Is space fundamental?

Question

Let's start with a definition of space, like

"Space is a three-dimensional continuum containing positions and directions"

If we delve deeper into such definitions, we come across terms like 'points','vectors',etc. And then if we go further into defining those terms, it kind of comes at a full-stop, like you cannot describe it more, sometimes it can become circular too. So that makes the whole concept of space fundamental, because you just need to start with it?? Are there any hypothetical forms of existence, where the concept of space is not fundamental or doesn't exist.

For instance, this makes me also wonder, if some reality exists with certain laws, where do the laws exist? They are not contained in space, right? That gives them an abstract notion. So similarly, could you have a reality where you don't have space, but rather different abstract concepts. So then space wouldn't be fundamental thing, where it implies that entities and interactions could be understood purely in terms of these abstract concepts, rather than spatially. I would really love if someone has something informative or a resolution for what I'm talking about...

Answer 1

A mathematical space is any ordered arrangement of different properties. As long as you have some properties, you can order them into a space, and there's nothing in principle more fundamental about any particular set of properties or scheme of ordering them.

However, geometrical distance-space is special in that:

• there are a small finite number of dimensions worth of similar properties, which makes 'computing' translations and rotations in the space trivial in places where those dimensions are approximately orthogonal
• the dimensions are approximately orthogonal most places in the universe - that is, you can change x position without significantly changing y, z, and (if you're using 4-space) ct position as they would be measured from the original position. (Or change radial position without changing polar and azimuthal angle, or whatever other coordinate system you prefer to use to represent spatial dimensions.)
• disruptions in this approximate orthogonality (gravity) are themselves spherically symmetrical, which preserves the approximate orthogonality across vast extensions of these dimensions
• information about the positioning of processes in geometric space is easy to get (from electromagnetic interactions, which exhibit symmetry in the way they propagate in any direction in distance-space)
• information about distance-space is especially salient to the survival and reproduction of machines that run on electromagnetic interactions
• because of the above symmetries, ability to obtain and act on information about distance-space remains salient across large displacements in distance-space and time, often even when environment changes.

Answer 2

Firstly, we think space and time are deeply connected, and objects that are at high energies partially rotate through space-time. See the great interactive explanations here: Inside Einstein's head

To unify relativity and quantum pictures, we know there is a conceptual conflict between the quantum picture where time is treated externally from the models, and relativity where time varies depending on observer dynamics. The limits of 'quantising' relativity are shown by canonical quantum gravity. But 'relativising' quantum theories has also been limited to combining special relativity. It is currently impossible to measure gravity at small scales appropriate to quantum behaviour, so where general relativity and quantum scales collide, in blackholes and in the early universe for instance, we don't have a clear account. Loop-quantum gravity, and Twistor theory, are examples of approaches with a more fundamental layer from which spacetime is emergent.

It's important to think about what space does. Noether's theorem shows us that conservation laws are directly equivalent to continuous symmetries under transformation. That is, we link it's shape to the paths objects will take with no forces acting on them, where momentum is conserved.

The other crucial property of space is expressed as the principle of locality: that an object is influenced directly only by its immediate surroundings, and signals are fundamentally limited by spatial seperation. This is another way of talking about the expectation there will be no action-at-a-distance, which has been a very useful guideline in developing and distinguishing physics from non-physics. Entanglement challenges locality, with the Bell Theorem showing if hidden variables lead to entanglement correlations they must be non-local. That has led to the EPR = ER hypothesis, the idea entanglement information travels down Einstein-Rosen bridges, often dubbed wormholes.

As @gs put more eloquently, a space in physics and math is just a way of ordering things. It's common to say causality makes the spacetime ordering the necessarily correct or fundamental one, but from the symmetry-conservation laws point, we can see that in line with Hume's Problem of Induction, what we have is not necessary connections, but Real Patterns. Discussed here: Is the idea of a causal chain physical (or even scientific)?

But, our intuitions that give rise to the symmetries we base our shared use of math on, relate to the necessarily shared experiences of space we have, in order for our chemistry and biology to behave the way they do. Discussed here: The Unreasonable Ineffectiveness of Mathematics in most sciences So space doesn't seem to be fundamental to the universe, but it does seem to be fundamental to how minds work, with 'Flatlanders' or higher-dimensional beings having radically fundamentally different phenomena to those we experience, and our language and learning is rooted in intersubjectivity and common experiences.

Answer 3

No--time creates space and not vice-versa, our phraseology has confused this relationship. Time is more fundamental than space, just as change is a grounds for non-change or permanence.

Take two philosophers: Kant and Whitehead (I include William James and Henri Bergson because Whitehead follows their radical empiricism). Kant writes in the Transcendental Aesthetic of his Critique of Pure Reason: "Time is a necessary representation that underlies all intuitions. As regards appearances in general [spatial relations], we cannot annul time itself, though we can quite readily remove appearances from time. Hence time is a priori. All actuality of appearances is possible only in time. Appearances, one and all, may go away; but time itself (as the universal condition of their possibility) cannot be annulled" (A31/B46).

In Process and Reality Whitehead argues that "presentational immediacy" or spatial relations depend upon and presuppose "causal efficacy" or temporal relations. The actuality of mobility is what makes the possibility of immobility actual, and that's what space is.

Answer 4

When we are born and begin to develop in the world, we possess an intuitive philosophical position called naive realism which is committed to the idea that any product of our senses is real, be they tables, forces, time, or space. From WP:

In philosophy of perception and epistemology, naïve realism (also known as direct realism, perceptual realism, or common sense realism) is the idea that the senses provide us with direct awareness of objects as they really are. When referred to as direct realism, naïve realism is often contrasted with indirect realism.

As we get older and go about our critical thinking, we discover that our senses are not always reliable. We confabulate and fall prey to illusions, or we begin to ask questions like 'what exactly are space and time?' So, we embark in the direction of the metaphysician and begin to explore what is real and what is not, which typically the provenance of ontology. We may also begin to read the works of famous philosophers, such as Aristotle, Leibniz, or Kant to advance our thinking. The question you ask is today often discussed in the philosophy of science, since space and time are of primary interest to physicists and philosophers of physics. Often times, physicists who are conceptually specialized technicians, presume their views, or the views of their research community are solutions to such questions, but while physics may inform philosophy, it does not replace it.

Whether or not space is real will bring you to a debate between scientific realism and instrumentalism. From WP:

Scientific realism is the view that the universe described by science is real regardless of how it may be interpreted... Within philosophy of science, this view is often an answer to the question "how is the success of science to be explained?" The discussion on the success of science in this context centers primarily on the status of unobservable entities apparently talked about by scientific theories. Generally, those who are scientific realists assert that one can make valid claims about unobservables (viz., that they have the same ontological status) as observables, as opposed to instrumentalism.

So, one has to start asking questions about how does one go about knowing whether space is real or what method can one show that space is real or not. This then leads into methodological and epistemological questions. Can you touch space? Can you weigh it? Does space have properties in common with bananas, dogs, and blankets? What does it mean if it doesn't?

While the philosophical canon and the exploration of the nature of space goes back to the Pre-Socratics, the modern mathematical physical definition owes a huge debt to two men in particular, Isaac Newton and Albert Einstein, the former for introducing Newtonian space, and the latter for introducing relativity. Add to the fray the views of Leibniz and Kant, and you have a robust, but highly technical discussion of what space might be both metaphysically and scientifically. The discussion of whether space is real is also complicated by the question of 'is mathematics real?' For instance, if you believe that numbers are real and have some sort of quasi-physical existence, then that colors your views on abstractions derived from them.

Many views exist on space and perception of it, and so I'll just respond to your question by giving a quick outline of nod in the direction of Immanuel Kant, whose position in transcendental idealism is that space and time are constructed by the mind. From the SEP article Kant's Views on Space and Time which quotes Kant directly:

Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally. (Ak 2: 403)

Kant, as per Kant and the Exact Sciences (GB) was involved in trying to merge Netwonian space and Leibnizian monads in his philosophy, and arrived at the conclusion that space and time are constructs of the mind. His most famous work, Critique of Pure Reason has a section entitled Transcendental Aesthetic which addresses his mature views on both space and time, and today, is defended by neo-Kantians who believe that space is not like bananas, dogs, and blankets, but comes to be because the mind constructs it. This sits comfortably with a number of philosophical traditions including nominalism (SEP), mathematical intuitionism (SEP), and embodied cognition (SEP) that center around the fact that there is nothing directly sensible about space. It cannot be touched with fingers, weighed by scales, or seen with the naked eye suggesting it is a byproduct of the mind. This, of course opens up a deep and transformative discussion about the nature of reality itself, often provoking knee-jerk reactions by some who attack the position as being equivalent to declaring that idealism is preposterous.

The point of this answer, however, is not to affirm or disconfirm space is real, but rather, to set you on the journey of finding the right words to continue a conversation that goes back to Ancient Greece. According to a recent PhilPapers survey, three quarters of philosophers consider themselves scientific realists. The question cannot truly be answered and defended until staking out a broad range of philosophical positions on diverse questions. Ultimately, if you come to the conclusion Kant is correct, then space is not fundamental, because it is constructed by the mind.

Answer 5

TL;DR According to science orthodoxy there is no space, only space-time, and space-time only applies to the 'normal', not reality which includes gravitational singularities. So what is fundamental?

OP: "For instance, this makes me also wonder, if some reality exists with certain laws, where do the laws exist? They are not contained in space, right? That gives them an abstract notion. So similarly, could you have a reality where you don't have space, but rather different abstract concepts."

Without the cognition of beings there is no existence and no beings (either living or inanimate). The ground of beings is being, therefore being is fundamental.

“All manifoldness of things is only so many different ways of limiting the concept of the highest reality, which is their common substratum, just as all figures are possible only as different ways of limiting infinite space. Hence the object of reason’s ideal, (…) is also called the original being (ens originarium); because it has nothing above itself it is called the highest being (ens summum), and because everything else, as conditioned, stands under it, it is called the being of all beings (ens entium).” [Kant, Critique of Pure Reason, A578/B606]

This concept is covered at length by Heidegger; here is a gestureal quote from Contributions to Philosophy (Of the Event) p.200

Beyng—the remarkable erroneous belief is that beyng must always "be" and that the more constantly and the longer it is, the "more eminently" it is.

But beyng "is" not at all; instead, it essentially occurs.

Then beyng, because it is the most unique, possesses the utmost rarity, and no one esteems the few moments in which it grounds a site for itself and occurs essentially.

p.203

Beyng is here not a supervenient genus, not an added cause, not something that encompasses beings by standing behind and over them. If that were the case, beyng would be degraded to the level of an addendum, whose accessory character would not be undone by any elevation to "transcendence."

Beyng or, rather, its essential occurrence—out of which and back into which beings as beings first come to be in a concealed and sheltered way (d. The grounding, on truth).