Motion in an expanding space

Lots of people have been talking about expanding space in the enormous thread Message 315. This thread is to explore a simple puzzle about expanding spaces. The solution may help folks understand what is going on a bit better.(Percy, you are going to love this one!)As background, be aware that astronomers observe that all galaxies are moving away from us, and the further they are away the faster they move.Modern physics explains this as expanding space. For every MegaParsec of separation distance between object in deep space, we get 70 new kilometres of space every second. (Actually it is 71, but let’s use 70 to keep calculations easy.) Thus galaxies that are 30 MegaParsecs away from each other are receding from each other, on average, at 2100 km/sec. A MegaParsec is about 3*10¹⁹ kilometres.On top of that, galaxies can be moving locally through space. A galaxy moving at 300 km/sec with respect to nearby galaxies will have this velocity added on to the recession velocity due to expanding space.People sometimes think that space pulls things along with it, somehow. Let’s see.Take two particles, and hold them at exactly the same (large) separation, while space is expanding. For simplicity, let particle "A" be at rest in the frame of background radiation, and let particle "B" be one MegaParsec away. Assume that these two particles are out in deep space, in one of the great voids. That is, there are no other galaxies anywhere near these particles to push or pull them with local gravitational attractions.Space between these two particles is expanding at 70 new kilometers every second. To remain at the same separation distance, therefore, particle "B" must have a local motion of 70 km/sec towards particle "A". That is, the particles have a local velocity towards each other that exactly matches and cancels out the rate at which space is stretching between them.Now release the particles, so that they are in free fall. Will the distance between them increase, or decrease, or stay the same?I’ll give the solution, but I want to give people the chance to think about it first. This is a good way to get a feel for whether your intuitions about expanding spaces are correct, or not.Cheers — SylasThis message has been edited by Sylas, 01-28-2005 18:31 AM

Thread moved here from the Proposed New Topics forum.

As there is no friction or gravity to mess with B won’t it continue to wards A at the same rate, and the expansion will continue at the same rate because their relative separation doesn’t change. Therefore won’t A&B maintain the holding pattern?(please note I failed o level math first time round and anything to do with numbers hurts my head, more of a pictures guy)

Very good! You have got the key point, which is that expanding space does not actually pull on the particles to drag them apart.There is a bit more to say than this. In fact, I did not quite give enough information to solve the puzzle! The description you have given is correct for inflationary expansion.The rate of expansion 70 km/sec/MPsec is called the "Hubble constant". The term is misleading, because the Hubble constant is not in fact a constant at all! It is a constant value through all space, but it changes with time.That is, anywhere in the universe (as far as we can tell) which is 13.7 billion years from the singularity, like we are, will see space expanding at 70 km/sec (sticking to this rather than 71 for helping any maths when we get around to it).But what happens as time passes? In a simple zero density case, a galaxy at 1 MegaParsec distance, which is receding with the Hubble flow at 70 km/sec, will continue to recede at that same rate, even as it moves further away. So, taking a MegaParsec as 3*10¹⁹ km, then after 4.3*¹⁷ seconds, the galaxy will be 2 MegaParsecs away. This is about 14 billion years.(Does than number sound familiar? It should! It is about the age of the universe, since the time when galaxies are at zero separation distance.)At that time, the Hubble flow rate will be only 35 km/sec/MPsec. In other words, the flow rate is inversely proportional to age.Now there are a few more quibbles. A "cosmological constant" tends to maintain the Hubble flow at a fixed rate. As galaxies move further away, therefore, the rate of recession increases. In the extreme case this is what happens in so-called "inflation". If we have an inflationary expansion, so that the Hubble constant remains at 70 km/sec/MPsec indefinitely, then your answer is correct. (I think! I've only been learning about this myself quite recently.)On the other hand, gravity from mass in the universe tends to retard expansion.At present, there seems to be a small cosmological constant, but not enough for inflation, and also a small mass density which acts to retard expansion rates. So to a first approximation, we can just use the zero density model. Assume that the expansion of space is such that objects moving with the flow of expansion continue to recede at the same velocity as they move further away.Cheers -- SylasThis message has been edited by Sylas, 01-28-2005 19:39 AM

Can you recommend any good books for a layman like myself? I have been lurking on the previous thread and would like to find out more - this is most interest.

Hi Sylas,Evolution is my thang, so I'm prepared to totally misunderstand this (I already hear the whooosh of something passing overhead). But is there a point, for two given masses at a certain distance (if such a thing is sensible), where they will move closer if inside that distance, or "expand" apart if outside it (ie gravity isn't strong enough to overcome expansion)? Am I thinking in the correct context?Go easy, brother, please!Mark

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There are 10 kinds of people in this world; those that understand binary, & those that don't

Recommendations and references coming soon. First, you have to make a stab at the question. The previous posts almost give the answer, but see if you can push it a bit further.Imagine a sequence of massless particles, A, B, C, D, E, F, G, ...Right now, imagine them all in a long line, at 1 MegaParsec separation. They are all at rest in the local Hubble flow; and so there is 70 km/sec recession between A and B, B and C, C and D, and so on, due to expansion of space, but with no other local movements.Imagine that the Hubble flow is such that the separation rate of these particles remains 70 km/sec, even as they recede from each other.But we have another particle "d", which is initially at the same location as "D", and moving back towards "C" at 70/km/sec to compensate for expansion between "C" and "D". That is, (initially at least) the "C" and "d" remain at a steady 1 MegaParsec separation, and "d" is moving past "D" at 70 km/sec.What happens to "d" as lots more time passes?Cheers -- Sylas the evil instructor

There is a reason I do "soft" social sciences!!!I'll have a think over breakfast in the morning.

This appears to imply that if all galaxies from every dimension or direction from planet earth move away from earth that earth would then be at the center of the universe. Is there a fairly simple explanation for this?

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In Jehovah God's Universe, time, energy and boundless space had no beginning and will have no ending. The universe, by and through him, is, has always been and forever will be intelligently designed, changed and managed by his providence. buzsaw

yes, the balloon analogy.Take a balloon and draw lots of dots on the surface. Now blow the balloon up slowly.You will notice that as the balloon expands all the dots move apart from each other. Take any dot and each one will see that all others are moving away from it at different speeds. Yet none are the centre of this expansion.

Thanks onhai. That makes sense. Your model is 2 dimensional, but as I think about it, it would also be so from a 3 dimension model with you/me being at any area inside the balloon.

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In Jehovah God's Universe, time, energy and boundless space had no beginning and will have no ending. The universe, by and through him, is, has always been and forever will be intelligently designed, changed and managed by his providence. buzsaw

Buz,You are so ready. You've got the key points. One more step and you'll begin to understand the need for expanding space.lfen

Sylas, If light returns as a curve and the object travels in a straight line, then your galaxies are 70 km/sec/MPsec closer.If this is the case then d starting out at D will be catching C, B, & passing A. It maybe the galaxies size and distance is inflated too, if light refracts as a curve in space.

There are indeed problems with the notion of distance in general relativity; but we don’t need to go into the matter. There is a concept called proper distance in cosmology, which I am using without bothering to define it in detail. This does make sense of having masses at a certain distance, so yes, it is sensible to speak of masses at a certain distance.The expansion of the universe means that objects at a given distance will recede from each other at a rate proportional to distance. Gravity can slow the universal expansion over time, and with a very dense universe it can even eventually reverse expansion and collapse the universe (the Big Crunch). All indications are that this model is wrong; there is not enough mass to stop expansion, and in fact there seems to be another effect at work that is accelerating expansion. So no, gravity in our universe does not seem to be strong enough to overcome expansion of the whole universe.What this thread is about is the effects of additional local motions. All of the above is referring to objects that are at rest (in a sense I have not fully defined) with respect to the rest of the universe. Objects at rest in this sense see all the rest of the universe expanding away from them. Two objects at rest in this sense will recede apart from each other due to the expansion of space between them.If massive objects are close together, then gravitational attraction will make them move; they end up in an orbit. One effect of this orbit is that the objects remains close together, so gravity does overcome the expansion of space just for these two objects, by keeping them moving in space to remain in a close orbit while all the rest of the universe that is not close enough to be gravitationally bound continues to recede.This means, for example, that the solar system remains the same size even despite the expansion of space.

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PS. For other participants in this thread. Kudos to ohnhai for a good explanation of centers (Message 10), and to buz for an excellent question (Message 9) and for comprehending the answer with such rapidity (Message 11). Well done folks. Remember, you don't have to agree with all aspects of a model to understand it! Anyone who starts to understand the model is doing very well, regardless of whether you accept that it corresponds to reality.Tom, I’m sorry, but your comments in Message 13 just make no sense at all. Light does not "return in a curve". The galaxies don't get closer; they get further apart. Light does not refract as a curve in space. Galaxy size is not inflated (or at least, not by any detectable amount) because gravity holds them together even as space expands within and around them. You need to learn a lot more very basic stuff. This thread is too advanced for you at present.Cheers -- SylasPPS. I'm still learning all this as well. I have made a couple of minor errors in the thread already. Specifically, I was wrong in Message 4 with the comment about Inflation. The actual conditions for "A" and "B" in the initial post to remain at a fixed separation are apparently the Ω=0 case. The reason why is still confusing me.This message has been edited by Sylas, 01-29-2005 04:29 AM

OK. What is a "local motion"? What reference frame defines "local motion" ? I don't get this at all. It doesn't fit with how I think about space. Would you mind to help me understand? I still don't get it. What is "local velocity" ? How is that different from "velocity" ? I can understand what it means for the two particles to be in the same inertial reference frame... but I think I'm missing something basic here. Well... really, I have no frickin' idea. But, since there's no forces on either particle, and since the particles have been put in inertail motions that maintain the distance between them, then I'd have to say that nothing changes when you release them. Of course this answer was greatly assisted by reading the other posts in this thread By the way Sylas, thanks for opening this thread. I'll look forward to your comments.Ben