Observable Universe and speed of light

Usually when you try and accelerate objects close to the speed of light their mass will begin to increase , making light speed almost impossible for ordinary objects . Also the energy required to accelerate an object to the speed of light would increase as the mass increases .
As already pointed out however the speed of light doesn't apply to the universe itself as a body .

Anyone have a simple answer as to why the the cosmic speed limit doesn't apply to the universe .

Panrich wrote: »

My simple question relates to two points side by side just after the big bang that are accelerating away from each other in opposite directions (forming the outer boundaries of the universe). At the speed of light, they can be no further than 28 billion light years apart now. In order to be 92 billion light years apart, they would have travelled faster than the speed of light.

animaal wrote: »

Sorry to be the "I don't know what a tracker mortgage is" guy, but I really don't understand...

If we see something that's 13 billion light years away, it means the light from it has taken 13 billion years to get to us. But 13 billion years ago, when the light was emitted by (or reflected off) that "thing", it was much closer to us (because the universe was so much smaller) - so how come the light is only getting to us now?

Obviously I just don't get it, but I'd appreciate if somebody could tell me where I'm going wrong.

Let's consider a few scenarios.

Suppose the universe is static and unchanging. Then there are no horizons because light has had an infinitely long time to reach us. However, if it is infinite in extent we have Olber's paradox and if it is finite it is unstable to gravitational collapse -- Einstein knew a static universe was problematic even before Edwin Hubble discovered the cosmological red shift.

Post Hubble, we know that the universe is expanding. Let's take a simple rubber band model of the expanding universe:



The pins in the rubber band are galaxies in space and we label them A, B, and C from left to right. Now pull the two ends of the rubber band away from each other. The galaxies move away from each other, and because the rubber stretches evenly along its length, the recession speed of any two points depends on how far apart they are: galaxies A and C recede from each other at twice the speed that either recedes from galaxy B.

Ok, suppose the picture above represents the scenario today,and that we're in galaxy A. It's possible that galaxy C is receding from us at greater than light speed, and galaxy B at sub-light speed. Assuming a constant rate of expansion, light emitted today from galaxy B must become visible to us sometime, whereas light emitted from galaxy C will never be seen. Strangely, this doesn't mean we can't see galaxy C. In the past it was closer to us, and the recession rate (which remember depends on distance) might have been lower than light speed. The distance at which the current recession speed becomes the speed of light is called the Hubble distance, and the volume it encloses is called the Hubble volume. Whether more and more galaxies are entering the Hubble volume as time goes on, or galaxies already within the Hubble volume are leaving it, depends on the expansion rate. We'll come back to this question. I am hesitant to give this link about the Hubble distance, since it claims the Hubble distance defines the edge of the visible universe, which is completely wrong, but it gives some useful introduction.

When we look at something a light year away, we see the light emitted from it a year ago. We say that the lookback time for this object is one year. Since the universe is about 13.7 billion years old, the maximum lookback time is 13.7 billion years. Light that reaches us from then has been travelling for 13.7 billion years. But it has travelled far further than 13.7 Gly. (The abbreviation Gly is often used for a billion light years). The space it has traversed has been expanding while it travelled. So to calculate the actual distance travelled we would have to chop up the path into tiny little segments and sum them all. The space traversed in the last year hasn't expanded all that much, so it only counts for about one light year. But the space traversed five billion years ago or ten billion years ago has expanded a lot since then. We have to do a bit of integral calculus along the whole path to get the overall distance. It works out that the furthest away objects we can see are at 46 Gly.

This is the present radius of the observable universe. The Hubble distance is only about 14-15 billion light years. So we can actually currently see lots of stuff that is now receding at greater than the speed of light. In that sense, the Hubble distance does not define our current cosmological horizon, which is the so-called particle horizon at 46 Gly.

Here we must correct another inaccuracy. The OP's link mentioned that "scientists might see a spot that lay 13.8 billion light-years from Earth at the time of the Big Bang". Well clearly that can't be right -- at the time of the Big Bang there was no earth, but even the point that the earth would eventually occupy wasn't 13.8 Gly from anywhere, since the universe itself was much smaller than that. I don't know if that's just a horrendous misunderstanding in the article, or whether they are talking about co-moving distance. Co-moving distance is defined so that objects moving apart with the Hubble flow (i.e. with the expansion of space) are at a constant co-moving distance. Their proper distance (i.e. the distance you would measure if you could instantaneously lay out measuring sticks along the path to them) varies with the expansion of space. The co-moving distance is defined to be equal to the proper distance today. To use our earlier rubber band analogy, we'll mark the pink backing paper in the picture with the locations of the pins in the rubber band today. The marks in the backing paper show the co-moving distance, which never changes, while the proper distance changes as the rubber band expands. Today the co-moving and proper distances to a galaxy at the current particle horizon are both 46 Gly. The co-moving distance to that galaxy has always been 46 Gly, whereas the proper distance was much smaller in the past and will be greater in future.

So now we come back to the question of what's going to happen to our cosmological horizon. We can see galaxies beyond the Hubble distance, so the implication is that they might eventually disappear, since the light leaving them now can never reach us. Except, that might not be true, because the expansion of the universe might have slowed down since the light left those distant objects. The Hubble distance expands as time goes by, since the maximum lookback time increases as the universe ages. Will this bring more galaxies into view as the expansion of the Hubble volume overtakes the expansion of the universe, or will galaxies leave the Hubble volume if the universe is expanding fast enough?

Paradoxically, the answer appears to be "both". This is because the expansion rate appears to have been changing over time. The expansion started very fast, but slowed because of the mutual gravitational attraction of the galaxies. During this phase the universe is said to have been matter dominated. However, about two billion years ago, something seems to have changed. Space itself seems to have an energy that acts like a repulsive force. Whereas the gravitational attraction between the galaxies gets weaker as the universe expands, the dark energy increases as the quantity of space increases. This means the rate of expansion has started to accelerate!

So now we have this weird situation -- when we look back to more than two billion years ago we are looking back to a time when the rate of expansion was decreasing, and new galaxies are thus appearing for the first time over our horizon. But in the future, the accelerated expansion will dominate and galaxies will start to disappear again. So there is a limit beyond the current particle horizon, called the cosmological event horizon, which is the furthest we will ever see at any time in the future. It is at a co-moving distance of about 60 Gly, although by the time it actually comes into view its proper distance will be much greater. After that time our observable universe will become emptier and emptier, until eventually there are no galaxies visible outside our local cluster in the sky.

ps200306 wrote: »

The pins in the rubber band are galaxies in space and we label them A, B, and C from left to right. Now pull the two ends of the rubber band away from each other. The galaxies move away from each other, and because the rubber stretches evenly along its length, the recession speed of any two points depends on how far apart they are: galaxies A and C recede from each other at twice the speed that either recedes from galaxy B.

Just to add one note: when we look into space, we see it expanding uniformly in all directions. This might suggest that we are at a special point, like pin B at the centre of the rubber band. But in fact, anyone anywhere in space would see the same thing, because the "rubber band" is effectively infinitely long and has no centre.

AugustusMinimus wrote: »

Added to that, objects which are past the cosmic horizon also don't exert a gravitational pull on us as gravitation also travels at the speed of light.

LeinsterDub wrote: »

This seems wrong , can anyone else confirm this?

It's correct. Gravity propagates at the speed of light. If the sun somehow instantly disappeared, we wouldn't notice for eight minutes, since both its light and its gravitational influence take eight minutes to traverse the 93 million miles between us.

So it's true that if the universe is expanding such that two points are receding from each other at greater than the speed of light, they can have no mutual gravitational attraction.

This gives rise to the so-called horizon problem -- if such regions of the universe have no radiative or gravitational connection, how come the universe is homogeneous and isotropic, i.e. looks the same on a large scale in all directions, since there is no way for things to have "smoothed out" since the Big Bang? That's the problem addressed by the theory of Cosmic Inflation.

mickmackey1 wrote: »

Because if gravity traveled at any other speed than that of light, the trajectories that are calculated for spacecraft would be wrong since they include gravitational influences that change as the spacecraft, Sun and planets change their positions.

(Admittedly I copied that from here)

I see your reference is written by an apparently bona fide "Doctor". But at the risk of appearing cocky, I remain to be convinced. First, because this fascinating article talks about how, although General Relativity was taken into account for calculating MESSENGER trajectories near the sun, it's generally not required for calculations in deep space. I'm pretty sure plain old Newtonian dynamics has been used for spacecraft trajectories in the past (except in those cases where there were special requirements, e.g. testing GR itself, or very precise timing requirements like GPS). Another interesting case is the famous Pioneer anomaly. In that case, anomalous accelerations in the two Pioneer spacecraft, although measured to exquisite precisions of billionths of a metre/sec² were unable to distinguish between GR and competing gravitational theories.

The other point is, I plain don't understand the language. Newtonian gravity has to take into account that the sun and planets change their positions. How is this a special case for GR? The force vector to the gravitating body is continually changing direction. I can see how a difference in the speed of light and the "speed of gravity" would cause the vector to point in a slightly different direction to where the the gravitating body appears to be. But he doesn't give any evidence that this is significant to the calculation of trajectories, and other references I've read suggest otherwise.

First to admit, though, I am coming from a position of ignorance.