisely, it is concluded that the content of Schrödinger’s equation is equivalent to propagation by a generalized Gaussian function, normalized in the sense of C [i.e. complex number system] with the norm conserved in time. The key role of the Gaussian is attributed to the central limit theorem, which extends to random vectors in infinite-dimensional separable complex Hilbert spaces."
"The change from interpreting quantum mechanics to reconstructions of it has been described by Grinbaum [...] as a paradigm shift. All the reconstructions rest on assumptions. Arguably the present assumptions are few in number, of a general nature and relatively simple: they consist of a Gaussian propagator, and norm conservation in C.
Randomness has been seen as a puzzle to which the many worlds interpretation [...] may provide a resolution. As the present treatment deals with Gaussian functions, which occur by virtue of the central limit theorem, randomness is implied, but it is indifferent as to possible sources of randomness."
I appeal here to physicists in a spirit of free and friendly discussion.
Last but not least, Schrödinger's equation has already been applied to image filtering (both low-pass and high-pass filtering) by means of the so-called Schrödinger Transform of Image introduced by Lou et al.:
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If we ignore fermions and bosons, what is your model of the pristine vacuum? One aspect of this question is designated the “cosmological constant problem”. The observable energy density in the universe is about 10-9 J/m3. This is the average energy density of ordinary matter, dark matter, and dark energy. However, one interpretation of quantum field theory says that the vacuum has zero-point energy density of about 10113 J/m3. This enormous energy density has been called “the worst theoretical prediction in the history of physics.” However, this enormous vacuum energy density is supported because it is used to make the most accurate theoretical prediction in all of physics (the electron’s anomalous magnetic moment).
Quantum field theory says that the vacuum is not empty because it contains all the fields required by the standard model of particle physics. However, the geometric interpretation of gravity from general relativity implies the vacuum is an empty medium that can be curved by matter. For example, the strong equivalence principle requires this geometric interpretation. If gravity is transferred by gravitons, then gravitational acceleration and physical acceleration would have different causes.
There have been hundreds of scientific articles written on the cosmological constant problem and most of these articles attempt to disprove the 10113 J/m3 energy density. There is no doubt that this is not observable energy, but could this be the undetectable fields required by quantum field theory? A field is undetectable until an “excitation” is introduced to create an observable particle (observable energy density). I have written several papers exploring this model. However, what is your vacuum model?
Wolfgang Konle General relativity (GR) is a top-down approach to understanding gravity, spacetime, the rate of time, etc. This approach has made wonderful progress, but it has its limitations. For example, GR does not attempt to describe the underlying physics of how a fundamental particle such as an electron creates curved spacetime. GR merely postulates that matter causes spacetime to curve and proceeds to mathematically describe this curvature.
I assumed John Wheeler's model of the quantum vacuum (Planck length oscillations at Planck frequency) and calculated the acoustic properties of this elastic quantum mechanical medium. I postulated this is the structure of a fundamental field. I tested this hypothesis by seeing if it was possible to build a model of an electron by introducing ħ/2 angular momentum "excitation" into this medium. After several steps, the model exhibited an electron's energy, inertia and de Broglie waves. However, then the model unexpectantly also generated an electron's gravity and electrostatic properties. Since a single model was generating both the electron's gravitational and electrostatic forces, it was also making predictions about how these forces should be related and other previously unknown characteristics of these forces.
GR still works at the scale of an electron, but equations are simplified because weak gravity approximations are highly accurate when dealing with an electron's mass/energy. In previous posts, I have given both equations and referenced papers on this subject. For example, one prediction that is easy to check is the predicted equation for the ratio of the gravitational force (FG) between two electrons divided by the electrostatic force (Fe) magnitude between the same two electrons. The equation incorporates the fine structure constant (α) and the electron's wave amplitude: Planck length (Lp) and the electron's Compton angular wavelength ƛc = ħ/mec.
FG/Fe = α-1Lp2c2
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I'm searching for a good collaborator or a research group that might want to tackle an interesting problem involving the relationship between quantum dots generating nanoparticle clusters and their DNA/proteins corral. This relationship is encapsulated by geometric proximity, that is I'm looking for someone who might know how quantum mechanics impacts something like these nanoparticles, such as how close a nanoparticle is to another nanoparticle or a protein and whether sized clusters form. Ping me if you're in the bio sciences, computational biology, chemistry, biology or physical sciences and think you might be able to shed some light on the above.
Navjot Singh This might surprise you but I recommend you analyse the problem without using quantum theory. If you take a look at the preprint linked below you will see a different approach to the analysis of molecular bonds:
This is based on the Spacetime Wave theory and shows how a stable bond is formed when the electrostatic and electromagnetic forces are in balance.
Richard
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On this eve of mahashivratri, I would like to share my opinion that, Soon quantum computations explore that, ingenral, bipartite graphs are not symmetric about the origin.
This may may lead new directions in the study of quantum mechanics, molecular biology in particularly genetic engineering.
Hi , can you prove that ????, Good luck
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Of course, as the frequency of electromagnetic waves increases, the magnetic force increases which people are not yet aware of. This fact is also responsible for creating the photoelectric effect. It's a mystery why people didn't realize this for the past 100 years.
This fact cannot be explained by classical electrodynamics as well as quantum mechanics.
It might be a good idea to study classical electrodynamics, the subjects are standard exercises.
Magnetic force on electric charges is described by the Lorentz force....
The photoelectric effect is beyond classical electrodynamics, but is, now, also, standard material.
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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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In quantum mechanics, it is always mentioned that a quantum particle can be at two places at the same time. In a similar way, we can also say that the actual particle has no location. can we say it?
When we say "location", we mean a point in spacetime. There is always non-zero probability for a quantum particle to be at any point in spacetime and according to quantum mechanics particle takes all these positions( or locations ) at the same time. So particle has location but it is probabilistic.
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Can these physical constants be traced to a source inside our universe? When I was in grade school, I was taught that an unseen deity created the laws of nature. This implies that there is no physical source of the constants because they are externally imposed on the universe. As physicists, we assume that everything in the universe has a logical explanation. For example, if we detect a steady negative electric field, we know this must be caused by an excess of electrons in the vicinity. However, when we find that constants G, c, and ħ exist everywhere in the universe, we usually do not search for the cause. Is the gravitational constant a property of space or a property of mass/energy? Angular momentum can only be transferred in integer units of ħ. What enforces this?
Since this is a discussion question, I will give my opinion. John Wheeler suggested that the empty vacuum is not empty. He states that on the scale of Planck length, the vacuum is the seat of the most violent physics. At this scale, the term “vacuum fluctuations” literally means the vacuum is undergoing undetectable Planck length expansion and contraction at Planck frequency. These lp and ωp fluctuations incorporate c, G and ħ. Therefore, in this model, the quantum vacuum has structure that incorporates these constants. What is your opinion? Do you believe the vacuum is an empty void and particles introduce these constants?
Hi @ Stefano,
Good to hear from you again. As you may recall, I carry this model of the quantum vacuum much further and develop a model of the universe where everything (including electric charge and gravity) is derived from this model of the quantum vacuum. The dielectric constant of the vacuum (εo) is addressed because I propose a new constant of nature, I call the “charge conversion constant”. This is Planck length (Lp) divided by Planck charge (Qp). This converts the units of Coulomb to polarized length. This will not make any sense in this brief post, but using this charge conversion constant, the Coulomb force constant (1/4εo) converts to Planck force Fp = c4/G. This is Eq. (28) in the paper below. This charge conversion constant also converts the impedance of free space (Zo ≈ 137 Ω) to the impedance of spacetime Zs = c3/G. This proves photons and gravitational waves encounter the same impedance.
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If something is next to something without extension that itself has no extension, it never manages to actually be SPACE.  Instead it is the juxtaposition of non extended singularities, manufactured into a matrix in whose connection singularities are impossible.  It makes no sense to me how space can be the juxtaposition of non extended and non extendable single locales who generate a system of ways of articulating spacial relations of all objects made up of material.
How can material be made of nothing more than frequency of strings working harmoniously.  It makes no sense quantum Mechanics...it must be wrong as a model goes, even though it's models are enormously precise in some of their predictions.
IF I am wrong and it is correct can anyone please explain to me how something non extended can be next to something else non extended to between the two of them form a displacement? It's impossible right?  So please explaing Quantum Mechanics to me then.
They cannot have extensions .They act in such a manner as to mathematically represent extensions .
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We assume the answer is yes.
Energy density fields, electric potential, thermal energy, sound, etc., have appropriate sources/sinks terms and Dirichlet/Neumann boundary conditions that are outside the scope of quantum mechanics.
It is known that the continuity equation in quantum mechanics, which is derived by taking into account the Schrodinger equation, relates the partial derivative of the probability density to the divergence of the probability current (probability flow). By adding an imaginary part to the potential, an extra term appears in the continuity equation, which is proportional to the imaginary part of the potential and describes the creation or annihilation of probability locally. The imaginary part of the potential can thus provide a (phenomenological) description of wells and sinks of probability or equivalently, of creation and absorption of quantum mechanical particles.
For more details, the following presentation may be useful
As for mixed boundary conditions, I suppose that in certain cases, they could be imposed to the probability flow.
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What quantum mechanical mechanism governs the super-hardness of the materials.
The diamond structure relies both on a diamond lattice structure as well as the covalent bond.(a form of carbon)
Covalent bonds are explained by QM effects. An electron hesitates between occuping two equivalent sites near one atom or another, this provoques a gap and energy lowering in the electronic spectrum, stabalizing this kind of structure.
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It is a common sense that there must be only one theory which can describe the entire universe. But we also know Quantum mechanics & Theory of Relativity are not compatible with each other. Isn’t is sufficient to say that either both theories are wrong (minimal chance) or are approximation of the same theory (stronger candidate)? Why we are not trying to write a theory from the scratch which may be compatible with both?
An international team of researchers developed a unified framework that would account for this apparent break down between classical and quantum physics, and they put it to the test using a quantum satellite called Micius. They published their results ruling out one version of their theory on Sept 19th in Science.
Einstein’s legacy left two completely justified and scientifically provable theories. However, when viewed together, the quantum mechanical model does not completely align with general relativity. This is where the fundamental dilemma arises: A major disagreement exists between physics’ two most important frameworks.Relativity treats objects as point particles that exist as independent masses in time and space. Quantum mechanics, however, treats matter as wave functions that do not possess positions as point particles do, but are probability distributions. Relativity’s predictions produce definite outcomes, whereas quantum mechanics’ predictions produce probabilistic ones. As a result, applying relativity to objects of the scale at which quantum mechanics operates fails to produce sensible answers.Robert Brandenberger, a professor in the department of Physics at McGill, completed his post-doctoral research under Hawking. Brandenberger now works on the cosmological aspects of string theory, a postmodern theory that thinks of particles not as definite points, but as one-dimensional ‘strings’ which propagate through space-time in constant interaction with one another.For matter to be described quantum mechanically, then gravity must be described quantum mechanically as well.” Brandenberger said.If both quantum mechanics and relativity work independently, then they also have to work in unison. Here lies the scientific grey area physicists face when trying to integrate quantum mechanics with relativity: They simply do not function properly.“It is not that they oppose one another, but general relativity has a limited range of applicability,” Brandenberger said. “Newtonian [classical] mechanics describes point particles very well except if you go down to very small scales.”The same drawback applies to quantum mechanics on a larger scale: It describes, with great accuracy, the inner workings of subatomic particles, but fails to precisely address particle properties in the grand scheme.“When you include quantum mechanics, you get corrections to Einstein’s original equation,” Professor of Theoretical Cosmology Jim Cline told the Tribune. “These corrections are very small when talking about the everyday applications of gravity, but at short distances and high energies the corrections that come from quantum mechanics become very big and are infinitely many.”He explained that the data required to discern a unified theory are incredibly, and maybe impossibly, hard to collect using current research methods.“The theory itself becomes un-predictive,” Cline said. “Scientists do not like that.”However, black holes in the outer-reaches of the universe may provide the answer to unifying these two theories, an argument Hawking himself supported in his hypothetical ‘theory of everything.’“If you want to consider the physics of something very massive, that is also very small, you would need to understand both general relativity and quantum mechanics simultaneously,” Maloney said.The density of black holes is so great that nothing, not even light, can escape their immense pull. If a black hole can exert gravitational effects on large masses like planets in the same way that it can pull in light—which has a mass of almost zero—then an explanation of the phenomena of black holes would, in theory, reveal how large, macroscopic particles can interact with tiny, nanoscopic ones.
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See the corresponding blog at https://restframe.blogspot.com
The detection of the existence of the Cosmic Microwave Background Radiation (CMBR) from everywhere around in the universe has puzzled theorists. Not least because of the discovery of a Doppler effect in the data that can only be interpreted as direct related to the velocity and the direction of the motion of the solar system. But if it is correct we have to accept that there exist a rest frame in the universe. Actually we can determine the existence of absolute space and that is not in line with the “belief” of most of the theorists.
There is another method to verify the results: counting the numbers and measuring the brightness of galaxies from everywhere around. The first results – using visible light – were not convincing. But a couple of days ago The Astrophysical Journal Letters published a paper from Jeremy Darling with results that were obtained with the help of radio waves: “The Universe is Brighter in the Direction of Our Motion: Galaxy Counts and Fluxes are Consistent with the CMB Dipole” (https://iopscience.iop.org/article/10.3847/2041-8213/ac6f08).
In other words, it is real. We can determine the existence of "absolute space". Moreover, we know from set theory (mathematics) that absolute space and phenomenological reality must share the same underlying properties otherwise we cannot detect the existence of absolute space. The consequence is that absolute space has a structure too, because phenomenological reality shows structure.
None of the grand theories in physics is founded on the structure of absolute space. Therefore we are facing a serious problem in respect to the foundations of theoretical physics (the conceptual framework of physics).
As we know, Einstein stated that aether is no longer absolute and used geodesic, it depends on the presence of matter and changes.Empty space has nothing physical and the basis of mechanics is not compatible with it For a system that floats freely in space, its relative position, relative velocity, and rotation are considered And physically it can be considered a feature in itself that is not related to the system The theory of relativity solved this problem by creating a neutral electrical behavior. The point of mass is governed by the law of geodesy, according to which the effects of inertia and gravity are no longer considered separately.In doing so, it attached characteristics to the aether which vary from point to point, determining the metric and the dynamic behaviour of material points, and determined, in their turn, by physical factors, namely the distribution of mass/energy. Thus the aether of general relativity differs from those of classical mechanics and special relativity in that it is not ‘absolute’ but determined, in its locally variable characteristics, by ponderable matter.
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I am using MP2/cc-pVDZ, MP2/cc-pVTZ, MP2/cc-pVQZ, QCISD/cc-pVDZ and QCISD/cc-pVTZ theories to calculate SPE of C2H4N4O4, but frequently met Error l502, that is likely to be caused by SCF convergence failure. Increasing the SCF cycle from default 128 to 512 doesn't help.
I understand that changing the convergence way to quadratically convergent SCF procedure (scf=qc or xqc) can solve my problem, and indeed it works. But it would influence the energy calculation results, making them obviously different from those obtained via normal SCF convergence way, and it will also increase the T1 Diagnostic of QCISD methods over an unacceptable value (eg. bigger than 0.05).
• Could any expert in QM calculation help me with problem? to allow me get the right SPE result and avoid the SCF failure error.
Part log files for your information
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Rare condition: small coef for last iteration: 0.000D+00
Rare condition: small coef for last iteration: 0.000D+00
Rare condition: small coef for last iteration: 0.000D+00
Rare condition: small coef for last iteration: 0.000D+00
>>>>>>>>>> Convergence criterion not met.
SCF Done: E(UHF) = -670.314163564 A.U. after 513 cycles
NFock=128 Conv=0.11D-03 -V/T= 2.0006
<Sx>= 0.0000 <Sy>= 0.0000 <Sz>= 0.5000 <S**2>= 0.9099 S= 0.5770
<L.S>= 0.000000000000E+00
Annihilation of the first spin contaminant:
S**2 before annihilation 0.9099, after 0.7656
Convergence failure -- run terminated.
Error termination via Lnk1e in /app1/centos6.3/gnu/apps/gaussian/g16a6/g16/l502.exe at Mon May 30 16:51:42 2022.
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Quadratic convergence (QC) algorithm has significantly higher probability to converge to unstable wavefunction than the default algorithm, therefore scf=qc or scf=xqc is not recommended to be considered as the first attempt when you encounter SCF convergence problem. All methods that may solve SCF unconvergence in Gaussian have been summaried in http://sobereva.com/61 (written in Chinese, you can use Google translator), please check.
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I have a quantum mechanics course in my Ph.D. program next semester but I never had this course before and I have to do good in this particular topic. Can someone suggest to me a few elementary books on quantum mechanics which might help me?
For an overall introduction and general reference to related issues, the best book I ever laid hands on on Quantum Mechanics is "Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles" by Robert Eisberg and Robert resnick. John Wiley & sons.
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It is like Puzzle to all my physics family. If any body gives valid discussion or answer it would be helpful.
let me ask a question: if time is one dimensional background, what is the position of a particle on this one dimensional background of time?
How do you calculate position of a particle without the violation of law of conservation of energy on this one dimensional background of TIME?
as long as qm continue to use classical variables, instead of its proper ones(unknown yet), it cannot avoid the uncertainity principle@
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It would seem to reconcile quantum mechanics with relativity we need perhaps more to find an equation that takes us between formal systems than to have a synthesis.
I agree with Prof. Sergey Shevchenko
We should not forget (even QED is not my first field) that in the 60s same Prof. Lev D. Landau & E. M. Lifshitz couple of books on quantum field theory were retired and instead, a new QED book appeared later.
History sometimes also helps, I consider non-relativist quantum mechanics, quite a complete theory, particularly elastic and non-elastic scattering theory (Profs. Landau & Lifshitz 3rd volume) as group theory ( Prof. Messiah book), but many ignore these two parts, and now use liquid crystals to explain solids when we know that in hydrodynamics the angular momentum L is not conserved, a big failure in superconductivity theories, unfortunately.
For years in solid state physics, researchers only wanted papers and not the truth, just now I see some papers trying to get back to the self-consistent part of that theory in the non-relativistic part.
Best Regards
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Time is what permits things to happen. However, as a physical grandeur, time must emerge as a consequence of some physical law (?). But, how time could emerge as a consequence of something if " consequence", " causation", implies the existence of the time?
A lot of science we termed “metaphysics” long ago is just mathematics nowadays (set theory). So maybe it is more realistic if I change the title of the question: “Is time a mathematical consequence of phenomenological physics?
Physics as a branch of science is a bit troublesome. It represents the scientific method to search for – and to describe – the mutual relations between all the observable and detectable phenomena in the universe. But since ≈1900 physics is also the continuation of the main aim of philosophy: understanding the nature of reality. Unfortunately the latter is not a “tangible” aim. Actually it must be some kind of a model that represents a mixture between philosophy, mathematics and physics. And last but not least, physics is not leading in this particular scientific process. Physics is providing assistance with the descriptions of the properties of the physical universe.
Time is not a “tangible” property itself because it is a kind of an experience. Not only for humans because everything in the universe experience time. Time only exists if there is change and it shows there is a continuous change everywhere in the universe. But if everything changes – and everything influence everything at exactly the same moment because our universe is non-local – change (time) is a basic “mechanism” of the structure of our universe.
The properties of our universe were once limited to the observable and detectable phenomena (classic physics). This in contrast to philosophy because from the beginning (≈ 600 B.C.) there was a concept about the existence of an underlying “mathematical” structure that was responsible for the creation of observable/detectable reality.
In physics classic physics was replaced by “quantum physics” (Planck’s constant as the constant of energy) and quantum physics evolved into quantum field theory. Nowadays the leading theorists are convinced that matter emerges from the basic properties of the universal quantum fields. For 3 decades theorists are also trying to incorporate gravity into QFT and the consequence is that space itself must have a “non-visible” structure, a metric. In line with ancient Greek philosophers who already created a comparable concept (Parmenides and followers).
Einstein’s opinion that time is relative, is not really helpful. We can measure the rate of change of a decaying particle at moderate speed and the same particle at nearly the speed of light. Einstein shows to be right: accelerating the particle is slowing down the process of decay. But is this process “time itself” or is it just the rate of change of a composite phenomenon? One should expect that every theorists can draw the conclusion that Planck’s constant in relation to the constant speed of light (the linear velocity of a free quantum of energy) determines that time is a universal constant (the constant of physical change). In line with the expectation that at the smallest scale size the complexity in nature is build on simplicity and logic (advocated by e.g. Steven Weinberg).
But in practice physics is about measurements and equations that describe the detected standardized mutual relations between the measurable phenomena. If there is a theoretical problem in relation to the outcome of certain experiments theorists frequently start to hypothesize the existence of a new particle or even a new field to dissolve the problem. Don’t ask a theorist about the “tangible” existence of Planck’s constant or the mechanism behind the speed of light. It seems that in physics every hypothetical concept is acceptable if it doesn’t violate the equations.
In other words, if we want to understand time we have to discuss the structure of the universe.
With kind regards, Sydney
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I'm wondering how many monomeric units of a conjugated polymer I need in order to accurately calculate the HOMO-LUMO difference using ab initio methods. Does anyone have experience with this or know of a good rule of thumb?
A conjugated polymer is a type of polymer that consists of alternating single and double bonds along the polymer chain. This alternating bond structure gives conjugated polymers their unique properties, such as high electrical conductivity and optical transparency. Ab initio calculations are a type of quantum mechanical calculation that uses the first principles of quantum mechanics to predict the properties of a system. These calculations are often used to study the electronic structure of molecules and materials. The HOMO-LUMO difference is the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a molecule. This energy difference is important because it determines the strength of the molecule's chemical bonds and the molecule's overall stability.
Here the issue is related to the definition of a unit cell of a polymeric chain and it is only partially affected by conjugation. From the point of view of a solid state DFT code, you should use the minimal unit cell since any larger cell will have exactly the same electrical properties. Now, for a polymer, a single monomer (or a pair of them for conjugation) might be not enough. This is because the angle between the monomers might be not well defined (the polymer might be not flat). This one may need to build short monomer chains to construct a reasonable unit cell of the polymer. For example, for carbazole, one might need to have chains of 8-12 monomers to build a single unit cells, since each monomer is rotated with respect to the previous one by an angle between 45 and 30 degrees. (Measurement of such an angle were difficult.)
Clearly, here I am also neglecting the other issue, namely that the polymer might be bending and folding at larger scale than what is currently possible with standard DFT methods.
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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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My understanding of the significance of Bell's inequality in quantum mechanics (QM) is as follows. The assumption of hidden variables implies an inequality called Bell's inequality. This inequality is violated not only by conventional QM theory but also by experimental data designed to test the prediction (the experimental data agree with conventional QM theory). This implies that the hidden variable assumption is wrong. But from reading Bell's paper it looks to me that the assumption proven wrong is hidden variables (without saying local or otherwise), while people smarter than me say that the assumption proven wrong is local hidden variables. I don't understand why it is only local hidden variables, instead of just hidden variables, that was proven wrong. Can somebody explain this?
Dear L.D. Edmonds , if I understand your question, you do not understand where in Bell's theorem the locality assumption is made.
In section “Bell’s theorem”, page 424, in “Introduction to Quantum Mechanics”, 2nd Ed., David J. Griffiths, we read:
"The argument is stunningly simple. Suppose that the “complete” state of the electron/positron system is characterized by the hidden variable(s) λ (λ varies, in some way that we neither understand nor control, from one pion decay to the next). Suppose further that the outcome of the electron measurement is independent of the orientation (b) of the positron detector – which may, after all, be chosen by the experimenter at the positron end just before the electron measurement is made, and hence far too late for any subluminal message to get back to the electron detector. (This is the locality assumption)…”
It is also worth noting that the Bell’s theorem was formulated to resolve a thought experiment called the EPR paradox. One of the key assumptions of the EPR paradox was that the result of a measurement at one point cannot depend on whatever action takes place at a far away point at the same time [1].
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Regarding my research in quantum mechanics and the Riemann zeta function if there was a quantum operator H such that H{function Psy} = E.function Psy derived from the Schrödinger equation (time independent equation) then the vital part of this analysis is to find a potential V(x,y,z) or any in some specific coordinate system (e.g., spherical, cylindrical or others), such that V() led to determine a system where the imaginary parts of the non trivial zeros of the Riemann Zeta function named levels of energy E in a physical context could be represented as the spectrum of this operator H.
We have examples of Harmonics oscillators, free particles, infinite dwell of potential etc., but I am asking myself and the public here which would be the nature of that potential - of course- there are many works regarding that, but a good start is to identify which way should be introduced for that potential V() and in which coordinates (I think so also in exotic ones like the TNB Tangential, Normal and Binormal system) or others.
It would be so interesting to know more literature of introducing these ways of potentials V() and other ideas since Berry‘s work and even the Hilbert- Pólya‘s Conjecture.
Prof. Carlos Hernan Lopez Zapata, I can't remember now any good one, but in addition to the right previous answers, please check the book:
Quantum Mechanics, Selected Topics by A. Perelomov & Y. Zeldovich, 1998, World Scientific Publishing.
Particularly chapter 4th on the inverse scattering problem, pp. 101 & also pp. 114 as Prof. Ivan I Yakovkin suggested which talks on isospectral deformations of the SE & KdV equations.
Best Regards.
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I use orca 5.0.3 and some times get error termination. There was an error code or return code in the end of the output file and if there is list of the codes its easier to understand it and solve the problem. I have searched it but still dont get it yet. Thanks
Hi Achmad. I couldn't get an error code list too. In the meantime, maybe this script helps in debugging your script. https://github.com/rjohns03/orca-scripts/blob/master/orcajobcheck
Diego.
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On the word of Stephen Wolfram, there is a “genuine impossibility” in mathematics. That is, within mathematics, we can explicitly prove that there are things that are genuinely infinite, and cannot meaningfully be reduced to something finite.
And, as it is shown in the paper arXiv:1506.00428, this mathematical impossibility directly corresponds to physical impossibility. Namely, the Hilbert space of an Ising model of a spin glass in thermodynamic limit cannot be converted decidedly (i.e., in the sense of Church-Turing thesis of computability) into the configuration space.
This could mean that in order to explain the emergence of classicality totally from the formalism of basic quantum mechanics, we would need something other than a Turing machine (TM). Therefore, the question arises, does exist there a computing device whose computational power strictly exceeds that of a TM?
What about systems in which the hardware and software is inseparable and on the top of it, the whole thing is adaptive. My estimate is that such systems are undescribeable by TM. By the way, such systems got the name: living.
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Dear all,
I have a technical question regarding the self-diffusion coefficient of water in an equilibrium state using Einstein relation in molecular dynamics simulation. If we consider an equilibrated medium of water/polymer, water molecules have Brownian motion as a result of thermal fluctuations. So their self-diffusion movements, related to the Einstein relation between diffusion coefficient and mobility are fully accounted for. But in addition to thermal fluctuations, an equilibrium fluid system has pressure fluctuations. At any instant, the pressure on one side of a volume element is not the same as the pressure on the opposite surface of the volume element, and the volume element will move as a whole in the direction of lower pressure. These pressure fluctuations are not included in the simulations. In macroscopic (but linear, i.e., small forces and flows) flow conditions, they would give rise to a flow described by the linearized Navier-Stokes equation. Isn't this correct? how does Einstein relation consider it? is it logical to use Einstein relation in this situation? Can you discuss it briefly?
Thanks a lot
Try the following article *, you have two different substances and a surface that plays a role, but not 2 isotopes of the same substance where the question of self-diffusion and pressure gradients are relevant:
* Isotope effect for self-diffusion in liquid lithium and tin Belashchenko D., Polyanskii R. & Pavlov R. Russian Journal of Physical Chemistry A. 2002. Т. 76. № 3. С. 454-461
We ought to remember that:
• 1st Fick´s law applies to diffusion
• 2nd Fick´s law applies to convection
I do not see how convection 2nd Ficks´ law can be used for your particular system
Best Regards.
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A rigid body with vertical proper length J rises along the Y direction in an inertial frame S(T,X,Y) with constant proper acceleration, therefore me may write the equation of hyperbolic motion of the body along the Y direction as:
1) J2 = Y2 - c2 T2
Using Born´s definition of rigidity, the proper length “J” must be invariant under Lorentz transformations between instant commoving inertial frames where the proper length (squared) J2 coincides with the line element (squared) along the Y direction: Y2 - c2 T2. It is straightforward to see that this is the case just for boosts along the Y direction. If the velocity of the body and its inertial commoving frames have an aditional constant component along the X direction, the line element is different, the vertical length J cannot be invariant in the inertial comoving frames and we get a violation of Born´s rigidity.
And it is a pitty that the students fail to take into account simultaneity of relativity since it is a straighforward consequence of the two more basic priciples of SRT:
1) Constancy of speed of light.
2) Equivalence of inertial frames.
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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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Consider two particles A and B in translation with uniformly accelerated vertical motion in a frame S (X,Y,T) such that the segment AB with length L remains always parallel to the horizontal axis X (XA = 0, XB = L). If we assume that the acceleration vector (0, E) is constant and we take the height of both particles to be defined by the expressions YA = YB = 0.5 ET2, we have that the vertical distance between A and B in S is always (see fig. in PR - 2.pdf):
1) YB - YA = 0
If S moves with constant velocity (v, 0) with respect to another reference s(x,y,t) whose origin coincides with the origin of S at t = T = 0, inserting the Lorentz transformation for A (Y = y, T = g(t - vxA/c2), xA = vt) into YA= 0.5 ET2 and the Lorentz transformation for B (Y = y, T = g(t - vxB/c2), xB = vt + L/g) into YB= 0.5 ET2 we get that the vertical distance between A and B in s(x,y,t) is:
2) yB - yA = 0.5 E (L2v2/c4- 2Lvt/c2g)
which shows us that, at each instant of time "t" the distance yB - yA is different despite being always constant in S (eq.1). As we know that the classical definition of translational motion of two particles is only possible if the distance between them remains constant, we conclude that in s the two particles cannot be in translational motion despite being in translational motion in S.
Larissa, I might be wrong but I believe that you wanted to post in another quest on dark matter and dark energy.
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We discover a constant that predicts hydrocarbons (the backbones of life) and determines a definition for the radius of the solar system, predicts the relative abundances of hydrogen and helium in the Universe from which the heavier elements were made, the relative abundances of oxygen and nitrogen in the earth atmosphere, and that predicts the radius of the proton within its experimental errors. Incredibly this all ties into the ancient Babylonian origins of the calendar and their sexagesimal counting system. While this reconciles a lot between Newtonian Gravity and Quantum Mechanics, it becomes as well an Archaeological problem.
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Ian Beardsley, I'm glad if you were interested. It is about virtual dimensional gaps (a-b), so I didn't try to figure it out in any other way. But maybe there are more ways to calculate it or more things to add to that equation. Thank you for your suggestion, and it's an excellent question.
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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 flat spacetime.
Christian Corda showed in 2019 that this effect of clock synchronization is a necessary condition to explain the Mössbauer rotor experiment (Honorable Mention at the Gravity Research Foundation 2018). In fact, it can be easily shown that it is a necessary condition to apply the Lorentz transformation to any experiment involving high velocity particles traveling along two distant points (including the linear Sagnac effect) .
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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 call g to the Lorentz factor for v and 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 assume that the origins coincide x = X = 0 at time tP = 0 we may write down the space-like component of the Lorentz transformation as:
3) X = g(x - vtP)
Assuming that both clocks are placed at the same point x = xP , inserting x =xP , X = XP , T = TP into 2)3) yields:
4) XP = g (xP - vtP)
5) TP = 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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Hi, Nice Project!
23 September I have presented my new Research Paper "Hydrogen Atom and Elliptic Curve" (attached) on Quantum Mechanics and Nuclear Engineering Conference in Paris.
And I wonder if my paper could be relevant to your Project somehow?
Looking forward to hearing from you sometime soon.
Best regards,
George Yury Matveev
Hello Everybody. One more thing:
It turned out that the new equation (actually Two Linked Elliptic Curves) provides the Mechanism required for the Quantum Entanglement to work!
Whenever EPR pair (aka Bell state) is created there are Two Quantum Elliptic Curves assigned to those particles reflecting their energy levels.
Because those two equations are Linked via simple quantum condition (see formula 41 in the Matveev-QuantumEllipticCurve2.0-DK.pdf attached) changes made to parameters of One curve will be INSTANTANEOUSLY REFLECTED in the Second curve!
And this is the MECHANISM required for the Quantum Entanglement!
Moreover, the QEC equation explains that the Mechanism can work via Both Discrete or Continuous change of those two elliptic curves parameters, which is what has been observed experimentally!
Quantum Entanglement Explained!!!
Best regards,
George Yury Matveev
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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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Reading some of David Deutsch's books convinced me that the multiverse is key to understanding quantum mechanics. Molecules are objects in the multiverse - can we use this knowledge to teach Hartree-Fock, Configuration Interaction, etc.? My hunch would be that using the multiverse consistently and from the beginning (instead of treating it as a possible "interpretation", to be tacked on at the end) would make quantum chemistry simpler to teach, instead of more difficult, if done right. I have not seen anything like this, though.
Yes, the interpretation won't change the result. But the question is: assuming the multiverse is real: would the derivation of all key results (HF wave function, full CI wave function, etc.) become more *intuitive* if the multiverse is used as the starting point? Same results but much easier to understand how they arise? An analogy to make my point: nobody needs Feynman diagrams. Schwinger didn't. But they make it much more intuitive to see what is going on.
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Why expectation value of angular momentum square operator <Jx2> = <Jy2> ? How can we prove this?
I don't claim that the real and imaginary part of the operator J+2 vanish; I claim that <J+2>=0 implies that the real and the imaginary part of the expression of <J+2>, which are both numbers vanish; x+iy=0 implies that x=y=0 IF both x,y are real, and in this case are, since Jx,Jy are Hermitian.
The expression <J+2>=< Jx2-Jy2> +i<JxJy+JyJx> results from the expression of J+2 by linearity; J+2 is linear.
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In QFT they are point like particles. But what are the observational contraints on their size?
I have watched that video and, basically, I agree. The point is that the experimental size of the electron is going to depend on the type of experiment one carries out.
However, there is a sense in which the Compton wavelength is the fundamental size: it signals the size below which creation of virtual electron-positron pairs becomes prevalent, forbidding the identification of one single electron. This is a QFT effect, which involves quantum mechanics and relativity.
I hope this clarifies my previous answer.
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We have learned in QM the famous U. Principle which is probably the most important thing in this branch.
We also have learned that space-time stays together in GR.
The problem of measurements in QM comes from U. Principle & vice-versa and why it is not present in GR, not in the same form but analog?
Thanks
The answer of Mark Kristian van der Pals is – in my opinion – correct (Planck’s constant and Heisenberg’s uncertainty principle are like the 2 sides of a coin).
The quantization of energy is not in line with the theoretical properties of the electromagnetic field (electric field and corresponding magnetic field). Because the electric field shows to be a topological field – responsible for the wave-like nature of the phenomena in the microcosm – and the magnetic field is a pure vector field. The topological deformation of a field structure is only possible within a continuum.
The consequence is that the quantum of energy and Heisenberg’s uncertainty principle are not basic properties of space itself, but induced properties (caused by the basic properties).
With kind regards, Sydney
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The typical harmonic or morse potential for modeling bonds model energy levels in a continuous fashion. Are there any molecular/bond models that recreate intermolecular collisions in such a way that energy exchange between the translational and vibrational levels happens as per the laws of quantum mechanics?
Please check the following Open Learn resource & references therein:
Infrared Spectroscopy. (2020). https://chem.libretexts.org/@go/page/1847
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"A successful unification of quantum mechanics and gravity has eluded physicists for nearly a century. Quantum mechanics governs the world of the small - the weird realm in which an atom or particle can be in many places at the same time, and can simultaneously spin both clockwise and anticlockwise. Gravity governs the Universe at large - from the fall of an apple to the motion of planets, stars and galaxies - and is described by Albert Einstein's general theory of relativity, announced more than100 years ago. The theory holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a force, said Einstein, but because space and time around the object are curved. Both theories have been abundantly verified through experiment, yet the realities they describe seem utterly incompatible." Here we show that the approach to resolve this incompatibility is the free particle Dirac equation that explains the intrinsic spin as a consequence of combining of quantum mechanics and special relativity. We found in my preprint
hat the experimental observation of this free Dirac particle intrinsic spin in Stern Gerlach experiment demonstrates the discretization of the space-time.
yes ,the experiment observation of spin in Stern Gerlach experiment demonstrates Discretization of Space-time by the Dirac equation for free particle
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A quantum mechanical operator acting on the abstract state space of Dirac kets maps vectors of the space to other vectors of the space.
Assuming for simplicity that the examined quantum system is one dimensional, in position space, the same operator is a function of momentum, which is a differential operator, and position, which is a variable.
If the expression, or representation, of the operator in position space has singular points; i.e. values of the position where the operator is not defined for some reason; for instance due to a pole, is there a property of the same operator in state space that distinguishes it from operators that do not have singularities in position space?
Τhe position space is realized by using the position eigenstates which do not belong to the state space since they are not normalizable, but since the state and position spaces are physically (and mathematically) equivalent, shouldn’t a property exist that distinguishes operators with singularities from operators without singularities in position space?
If I undertsand your question, you consider two different bases: One being the base consisting of delta(x) and the other let's say the hydrogen bound wavefunctions plus free (scattering ) states. You can transform, of course between these base states via the coefficients <x|a> where x is a position eigenstate and a a hydrogen bound or scattering state. You can also take matrix elements and expectation values of any operator in either base and transform. If you compute the matrix element in one basis and it diverges e.g. <x=0|V|x=0>, you should also get the same result by summing over a1,a2 <x=0|a1><a1|V|a2><a2|x=0>. Else your basis is not complete. If you are using complete sets of states, the properties of an operator do not depend on the choice of basis.
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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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Radial gravitational wave study, physical interpretation of the fine-structure constant, resolution of the problem of wave-particle duality for electromagnetic radiations, and quantization of space-time :
Have a nice day :)
the radial gravitational wave depends on amplitude , potential of energy .It introduced a good idea about dilations of space and the radiation.
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A system of ideal gas can always be made to obey classical statistical mechanics by varying the temperature and the density. Now a wave packet for each particle is known to expand with time. Therefore after sufficient time has elapsed the gas would become an assembly of interacting wavelets and hence its properties would change since now it would require a quantum mechanical rather than classical description. The fact that a transition in properties is taking place without outside interference may point to some flaw in quantum mechanics. Any comments on how to explain this.
Wigner probabilistic distributions, Prof. Sohail Khan
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As we all know, the wavefunction of such a particle has a certain number n of zeros due to boundary conditions. If at these points the wavefunction is zero, then, since the probability of finding the particle there is equal to the square of the wavefunction, it follows that the particle cannot ever be there. However, there is nothing physical at those points that would prevent the particle from being there at some instant.
Moreover, a wavefunction psi_n corresponds to an energy level E_n. As you change to a higher energy level, the index n grows, and we have more nodes of the wavefunction; i.e., more places where the particle cannot be. Again, there is nothing physical at these points.
I guess, the meaning is in the Kronig-Penney model, Prof. Raul Simon
I don't have with me my notes from my Moscow Supervisor, I lost them when I run in Venezuela...
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Suppose one has a flux of electrons with speed not exceeding 10 m/sec falling one at a time on a plate with an aperture of 100 nm. If some electrons can pass one would have a statistics of many electrons passed through the slit but their speed can not exceed 10 m/sec because the aperture is a passive medium unable to accelerate the electrons. HUP (Heisenberg Uncertainty Principle) says that the momentum in x direction should be from 0 to 7 km/sec and more. {dp.dx>h --- dv=h/mv ---dv=7.10(^-34)/10(-30).10(-7)= 7.10(^3)= 7 km/sec}. So if electrons pass there is a contradiction with HUP?
There’s an uncertainty relation for energy, but the statements made about the electron in the statement just don’t make any sort of sense, anyway. So itks not surprising that they lead to equally meaningless c9nclusions.
This material isn’t new, it’s covered in any textbook on quantum mechanics. J7st solve the Schrödinger equation, deduce the probability density and compute any average value. It’s straightforward to check the validity of the uncertainty principle for canonically conjugate variables.
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This paper is a project to build a new function. I will propose a form of this function and I let people help me to develop the idea of this project, and in the same time we will try to applied this function in other sciences as quantum mechanics, probability, electronics …
Are you sure you have defined your function correctly?
1. Usually z=x+iy. But in your function z is in the limit, thus being in both the arguments and what the integral is computed against. If z is not x+iy, the function is not a function of (x,y).
2. What do you mean by limit? Do you want to compute the case when z->0?
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Our answer is YES. This is, however, a frequent question, and the answer has been: no. For context, see the video 2016 Patrusky Lecture by Steven Weinberg, on "What's the matter with quantum mechanics?"
We take the reasoned position: yes. Thinking otherwise would be to give up on deductive reasoning, on physics, on causality.
IM: A wave brings in the amplitude paradigm, important as we see in a simple beach. A particle is a localized vibration. For particles, what is important is the frequency, like in the photoelectric effect..
Experimentally, this and other particle properties of photons win, the wave properties lose. The Maxwell Equations (ME) represent the wave properties, only. Photon spin is the particle description of light polarization, where spin +1 and spin −1 represent two opposite directions of circular polarization. Thus, light of a defined circular polarization consists of photons with the same spin, either all +1 or all −1.
Stimulated emission, and its coherence, are the foundations of the laser, and are not represented in the ME, even when represented by relativistic equations for the field strength tensor, with B and E using the same units. There are other examples, like diamagnetism
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The special theory of relativity assumes space time is formed from fixed points with sticks and clocks to measure length and time respectively. The electromagnetic waves are transmitted at the speed of light through this space time. This classical space time does not explain the mysteries of quantum mechanics. Do you think that maybe there is more than one space time?
Humans have two kinds of space-time observers: the chord (tonality) observer and the non-chord (atonality) observer. They observe two kinds of space-time: chord space-time and non-chordal (atonality) space-time. Space-time is two The second level of existence.
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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.
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Schrodinger’s Enemy Experiment
Schrodinger decided to replace the cat by his enemy in his famous “Schrodinger’s Cat Experiment”.
Schrodinger didn’t reveal any details regarding the experiment to his enemy except instructing him to come out of the box (bigger than the one used for the cat) exactly after one hour. Therefore, as long as the enemy is inside the box, his situation is the same as that of the cat, except for the instruction he received from Schrodinger.
Earlier, in the original Schrodinger’s cat experiment, after one hour (half-life of a radioactive atom), the cat was in a superposition of |dead> and |alive> states, until Schrodinger opened the box. The moment the box was opened, the superposition collapsed either to |dead> or |alive> state. The important point here to note is that, after one hour, there was a superposition which collapsed only due to the act of opening the box.
But, in the present Schrodinger’s enemy experiment, there is no superposition to start with `after one hour'. Schrodinger is sure about the state to be observed after one hour, i.e. if his enemy comes out of the box, then he is in |alive> state. Otherwise, he is in |dead> state.
***
After an hour, his enemy didn’t come out of the box. Therefore, Schrodinger concluded that his enemy is in |dead> state. He opened the box, and to his surprise, his enemy woke up just that same moment from a lovely nap. Now, Schrodinger’s already inferred |dead> state suddenly changed to |alive> state.
In Schrodinger’s cat experiment, `after one hour’, there was a superposition which collapsed due to the act of observation, i.e. opening the box. In the present Schrodinger’s enemy experiment, there is no superposition `after one hour’ to start with, but, a definite inferred state which changed into another observed state upon opening the box (of course, if Schrodinger had found his enemy in |dead> state, then his inferred state would have been the same as the observed state). How to reconcile these two situations using quantum mechanics? Is there any interpretation or is there any need for any interpretation for the reconciliation?
Dear RG members,