Reconciling the Paradox of Age and Size in a Finite Universe

[Quincy]

If the Universe is 96 billion light years across and 13.7 billion years old, then doesn't that mean that the Universe has expanded faster than the speed of light? How can that be if speed of light is the speed limit of the Universe?

 

[DaveC426913]

I am driving between two towns 60 miles apart, traveling at 60mph - the speed limit.
This road is special - it is not fixed, it is expanding. Every moment I drive, the distance between the towns grows by 100 miles every hour.

At no time am I moving at more than 60mph, nor is any local part of the road expanding at greater than 60 mph.

 

[Quincy]

Driving from town A to town B @ constant velocity of 60 mph and the distance between town A to town B is 60 miles and is increasing 100 miles every second. Then after 1 hour, the total distance between the town would be 160 miles and you'll be somewhere in between the towns... sorry, I'm not really seeing the connection between this and my question...

 

[marcus]

This is a good example to get the idea of expansion across! The image is a good one to focus on. Have you estimated how long it will take the driver to get from Quasar to Milktown?

I am driving between two towns 60 miles apart, traveling at 60mph - the speed limit.
This road is special - it is not fixed, it is expanding. Every moment I drive, the distance between the towns grows by 100 miles every hour.

At no time am I moving at more than 60mph, nor is any local part of the road expanding at greater than 60 mph.

It is a great example! We are in Milktown and the city of Quasar is 60 miles away.
Hubble parameter is 100 mph/60 miles so Hubble radius is 36 miles.
The Hubble radius is the distance from us (Milktowners) at which a point on the road is receding at 60 mph.

At first the driver is being swept back at about 40 mph but this gradually lessens as the Hubble parameter decreases.

After one hour the driver is LESS THAN 100 MILES FROM MILKTOWN. Because he started at 60 miles and is swept back slower than 40 mph! A fair guess would be that he is actually LESS THAN 90 miles from us, because on average being swept back at considerably less than 40 mph. The figure of 40 was only right at the start of his trip.

Now after the first hour of driving, the Hubble radius is only 96 miles! So the driver is NO LONGER OUTSIDE THE HUBBLE RADIUS! Great, so he is no longer beings swept back at all. He is actually making forwards progress towards Milktown. And he will eventually get there.

If the Universe is 96 billion light years across and 13.7 billion years old, then doesn't that mean that the Universe has expanded faster than the speed of light? How can that be if speed of light is the speed limit of the Universe?

Quincy the OBSERVED universe is said to have a radius of around 47 billion LY. The socalled "particle horizon" is about 47 billion LY. We are now seeing stuff that is currently about 46 or 47 billion LY away.

That is not the size of the universe. The universe is larger. We really shouldn't say that the universe is 96 billion LY across because it confuses people. If we are talking about what has so far been observed we should say OBSERVABLE universe. Believe me I have seen people get awfully confused just because someone left off the word 'observable' and they got the wrong impression.

Large distances are permitted by Einstein's relativity to expand faster than the speed of light.

In a large universe like ours, relativity REQUIRES there be distances changing faster than the speed of light. If large distances weren't expanding FTL as they are for us, they would be contracting.

You may have gotten the wrong impression about the LOCAL SPEED LIMIT because somebody talking to you left out the word 'local'. The special relativity speed limit only applies to local motion-----shortrange distances between things in a local, approximately flat patch of space.

 

[marcus]

Driving from town A to town B @ constant velocity of 60 mph and the distance between town A to town B is 60 miles and is increasing 100 miles every second. Then after 1 hour, the total distance between the town would be 160 miles and you'll be somewhere in between the towns... sorry, I'm not really seeing the connection between this and my question...

Quincy I didn't see this when I was answering just now. Please look back at what I said to you. Maybe I didnt make things clear enough. I have to go out for now but will try again later.

Typical recession speeds are faster than light, this is allowed by relativity (you might even say required), and light has been able to get here, despite being emitted by things receding FTL. Dave was explaining how that happens.

 

[DaveC426913]

Driving from town A to town B @ constant velocity of 60 mph and the distance between town A to town B is 60 miles and is increasing 100 miles every second. Then after 1 hour, the total distance between the town would be 160 miles and you'll be somewhere in between the towns... sorry, I'm not really seeing the connection between this and my question...

The towns are now 100 miles farther apart - even though only one hour has passed.

You're asking how the country can be expanding at 100 miles per hour, when the speed limit for our cars is only 60mph.

I'm pointing out that there is a speed limit on cars (and the towns) but there's no speed limit on the rate of road expansion.

 

[Quincy]

I'm pointing out that there is a speed limit on cars (and the towns) but there's no speed limit on the rate of road expansion.

Large distances are permitted by Einstein's relativity to expand faster than the speed of light.

In a large universe like ours, relativity REQUIRES there be distances changing faster than the speed of light. If large distances weren't expanding FTL as they are for us, they would be contracting.

You may have gotten the wrong impression about the LOCAL SPEED LIMIT because somebody talking to you left out the word 'local'. The special relativity speed limit only applies to local motion-----shortrange distances between things in a local, approximately flat patch of space.

ohhh, I get it now; thanks

 

[marcus]

ohhh, I get it now; thanks

HEY GREAT! It is so wonderful when someone comes in with an open mind and a real question and we can manage to help.

Have you read this fine article in the March 2005 Scientific American called Misconceptions about the Big Bang?

there is a Princeton astronomy course for nonmajors that uses it as course reading so it is available at princeton.edu, as well as at the SciAm website.
Lineweaver and Davis' Scientific American article Misconceptions about the big bang March 2005.
AS LONG AS THIS PRINCETON LINK WORKS IT IS BETTER THAN THE OTHERS

http://www.astro.princeton.edu/~aes/AST105/Readings/misconceptionsBigBang.pdf

Here are the links to the same article at the SciAm website. But these links have been going dead or else the GRAPHICS that you used to get have been disappearing. So these SciAm links may not be as good as the Princeton one

http://www.sciam.com/article.cfm?chanID=sa006&colID=1&articleID=0009F0CA-C523-1213-852383414B7F0147

The Lineweaver Davis article had some very useful SIDEBARS giving pictorial diagrams with a question together with right and wrong answers explained. For easier access, here are links to individual sidebars.
http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p39.gif
What kind of explosion was the big bang?

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p40.gif
Can galaxies recede faster than light?

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p42.gif
Can we see galaxies receding faster than light?

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p43.gif
Why is there a cosmic redshift?

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p44.gif
How large is the observable universe?

http://www.sciam.com/media/inline/0009F0CA-C523-1213-852383414B7F0147_p45.gif
Do objects inside the universe expand, too?

Some of these sidebars are just pictures, but the pictures can be very helpful with visualizing.
If you haven't seen the Lineweaver Davis article, you might really get something out of it. If you have, let me know and I will come up with something just a tad more advanced. Like these calculators and a UCLA tutorial.

Ned Wright's cosmology tutorial
http://www.astro.ucla.edu/~wright/cosmolog.htm

Ned Wright's cosmology FAQ
http://www.astro.ucla.edu/~wright/cosmology_faq.html

Ned Wright's most basic cosmology calculator
http://www.astro.ucla.edu/~wright/CosmoCalc.html
(he has links to some more advanced or specialized calculators)

Morgan's calculator
http://www.uni.edu/morgans/ajjar/Cosmology/cosmos.html

 

[sulymani]

age of universe is millions of years no body can tell. it's like a cycle ..

 

[drewterry]

What if the concept of age was an illusion?

Everything is exactly as Einstein said it was, except at any given moment in time E=MC^2 is infinite distance in lightyears?

The infinite distance is the same thing as lightyear.

The passing of time (duration) then becomes accumulated infinite change in matter in space experienced in sequence relative to the observer.

I intend not to offend anyone, so please be reassured that I apologize in advance if I am flirting with dangerous territory.

At quantum states, if motion is nearly instantaneous, yet contained in the quantum dimension, that is infinite (time) contained within a finite singularity?