What Happens When Space Bends?
Hi,
Suppose there is some space and a small corner of it moves, now there is no space in that corner which means the space in that corner is non-existent. Correct me if I am wrong.
Suppose there is some space and a small corner of it moves, now there is no space in that corner which means the space in that corner is non-existent. Correct me if I am wrong.
Comments (52)
It just means that part of the space moves to a different part. Suppose part A moves to part B of the space, now part A of that space is in part B of the space.
There isn't any corner either: the corner's moved with the space. Or: the space moving is the corner moving.
(I edited by posted in response to your edit! Now things look strange).
That is what I was thinking, but I am not quite what Einstein was saying when talking about space bending.
If space was curved enough, it would mean that going in a straight line without turning would evenutally lead you back to where you began (just like travelling in a straight line on Earth would). There are probably some cool youtube videos on this, if you search for space-time curving, or the geometry of the universe or something similar. Probably good to visualize it.
I can't wrap my head around your question :rofl:
You should've asked Einstein/Minkowski this question.
They would've laughed or wept.
I don't know which. I hope they would've wept in joy. Now all of us are happy :grin:
Methinks it works like how a 2D space (a flat sheet of paper) bends in 3D space and leaves behind 3D space. So, a nD space bending would leave behind (n+1)D space in the place it bent away from. This makes sense since bending 3D space causes time (4th dimension) to behave differently.
Space doesn't bend, spacetime curves around a mass. This means that a clock located within the proximity of a mass will run slower than a clock located away from the mass. It also means that any matter or energy traveling in the proximity of that mass will be influenced by this curvature and its path will bend. We call that curvature gravity.
Ok, thanks for clearing that up. I must have misunderstood people talking about space curving.
Spacetime isn't an actual observable thing either, it's a mathematical tool, to say spacetime curves is not to say there is something actually curving out there, well those who do say that commit the fallacy of reification. Gravity can also be modeled precisely without invoking a curved 4-dimensional mathematical manifold. For instance the phenomenon of gravitational lensing can be explained by saying that it is the trajectory of light that bends, rather than some undetectable space or spacetime.
So that thing that creates the separation between objects is only a mathematical tool.
Quoting leo
And whatever it is that magically bends the light is more detectable than the curvature of "non existent" spacetime.
Yeah Einstein was an idiot
I was talking about spacetime, the 4-dimensional manifold of general relativity.
Regarding space itself, it doesn't create the separation between objects, you could say that it is the volume between objects. Now when you say that this volume bends or curves, all you're saying is that the relative positions of the objects have changed, there is no need to reify the volume as an actual substance or entity that has bent or curved and that is responsible for the motion of the objects.
Otherwise you might as well say that a rock falls to the ground because the space between the rock and the ground shrinks. See the fallacy?
Quoting staticphoton
Not "bends the light", "bends the trajectory of light". When you launch a ball horizontally its trajectory gets bent right? Same idea. Even in Newton's theory of gravitation it is predicted that light gets deflected by gravity, its prediction is simply less accurate.
Quoting staticphoton
Einstein agreed that spacetime is a tool of thought, not an actual thing, it's people like you who don't understand him.
Where is your explanation for the reason the "trajectory of light" bends? You accuse me of reification and yet you are treating a "trajectory" like it is a thing. It is not.
And the reason Newton predicted light bending is because he believed light to be strictly a particle.
The theory of general relativity offers a wonderful explanation of how matter and energy move around other matter, it is not "the truth", but a well crafted model that works extremely well within its limits.
Quoting leo
The effects of time-space shrinking as you approach a massive object are well demonstrated. Time dilation is real.
May I ask how familiar are you with General Relativity? Are you mathematically trained to understand Einstein's application of differential calculus, tensors, and geodesics to develop the concept of space-time curvature? Because if not then you are just repeating somebody else's interpretation.
Quoting leo
And I'm sure you understand Einstein really well, maybe as not to derail this thread you can start your own thread to school me about the real Einstein.
There's not a "thing" that creates separation between objects. There's just the facts of their extensional relations.
Have you ever heard of matter-antimatter pair production out of the vacuum of space?
Yes. And what we're talking about--or, what's really going on in that talk, rather--is doing things with mathematical equations.
When I say the trajectory bends it's a figure of speech, it's the same as saying that light doesn't travel in straight lines. Whereas you're saying lights travel in straight lines in curved space or spacetime.
Quoting staticphoton
Whatever light is, when it passes by a massive body it doesn't travel in straight lines and its two-way velocity is not constant. You can say that it really travels in straight lines at a constant velocity but it doesn't appear to because it travels through some 4-dimensional medium that is curved in an undetectable way, or you can simply say that it doesn't travel in straight lines at a constant velocity in the presence of massive bodies.
If you see the 4-dimensional medium as a mathematical tool then that's okay. But if you pretend it's a real thing out there that really curves, that's wrong. There is zero evidence of that, any observation can be explained without invoking a curved space. And it's misleading to say that it explains gravity, it's misleading to say that planets move around the Sun because they follow straight lines in curved spacetime.
Quoting staticphoton
Why do planets move around stars and things fall to the ground? We don't know, they just do, and we describe that through mathematical equations under the moniker of gravity. We can describe their trajectories in Euclidean space, or in other geometrical spaces.
Einstein wanted mathematical elegance, he wanted to generalize Newton's first law of motion by including gravity (in other words he wanted things to have a uniform motion in straight lines even in the presence of gravity), in order to do that he had to invoke a 4-dimensional geometrical space that curves.
Einstein's model does not explain any more why planets move around stars and objects fall to the ground. They don't move that way because they follow straight lines in curved spacetime, rather they move the way they do and one way to represent that is to imagine they're following straight lines in a curved spacetime, that's a representation that's not a cause. Another more intuitive way is not to invoke any space curving or bending.
Quoting staticphoton
Clocks run at different rates in different places sure, that's not in any way evidence that they run at different rates because they are embedded in a 4-dimensional manifold that curves.
Quoting staticphoton
Sure, I have also read Einstein's historical papers on special and general relativity, have you? I'm not repeating somebody else's interpretation, you know very well what the popular interpretation is, that's the one you're repeating, but sadly it's wrong. It took me years to grow out of it myself, it's not easy when everyone keeps repeating it, everywhere, in books, textbooks, news articles, ...
Quoting staticphoton
No need for a thread, I'll just leave a few quotes from the man himself:
We have attempted to describe how the concepts space, time and event can be put psychologically into relation with experiences. Considered logically, they are free creations of the human intelligence, tools of thought, which are to serve the purpose of bringing experiences into relation with each other.
The only justification for our concepts and system of concepts is that they serve to represent the complex of our experiences; beyond this they have no legitimacy.
You imagine that I look back on my life’s work with calm satisfaction. But from nearby it looks quite different. There is not a single concept of which I am convinced that it will stand firm, and I feel uncertain whether I am in general on the right track.
And somehow people have come to believe that Einstein has proved that gravity is curved spacetime, that planets really follow straight lines in curved spacetime, that we live within a 4-dimensional spacetime that is really curving and expanding. Einstein knew very well spacetime is a human creation, a tool of tought, that curved spacetime doesn't explain gravity, it's just one complicated but mathematically elegant way to describe it.
As to why I care, I care about understanding, not blindly believing what I'm told.
Anyway I'll leave it at that, if you aren't convinced there isn't much more I could say to convince you, and most people just want to stick to the popular story even if it is incorrect.
I'm an old engineer with a physics minor, and understanding Einstein's theory has been a personal pursuit of mine for the last 30 years. Not by reading historical papers but by painstakingly working through and understanding the mathematics behind it, and building my intuitive thoughts on the matter based on that.
As I said, his theory is no different than any other theory in the fact that it is only a mathematical model used to represent physical phenomena.
You on the other hand seem to be the owner of the truth, thank you for illuminating me and clearing it all out for me.
I am no Einstein expert, and I don't pretend to deeply comprehend his theory, but what you are saying runs contrary to the impression I've gotten. Can you point me to a place where he expressed such thoughts?
For one thing, Einstein's theory is often appreciated for restoring a local picture of gravity, of solving this problem that Newton expressed:
If we understand massive objects to actually distort spacetime where they sit in it, with distortions spreading out from there in the fabric of spacetime, the influence is once again entirely local, with no "spooky action at a distance", which is famously something Einstein didn't believe in. You've probably encountered the old analogy of the rubber sheet or trampoline on which a bowling ball is placed, which is then distorted, with these distortions then causing marbles placed nearby to roll into the bowling ball. Obviously, the analogy is flawed, because you need downward gravitational pull to make the bowling ball form an indentation in the trampoline!
Regardless, the analogy is useful for something else, the way in which it gives us an intuition of how gravity could be communicated entirely locally. How is this? Well, the bowling ball only affects what it is "touching". And the marbles at some distance from it are only affected by what they are touching. The tilt in the surface of the trampoline under the marbles is the reason they start to roll toward the bowling ball. It is not a force of attraction at all. But this influence can only be communicated if the trampoline surface (spacetime) is "something", if it has a fabric, if you will. One part in it pulls down on an adjacent part, which pulls down on the next adjacent part, and so on. It is like a chain, with each link pulling the next. If I pull on a chain you are attached to, this is not spooky action at a distance. It is entirely local. Every causal influence involves contact action.
Also, notice that we recently measured gravitational waves, or ripples in spacetime. Can we make sense of this if space is as @Terrapin Station describes?
Quoting Terrapin Station
What would it mean for there to be a ripple in "the facts of their extensional relations"?
I don't think physicists actually think that any bending of space of n dimensions needs to involve a flat spacetime of n+1 dimensions surrounding it. Think about it like this. Suppose you are writing a computer program in which you define a series of variables that are sort of connected in a chain, where some sort of information can be moved from one to another through a "link". Information is not allowed to skip over links. So, for example, you might define one like the following. A is connected to B and B is connected to C and C is connected to D and D is connected to A. Information cannot move directly from A to C. It must first go through B or through D. You could visualize it as a loop, like this:
But to visualize it this way is a bit misleading, as we are "bending" it in two dimensions. And the way we have defined it, we haven't defined any space at all. We have only defined how the elements are connected, what is linked to what. You could go on to define much more complex networks like this with any imaginable space-like topology. You can imagine easily creating one that is like the surface of a cylinder. Just define something like a grid and then connect all the nodes along one edge to all the nodes along the opposite edge. But notice that space language like "grid" is still misleading, as we wouldn't be drawing a grid or a cylinder. We would just define "adjacencies". A1 is connected to B1 and to A2. B1 is connected to A1 and C1 and also to B2. B2 is connected to B1, B3, A2, and C2. Get the idea? No space. Just connections.
But consider if there were an incredibly large network like this, with a astronomical number of nodes. You could do things like Conway's Game of Life in this network. But you could have any imaginable topology. And the topology could change according to certain dynamical rules. Connections could be formed and broken. Nodes could be created or destroyed. The effective topology could have any number of "dimensions" and any imaginable "curvature".
Imagine that, like Conway's game of life, changes propagate through the network at a max speed of one link per clock cycle. Clearly, you can't skip links. This establishes a speed limit. And interestingly, this speed limit is one link per clock cycle. It seems conspicuously like the speed of light in a way, which is 1 Planck length per Planck time. In other words, it is equivalent to the smallest possible step in the smallest possible duration.
Perhaps the space we live in is like this. What is "closer" is simply what involves fewer links.
There are actually some new ideas in physics that try to marry quantum mechanics and general relativity that treat spacetime as a network. Such an approach is showing some promise. One is loop quantum gravity. Another is EPR=ER. The latter is especially interesting to me. An interesting article on it:
https://www.nature.com/news/the-quantum-source-of-space-time-1.18797
There is also this one I just came across (from: link
By the way, the PacMan gameworld has a cylindrical topology. Go off the right side of the screen and you'll come in on the left. But this space is not bent through 3D space to do that. In fact, even the 2D space you see when playing is only there because it is mapped onto a screen for you to see what's happening. The way the information is being processed doesn't involve any space. It is more like the node network I've been describing.
Regardless of whether our space is discrete and network-like or not, what I am saying here about networks might help make more intuitive how a space could have geometry other than the familiar flat Euclidean while not being "bent" inside some higher space. Rather, it might just have to do with the causal structure of the universe.
What do you make of physicists saying that with Einstein's theory, space acquired its own degrees of freedom?
Here is a quote from Andrei Linde, who, along with Alan Guth, among others, formulated inflation theory:
Speaking of degrees of freedom of space, what about standard big bang theory? Scientists speak of the space itself between galaxies expanding, even accelerating in its expansion. It apparently isn't simply a matter of them having been close together and then moving apart. The analogy often given is of drawing dots on balloon and then blowing it up. This is why galaxies far apart can be "moving" away from one another faster than the speed of light, and thus falling behind the cosmic event horizon. The objects can't move faster than light. But space can expand fast enough to make distances between objects grow at such a rate that light cannot cross it fast enough to bridge the gap. How would you understand any of this without thinking of space as "something" which changes its form?
I see it as reifying mathematics and other instrumental theoretical constructs, and subsequently doing bad philosophy. A lot of it amounts to the equivalent of positing epicycles to account for planetary motion, to avoid having to change paradigms.
As long as we're talking about something observational and not simply something we can do with mathematical constructs, it would mean that you're observing particular dynamic changes in the extensional relations of objects.
Anyway the reason I said what I said about an N dimensional space bending in an (N+1) dimensional space is for a reason that appeals to my and hopefully other's intuitions. If a particular N dimensional space is to "bend" then it requires the next higher dimension to do it in. Now that I think of it might just be the right interpretation because take a flat sheet of paper (2 D space) and "bend" it. What do you notice? It acquires a 3 D form.
I'd like to know more about what you said though. "Nodes", "topology", "connection", "network" were some of the words you used and I'm familiar with them I couldn't understand what it is that you wanted to say.
PS: Gravity bends/curves 3 D space and time (4th dimension) behaves differently/accordingly depending on how well you understand Einstein.
Not at all. Imagine a string lying in a straight line on a sheet of paper. Now bend the same string and it continues to lie flat on the piece of paper. It does not acquire a 3 D form.
Cosmologists say the form of the universe could be open, closed or flat. For decades, they mostly assumed it was closed. More recent measurements, which always come with error bars, indicate the universe is very close to flat. In fact, the universe is so big we will never be able to prove the universe is not flat. But the universe could have been closed, which means space would be curved on itself so that if you went in one direction you would end up back where you started. The 4 D spacetime continuum warps and bends due to massive objects. This does not require a fifth dimension.
I'm new to the forum. This is my first post, so please forgive me if I make any newbie errors of etiquette.
I have two comments to make. The first is that I found Petrichor's posts very thought-provoking. The second is that I noticed some of you are tending to argue with each other in a personal way, rather than trying to work together to help our collective understanding.
I think that part of the difficulty with understanding curved spacetimes, or curved geometries generally, is that we have Euclidian geometry drummed in to us when we are young, and the local space around us seems Euclidian, so our minds are programmed to accept the Euclidian picture by default, and we have to make an extra effort to abandon that default position in order to picture and accept non-Euclidian geometry. Given that, if anyone is struggling to understand the concept of curved spacetimes then I would strongly endorse the advice given by another member to look at the many excellent resources elsewhere on the net.
I gave 3 quotes of his in my previous post, the first one is from his book Ideas and Opinions, the second one from his book The Meaning of Relativity, the third one is from a letter to his friend Maurice Solovine.
Quoting petrichor
You probably know that customarily electromagnetism and other forces aren't represented as a curvature of space or spacetime, they are represented as a propagation of fields or force carriers. There is no necessity to model gravity as a curvature of space, it's simply what Einstein chose to do.
As to why he chose to do that, at the beginning of the 20th century Minkowski came up with the concept of spacetime to formulate special relativity in a mathematically elegant way, then when Einstein came up with the equivalence principle (which he called the happiest thought of his life) he came to realize that he could fit it into Minkowski's construction by making that spacetime curve. I think it's fair to say that if no one had come up with the concept of spacetime back then then Einstein would have formulated general relativity without a curving spacetime. The useful predictions of general relativity fundamentally do not necessitate a curving spacetime, rather they follow from special relativity's postulates and from the equivalence principle.
Quoting petrichor
"Ripples in spacetime" is how the media describe it, it's how many physicists describe it too, but if you look at the experimental set-up they measured no such thing. Basically they send light traveling on two different paths of equal length, and they measure precisely the difference between the times of arrival, which are supposed to be the same. Tiny vibrations such as from cars traveling on a nearby road cause a detectable difference, so they attempt to filter out all such vibrations.
Then when they do detect an oscillating signal, they don't detect "ripples in spacetime", what they detect is an oscillating difference between the times of arrival of light following two different paths of equal length. And there is no need to invoke curved spacetime or ripples in spacetime to explain that.
Fundamentally a gravitational wave is not a "ripple in spacetime", it is a gravitational influence of oscillating intensity that propagates. So for instance if a gravitational wave passes through your room, what that means is that the gravity in your room changes in an oscillating manner. And since gravity has an influence on the propagation of light (as evidenced by phenomena such as gravitational lensing and the Shapiro time delay), this is what they assume their experiment detected: gravity changing in an oscillating manner, in other words a gravitational wave.
As further evidence that gravitational waves are not "ripples in spacetime", any theory in which gravity propagates at a finite velocity implies the existence of gravitational waves, and pretty much any such theory in which gravity has an influence on the propagation of light can explain the results of the LIGO experiment. Curving spacetime is not a necessity to explain what we do observe.
Quoting petrichor
Yes many talk of space expanding between galaxies, and that's again the fallacy of reification. If two projectiles move away from one another, that doesn't imply they move away from each other because there is some substance between them that is expanding. The balloon analogy is misleading. This is a good paper that explains the issues with thinking there is a concrete thing expanding between galaxies : https://arxiv.org/pdf/0707.0380.pdf
"[i]Galaxies move apart because they did in the past.
The expansion of space does not cause the distance between galaxies to increase, rather this increase in distance causes space to expand, or more plainly that this increase in distance is described by the framework of expanding space.[/i]"
For instance consider the following thought experiment: let's say we hold a galaxy at a constant distance from ours, and then we release it, what happens? If space was really expanding between galaxies, then that galaxy would start moving away from us, but that's not what the theory predicts: rather the galaxy starts moving towards us because of gravity.
And that's a perfect example of the problem with bad analogies: people (physicists included) come up with an analogy to explain a theory, yet that analogy makes predictions that contradict the predictions of the theory. Seeing space as something concrete that is expanding between galaxies is a bad analogy.
The idea that "space can expand faster than light" is misleading too, this is also addressed in the paper. Of course if we extrapolate Hubble's law to arbitrarily large distances then at some point we have galaxies receding faster than light, but us making that extrapolation doesn't imply that this is what actually happens, we don't observe galaxies receding faster than light in any way, if you run faster and faster I can extrapolate that at some point you'll be running the 100 metres under one second, but me making that extrapolation doesn't imply you'll ever run it under one second.
There again "space expanding faster than light" is a bad analogy that contradicts the theory, what the theory actually predicts is that if you send light towards a galaxy that is supposedly receding faster than light, the light eventually reaches it.
Personally this is why I think it would be better to do away with the concepts of curving spacetime and expanding space, because they lead to bad analogies, which are spread by popular physicists and by the media, and then people come to believe things that contradict what the theory actually says.
Thanks for your thoughts. I read some of the paper. I'm cogitating on it.
I tend to think space has to be something. And I strongly tend toward a belief that all forms of causality must be local and work by contact action. This, for me, makes the notion of spooky action-at-a-distance problematic. I strongly sympathize with Newton in the quote I gave earlier.
I think it will turn out that all forces are communicated through something like the medium of space itself, with space being perhaps like a network, as in ER=EPR.
Have a look at this interesting article by Stephen Wolfram:
What Is Spacetime, Really?
You can have contact action without assuming space to be a concrete substance. As an analogy, if I throw a ball at you and it hits you there is no spooky action-at-a-distance, the contact action occurs when the ball hits you. In the case of gravity we can assume there are things traveling between bodies attracting one another, which have an influence when they reach the bodies.
These things traveling are theoretical entities, like space, they aren't things that we actually observe. But we can say that the things we do observe behave as if there are invisible things traveling between them and having a specific influence, or if you want you can model that influence as a propagating perturbation of an underlying space. Both views are theoretical models, and in both there is no action-at-a-distance.
But it is wrong to say that just because we can model what we do observe as perturbations of an underlying space, then that implies that space really is a substance curving or expanding or stretching, it's a theoretical model out of many possible, it's not something we actually observe or detect, and it's not the only way to explain what we do observe.
Fundamentally what is physics? We observe change and we attempt to model that change. Then you can model that change however you like, by invoking invisible particles, or invisible waves, or an invisible space, or an invisible network, ..., no matter what these remain theoretical entities, tools of thought used to model the change we observe.
So I don't disagree that we can come up with a consistent model that invokes an all-pervading changing space. But I'm saying that this space is not something we observe or detect or prove to exist beyond our imagination, and that popular analogies of space expanding and curving lead to false interpretations of what the theory actually says, and lead people to have a flawed idea of what we know and what we don't, of what we observe and what we imagine.
I would rather recommend John Norton articles, such as What Can We Learn about the Ontology of Space and Time from the Theory of Relativity?
You can't exactly model it "however you like", as some models work better than others. It is difficult, for example, to understand why interference patterns develop on the screen in the double-slit experiment if you model everything as particles.
I appreciate what you are saying though, and I am familiar with this sort of thinking. But it seems to me that at some point, if a model works well enough, it is sensible to just accept that that's how things are.
Consider that in the end, everything we understand about the world amounts to models. The idea of a round Earth, for example, is just a model, and is subject to your criticism every bit as much as the idea of bending spacetime. Is there actually a round Earth out there in the objective world? Going along your lines, all we can say is that this model has a lot of explanatory power, but in the end, it's just a model. It allows us to make successful predictions about what we'll see next when we fly in an airplane or launch a rocket, but this never demonstrates that the Earth is actually round. There could conceivably be a another model that explains all that we observe equally well, one that paints quite a different picture of what's out there. A round earth could be like epicycles. There might even be a simpler but much different model, one that we just haven't thought of yet.
You get my point. Strictly speaking, round earth is just a model, but I think we can all agree that the model works so incredibly well and is so parsimonious and elegant an explanation for what we observe that it is probably how things actually are. Earth probably is actually round (well, not exactly spherical). Consilience might be the best indicator here that we are on the right track. Many independent lines of evidence lead us to the idea of roundness.
Your objection is something we ought to keep in mind much more when we are dealing with the barely known, like the very, very small, the very, very large, the deepest fundamentals of nature, and so on. This is so especially when consilience is low.
I hear you. Your criticism of Wolfram might be valid, and I am not devoted to any of his ideas. That article I linked to, however, is rather interesting! But I am partial to modeling space as a network, so I like his thinking there. I'll take a look at your Norton article.
Well you can, it's just some models are simpler than others. But "simpler" is subjective, and it doesn't mean "closer to truth". The double-slit experiment can be understood in terms of particles, for instance with the pilot wave theory in which particles are guided by a wave. Yes there is a "wave", but a wave can be seen as made of a lot of smaller particles, so that experiment and others can be explained purely in terms of particles. I was working on something like that, I will publish it some day when I get the time to finish it, the upside is that you can explain experiments much more intuitively than the usual interpretations of quantum mechanics, you don't have to talk of a thing going through both slits at the same time or not having a definite location or trajectory and all that quantum weirdness. To me, more intuitive is "simpler", while for some other people neat and elegant mathematical equations are "simpler" even if they imply a completely non-intuitive picture of the universe. In the end what matters is whether the model works.
Quoting petrichor
Yes precisely, this is actually an example I mention every now and then, it's possible to come up with non-round Earth models that work just as well and allow to fly an airplane or launch a rocket successfully because they make the same observable predictions. For instance these models would predict that the Earth would appear round from space (same observable prediction) but they would treat it as an optical illusion (one doesn't have to assume that light travels in straight lines in space, it's not something that can be proven without making other unprovable assumptions).
Quoting petrichor
I agree that it is the simplest we have, but I wouldn't go as far as to say that it implies it is "probably how things actually are". Could be that "how things really are" is something that would appear very complicated to us, or could be that there is no such thing as "how things really are" independently of us.
Quoting petrichor
I think we ought to always keep it in mind, for instance I see people getting attacked harshly for believing that the Earth is flat or that the Sun revolves around the Earth, well their beliefs aren't proven false, they can be made compatible with observations, yet these people are treated as heretics by the scientific establishment.
I don't mind that most people use some model, but they ought not to treat it as truth and dismiss other models that can explain the same observations differently. And in the case of the model of space curving and expanding, I actually think that focusing on this model alone while dismissing alternatives has prevented a lot of progress, as it created numerous misconceptions and put physics on a path of ever-increasing complexity privileging mathematical elegance at the cost of intuitiveness. I strongly believe there is a lot to gain by allowing alternative models to flourish, instead of presenting one model as "truth" or as "closest approximation to truth" and having everyone work on it or believe in it.
Physics has become more focused on the realm of theoretical entities than on actual observations. Again look at the example of space curving and expanding, instead of seeing it as a tool of thought people have come to see it as an actual thing that was observed or detected in experiments, and then through that reification they reach conclusions that contradict what the theory actually says. That hinders progress in many ways.
I find that attempting to understand a theory to understand how the universe works is doing it backwards. The theory didn't come out of thin air, it stemmed from observations and experiments, and it makes assumptions that aren't necessarily true. There is more to understand in learning how the theory was developed than in learning the theory itself. Then when you do that you realize that things could have been done differently, different paths could have been explored and weren't, while the succeeding generations only learnt the theory and built on top of it. In my view physics and science in general would be more effective if scientific education was more focused on learning about observations and experiments that were made, and how theories were developed to account for them, rather than on learning the theories and how to apply them. And then physicists would be more open to alternative models and not so dogmatic about the one that they use.
The problem is not so simple though. One object hitting another is nothing but a transferal of force or energy from on solid body to another. But when we look at what constitutes a solid body, it is tiny parts, with space between them. So we need to account for how the tiny parts of one body interact with the tiny parts of another body, as if the two bodies are each a coherent, massive whole, instead of the tiny parts simply interacting with each other, as independent bodies.
Now, since the space occupied by a massive whole is mainly empty space, with tiny parts precisely positioned to make a whole massive body, all that "empty space" must be modeled as part of the body. This is why the centre of gravity (or, centre of mass) is an important concept in physics, it allows that numerous particles with various spatial relations, can be treated as one cohesive body. However, this way of modelling things necessarily reifies the space within that body, as part of the body. and clouds the issue of how the parts of the body interact with the parts of another body, in the transferal of force. The concept of placing the force at a point has literally been abused by physicists to produce nonsensical things like point particles.
Quoting leo
I believe that this is an incorrect assumption, and that there is really no way to adequately or accurately model motions and interactions of bodies without representing "space" as a real underlying substance. As described above, there is no way to even account for the existence of a body without representing its internal "space", as part of the body, and therefore substantial.
You can also talk of the center of gravity of two distinct bodies such as binary stars, and treat them as one cohesive body, but it's not necessary, you can simply model the motion of each star individually without referring to a center of gravity, which is a tool of thought and not a tangible thing. So I don't agree that talking about the center of gravity of a body implies that space is a tangible substance that can curve or expand, in principle we could also model each part of the body individually and never talk of a center of gravity.
If we define space as the unoccupied volume between tangible objects, then when the shape of that volume changes it's simply that the tangible objects are moving, we don't need to say that the volume is made of an underlying substance that is changing shape and dragging the objects with it.
As I explained, a body is full of empty space, and that empty space is treated as part of the body, and therefore substantial. You might model the motion of a body without referring to its centre of gravity, but it is implicit within the way that the multitude of parts which compose "the body", is treated as one whole.
Quoting leo
This is not an acceptable definition for physicists though, because physics deals with objects which are very tiny and therefore not tangible. A tangible object is made up of parts which are not tangible. And even if you define "tangible" in such a way that all these tiny parts are said to be tangible, there is the issue of having to deal with the "space" within a large tangible object. The "space" within an object allows its parts to be moving.
The "space" within tangible objects is outside your proposed definition of "space". If we say that when we are talking about its constituent parts, the "space" within the whole is "space", and when we are talking about the object as a whole, it is not "space", then the same area is treated in one context as "space", and in another context not as space, and this is contradictory. So we cannot define "space" in that way without the consequence of contradiction. .
And as I explained, that's the same as saying that a binary star is full of empty space, rather than simply saying that it is two stars orbiting one another. Just because we call two stars orbiting one another a "binary star" and can treat it as one whole, does not suddenly imply that space is a substance that can curve or expand and that it refers to anything more than the unoccupied volume between things.
How do you get from "space refers to the unoccupied volume between things" to "space is a substance that can curve and expand"?
Quoting Metaphysician Undercover
Well on the one hand we have the space that we do see, the unoccupied volume between tangible objects, that's where our very notion of space comes from. And on the other hand at some point we come to model tangible objects as having mostly unoccupied volume within them, but that space we do not see. Let's call the first one space1 and the second one space2 if you like.
So what I was doing, is that I used the notion of space1 to explain that when the shape of space1 changes, it's merely that the tangible objects (which define the very shape of space1) are moving, so we don't need to say that space1 is a substance that curves or expands and that is responsible for making the objects move. When we talk of space1 curving or expanding, we're not doing anything more than describing the motions of the tangible objects, there is no need to reify space1 as a substance.
Then usually the notions of space1 and space2 are conflated, that is usually we imagine that the tiny invisible particles that make up a tangible object are real things and not just theoretical entities, so in that context we can apply the same reasoning as in the paragraph above to say that the space between these particles refers merely to the unoccupied volume between them, that it is not a substance that has any causal influence on the motions of these particles.
If you want you can define space in general as the unoccupied volume between things, whether these things are tangible objects or theoretical entities imagined to be real objects.
All it boils down to really is that the space between tangible objects and the space that is imagined to be within tangible objects does not need to be reified as a substance that has any causal influence on the objects. The shape of that space changes because the objects are moving, not the other way around. If we want to say that the objects are moving because space is changing shape, then we would have to show that space is a tangible thing that is dragging or pushing or pulling the objects, but we don't observe that.
That analogy doesn't provide a solution to the problem. The problem is that not only is there space between objects, but objects also occupy space. You might say that the only real objects are point particles, which occupy no space, but then you rob objects of their reality, only to hand it to space.
Quoting leo
I think you have this wrong, not only do we not "see" space (it is conceptual), our notion of space comes from measuring objects, and this means it is derived from the "space" occupied by things, not the space between things. Consider the development of ancient geometry, the right angle was developed for the purpose of measuring land for example, and the principles of a "circle" are the principles of a thing.
But history has shown that when we apply these principles produced for the purpose of measuring things, to measuring the "space" between things, there is a problem. That problem is that things are moving in relation to each other. This adds another "dimension" to the problem of "space", because "space" is now not the static area occupied by a thing, it is the changing distance between things.
The issue, as I pointed out earlier is that the "space" occupied by a thing is fundamentally different from the "space" between things. The two concepts of "space" are incompatible because the space occupied by a thing is static and the space between things is changing. When we move to allow that the thing is changing, and therefore the space occupied is not static, we describe the changing thing, as parts moving relative to each other. But then we're not talking about the original "thing" anymore, as the parts are now things in themselves, the subjects of discussion.
So I'd reverse your order of space 1 and 2
Quoting leo
You can't do this with "space 1" though. In space 1, space is the thing measured, so if the distance between objects changes, then the measurement changes, therefore space, as the thing measured, changes.
Quoting leo
So this is false too. You are actually removing "substance" from the things, making them point particles, and making space, as the thing measured, into the substance. Since space is the thing measured, you cannot interpret this model as saying that space is not substance.
We're talking past each other here. Sure if you want let's say that there is space between objects and that objects occupy space. You agree that this space is conceptual, that it comes from measurements, either measurements between objects or measurements of objects themselves.
So what does it mean to say that space "bends", or "curves", or "expands"? It simply means our measurements are changing, that is the distance between objects changes, or the shape of the objects change. It decidedly does not mean that space is not merely a concept but a tangible substance that physically bends or curves or expands and is responsible for the changing distance between objects. An object is a tangible thing, a measuring device is a tangible thing, space is not, you said it yourself it's a concept, you can't take a spoon of space, you can't boil space or cut it in half, you can't throw space, you can't lick space, ...
So, when people say that planets revolve around the Sun because they follow straight lines in a curved space, that's wrong, the curved space is not the cause, it is a model, a representation, we don't detect a space substance that is physically curved, and we are not forced to invoke a curving space to model the motions we observe. To say that curved space is a cause of the motions we observe is to give an illusion of explanation and to reify space as a tangible thing.
We're talking past each other because you are not listening to what I am saying. The point I was making, is that the space which is between objects (which is how you define "space"), is apprehended, or conceived of as being substantial. When you measure, there is necessarily something which is being measured. When you measure the distance between objects that something is space.
Quoting leo
So this is wrong, when we say that space bends, curves, or expands, we are saying that space is substantial, and these are the properties that it has. Yes, "space" is a concept, but within that concept, as necessarily implied, or dictated by the concept, is that space is something real, substantial. This can be readily understood through what I said above. When we measure, there must be something which is measured or else the measurement is meaningless. It is invalid as an actual measurement if there is nothing substantial which is being measued. So when we measure the distance between objects, we presuppose the substantial existence of "space", as the thing being measured.
Objects move and change, because time is passing. In our attempts to understand and conceptualize these changes we've come to the conclusion that space curves, bends, and expands. This is what happens to space, as time passes, and this new, more comprehensive way of understanding space has left the ancient concept, of a static space, as inadequate for the progression, and evolution of knowledge. But it is implied within this new concept of space, that space is real, substantial, as the thing with these properties.
Quoting leo
Everything that we say about things is a model, or representation, that's just a fact of how we speak. But that doesn't mean that we are not speaking about, referring to, what we believe are real, substantial things. One might say "the sky is blue", and that's a model or representation, but 'the sky" is referred to as a real thing. You might say, that "the sky" is not a real thing, by your ontological principles, but in that model, the sky is a real thing, the thing referred to as being blue. It would require that you produce another model, one which doesn't hold 'the sky" as the real thing being referred to, in order to support your ontological principles. But it's inconsistent, and contradictory to use the model, and also claim that the sky is not a real thing.
Likewise, you use a model which represents "space" as a real, substantial thing, the thing that exists between objects, which is measured when we measure distances, but you claim to hold as an ontological principle that space is not real or substantial. Well, to support your ontology, you need a model of "space" which does not represent space as something real, substantial. What is it that exists between objects, that is being measured when we measure distance, an aether o something? In other words, you might insist that we ought not reify space, but this is irrelevant to the fact that the model you use actually does reify space.
If space can bend, what is the space that it is bending in? If there is no space outside of it, then there is no framework for bending to occur in.
Gaussian curvature
Curved Space
I hear what you’re saying, but I disagree, which is another instance of us talking past each other, and you’ll probably disagree with me disagreeing, which will be yet another instance, and so on.
Quoting Metaphysician Undercover
I disagree, when you put a ruler between two objects you’re not measuring space, you could simply say “this object that I call a ruler visually fits between these two objects”, no need to invoke a separate substance that is supposedly measured.
Quoting Metaphysician Undercover
Now you’re refying time. It’s the other way around, we observe change, and then we come up with the concept of time. There is no entity called “time” that we have identified that is responsible for the change we observe. We simply relate change to some reference change that we call a clock. We don’t observe “time passing”, we observe objects that we call clocks change.
Quoting Metaphysician Undercover
That’s wrong, considering there is no need to talk of space curving or bending or expanding to describe precisely how planets and galaxies and light move. The same observations can be modeled as precisely in a space that curves and in a Euclidean space that doesn’t. Observations don’t lead us to the conclusion that space curves.
Your point of view implies among other things that if two objects get closer to each other it’s because space is shrinking between them. I disagree.
Quoting Metaphysician Undercover
You can define the sky as the area above the Earth as seen from the Earth. You do see blue when you look up. In what instances do you see space curving or bending or expanding?
I've provided arguments for my position, based on the definition of "space" which you gave, evidence that I'm not "talking past" you. If anyone is talking past the other, it is you, asserting that "space" as it is commonly understood, is not something substantial, in complete ignorance of what the models, and your definition of "space" indicate.
Quoting leo
Placing object Y between object X and Z, is not a case of making a measurement. This is a diversion, a ruse, or distraction created by you, in an effort to avoid the point of my argument. For me to construe this as a measurement, you'd need to produce a scale by which the degree of "fits" is being judged.
To measure is to determine the quantity, extent, or size of something. To measure the distance between two objects, which is a common practise, requires that the quantity, extent, or size of something is being determined. That something is space. To place a ruler between objects X and Z, and say that the ruler fits between objects X and Z, is not a case of measurement unless the quantity, extent, or size of something is being determined. If the ruler placed between X and Z is being used to measure, it is being used to determine the quantity, extent, or size of something. If it is not determining the extent of the space between the two, then what is it determining the size of?
Quoting leo
Of course time is reified. Time is understood as a dimension of space, and space is necessarily reified according to the concepts we use to measure it, as explained above. Therefore time is necessarily reified as well. But it's not me who is reifying these, they are already reified by the concepts we use to understand time and space. I am just explaining this fact to you. This is a fact which you are having a hard time apprehending because you seem to hold as an ontological principle, that space and time are not substantial. And, despite me demonstrating that this ontological principle is not supported by the concepts of "space" and "time" in common usage, you have provided no support for your personal ontological principle.
Quoting leo
OK, that's fine, you disagree. I already know that, because that's what you keep asserting. Now support your principles, justify your disagreement. Suppose we measure the distance between X and Z at one time, and we measure the distance between X and Z at a later time, and find that the distance is less. If this is not a case of the space between them shrinking, what is it? Don't say that it is a case of the objects moving relative to each other, because that is exactly what movement is, a change in the space between objects. I want you to justify your belief by explaining how objects could move without there being a real substantial space which changes when objects move.
Space can be defined in various ways, let's go with your definition (state it precisely so we can be on the same page).
Strictly speaking I wouldn't say there is space between objects and that objects occupy space, when I do that it's a figure of speech, just like I would say there is love between two people, I don't literally mean that somewhere between these people there is some entity or substance called love that I have observed.
We're also talking past each other because we don't seem to give the same meaning to the word "substance", by substance I mean some sort of liquid or solid or gas, something detectable in some way, space is none of that, to me space isn't a substance just like an idea isn't a substance. You seem to consider that anything that can be thought is substantial, that's not how I'm using the word substance here.
Quoting Metaphysician Undercover
Plenty of measurements precisely involve placing an object between or along other objects.
Quoting Metaphysician Undercover
No, that's you believing I'm creating a diversion/ruse/distraction and attempting to avoid the point of your argument, whereas I disagree with your argument and I'm trying to make you see why while you don't see. Misinterpreting and misrepresenting my intentions and thoughts leads to talking past each other.
Quoting Metaphysician Undercover
Measurements boil down to comparisons. At some point you're judging whether something fits, you're making a comparison when you make a measurement, you can't escape that.
When you place a ruler along two objects, you're judging how the objects fit next to the ruler, you aren't forced to invoke an underlying space that you are supposedly measuring.
Quoting Metaphysician Undercover
No, you and some other people reify time, and you and some other people "understand" time as a dimension of space. Time doesn't have to be reified, and time doesn't have to be treated as a dimension of space. You can do that if you like (as long as you understand it's a model, otherwise you're committing a logical fallacy), but stop pretending it's a necessity.
Quoting Metaphysician Undercover
And I explained why I disagree.
Quoting Metaphysician Undercover
Are you saying that space and time are substantial because in common usage they are treated as substantial? So if something in common usage is treated as substantial then it becomes substantial? If in common usage pink elephants on the moon are treated as substantial then there are pink elephants on the moon? Either you're committing the very fallacy of reification, or you're playing with semantics.
Whereas you know why I don't treat space and time as substantial? Because I don't see space nor time, I see objects, rulers, clocks. The concepts of space and time stem from observations of these substantial things, not the other way around, and that you don't seem to get despite me explaining it to you again and again.
Quoting Metaphysician Undercover
If I'm looking at two objects moving towards each other that's what I see, two objects moving towards each other, I can imagine putting a ruler next to them and reading a decreasing measurement, but I don't see any substance between the objects that shrinks.
Would you say that they move towards each other because space is shrinking between them? That would be again the fallacy of reification.
If I wasn't looking at them moving and I only saw them at rest and I made two measurements and the second one was less, I would say that the objects have got closer to one another, I wouldn't say that some space substance has physically shrunk between them.
If you like you can say that the distance between them has decreased, or you can even say that the space between them has decreased, as long as you understand space to be a concept, an idea, a tool of thought, and not a physical thing like the objects, not a substance. Just like a distance isn't a substance, it's a concept, a tool of thought.
Also, realize that if you consider that when objects move relative to each other it's because space is shrinking or expanding between them, then in your view objects never move relative to space, they are always at rest in space, and that's surely not the concept of "space" in common usage, it's your idiosyncratic one.
There is no single acceptable definition of "space". We discussed this already, there are two distinct conceptions of space. One is derived from our measurements of objects, and this produces the "space" which is occupied by an object, and the other is derived from the measurements of distance between objects, and this produces the "space" between objects. As I explained, these two conceptions of "space" are incompatible, because the former sees space as static, and the latter sees space as active.
Quoting leo
You misunderstand the meaning of "substance" if you believe that substance must be sensible. What is sensible is the form of a thing, it's shape, colour, etc. We do not sense a thing's material substratum, what makes it a real thing, its substance. "Substance" is a concept introduced by Aristotle to validate our assumptions that the material world must be real. So it is not something whose existence we detect, we conclude through logic, that there must be "substance", or else the sensible world would be an illusion. So things which we assume to have real material existence, we say have substance.
Quoting leo
Yes, that's true many measurements involve placing one object beside another, but there is more to a measurement than just that. And that's not relevant, what is at question here, is the fact that if a measurement is made, there is necessarily something which is measured. Why do you resist the idea that when we measure the distance between two objects, what is being measured is the space between them? This is not speaking metaphorically, because the thing being measured (space in this case) must have substantial existence or else the measurement is invalid, it's just an illusion. Therefore "space" must have real substantial existence to validate measurements of distance.
Quoting leo
What are you talking about here, measuring objects, or measuring the distance between objects? If you are measuring the objects, there is no need to assume an underlying space, the substance measured is the object itself. But if you are measuring the distance between them, you are not measuring the objects, and therefore you must assume "space" as the thing which you are measuring. Otherwise you are not measuring anything, and your measurement is not a valid measurement because there is nothing which has been measured.
Quoting leo
You don't seem to understand, a model must model something, or else it's not a model, just like a measurement must measure something or else it's not a measurement. Therefore it really is a necessity that the thing modelled must be real, substantial, or else the model is invalid, meaningless nonsense, because you have a model which doesn't model anything real.
Quoting leo
But pink elephants on the moon are not treated as substantial, so you have no point here. Again, you don't seem to understand. The things which are treated as substantial are the things which are believed to be substantial. What other possibility is there? If time and space are treated by us as having substantial existence, then they are believed by us to have substantial existence. What more is there that I am missing? What you are missing is that it is contradictory to treat space and time as having substantial existence (as you do), yet claim to believe that they do not have substantial existence (as you do).
Quoting leo
But you do treat space as substantial, you defined it as "the unoccupied volume between tangible objects", and spoke about measuring that volume. It just appears now, that you have a misunderstanding of what "substance" means, such that you believed that substance was necessarily something you could see. I hope you now realize that this is incorrect, we see colours, and different shapes, but we don't see substance.
Quoting leo
This is false. As I explained, under your conception of "space", space is necessarily something real, substantial, so there is no fallacy of reification here. The space between the two object is shrinking, or else your measurements are invalid because they are not measuring anything.
Quoting leo
It's fine and acceptable to talk about them being closer to each other, but then you do not mention "space". As soon as you mention "the space between them", you have referred to a real substantial thing which lies between them. What sense does it make to talk about "the space between them" unless you are actually referring to the space between them?
Quoting leo
I don't think that anyone conceives of motions as objects moving relative to space, so I think it's you who has a rather idiosyncratic concept of "space".
I don't know why you make a distinction there. In both cases measurements are involved, in both cases the measurements can change (the shape of an object can change, so can the distance between objects).
There are other conceptions of space. The one customarily used in physics is something like:
a boundless three-dimensional extent in which objects and events occur and have relative position and direction (Merriam-Webster dictionary)
the dimensions of height, depth, and width within which all things exist and move (Oxford dictionary)
Notice how these definitions do not refer specifically to measurements of objects or measurements between objects, they refer to a thing within which objects exist and move.
Quoting Metaphysician Undercover
As above, in physics the very customary thing to do is to conceive of motions as objects moving in space. In classical physics you have objects moving within Euclidean space. In general relativity you have objects moving within curved space.
For instance in classical physics, when two objects move towards each other they move in space, space doesn't shrink between them. Sure the distance between them decreases, the unoccupied volume between them shrinks, but the reference background relative to which objects are tracked, space, doesn't shrink.
Now of course that reference background is not something we observe or detect, it is a reference frame that is defined from things we do observe, which is why I say that this background is not something tangible, is not a material substance, it's a concept, a tool of thought, and to treat it as tangible like an object is the fallacy of reification.
Quoting Metaphysician Undercover
I do not misunderstand the meaning of "substance", rather I use a definition of "substance" different from yours, your definition is not the only one that exists, and it isn't the most widespread either.
The definition I use would be something like a material with particular physical characteristics (Cambridge dictionary), whereas your definition seems to be something like the essential nature underlying phenomena (Oxford dictionary). So obviously if we're not using the same definition we talk past each other when we talk about substance.
Now that you know in what sense I use the words "space" and "substance", and so as to not get too carried away, the whole point of the discussion is what does it mean to say that space curves? Plenty of people say that gravity is the curvature of space, that planets orbit the Sun because space is curved around the Sun and because they follow straight lines in curved space, people are made to believe that we have found the cause of gravity, that this cause is that space is curved, as if space was a tangible thing, a tangible material, a tangible substance that we have detected to curve, and as I keep saying this is false, we have detected no such thing, the curvature of space is an abstraction, a concept, a tool of thought, not something that is physically detected in any way, and to treat that abstraction as a material thing is the fallacy of reification.
People are made to believe that we can't model gravity precisely without invoking a curved space, as a supposed proof that space really is a tangible material that really does curve even though we don't directly observe it, this is false, we can model observations as precisely without invoking a curved space.
And when I say that space is not a tangible material that curves or expands like a sheet curves or a balloon expands, I'm not saying that we don't perceive objects that are visually separated. And when I say that time is not a tangible material that passes or flows like a train passes or water flows, I'm not saying that we don't perceive change.
Do you not see a difference between measuring an object, and measuring the distance between two objects? In the first case, you would be dealing with the properties of one individual object, and in the second case you would be dealing with a relation between two objects.
Quoting leo
If space is "a thing within which objects exist and move", how can it not be a substance? You are saying that it is a thing, like a medium, within which objects exist, like they exist in water, or air. How could there be a thing, with objects existing within it, and this thing does not have substantial existence?
Quoting leo
OK, so there is a thing, with objects moving within it, just like objects move in water or air, but this thing is called "space". How can the objects move within this "space" without changing this thing? If an object moved, wouldn't some of the space be displaced, and therefore itself be moved? If the objects moved closer to each other, than the amount of space between them would necessarily shrink, as some would have to move aside, or else it might compress.
Quoting leo
Now you are contradicting what you said above. You said that space is a thing within which objects exist. How could this thing (space) be just a concept, or tool of thought? Either there is a thing (space), within which objects exist, or space is just a concept, a tool of thought. But it doesn't make sense to say that the thing within which objects exist, and move around, is a concept. Which do you believe? Is space a medium which has objects within it, as you say is the customary definition in physics, or is space just a concept or tool of thought, as it is in you ontology?
This is the problem I told you about already. Our definitions, concepts and models, treat space as a real, substantial thing, a medium within which objects exist,. Also, you use and refer to those concepts in your argumentation. Yet you assert an ontological principle which contradicts this, that space is only conceptual. Do you not realize that the definitions you cite do not support, and are actually opposed to the principle you assert?
Quoting leo
OK, since we have different ideas of what substance means, lets leave that word. Let's just focus on your definition of "space" as a thing within which objects exist, and we'll forget about whether this thing is properly called a substance or not. Clearly you must see that this thing is not merely conceptual. How could objects exist within it if it were only conceptual?
Quoting leo
OK, now according to your definition, space is a thing, like a medium, within which objects exist and move. Would you agree that there is a property of this medium (space) which causes things to move in a curved trajectory when we would otherwise think that these things ought to travel in a straight line, and that this is why some people talk about a curved space? If it is not a property of this thing, called space, then what could it possibly be that causes this? It cannot be that the concept of space, or that the tool of thought causes this curved motion, because the concept is simply supposed to represent, model, or demonstrate an understanding of this curvature.
Quoting leo
OK, let's suppose that this is true, space can be modeled with or without the curvature, and each model is as accurate, and reliable as the other. What does this indicate other than the fact that we really don't know what space is?
Quoting Metaphysician Undercover
I meant why the distinction between static space and active space, since the shape of an object is not necessarily static.
Quoting Metaphysician Undercover
No I'm not saying that, I said that the definitions refer to it like a thing, some sort of container in which objects move. In physics space used to be thought as a medium (the luminiferous aether), then failures to detect it experimentally led to abandon the idea of it as a medium (as Einstein did with special relativity in which there is no more reference to an absolute space but instead to relative reference frames), and then Einstein reintroduced it as some sort of a medium in general relativity since in it space has properties such as curvature. But even though in his theory space has properties, Einstein was well aware that space is a "tool of thought" (that's his own words), in no way did he pretend that his theory somehow proved that space is an actual medium that really does curve, only people who misinterpret him and misinterpret the function of scientific theories say that.
It could be that there really is a medium that permeates everything, or it could be that there is pure void between things, both ideas are compatible with what we observe. If there is pure void between things then space isn't a medium, it isn't an actual thing.
Quoting Metaphysician Undercover
It does make sense if it is said conceptually and not literally. We can imagine that planets follow curved trajectories in a flat space, or straight trajectories in a curved space, or some other trajectories in some other space, the conceptualization itself doesn't imply that space is an actual thing that is flat or curved, otherwise that leads to senseless conclusions, space would be at the same time flat and curved when one person conceptualizes it as flat and some other person as curved.
Yourself you have even come up with a concept of space in which objects don't move even when we perceive them to move. Do you conclude from that that space is an actual thing that shrinks and expands whereas objects remain at rest, or that it's a concept you have invented?
If simultaneously one person can imagine space as flat, some other person as curved, some other person as shrinking and expanding, some other person as being displaced by objects, do you not see that space is a concept, and that people conceptualize it by analogy with what they do observe? People observe flat surfaces, people observe curved surface, people observe balloons shrinking or expanding, people observe water displaced by objects moving within it, then they conceptualize space by analogy with what they have observed, but they can conceptualize it however they want, all their conceptions are compatible with observations, the very same observation can be translated in one conceptualization as an object having a straight trajectory, in another conceptualization as the object having a curved trajectory, in yet another as being at rest, all are valid depending on the concept you use.
So if space can be anything we want it to be, what is it? It's a creation of the imagination, a tool of thought, a concept. Yes we perceive objects, yes we perceive change, but I think if you trained your mind you could come to see all objects at rest while imagining (or seeing) space shrinking or expanding between them. Maybe then you would come to see space as a real tangible thing, and motions of objects as an illusion. Sometimes the line between reality and imagination can be blurry, who knows if we aren't the ones who impose that delimitation ourselves.
So I won't claim it's impossible to see space as a real tangible thing, after all I'm not in your mind. But I'll keep saying that it's possible to imagine it as flat, or curved, or as nothing at all, and as such that it is false to claim that planets revolve around the Sun because they follow straight lines in curved space as if we had detected space to be something that curves, conceptually we can see planets as following straight lines in curved space, but conceptually we can also see them as having curved trajectories in flat space or as some other thing.
Quoting Metaphysician Undercover
I think really your question boils down to why is there something rather than nothing. Because as soon as you identify several things within what you see you can come up with a concept of distance, and then a concept of space. Only if your experience was uniform (say you didn't experience anything except the color white, no sound no smell no taste no touch, no screen around the white just white) then you wouldn't come up with the concept of space. The concept is used to relate things that are identified as distinct.
So I would say our thoughts create the concept of space. And then I wonder to what extent our thoughts create what we see, to what extent they decide what's reality and what's imagination, to what extent they have created what they classify as reality...
Well I went through this already. An object must really be a static thing, because if it changes it is no longer the same object. Sure we say that it is the same object, only changed, but logically if it has changed, it can no longer be the very same thing. Aristotle tried to deal with this problem by employing the concept of matter, which allowed that the object would remain the same object, despite changing its form, so long as its matter stayed the same.
So Aristotle distinguished change of shape or form, from locomotion, as two distinct types of activity. In modern times, we have come to understand change of shape as the locomotion of a thing's parts. So we no longer have these two distinct types of activity, all is understood under the terms of locomotion. Change of the shape of an object, is supposed to be the movement of parts relative to each other. But then the parts are themselves objects, moving relative to each other, and there is no justification for the claim that a multitude of objects is really one object, the original "object". Either the circumstances being observed is a multitude of objects, or it is one object, but it can't be both at the same time because this is contradictory.
That is the problem with the part/whole ontology. Saying that an entity, an object which exists as a single, individual unity, is composed of other objects which are parts, is really contradictory. This is because we then consider the same thing to be both one object, and a multiplicity of objects, at the same time, and this is contradictory, like saying 1 is at the same time, 2. If we divide the one unity into parts, then it is no longer one unity. It cannot be divided and whole at the same time. So the one object, as a unity is divisible into parts, but it cannot actually be composed of parts, if the parts are considered to be objects themselves.
If the object, as a unity is not composed of parts, then it cannot be changing. If it is composed of parts, and changing, then the parts cannot be considered to be objects, and their activities cannot be understood as objects moving relative to each other.
Quoting leo
I accept this description, but it does not explain how objects exist within space, yet space is just a tool of thought. The inconsistency, or contradiction, remains. If the conceptions of "space" model space as a medium within which objects exist, then it is absolutely incorrect to say that space is a "tool of thought". Space is something which is modelled as a medium within which objects exist. It is not modeled as a tool of thought, so it is incorrect to say that space is a tool of thought, because it is represented by the models as a medium within which objects exist. If we model water as something we can swim in, then it is incorrect to say that water is a tool of thought, that is not how it is modelled.
Quoting leo
It doesn't matter if you call this medium "pure void", it's still a medium. So your claim of two possibilities, medium, and pure void, is inaccurate because "pure void" is really just a special type of medium, and so there is really only one choice, medium. Many people speak of "pure void" as if it were something other than medium. But when we come to realize that "pure void" just refers to a special type of medium, an absolute medium which consists of absolutely nothing but itself, then we realize that it doesn't make sense even to speak of "pure void".
Quoting leo
I don't understand this distinction. Do you recognize that a model must model something? If one were to make a model, and it didn't model anything, it would just be random nonsense, and not a model at a all.
So if you model planets as moving through space, it makes no sense to say that this is just what the model shows, and the planets are not really moving through space, we've just modelled them that way. If you model planets as moving through space, and insist that the planets aren't really moving through space, it's just that the model shows them as moving through space, then all you are doing is asserting that the model is wrong.
Quoting leo
Not at all. What I would conclude from this is that space is a real thing, because many people are talking about it, but they just don't understand it, and this is evident because their concepts of it vary. It's very similar to when a few people try to recount an incident from many years ago. Some will remember it in one way, others in another way. This doesn't mean that the incident isn't a real thing which really happened, it just means that the people haven't conceptualized it well.