It is thought that the universe is roughly 14 billion years old (soon) and that all matter came from a singularity (big bang). But even if we assume that all matter moved at the speed of light at some point, there simply wasnt enough time for the matter to spread over the area it is today in under 14 billion years.
I attended a talk at Bell Labs in New Jersey by Alan Guth and he mentioned the time he calculated to go from what was essentially a point size to about the size of a basketball, and I did the numbers on that and saw the size increased at a rate 22 orders of magnitude greater than the speed of light. In a question and answer period I asked him how that could be, and his answer: "You did your arithmetic right!" and went on to explain that space does not follow the same rules of velocity as matter and is not limited to the speed of light. In fact, even after 14 odd billion years the speed of expansion is still several times the speed of light. So the background radiation the satellites have measured shows the age of the universe but not its full size which is estimated at around 50 billion light years, which is the case of light just not having enough time to have reached Earth so we can only see about 14 billion light years out.
That is the usual explanation, but the relationship between inertial mass and the expansion of space still seems very curious. What aspect of empty space expansion acts on the mass to make it move? If inertial mass acceleration is only related to relative displacement from fixed coordinates in an expanding coordinate system, the concepts of inertia, force, and acceleration would seem to be less related to mass and more related to the coordinates. In other words, how is it that all inertial frames of reference are in apparent mutual relative acceleration?
I'm certainly no expert. but there is a big difference between accelerating from us and expanding from us. The space between non gravitationally bound objects is expanding from us. That does not mean they have acceleration. Merely that the space between us and them is expanding. As its an expansion its not limitted by light speed where as acceleration/velocity is.
If space is expanding it is accelerating from us... If distant objects are resting in inertial frames, and space is expanding and accelerating from us, I'm inclined to think those objects must also be accelerating from us. It is clear that the coordinates of those objects are accelerating from us, not so clear why the objects move with the coordinates rather than stay put and appear to shift coordinates towards us as the coordinate system expands. I must be missing something because if space expands, it expands at some rate of expansion; but then that magnitude rate of expansion would be measured against an expansion rate of zero, which would likewise have inertial frames distributed all over; but with zero expansion the time light took to travel from A to B would match the metric for time and distance. I guess I'm missing how assigning a rate of expansion avoids the problem of having to assign an absolute space to which the expansion rate is measured.
The term acceleration implies a force being exerted. In one sense your correct as the force would be dark energy. In the Geometric expansion the term accelerating isn't the best description as the objects are not moving, rather the spacetime geometry is changing. this is from Wiki metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself is changed. That is, a metric expansion is defined by an increase in distance between parts of the universe even without those parts "moving" anywhere. This is not the same as any usual concept of motion, or any kind of expansion of objects "outward" into other "preexisting" space, or any kind of explosion of matter which is commonly experienced on earth. Later on on the same wiki page it includes dark energy as a force. I'll post the page reference it may answer some of your questions. Keep in mind I'm definetely no expert lol. http://en.wikipedia.org/wiki/Metric_expansion_of_space here is a recent article I just happened upon. don't know its full validity but found it interesting http://phys.org/news/2013-01-dark-energy-symmetrons.html
I have non-authoritative issues with this myself by a slightly different reasoning. My issues is related to the notion of how size is defined. Consider an observer at a point of origin observing two spaceships going 3/4 c in opposite directions. We certainly don't make the mistake of assuming this means the spaceships are receding from each other at 1.5 c relative to each other. Yet, right or wrong, this is generally analogous to the assumption made when we talk about expansion. Thus even though I can't reject Guth's contention outright I'll need more than provided so far to accept the claim as authoritative.
perhaps these links decribe it better than I ever could. http://www.mso.anu.edu.au/~charley/papers/LineweaverDavisSciAm.pdf https://www.physicsforums.com/showthread.php?t=261161 the second describes the balloon analogy started by Marcus its well written. http://www.astro.ucla.edu/~wright/cosmology_faq.html#CC this tutorial covers the OP question
Yeah Wiki isn't the greatest reference lol. Think of it as the geometry between the two Large structure objects increasing rather than accelerating due to some force or exertion moving the objects apart. The Ballon analogy links should answer those questions better than Wiki
OK, I'm thinking about what increasing the geometry means... From what I gather, the expansion of space does not include the expansion of the material objects in that space, for if it did the proportion would be constant. So if space is expanding, is it the unit of measure or the number of units between the two objects that is expanding or increasing? If it means the unit of measurement is increasing in size between the two objects, then fewer units would be measured later between the "non-moving" objects and would cause the observation that the distance (measured in these increasing units) between the objects was decreasing and space was not expanding, but contracting. If it means that the number of units between the two "non-moving" objects is increasing, then the size of these units must be decreasing, which really might better be considered a contraction of space (or a contraction of the units of space - contraction of the metric) rather than an expansion. The whole idea is very peculiar - especially the way the units of space measurement are held separate from the units of measuring the size of the objects in that space. What kind of units of distance are these that apply to one but not the other? The balloon analogy to me is inadequate; the balloon is a three dimensional object, but in the analogy one is asked to consider only the surface (distances measured from one point on the surface to another by traveling the surface rather than straight through the volume of the sphere), and not consider that surface as a true three dimensional surface (sphere) but as a two dimensional analog of a three dimensional space, and to ignore the curvature. The raisins in the bread dough analogy is better in that it is three dimensional, but it still fails because the raisins are certainly accelerating apart, but the expanding space concept asks one to hold that the individual locations are "non-moving". If one seeks light speed as a guide, it seems that an expanding space where the unit size is decreasing and the number of units between "non-moving" objects is increasing would suggest that the speed of light between the two "non-moving" objects is slowing down through time if the speed of light is held to a measured constant of distance/time. It will take light increasingly longer times to cover the increasing number of units between the two "non-moving" objects. On the other hand, if the travel time of light between the two "non-moving" objects is held constant, then the expanding space in which the units are decreasing and the number of units between objects is increasing would suggest that the speed of light is actually increasing through time. The same travel time for the light will be covering increasing numbers of units in the same time period so as to make the light speed (distance/time) increase through time. Surely someone has thought about this and can clarify what I'm missing.
I understand the argument, and can make no claim that it's wrong, but the balloon analogy is useful to explain why it's logically suspect. The balloon analogy allows FTL on the basis nothing in space actually exceeds c. Yet under SR the two spaceships doing 3/4 c in opposite directions relative to a point of origin can each be defined to be at rest in space. Also the notion that nothing in space actually exceeds c under the balloon analogy is predicated on not exceeding c with respect to the space it occupies. SR doesn't define the spaceships to have any speed with respect to space either. Hence the notion that an expansion of space allows a mass to exceed c with respect to some other mass as a result of expansion is based on a suspect logic. The fundamental question, for which there is as yet no empirical answer I am aware of, is whether or not the composition law for velocities is relevant to expansion with respect to how a pair of observers measure their mutually observed velocities. Consider the following thought experiment. For a present day observer let's assume an observation horizon 14 billion light years away. For an observer passing Earth at 86% c this horizon we define will be 7 billion light years away in their relative direction of travel. The relativity of simultaneity allows a wide margin of disagreement, but it's not going to account for 7 billion years difference. Of course the problem goes away if the same horizon is in effect, but the interim space simply appears stretched to fit a different curve defined by the addition of velocities. Seems like this should be testable in some way. Perhaps using orbital velocities to see how the apparent distance of a pair of distant standard candles varies with respect to a local observer at differing relative velocities.
bahamagreen, Although some researchers investigate the idea that the speed of light changes with expansion, most still work from the assumption that the local speed of light for any observer remains constant. Under GR the speed of light is not an absolute constant, but rather a relational constant. Hence a changing speed of light could just as well be defined constant such that it was related constants that actually changed, or merely the gravitational depth of the Universe increased. In effect if the local speed of light changes then so does the local metric of space and time such that the apparent local speed of light remains constant for a local observer. This is precisely what GR prescribes under a changing gravitational depth, which is not dependent on the local value of g. If you assume that expansion can be fully modeled by a global change in gravitational depth, as defined by GR, that would indicate that expansion does not result in any effective change in distance over time, even though expansion is occurring. The redshift would still be observable due to the relativity of simultaneity, since observers are limited to speed of delays in their observations of distant objects. But we can't know that either, since we don't know enough about how nature generates a local metric of space and time I don't think anybody actually knows. It's really matter of whether the ratios of the constants change, or whether this ratio is maintained by a simple change in volume, etc. None of which happens under standard GR without the Robertson-Walker metric and its assumptions.
yes, it makes sense to me. You have to get the idea of general relativity. If you think of it the Newton/Descartes way they taught you in school then it will never make sense. You have to think about it differently. I spent so much time writing a post about this that the system timed out and threw it in the trash, so this short reply will have to do.
I'm more interested in the response of inertial mass to the expansion of space than the light effects. Light seems to operate so strangely that its properties don't surprise me so much (but still mystify me). What does surprise me is that matter responds to expanding space by moving with it... and co-accelerating with it. How is it that inertial matter would "stick" to the expanding coordinates of space rather than stay put? What does this mean for the "non-relativity" of acceleration? Why can't space expand past matter without somehow dragging it along and somehow keeping it inertial? Basically, if the inertia of mass is not intrinsic to the mass but is intrinsic to its relative position in the moving coordinates of expanding space, then I don't think inertia is well defined. In other words, how is it that two reference frames in mutual relative acceleration can both be inertial reference frames? It seems to me that as soon as one assigns expansion to space, one has implicitly defined and promoted the non-expanding space against which the expansion is defined as a kind of special absolute space. As an aside, I see lots of explanations and quotes from references around here that take the improper form "A is not A" based on the meaning of the terms. It would help a lot if when these kind of things are presented the necessary changes to the definition of the terms are included so as to not make the thing look flatly illogical on its face.
You keep thinking in terms of Inertia. Here is the problem with that thinking. In metric expansion. Only the non gravitationally bound areas are expanding. So the only thing that is changing is the distance between two large scale structures. This does not mean that the expansion is causing a force to move the large scale structure it merely increases the distance. Inertia requires a force. F=MA. In expansion the scale of space itself is increasing. For example if expansion suddenly stopped. By Newtonian laws the large scale structures should keep expanding until an opposing force stops it. We all know this isn't what will happen. The acceleration of objects moving away from each other in an expanding universe is not the sort of acceleration which can be associated with a force as in Newton's Second Law because the expansion is an intrinsic property of the way space and time are measured rather than being due to dynamical interactions. A metric defines how a distance can be measured between two nearby points in space, in terms of the coordinates of those points. A coordinate system locates points in a space (of whatever number of dimensions) by assigning unique numbers known as coordinates, to each point. The metric is then a formula which converts coordinates of two points into distances. Now thinking of metric and the above. the coordinates are not changing. The only change is the distance between two coordinates. Hence as the coordinates are not changing we state that it is not moving. As their is no force acting upon the body stating that its accelerating is misleading. as acceleration requires constant force. Unfortunately thats one of the hickups with lanquage and its restrictions on usage. They would rather see a word poorly used than a new one created lol. Hubble's Law demonstrates that the Universe is expanding in a systematic way: The further away a galaxy is from us, the faster it appears to be moving away from us. Hubble Parameter: Rate of expansion of the Universe H0 is the value of the Hubble Parameter today. Hubble's Law v = recession velocity in km/sec d = distance in Mpc H0 = expansion rate today (Hubble Parameter) The more distant a galaxy, the faster its recession velocity what is recession velocity well simply put its NOT motion through space but rather its Expansion of spacetime: galaxies carried along Hope that helps as I cannot think of any other way to answer your confusion. Hopefully others can better.