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Thread: Clarification needed on exactly what accelerating vs constant expansion means

  1. #1 Clarification needed on exactly what accelerating vs constant expansion means 
    Administrator KALSTER's Avatar
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    I have just finished making an arse of myself by confidently talking about expanding space, unknowingly misrepresenting how it actually works.

    I'll quote SpeedFreek's post explaining the misconception:

    Quote Originally Posted by SpeedFreek View Post
    Wow. Firstly, I had not realised the scenario was supposed to represent the expansion of the universe, and secondly, KALSTER's recent replies are actually describing accelerating expansion, rather than constant expansion.

    Firstly, we cannot use the relativistic velocity addition formula for this.

    Secondly, when cosmologists refer to constant expansion (which is the state between an accelerating and a decelerating universe), it means that objects recede at a constant speed (which is actually how zinjanthropos described the scenario), NOT that the hubble parameter remains constant. This is important, because it means that we can see galaxies who have always had recession speeds faster than light.

    Even as the expansion of the universe accelerates, the Hubble parameter is still decreasing. Confusing eh?

    All the Hubble constant represents is the average of the rate at which the universe has expanded over the age of the universe. It represents how much the universe would have had to expanded, over the past 13.7 billion years, for it to reach the size it is today. It would have had to have expanded at an average of around 70km/s/Mpc to do so.

    The thing to remember is that when cosmologists talk of constant expansion, it means that objects recede at a constant speed, and that speed increases with distance. The further away something is, the faster it recedes, and it continues to recede at that speed. More distant objects will recede at a faster but constant speed and closer objects will recede with a slower but constant speed.

    Objects only accelerate away from us in an accelerating universe (in a universe with no cosmological constant, only gravity, what is there that would make an object accelerate away from us?), and only in an accelerating universe is there a cosmic event horizon which objects pass beyond and become invisible. That horizon is not where the object recedes at the speed of light (known as the Hubble distance), it is the distance beyond that where the light from a distant event cannot make it to our Hubble distance, and it is known as the cosmological event horizon, or the light horizon.

    We can see galaxies that are, and always have been, receding faster than light, but due to the acceleration of the rate of expansion there is a limit to how far past the Hubble distance we can see an event from.

    The Hubble constant only actually remains constant during certain extreme forms of exponential expansion, like for instance the inflationary epoch or the ultimate fate of an accelerating universe.

    I am not denying the "expansion of space" can make objects accelerate away from us, I am only denying that constant expansion (the state between deceleration and acceleration) does so.

    Not such a quick question, this one.

    So, I have a few questions:

    1) The Hubble parameter gives a simple relation of what recession velocity one can expect per unit distance. So, with a constant Hubble parameter, one can choose a comoving point far distant and might observe a succession of galaxies passing that point, each having more or less the same recession velocity.

    In an accelerating universe, one would expect each successive galaxy to be moving faster relative to us and with a decelerating universe, the opposite.

    Correct?

    2) We now keep our sights on a single galaxy moving past two points separated by a parsec and with a constant Hubble parameter. At point A it will be receding at a certain velocity, but after some time it will pass point B, but will be receding at a faster rate at that distance, thus we see that particular galaxy as accelerating away from us.

    Correct?

    In the quick question thread I was trying to relate the second condition. If a galaxy passes point A at near c and reaches a recession velocity of c at point B, would it not disappear?


    All of this is with the given that once we receive the light and make the measurements of recession velocity, those measurements are taken as the recession velocity of the object an x number of years ago when the light was emitted. So, we might see a galaxy now that might have gone past the Hubble sphere in the time the light has taken to get here.



    Did I make a mistake somewhere? This is more or less how I have understood it.

    Thanks


    Last edited by KALSTER; September 21st, 2012 at 08:16 PM. Reason: typo
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    Quote Originally Posted by KALSTER View Post
    1) The Hubble parameter gives a simple relation of what recession velocity one can expect per unit distance. So, with a constant Hubble parameter, one can choose a comoving point far distant and might observe a succession of galaxies passing that point, each having more or less the same recession velocity.

    In an accelerating universe, one would expect each successive galaxy to be moving faster relative to us and with a decelerating universe, the opposite.

    Correct?
    With a constant Hubble parameter, you already have an accelerating universe.

    A constant Hubble parameter, over time, means that the distance where an object recedes at a c remains constant. Galaxies accelerate towards that distance and reach c at that distance. This is known in cosmology as exponential expansion, as the universe would scale up exponentially, continually doubling in size over the same repeating period of time. This is an accelerating universe. It is an extreme form of accelerating universe.

    It is easiest to consider the horizon itself. With constant expansion (the cosmological definition), the Hubble distance is always equal to the age of the universe, so it recedes at the speed of light, rather than remaining at a constant distance. A galaxy at the Hubble distance will remain at the Hubble distance, constantly receding at c. All galaxies recede at a constant speed, which increases with distance. The Hubble parameter is always decreasing.

    Consider the comoving view - each galaxy moves away from its neighbour at a constant speed. And so does the next one, and the next... this is where the "cumulative effect" comes from, but with constant expansion all the speeds remain constant, only the distances increase.

    So, with constant expansion, the Hubble distance recedes at c and always equals the age of the universe in light-years, and a galaxy at the Hubble distance will also recede at c and remain at that speed.

    With decelerating expansion, the Hubble distance recedes faster than c and is larger than the age of the universe in light-years. A galaxy at the Hubble distance will be decelerating in relation to us, so it comes into our Hubble sphere. All galaxies are receding from us, and their speed is larger the further away they are, but as time goes on they all slow down.

    With accelerating expansion, the Hubble distance recedes slower than c and is smaller than the age of the universe in light-years. A galaxy at the Hubble distance will be accelerating in relation to us, and it passes out of our Hubble sphere. All galaxies are receding from us, and their speed is larger the further away they are, but as time goes on they all speed up.

    With extremely accelerating expansion, the Hubble distance does not recede at all, but can remain at the same distance, or even come back towards us (which ends in a Big Rip scenario).

    Quote Originally Posted by KALSTER View Post
    2) We now keep our sights on a single galaxy moving past two points separated by a parsec and with a constant Hubble parameter. At point A it will be receding at a certain velocity, but after some time it will pass point B, but will be receding at a faster rate at that distance, thus we see that particular galaxy as accelerating away from us.

    Correct?
    Yes. The constant Hubble parameter means the galaxy is accelerating away from us, so we have accelerating expansion.

    Quote Originally Posted by KALSTER View Post
    In the quick question thread I was trying to relate the second condition. If a galaxy passes point A at near c and reaches a recession velocity of c at point B, would it not disappear?
    Yes. But only with a constant Hubble parameter, which is a state of affairs that might have occurred during the inflationary epoch, or at the end of the universe with a positive (but not increasing) cosmological constant. It doesn't apply to our actual observations of galaxies any time in between. In a (non-exponentially) accelerating universe, the galaxy does disappear, but at point C which is more distant than point B.

    Quote Originally Posted by KALSTER View Post
    All of this is with the given that once we receive the light and make the measurements of recession velocity, those measurements are taken as the recession velocity of the object an x number of years ago when the light was emitted. So, we might see a galaxy now that might have gone past the Hubble sphere in the time the light has taken to get here.
    We see galaxies that were beyond our Hubble sphere (as it was) and thus had apparently receded faster than light when the light was emitted.

    Have a good read of this (including the footnotes, where they talk specifically about how the Hubble distance relates to accelerating expansion):
    [astro-ph/0310808] Expanding Confusion: common misconceptions of cosmological horizons and the superluminal expansion of the Universe

    Exponential expansion, such as that found in inflation, has q = −1.
    Therefore the Hubble sphere is at a constant proper distance and coincident with the event horizon.
    This is also the late time asymptotic behaviour of eternally expanding FRW models with ΩΛ > 0


    Last edited by SpeedFreek; September 21st, 2012 at 09:41 PM. Reason: Added relevant quote from paper
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    Quote Originally Posted by KALSTER View Post
    I have just finished making an arse of myself by confidently talking about expanding space, unknowingly misrepresenting how it actually works.
    Not really. The principle you were trying to convey was correct, but you were unknowingly using an extreme example of expansion to illustrate it. And I think I know why...

    A lot of popular descriptions of expansion, including my own descriptions, work through the use of analogy and simplification. The balloon analogy and the raisin bread analogy are two examples. Take the example in the applet below:

    http://spiff.rit.edu/classes/phys301/lectures/expand/RaisinBread.swf

    Click on a raisin and then hit the bake button to start the expansion. Then hit the graph button periodically, to see how the distance to the raisin and the velocity increases.

    Now what that raisin bread example fails to make clear is that it does not represent the constant expansion of the universe, it represents a constant Hubble parameter - an accelerating universe! The raisins are accelerating away from each other.

    There are a lot of these kinds of descriptions around. They do convey the basic principles, but are based on an idealised case to make the numbers easier.

    I am somewhat guilty of this myself, and I reckon it was one of my earlier descriptions of expansion that might have led you to the (slightly) wrong conclusion. Here it is:

    Quote Originally Posted by SpeedFreek View Post
    Let's make a model.

    Now to model an expanding space we need to assign coordinates within that space. For the moment, forget about any edges to that space, we don't need edges, we just need coordinates in order to measure the expansion of space. Galaxies come later, so for now just imagine a 3 dimensional grid. At each grid intersection we will assign a coordinate, a point, a dot. Let's say each intersection point is 1 meter apart.

    Put yourself on a point somewhere in this space. Whatever axis you look along you see neighbouring points 1, 2, 3, 4, 5 etc meters away, receding off into the distance. Then we introduce some expansion. Let's say the space grows to 10 times its original size in 1 second! That seems fast perhaps, but this is just a model with easy numbers. The key thing to remember is that the grid expands with the space.

    So, here we are, still sitting on our point (but it could havebeen any point!) 1 second later. Now lets look along an axis. We see those neighbouring points are now 10, 20, 30, 40, 50 etc meters away. The space increased to 10 times its original size, and so did the distance between each intersection point on that grid.

    Our nearest neighbouring point has receded from 1 to 10 meters in 1 second, so it has receded at 9 meters per second. The next point away has receded from 2 to 20 meters in 1 second, so that point receded at 18 meters per second. The fifth point has moved from 5 to5 0 meters away in 1 second, so that one has receded at 45 meters per second. The further away you look, the faster a point will seem to have receded!

    And the view would be the same, whatever viewpoint you choose in the grid! There is no "centre" of expansion, no origin point within that grid - the whole thing, the whole space has expanded from something where the spaces between things were really small to something where the spaces between things are much larger. The expansion of that space has carried matter and energy along for the ride.

    Remember I said the grid of points receded off into the distance.. well a point that was initially 33,000,000 meters away will have moved away to 330,000,000 meters in 1 one second, meaning that it has receded at 300,000,000 meters per second - the speed of light! Any point initially more distant than 33,000,000 meters away from another point will have receded from that point faster than the speed of light. That is the distance were an object recedes at light speed in this "little" model of expansion. If you look at a point that has receded at the speed of light, then from that point, the point you are on has receded at the speed of light. But no object would be moving through space faster than light, no photon would ever overtake another photon, it all just gets carried along by the cosmic flow.

    Now I know this is a very simple model, dealing with a simple 10 times expansion in 1 second. This might seem very different from a universe where the rate of expansion was slowing from immense speed and then starting to accelerate, but if you start your grid very small and apply different rates of expansion to that grid, incrementally, over different lengths of time, to simulate slowing it down and then speeding it up, when you look at the end result it is essentially the same. (Whenever there is a change in the rate of expansion, it is the rate of expansion for the whole grid that changes).

    You might be asking how useful this model actually is. Well you can substitute different distance measures and time-scales if you like but the principle remains. If you sprinkle galaxies throughout the grid and then expand that grid such that the galaxies move with the expansion, you would find that galaxies interact gravitationally with their near neighbours. The further apart galaxies are when they form, the less the gravitational attraction between them. If they are less than a certain distance apart, the galaxies will move towards each other and cluster together, but if there is enough distance they will be moved apart by the expansion of the universe.

    We end up with clusters of gravitationally-bound galaxies and increasing distance between the centres of those clusters, in a universe where there is no "origin point" or centre of expansion. The whole thing was the origin point and we have no way of knowing how much larger than our observable part of it the whole thing is. We don't even know if it has an edge, and it doesn't actually need one, mathematically. It is not quite as simple as saying "if it has an overall shape, it must have a centre", unfortunately.
    In that example, which I know you read, the space expands to 10 times its size in one second, but we are looking at that expansion after it has happened and are calculating the average rate of expansion. It doesn't matter how the expansion accelerated or decelerated, as we are only looking at the end result. In the time it took a point to move from 1 to 10 metres, a more distant point moved from 5 to 50 metres. This is all okay as long as nobody infers from this that, with a constantly expanding universe, it expands another 10 times over the next second! I never said that, but I can see how it might be taken to mean that.

    What I was trying to convey is that the first point moved away at 9 m/s and the fifth moved away at 45 m/s, so the further away a point is, the faster it recedes. What I perhaps did not make clear is that, with constant expansion, the points continually move at those speeds, so it takes a lot longer than a second for the size to increase by another 10 times.

    Have a look at the graph below - it shows how the different kinds of expansion affect the average distance between galaxies.



    There might be confusion if one tries to equate this with the graph in the raisin bread applet. In the applet the vertical axis represents velocity, whereas here it represents the increase in the average distance between galaxies. With constant expansion (omega=0, or an empty universe with no gravity to cause deceleration!) that increase is linear, so the galaxies are moving apart at a constant speed.
    Last edited by SpeedFreek; September 22nd, 2012 at 07:18 AM.
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    Look at it like a matrix:

    Untitled.jpg

    With you in the center, if the yellow galaxy moves away from you at a speed of c, the green galaxy moves away from the yellow galaxy at a speed of 2c and 3c from you. Similarly, the black galaxy moves away from the opposite black galaxy at a speed of 10c. What accelerating expansion means is that the speeds I mentioned, likec, 2c, 3c and 10c increase with time. This means that, after enough time, the 2 black galaxies may be moving away from eachother at speeds defying everything we know, assuming the acceleration will continue and not stall or reverse.

    A fair theory is that our reality is a hollogram and we are sliding away from eachother on a "soapy" bubble sphere and that the acceleration is due to us moving onto a larger diameter of the sphere following the big bang until we eventually reach the equator and begin to converge again on the other side. So the dark energy driving us away may actually not exist and be of a geometrical nature. Or, that we are nailed in, not moving away but the bubble is growing.
    Last edited by Oxycodone; September 22nd, 2012 at 03:38 PM.
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    Forum Radioactive Isotope zinjanthropos's Avatar
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    SpeedFreek, you are the man. I think I'm getting it, still will take a few more reads to nail the concepts. One thing, all the different expanding universe scenarios tell me that there's no real proof of one that we can say without doubt represents the truth. From what you know, which is the most accepted?
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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    Quote Originally Posted by zinjanthropos View Post
    SpeedFreek, you are the man. I think I'm getting it, still will take a few more reads to nail the concepts. One thing, all the different expanding universe scenarios tell me that there's no real proof of one that we can say without doubt represents the truth. From what you know, which is the most accepted?
    The 2006 Shaw Prize in Astronomy and the 2011 Nobel Prize in Physics were both awarded to Saul Perlmutter, Brian P. Schmidt, and Adam G. Riess for the 1998 discovery of the accelerating expansion of the Universe through observations of distant supernovae.

    I think we pretty much know that the universe is accelerating, we are past acceptance. Soon, we will be very lonely in our galaxy. All galaxies would be stripped from the night sky and there won't be an inch of a clue left that they were ever there. I wonder how many other things like this we missed. Maybe we are more lonely than we think we are. Maybe there's nothing out here, but us.
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    Quote Originally Posted by zinjanthropos View Post
    SpeedFreek, you are the man. I think I'm getting it, still will take a few more reads to nail the concepts. One thing, all the different expanding universe scenarios tell me that there's no real proof of one that we can say without doubt represents the truth. From what you know, which is the most accepted?
    As Oxycodone has already said, it is accepted that the expansion of the universe is now accelerating.

    But one thing I would like to make clear is that it wasn't always accelerating. You mention all the different expanding universe scenarios we have been discussing (deceleration, constant or accelerating) and in fact the universe has done all of them!

    The universe started out decelerating from the incredibly fast expansion rate left over at the end of the inflationary epoch. It continued to decelerate for billions of years, until around 5 or 6 billion years ago. So, all our observations of distant galaxies are observations of a decelerating universe (and when I say "distant", I mean all redshifts from z~0.5 out to the largest redshifts we have seen so far at around z~10).

    It is easiest to quantify the redshifts at those distances, as they are dominated by the expansion of the universe, but when we look closer to home the cosmological redshift gets smaller and smaller and starts to get mixed up with the peculiar motions of the galaxies due to gravity. So, as we looked to the distant universe we could easily see it was decelerating, but measurements of the expansion become more difficult the closer to home we look.

    It was easy to understand why the expansion of the universe was decelerating - this was due to gravity slowing down the rate at which galaxies recede from each other. The question was, would the deceleration slow towards a constant speed, or slow towards a halt, or slow to a halt and then turn into a collapsing universe? This was the main question in cosmology a couple of decades ago.

    Then, in 1998, we discovered that around 5 - 6 billion years ago the deceleration had turned into an acceleration (which means it passed "momentarily" through a phase of constant expansion!). It looked as if the deceleration of the expansion was tending towards a constant speed, but instead it turned in the other direction and started to accelerate!

    That meant that there was more than just gravity affecting the rate of expansion. It meant that there was something acting against gravity, something we call dark energy, for want of a better term.
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    Even though there has been deceleration and acceleration, space has always been expanding, except now it's speeding up. Correct?

    A couple things before I get more inquisitive:

    Is the consensus that both space and matter came out of the BB at time zero to form a universe? If so then would it be logical to assume that space expanded at a rate greater or equal to c in order to accommodate the influx of matter? The reason I ask this is because space wouldn't have much of a choice to do anything else if it was to form a universe, would it? I'm imagining space more like something once compressed than say as an actual free flowing entity.
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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    Quote Originally Posted by zinjanthropos View Post
    Even though there has been deceleration and acceleration, space has always been expanding, except now it's speeding up. Correct?
    Yes, the observable universe has always been expanding, and whilst the speed it expanded was slowing down for billions of years, now it is speed up.

    Quote Originally Posted by zinjanthropos View Post
    Is the consensus that both space and matter came out of the BB at time zero to form a universe?
    That has been the working hypothesis, as General Relativity leads us towards a singularity at t=0. The general consensus however, is that we need a better theory than just GR in order to understand better the origins of the universe - a theory of quantum gravity.

    Quote Originally Posted by zinjanthropos View Post
    If so then would it be logical to assume that space expanded at a rate greater or equal to c in order to accommodate the influx of matter? The reason I ask this is because space wouldn't have much of a choice to do anything else if it was to form a universe, would it? I'm imagining space more like something once compressed than say as an actual free flowing entity.
    The mainstream view is that the universe has always been expanding at a rate greater than c, and that it still is. The question is, at what distance does a place recede at c.

    Perhaps it would be better not to ascribe too many physical properties to "expanding space", until we understand the situation better. These are the kind of assumptions that the paper "Expanding Space: the Root of all Evil?" warns us about.
    Last edited by SpeedFreek; September 24th, 2012 at 07:39 PM. Reason: noticed a typo!
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    Quote Originally Posted by SpeedFreek View Post
    Perhaps it would be better not to ascribe too many physical properties to "expanding space", until we understand the situation better.
    I better keep quiet then.

    This is the part of science I enjoy the most. Surely many people have their collective thinking caps on and it will be interesting because now we have to deal with the human element.....who will stick their neck out first or put everything on the line against mainstream science. It's obvious I really don't know much about this stuff but I will be looking forward to reading about new ideas. However this will also spawn crackpot theorists and I wonder how experts in the field deal with such people when you yourself are aware that something has to change. Sounds like fun times ahead.
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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    I wouldn't go as far as to say "something has to change" - there is nothing wrong with general relativity that we know of, except that there are certain conditions, like those at the beginning of the universe, that it does not explain.

    Just as Newtonian gravity has been shown to be only an approximation with a limited domain of applicability, I am sure the same will end up being true for GR, but we already know that the domain of applicability of GR is far wider than that of Newtonian gravity.

    As for "expanding space", the jury is still out on the mechanism, but the observational results tell us that there is definitely more than just motion through space going on.
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    Quote Originally Posted by SpeedFreek View Post
    I wouldn't go as far as to say "something has to change"
    Call it a euphemism for 'something's missing'. Thanks for all your patience.
    All that belongs to human understanding, in this deep ignorance and obscurity, is to be skeptical, or at least cautious; and not to admit of any hypothesis, whatsoever; much less, of any which is supported by no appearance of probability...Hume
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