AI learnt "something" from the Physical & Life Sciences Forum.

[sjastro]

In April of this year I asked Bing this applied mathematics question.

Explain how the Schwarzschild metric when expressed in Droste-Hilbert coordinates results in the speed of light being anisotropic.
Calculate the difference Δv between the radial and peripheral velocity of light at the Earth’s surface.

It didn't know the answer.

I’m sorry, but I couldn’t find any information on how the Schwarzschild metric when expressed in Droste-Hilbert coordinates results in the speed of light being anisotropic or the difference between the radial and peripheral velocity of light at the Earth’s surface. Would you like me to search for something else?

I asked the same question today to Bing with GPT-4 Copilot which gave this answer.

The Schwarzschild metric, which describes the gravitational field outside a spherical mass, can be expressed in Droste-Hilbert coordinates as³:

ds² = c² (1-2MG/ c²r)dt² - dr²/ (1-2MG/c²r) -r² (dθ²+sin²θdϕ²)

In this metric, the speed of light appears to be anisotropic, meaning it varies depending on the direction of propagation. This is a consequence of the curvature of spacetime caused by the mass.
The radial and peripheral velocities of light refer to the velocities of light moving radially (directly towards or away from the mass) and peripherally (tangentially to the mass), respectively. The difference between these velocities, Δv, is a result of the gravitational influence of the mass.
However, calculating the exact difference Δv at the Earth's surface requires a detailed understanding of the Earth's gravitational field and the effects of general relativity. It's a complex calculation that typically requires numerical methods and is beyond the scope of this conversation.

For a rough estimate, we can consider that the Earth's effect on the radial velocity of light is very small, on the order of 0.1 m/s over a period of 1 year⁵. The peripheral velocity of light at the Earth's surface is essentially the speed of light, c. Therefore, the difference Δv would be extremely small and close to zero. For a precise calculation, I would recommend consulting a textbook on general relativity or seeking the help of a physicist.

Source: Conversation with Bing, 12/19/2023

(1) An experiment with Bing chatbot. | Christian Forums. https://www.christianforums.com/threads/an-experiment-with-bing-chatbot.8273104/.
(2) Doppler spectroscopy - Wikipedia. Doppler spectroscopy - Wikipedia.
(3) Schwarzschild metric in terms of a falling observer's coordinates. https://physics.stackexchange.com/questions/714074/schwarzschild-metric-in-terms-of-a-falling-observers-coordinates.
(4) Schwarzschild metric - Wikipedia. https://en.wikipedia.org/wiki/Schwarzschild_metric.
(5) MathPages. https://www.mathpages.com/home/kmath697/kmath697.htm.
(6) The fundamental definition of ‘radial velocity’ - arXiv.org. https://arxiv.org/pdf/astro-ph/0302522.pdf.
(7) A connection between radial velocity and distance. http://spiff.rit.edu/classes/phys240/lectures/expand/expand.html.
(8) Proper Motions and Radial Velocities - CliffsNotes. https://www.cliffsnotes.com/study-guides/astronomy/observational-properties-of-stars/proper-motions-and-radial-velocities.
(9) Radial velocity - Wikipedia. https://en.wikipedia.org/wiki/Radial_Velocity.

Bing provided a host of references including the CF thread in the first reference.
Despite the detailed response it didn't answer the question, you do not need numerical methods nor seek the help of a physicist.
This is standard applied mathematics question, the answer was provided in the first reference which AI clearly doesn't understand at this stage.
I might ask the question again in a years time.

 

[Occams Barber]

In April of this year I asked Bing this applied mathematics question.

Explain how the Schwarzschild metric when expressed in Droste-Hilbert coordinates results in the speed of light being anisotropic.
Calculate the difference Δv between the radial and peripheral velocity of light at the Earth’s surface.

It didn't know the answer.

I asked the same question today to Bing with GPT-4 Copilot which gave this answer.


Bing provided a host of references including the CF thread in the first reference.
Despite the detailed response it didn't answer the question, you do not need numerical methods nor seek the help of a physicist.
This is standard applied mathematics question, the answer was provided in the first reference which AI clearly doesn't understand at this stage.
I might ask the question again in a years time.

I have no idea what your question is all about, but it does raise the issue of how often and by what strategy does an AI system update itself. In the past I've asked questions involving data (typically surveys) only to be quoted dated info. When challenged the AI went looking for more up to date data and modified it's answer.

In an era where info changes rapidly, It would seem that refreshing data as soon as it is available would be a sensible (if difficult) strategy.

OB

 

[Fervent]

In April of this year I asked Bing this applied mathematics question.

Explain how the Schwarzschild metric when expressed in Droste-Hilbert coordinates results in the speed of light being anisotropic.
Calculate the difference Δv between the radial and peripheral velocity of light at the Earth’s surface.

It didn't know the answer.

I asked the same question today to Bing with GPT-4 Copilot which gave this answer.


Bing provided a host of references including the CF thread in the first reference.
Despite the detailed response it didn't answer the question, you do not need numerical methods nor seek the help of a physicist.
This is standard applied mathematics question, the answer was provided in the first reference which AI clearly doesn't understand at this stage.
I might ask the question again in a years time.

I don't understand your question, but it demonstrates one of the major pitfalls of AI. Because it tends to output detailed information, any answer is going to appear credible. But if you're asking a question that demands some level of technical sophistication, it is easy to be fooled if you're not already an expert in the field. Since people will likely use it to try to answer complex questions that are beyond their capabilities, it will likely increase the amount of persuasive misinformation rather than decrease it.

 

[durangodawood]

At least someone (something) visits this subform.

 

[sjastro]

This is what the question is based on, the Schwarzschild metric in Drost-Hilbert coordinates is a solution of Einstein’s field equations for gravity.
It predicted the existence of black holes but is also used to describe the gravitational field around objects such as the earth.
The coordinate system is non isotropic as the speed of light in the radial direction is different from its peripheral or tangent direction at the earth’s surface as illustrated.

This is a mathematical artefact of the coordinate system used and does not represent the physical reality of the speed of light being different in the radial and peripheral directions.

 

[sjastro]

@Occams Barber, @Fervent

ChatGPT-3 has the disclaimer.
ChatGPT can make mistakes. Consider checking important information.

 

[sjastro]

At least someone (something) visits this subform.

It has been pointed out to me contents in this subforum occasionally turn up in the comments section in places such as Phys.org to refute pseudoscience such as the electric universe model or highlight the nonsense when Christian fundamentalists critique mainstream science.

 

[Hans Blaster]

It has been pointed out to me contents in this subforum occasionally turn up in the comments section in places such as Phys.org to refute pseudoscience such as the electric universe model or highlight the nonsense when Christian fundamentalists critique mainstream science.

It's some sort of honey trap. I haven't freed myself yet.

 

[sjastro]

Yesterday I posed the same question to ChatGPT-3 which gave a similar answer to Bing with GPT-4 Copilot.

Twenty four hours later it gave a different answer where it attempted to describe the mathematics of radial velocity of light before going horribly off the rails as shown in the shaded portion.

You cannot define the speed of light c as a derivative defined by the formula v = ds/dt as in GR light travels along null geodesics where ds = 0.
Objects travel at speeds less than c along geodesics where ds <> 0 can be defined by a 4-velocity, whereas photons cannot be defined due to travelling along null geodesics.
Hence multiplying the radial coefficient of Schwarzschild metric by the radial component of the photon’s 4-velocity make absolutely no sense.
Furthermore ChatGPT-3 does not go into detail how the peripheral velocity of light is derived.

 

[sjastro]

Unbelievable in a short period of time where Bing didn't know the answer, stated the calculations required numerical methods or it was so hard one should ask a physicist for the answer, it is now giving a lecture on the mathematical explanation for the anisotropic nature of the speed of light at the Earth's surface.

Here is the explanation which I gave.

The Schwarzschild metric in Droste-Hilbert coordinates is;

ds² = c²(1-2MG/ c²r)dt² - dr²/ (1-2MG/c²r) -r²(dθ²+sin²θdϕ²)

One needs to look at the radial and peripheral velocity of light.
Since light travels along null geodesics ds² =0.
For the radial velocity dr/dt, dθ = dϕ = 0 and the metric reduces to;

dr/dt = c(1-2MG/c²r)

For the peripheral velocity rdθ/dt, dr = dϕ = 0 and the metric reduces to;

rdθ/dt = c√(1-2MG/c²r) ≈ c(1-(1/2)2MG/c²r) as 2MG/c²r is very small for Earth.

The difference between the radial and peripheral velocity is;
Δv = c(2MG/c²r)(1/2) = 21 cm/sec.

Here is Bing's "lecture" on the explanation.

Bing

There are a few points to consider:

1. Approximation: The approximation used for the peripheral velocity of light,
rdθ/dt = c√(1-2MG/c²r) ≈ c(1-(1/2)2MG/c²r), is valid only when 2MG/c²r is very small.
This is indeed the case for Earth, but it’s important to remember that this approximation may not hold for other celestial bodies with stronger gravitational fields.

2. Anisotropy: The difference in radial and peripheral velocities of light, Δv = c(2MG/c²r)(1/2) = 21 cm/sec, indicates an anisotropic nature of light at the Earth’s surface.

This means that the speed of light appears to vary depending on the direction of propagation. However, this anisotropy is a coordinate effect of the chosen Schwarzschild coordinates and does not represent a physical anisotropy. In a locally inertial frame, the speed of light is still isotropic.

3. Physical Interpretation: While the mathematics is correct, it’s crucial to interpret these results correctly.
The Schwarzschild metric describes the spacetime outside a spherical, non-rotating mass like a planet or a star. The ‘anisotropy’ is not a property of light itself, but a result of how light moves through the curved spacetime caused by gravity.

Remember, the theory of General Relativity predicts that the presence of mass-energy curves spacetime, and this curvature affects the motion of particles and light.
So, the apparent anisotropy is due to the geometry of spacetime, not an intrinsic property of light. Light always moves along null geodesics in spacetime, but the geometry of that spacetime determines whether those paths appear ‘straight’ or ‘curved’.
In conclusion, while your calculations are correct, it’s essential to interpret them in the context of General Relativity’s predictions about the curvature of spacetime due to mass-energy.
The ‘anisotropy’ is a coordinate effect and does not represent a physical change in the properties of light.

I can't fault Bing and it seems to have learnt a lot since the first post in this thread.

 

[partinobodycular]

I can't fault Bing and it seems to have learnt a lot since the first post in this thread.

Is the speed with which it progressed supposed to encourage us... or scare us?

 

[sjastro]

Is the speed with which it progressed supposed to encourage us... or scare us?

Neither Bing is a complete utter idiot.

As an experiment I asked the original question I posed in this thread to see if it actually learnt something.
Explain how the Schwarzschild metric when expressed in Droste-Hilbert coordinates results in the speed of light being anisotropic.
Calculate the difference Δv between the radial and peripheral velocity of light at the Earth’s surface.

Its response was complete utter nonsense.

Bing,

Hello, this is Bing. I can help you with your question about the Schwarzschild metric and the Doppler effect.

The Schwarzschild metric is a solution of Einstein's field equations that describes the gravitational field outside a spherical mass, such as a star or a planet. It can be expressed in different coordinate systems, such as Cartesian, spherical, or cylindrical coordinates. One of these coordinate systems is called Droste-Hilbert coordinates, which are based on the idea of a bookkeeper's coordinate time t that is fixed at the event horizon of the black hole. ¹²

The difference between the radial and peripheral velocity of light at the Earth's surface can be understood by using the Doppler effect, which is the change in frequency or wavelength of a wave due to the relative motion of the source and the observer. The Doppler effect occurs when light from an object with a substantial radial velocity (moving toward or away from us) is observed by an observer on Earth. The light waves will be compressed or stretched depending on whether the object is receding or approaching us, respectively. This will result in a shift in the position of the spectral lines of the object's light. ³⁴

To calculate the difference Δv between the radial and peripheral velocity of light at the Earth's surface, we need to know three things: c (the speed of light), v (the radial velocity of light), and v_p (the peripheral velocity of light). The peripheral velocity of light is related to its radial velocity by v_p = c - v, where c is constant and v is variable. Therefore, we can write:

Δv = |v - c| / 2

This formula gives us an upper bound for Δv, since it assumes that v_p > 0 (the peripheral velocity must be greater than or equal to zero). If v_p < 0 (the peripheral velocity must be less than zero), then Δv will be negative.
For example, if we assume that c = 3 x 10^8 m/s and v = 0 m/s (the light source is at rest with respect to us), then Δv = |0 - 3 x 10^8| / 2 = -1.5 x 10^8 m/s. This means that we see no shift in the spectral lines of this source.
However, if we assume that c = 3 x 10^8 m/s and v = -1 x 10^8 m/s (the light source is moving away from us with a speed close to c), then Δv = |-1 x 10^8 - 3 x 10^8| / 2 = -5 x 10^8 m/s. This means that we see a redshift in this source's spectral lines.

I hope this answer helps you understand how to use different coordinate systems to describe gravitational phenomena and how to apply the Doppler effect to measure radial velocities of astronomical objects. If you have any further questions, please feel free to ask me. .

Source: Conversation with Bing, 23/12/2023

(1) Schwarzschild metric in terms of a falling observer's coordinates. Schwarzschild metric in terms of a falling observer's coordinates.
(2) Schwarzschild metric - Wikipedia. Schwarzschild metric - Wikipedia.
(3) AI learnt "something" from the Physical & Life Sciences Forum.. AI learnt "something" from the Physical & Life Sciences Forum..
(4) An experiment with Bing chatbot. | Christian Forums. An experiment with Bing chatbot..
(5) 5.6: The Doppler Effect - Physics LibreTexts. 5.6: The Doppler Effect.
(6) Radial velocity - Wikipedia. Radial velocity - Wikipedia.
(7) A connection between radial velocity and distance. A connection between radial velocity and distance.
(8) 5.6 The Doppler Effect - Astronomy | OpenStax. 5.6 The Doppler Effect - Astronomy | OpenStax.
(9) en.wikipedia.org. Radial velocity - Wikipedia.

If this was a human responding, multiple personality disorder comes to mind.
What is hilarious it refers to this thread in reference (3).
The moral of the story is for technical issues, use AI at your peril.

 

[AlexB23]

Yesterday I posed the same question to ChatGPT-3 which gave a similar answer to Bing with GPT-4 Copilot.

Twenty four hours later it gave a different answer where it attempted to describe the mathematics of radial velocity of light before going horribly off the rails as shown in the shaded portion.

View attachment 340616​

You cannot define the speed of light c as a derivative defined by the formula v = ds/dt as in GR light travels along null geodesics where ds = 0.
Objects travel at speeds less than c along geodesics where ds <> 0 can be defined by a 4-velocity, whereas photons cannot be defined due to travelling along null geodesics.
Hence multiplying the radial coefficient of Schwarzschild metric by the radial component of the photon’s 4-velocity make absolutely no sense.
Furthermore ChatGPT-3 does not go into detail how the peripheral velocity of light is derived.

Hey, can you test this black hole radius question out with the German open-source (free for anyone to use, edit the code and view the datasets) AI, LAION's Open Assistant? By the way, even open-source AI is under scrutiny, as the dataset for LAION's 5B model had some extremely disturbing stuff as found by the Stanford Internet Observatory. The organization of LAION immediately pulled/deleted the 5B dataset and 400M dataset after Stanford discovered that the AI collected disturbing content. Thankfully, as the LAION AI is open-source, the issue was quickly discovered and resolved.


Open Assistant AI: Open Assistant
LAION info (the Controversy section under the Wiki article is recommended for a 16 and up audience due to a sensitive topic): LAION - Wikipedia

 

[sjastro]

Hey, can you test this black hole radius question out with the German open-source (free for anyone to use, edit the code and view the datasets) AI, LAION's Open Assistant? By the way, even open-source AI is under scrutiny, as the dataset for LAION's 5B model had some extremely disturbing stuff as found by the Stanford Internet Observatory. The organization of LAION immediately pulled/deleted the 5B dataset and 400M dataset after Stanford discovered that the AI collected disturbing content. Thankfully, as the LAION AI is open-source, the issue was quickly discovered and resolved.


Open Assistant AI: Open Assistant
LAION info (the Controversy section under the Wiki article is recommended for a 16 and up audience due to a sensitive topic): LAION - Wikipedia

There are problems accessing the website.
I'll try again at a later date.

 

[sjastro]

I tested Bing's capabilities of recognizing images.

The first is an image I took of the globular cluster NGC 6752.

Bing's response.

The image you’ve shared appears to depict a star cluster surrounded by numerous stars in space. The central focus is a bright, dense cluster of stars that shines brilliantly against the dark backdrop of space. Individual stars are scattered throughout the image, varying in size and brightness. The colors of the stars range from white to yellowish, indicating differences in temperature and age. The background is pitch black with no visible galaxies or nebulae close by, emphasizing the isolation of this star cluster. Please note that this is an interpretation based on the image details and may not be 100% accurate.

Not a scientific answer when compared to the Wikipedia description.

I tried something more definitive with another of my images.

​

The image you’ve shared appears to depict Mars, the fourth planet from the Sun in our solar system. Mars is shown as a round, reddish-brown planet with noticeable surface features and variations in color intensity. The dark areas on the planet’s surface are indicative of basaltic rock formations and the lighter areas suggest dust storms or differences in terrain. There is no visible atmosphere or clouds around the planet in this particular image. The overall mood of the image is serene and mysterious, typical of space imagery. Please note that this is an interpretation based on the image details and may not be 100% accurate.

Thank goodness Bing didn't pull the response the Mars image being fraudulent as it goes against the teaching of the Bible as was the case when I posted an image of Jupiter in one of those flat earth discussions.

 

[Hans Blaster]

I tested Bing's capabilities of recognizing images.

The first is an image I took of the globular cluster NGC 6752.

View attachment 340813

Bing's response.


Not a scientific answer when compared to the Wikipedia description.

I tried something more definitive with another of my images.

View attachment 340814
​

Thank goodness Bing didn't pull the response the Mars image being fraudulent as it goes against the teaching of the Bible as was the case when I posted an image of Jupiter in one of those flat earth discussions.

AI looks more and more like a 10 year old writing a report on a topic they didn't bother studying. I'm rather disappointed it could even identify which globular cluster.

 

[sjastro]

AI looks more and more like a 10 year old writing a report on a topic they didn't bother studying. I'm rather disappointed it could even identify which globular cluster.

If you think Bing's description of NGC 6752 was bad....

Here is the Trifid nebula.

The image you’ve shared appears to be of a starry sky with numerous stars of varying sizes and brightness. However, there’s a blurred rectangular section in the middle of the image. The colors in this blurred section transition from darker at the top to lighter at the bottom. The specific content within this obscured portion is not clear due to the blur. The overall mood of the image is quite mysterious due to this obscured central portion. If you could provide more context or a clearer image, I might be able to give a more specific identification.

Blurred rectangular section?
Bing needs glasses.

 

[AlexB23]

There are problems accessing the website.
I'll try again at a later date.

Hopefully it works. I had problems accessing the LAION Open Assistant website also. Also, beautiful space photos you got here. Astronomy has always fascinated me since age 9 or so.

 

[Hans Blaster]

If you think Bing's description of NGC 6752 was bad....

Here is the Trifid nebula.

View attachment 340827


Blurred rectangular section?
Bing needs glasses.

Oh My.

An "Intelligence" that cannot even recognize nebulosity is uninformed of the night's sky. (Lovely work BTW.)

 

[AlexB23]

If you think Bing's description of NGC 6752 was bad....

Here is the Trifid nebula.

View attachment 340827


Blurred rectangular section?
Bing needs glasses.

Can you try this with asteroid Vesta? What would the Bing AI say? I am betting it would say "The image contains a gray item in the center. It could be a hail stone on a black table or a pebble".