Why Understanding Space Is So Hard
nautil.us
nautil.us
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.
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.
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".
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?
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.
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.
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.
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.
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.
Mind you, I'm not arguing that space doesn't exist, only that Newton's argument is flawed.
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.
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.
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.
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 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.
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.
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.)
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.
This would also be true of any system such that the size is large enough to render the quantum spins statistically close to zero.
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.
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.
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.
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.
http://www.reddit.com/r/askscience/comments/42u57e/how_can_a...
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.
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.
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).
/s ;-)