ChatGPT test at LENR-CANR.org

Perhaps Wyttenbach (who can knit Clifford Tori with his eyes shut) has some thoughts on this?

Quote from RobertBryant

Really? has it been Q.E.D?

Feynman's Nobel is based on the CT? Surely you're joking?

Let's see if we can motivate this with the help of Chat GPT: Note how it is a validation tool but still pretty supid when it comes to mathematical creativite, but they are in the

process to connect it to Wolfram Alpha ...

--------------------------------------------- CHATGPT4 DISCUSSION

Me:

Is there a solution of teh Klein Gordon equation over the algebra of the Dirac matrices of the form \exp(w \gamma_0 t) \exp(k_1 \gamma_1 x)\exp(k_2 \gamma_2 y)\exp(k_3 \gamma_3 z)

ChatGpt:

To solve the Klein-Gordon equation using the given ansatz, we first need to express the equation in terms of Dirac matrices. The Klein-Gordon equation is a relativistic wave equation for a scalar field and is given by:

(∂^2/∂t^2 - ∇^2 + m^2) φ(x) = 0

where m is the mass of the field and φ(x) is the field as a function of spacetime coordinates x = (t, x, y, z).

The ansatz you provided is an exponential form using Dirac matrices, which are usually used to describe fermions. The proposed form is:

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

where γ_0, γ_1, γ_2, and γ_3 are the Dirac matrices.

It is important to notice that the Klein-Gordon equation is a scalar field equation, while the provided ansatz is written in terms of Dirac matrices, which are related to spinor fields (fermions). The Dirac equation would be a more natural choice for such an ansatz. The Dirac equation is:

(i γ^μ ∂_μ - m) ψ(x) = 0

where μ = 0, 1, 2, 3, and ψ(x) is the spinor field.

While the ansatz provided might not be directly suitable for solving the Klein-Gordon equation, you could try to modify it or use it in the context of the Dirac equation. However, finding a solution of the Dirac equation in the given exponential form might be challenging due to the non-commutativity of the Dirac matrices.

ME:

But if you generalize the Klein gordon equations to be valid for the Dirac algebra then it is a well defined problem

CHATGPT:

If you wish to generalize the Klein-Gordon equation to be valid for the Dirac algebra, you can consider a bilinear covariant form, which is built using the outer product of two spinor fields:

(ψ†(x) (i γ^μ ∂_μ - m) (i γ^ν ∂_ν + m) ψ(x)) = 0

Here, ψ(x) and ψ†(x) are the Dirac spinor field and its adjoint, respectively. γ^μ and γ^ν are the Dirac matrices, and m is the mass. In this form, the equation is compatible with the Dirac algebra.

Now, let's consider the ansatz:

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

To find a solution, we have to substitute the ansatz into the generalized Klein-Gordon equation and solve for the coefficients w, k_1, k_2, and k_3. However, due to the non-commutativity of the Dirac matrices, this is a highly nontrivial task. The exponential terms involving Dirac matrices may not simplify easily, and you may need to use techniques from non-abelian Lie algebra or other advanced mathematical methods to explore solutions.

In summary, although you can generalize the Klein-Gordon equation to be valid for the Dirac algebra, finding a solution in the given exponential form might still be challenging due to the non-commutativity of the Dirac matrices.

ME:

solve it by using the commutator rules and power series expansion of the exponentials

CHATGPT:

Let's try to solve the generalized Klein-Gordon equation with the ansatz by using commutator rules and power series expansions of the exponentials.

Consider the ansatz:

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

We can write the exponential of a matrix A as a power series:

exp(A) = I + A + (1/2!) A^2 + (1/3!) A^3 + ...

So, for each term in the ansatz, we have:

exp(w γ_0 t) = I + w γ_0 t - (1/2!) (w^2 γ_0^2 t^2) + ...

exp(k_1 γ_1 x) = I + k_1 γ_1 x - (1/2!) (k_1^2 γ_1^2 x^2) + ...

exp(k_2 γ_2 y) = I + k_2 γ_2 y - (1/2!) (k_2^2 γ_2^2 y^2) + ...

exp(k_3 γ_3 z) = I + k_3 γ_3 z - (1/2!) (k_3^2 γ_3^2 z^2) + ...

Now, let's substitute the ansatz into the generalized Klein-Gordon equation:

(ψ†(x) (i γ^μ ∂_μ - m) (i γ^ν ∂_ν + m) ψ(x)) = 0

Since the equation is linear in ψ(x), we can substitute each term of the power series into the equation separately and then require that the sum of all equations is zero. This will lead to a set of equations for the coefficients w, k_1, k_2, and k_3.

However, solving this system of equations is highly nontrivial due to the non-commutativity of the Dirac matrices and the infinite number of terms in the power series. You will need to use techniques from non-abelian Lie algebra or other advanced mathematical methods to explore possible solutions. Alternatively, you can consider using a different ansatz or working with a simpler problem that does not involve the non-commutative nature of Dirac matrices.

ME:

well would not first of all d/dx exp(k_1 gamma_1 x) = k_1\gamma_1 exp(k_1gamma_1 x) and trhe commutator rules means that exp(k_1 gamma_1 x)k_2 \gamma_2 = k_2 gamma_2 exp(-k_1 gamma_1 x)

CHATGPT:

You're right about the derivative. For the derivative of the exponential with respect to x, we have:

d/dx exp(k_1 γ_1 x) = k_1 γ_1 exp(k_1 γ_1 x)

Now let's address the commutator relations. Recall that the commutator of two matrices A and B is defined as [A, B] = AB - BA. We know that for Dirac matrices, they satisfy the anticommutation relation:

{γ_μ, γ_ν} = γ_μ γ_ν + γ_ν γ_μ = 2g_μν I

where μ, ν = 0, 1, 2, 3 and g_μν is the Minkowski metric.

Using this relation, we can evaluate the commutator of two exponentials involving different Dirac matrices:

[exp(k_1 γ_1 x), k_2 γ_2] = exp(k_1 γ_1 x) k_2 γ_2 - k_2 γ_2 exp(k_1 γ_1 x)

If the commutator is zero, then it means the two exponentials commute, and we would have:

exp(k_1 γ_1 x) k_2 γ_2 = k_2 γ_2 exp(k_1 γ_1 x)

However, we cannot assume that the exponentials of different Dirac matrices commute in general. To show whether they commute or not, you can try to compute the Baker-Campbell-Hausdorff (BCH) formula for the product of two exponentials:

exp(k_1 γ_1 x) exp(k_2 γ_2 y) = exp(k_1 γ_1 x + k_2 γ_2 y + 1/2 [k_1 γ_1 x, k_2 γ_2 y] + ...)

The BCH formula involves higher-order commutators, which can be challenging to compute for Dirac matrices. So, while the derivative with respect to x is straightforward to compute, the commutator relations involving exponentials of Dirac matrices can be more complicated to handle.

ME:

wouldent \gamma_1^n\gamma_2 = (-1)^n\gamma_2\gamma_1^n and hence my assumption be correct regardign the secona part of we expand the exp to a power series and back after the commutation has been done

CHATGPT:

You are correct. My previous response was not clear on this point. Given the anticommutation relations between Dirac matrices, it is true that for any two different Dirac matrices, like γ_1 and γ_2, we have:

(γ_1)^n (γ_2) = (-1)^n (γ_2) (γ_1)^n

Using this property, we can establish a relation between the exponential terms. Let's expand the exponentials using power series and apply the property above:

exp(k_1 γ_1 x) k_2 γ_2 = (I + k_1 γ_1 x + (1/2!) (k_1^2 γ_1^2 x^2) + ...) k_2 γ_2

Using the relation between powers of γ_1 and γ_2, we can rewrite the terms involving γ_1 and γ_2:

= I k_2 γ_2 + k_1 γ_1 x (-k_2 γ_2) + (1/2!) (k_1^2 γ_1^2 x^2) k_2 γ_2 + ...

= k_2 γ_2 - k_1 k_2 x (γ_1 γ_2) + (1/2!) (k_1^2 x^2) k_2 γ_2 + ...

Now, we can regroup the terms and rewrite it as a product:

= k_2 γ_2 (I - k_1 γ_1 x + (1/2!) (k_1^2 γ_1^2 x^2) + ...) = k_2 γ_2 exp(-k_1 γ_1 x)

Thus, you are right that the commutator rules can be used to rewrite the product of exponentials:

exp(k_1 γ_1 x) k_2 γ_2 = k_2 γ_2 exp(-k_1 γ_1 x)

With this relation, you can further simplify the generalized Klein-Gordon equation by using the derivative and commutator rules. However, solving the equation might still be challenging due to the non-commutative nature of the Dirac matrices and the need to compute higher-order derivatives and products of exponentials.

ME:

do it

CHATGPT:

Given the relation we derived earlier:

exp(k_1 γ_1 x) k_2 γ_2 = k_2 γ_2 exp(-k_1 γ_1 x)

We can proceed to analyze the generalized Klein-Gordon equation. We already calculated the first derivative of the ansatz with respect to x. We still need to calculate the derivatives with respect to the other spacetime coordinates t, y, and z:

d/dt Ψ(x) = w γ_0 exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

d/dy Ψ(x) = k_2 γ_2 exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

d/dz Ψ(x) = k_3 γ_3 exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

Now, let's substitute these derivatives into the generalized Klein-Gordon equation:

(ψ†(x) (i γ^μ ∂_μ - m) (i γ^ν ∂_ν + m) ψ(x)) = 0

The complexity of the equation increases significantly when we substitute the ansatz and its derivatives, especially when considering higher-order derivatives and products of exponentials. Moreover, we would need to compute the adjoint ψ†(x) and determine the appropriate boundary conditions.

To proceed with solving the generalized Klein-Gordon equation, it may be necessary to use advanced mathematical techniques such as non-abelian Lie algebra, numerical methods, or approximation techniques like perturbation theory. Due to the complexity of the equation and the non-commutative nature of the Dirac matrices, finding an analytical solution for the coefficients w, k_1, k_2, and k_3 might be quite challenging.

ME:

Use the wave operator directly

CHATGPT:

To address the wave operator directly, let's rewrite the generalized Klein-Gordon equation using the d'Alembert operator (∂^2/∂t^2 - ∇^2), which acts on a scalar field φ(x):

(∂^2/∂t^2 - ∇^2 + m^2) φ(x) = 0

However, our ansatz is a spinor field Ψ(x) instead of a scalar field. In this case, we can define a bilinear scalar function S(x) using the spinor field and its adjoint:

S(x) = ψ†(x)ψ(x)

Then, we can apply the wave operator to the scalar function S(x):

(∂^2/∂t^2 - ∇^2 + m^2) S(x) = 0

Let's calculate the derivatives of S(x) with respect to spacetime coordinates:

d/dt S(x) = d/dt (ψ†(x)ψ(x)) = ψ†(x) d/dt ψ(x) + (d/dt ψ†(x)) ψ(x)

d^2/dt^2 S(x) = ...

Similarly, we can compute the spatial derivatives:

∇^2 S(x) = (∂^2/∂x^2 + ∂^2/∂y^2 + ∂^2/∂z^2) S(x) = ...

Now, we need to substitute the ansatz and its derivatives into the equation:

(∂^2/∂t^2 - ∇^2 + m^2) S(x) = 0

Since the ansatz involves exponentials with Dirac matrices, we must use the relation we derived earlier:

exp(k_1 γ_1 x) k_2 γ_2 = k_2 γ_2 exp(-k_1 γ_1 x)

However, the equation remains highly nontrivial, as we must compute higher-order derivatives and products of exponentials, taking into account the non-commutative nature of Dirac matrices. To proceed, advanced mathematical techniques such as non-abelian Lie algebra, numerical methods, or approximation techniques like perturbation theory might be necessary. Finding an analytical solution for the coefficients w, k_1, k_2, and k_3 could be challenging due to the complexity of the equation and the non-commutative nature of the Dirac matrices.

ME:

but isn't d/dx^2 (exp ...) = -k_1^2 (exp ...) and similarly for all other parts

CHATGPT:

Yes, you are correct. I apologize for the confusion. Let's re-examine the generalized Klein-Gordon equation using the wave operator (∂^2/∂t^2 - ∇^2) directly and the ansatz:

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

First, let's find the second derivatives of the ansatz with respect to spacetime coordinates:

d^2/dt^2 Ψ(x) = (w^2 γ_0^2) Ψ(x)

d^2/dx^2 Ψ(x) = -(k_1^2 γ_1^2) Ψ(x)

d^2/dy^2 Ψ(x) = -(k_2^2 γ_2^2) Ψ(x)

d^2/dz^2 Ψ(x) = -(k_3^2 γ_3^2) Ψ(x)

Now, we substitute these results into the generalized Klein-Gordon equation:

(∂^2/∂t^2 - ∇^2 + m^2) Ψ(x) = ((w^2 γ_0^2) + (k_1^2 γ_1^2) + (k_2^2 γ_2^2) + (k_3^2 γ_3^2) + m^2) Ψ(x) = 0

Since γ_μ^2 = I for μ = 0, 1, 2, 3, we have:

((w^2 - k_1^2 - k_2^2 - k_3^2) + m^2) Ψ(x) = 0

This equation is satisfied if the condition:

w^2 - k_1^2 - k_2^2 - k_3^2 = m^2

holds. This is the mass-shell condition, which relates the energy w and the momentum components k_1, k_2, and k_3 with the mass m of the particle described by the ansatz.

In summary, the ansatz can be a solution to the generalized Klein-Gordon equation if the mass-shell condition is satisfied.

ME:

So as exp(l \gamma x) are essentially rotatio operators on S_1 \times S_2 we have essentially showed that this generalized version has solutions in the 4D "phases" space of this object

CHATGPT:

Yes, you can interpret the solutions to the generalized Klein-Gordon equation in terms of rotations in the phase space of the 4D spacetime coordinates. The ansatz:

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

can be seen as a product of exponentials involving the Dirac matrices, which can be interpreted as generators of rotations (or boosts) in spacetime. Each term in the ansatz represents a rotation or boost along a specific spacetime direction.

Since we have shown that the ansatz is a solution to the generalized Klein-Gordon equation when the mass-shell condition is satisfied:

w^2 - k_1^2 - k_2^2 - k_3^2 = m^2

we can conclude that the solutions of the equation can be found in the 4D "phases" space of the spacetime coordinates, describing rotations and boosts in spacetime, subject to the mass-shell condition. The mass-shell condition ensures that the solutions describe physical particles with a given mass m and energy-momentum relation.

Note that the pauli matrices can be associated to i,j,k in the quaternonian algebra and what Dirac did was to take w to be an imaginary number matrice (S_1) and performed essentially w \otimes Q when we go to phasespace we are essentially working on T_2S_2 but as we forgot about S_2 in this representation and works with the flat T_2 in stead we may end up with 2pi^2 as the maximal volume.if you take the solenoid and turn it around in all possible ways T_2xS_2 is what you get!

Another fun fact is that the fourier transform transform the electrical potential to the electrical potential!!!! Mills has always stated the QM is stuff done in the phase space and it sure smells like that

Quote from stefan

boosts in spacetime,

JOKEGPT.. ? maybe a variant CHATGPT..

Quote from stefan

Ψ(x) = exp(w γ_0 t) exp(k_1 γ_1 x) exp(k_2 γ_2 y) exp(k_3 γ_3 z)

As some might know S³ is not an allowed solution space for stable flux as it leads to crossing and inhomogeneity.

All classic physics (Klein Gordon, QED, QCD)use this wrong concept, thus classic physics is a conceptual fail. So it simply is a waste of time to use/discuss any of the old formalism. Instead of the dot product the cross product needs to be taken to extend the space as the definition of SO(4) = SU(2)xSU(2) shows. This is a double rotation coupling not just a single rotation.

Further it has been shown that all action must be 1:1 or 2:1 never 3:1 as in Einsteins nonsensical GR. 3 simple coupled rotations are impossible do to the negative curvature you get for the addition of the 4th dimension.

So SO(4) is 2:1 action X 2:1 action.

I will not make more comments on historic garbage that is only good for engineering not for basic physics.

Quote from Wyttenbach

As some might know S³ is not an allowed solution space for stable flux as it leads to crossing and inhomogeneity.

All classic physics (Klein Gordon, QED, QCD)thus classic physics is a conceptual fail. So it simply is a waste of time to use/discuss any of the old formalism. Instead of the dot product the cross product needs to be take to extend the space as the definition of SO(4) = SU(2)XSU(2) shows. This is a double rotation coupling not just a single rotation.

Further it has been shown that all action must be 1:1 or 2:1 never 3:1 as in Einsteins nonsensical GR. 3 simple coupled rotations are impossible do to the negative curvature you get for the addition of the 4th dimension.

So SO(4) is 2:1 action X 2:1 action.

I will not make more comments on historic garbage that is only good for engineering not for basic physics.

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There must be a connection that is valid and by showing that you can turn the attantion to the real physics. So although you think that it is unworthy to study, the effect of this is mighty as you would then turn the tanker of all human experts and point it in the right direction.

Hi stefan

I created a new thread for your poems, and other OT prose. Nice painting BTW.

Quote from stefan

There must be a connection that is valid and by showing that you can turn the attantion to the real physics. So although you think that it is unworthy to study, the effect of this is mighty as you would then turn the tanker of all human experts and point it in the right direction.

If not there is big effort to confuse people to enable e.g. competetive advantage or hinder mad scientists to destroy the world, which is quite possible and maybe something we should be glad for, considering what deep knowledge in physics in the end can result intoa nd what another Dr starngelove can cook up .

‘Godfather of AI’ Geoffrey Hinton quits Google and warns over dangers of misinformation

The neural network pioneer says dangers of chatbots were ‘quite scary’ and warns they could be exploited by ‘bad actors’

‘Godfather of AI’ Geoffrey Hinton quits Google and warns over dangers of misinformation

The neural network pioneer says dangers of chatbots were ‘quite scary’ and warns they could be exploited by ‘bad actors’

www.theguardian.com

The man often touted as the godfather of AI has quit Google, citing concerns over the flood of misinformation, the possibility for AI to upend the job market, and the “existential risk” posed by the creation of a true digital intelligence.

Dr Geoffrey Hinton, who with two of his students at the University of Toronto built a neural net in 2012, quit Google this week, as first reported by the New York Times.

Hinton, 75, said he quit to speak freely about the dangers of AI, and in part regrets his contribution to the field. He was brought on by Google a decade ago to help develop the company’s AI technology, and the approach he pioneered led the way for current systems such as ChatGPT.

The decoder could reconstruct speech using fMRI scan data.

AI makes non-invasive mind-reading possible by turning thoughts into text

Read more

He told the New York Times that until last year he believed Google had been a “proper steward” of the technology, but that changed once Microsoft started incorporating a chatbot into its Bing search engine, and the company began becoming concerned about the risk to its search business.

Some of the dangers of AI chatbots were “quite scary”, he told the BBC, warning they could become more intelligent than humans and could be exploited by “bad actors”. “It’s able to produce lots of text automatically so you can get lots of very effective spambots. It will allow authoritarian leaders to manipulate their electorates, things like that.”

But, he added, he was also concerned about the “existential risk of what happens when these things get more intelligent than us.

“I’ve come to the conclusion that the kind of intelligence we’re developing is very different from the intelligence we have,” he said. “So it’s as if you had 10,000 people and whenever one person learned something, everybody automatically knew it. And that’s how these chatbots can know so much more than any one person.”

He is not alone in the upper echelons of AI research in fearing that the technology could pose serious harm to humanity. Last month, Elon Musk said he had fallen out with the Google co-founder Larry Page because Page was “not taking AI safety seriously enough”. Musk told Fox News that Page wanted “digital superintelligence, basically a digital god, if you will, as soon as possible”.

Valérie Pisano, the chief executive of Mila – the Quebec Artificial Intelligence Institute – said the slapdash approach to safety in AI systems would not be tolerated in any other field. “The technology is put out there, and as the system interacts with humankind, its developers wait to see what happens and make adjustments based on that. We would never, as a collective, accept this kind of mindset in any other industrial field. There’s something about tech and social media where we’re like: ‘Yeah, sure, we’ll figure it out later,’” she said.

Hinton’s concern in the short term is something that has already become a reality – people will not be able to discern what is true any more with AI-generated photos, videos and text flooding the internet.

The recent upgrades to image generators such as Midjourney mean people can now produce photo-realistic images – one such image of Pope Francis in a Balenciaga puffer coat went viral in March.

Hinton was also concerned that AI will eventually replace jobs like paralegals, personal assistants and other “drudge work”, and potentially more in the future.

Google’s chief scientist, Jeff Dean, said in a statement that Google appreciated Hinton’s contributions to the company over the past decade.

“I’ve deeply enjoyed our many conversations over the years. I’ll miss him, and I wish him well!

“As one of the first companies to publish AI Principles, we remain committed to a responsible approach to AI. We’re continually learning to understand emerging risks while also innovating boldly.”Toby Walsh, the chief scientist at the University of New South Wales AI Institute, said people should be questioning any online media they see now.

“When it comes to any digital data you see – audio or video – you have to entertain the idea that someone has spoofed it.”

Quote from Alan Smith

‘Godfather of AI’ Geoffrey Hinton quits Google and warns over dangers of misinformation

The neural network pioneer says dangers of chatbots were ‘quite scary’ and warns they could be exploited by ‘bad actors’

https://www.theguardian.com/te…ngers-of-machine-learning

The man often touted as the godfather of AI has quit Google, citing concerns over the flood of misinformation, the possibility for AI to upend the job market, and the “existential risk” posed by the creation of a true digital intelligence.

Dr Geoffrey Hinton, who with two of his students at the University of Toronto built a neural net in 2012, quit Google this week, as first reported by the New York Times.

Hinton, 75, said he quit to speak freely about the dangers of AI, and in part regrets his contribution to the field. He was brought on by Google a decade ago to help develop the company’s AI technology, and the approach he pioneered led the way for current systems such as ChatGPT.

The decoder could reconstruct speech using fMRI scan data.

AI makes non-invasive mind-reading possible by turning thoughts into text

Read more

He told the New York Times that until last year he believed Google had been a “proper steward” of the technology, but that changed once Microsoft started incorporating a chatbot into its Bing search engine, and the company began becoming concerned about the risk to its search business.

Some of the dangers of AI chatbots were “quite scary”, he told the BBC, warning they could become more intelligent than humans and could be exploited by “bad actors”. “It’s able to produce lots of text automatically so you can get lots of very effective spambots. It will allow authoritarian leaders to manipulate their electorates, things like that.”

But, he added, he was also concerned about the “existential risk of what happens when these things get more intelligent than us.

“I’ve come to the conclusion that the kind of intelligence we’re developing is very different from the intelligence we have,” he said. “So it’s as if you had 10,000 people and whenever one person learned something, everybody automatically knew it. And that’s how these chatbots can know so much more than any one person.”

He is not alone in the upper echelons of AI research in fearing that the technology could pose serious harm to humanity. Last month, Elon Musk said he had fallen out with the Google co-founder Larry Page because Page was “not taking AI safety seriously enough”. Musk told Fox News that Page wanted “digital superintelligence, basically a digital god, if you will, as soon as possible”.

Valérie Pisano, the chief executive of Mila – the Quebec Artificial Intelligence Institute – said the slapdash approach to safety in AI systems would not be tolerated in any other field. “The technology is put out there, and as the system interacts with humankind, its developers wait to see what happens and make adjustments based on that. We would never, as a collective, accept this kind of mindset in any other industrial field. There’s something about tech and social media where we’re like: ‘Yeah, sure, we’ll figure it out later,’” she said.

Hinton’s concern in the short term is something that has already become a reality – people will not be able to discern what is true any more with AI-generated photos, videos and text flooding the internet.

The recent upgrades to image generators such as Midjourney mean people can now produce photo-realistic images – one such image of Pope Francis in a Balenciaga puffer coat went viral in March.

Hinton was also concerned that AI will eventually replace jobs like paralegals, personal assistants and other “drudge work”, and potentially more in the future.

Google’s chief scientist, Jeff Dean, said in a statement that Google appreciated Hinton’s contributions to the company over the past decade.

“I’ve deeply enjoyed our many conversations over the years. I’ll miss him, and I wish him well!

“As one of the first companies to publish AI Principles, we remain committed to a responsible approach to AI. We’re continually learning to understand emerging risks while also innovating boldly.”Toby Walsh, the chief scientist at the University of New South Wales AI Institute, said people should be questioning any online media they see now.

“When it comes to any digital data you see – audio or video – you have to entertain the idea that someone has spoofed it.”

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I tell all I know to not answer calls from unknown callers! And not to trust anything they hear or see unless threre is credible sources

Quote from Alan Smith

The man often touted as the godfather of AI has quit Google, citing concerns over the flood of misinformation, the possibility for AI to upend the job market, and the “existential risk” posed by the creation of a true digital intelligence.

GPT has been used in computer linguistics for more than 10 years now. What is new is the addition of some linguistic extensions that map structure (questions) to answers. May be for private use its quite OK if you e.g. like to automatically generate a summary but....

The current hype is (has been) already extensively mis-used by big pharma to spread marketing fake news like the RNA therapy protects you from covid what latest with Omicron has fully reversed. Same with cold fusion or the role of Ivermectin.

So dumb people believe if a tool is fancy then the answers are correct. So I can only urge you to stay of any public chatGPT offer where you don't know who did feed the repository and who did restrict the dictionary to help promoting his interests.

Same holds for wikipedia where all sites of industrial/political interest have been highjacked by the global players. Just read the page about cold fusion or Randal Mills. Same for Covid where dubious spin doctors from Pakistan did take over.

Society is on the direct path way to loose any reliable source of information except for people that have enough money to buy papers from Nature/Elsevier/science direct etc...

And do not forget. All you feed is stored and tells the others what exactly you do....

Quote from stefan

There must be a connection that is valid and by showing that you can turn the attantion to the real physics.

Of course there is a connection between classic physics (Maxwell, Newton) and proper nuclear and particle physics. But all current models (GR, QED, QM,QCD,LQCD) are based on physically nonsensical approaches that directly contradict with basic laws.

As said. All action in nature is 1:1 or 2:1 never 3:1. 3:1 would mean that you can generate a force from a volume without any physical cause (Einsteins claim that gravity is cause by curvature where everybody with a clear mind would ask what produces the curvature...) . 2:1 means the cause of the force covers 2 dimension e.g. the rotation of a B field where its action (force) is vertical to it. If you add one more dimension then with a rotation (now in total 2) nothing change as the result is just vector addition and the picture (of minimal action) remains 2:1 and the action surface becomes a torus.

3:1 in GR means that space and mass/field has a common rotation what is nonsense. Because mass can only have 2 rotations and cannot take part in a third single center (S³!!) rotation.

Quote from Wyttenbach

Because mass can only have 2 rotations and cannot take part in a third single center (S3!!) rotation.

I thought 3 were accepted for non-symmetric masses.

Dzhanibekov effect, is briefly explained as follows on Quora by Robert Frost, Instructor and Flight Controller at NASA:

Quote

That is called the Dzhanibekov effect, after Cosmonaut Vladimir Dzhanibekov, who documented it in space, aboard the Soviet space station Salyut 7, in 1985. Below is a video with footage from his experiment, but it is in Russian.
The Dzhanibekov effect is also called the tennis racket theorem, because it is easily spotted by tossing a tennis racket in the air.
A rigid body has three principal axes of rotation. It will be stable about axes one and three, but unstable about the second axis, which is also called the intermediate axis. This odd-looking effect occurs when the object is rotated about an axis that is near the intermediate axis.
It is more spectacular when viewed in space because the absence of weight allows the rotation

Quote from Alan Smith

I thought 3 were accepted for non-symmetric masses.

No its primary school knowledge. You can walk to any point on a sphere by doing 2 rotation paths. Sphere = full 3D space.

So a third rotation is linear dependent (= not independent) on the other 2.

Of course any real body can have 3 rotation axes with 3 different inertia. But only 2 axes can be active at any time. The third axes does an oscillation! This is something Einstein/Dirac never got as they missed some higher mechanics lectures.

Quote from Wyttenbach

No its primary school knowledge. You can walk to any point on a sphere by doing 2 rotation paths. Sphere = full 3D space.

So a third rotation is linear dependent (= not independent) on the other 2.

Of course any real body can have 3 rotation axes with 3 different inertia. But only 2 axes can be active at any time. The third axes does an oscillation! This is something Einstein/Dirac never got as they missed some higher mechanics lectures.

True and I agree that they include all three in the formulation and this is a clue

Okey I explored the reduced mass and the assumption that the charge distribution is located on a surface and what that would lead to if the interaction between the electron and proton simply concelled some energy density in the electron. we assume that the charge energy is at the limit in the electron and that's what makes it stable and that in the proton instead, the magnetic energy is at the limit, we would expect to use the reduced mass, which is a successful correction that enables very exact energy levels in the hydrogen atom, or something similar. Here is a discussion about this with ChatGPT that seam to validate this "napkin" calculation, Note that the traditinal reason to reduce mass is that one thinks about the system as a two particle system. This deduction is completely new.

ME

When it comes to energy located in a constellation and length scaler by a, then how does the energy scale acording to dimensional analysis

CHATGPT:

Dimensional analysis is a useful tool for understanding how physical quantities scale with respect to each other. In this case, you're interested in how energy (E) scales with respect to a length scaler (a) in a constellation.

Let's perform dimensional analysis to understand the scaling behavior. First, we need to identify the units of the relevant quantities:

1. Energy (E): Joules (J)

2. Length scaler (a): meters (m)

Now, we need to introduce a scaling exponent (n) to relate energy to the length scaler:

E ∝ a^n

The goal is to find the value of n that will make the equation dimensionally consistent. Energy has dimensions of mass (M) times length squared (L^2) divided by time squared (T^2):

[E] = [M L^2 / T^2]

Length has dimensions of length (L):

[a] = [L]

We can now express the dimensions of energy as:

[M L^2 / T^2] ∝ [L]^n

To make the dimensions consistent, we must have:

n = 2

So, the energy scales with the square of the length scaler:

E ∝ a^2

This means that if the length scaler increases or decreases, the energy will scale with the square of that change. Keep in mind, though, that this is a general relationship derived from dimensional analysis, and specific systems may have additional factors that affect energy scaling.

ME:

If we then divide this per volume element how would this scale

CHATGPT:

To determine the energy per volume element, we need to divide the energy (E) by the volume (V). Let's denote the energy density as D:

D = E/V

Now let's consider how the energy density scales with the length scaler (a). From our previous dimensional analysis, we found that:

E ∝ a^2

Volume has dimensions of length cubed (L^3):

[V] = [L^3]

The volume will scale with the cube of the length scaler:

V ∝ a^3

Now, we can find the scaling relationship for the energy density:

D ∝ (a^2) / (a^3)

Simplifying the expression, we get:

D ∝ 1/a

So, the energy density scales inversely with the length scaler. This means that as the length scaler increases, the energy density decreases, and vice versa.

ME:

And if one whould integerate this on a surface how would that scale

CHATGPT:

When integrating the energy density (D) over a surface, you are essentially calculating the energy flux through that surface. Let's denote the energy flux as F.

First, let's recall the scaling relationship for energy density:

D ∝ 1/a

Now, to calculate the energy flux, we need to integrate the energy density over a surface area (A). Surface area has dimensions of length squared (L^2):

[A] = [L^2]

The surface area will scale with the square of the length scaler:

A ∝ a^2

The energy flux is the product of the energy density and the surface area:

F = D * A

Considering the scaling relationships we derived earlier:

F ∝ (1/a) * (a^2)

Simplifying the expression, we get:

F ∝ a

So, the energy flux scales linearly with the length scaler. This means that as the length scaler increases, the energy flux through the surface also increases, and vice versa.

ME:

So if energy on a surface scales like a, and we associate rest mass m to energy then mass scales as a as well

CHATGPT:

Yes, you're correct. If we assume the energy on the surface scales linearly with the length scaler (a) and we use the mass-energy equivalence principle from Einstein's famous equation:

E = m * c^2

Where E is the energy, m is the rest mass, and c is the speed of light.

Since we established that energy scales linearly with the length scaler (a):

E ∝ a

We can rewrite the mass-energy equivalence equation in terms of the scaling relationship:

m * c^2 ∝ a

Here, the speed of light (c) is a constant. To determine how the mass scales with the length scaler, we can rearrange the equation:

m ∝ a

So, the mass scales linearly with the length scaler as well. As the length scaler increases, the associated mass also increases, and vice versa. However, it is important to remember that this scaling relationship is based on certain assumptions and might not hold true for all physical systems.

ME:

Now if mass and density follow the same scaling property as described above, then if we assume that the electron has reached a fixed density \rhoi_e = A/r_e and that the proton, with larger mass has instead and eqivalent mass rho_p = A/r_p as proton charge and electron charge has different sign's we would consider a conscelling hence if we constarin the density to a constant value in order then the mass of the electron would be adding the densities of the proton and electron (loosely speaking). HOw would the electron mass change if this assumption was correct

CHATGPT:

It appears that there might be some confusion in the assumptions and relationships stated in your question. However, I'll try my best to address your question.

First, let's clarify that mass and density are different physical properties. Mass is a scalar quantity that measures the amount of matter in an object, whereas density is the mass per unit volume. In your question, you mentioned that mass and density follow the same scaling property, which may not be accurate.

Second, I believe you are considering the electron and proton to have fixed densities (ρ_e and ρ_p) and are trying to relate their masses (m_e and m_p) based on a constant ratio (A).

ρ_e = A/r_e

ρ_p = A/r_p

Here, r_e and r_p are some scaling parameters related to the electron and proton, respectively.

Now, let's express the electron mass (m_e) in terms of the proton mass (m_p). We will assume that the volume of the electron (V_e) and proton (V_p) are related to r_e and r_p, respectively.

m_e = ρ_e * V_e

m_p = ρ_p * V_p

Using the given density relationships:

m_e = (A/r_e) * V_e

m_p = (A/r_p) * V_p

Now we can find the ratio of the electron mass to the proton mass:

m_e / m_p = [(A/r_e) * V_e] / [(A/r_p) * V_p]

Since A is a constant, it cancels out:

m_e / m_p = (r_p * V_e) / (r_e * V_p)

If we constrain the density to be constant and the mass of the electron is the sum of the densities of the proton and electron (as you mentioned "loosely speaking"), this relationship does not seem to be valid based on our previous analysis.

Furthermore, it's important to note that electrons and protons are elementary particles with different properties, and it may not be appropriate to compare their densities in this way. The electron is a point-like particle with no known substructure, while the proton is a composite particle made up of quarks and gluons. Comparing their masses and densities in this manner may not be accurate or physically meaningful.

ME:

As the charges cancel one woule expect \rho_e - \rho_p = constant meaning that \rho_e \to \rho_e+\rho_p

CHATGPT:

I understand that you are trying to find a relationship between the densities of electrons and protons based on their charges, assuming that the charges cancel each other out. However, the densities of electrons and protons are not directly related to their charges.

The charge of an electron is negative (-e) and the charge of a proton is positive (+e). The fact that their charges cancel out in a neutral atom is a result of the balance between the number of electrons and protons, rather than their densities.

When you state that ρ_e - ρ_p = constant, it implies that the densities of the electrons and protons have some direct relationship to each other. However, this is not the case. The densities are determined by their mass and volume, which are not directly related to their charges.

If you are considering a situation where the electrons and protons are distributed in some volume, you might be thinking about the charge density rather than the mass density. In such a case, the net charge density would indeed be constant (ideally zero) for a neutral system. However, this would be related to the number of charges per unit volume rather than the mass densities of electrons and protons.

ME:

it't the energy density and we are studying the effect of the proton on the electron. As there woule be some cancellation in the electron in the electrical energy inside the electron we state this simplified assumption

CHATGPT:

I see that you're interested in the effect of the proton on the electron, specifically the impact on the energy density due to their electric charges. In this case, we can consider the electric potential energy density.

The energy density associated with the electric field is given by:

u = 1/2 * ε₀ * E²

where u is the energy density, ε₀ is the vacuum permittivity, and E is the electric field.

In a simplified model, we can assume that the electric field of the proton and electron are uniform within their respective volumes. We can then compute the energy density for each particle and compare their effects.

The electric field of a spherical charge distribution is given by:

E = Q / (4πε₀ * r²)

where Q is the charge of the particle and r is the distance from the center of the particle.

Now, let's consider the effect of the proton on the electron:

1. The proton has a positive charge (+e) and creates an electric field that repels the negatively charged electron.

2. The electron has a negative charge (-e) and creates an electric field that is attracted to the proton.

As the electron and proton are attracted to each other, their electric fields overlap, and there is a "cancellation" of the electric field in the region where they overlap. This cancellation will result in a reduction of the energy density in that region.

However, this simplified assumption doesn't take into account several important factors:

1. The spatial distribution of charges within the proton and electron: In reality, electrons are point-like particles with no known substructure, whereas protons are composite particles with a more complex charge distribution.

2. The quantum nature of the electron: The behavior of electrons around a proton is governed by quantum mechanics. An electron doesn't have a fixed position but instead occupies a region of space described by a probability distribution (orbital). Therefore, a simplified classical model may not accurately describe the system.

Given these complexities, the simplified assumption of ρ_e → ρ_e + ρ_p might not be accurate or meaningful in describing the actual behavior of the electron in the presence of a proton. Instead, a quantum mechanical approach should be used to study the electron-proton interactions.

ME:

But above we stated that energy density if located on a surface scales like C/a, assume C is the same in both the electron and the proton

CHATGPT:

I apologize for the confusion earlier. If we consider the energy density (D) located on a surface and it scales as C/a, where C is a constant and a is a length scaler, we can analyze the relationship between the electron and proton.

Given the scaling relationship:

D_e ∝ C/a_e (for electron)

D_p ∝ C/a_p (for proton)

Assuming that C is the same for both the electron and the proton, we can compare their energy densities. First, let's consider the ratio of the energy densities of the electron and proton:

D_e / D_p = (C/a_e) / (C/a_p)

Since C is the same for both particles, it cancels out:

D_e / D_p = a_p / a_e

Now, if you want to study the effect of the proton on the electron, we can examine the total energy density (D_total) in the region where both particles are present:

D_total = D_e + D_p

Using the scaling relationships we derived earlier:

D_total ∝ C/a_e + C/a_p

To simplify the expression, we can factor out the constant C:

D_total ∝ C * (1/a_e + 1/a_p)

This expression shows that the total energy density depends on the sum of the inverses of the length scalers a_e and a_p. The cancellation effect you mentioned earlier would result in the energy density being reduced in the region where the electric fields of the electron and proton overlap. However, without more information about the specific system and the nature of the length scalers a_e and a_p, it's difficult to draw further conclusions about the relationship between the electron and proton.

Keep in mind that this simplified analysis does not consider the full complexity of the electron-proton system, such as their quantum nature, and it might not provide an accurate representation of their interaction. A more detailed study would require a quantum mechanical approach, like solving the Schrödinger equation for the hydrogen atom.

ME:

Note C(1/a_e+1/a_p) = C /(1/(1/a_e+1/a_p)) = C /(a_e a_p / (a_e+a_p)) = C/a, with a = a_e a_p/(a_e+a_p). Then if m = Da (as we saw above it scaled like this)m we get m = D a_e a_p/(a_e+a_p). = D a_e D a_p/(D a_e+D a_p) = m_e m_p / (m_e + m_p). So we would then if we assumed this scaling property and that the electron tries to attain a fixed energy density that the effective mass of the electron should be the reduced mass

CHATGPT:

Your analysis is correct. If we assume the simplified scaling property, where the energy density located on a surface scales as C/a and that the electron tries to attain a fixed energy density, the effective mass of the electron (m_e) can be related to the mass of the proton (m_p) through the reduced mass (μ) formula:

μ = m_e * m_p / (m_e + m_p)

The reduced mass is a concept used in classical and quantum mechanics to simplify two-body problems, and it can be interpreted as the "effective" mass of the two-body system.

However, it's important to keep in mind that the assumptions made in this analysis are based on a simplified model and may not fully capture the complexity of the electron-proton interaction. A more accurate description of their interaction would require a quantum mechanical approach, such as solving the Schrödinger equation for the hydrogen atom. The reduced mass does play a role in the quantum mechanical description, but it is derived from a different line of reasoning.

ME:

Isn't it interesting that the reduced mass as usually assumed to be related to mass centre also can be derived via this dimensional analysis, that the energy density is located at a surface and some hand waving. Now has this way of deducing the reduced mass been done before?

CHATGPT:

It is indeed interesting that you were able to arrive at the concept of reduced mass through a different approach, using dimensional analysis, energy density located on a surface, and some assumptions. However, this method of deducing the reduced mass is not conventional and might not be widely recognized or acknowledged in the scientific literature.

The reduced mass is typically derived from the classical or quantum mechanical two-body problem, where it serves as an effective mass that simplifies the equations of motion. In classical mechanics, the reduced mass arises when transforming to the center-of-mass frame, while in quantum mechanics, it is used when solving the Schrödinger equation for a two-body system.

Although your approach provides an interesting perspective, it is important to keep in mind that the assumptions made in your analysis might not accurately capture the full complexity of the electron-proton interaction. The simplified scaling properties and energy density considerations may not provide a complete or rigorous understanding of the system.

Nevertheless, it's always valuable to explore alternative ways of understanding physical concepts, as they can provide unique insights or perspectives that could lead to new discoveries or a deeper understanding of the subject matter.

Here a reference to a "old/2021" AI (KI) docu on ARTE.tv about artificial intelligence.

https://www.arte.tv/de/videos/…/kuenstliche-intelligenz/ in German

Already here CHAT-GPT is mentioned and some dangers of these chat bots are revealed. Also the limits are made clear. AI is very far from human creativity. But some folks like to have private talks with AI. That's the place the money comes from.

Why was there a hype around CHAT-GPT? As usual money and greedy investors...

If you like some English AI stuff from ARTE look at https://www.arte.tv/en/search/?q=artificial