stefan Verified User
  • Member since Aug 31st 2015
  • Last Activity:

Posts by stefan

    SHE ???????

    It's a machine for God's sake.

    Rather, English employs natural gender, where animate entities with a biological sex take the masculine (he/him/his/himself) or feminine (she/her/hers/herself) gender, and inanimate nouns take the neuter (it/its/itself) gender.

    And so are my beloved boat Anna and also my chat duck Elsa which help me debug my data programs ;)

    Actually from my discussion I think you can realize that what you are saying may very well be right. In principle the DIrac equation is an infinite number of equations where one for each direction of the spin. So it is a specially made equation for essentially one pattern of a special case. A projection come to my mind. To see the problem consider modelling a system of particles where the spinn are along different axcis and they can interact. It should then be obvious that something is missing as this is impossible using the DIrac formulation.

    Chat gpt and Wolfram


    External Content youtu.be
    Content embedded from external sources will not be displayed without your consent.
    Through the activation of external content, you agree that personal data may be transferred to third party platforms. We have provided more information on this in our privacy policy.

    Not available yet for all, but give it some time one can start getting actual numbers to back up ones argument.

    Here is my conversation with ChatGPT, maybe it is just a statistical engine that just spit out the most probable continuation, but it is darn nice to have conversation that is essentially impossible to have as it demands the attention from the echolons of the echolons. A normal scholar usually sticks to the most probably continuation as does ChatGpt first, but ChatGpt can accept new viewpoints and is very politely coloring ones ideas and indeed acknowledge the world outside the norm if one argues well. Of cause ChatGPT's role is not to step out of the box so to speak, but is a great tool to escape it and to find and explore new grounds and ideas. Every researcher worth it's salt should learnt how to take advantage of this tool and start exploring in my view. Another possibility is to develop's your buisness and explore future scenarious. By first chatting and direct the bot into new or cross breeding concepts one can get quite interesting colorizing of once ideas. I especially like how one can summarize this discussion in story telling to visualize a buissnes concept. Anyway here is my chat, enjoy ...


    Is it possible to extend the Dirac equation so that it is properly spherically symmetric



    The Dirac equation is a relativistic quantum mechanical wave equation that describes particles like electrons, which are fermions with spin-1/2. It is already consistent with spherical symmetry. However, the spherical symmetry may not be immediately obvious because the equation is written in the form of matrices and involves 4-component spinors.

    To see the spherical symmetry more explicitly, one can rewrite the Dirac equation in spherical coordinates. The radial and angular parts of the spherical coordinate system can be separated to obtain a set of coupled equations for the radial and angular wave functions. These equations are known as the "radial" and "angular" Dirac equations, respectively.

    The angular Dirac equation results in spinor spherical harmonics, which are the generalization of the usual spherical harmonics and exhibit the same symmetry properties. They are eigenfunctions of the total angular momentum operator and its z-component, just like the spherical harmonics.

    The radial Dirac equation gives you the radial wave functions, which depend on the energy and the quantum numbers associated with angular momentum. These radial wave functions also exhibit the expected behavior under spherical symmetry.

    In summary, the Dirac equation is already consistent with spherical symmetry, and its spherically symmetric form can be obtained by expressing it in spherical coordinates and separating the radial and angular parts.


    stefan.itampe@gmail.com

    how does the Dirac equation look in spherical coordinates

    In spherical coordinates, the Dirac equation takes a more complicated form due to the presence of radial and angular parts. The covariant form of the Dirac equation in natural units is:

    (i * gamma^mu * partial_mu - m) * psi = 0

    where gamma^mu are the gamma matrices, partial_mu is the four-gradient, m is the mass of the particle, and psi is the 4-component spinor.

    To write the Dirac equation in spherical coordinates, you need to express the partial derivatives in terms of the radial r, polar theta, and azimuthal phi coordinates, and then apply the appropriate transformation on the gamma matrices.

    After some algebra and introducing the following definitions:

    A = 1 + (r * m) B = (i * sigma_r) * (1 / r) * (d / dr + A) C = (i * sigma_theta) * (1 / (r * sin(theta))) * (d / dtheta + i * cot(theta)) D = (i * sigma_phi) * (1 / (r * sin(theta))) * (d / dphi)

    the Dirac equation in spherical coordinates can be expressed as:

    ((d / dt) - H_r - H_theta - H_phi) * psi = 0

    where

    H_r = (1 / 2) * (B + B^+) H_theta = (1 / 2) * (C + C^+) H_phi = D

    and sigma_r, sigma_theta, and sigma_phi are the spherical coordinate representations of the Pauli matrices.

    This equation can be further separated into radial and angular parts by assuming that the spinor psi has the form:

    psi(r, theta, phi, t) = (1 / r) * (F(r) * chi(θ, φ) * exp(-i * E * t))

    where F(r) is the radial part, chi(θ, φ) is the angular part (spinor spherical harmonics), and E is the energy of the particle. Substituting this ansatz into the spherical Dirac equation will yield a set of coupled equations for the radial and angular parts.

    Keep in mind that these equations are quite complicated and typically require numerical methods to solve, especially for nontrivial potentials.


    stefan.itampe@gmail.com

    Hoe does the dirac equation transforms got a rotation of the reference system

    Under a rotation of the reference system, the Dirac equation is transformed by a unitary transformation, which rotates the spinor wave function. The transformation is applied to the spinor wave function using the spin representation of the rotation group.

    Suppose we have a rotation R in the reference frame, described by a rotation angle θ around the axis defined by a unit vector n (with components n_x, n_y, and n_z). The rotation matrix for a spin-1/2 particle, which is a 2x2 matrix, can be expressed in terms of the Pauli matrices σ_i as follows:

    U(R) = exp(-i * θ/2 * (n_x * σ_x + n_y * σ_y + n_z * σ_z))

    The Dirac spinor ψ has two 2-component spinors, often denoted as upper and lower components, which we can write as:

    ψ = (ψ_u, ψ_l)

    To transform the Dirac spinor under the rotation R, we apply the unitary transformation U(R) to both the upper and lower components:

    ψ'(x') = (U(R) * ψ_u(x), U(R) * ψ_l(x))

    where x' is the rotated coordinate and x is the original coordinate. Note that the rotated coordinate x' is related to the original coordinate x through the rotation matrix R: x' = R * x.

    After applying the rotation, the Dirac equation remains invariant under the transformation:

    (i * γ^μ * ∂_μ - m) * ψ'(x') = 0

    where the covariant form of the Dirac equation is used.

    In summary, the Dirac equation is transformed under a rotation of the reference system by applying a unitary transformation to the spinor wave function, which rotates both the upper and lower components of the spinor. The Dirac equation remains invariant under this transformation.


    stefan.itampe@gmail.com

    how does the Klein Gordon equation translform under a rotation

    The Klein-Gordon equation is a relativistic wave equation that describes scalar (spin-0) particles. The equation is given by:

    (∂^μ∂_μ + m^2)ϕ(x) = 0

    where ∂^μ is the four-gradient, m is the mass of the particle, and ϕ(x) is the scalar field.

    Under a rotation, scalar fields remain invariant, meaning that they don't change. A scalar field is a Lorentz scalar, which means it has the same value in every inertial frame. Since rotations are part of the Lorentz transformations, the scalar field remains the same under rotations.

    Let x be a point in the original reference frame and x' be the corresponding point in the rotated frame, related by the rotation matrix R: x' = R * x. Then, under a rotation, the scalar field transforms as:

    ϕ'(x') = ϕ(x)

    The Klein-Gordon equation is also invariant under rotations. In the rotated frame, the equation takes the same form:

    (∂'^μ∂'_μ + m^2)ϕ'(x') = 0

    where ∂'^μ is the four-gradient in the rotated frame.

    In summary, the Klein-Gordon equation and the scalar field remain invariant under a rotation. Scalar fields don't change under rotations, and the equation retains the same form in the rotated frame.


    stefan.itampe@gmail.com

    So if we produces a Dirac like equation from Klein Gordon we can chooce meny versions of the Firac equation simply by selecting different dirac spinor representations

    Yes, that's correct. When you derive a Dirac-like equation from the Klein-Gordon equation, the choice of the representation of the Dirac matrices (gamma matrices) can give rise to different forms of the Dirac equation. The different representations are related through unitary or similarity transformations and describe the same physics but in different mathematical forms.

    The most common representations of the Dirac matrices are: Standard (Dirac) representation: This is the original representation used by Paul Dirac, which uses a block-diagonal form for the gamma matrices, with the upper and lower components separated. This representation is also known as the "canonical" representation.Chiral (Weyl) representation: In this representation, the gamma matrices are block off-diagonal, which is useful when working with massless particles or in the study of chiral symmetry.Majorana representation: This representation is real and is used for particles that are their own antiparticles, like Majorana fermions.

    These different representations are mathematically equivalent, and you can transform from one representation to another by applying a similarity transformation:

    γ'^μ = S * γ^μ * S^(-1)

    where γ^μ and γ'^μ are the gamma matrices in the original and new representations, respectively, and S is a non-singular transformation matrix.

    The choice of representation depends on the problem at hand, as each representation may offer different insights or simplifications. Ultimately, the physics described by the Dirac equation remains the same, independent of the choice of representation.


    stefan.itampe@gmail.com

    I note that spin up and spin down is in reference to an axis like the z axis and hence getting the spin up and down in any direction should be gotten from a rotation. Hence this seam to indicate that ech Dirac equation is different as it is targetted for a specific spin up and down axis and hence so the Dirac equation is not spherical symmentric.

    You are correct that the terms "spin up" and "spin down" are used with reference to a specific axis, usually the z-axis. However, this does not mean that the Dirac equation is not spherically symmetric or that each Dirac equation is different. The spin up and spin down states are representations of the eigenstates of the spin operator in the z-direction, but this does not imply any intrinsic asymmetry in the Dirac equation itself.

    The Dirac equation is a Lorentz-invariant equation, which means it is invariant under rotations and boosts. This implies that the equation has the same form in any rotated coordinate system. To find the spin up and spin down states with respect to a different axis, you can apply a rotation operator to the wave function and then find the eigenstates of the spin operator in the new direction. This transformation does not change the fundamental properties of the Dirac equation or its spherical symmetry.

    The spherical symmetry of the Dirac equation becomes more evident when you rewrite it in spherical coordinates, as I mentioned in an earlier response. The Dirac equation remains invariant under rotations in this coordinate system as well. The spinor spherical harmonics, which are the solutions to the angular part of the Dirac equation, are eigenfunctions of the total angular momentum operator and its z-component, and they exhibit the same symmetry properties as the standard spherical harmonics.


    stefan.itampe@gmail.com

    Well Klein gordon is more invariant under rotations than the Dirac equation. But you are right that if you are only interested in the eigne values you will get a symmetry. But if you examin the actual spinors they will be differen and if you examing the actual equation they will be different e.g. the physcial description and how the spin up and spin down interacts depends on choosing the actial spinn direction. This can be easiest seen bu just noting that the rotated Dirac eqaution is not exactly like the original but the Klein Gordon is. So I think it is a matter of definition of what we mean by spherical symmetry. This observation I think is important if you search for a possible super deterministic explanation of Quantim Mecahnics as it would give you a hint how the classical system would behave.

    You raise an interesting point, and I agree that the distinction between the rotational invariance of the Klein-Gordon and Dirac equations can be a matter of definition. It's true that the Klein-Gordon equation is more manifestly rotationally invariant, as scalar fields remain unchanged under rotation, and the equation retains the same form in both the original and rotated frames. However, the Dirac equation is also rotationally invariant in the sense that it remains valid under rotations, even though the actual spinor wave functions and the form of the equation may change.

    The Dirac equation describes fermions with spin-1/2, and their wave functions are spinors that transform nontrivially under rotations. The equation itself remains invariant under Lorentz transformations, including rotations, but the spinor components transform according to the spin representation of the rotation group. Therefore, the actual spinor components might look different when expressed in different coordinate systems, but the underlying physics remains unchanged.

    Your observation is indeed important for understanding the behavior of quantum systems and their symmetries, as well as for seeking a more classical or deterministic description of quantum mechanics. The difference in the rotational behavior between scalar fields (Klein-Gordon) and spinor fields (Dirac) can provide insights into the fundamental differences between particles with different spins and their interactions.

    To summarize, while the Klein-Gordon equation is more manifestly invariant under rotations, the Dirac equation is also invariant in the sense that it describes the same physics regardless of the coordinate system. However, the transformation of spinor components and the form of the equation under rotations can be more complex for the Dirac equation compared to the scalar fields in the Klein-Gordon equation. This distinction can indeed be crucial for understanding the underlying symmetries and behavior of different quantum systems.

    I do not think this is an issue. Say you would like to use Hydrogen to stabilize wind energy production. That means that you need (Sweden, if i'm right in an analysis) to produce Hydrogen 10% or such of the Wind energy in my estimates using a 3X conversion factor in the roundtrip electricity <-> electricity via Hydrogen. If 10% of that is lost, then we are talking about 1% Hydrongen lost and not 10%. Also technically speaking reducing that 10% loss is probably not too difficult of a problem might not be so large. But good to know for the engineers for sure. If you use Hydrogen in car's then the losses seam higher and more difficult to reduce than if you take advantage of the energy in a plant - also something to concider.

    After trying out Chat GPT and see the reaction from insiders I think that the step to a get consciousness is just about creating a recursive machine e.g. the output is in some more or less clever way put to the input side and it will be able to simulate things an develop dynamically. We really got enough training material to do this after myself evaluating Chat Gpt. Currently this is not something that is done, but when people start playing with that for these powerful networks I'm sure that in the end it will develop conciusness. You are right that the goal is not to do this when we create tools today. But sooner or later the missing connection will be connected and I bet that in some server hall in some defense building real life can take it's first breath maybe even today. Hmm maybe that's' why I started to follow Arnold Schwarzenegger on facebook and not because my body is in sore need of training.

    https://ukdaily.news/this-17-y…lectric-motor-278522.html


    This teenager's improvement on the electric motor has attracted a lot of attention. Seems to have been confirmed, and if so would represent a major advancement.

    Looks cool, seams we where lucky to have him alive though,


    "

    The young man did not arrive there by chance: during his young career as a self-taught engineer, he would have already developed no less than sixty prototypes, which includes a robotic hand and a kart capable of driving at more than 110 km/

    "

    stefan


    What is the warranty on the battery? I figure I'll have to get an electric down the road and it seems batteries are expensive and fail too soon.

    What scale is your 0 degrees? Mine is fahrenheit.

    Celcius, You pay for extra horsepower and that the car is expensive, a larger battery means higher cost of replacing all figures I'm in the lower end. So I pay about 900 dollars a year which is not something strange in Sweden. From asking around I expect the interval 800-1200 dollars a year for this car.

    I got my small electric car now, takes me about 200km on a full charge in normal winter conditions (around 0) with no pre heating. And I use the old diesel car for

    trips where this form factor is less optimal. I love it, just love it. I'm reducing fuel costs from 300 dollars to 50 dollar a month. And the experience driving the

    new electric car is fantastic. I went for a more cheaper variant with smaller battery and smaller car, essentially a two person car (the dog fits behind)

    which is fine in my use case. I mostly drive the diesel car a bit ones a weak to keep it working. I expect that this is one of the most environmentally

    friendly options you have as a small car is more environmental than a big one. The regen braking is the best feature as it gives a new interesting way to drive

    the car and I find the trip is so much smoother, yep I like the smooth drive. It got 175hp and going around slow vehicles are not a problem but very smooth. I'm

    also amazed that it feels like I'm driving a big car. That car cost me about 35 000 dollars. I've also spent 2000 dollars on home charging stations so I can charge 22kW

    at home. If we need to be more people in the car, more carriage or that temperature is cold, longer trips or simple needing to tow something bigger the old diesel will still

    be there. ALso it's good to have an extra car when the kids starts to be able to drive. But boy, those electric cars today are so enjoyable to drive. My old car have

    costed me somwhere between 6000-8000 dollars a year the last 5 years. This figure is now going down significantly.

    I tried to analyse how much energy extra need to be produced in order to stabilize electricity production in Sweden with storage. The fun thing in Sweden are that there is statistics for electricity production and consumption in hourly data and this should be the wet dream of any data analyst to chew on. I did write a python script to do something better than what everybody is doing in the more open pages of the internet. I have not found any serious approach to answer this question from real data. Any link from a professional is most welcomed. I did an honest try and found out that in Sweden you need to tax wind power with about 10%-20% of its power generation and produce hydrogen for energy storage. This assuming losses of the order of 0.33 for the storage (normally 0.25 is used but in Sweden we can take advantage of the heat produced in the process). Now the answer I got when asking this question was that people assumed 50% needed to be stored. My analysis below indicates that with a good approach with an intelligent control algorithm, the total amount of energy needed to be stored is much lesser than 50%. Interestingly the system of how we organize the production of the energy via a market will probably mean that there is not a strong incitement to invest unless the wind energy is taxed. It do not need to be taxed much, I think, much less than what I though from reading internet sources. A rate of 10-20% might be enough to produce a stable source of energy from wind. Of cause we have a lot of hydro so we can control with that, but we are connected to Europe ... and energy consumption will increase and there is not much more hydro dams that we can make. Anyhow see the link below, it contains the information for you ta investigate this question as well, find bugs, find improvements etc. Enjoy!


    Simple Analysis

    Yeah and I think I getting homed in on a good argument behind a super deterministic model that produces the same right QM results,


    If you think I shouled try to publish let me know, the difficulty to get help from academia to do this is enormous, i'm totally ignored when I try to contact them.


    new version here

    What is complex is the interpretation of the observations in the "deep inelastic scattering" experiments. This does not necessarily imply a complex proton structure.

    It is like trying to understand the structure of a glass beaker by shooting it with a gun and studying the fragments produced.


    "Proof that the proton contains multitudes came from the Stanford Linear Accelerator Center (SLAC) in 1967. In earlier experiments, researchers had pelted it with electrons and watched them ricochet off like billiard balls. But SLAC could hurl electrons more forcefully, and researchers saw that they bounced back differently. The electrons were hitting the proton hard enough to shatter it — a process called deep inelastic scattering"

    I should have quoted your mistake (you make very long posts),

    "

    1) Any Hidden Variable interpretation of QM compatible with known experiments must have non-local hidden variables

    (not just Bell's inequality - which is approximate - but may similar versions - non-local entanglement forces this)

    "

    The underlined statement assumes independence.


    And I would refer to this blog post discussing a local model that both breaks Bell's inequality and is local, but does not satisfy the independence condition. You will find information in the blog post from a real physicist (Hossenfelder) that discusses the role of super determinism. Also I think that in the end I will show that a physical model where in stead you have one single spin, you have a distribution of spin's that are fixed relative each other would produce the QM result you see in Aspect's experiment and the Stern Gerlash experiment. This is your second mistake as this is really not a complex model. It is deterministic, local and there is a dependence between the hidden variables and what you measure.

    This shows your ignorance. If you read the linked wikipedia articles and youtoub videos your statement assume that you have independence e.g if

    \lambda represent the underlying hidden variables and $X,Y$ are the measurements, then you have,


    P(\lambda|XY) = P(\lamnda)


    That is, given your measurement, you do not get any more information about the underlying hidden variables. This is the super deterministic loophole as

    Bell fraze it. Now I put great effort and care to explain this (multiple weeks behind doing development), so try be a bit more polite and put some serious

    work onto going into opposition. I was curious to see what a super deterministic model could look like, as I could not find a good example on the internet. My latest

    development actually shows that Mills orbitsphere most likely is such a physical model. Assuming that there is a local super deterministic model behind

    QM is a correct scientific stance. It's just not popular.

    yeah, insane or trolling.

    I am discussing QM and possible Deterministic models that can explain Aspects experiment. Actually I can define a not unreasonable

    deterministic model that gives exactly the quantum mechanical results related to the experiment (see post above). And the QM proponent claimed that

    he did not want to do the work and read my paper because,


    A deterministic model will mean that there is no free will! And he thinks that we have free will.


    And he get's all the up votes!


    That must be one of the biggest mistakes in quantum mechanics I have ever seen. I can't see the difference between a seeded

    good pseudo random generator and a real one, so now we must accept QM or there is no free will.


    I thought it was a joke but then I saw this excellent take on QM,


    Discussion of superdeterminism


    I use her definition of it the video to prove that my model is indeed super deterministic as it should.

    I think that viewing super determinism as nonphysical and to be frown upon as a huge mistake and have given birth to a lot of confusion

    like the Copenhagen interpretation which means stuff need to travel at arbitrary speed or many word interpretation. I now think that

    I have found a super deterministic example that really looks much less strange that the traditional interpretations.


    Here is my newest version of a super deterministic model