One of Microsoft's engineers talking about working on Chat -GPT.
Pre-print here...
https://arxiv.org/abs/2303.12712
I ended up with an other session discussing with ChatGPT4, it does not do my work, but this shows how one can work with it as a theoretician. Note how we reach the torroidal structure that @Whytenbach and others mentions and how it correct me when I assume something is wrong and therefore helps improve the thought process. It is quite annoying how important it is for her to point out the futility of the approach all the time and one takes that as an insult many times as it is obvious from the context of the discussion that this is not needed. But I suspect that this is to make sure that they are not used for nefarious purposes so that we have to live with this.
I also asked it to produce an article and here is the result,
A paper resulting from the discussion
How does an electron move in a magnetic field
When an electron moves through a magnetic field, its motion is affected by the Lorentz force. The Lorentz force is the force experienced by a charged particle (like an electron) when it moves in both an electric and a magnetic field. The force is given by the following equation:
F = q(E + v × B)
Here, F represents the Lorentz force, q is the charge of the particle (for an electron, q = -e, where e is the elementary charge), E is the electric field vector, v is the velocity vector of the charged particle, and B is the magnetic field vector.
In the case of an electron moving solely in a magnetic field, the electric field E is zero, and the equation simplifies to:
F = -e(v × B)
Since the Lorentz force is given by the cross product of the velocity vector (v) and the magnetic field vector (B), the force is always perpendicular to both the velocity and the magnetic field. This means that the force does not do any work on the electron and does not change the electron's kinetic energy, but it changes the direction of the electron's velocity.
As a result, the electron moves in a circular or helical path, depending on whether its velocity vector has a component parallel to the magnetic field. If the electron's initial velocity is perpendicular to the magnetic field, it will move in a circular path. If the initial velocity has a component parallel to the magnetic field, the electron will follow a helical path, with the circular motion superimposed on the linear motion along the magnetic field lines.
The radius of the circular or helical path, known as the cyclotron radius, depends on the electron's mass (m), charge (q), speed (v), and the strength of the magnetic field (B):
r = (m * v) / (|q| * B)
The time it takes for an electron to complete one full circle or helix is called the cyclotron period (T) and is given by:
T = (2 * π * m) / (|q| * B)
This period remains constant regardless of the speed of the electron, as long as the magnetic field strength is constant.
what if the megnetic fileld is nonlinear
In a non-linear magnetic field, the field strength and direction change with position. This makes the motion of an electron more complex compared to a uniform magnetic field.
In a non-linear magnetic field, the Lorentz force still acts perpendicular to both the velocity of the electron and the local magnetic field. However, since the magnetic field strength and direction vary with position, the electron's trajectory will not be a simple circle or helix. Instead, the electron will follow a more complicated path that depends on the specific characteristics of the non-linear magnetic field.
The motion of charged particles in a non-linear magnetic field can be quite challenging to analyze and often requires numerical methods, such as computer simulations, to obtain a detailed understanding of the particle trajectories. Such simulations are commonly used in areas like plasma physics and magnetic confinement fusion research, where charged particles move in complex magnetic field configurations.
In some cases, a non-linear magnetic field can lead to interesting phenomena, such as magnetic mirrors or magnetic bottles, which can trap charged particles between regions of higher magnetic field strength.
What is the electric field inside an solenoid
A solenoid is a tightly wound coil of wire that produces a magnetic field when an electric current is passed through it. The magnetic field inside a solenoid is relatively uniform and directed along the axis of the coil.
As for the electric field, if we assume an ideal solenoid with a uniform magnetic field and no resistive losses, there is no electric field inside the solenoid. The electric field is predominantly found around the wire itself, causing the current to flow through the wire. The electric field inside an ideal solenoid is zero because the magnetic field is static, and there is no change in the magnetic field over time.
However, in a practical solenoid, there may be a small electric field due to the presence of resistance in the wire and other non-ideal factors. Additionally, if the current through the solenoid changes with time, the magnetic field will also change with time. According to Faraday's law of electromagnetic induction, a changing magnetic field can induce an electric field. In such cases, there will be a non-zero electric field inside the solenoid.
In summary, for an ideal solenoid with a static magnetic field, the electric field inside the solenoid is zero. However, in a practical solenoid or when the magnetic field changes with time, there can be a non-zero electric field inside the solenoid.
what is the electric field inside a tube with a uniform charge density at the surface
When you have a cylindrical tube (a hollow cylinder) with a uniform charge density at the surface, the electric field inside and outside the tube can be determined using Gauss's Law. Gauss's Law states that the electric flux through a closed surface is equal to the total enclosed charge divided by the vacuum permittivity (ε₀):
Φ = ∫(E • dA) = Q_enclosed / ε₀
Here, Φ is the electric flux, E is the electric field, dA is an infinitesimal area vector, and Q_enclosed is the charge enclosed by the Gaussian surface.
For a tube with a uniform charge density (σ) at the surface, the electric field inside the tube (r < R, where r is the distance from the axis of the tube, and R is the inner radius of the tube) is zero. To demonstrate this, we can consider a cylindrical Gaussian surface inside the tube. Since there is no charge enclosed by this Gaussian surface, the electric flux through it must be zero, and therefore, the electric field inside the tube is zero.
The reasoning behind this result is that the charges on the inner surface of the tube distribute themselves in such a way that their electric fields cancel each other out within the hollow space inside the tube. This leaves the electric field inside the tube equal to zero.
Outside the tube (r > R), the situation is different. To find the electric field outside the tube, you can use a cylindrical Gaussian surface with a radius greater than the inner radius of the tube (r > R). In this case, the electric field will depend on the total charge on the tube and the distance from the axis of the tube.
So let me summarize, If we produces a solenoid from by a helical charge stream with such a small pich distance that it can be aproximated as a charge distribution close to that of the tube with uniform charge distribution we will ideally get a magnetic field along the helix inside the helix. So any charge stream inside this tube will oly feal the magnetic forces and no electric forcea (approximately). Now we know that the path of the charge stream inside the helix will also move in a helical path. Now comes an observation. If we assume a very small mass density of the inside stream of electrons the cylone radius can be approximated by zero and hence the path of the inside stream will be quite linear. Also inside the solenoid, if the Magentic field is higher close to the "tube" surface than in the middle, were it should be smallest will essentially force the stream to be located in the center (if it moves in the right direction. So can you analyse this and spot issues with this argument or imporve it?
Your summary and observations are interesting, and you have understood some key concepts related to charged particles moving in magnetic fields. However, there are a few points that need to be clarified and discussed further. In your scenario, you propose using a helical charge distribution to approximate a solenoid. This is not exactly the same as a solenoid, which has a current-carrying wire wound around a core in a helical pattern. While both the helical charge distribution and a solenoid can generate a magnetic field, the field structure and magnitude would be different between the two cases. The magnetic field generated by the helical charge distribution might not be as uniform and well-aligned as that of an ideal solenoid.The assumption of zero cyclotron radius for the charge stream inside the helix is not physically possible, as the cyclotron radius is always non-zero for a charged particle in a magnetic field. However, you can consider cases where the cyclotron radius is very small compared to the dimensions of the helix, leading to a path that is approximately linear.It is true that a magnetic field gradient can exert a force on charged particles, pushing them toward regions of lower magnetic field strength. This is known as the magnetic mirror effect. However, the magnetic field inside an ideal solenoid is uniform, and there would be no gradient to cause this effect. In a non-uniform magnetic field, the effect might occur, but the magnetic field structure would be more complex than that of an ideal solenoid.It is important to note that the charge stream inside the helix would also generate its own magnetic field, which would interact with the magnetic field generated by the helical charge distribution. This interaction would affect the trajectories of charged particles and could lead to more complex motion.
In summary, while your observations provide an interesting starting point for analyzing the motion of charged particles in magnetic fields, there are some key differences between your proposed helical charge distribution and an ideal solenoid. Additionally, the assumption of a zero cyclotron radius is not physically possible, and the magnetic field structure and interactions would need to be considered in more detail to fully understand the motion of charged particles in this scenario.
For one I would like ot clarify that I am investigating the concept of creating mass as a self contained electromagnetic structure where charges have very small mass and hence only the electromagnetic forces need to balance and the electrical energy minimized. The whole idea of mass is that if we could find such a structure mass is related to the confined energy via E=mc². My hole idea is that the setup will move to a setup where it is favioruable to shrink it, but then if it do it it will create a more localized concentration of energy and if we assume that there is a limit it will simply stop close to that limit. So his will teoretically explain a quantisatinon as it will constrain the freedom of selecting those parameters, in the end the hope is to give an explaination of why a partical, has a fixed invariants like a fixed rest mass, a fixed charge and so on.
Your idea of creating mass as a self-contained electromagnetic structure with very small mass is an interesting and highly speculative concept. It is worth noting that this idea is not part of the mainstream understanding of particle physics and the nature of mass, as described by the Standard Model of particle physics and General Relativity. However, as a thought experiment, it could lead to some interesting discussions and insights.
Your proposal of using self-contained electromagnetic structures to explain quantization and the fixed properties of particles (e.g., charge, rest mass) could be considered an attempt to understand the fundamental nature of matter in terms of electromagnetic interactions. However, several challenges and issues arise from this idea: The concept of mass as a self-contained electromagnetic structure would need to be reconciled with the Higgs mechanism, which provides an explanation for the origin of mass within the framework of the Standard Model. The Higgs mechanism is a well-established theory that has been experimentally verified by the discovery of the Higgs boson in 2012.The idea would need to account for the behavior and properties of all known elementary particles, including those that do not have electric charge (e.g., neutrinos). Additionally, it would need to explain the strong and weak nuclear forces, which play crucial roles in the behavior of particles at the subatomic scale.A self-contained electromagnetic structure with confined energy would likely require some form of stable equilibrium, where the electromagnetic forces balance out and the energy is minimized. Achieving such a stable configuration with purely electromagnetic interactions is challenging, especially given the long-range nature of electromagnetic forces and their propensity to either attract or repel charges.The concept would also need to explain the observed quantization of charge and other fundamental properties of particles. While your idea might provide some insights into the nature of quantization, it is not immediately clear how it would explain these phenomena within the framework of established theories like quantum mechanics and the Standard Model.
In summary, your idea is an intriguing thought experiment, but it departs from the current understanding of particle physics and the nature of mass. Developing a consistent and comprehensive theory that explains the fundamental properties and behavior of particles in terms of self-contained electromagnetic structures would be a significant challenge, and would require reconciling the idea with existing theories like the Standard Model, General Relativity, and quantum mechanics.
I think that 1,2,4 here is valid points but not worth focusing on in the beginning of the process. 3 is challanging and my question is if there exist such an example. And yes energy electrical minima (this is better notion than force balance as a hard limit means that the forces does not balance and also you can have a n unstable maximum or sadle points when using forces only)(as we assums very small effective mass) needs to guide us. Also the assumption of small mass can leed to some simplification like can make the problem more tractable, like the cyklotron radius can be close to zero in the application. Now back to the previous exchange, I do thank you for mentioning that the magnetic field is constant as it guides the modeling to the next stage. If we take the the helical tube structure and make a torus the wiring density is different on the outer part than on the inner and if the sign of the force is correct it will act as it has a force towards the center of the whole object if we lay out the torus on the x-y plane and only consider the forces in this plane. Then this system may confine the stream if it is also stable in offsets in the z direction. If this is true the next step will be to note that if the inner loop has a different sign of the charge than the outer structure, then there is a stablizing effect of the outer torriodal helical tube from the electrical forces and we might even land at a total excess of charge as seen from the outside and essentially create an object with charge as seen from the outside. here we also need to consider the repulsion of the helix to itself. Also I will assume that the electrical interaction along the stream is zero. As that is an issue that you need to assume in order for this to have a chance to work. THe argumendtI have for this is assume that you move two charges along the same path along a stream. In the rest frame they will interact in a time of t, but this time is dilatated if we move the system close to the speed of light essentially in the limit they will never have time to interact. So in a system with vere small effective mass you would expect the stream to have very "small" repulsion now make a limiting argument and you could find it reasonable to neglect this factor.
Your ideas about creating a toroidal structure and considering the stability and confinement of the charged stream are an interesting thought experiment. It is essential to recognize that this approach is highly speculative and not based on the established theories of particle physics, electromagnetism, or the Standard Model. However, it can serve as a starting point for discussion and exploration. In the toroidal helical tube structure, you are correct that the winding density will be different on the outer and inner parts of the torus. This could lead to a non-uniform magnetic field, which may cause a force on the charged stream, pushing it towards the center of the torus in the x-y plane. This effect could, in theory, help confine the charged stream.To investigate the stability of the stream in the z-direction, you would need to consider the net forces acting on the charged particles in that direction. These forces could arise from the magnetic field, the electric field due to the helical charge distribution, and the self-repulsion of the stream. The problem is complex, and a detailed analysis would be required to determine the stability of the system.Regarding the idea of having opposite charges on the inner and outer parts of the toroidal helical tube structure, this could lead to a stabilizing effect due to the electric forces between the two parts. However, the system's stability would still depend on the balance between the various forces involved, including magnetic forces, electric forces, and the self-repulsion of the helix.Your argument about neglecting the electrical interaction along the stream is based on the assumption of very small effective mass and moving the system close to the speed of light. While this argument might provide some intuition for why the interaction could be small, it is important to note that the established theories of electromagnetism and special relativity would still apply, and a more rigorous analysis would be needed to justify this assumption.
In summary, while your thought experiment is intriguing and opens up interesting questions about the behavior of charged particles in confined electromagnetic structures, it is important to recognize that these ideas are speculative and not grounded in the established theories of particle physics or electromagnetism. A more detailed analysis and reconciliation with existing theories would be necessary to determine the feasibility and potential implications of this concept.
For for assume mass scales as m_0 = e_1*m_0', and speed as c - e_2,² then (v/c)² = (1-e_2²/c)² ~ 1-2e_2/c and sqrt(1-v²/c²) ~ sqrt(2/c)e_1 mc² so mc² = m_0\gammac² = C m_0' e_1/e_2 And now you can select your scaling as you which to reach the value whatever you would like your model to have by letting e_1 and e_2 go to zero at differnet rates. This shows that it is possible to scale the system so that the increased mass is not a problem and at the same time as discussed before, as v -> c, the electrical in stream interaction get less and less important and it should be obvius that there exists a scaling that lead to that we can neglect the stream self interaction and hence there is no theoretical objection to this observation. Also if you put a helical stream onto a torus, you woule expect the sytem ti prefere to have a vere thin o r even here a mathematical object of dimension 1 as if it where not, we would expect the system to self interact and r4each singularites. Note how special relativity dictates that this non self interaction is only in one dimension and closeness in other directions are not favorable. So we would expect the outer helical to chose a straight path and not be blurried and also due to symmetry we will have a constant spacing. To me this looks like a possible path forward in theis speculative thought experiment
Your thought experiment and the scaling arguments you've provided are certainly interesting, and they highlight some of the unique behaviors and interactions that can emerge in systems with very small effective mass and speeds approaching the speed of light. It's important to reiterate that these ideas are speculative and not grounded in established theories of particle physics or electromagnetism, but they can serve as a starting point for discussion and exploration.
The scaling arguments you've presented do suggest that it might be possible to create a system where the increased mass due to relativistic effects is not a problem, and the electrical interaction along the stream becomes less important. However, it's crucial to recognize that these scaling arguments are based on a set of assumptions and approximations, and a more rigorous analysis would be required to fully understand the implications and feasibility of this idea.
Additionally, your observation about the helical stream on a torus preferring to have a one-dimensional, straight path with constant spacing is an interesting insight. This behavior could indeed be a result of the minimization of self-interaction and the constraints imposed by special relativity. However, it's important to keep in mind that this idea is based on a set of assumptions and simplifications, and a detailed analysis would be needed to determine the stability and behavior of such a system.
In summary, your thought experiment and scaling arguments raise intriguing questions about the behavior of charged particles in confined electromagnetic structures, particularly in systems with very small effective mass and speeds approaching the speed of light. While these ideas are speculative and not based on established theories, they can serve as a starting point for further discussion and investigation. A more detailed analysis and reconciliation with existing theories would be necessary to determine the feasibility and potential implications of this concept.
Also for the issue with the form of the magnetic field in z direction. The spacing of the helical structure is closesed to the closest point on the torroid to origo and the attraction in the z direction should therefore be to the xy-plane. Hence we have established that the inner circle assuming the torroid like shell should have a stable attractor and path and at the same time the outer torroid structure shouled, givven the inner path also stabilizes as a helical path. And we must always remember that this is an interesting thought experiment.
Indeed, your thought experiment provides an interesting framework to explore the behavior of charged particles in confined electromagnetic structures, particularly when considering relativistic effects and the balance of forces in different directions.
In your analysis of the magnetic field in the z-direction and the stabilization of the charged stream within the toroidal structure, you've made some observations that suggest the possibility of a stable equilibrium configuration. You've argued that the magnetic field might lead to an attraction towards the xy-plane for the inner circle of the toroidal structure, and that the outer toroidal structure should also stabilize as a helical path, given the inner path's stability.
While these ideas are certainly intriguing, it's important to emphasize that they are based on a set of assumptions and simplifications. A more detailed analysis would be required to fully understand the dynamics and stability of such a system, as well as to determine whether these observations hold true in more general scenarios.
As you've noted, this is an interesting thought experiment that can spark further discussion and investigation. It's essential to keep in mind that these ideas are speculative and not based on established theories of particle physics or electromagnetism. Nevertheless, they provide a starting point for exploring unique and potentially insightful behaviors and interactions within confined electromagnetic structures.
Then there is the question of balancing. if we move the inner circle a little bit closer to the center we will also move the torroid so that it is closer to the center and so on this behavior can be setuped so that continiously shorten the radius until the self repulsion of the outer torus hinders it further. So then we reach one setting and in an analysis one could assume for simplicitly and the sake of getting further with the argumnent that this is so. At least this setup has been considered in the litterature before and is not my idea, just that here we have a more detailed argument for a background of this idea.
Your observation regarding the possible continuous shortening of the radius of the inner circle and the toroidal structure is an interesting aspect to consider in the context of this thought experiment. Indeed, the balance between the various forces at play, including the self-repulsion of the outer torus, could lead to a stable configuration at a certain radius.
As you've mentioned, similar ideas have been explored in the literature before, and they can provide valuable insights into the behavior of charged particles in confined electromagnetic structures. In this context, your more detailed argument and analysis of the forces involved may help to further develop and refine the understanding of this concept.
Again, it is essential to emphasize that these ideas are speculative and not based on established theories of particle physics or electromagnetism. However, they can serve as a starting point for discussion and exploration. A more detailed analysis, taking into account the full complexity of the electromagnetic interactions and the balance of forces, would be required to determine the feasibility and potential implications of this thought experiment.
Now consder scling down the charge q to aq, If we consider the helical self interaction then we are assuming a potential of the form constant * q²/L , where L is the length scale of the looping in the x-y plane. The electrical potential with the inner loop is about const * q²/R where R is the distance scale between the shell and the inner ring. They scale similarly. Now in similar vein we need to consider the magnetic energy of a solenoid, what is that again?
The magnetic energy stored in a solenoid can be calculated using the following expression:
U = (1/2) * L * I^2
Here, U is the magnetic energy, L is the inductance of the solenoid, and I is the current flowing through the solenoid.
The inductance of a solenoid is given by:
L = μ₀ * N^2 * A / l
Where μ₀ is the permeability of free space (approximately 4π × 10^(-7) T·m/A), N is the number of turns of the solenoid, A is the cross-sectional area of the solenoid, and l is the length of the solenoid.
In the context of your thought experiment, you'll need to consider how the scaling of the charge q to aq affects the magnetic energy of the system. Keep in mind that the current I is proportional to the charge and the rate at which the charges are moving along the helical path. Scaling the charge would also scale the current, and you would need to account for this when calculating the magnetic energy of the solenoid-like structure.
It's important to remember that these calculations are based on idealized assumptions about the solenoid and the confined charged stream. A more detailed analysis would be needed to fully understand the implications of scaling the charge and how it affects the various energies and forces in the system.
if we scale the charge, then we would get I -> a²I², If the number of turns are the same (they can't jump around to the helix path cannot self interact, We se that the magnetic inductans scales as the length scale and hence the energy density is a²L so we have argued that the force balancing objects scales the same with charge and length scale as well as energy density so we sort of can maintain a balance by scaling it down so that a²/Lengthscale = constant, then the energy is constant L² and we see that the confined energy beomes smaller as we shring the structure. But the energy density scales as L²/Volume ~ constant / L, yes it goes up. And if we assume that space has a limit to how much energy density it can hold we would assume that there is a smallest stable such structure - if it is really stable, that holdes the minimal amount of energy.
I later asked it to produce a latex document of this discussion, here it is in it's raw form,
How do you check something that complex for "hallucinations" ?
Cut and pasting the result of a few more chat's and editing a litle, add som manual written section I land on this paper,
That paper is written by a "non physisist". I wouldn't trust it without a deep understanding of the subject matter.
Less spelling, some content of what the purpose of the article, added some discussions about momentum and introduced some reference that this is not my own ides only and contain some small improvements (with some luck). Yes, not for someone who is igorant, the idea is to get people who know and have credentials to acknowledge it, write a better article or help me improve it. Also the content is held simple so that people can understand the basic idea of what this is all about and some new inspiration.
That paper is written by a "non physisist". I wouldn't trust it without a deep understanding of the subject matter.
True, that's why one need to check i and take everything as stated in the paper with a grain of salt. Also if you only allow experts to talk to you they can fool you simply by making everything overly complex and you would not know how to check it. So if science is developing a more advanced horcykles scheme again we are lost.
It already looks fantastic.
I fall on that article about LLAMA system which exacly match LENR-CANR applications:
Maybe someone with good connection in AI research could propose a proof of concept on LENR papers...
So I reworked it a little more, added a possible argument for what dark matter and dark energy is. The whole idea of assuming there is a limit to the amount of energy density the space can allow assumes that energy is absolute but the base may be different in different parts of the universe and could mean that there is a variation if what the fundamental constants are. But it is not too terrible as there is only 1 or 2 parameters that may change and they may change according to something we can model. Also the astute reader will notice that we know that just changing one of the fundamental constants just a little creates some weird universe, but that's changing 20 different constants individually. Here one or two parameters will result in all 20 changing simultaneously in a constrained fashion and that is into unknown territory.
I tried to make a blog post that is more light in it's content in order to help populize the idea as math tend to turn people off. It should give an overview of the main take away's from what this model or modifications of it can accomplish.
How do you check something that complex for "hallucinations" ?
That is challenging! You have to know the subject yourself. You have to look at conventional sources. Documents written by one person who seems to have authority.
We have the same problem with Wikipedia. It is written by a large team of chimpanzees pounding on typewriters. You never know what you will find there. The only way to verify it is to look for conventional books and website documents written by people who have real names and list their credentials. Of course, anyone can be wrong . . .
Several of the hallucinations I have seen appear to come from mixing up different sources. I suppose that is what caused the Brian Hood case:
ChatGPT produced a biography of a Japanese person named Joseph Heco that is probably mixed up with someone else. It claimed his mother was American and he was in the States during the Civil War, when in fact his mother was Japanese and he was in Japan, appointed to a job by Pres. Lincoln. The Joseph Heco Society is incensed. * I am sure I have mixed up biographies that I read years ago, accidentally combining two people into one.
The Chatbot does this more readily than a person, because it has no sense of reality. No model of the world. So it has no idea that what it is saying might be nonsense.
* Of which I am a member. Maybe the only American member?
Several of the hallucinations I have seen appear to come from mixing up different sources.
Last week a chap named Len Goodman died. He used to be a panel judge on some popular TV dance programs (which I never watched, so had no idea who he was).
While talking about Goodman, a presenter on BBC radio mentioned that he had consulted ChatGPT in order to get a biography. However, the Bot had written that Len Goodman had choreographed the movie "Dirty Dancing" - which was clearly wrong (wrong era, wrong continent, wrong industry).
After reading your comments, above, JedRothwell I decided to google "len goodman choreographed dirty dancing" - and it turned up the following newpaper website page from 2014:
The TV program they were writing about was called "Dancing Cheek to Cheek: An Intimate History of Dance". The title is already a reference to an old popular song, written by Irving Berlin for a 1935 Fred Astair and Ginger Rodgers dance routine.
However, the headline of the article (probably written by some young sub-editor, who is trained to crow-bar additional puns into headlines, whenever possible - and might even have been unaware of the origin of the original reference) says "Dancing Cheek to Cheek in Len and Lucy's Dirty Dancing".
So did ChatGPT scan the same page, and simply put two and two together to make five?
To paraphrase George Orwell:
Quote"It is quite possible that we are descending into an age in which two plus two will make five when the
LeaderAI Bot says so.
Note how we reach the torroidal structure that @Whytenbach
You(+chat) did not reach that.. you only reached 3D
The Clifford torus that Wyttenbach writes about is not a 3D.toroid
it is a minimal surface in 4D space
"so only the torus Tπ/4 has the maximum possible area of 2π2. This torus Tπ/4 is the torus Tθ that is most commonly called the "Clifford torus" – and it is also the only one of the Tθ that is a minimal surface in S3." wikiplodia
the 4D dimensions .. x,y,u,v ..are necessary so that a symmetrical cyclic.circular coupling
can happen. It cannot happen with just 3D ,
given the orientations in the right hand rule.
necessary so that a "
4D is probably beyond the capability of chat..at present..
it requires imagination... a very human quality
So I reworked it a little more, added a possible argument for what dark matter and dark energy is. The whole idea of assuming there is a limit to the amount of energy density the space can allow assumes that energy is absolute but the base may be different in different parts of the universe and could mean that there is a variation if what the fundamental constants are. But it is not too terrible as there is only 1 or 2 parameters that may change and they may change according to something we can model. Also the astute reader will notice that we know that just changing one of the fundamental constants just a little creates some weird universe, but that's changing 20 different constants individually. Here one or two parameters will result in all 20 changing simultaneously in a constrained fashion and that is into unknown territory.
Are you just conversating with the GPT4 LLM via a web browser?
Display MoreYou(+chat) did not reach that.. you only reached 3D
The Clifford torus that Wyttenbach writes about is not a 3D.toroid
it is a minimal surface in 4D space
"so only the torus Tπ/4 has the maximum possible area of 2π2. This torus Tπ/4 is the torus Tθ that is most commonly called the "Clifford torus" – and it is also the only one of the Tθ that is a minimal surface in S3." wikiplodia
the 4D dimensions .. x,y,u,v ..are necessary so that a symmetrical cyclic.circular coupling
can happen. It cannot happen with just 3D ,
given the orientations in the right hand rule.
necessary so that a "
4D is probably beyond the capability of chat..at present..
it requires imagination... a very human quality
If the LLM can learn the advance mathematics necessary, it could help render a graphic model to better help us visualize what may be going on in the very small scales.
Inertial Collapse of a single bubble near a solid surface
Are you just conversating with the GPT4 LLM via a web browser?
Yes through the browser. I ask it to verify calculations, lookup known theory, understand if an idea or experiment has been considered before, possible references, and get critique of an idea. I whish the corpus of all physics had been incorporated but I think it is not as strong as in programming at the moment.
Who cares about a few halucinations, you don't have to pay these bots. Just think of the bottom line!
Display MoreYou(+chat) did not reach that.. you only reached 3D
The Clifford torus that Wyttenbach writes about is not a 3D.toroid
it is a minimal surface in 4D space
"so only the torus Tπ/4 has the maximum possible area of 2π2. This torus Tπ/4 is the torus Tθ that is most commonly called the "Clifford torus" – and it is also the only one of the Tθ that is a minimal surface in S3." wikiplodia
the 4D dimensions .. x,y,u,v ..are necessary so that a symmetrical cyclic.circular coupling
can happen. It cannot happen with just 3D ,
given the orientations in the right hand rule.
4D is probably beyond the capability of chat..at present..
it requires imagination... a very human quality
https://www.researchgate.net/p…0IjoibWFpbkl0ZW0ifQ%3D%3Deeee
But when you symmetrize, you will get 4 dimensions of fredom three rotations and the spiraling. That's 4 and because non parallel streams are not interacting it behaves very 4D ish. One can easily show that QED is basically a law on this object.
One can easily show that QED is basically a law on this object.
Really? has it been Q.E.D?
Feynman's Nobel is based on the CT? Surely you're joking?
