@Kristian Berry Your question touches two important issues. They deal with the relation between philosophy and science in explaining fundamental questions of our worldview. Nevertheless, for me your text mixes up two issues which better stay in separation:

1. What does Kant want to show with the second antinomy?
2. Which models are discussed in contemporary physics for the conception of space?

Ad 1) As @PhilipKlöcking has shown there are some snares in Kant’s formulation. They prevent a quick understanding of what Kant means and against which positions he argues.

For a better understanding of Kant’s text one needs an accurate comment. It has to show which concepts of his forerunners Leibniz and Wolf Kant references on the philosophical side of the antinomy. And which Newtonian concepts Kant references on the side of science.

Ad 2) The concept of a scalar field is totally secondary for the concept of space: You name as example a temperature field, you could also name the field of atmospheric pressure on earth. The simple characteristic of a scalar field is that the physical quantity in question depends on 1 (one) parameter, but not on 2 or 3 or …

Special Relativity conceptualizes space as one part of the 4-dimensional spacetime. And General Relativity treats the latter as the gravitational field.

A different view on spacetime has been favoured by Wheeler’s geometrodynamics. The latter has been further developed by Rovelli’s formulation of loop quantum gravity. In loop quantum gravity space is quantized on the Planck scale and treated by methods of quantum theory.

Concerning matter: An ongoing splitting of matter to find smaller and smaller units of matter is impossible: The decomposition of elementary particles needs high energies. These energies generate new particles which are not smaller than the original ones.

@Kristian Berry Your question touches two important issues. They deal with the relation between philosophy and science in explaining fundamental questions of our worldview. Nevertheless, for me your text mixes up two issues which better stay in separation:

1. What does Kant want to show with the second antinomy?
2. Which models are discussed in contemporary physics for the conception of space?

Ad 1) As @PhilipKlöcking has shown there are some snares in Kant’s formulation. They prevent a quick understanding of what Kant means and against which positions he argues.

For a better understanding of Kant’s text one needs an accurate comment. It has to show which concepts of his forerunners Leibniz and Wolff Kant references on the philosophical side of the antinomy. And which Newtonian concepts Kant references on the side of science.

Ad 2) The concept of a scalar field is totally secondary for the concept of space: You name as example a temperature field, you could also name the field of atmospheric pressure on earth. The simple characteristic of a scalar field is that the physical quantity in question depends on 1 (one) parameter, but not on 2 or 3 or …

Special Relativity conceptualizes space as one part of the 4-dimensional spacetime. And General Relativity treats the latter as the gravitational field.

A different view on spacetime has been favoured by Wheeler’s geometrodynamics. The latter has been further developed by Rovelli’s formulation of loop quantum gravity. In loop quantum gravity space is quantized on the Planck scale and treated by methods of quantum theory.

Concerning matter: An ongoing splitting of matter to find smaller and smaller units of matter is impossible: The decomposition of elementary particles needs high energies. These energies generate new particles which are not smaller than the original ones.

@Kristian Berry Your question touches two important issues. They deal with the relation between philosophy and science in explaining fundamental question of our worldview. Nevertheless, for me your text mixes up two issues which better stay in separation:

1. What does Kant want to show with the second antinomy?
2. Which models are discussed in contemporary physics for the conception of space?

Ad 1) As @PhilipKlöcking has shown there are some snares in Kant’s formulation. They prevent a quick understanding of what Kant means and against which positions he argues.

For a better understanding of Kant’s text one needs an accurate comment. It has to show which concepts of his forerunners Leibniz and Wolf Kant references on the philosophical side of the antinomy. And which Newtonian concepts Kant references on the side of science.

Ad 2) The concept of a scalar field is totally secondary for the concept of space: You name as example a temperature field, you could also name the field of atmospheric pressure on earth. The simple characteristic of a scalar field is that the physical quantity in question depends on 1 (one) parameter, but not on 2 or 3 or …

Special Relativity conceptualizes space as one part of the 4-dimensional spacetime. And General Relativity treats the latter as the gravitational field.

A different view on spacetime has been favoured by Wheeler’s geometrodynnamics. The latter has been further developed by Rovelli’s formulation of loop quantum gravity. In loop quantum gravity space is quantized on the Planck scale and treated by methods of quantum theory.

In any case, an ongoing splitting of matter to find smaller and smaller units of matter is impossible: The decomposition of elementary particles needs high energies. These energies generate new particles which are not smaller than the original ones.

@Kristian Berry Your question touches two important issues. They deal with the relation between philosophy and science in explaining fundamental questions of our worldview. Nevertheless, for me your text mixes up two issues which better stay in separation:

1. What does Kant want to show with the second antinomy?
2. Which models are discussed in contemporary physics for the conception of space?

Ad 1) As @PhilipKlöcking has shown there are some snares in Kant’s formulation. They prevent a quick understanding of what Kant means and against which positions he argues.

For a better understanding of Kant’s text one needs an accurate comment. It has to show which concepts of his forerunners Leibniz and Wolf Kant references on the philosophical side of the antinomy. And which Newtonian concepts Kant references on the side of science.

Ad 2) The concept of a scalar field is totally secondary for the concept of space: You name as example a temperature field, you could also name the field of atmospheric pressure on earth. The simple characteristic of a scalar field is that the physical quantity in question depends on 1 (one) parameter, but not on 2 or 3 or …

Special Relativity conceptualizes space as one part of the 4-dimensional spacetime. And General Relativity treats the latter as the gravitational field.

A different view on spacetime has been favoured by Wheeler’s geometrodynamics. The latter has been further developed by Rovelli’s formulation of loop quantum gravity. In loop quantum gravity space is quantized on the Planck scale and treated by methods of quantum theory.

Concerning matter: An ongoing splitting of matter to find smaller and smaller units of matter is impossible: The decomposition of elementary particles needs high energies. These energies generate new particles which are not smaller than the original ones.