Hans

Assume we have an accurate Hubble's Constant and infer from that constant that the fictional quasar "X" is 10 billion light years from our location.

If I understand my physics correctly (subject to debate of course), then we must argue that 10 billion years ago quasar X was at a distance of 10 billion light years from us.

Also, If I'm correct we must also assume that the universe is at least 10 billion years old because it took 10 billion years for the light from quasar X to reach us.

Now if I understand my sequence of events correctly we have: a) The big bang. b) The time it took quasar X and ourselves to be separated by a distance of 10 billion light years. And c) 10 billion years for the light from quasar X to reach us.

Finally, if I understand relativity correctly (also subject to debate) no object can move at a speed greater than the speed of light in a vacuum relative to another object (or is that just can't be "observed" to travel faster than the speed of light?). If so, then we must assume that the time it took quasar X and ourselves to be separated by a distance of 10 billion light years is somewhere greater than 10 billion years.

If I'm correct then must we not assume under the big bang model that the universe's age in years is at a minimum greater than double the distance in light years of the furthest object we can observe?

Bluenose

Hi Hans, What you just posted is the "horizon problem" which led to Guth et al postulating "inflation" to get around the simple math of signal time + separation time argument. The beauty of the inflationary models is that they avoid this little bind by requiring that quasar to have never been close enough to us until now for the light (emr) to reach us. OTOH If we could have seen that quasar a 100 million years ago, it might show a very different energy output and spectrum and appear to be 9.9 billion light years away and very different... I may have not have said it as well as the prople who write the books, but that's why I'm not a writer or frequent poster.

Hans

Bluenose,

I found an Alan Guth of MIT who describs an infationary model here:

<a href="http://www.physics.sunysb.edu/itp/OWP/talks/aguth/Guth.pdf" target="_blank">http://www.physics.sunysb.edu/itp/OWP/talks/aguth/Guth.pdf</a>

In the document on pages 3 and 4 I find the following:
In summary, inflation, according to the theory, started and ended near the very beginning of the big bang and ended at a time when the universe was about the size of a marble. Then standard big bang evolution prevailed. Is this the same Guth you refered to? If so is there something left out of the description that is offered in the document?

If they argued that inflation expanded the universe to a size that is say billions of times the size of the observable universe then I could see where attempts at placing a minimum age to the universe via observed distances would be nill. But the theory doesn't seem to offer that.

The Lone Ranger

This might seem strange at first, but keep in mind that space itself is expanding, at least in a sense. I'd have to go back and read up some more on the topic well, but Lawrence Krauss, among others has explained it this way.

During an early "inflationary" period in the universe's history, it was probably expanding faster than the speed of light -- that is, space itself was expanding faster than light. While no physical object can move at FTL speed, there's no reason that space cannot expand at FTL speed.

Think of it this way:
Suppose that I'm in a starship, and 1 light year from Earth. Theoretically, it would take at least a year to reach Earth from this position, but suppose I fire up the "warp engines" and using unimaginably vast amounts of energy, I compress the space between me and Earth. In theory, this could be done, if enough energy were available. So, after performing my "space warp", I suddenly find myself just a few million miles from Earth, though only a few minutes' time has passed.

Here's the kicker. Technically, my ship hasn't moved at all; I've simply used its engines to shorten the distance between Earth and where it originally was. To an outside observer, it would look like my ship was travelling at FTL speeds, but in fact it never did.

***

Anyway, it may well be that because the universe itself is expanding, including the space/time matrix that it is embedded in, under certain circumstances some sufficiently-distant objects might appear to be moving away from us at FTL speeds, or to have been doing so in the past.

Krauss' The Physics of Star Trek provides a much better explanation than I just did.

Cheers,

Michael

Bluenose

AAAA Yes, author of "The Inflationary Universe" 1997, maybe still in print. It's forward is by Alan Lightman the author of "Origins" 1990 which is a series of interviews of scientists discussing cosmology.

Bluenose

OK, let's go back to the original problem with a little old math class mental exercise. IF we look at the universe as a 3d circle (sphere) we can illustrate the problem on 2d graphpaper using standard x and y axes with our quasar Q traveling to the right and US traveling to the left of the big bang at zero. The distance between US and Q is 10 gly but that leaves both at only 5 gly from the BB at zero. This works only if both moved at 1/2 c......BUT we don't know the ratio of proper motion to the appearance of Hubble expansion which can approach c at the greatest distance. This example illustrates a model universe of "us" and only one other light source Q.....Does this help muddy the water? I was hoping one of our more articulate folks would post so I wouldn't have to, but cosmology has been near the top of my short favorite book list for a long time.

Hans

The Lone Ranger,

The infationary model successfully reduces separation time. But Signal Time + Separation Time would still apply, only seperation time would be smaller.

It would seem to look something like this:

Signal Time + Separation Time + Inflation Time = Age of Universe
Where separation time is the observed Hubble's Constant

The infationary model offered by Alan Guth suggests the infationary period lasted for only a miniscule fraction of a second and encompassed a distance of less than that of a marble. Given the scale of billions of trillions of miles and billions of years, the inflationary period can be ignored when making an approximate date of the big bang.

Friar Bellows

OK.

No. The redshift doesn't measure a Doppler effect. It measures the expansion of space during the entire period between the emission and reception of light. So when we receive a photon whose redshift implies a distance of 10 billion light years, we're talking about the distance NOW.

If you're worried about how in a 15 billion year old universe we can see objects (say) 30 billion light years away, the explanation is simple. The photon didn't travel 30 billion light years. It travelled no more than 15 billion light years (probably less). But space EXPANDED during the course of the trip.

The expansion of space is not bounded by the speed of light limit. The cosmological distances and times you are talking about do not correspond to those used in the equations of special relativity. In fact, there are quite a few "distances" we use in cosmology. They are described <a href="http://www.astro.ucla.edu/~wright/cosmology_faq.html#ct2" target="_blank">here</a>, <a href="http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD" target="_blank">here</a>, and <a href="http://www.astro.ucla.edu/~wright/CosmoCalc.html" target="_blank">here</a>.

Hans

Friar:

Thank you. I'll spend some time digesting the links you provide for sure.