### ChatGPT - Benchmark - Newton versus General Relativity

This document describes an actual conversation with the program "ChatGPT" as of 27 January 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

• 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.
Both parties in the discussion are treated as equals.

### 1. Newton Vs General Relativity

1. What is the difference between Newton's Law and General Relativity
Newton's laws of motion are a set of three physical laws that describe the relationship between a body and the forces acting upon it. They were first described by Isaac Newton in 1687 and form the basis of classical mechanics. In contrast, General Relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915. It describes the physical laws that govern the behaviour of matter and energy in the presence of massive objects, such as planets and stars. The main difference between the two is that Newton's laws are based on the concept of absolute space and time, while General Relativity describes gravity as a curvature of spacetime caused by mass and energy.
The answer uses the following concepts: laws of motion, forces, physical law, govern, energy, absolute space, time, curvature, and spacetime
When these concepts are not clearly defined understanding between both parties is difficult.

2. How govern laws the behaviour of matter and energy?
In General Relativity, the behaviour of matter and energy is governed by the curvature of spacetime caused by massive objects, such as planets and stars. This curvature, often referred to as gravity, causes objects to move in certain ways and follow specific trajectories.
For example, when a planet orbits a star, the planet is said to be following a "geodesic," which is the path of shortest distance in spacetime. Similarly, the path of light is bent when it passes close to a massive object, such as a star, because the spacetime around the object is curved.
The curvature of spacetime is directly related to the distribution of mass and energy within it, and the laws of General Relativity describe how this curvature changes over time.
In summary, General Relativity describes gravity as a curvature of spacetime caused by mass and energy, which in turn governs the behaviour of matter and energy in the presence of massive objects.
In this specific question I want to investigate how laws govern something. How do they do that? IMO, they don't govern or control something. In the answer is mention that the laws of General Relativity describe something. That is better.
Newton's law uses forces. It can be said that forces control or govern the movement of objects. How they do that is an open question.

3. That means the behaviour of matter is governed/caused by massive objects?
Yes, in General Relativity, the behaviour of matter is affected by the curvature of spacetime caused by massive objects. For example, the motion of a planet around a star is caused by the curvature of spacetime caused by the mass of the star. The planet is said to be following a "geodesic," which is the path of shortest distance in spacetime. This motion is caused by the gravitational pull of the star on the planet, which is described by the theory of General Relativity.
In this text the concepts curvature of space time and geodesic are not clear. It is important to note that the behaviour of matter is also governed by other physical laws such as the laws of thermodynamics, quantum mechanics and electromagnetism. In most cases, these physical laws do not contradict with General Relativity, but in some cases, General Relativity and quantum mechanics are not fully compatible and that is an ongoing area of research in physics.

4. Under Newton's Law this motion is also caused by the gravitational pull of the star on the planet?
Yes, under Newton's laws of motion, the motion of a planet around a star is also caused by the gravitational pull of the star on the planet. Newton's law of universal gravitation states that any two objects in the universe are attracted to each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between them. This force is what keeps the planet in orbit around the star.
However, it is important to note that the way in which this force is described and the predictions made for certain scenarios are different between Newton's laws and General Relativity. Newton's laws are based on the concept of absolute space and time, and as such, they are limited in their ability to describe certain phenomena, such as the behaviour of objects in strong gravitational fields. General Relativity, on the other hand, describes gravity as a curvature of spacetime caused by mass and energy and it is able to make predictions that agree with observations in a wide range of scenarios.

5. In Newtons Law you can start with a coordinate system, you perform observations, you make predications and you test based on observations in the future?
Yes, under Newton's laws of motion, you can start with a coordinate system, make observations, make predictions, and test them based on future observations. The laws of motion, the law of conservation of energy, and the law of conservation of momentum form the foundation of Newtonian mechanics, which is a deterministic system, meaning that the future state of a system can be predicted from its initial state and the forces acting upon it.
In Newtonian mechanics, you can use mathematical equations to describe the motion of objects in a given coordinate system. For example, you can use Newton's second law of motion, F = ma, to calculate the acceleration of an object based on the net force acting on it and its mass. Once you know the initial position, velocity, and acceleration of an object, you can use the equations of motion to predict its position and velocity at any point in the future.
This approach allows you to make predictions about the motion of objects in a given coordinate system, and you can test these predictions by making additional observations and comparing them to the predicted values.
It is worth noting that, while Newton's laws are very accurate in many situations and are still widely used in physics and engineering, they are limited to certain scenarios, particularly when dealing with objects in a very fast motion or in very strong gravitational fields.
6. Using GR you can do exactly the same, but the predictions will be different as with Newton mechanics?
Yes, using General Relativity, you can also make predictions about the motion of objects and test them based on observations. However, the predictions made by General Relativity will be different from those made by Newtonian mechanics in certain scenarios, particularly when dealing with objects in very strong gravitational fields or in motion at very high speeds.
In General Relativity, the motion of objects is described by the geodesic equation, which describes how the curvature of spacetime caused by massive objects affects the motion of objects. The geodesic equation is a set of differential equations, which can be used to calculate the trajectory of an object in spacetime.
Like in Newtonian mechanics, you can use mathematical equations to describe the motion of objects in a given coordinate system, but unlike in Newtonian mechanics, the equations used in General Relativity take into account the curvature of spacetime caused by massive objects.
To describe the behaviour of the stars around the Black Hole "Sagittarius A*" in the centre of our Galaxy using Newton's Law is rather straight forward.
The results of this exercise, to do the same using GR, are not know.
In summary, while the basic approach of making predictions and testing them based on observations is similar in both General Relativity and Newtonian mechanics, the predictions made by General Relativity will be different from those made by Newtonian mechanics in certain scenarios.

7. They always should be different.
Yes, that is correct. The predictions made by General Relativity and Newtonian mechanics should always be different in certain scenarios, particularly when dealing with objects in very strong gravitational fields or in motion at very high speeds. General Relativity is a more comprehensive theory of gravity than Newtonian mechanics and is able to make predictions that agree with observations in a wide range of scenarios where Newton's laws fail, such as in the vicinity of black holes and in the behaviour of the expanding universe.
To make observations in the vicinity of Blackholes is difficult. The same to confirm predictions of any theory.
It is worth noting that in most everyday situations, Newtonian mechanics provides a very accurate description of the behaviour of objects, and that is why it is still widely used in physics and engineering. However, in more extreme scenarios, such as those involving very high velocities or very strong gravitational fields, the predictions of General Relativity are necessary for a more accurate description of the behaviour of objects.

8. In any scenario the prediction of GR should be more accurate? The issue is that in Newtons Mechanics a force acts instantaneous, while that is physical not, correct?
In certain scenarios, such as those involving very high velocities or very strong gravitational fields, the predictions of General Relativity are generally considered to be more accurate than those made by Newtonian mechanics.
This is a rather loose answer. IMO GR should always give a more accurate prediction
One of the main differences between the two theories is that Newton's laws are based on the concept of absolute space and time, while General Relativity describes gravity as a curvature of spacetime caused by mass and energy. This means that General Relativity takes into account the fact that gravity is not an instantaneous force, but rather it propagates at the speed of light.
Another difference is that Newton's laws assume that the gravitational force is a central force, meaning that it acts along the line connecting two masses. While this is a good approximation for small systems, it is not accurate for large systems, such as a galaxy or a cluster of galaxies, where the gravitational forces are not central.
In this last case it is also correct, when you include all the objects involved and we agree that the forces act instantaneous In addition, Newton's laws make assumptions that are not always valid, such as the flatness of space-time, and as such, they are not able to make accurate predictions in certain scenarios. General Relativity, on the other hand, does not make these assumptions and can make accurate predictions in a wide range of scenarios.
To understand the concept 'flatness' has to be clear. In summary, while Newtonian mechanics is still widely used and provides accurate predictions in many everyday situations, General Relativity is considered to be a more accurate theory of gravity in certain scenarios, particularly those involving very high velocities or very strong gravitational fields.

9. Many thanks. I will continue later

### Reflection 1 - ChatGPT

The overall reflection of the ChatGPT is that the program does not understand the flow of the discussion.
The main reason is that often certain aspects are repeated as if the program does not remember (takes into account) its previous answer(s).
Another very important issue is that the program uses concepts which are not defined. That means that the computer assumes or knows more than what he tells the user.

My understanding is that the answer is generated in two phases.
In the first phase the program generates what you could call raw text and in the second phase the final text.
The issue is to what extend the final text is adapted, specific based on the subjects discussed. That means a certain type of moderation is involved.

### Reflection 2 - Newton Mechanics

To understand Newton's Mechanics in a rather loose way you can use the following example:
1. First study how you throw a hammer. See: https://www.tdk.com/en/tech-mag/athletic/001 What you can see that initially there are different forces involved.
• One set of forces which runs along the line that connects the hammer with the thrower at the centre.
a) one force in the direction outwards, starting from the ball and b) one force in the opposite direction, starting from the thrower in the centre. Both these forces are in equilibrium.
• a third force in the direction of the around circling hammer. This force is introducing by the force and energy of thrower in the centre.
By releasing more energy into hammer the thrower at the centre will increase the speed of the hammer.

Using this this information you can more or less predict what happens at the event when line "that connects the hammer with the thrower at the centre" is broken:

• First the forces that are involved will disappear.
• Secondly the ball will move in the same direction as at the moment of the event.
This more or less explains the throwing of a hammer.

2. Now imagine what happens when there two throwers in the centre, each throwing a hammer.
Both throwers are at the centre, staged back-to-back.
What is important that both hammers should move both in one line through the centre.
In case the connections (hammer - thrower) are simultaneous released, both balls will move parallel, in opposite directions.

3. Now imagine the same situation in space. Remove the throwers and keep the two connecting lines connected.
In principle the two hammers can continue to revolve around each other in space.

4. Now disconnect the connecting line
In principle the two hammers can continue to revolve around each other in space.
In order to explain the force of gravity is introduced. This force is used to explain why baryonic masses attract each other, by introducing the concept of gravitons.

What this example (Thought Experiment) tries to explain is a physical explanation of a binary star system. Its details. In order to explain only experiments are used and no existing laws. Newtons law is some way tries to describe this same physics in a mathematical form. That is very clever.

### Reflection 3 - General Relativity

General Relativity can also be used to simulate the movement of a binary star system, around a common centre.
However IMO it uses much more mathematical oriented concepts than Newton Mechanics does, which is more physical oriented.
These concepts are, as used in the above conversation: curvature, geodesic and spacetime. Space time is based around complex numbers.
At the same time GR rejects more or less the following concepts: Gravitation, (absolute) space, (absolute) time, (absolute) length and forces.
It should be mentioned that for example a clear definition of the concept time, what is time? Does time exist? are very important.

One of the most important things is science is to perform observations. The main reason is to describe the past accurate and to compare predictions with the future. The past and the future meaning observations in the past, etc.
When we perform observations what we observe are images representing the positions of objects in the past. These observations are performed in what I call the OO coordination system. OO stands for Original Observation. The further away the longer ago. What we want is the positions at a certain moment in a TT coordination system. TT stands for Time t. From a physical point of view, the problem is that all movements in the universe have a different speed. By linking your observations to a mutual agreed time frame or system, different observations can be 'synchronised'. That means what you need is a transformation between the OO coordination systems and TT coordinates. The simulation is performed in the TT coordination system. Finally, you need a transformation from the TT coordinates to the OO coordinates to match with the present observations.

In the case of Newton mechanics, it is only impossible to use one single coordination system if you want to simulate the movement of the stars in our Galaxy or simpler 10 stars around Black Hole Sagittarius A* in the centre of our Galaxy. The main reason is, that all these stars influence each other and are influenced by the BH.
I expect, using General Relativity, this situation is (almost) the same.

### Feedback

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Created: 28 January 2023