### ChatGPT - Benchmark - Newton versus General Relativity Part 2

This document describes an actual conversation with the program "ChatGPT" as of 2 February 2023.
To use ChatGPT select: https://openai.com/blog/chatgpt/

### Reflection

In case, if part of is document is used by ChatGPT, the url of this document has to be mentioned.

### Introduction

The discussion consists of a series of Questions, Answers and Comments.
• A question is normally a follow up based on the previous question. The purpose is to get an explanation or more detailed about the previous Answer.
• An answer is the reply by the computer.
• A comment are thoughts about the answer. All comments are in red.
Both parties in the discussion are treated as equals.

### 2. Newton vs General Relativity Part 2

1. What is the difference between Newton's Law and General Relativity
Newton's law and General Relativity are two different physical theories that describe the behaviour of objects in the universe.
Newton's law, also known as Newton's law of gravitation, states that every point mass attracts every other point mass by a force pointing along the line intersecting both points. This law is expressed mathematically as
 F = G * (m1 * m2) / r^2
, where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the objects, and r is the distance between them. Newton's law provides an accurate description of gravity in most everyday situations, such as the motion of the planets and the fall of an object under Earth's gravity.
General Relativity, on the other hand, is a theory of gravitation that describes gravity as a curvature of spacetime caused by the presence of massive objects.
According to General Relativity, massive objects cause spacetime to curve, and objects move in this curved spacetime according to the shortest possible path, which we perceive as gravity. This theory predicts many of the same results as Newton's law in weak gravitational fields, but provides a more accurate description of gravity in strong gravitational fields, such as those near black holes.
In summary, Newton's law is a simple mathematical description of gravity, while General Relativity is a more complex and sophisticated theory that explains gravity in terms of the curvature of spacetime.
In summary both Newton Mechanics and General Relativity are caused by massive objects.
How ever to mention massive objects is a misnomer. Newton Mechanics is applicable for all sizes of objects. Average sized objects, Small objects like meteors and grain sized particles and large objects like Black Holes.
General Relativity is a much more complex explanation because in addition it requires concepts like curvature and spacetime. What makes this tricky is that spacetime is a mathematical concept.
What you most of all need is a physical explanation of why planets move around the Sun accordingly to Newton's Law and General Relativity. See also Reflection 2 - Newton Mechanics

2. In short Newton mechanics states that point masses attracts each other. However, IMO point masses don't exist.
You are correct. In physics, the concept of a point mass is an idealized abstraction used for mathematical convenience. In reality, all objects have a finite size and internal structure. However, for objects with a small size compared to the distances between them, such as planets and stars, the approximation of a point mass is a good one and yields accurate results.

3. To continue along that same line: How does it physical works that masses attract each other. They cannot see each other.
The force of gravity between two masses is not due to a direct interaction or "sight" between them. Instead, it is a result of the curvature of spacetime caused by the presence of the masses.
The answer does not mention the case of Newton Mechanics.
According to General Relativity, massive objects cause spacetime to curve, and objects moving in this curved spacetime will follow the shortest possible path, which is perceived as a force of gravity. This means that even though two objects may not be in direct contact with each other, their presence can still affect the spacetime around them, causing other objects nearby to follow a curved path and experience a gravitational pull.
In essence, the force of gravity between two masses is a result of their effect on spacetime, rather than a direct interaction between them. The mathematical description of this effect is complex, but it has been confirmed by many experiments and observations, including the orbit of the planets, the motion of stars, and the observation of gravitational lensing.

The question is more complex. The problem is that the movement of the planets has nothing to do with light or the speed of light. As such the concept of the visible universe is not important for their behaviour.
In the case of Newton Mechanics the force of gravity and the speed of gravity are important. The speed of gravity is the reason that the movement of two objects does not point to their present position but towards a position in the past.

4. How does it physical works, using Newton Mechanics that masses attract each other.
This question is tricky. Newton Mechanics has nothing to do why masses attract each other.
In Newtonian mechanics, the force of gravity between two masses is described by Newton's law of gravitation. This law states that every point mass attracts every other point mass by a force that is proportional to the product of their masses and inversely proportional to the square of the distance between them. The mathematical expression for this force is:
 F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between them.
In this description, the force of gravity is a result of an attractive force between the two masses, much like the attractive force between two charged particles in electrostatics. However, unlike electrostatics, the force of gravity is much weaker and acts over much larger distances.
This simple mathematical description has been found to be a good approximation for many everyday situations, such as the motion of the planets and the fall of an object under Earth's gravity. However, for more extreme situations, such as the motion of objects near black holes, General Relativity provides a more accurate description.

5. That means as far as you know, using Newton's law, there exist no physical explanation why masses attract each other.
In Newtonian mechanics, there is no underlying physical explanation for why masses attract each other. Newton's law of gravitation is a empirical law, derived from observations and experiments, that describes the behavior of masses under the influence of gravity. It provides a mathematical formula for the force of gravity between two masses, but does not explain the underlying cause of this force.
However, it should be noted that Newton's law has been extremely successful in explaining a wide range of phenomena related to gravity, and continues to be used in many areas of physics and engineering. The law's predictive power and accuracy in a variety of situations have made it a cornerstone of our understanding of the physical world.
The concept of gravitons can be used to describe these forces.

6 How does it physical works, accordingly to GR, that massive objects cause spacetime to curve?
According to General Relativity, the presence of a massive object causes spacetime to curve. The basic idea is that massive objects create a sort of depression or well in spacetime, and objects moving nearby will "fall" into this well and follow a curved path.
This does not explain the cause of these wells
This curvature of spacetime can be described mathematically using the concept of a metric tensor, which defines the geometry of spacetime. The metric tensor is determined by the distribution of mass and energy in the universe, and can be represented as a set of equations known as the Einstein field equations.
Mathematics has nothing to do with any physical explanation.
Solving these equations for a given distribution of mass and energy allows us to calculate the curvature of spacetime and predict the motion of objects moving in this curved spacetime. This description of gravity has been confirmed by a wide range of experiments and observations, including the orbit of the planets, the motion of stars, and the observation of gravitational lensing.
In case of Newton's Law, this is completely the other way around. First you need observations over a long period of time of a stable configuration to calculate the masses in volved. Secondly you can use Newton's Law to predict the future.
In the case of GR this is the same, except that number of parameters involved is much larger.

It is important to note that General Relativity is a highly abstract and mathematical theory, and the underlying physical mechanisms causing spacetime to curve are not fully understood. However, despite its abstract nature, the theory has been extremely successful in explaining a wide range of phenomena related to gravity and is considered one of the pillars of modern physics.

7. Consider two binary massive objects, revolving around each other. Consider a third object approaching these two. Where are the 3 wells?
According to General Relativity, each massive object creates its own depression or well in spacetime, representing a curvature of spacetime caused by its presence. These wells are not static, but change in shape and size as the objects move and interact with each other.
In the case of two binary massive objects revolving around each other, each object creates its own well in spacetime, and the combination of these wells causes spacetime to be curved in the region between the objects.
When a third object approaches these two binary massive objects, it will experience the combined effect of the wells created by each of the binary objects, and will follow a path determined by the combined curvature of spacetime. This path will be influenced by the masses and positions of the binary objects, as well as the velocity and trajectory of the third object.
In essence, the presence of the three objects creates three wells in spacetime, each representing the curvature of spacetime caused by the presence of one of the objects. The combined effect of these wells determines the path followed by each object.
When you compare this with Newton Mechanics, the last is the simplest because the cause are forces. The problem at every instant is, where is the position of object that causes the force and secondly what is the speed of this force. It should be mentioned that gravity and specific physical the speed of gravity has nothing to do with the speed of light.
In fact light has nothing to do with the behaviour of objects.

### Reflection 2 - Newton Mechanics vs General Relativity

The most important challenge of physics is to understand why there are objects and why for example two objects can circulate around each other.
In case of Newton's Mechanics, to explain this behaviour forces are introduced. Forces are not unique. They are also used to explain electrical and magnetic phenomena.

In the case of General Relativity the concept curvature of spacetime is introduced. Both concepts are mathematical concepts and as far as I understand can not be observed. Newton's mechanics also uses the concept and gravitational fields and specific in case of a binary system these fields propagate, from the center of gravity of both objects, away from the outside of both planets. Inside both planets the force of gravity acts almost instantaneous towards each other. That means Newton mechanics does not use the concept of curvature of space.
It is important that any theory depents in principle on observations in the past and observations in the future. The use of any theory or law is that the observations performed in the past should be used to predict the observations in the future. The theory or law that makes the most accurate predictions is the best.
In the case of Newton mechanics the only observations are the positions of the each object involved as a function of a sequence of time steps, partly in the past and partly in the future. Using Newton mechanics first the masses of the objects are calculated.
Newton mechanics also calculates velocities and accelerations but these parameters are not 'physical important'.
In the case of General Relavity more or less the same strategy should be followed. That means if the objects have a mass than first the masses should be calcualted using GR. My understanding is that concepts like spacetime and curvature are not important. What is important are the predicted positions in the future using GR.

### Reflection 3 - Astronomy - magazine.

In the Astronomy magazine of march 23, in the article 'Astronomical fossils' at page 55 we can read:
Einsteins theory of general relativity states that space and time are interwoven into a single continuum.
Space is an almost empty 3D physical concept, in which physical objects exist and move at different speeds, in time. Time is not a physical concept in the same sense as space and objects. As such time cannot be interwoven with space. In order to measure speeds it is important that all clocks in use should be fixed to the reference frame in use.
The gravitational pull of massive celestial bodies like stars or blackholes corresponds to distortions in this space-time fabric. Black holes cause extreme warping of space-time
No comment
- they are ojects that have so much gravitational pull, not even light can escape. The point of no return is called the event horizon.
The fact that black holes are invisible is not important. What is important that they emit gravitons, i.e. gravitational field, which is interpreted as a pull when received.
There are two main classes of Blackholes. Smaller blackholes that form from the deaths of masive stars or the mergers of stellar remnants are called steller-mass black holes. This type weighs tens of solar masses to 100 solar masses. Supermassive black holes, on the other hand, live in the centers of galaxies and are millions to billion of times heavier than the Sun.
Around the Black hole in the center of the Milky way, called Sagittarius A*, there are also large stars, orbitting around this center. For more detail select this link:
As pairs of black holes orbit one another, they produce ripples that propagate through the space-time fabric at the speed of light. These ripples are called gravitational waves. These waves carry away the systems energy causing the orbit to shrink. as a result the black holes orbit faster and faster increasing the frequency of the gravitational-wave signal.

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Created: 10 February 2023

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