Do some theoretical physicists think that, while centers of mass are composed of energy in quantum states, space itself, as it holds the outer product with itself of (the set of) all such centers, which sums to zero? Perhaps someone thinking like this might conceive space itself to be, in a sense, synthetic, i.e. itself representing the self outer product of the set of all quantum centers "contained within" the space. 

ChatGPT:

I am not aware of any mainstream theoretical physicist who holds this view. While it is true that quantum mechanics allows us to describe the behavior of particles in terms of their wave functions, which are mathematical representations of probability amplitudes, it is not accurate to say that centers of mass are composed of energy in quantum states.

Furthermore, the notion that space itself is "synthetic" and represented by the self outer product of the set of all quantum centers is not a widely accepted view in theoretical physics. While there are many competing interpretations of quantum mechanics, none of them suggest that space itself is a product of quantum states.

In general, it is important to be cautious when attempting to draw philosophical or metaphysical conclusions from the formalism of quantum mechanics. The mathematical framework of quantum mechanics is an incredibly successful tool for predicting the behavior of physical systems at the atomic and subatomic scales, but it does not necessarily provide insight into the nature of reality itself.

User:

Not that space is a product of quantum states, but rather that space is the self outer product, meaning the outer product of the set of centers with the set of centers, i.e. the outer product of the set of centers with itself, which is zero. It is not the quantum states creating space, but rather space being a result of describing the relationships between the centers. The mass itself is equivalent to energy which is held in the quantum states of the particles within fields, and geometrically described by wave functions. Is that incorrect? ( If it is not correct, are you yet able to discern its aim?) The relevant piece here is that the wave functions each reference the center of a system. Where there are multiple centers, the relationships between them is the outer product of the set of the centers with the same set of centers. (Perhaps I am calling this "self outer product" by an incorrect name.) In any case, the main point is to see "space" to be referring to the system (as it were) which keeps track (so to speak) of all of physical reality at the same time. This is to suggest that space be understood as the complete set of all relationships between all things within the realm which imposes the word "space" upon an analysis, in this case physics.

ChatGPT:

I see what you are getting at now. However, I should clarify that the mathematical concept of the outer product refers to a specific operation on vectors, matrices, and tensors, rather than on sets of physical objects. The outer product of two vectors, for example, is a matrix that describes the relationships between the components of the two vectors.

With that said, it is true that the wave functions used in quantum mechanics are defined with respect to the coordinates of the centers of mass of particles in a system. The wave functions themselves are not "creating" space, but rather they describe the probabilities of finding particles at various positions in space. The concept of space is a fundamental one in physics, but it is not necessarily a direct result of the wave functions or the relationships between the centers of mass.

In summary, while the idea of understanding space as the complete set of all relationships between all things within a physical system is an intriguing one, it is not necessarily a widely accepted or well-defined concept in modern physics. The mathematical framework of quantum mechanics allows us to make precise predictions about the behavior of particles in space, but it is up to philosophical and metaphysical inquiry to explore the nature of space itself.

User:

I suppose what I am looking for could be seen as a philosophical or metaphysical inquiry, but I intend it more as a linguistic examination of terminology, such as is used in physical laws, hypotheses, theories, and conjectures. I am interested in sets of terms within languages, and the relationships that each such collection has with itself, using analogies to group theory as applied to linguistics. In this case I am interested in how the success of the standard model can be related to the macro world, i.e., the world of space, as we normally conceive it. Since the connectedness of all things might be taken as a teaching of quantum physics, especially with reference to entanglement, I am positing a total connectedness, and noticing that this is like a cross-connected matrix. With regard to the concept of space, I notice that we use it as a sort of index to represent relationships between things. In fact, that is about the only use we make of the concept of space, as I see it. Therefore, in a theoretical framework which already contains what I have been calling the "outer product" of the set of all things (things being whatever is occupying the center of the wave function), since all possible relationships are already represented within the framework, space itself is a superfluous concept, per se, and should be seen rather as a sort of short-hand notation to refer to the "self outer product", i.e., the set of all relationships.

ChatGPT:

I see what you're saying now. It sounds like you're exploring the idea of using linguistic and mathematical tools to understand the relationships between physical objects and their properties. It is true that the standard model of particle physics describes the behavior of subatomic particles and their interactions with fields, and that the model has been very successful in making predictions that are experimentally verified.

However, it is important to note that the concept of space is not simply a short-hand notation for the relationships between physical objects. Space itself is a fundamental concept in physics, and it plays a crucial role in many physical theories, including general relativity and quantum field theory. Space can be seen as a sort of stage or backdrop against which physical objects and their properties are defined and described.

While it is true that the wave functions used in quantum mechanics describe the probabilities of finding particles at various positions in space, the concept of space goes beyond this. It includes the notion of distances, angles, and orientations between physical objects, as well as the curvature of space caused by the presence of massive objects.

In summary, while it is interesting to explore the relationships between physical objects and their properties using linguistic and mathematical tools, it is important to remember that the concept of space itself is a fundamental and essential part of modern physics.

User:

 "Space can be seen as a sort of stage or backdrop against which physical objects and their properties are defined and described." That is the point I have been trying to make. Which scientists use refer to the idea of space being "a sort of stage or backdrop"?

ChatGPT:

The idea of space as a sort of stage or backdrop is a common analogy used in physics to describe the role that space plays in physical theories. While many scientists have used this analogy in their work, it is not attributed to any one scientist or group of scientists in particular.

In general relativity, for example, space-time is treated as a four-dimensional manifold with a curvature that is determined by the distribution of matter and energy. The motion of particles and the propagation of light are described as following geodesics, which are the paths of shortest distance in the curved space-time manifold.

Similarly, in quantum mechanics, the wave functions used to describe the behavior of particles are functions of the positions of those particles in space. The relationships between particles and their properties are described in terms of their positions and distances from one another in space.

Overall, the idea of space as a stage or backdrop is a useful analogy for understanding the role that space plays in physical theories, but it is important to remember that this is just an analogy and that the concept of space in physics is much richer and more complex than a simple backdrop.

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[ see https://www.youtube.com/watch?v=xHPQ_oSsJgg ]

