## What Happens When Space Bends?

• 53
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.
• 53
What does this mean?.

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.
• 4.7k
now there is no space in that corner

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).
• 53
There isn't any corner either: the corner's moved with the space. Or: the space moving is the corner moving.

That is what I was thinking, but I am not quite what Einstein was saying when talking about space bending.
• 4.7k
Imagine rolling a ball in a straight line. If space itself is curved, the 'straight line' itself will be bent. Or obversely, if you really wanted the ball to move in a straight line, you would have to actively correct its trajectory as it rolled.

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.
• 4.9k
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.

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.
• 13.8k
What happens when space bends? Nothing. Space isn't a thing in itself that can bend. Space supervenes on the extensions of matter and the extensional relations of matter. It's not actually anything like a substance or a container or anything like that.
• 130
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.

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.
• 53
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.
• 813
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.
• 13.8k
Here's an illustration of what happens when Bender spaces:

• 130
Spacetime isn't an actual observable thing either, it's a mathematical toolleo

So that thing that creates the separation between objects is only a mathematical tool.

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 spacetimeleo

And whatever it is that magically bends the light is more detectable than the curvature of "non existent" spacetime.
Yeah Einstein was an idiot
• 813
So that thing that creates the separation between objects is only a mathematical tool.

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?

And whatever it is that magically bends the light is more detectable than the curvature of "non existent" spacetime.

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.

Yeah Einstein was an idiot

Einstein agreed that spacetime is a tool of thought, not an actual thing, it's people like you who don't understand him.
• 130
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 accurateleo

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.

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?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.

Einstein agreed that spacetime is a tool of thought, not an actual thing, it's people like you who don't understand himleo

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.
• 13.8k
So that thing that creates the separation between objects is only a mathematical tool.

There's not a "thing" that creates separation between objects. There's just the facts of their extensional relations.
• 130
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?
• 13.8k
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.
• 813
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.

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.

And the reason Newton predicted light bending is because he believed light to be strictly a particle.

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.

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.

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.

The effects of time-space shrinking as you approach a massive object are well demonstrated. Time dilation is real.

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.

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.

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, ...

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.

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.
• 130
Sure, I have also read Einstein's historical papers on special and general relativity, have you?leo

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.
• 242
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.leo

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:

It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.[5]
— Isaac Newton, Letters to Bentley, 1692/3

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?

There's not a "thing" that creates separation between objects. There's just the facts of their extensional relations.

What would it mean for there to be a ripple in "the facts of their extensional relations"?
• 242
Methinks it works like how a 2D space (a flat sheet of paper) bends in 3D space and leaves behind 3D space.

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:

A--B
|  |
D--C


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

Another approach that aims to reconcile the apparent passage of time with the block universe goes by the name of causal set theory. First developed in the 1980s as an approach to quantum gravity by the physicist Rafael Sorkin — who was also at the conference — the theory is based on the idea that space-time is discrete rather than continuous. In this view, although the universe appears continuous at the macroscopic level, if we could peer down to the so-called Planck scale (distances of about 10–35 meters) we’d discover that the universe is made up of elementary units or “atoms” of space-time. The atoms form what mathematicians call a “partially ordered set” — an array in which each element is linked to an adjacent element in a particular sequence. The number of these atoms (estimated to be a whopping 10240 in the visible universe) gives rise to the volume of space-time, while their sequence gives rise to time. According to the theory, new space-time atoms are continuously coming into existence. Fay Dowker, a physicist at Imperial College London, referred to this at the conference as “accretive time.” She invited everyone to think of space-time as accreting new space-time atoms in way roughly analogous to a seabed depositing new layers of sediment over time. General relativity yields only a block, but causal sets seem to allow a “becoming,” she said. “The block universe is a static thing — a static picture of the world — whereas this process of becoming is dynamical.” In this view, the passage of time is a fundamental rather than an emergent feature of the cosmos. (Causal set theory has made at least one successful prediction about the universe, Dowker pointed out, having been used to estimate the value of the cosmological constant based only on the space-time volume of the universe.)

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.
• 242
Space isn't a thing in itself that can bend.

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:

The general theory of relativity brought with it a decisive change in this point of view. Space-time and matter were found to be interdependent, and there was no longer any question, which was the more fundamental of the two. Space-time was also found to have its own inherent degrees of freedom, associated with perturbations of the metric - gravitational waves. Thus, space can exist and change with time in the absence of electrons, protons, photons, etc.; in other words, in the absence of anything that had previously (i.e., prior to general relativity) been subsumed by the term matter.

A more recent trend, finally, has been toward a unified geometric theory of all fundamental interactions, including gravitation. Prior to the end of the 1970’s, such a program seemed unrealizable; rigorous theorems were proven on the impossibility of unifying spatial symmetries with the internal symmetries of elementary particle theory. Fortunately, these theorems were sidestepped after the discovery of supersymmetric theories. In these theories all particles can be interpreted in terms of the geometric properties of a multidimensional superspace. Space ceases to be simply a requisite mathematical adjunct for the description of the real world, and instead takes on greater and greater independent significance, gradually encompassing all the material particles under the guise of its own intrinsic degrees of freedom. In this picture, instead of using space for describing the only real thing, matter, we use the notion of matter in order to simplify description of superspace. This change of the picture of the world is perhaps one of the most profound (and least known) consequences of modern physics.

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?
• 13.8k

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.
• 13.8k
What would it mean for there to be a ripple in "the facts of their extensional relations"?

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.
• 4.9k
You went to great lengths to explain your point of view but I'm afraid it went over my head. My fault. Not yours.

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.
• 174
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.

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.
• 1
Hi Everyone,

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.
• 813
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?

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.

For one thing, Einstein's theory is often appreciated for restoring a local picture of gravity, of solving this problem that Newton expressed

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.

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.

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?

"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.

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?

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

"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.
"

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.
• 13.8k
• 242

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?
• 813
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.

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.
bold
italic
underline
strike
code
quote
ulist
image
url
mention
reveal