Author Topic: size of the universe  (Read 4917 times)

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Offline Undecided

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Re: size of the universe
« Reply #15 on: March 11, 2012, 11:42:11 am »
Let's say I am the omnipotent God of a giant rubber balloon and two miniature men that live on it, which I'm going to call Adam and Steve. Adam and Steve have just finished their lunch date at a fancy bistro and are now just starting their journey home. At the moment, they live in opposite directions and about 3 meters away from the restaurant. The universal speed limit that I have set on this balloon is 4 meters per hour, and so that is how fast they will travel. Normally, then, you could expect their trips home to take about 45 minutes.

Now, I'm a vengeful and homophobic God, and I've decided to punish Adam and Steve for their "infraction" by making their journey more difficult. I eventually decide on inflating the balloon at a constant rate so that its volume octuples over the course of, say, 56 minutes. That means that the distance that Adam and Steve each have to travel doubles from 3 meters to 6 meters. But the ground underneath them is expanding as they travel! Using these facts, I can show that instead of taking 45 minutes, their trips home take 56 minutes (I had to use calculus for this part). Since Adam and Steve each travelled at a constant speed, I can calculate the distance that each traversed using multiplication: (56 minutes)*(4 meters per hour)=3.73 meters.

In other words, even though the restaurant and each man's apartment are currently 6 meters apart, each man only travelled 3.73 meters. It might appear that they violated my speed limit by travelling at an average speed of (6 meters)/(56 minutes) = 6.42 meters per hour; it should have taken them 90 minutes to get home, right? But in reality, they were both following my speed limit the whole time, and most of the apparent increase in speed is due to the inflation of this balloon world of mine.

Now, Adam and Steve are dismayed by this setback to their romance, but they nevertheless plan another date, this time at another restaurant right next to the first one. I decide to destroy their future using permanent and quicker inflation of the balloon. I get my magical balloon pump and use it to double the circumference of this balloon microcosm every 30 minutes. Now, no matter what, Adam and Steve can never reach each other: once each has travelled 30 minutes, there is more distance between them than there was at the beginning of their trip. Having contented myself with dashing their hopes, I destroy their Universe with a wave of my analogy wand.


The first part of this analogy concerns "normal" inflation, where the expansion of the Universe implies that we see parts of the Universe that are farther away right now than the universals speed limit would appear to allow. The second part concerns inflation which occurs at such a fast rate that certain parts of the Universe will never be visible to each other.



edited to add:
Yla, m52 is right (although I wouldn't quite the resolution that way; I think this issue merits a double post).

The universal speed limit of relativity is just that: a universal speed limit. The time rate of change of the distance between two objects moving in opposite directions is not a speed. However, if you are moving with one of the spaceships so that it appears at rest and then measure the time rate of change of the distance between yourself and the other spaceship, then you are measuring a speed. In Newtonian theory, these two quantities have the same value, but in relativity they do not.
« Last Edit: March 11, 2012, 12:10:49 pm by Undecided »
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Offline Yla

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Re: size of the universe
« Reply #16 on: March 11, 2012, 01:03:30 pm »
In Newtonian theory, these two quantities have the same value, but in relativity they do not.
I think that was my point.

Say you have two space ships that take off in opposite directions, each travailing at the sped of light or C.  The rate at which they are moving away from each other would be 2C.
Actually, that's wrong. They distance they move apart from each other would be 1C, not 2C. Galileian laws of motion are no longer applicable at relativisitic speeds.
The only way they can beat C is by universal expansion, i.e. they move at C, and due to the expansion of space itself, the distance between them increases. Relation between distance traveled and time needed can rise above C this way.

Neither ship would be traveling at greater than C. You have to remember that C is calculated from a fixed point.  When we are looking at the rate at which the two ships are moving apart we no longer have a fixed point.

Think about it.  If the ships both traveled in opposite directions at C for on light year they would each be one light year away from the starting point, and thus two light years from each other.  Meaning that they where traveling apart at 2C. 
Again, nope. Perceived from Ship A, Ship B travels away form it at speed c.
Since they're travelling at c, Ship A only sees the light/information Ship B sent out when it was still at the starting point, and appears at rest towards a hypothetical absolute frame of reference(which doesn't exist). With A travelling at c, this comes out to an apparent velocity of c. There is no absolute frame of reference.

Last-minute edit: ...but there is the observer you're introducing to make your 2c statement. Sorry, I seemed to have misunderstood you.
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