# Questions about the accelerating universe

• serp777
In summary: The apparent velocity is simply a logical conclusion: because of acceleration, at a certain point, the distance at which the galaxy moves over a period of times is greater than light would travel normally. Since the two galaxies accelerate at the same rate, you can calculate every instantaneous position from a central reference point, and thus you know the two galaxies relative speed, which looks v>c.
serp777
Since the most distant galaxies appear to be faster than the speed of light, due to the insertion of new space, does this mean that galaxies haven't actually gained any velocity as the universe accelerates?

Usually you want to calculate velocities locally. Calculating relative velocity of something which is half way across universe will not work like you'd expect, because velocity is a vector, which lives on a curved surface. If you want to compare velocities on two different points, you have to first move them to the same point (parallel transport, if you're familiar with the jargon), and if you do this in the case of expanding universe, you find that on average, the galaxies are not moving.

Of course, nothing stops you from talking about some sort of apparent velocity, where you forget about the curvature of the universe and just calculate what you see. You just cant' expect the apparent velocity to satisfy the usual rules, like v<c.

clamtrox said:
Usually you want to calculate velocities locally. Calculating relative velocity of something which is half way across universe will not work like you'd expect, because velocity is a vector, which lives on a curved surface. If you want to compare velocities on two different points, you have to first move them to the same point (parallel transport, if you're familiar with the jargon), and if you do this in the case of expanding universe, you find that on average, the galaxies are not moving.

Of course, nothing stops you from talking about some sort of apparent velocity, where you forget about the curvature of the universe and just calculate what you see. You just cant' expect the apparent velocity to satisfy the usual rules, like v<c.

I was thinking of galaxies that are only moving away from each other in one dimension, like another galaxy at the other end of the universe moving oppositely away. The apparent velocity is simply a logical conclusion: because of acceleration, at a certain point, the distance at which the the galaxy moves over a period of times is greater than light would travel normally. Since the two galaxies accelerate at the same rate, you can calculate every instantaneous position from a central reference point, and thus you know the two galaxies relative speed, which looks v>c. Its the same way you would calculate regular speed: distance/time. However, i said apparent velocity, because if things were actually gaining kinetic energy, it would violate special relativity.

serp777 said:
The apparent velocity is simply a logical conclusion: because of acceleration, at a certain point, the distance at which the the galaxy moves over a period of times is greater than light would travel normally. Since the two galaxies accelerate at the same rate, you can calculate every instantaneous position from a central reference point, and thus you know the two galaxies relative speed, which looks v>c.

So let's take a concrete example. Suppose you're an observer on the north pole of the earth, and a car is driving at a constant velocity southwards. Now, if the surface of the Earth were a manifold, the car would always move on a straight line in it's own reference frame. But viewed from north pole, it seems that it's motion is accelerating because it's moving on a curved surface. The apparent velocity of the car changes, while physical (local) velocity remains constant.

clamtrox said:
So let's take a concrete example. Suppose you're an observer on the north pole of the earth, and a car is driving at a constant velocity southwards. Now, if the surface of the Earth were a manifold, the car would always move on a straight line in it's own reference frame. But viewed from north pole, it seems that it's motion is accelerating because it's moving on a curved surface. The apparent velocity of the car changes, while physical (local) velocity remains constant.

This makes sense, but doesn't this assume that the universe is in fact curved, and not infinite etc?

serp777 said:
This makes sense, but doesn't this assume that the universe is in fact curved, and not infinite etc?

It's just an analogy, not a model of the universe :) If you want, you can imagine the car to be driving on whatever surface you can think of and visualize. I just wanted to keep it as simple as possible. Also, the Einstein equations imply that spacetime has to be curved if there is stuff in it, so that assumption is in the end not very constraining. If the spacetime is flat, then there's no distinction with apparent and real velocities, no gravity and everything works everywhere by the rules of special relativity.

serp777 said:
Since the most distant galaxies appear to be faster than the speed of light, due to the insertion of new space, does this mean that galaxies haven't actually gained any velocity as the universe accelerates?

Google "Metric Expansion" for a full discussion.

Last edited by a moderator:

## 1. What is the accelerating universe?

The accelerating universe is a concept in cosmology that describes the expansion of the universe at an increasing rate. This is contrary to the previous belief that the expansion was slowing down due to the force of gravity.

## 2. What evidence supports the idea of an accelerating universe?

One of the main pieces of evidence for an accelerating universe is the observation of Type Ia supernovae, which are exploding stars that can be used as standard candles to measure distances. The observations of these supernovae showed that the expansion of the universe is accelerating rather than slowing down.

## 3. What is causing the acceleration of the universe?

The cause of the acceleration is still a subject of ongoing research and debate. One of the leading theories is the presence of dark energy, a mysterious force that is thought to make up about 70% of the total energy in the universe. Other theories include modifications to Einstein's theory of general relativity or the possibility of a cosmological constant.

## 4. Will the universe continue to accelerate forever?

It is currently unknown whether the acceleration will continue indefinitely or if it will eventually slow down. Some theories suggest that the acceleration may eventually stop and the universe will begin to contract, leading to a "big crunch." Other theories propose that the acceleration will continue to increase, leading to a "big rip" where the expansion of the universe becomes infinite.

## 5. How does the accelerating universe impact our understanding of the universe and its fate?

The concept of an accelerating universe has significant implications for our understanding of the universe and its fate. It suggests that the universe is expanding at an ever-increasing rate, which could lead to a very different future than previously thought. It also challenges our understanding of the fundamental forces and components of the universe, such as dark energy. Further research and observations are needed to fully understand the implications of an accelerating universe on our understanding of the cosmos.

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