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# Quantum Mechanics - Science topic

Explore the latest questions and answers in Quantum Mechanics, and find Quantum Mechanics experts.

Questions related to Quantum Mechanics

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?

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 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.

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

how can fermi energy explain the conductivity of Cu and Nickle

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?

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?

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.

Can someone please help how to write Klein-Gordan equation for massless particles and also its action or Euler–Lagrange equation for massless particles?

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.

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 particlesif 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

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.

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.

- 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

In Atomic and molecular Physics, there are two notable selection rules 1)

**∆l=±1**and 2)**∆m**for a spherically symmetric potential. What is the logic behind these two rules?How do they come/derived?_{l}=0,±1I 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?

If ever confirmed, the applicative potential would be tremendous...

I refer here to Grinwald's publication:

- P. M. Grinwald, "
**Schrödinger’s Equation as a Consequence of the Central Limit Theorem Without Assuming Prior Physical Laws**", 2022 - https://www.researchgate.net/publication/360150783_Schrodinger%27s_Equation_as_a_Consequence_of_the_Central_Limit_Theorem_Without_Assuming_Prior_Physical_Laws

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.

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*/*m^{3}. 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 10^{113}J*/*m^{3}. 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 10

^{113}J/m^{3}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?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.

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.

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.

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.

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?

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

*l*_{p }and ω_{p}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?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.

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.

What quantum mechanical mechanism governs the super-hardness of the materials.

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?

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).

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

-----------------------------------------------------------------------------------------------

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.

-----------------------------------------------------------------------------------------------

I appreciate your kind help.

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?

Thanks in advance

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?**

Deleted research item The research item mentioned here has been deleted

Preprint Il Reconciliato And Explorations

**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.**

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?

*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.

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^{-13}m. What is your solution to the electron’s spin problem?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?

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.

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

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?

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

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) J

^{2 }= Y^{2}- c^{2}T^{2}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) J

^{2 }coincides with the line element (squared) along the Y direction: Y^{2}- c^{2}T^{2}. 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.The following Binary Physics project challenges your knowledge about quantum mechanics, quantum field theory, gravity, astronomy, Dark Matter, Dark Energy, Elementary Particles, forces, etc:

Preprint Verifying The Origin Of Everything

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?

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 (X

_{A}= 0, X_{B}= 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 Y_{A}= Y_{B}= 0.5 ET^{2}, we have that the vertical distance between A and B in S is always (see fig. in PR - 2.pdf):1) Y

_{B}- Y_{A}= 0If 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 - vx

_{A}/c^{2}), xA = vt) into Y_{A}= 0.5 ET^{2}and the Lorentz transformation for B (Y = y, T = g(t - vx_{B}/c^{2}), x_{B}= vt + L/g) into Y_{B}= 0.5 ET^{2}we get that the vertical distance between A and B in s(x,y,t) is:2) y

_{B}- y_{A}= 0.5 E (L^{2}v^{2}/c^{4}- 2Lvt/c^{2}g)which shows us that, at each instant of time "t" the distance y

_{B}- y_{A}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.More information in:

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.

Deleted research item The research item mentioned here has been deleted

Deleted research item The research item mentioned here has been deleted

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 x

_{P}to be t_{P}. Let the offset (t – t_{P}) between the two clocks be:1) (t – t

_{P}) = v (x - x_{P})/c^{2}where (t-t

_{P}) 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/c^{2}) we get:2) T = g (t

_{P}- vx_{P}/c^{2})On the other hand, if we assume that the origins coincide x = X = 0 at time t

_{P}= 0 we may write down the space-like component of the Lorentz transformation as:3) X = g(x - vt

_{P})Assuming that both clocks are placed at the same point x = x

_{P , }inserting x =x_{P}, X = X_{P ,}T = T_{P }into 2)3) yields:4) X

_{P}= g (x_{P}- vt_{P})5) T

_{P}= g (t_{P}- vx_{P}/c^{2})which is the local Lorentz transformation for an event happening at point P. On the other hand , if the distance between x and x

_{P}is different from 0 and x_{P}is placed at the origin of coordinates, we may insert x_{P}= 0 into 2)3) to get:6) X = g (x - vt

_{P})7) T = g t

_{P}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.

More information in:

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

Please, see the attached file RPVM.pdf. Any comment will be wellcome.

More on this subject at:

You can find the wording in the attached file PR1-v3.pdf. Any comment will be wellcome.

More on this topic at:

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.

Why expectation value of angular momentum square operator <J

_{x}^{2}> = <J_{y}^{2}> ? How can we prove this?In QFT they are point like particles. But what are the observational contraints on their size?

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 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?

"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.

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?

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.

Experiment Findings The Quantized Photon Field Experiment

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 :)

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.

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.

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?

*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 …*

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.

What is your qualified opinion?

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?

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?

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?

**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,

Please let me know your valuable responses, comments and answers.

Thanking you and best regards,

N.G.

What are the quantum materials? Quantum phenomenon takes place in every material at atomic level. then how to define quantum materials? is Iron (magnetic materials) quantum material as it shows magnetism which is the quantum phenomenon? if not then what are quantum materials?