The question "would space still exist if matter disappeared" is posed with an ontological bias which influences the answer.
A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.)
The question creates a bias because when we imagine matter being removed from the universe, we firstly imagine the removal as an event unfolding in time. Secondly, we continue to imagine the locations where pieces of matter used to be, and those locations continue to be separated by the abstract space which we continue to imagine.
> does a universe in which there is nothing (and never has been) still contain space?
Within the framework of our best current theories, the answer is yes, in the sense that flat Minkowski spacetime, containing no matter or energy anywhere, is a valid solution of the Einstein Field Equation of general relativity.
Physicists have been thinking about this for a long time, and I seem to recall having seen it pointed out before that the question of a space-time that never had matter in it could be different than one that had it but somehow had it removed. Which then implies the possibility that the space-time has a state in it, in which case, where did it come from and where is it being stored?
Given our current state of understanding, there really isn't a need to insist that one question is wrong and some other question is better, seeing as we are currently equally incapable of answering any of them.
Think of the exact same system performing the same intra-system permutations (changes) but in two different reference frames (one relativistic and the other not). The changes are identical but the time required by each will be different due to their different reference frames. If time was simply a measure of change than you would expect the time taken by these two systems to be identical. Time then takes on a quality (or rather perhaps has a dependency) that exists beyond simply a "measure of change".
I've struggled several times to formulate this question properly. I'm not convinced by your formulation. I'll give it an other try.
Does space have an existence per se, that is regardless of the matter it contains, or is it just a mathematical framework for the interactions between particles?
This requires a definition of space. For your question to be logical, space should be taken as the thing that is among and around matter. Then on it may be researched physically. Buf if space is taken to mean the thing that exists among and around perceivable matter, then your question becomes obscure, as this means that space is matter, but just not perceivable. And therefore it exists, also without relation.
We know what space is, at least operationally. Or rather space-time. Space is what can be measured with rigid rods. Time is what clocks measure. Einstein painstakingly defined those concepts this way.
Plank's question is more metaphysical : beyond what it means experimentally, does space have a -physical- existence per se, even in a completely empty universe? In other words, is an empty universe different than no universe at all? If not, one way to look at space it is to consider it as a set of abstract rules regarding the possible interactions between particles, those rules being very close to what we call geometry.
Nothing is an abstract concept that we use for various things, when we say nothing is just a way of saying the absence of something we know, our own existence (Descartes) is proof that absolute nothingness is not possible.
Space is big. Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the road to the chemist, but that's just peanuts to space.
52! is the number of different ways you can arrange a single deck of cards. Let's try to wrap our puny human brains around the magnitude of this number with a fun little theoretical exercise. Start a timer that will count down the number of seconds from 52! to 0. We're going to see how much fun we can have before the timer counts down all the way.
Start by picking your favorite spot on the equator. You're going to walk around the world along the equator, but take a very leisurely pace of one step every billion years. Make sure to pack a deck of playing cards, so you can get in a few trillion hands of solitaire between steps.
After you complete your round the world trip, remove one drop of water from the Pacific Ocean. Now do the same thing again: walk around the world at one billion years per step, removing one drop of water from the Pacific Ocean each time you circle the globe. Continue until the ocean is empty.
When it is, take one sheet of paper and place it flat on the ground. Now, fill the ocean back up and start the entire process all over again, adding a sheet of paper to the stack each time you’ve emptied the ocean. Do this until the stack of paper reaches from the Earth to the Sun.
Take a glance at the timer, you will see that the three left-most digits haven’t even changed. You still have 8.063 × 10⁶⁷ more seconds to go. So, take the stack of papers down and do it all over again. One thousand times more. Unfortunately, that still won’t do it. There are still more than 5.385 × 10⁶⁷ seconds remaining. You’re just about a third of the way done. [1]
Well, the volume of the visible universe is 3.4 × 10⁸⁰ m³ and therefore another factor of 4.2 trillion larger than 52!. And then the entire universe is estimated to be at least another 150 or 250 times larger than the visible universe. In diameter, not volume.
If one wants to get a sense of how far things are, it's probably more helpful to imagine all bodies besides the moon as being infinitely far away.
At 4km per hour, it takes 11 years of continuous walking to walk the distance between Earth and the Moon; 4252 years to the Sun; 214041 years to Pluto; 1.17 billion years to Alpha Centauri.
Assuming single celled organisms travel very slowly, that means if you have been walking your entire lifetime to Alpha Centauri, and your parents did the same and gave birth to you on their way to Alpha Centauri, and their parents gave birth to them on their way to Alpha Centauri, ancestors all the way back to the first biotic life form, you'd be just about arriving, now.
It does also mean, the sum of all distance traveled by all lifeforms on Earth is longer than the distance between Earth to Alpha Centauri and back by quite a few times, that can likely be measured in the billions.
I was walking along the other day after a class about mathematical modelling of biomolecules and was suddenly struck by the thought that space doesn't really even exist. This came from the observation that when we calculate van der Waals interactions there are two terms [0] and the term raised to the 12th power is an approximation to account for the fact that down at the quantum level two electrons cannot occupy the same orbital. We can map electron orbitals onto space but then we get something funky like the Pauli exclusion principle and suddenly a force that appears to be 'spatial' in origin is now a consequence of a completely non-spatial phenomenon. We use space as a convenient intermediate in many measurements but it is not clear to me that the fundamental accounting system of the universe actually needs it (though as the article points out, general relativity seems to suggest that space-time does exist or at least provides a pretty reliable coordinate system).
Spinning motion is an illusion and doesn't exist as a fundamental form of movement, similar to how lack of gravity in orbit is an illusion, in that you are continuously falling downward but missing the earth.
Spinning objects are made of particles that are all actually going in straight lines but forces against each other are causing them to change direction, cummulatively appearing to be spinning, like an extremely coherent eddie current or vortex. Their movement is in relation to each other, and there is no need for an objective space in which to spin.
> Spinning motion is an illusion and doesn't exist as a fundamental form of movement
If there is no objective space, then "movement" in general is not a fundamental concept; but you are assuming that at least some kinds of movement are fundamental (tarikjn points out something similar to this).
> similar to how lack of gravity in orbit is an illusion, in that you are continuously falling downward but missing the earth.
Actually, you have this backwards; it's the "falling downward" because of "gravity" that is the "illusion", according to our best current theory, general relativity. In a free-fall orbit, you are moving in a straight line through spacetime; you can tell this by the fact that you are weightless.
Regarding gravity, that was probably a bad analogy. Regarding movement, movement relative to other objects is fundamental. You are begging the question by assuming objective space is required for movement.
Mind you, I'm not arguing that space doesn't exist, only that Newton's argument is flawed.
> movement relative to other objects is fundamental
I agree that "objective space" in the sense of "a space that is the same for everyone", is not required to give an account of movement of objects relative to other objects. However, the only reason we know that is that we have an alternative: a theory of objective spacetime that gives an account of movement of objects relative to other objects.
In other words, according to our best current classical theory, general relativity, Newton's argument was flawed not because nothing objective is needed to account for the bucket experiment, but because he got wrong what thing was objective: he thought it was space, but it's actually spacetime. More precisely, it's the geometry of spacetime.
On the GR viewpoint, we can indeed view the rotation of Earth, for example, as relative in this sense: we can adopt a "cosmic" frame in which the Earth is spinning and the rest of the universe is at rest; or we can adopt a "geocentric" frame in which the Earth is at rest and the rest of the universe is spinning. Both frames are valid; neither one is "preferred" by the laws of physics. But both frames are describing the same underlying objective thing: the same geometry of spacetime. They are just describing it from different viewpoints.
Physicists are rather aware of these things, seeing as you they are the ones who taught them to you in the first place. This is an old, venerable question that, as the article says, dates back to before Einsteinian relativity and remain unresolved to this day. Physics 101 is not capable of resolving the matter.
"Appeal to authority" is more than "mentioning the existence of authorities". This is not an appeal to authority.
The point is, if the answer was as simple as that, it wouldn't be a problem. This is not news. This is a century+ old conundrum, and you can't solve it by simply reciting Physics 101 as if that's it, book closed. It's the equivalent of listening to a operating systems researcher describe a thorny problem in the creation of a multitasking operating system on a hundred-core NUMA system, and then pedantically, slowly, patronizingly explaining back to them how functions work by pushing things on to a stack and then popping them afterwards.
When they favor you afterwards with a deeply shocked expression, it's not in amazement at your penetrating insights.
Still sounds like "Appeal to authority" to me. To speak to your analogy, I am involved in the field of computers, and I've seen first hand "experts" in this field build big complicated systems, that maybe had some merit at some point in time, but as the context changed with new developments and technologies, a young upstart built something much more simple that made the expert's system look like a mess. This is relevant because the context of what we understand is very different from Newton's time. School children have a more accurate depiction of the laws that govern our reality than the tops minds at the time, who believed in such things as phlogiston and the earth-centric universe.
I am actually not sure that this is true. I used to think exactly like you, that rotations are just piles of small translations with time varying directions, but there is a problem with this, linear momentum and angular momentum are two different conserved quantities. If it were the case that rotations are just translations then you should be able to get rid of angular momentum and its conservation and explain it in terms of linear momentum and I don't think that you can do that. Linear momentum is tied to the homogeneity of space while angular momentum is tight to the isotropy of space. You could actually do the exact opposite, say that translations are just rotations about a point infinitely far away, but I think that won't work either. I really don't know for sure, I mean I am not really, really, really confident about it, but as far as I can tell rotations and translations are fundamentally different.
Unaccelerated translations make only sense as relations between two objects but you don't need any reference to detect acceleration, you can just release an object from your hand and see if it drops to the floor because of gravity, hits the wall behind you because your space ship is accelerating or flies away tangentially because you are on a carousel. Rotation requires continuous acceleration (I am avoiding the term constant acceleration because only the magnitude is constant but not the direction) of all the particles towards the center of rotation or otherwise they would fly away tangentially. But if rotation requires continuous acceleration and you can always detect acceleration without reference to some other outside objects then you can always detect rotations and that is not true for translations, you can not detect unaccelerated translations.
It is the difference between velocities and accelerations and the fact that rotations always require accelerations that makes rotations more than just a pile of translations. You won't notice any difference if you translate everything in space by the same amount, you won't see any change if you rotate everything in space by the same amount, there is also no difference if you change the velocity of everything by the same amount but you will immediately notice if you change the acceleration of everything.
Or maybe that is at least partially nonsense, unfortunately I haven't yet mastered that topic myself.
Centrifugal force is an abstraction, but angular momentum has physical reality at the subatomic level. See Feynman, chap. 17.[1] Photons have angular momentum, even though they don't have a meaningful size. This is strange, but it's reality.
That is a trivial fact, the wave function of a system completely describes the state of the system and that of course includes the angular momentum. But the wave function has nothing to do with a physical wave with physical properties, it is a pretty abstract construction and the physical properties are essentially encoded in the base vectors of the Hilbert space. I only skimmed the paper but I didn't come across something that plausibly argued that the wave function is the fundamental physical entity.
Not meaning to argue that the wave function is a physical entity but rather that particles aren't required to "exist" as a physical entity to explain experimental data.
I would say nothing is required to exists. Just take the idea that our universe may be a simulation, then nothing in the universe is real. It could then be that the real universe out there is similar to ours or we could be the Game of Life of the real universe which could be totally incomprehensible to us with concepts that aren't even imaginable in our little world. Or take Last Thursdayism, the idea that the universe somehow came into existence last Thursday with fake memories of the past in our all heads and so on. Or Solipsism. There is no way you could ever find out that something like that was true or not.
We just have to make some assumptions about the nature of the universe and accept them as axioms, otherwise you can not even start to draw conclusions. Some assumptions may look more reasonable then others but I guess that is more or less an illusion, last Thursdayism looks only unreasonable because you have already rejected the idea and accepted some other assumptions.
So what is real? Particles? Fields? Wave functions? We pretty surly don't know. Some will say the fields are the real things because they give us virtual particles and that matches experiments, others will say that fields are not real because they have gauge symmetries - gauge redundancies - and how can something that is underdefined be real? It seems certainly possible that we will be able to rule one or another view out in the future because they can not accommodate some new discovery but we are probably not yet there and there is definitely no consensus.
Not to forget that there are quite a couple of new directions in the last years and decades, like space and time emerging from entanglement, the holographic principle, gravity as an entropic force and what not. There is probably a good chance that some or all our fundamental concepts of physics as of today will not survive the next century, millennium or million years. I mean they will still exist as useful approximations but no longer been seen as fundamental.
I'm not in disagreement. I certainly could have been more careful with my original wording.
I had a gut reaction to the original commenter's statement that angular momentum was a "physical reality at the subatomic level" and should have been more direct in my response.
No, they're the same thing. Feynman: "Now we would like to discuss the idea of angular momentum in quantum mechanics—or rather, the characteristics of what, in quantum mechanics, is called angular momentum. You see, when you go to new kinds of laws, you can’t just assume that each word is going to mean exactly the same thing. You may think, say, “Oh, I know what angular momentum is. It’s that thing that is changed by a torque.” But what’s a torque? In quantum mechanics we have to have new definitions of old quantities. It would, therefore, be legally best to call it by some other name such as “quantangular momentum,” or something like that, because it is the angular momentum as defined in quantum mechanics. But if we can find a quantity in quantum mechanics which is identical to our old idea of angular momentum when the system becomes large enough, there is no use in inventing an extra word. We might as well just call it angular momentum. With that understanding, this odd thing that we are about to describe is angular momentum. It is the thing which in a large system we recognize as angular momentum in classical mechanics."[1]
Yes, it's weird. Yes, it's not intuitive. But it's very real. Many experiments, such as the classic two-slit experiment, have confirmed the stranger predictions of quantum mechanics.
I think something is being lost in translation here. An object made of multiple particles could potentially have one at dead center that is spinning perfectly, and this would be of the same sort of angular momentum as that at the quantum level. But a particle sitting out on the edge of an object is subject to the forces of those surrounding it, keeping it moving in a circle instead of a straight line. Instead of microscopic particles, imagine a bunch of marbles connected by loose springs in a 3D mesh. If you spin this around, are you suggesting that something is happening besides the simple fact that springs are tugging and pushing at marbles to constantly affect their linear motion to appear circular? It's like suggesting somehow that a line on a screen is not made of pixels.
Spin angular momentum seems to be a pretty intrinsic property of (fundamental) particles. What do you understand as inherent properties of objects? Position? Charge? Mass? Velocity? Energy? Linear momentum? Spin? And why? What if the object is composite? What about quantum physics, e.g. superposition states?
The angular momentum of a spinning bucket of water has approximately nothing to do with the intrinsic angular momentum of the particles, though. Statistically, we'd expect all of the intrinsic spins of the electrons and quarks to cancel out entirely.
Rather, the angular momentum is due to the fact that the straight-line motion of all the atoms on the left side of the bucket is opposite in direction to the straight-line motions of all the atoms on the right side of the bucket. (With respect to the reference frame of the center of gravity of the bucket, etc, etc.)
They are nonetheless related, if you would align the spins in the water and the (metal) bucket you would make the bucket and/or water spin to conserve the angular momentum. [1] They are surly different but it is not some accident of history that both are called angular momentum, they are really both angular momentum.
What is the point you're arguing against? I know perfectly well that conservation of angular momentum is a thing. I know perfectly well that the intrinsic property that we call 'spin' of an electron is really angular momentum. I know that a spinning bucket also has real angular momentum.
So, I'm not sure what you're trying to tell me.
The central point made by colordrops is that angular momentum in a macroscopic object is 100% (accurate to at least ten decimal places) due to synchronicity of linear momenta.
What colordrops wrote at least suggest that he thinks that circular motion and angular momentum are not fundamental but can be expressed or understood in terms of linear motion and linear momentum. As far as I can tell today this is not true, they are independent concepts and one can not be fully understood in terms of the other, neither by looking at circular motion as piecewise linear motion nor by looking at linear motion as circular motion about a point infinitely far away. I only brought up spin because it makes the point pretty clear - or maybe not - that angular momentum is a fundamental concept that can not be recast in other terms, especially it is not just the sum of many linear momenta.
Look at the 2-body gravitational system -- let's say Earth-Moon. Let's put our non-rotating reference frame at the barycenter. At any given moment, Earth has a definite position and velocity, and the Moon has a definite position and linear velocity. If we know these positions and velocities (and masses), we can derive anything else we'd like to know about the system. Including its angular momentum.
This would also be true of any system such that the size is large enough to render the quantum spins statistically close to zero.
Sure but you make an arbitrary choice here, you choose to use Cartesian coordinates. Lagrangian and Hamiltonian mechanics make it more clear that this is more or less an arbitrary choice and that there are other sets of generalized coordinates to describe the problem, something that is in some sense less obvious in Newtonian mechanics because things usually become pretty hard to deal with.
Yes, every choice of coordinates is capable of describing the physics of a system. Yes, you could certainly argue that Cartesian coordinates are a natural choice or in some sense special, derivatives are especially simple and whatnot. But I still think that something is lost when one disregards rotations and angular momentum, they seem to capture an important aspect of the structure of space, its isotropy.
Then again every equivalent description should capture the same things, just maybe not in an obvious way. And then again the existence of spin angular momentum hints at the fact that there is really more to it. As I said, I am really not sure. I used to think of rotations as emergent from translations and I kind of changed my mind but I am probably still on the edge.
Suppose your object is the only thing in space, how do you tell that it is spinning? How do the particles in the object can tell that the object as a whole is spinning?
What you describe are particules going in straight lines, but over what space/grid are they going on a straight lines? If they are going over straight lines on something then your description is one of an objective space.
If pulling forces are still exerted on its edges in proportion to said "spinning", then there exist a static field in space for which the object is in static alignment when the pulling force are at minima.
Interestingly the same observation could be made of two objects in orbit or the electrons orbiting individual atoms in the object, with the static alignment being observed when the acceleration between the objects is at a maxima i.e. they are falling into one another.
They are going in straight lines in relation to the other particles in the object. Then the force of one particle exerts on another particle as they get closer or further from each other, causing them to change direction. This happens for innumerable numbers of particles, appearing like a singular object that is spinning, since the forces are too great to pull the object apart. If you spin it fast enough, the particles will overcome the atomic forces holding it together, and the object will break apart, with the individual pieces continuing to move in a straight line.
Julian Barbour's The Discovery of Dynamics goes into great detail on absolute vs. relative pre-Einstein. His The End of Time reviews the ideas at a more popular level and continues the story into the 20th C.
Do you have the paperback? If so, is it well-constructed? I'm interested, but with so many pages I'm wary of the format. I'd usually buy something like this in hardcover but the paperback's not cheap and the hardcover's far more expensive, and seemingly out of print.
I'm afraid I don't know -- I read a pdf, and a library hardback for the latter book. That one shouldn't be hard to find from a U.S. library, and would tell you whether you want to delve into the former. (Which I found really interesting, though it's maybe too ready to valorize Ptolemy just because we know so little about his predecessors.)
At human scales Matter and energy behave as if space was 3-dimensional. That does not mean space is 3-dimensional.
This may seem pedantic, but a lot of assumptions brake down when you look at tiny or high energy things. So, it's really important to mark down all your assumptions.
The mathematics that model space fit conveniently in 3 dimensions without becoming unmanageably complex.
However, by employing additional dimensions, particularly dimensions in which the basis vector multiplied by itself is a product other than itself, you can sometimes simplify the math that describes portions of the universe to a shocking extent. For instance, using geometric algebra with one dimension that squares to positive one and three that square to negative one, Maxwell's Equations reduce to "nabla field_bivector = free_space_permeability * speed_of_light * current_vector".
Sometimes, introducing special-purpose dimensions with interesting geometries and constraints upon the multidimensional representation makes certain types of math easier. For instance, conformal representation employs two dimensions that square to zero to represent the origin and infinity, and regular space is represented as a curved subset of the hyperdimensional space. Otherwise complicated operations become simpler, as a translation and rotation through dimensions that do not exist that almost coincidentally lands the result right back on the constrained hypersurface that represents 3-dimensional space.
When we invent these extra dimensions for the purposes of doing the math, we have no good way of knowing whether they are entirely imaginary or just undetectable and inaccessible to us at our current level of technology. If the universe had a round dimension with a diameter of less than the Planck distance, we would not be able to detect it, because we can't measure a distance that small. But maybe certain properties in the particle zoo can be more easily explained using an angular phase value on a tiny round dimension perpendicular to everything else.
Anthropic arguments such as this are good for examining reasons why spacetime with a different number of dimensions might not support interesting universes, but they fail to ask answer the question why we have a spacetime with 3 dimensions.
Some non-string theory attempts at formulating quantum gravity have started without an assumption of space-time and attempted to make it an emergent property, and given 3-dimensional space's quite unique properties that feels like it might ultimately be a better course of reasoning.
Couple that with Max Tegmark's ideas about multiverses. The idea is that all possible combinations of dimensions exist as a universe. We see 3+1 dimensions because this is the one combination that's most likely to develop life.
Consider the outside of a straw. The surface is a curved two-dimensional space which is bounded in one direction only by the length of the straw, but is quite small in the other (the circumference of the straw). If the straw is very long and very thin then it may appear to be essentially 1-dimensional, but the surface is still two dimensional.
Nice example. Wouldn't there be easily measurable evidence of this? Imagine a flattened caterpillar like creature living on such a straw. Unwittingly, one day it might wrap itself round the straw many times. Looking back, seeing itself turned round the straw in this way, wouldn't it see slices of itself rather than a whole?
Well, how can you go on forever without falling off the edge of the Earth? The surface of the Earth two-dimensional, and approximately flat... but there's small positive curvature, so you're continuously wrapping around to a different part of the space. The surface of the Earth can be meaningfully understood as a two-dimensional surface that possesses finite dimension.
A three-dimensional space can be close to flat but have positive curvature as well (or negative curvature, for that matter). Some proposals give our universe positive curvature, rendering its space finite, though still stupidly-big. (I'm not aware of there being a final word on the subject, though). And if different dimensions can have different curvatures, some of them could be much smaller than others.
My understanding is that we have conducted experiments to measure the curvature of the universe, and come up with answers that are withing the experimental error of being flat. Without any theoretical reason why the universe should be flat, it is still possible that the universe is curved, but to slightly for us to detect, however, but the simplest interpretation is to say that the universe is flat.
Of course, if we a assume a multiverse with universes having regularly distributed, positive curvatures, then, the size of the universe would grow asymptotically as the curvature approached flat, so, statistically, life is more more likely to arise on the flatter universes.
Is it possible, or in any way related, that a small but non-zero curvature could be responsible for the accelerated expansion of the universe? I don't know, it's hard to picture. But I'm thinking the idea that you can look at a sphere as a 2 dimensional space that curves and eventually wraps around such that things going opposite directions on its surface eventually can run into each other again.
That would probably be more easily measured though. I don't know.
A small non-zero curvature would correspond to a non-zero cosmological constant, which is precisely what seems to be driving the accelerated expansion of the universe (there are other explanations but this is the simplest one).
Infinite is a big word :) . As explained above, the extra spacial dimensions would need to be compact, which implies them being finite in size. Perhaps the simplest example of compact manifold is the circle: you can imagine one extra dimension to be closed on itself. Going around the circular dimension one circumference length, you will find yourself where you started. The size of the dimension then refers to the characteristic size of the circle, i.e. the circumference.
Space is infinite. It seems most humans cannot comprehend/accept infinity. Without understanding infinity you will have a hard time understanding space.
That is not a known fact, we have no idea whether space is finite or infinite, whether it has boundaries or not. Admittedly at least a finite universe with boundaries seems kind of a strange idea, but who knows.
A better question is: does a universe in which there is nothing (and never has been) still contain space? (Though a better question, I wrecked it by introducing "never", which presupposes that the universe has time---even though it contains nothing, and therefore no events take place.)
The question creates a bias because when we imagine matter being removed from the universe, we firstly imagine the removal as an event unfolding in time. Secondly, we continue to imagine the locations where pieces of matter used to be, and those locations continue to be separated by the abstract space which we continue to imagine.