Warp speed is not required for Earth's population to engage in galactic colonization.
http://vimeo.com/38431018
However, according to Relativity, which doesn't say you cannot go faster than light, Einstein said material objects cannot travel AT the speed of light, it should be remembered that any attempt to go faster than light is equivalent to attempting to travel backward in time.
The good news is time travel is possible within an ergosphere of a spinning supermassive black hole, and we have such a black hole at the centre of our galaxy known as Sagittarius A*.
http://en.wikipedia.org/wiki/Sagittarius_A*
This has been known since 1936
http://www.lorentz.leidenuniv.nl/history/stockum/Proc_R_Soc_Edinb_57_135_1937.jpg
This is a special case in what was later known as a Penrose Mechanism.
In a practical sense the only thing we can dispatch at the speed of light across the galaxy with any hope of reaching Sag A* are microwaves emitted between the H and OH emissions lines using today's Radio Telescopes. If we sent a message to Sag A* there is some probability that we would receive IMMEDIATELY a response from Sag A*.
How does that work?
First, a microwave burst is sent to Sag A* from Sol. It makes its way to the spinning black hole in 25,600 years. A portion of the energy falls into the ergosphere at just the right place and at just the right angle to emerge amplified pointing back at Earth and emitted 51,200 before the original pulse arrived. The narrow band reflection through time is picked up at Earth the moment it left.
Now the gain of a large radio telescope like OSU's Big Ear or Arecibo is on the order of 68dBi to 73dBi depending on frequency used. Now while a 1 cm microwave signal leaving a 305 meter diameter dish can be focused to a beam only 8 arc seconds wide, after travelling 25,600 light years the beam is slightly more than 1 light year wide! And its energy is spread over the entire area.
Now if this seems incredibly weak, consider that the gain of Arecibo (or Big Ear when it was in operation) was quite capable of mapping hydrogen ion distribution at this distance and with this accuracy. So, when properly equipped with a narrow band analyzer like a FFT spectral analyzer used for SETI, these telescopes can easily detect a narrow band signal reflected off an object the size of Sag A* (which is the size of the ORBIT of Mercury!)
Now while one can concoct a process whereby it might be possible to get a reflection through time of a signal from Earth, how likely is it to actually occur?
Well, it may already have been done!
http://en.wikipedia.org/wiki/Wow!_signal
The WOW! Signals was received at Ohio State University's Radio Observatory in 1977, when the telescope was pointed into the vicinity of Sagittarius. What has not been widely reported is that after several days of trying to pick up the signal again students transmitted a narrow band burst in passing, which may very well have caused the original signal as a reflection in time.
There was no official record made, but I can report it anecdotal since I was there at the time;
http://www.bigear.org/JDKpassage-articles.htm#Dispatch20040723
Now, whether or not this is the explanation for Big Ear's WOW! Signal, we can say that if we are capable of structuring signals so that they can reliably arrive at times before they were sent, even a short distance in the past, we have a whole new approach to signalling and computing.
http://www.frc.ri.cmu.edu/~hpm/project.archive/general.articles/1991/TempComp.html
First and foremost, for this group, we can send remotely operated probes to the stars, and control them in real time. Even if it takes hundreds or thousands of years for a probe to reach its destination, we can still get real time data from it using this technique, even as its travelling to its destination.
As Dr. Moravec points out in the article above, sending signals through time allows us to construct goal directed programs that actually interrogate the future to determine what to do now. This makes AI much easier to achieve than present prediction by modelling.
Finally, signalling through time gives us tremendous logistical advantages. In the 1980s we had Just In Time inventory management using computing. Time travel logistics work like this. You walk into a store. You order something. They take it off the shelf because it arrived before you did. All they needed was the buyer. That is, you walk into a restaurant order a meal, and as one waitron enters your order in the computer, the other waitron takes your order to you. How did they know? Because the order was entered into a network, sent to a large Radio Telescope at 660 AU from Earth. There it was beamed around the Sun, using the Sun's gravity to focus the beam on to a precise spot at Sag A*. The signal bounces back through time and arrives before it left Earth, to arrive back at the restaurant fifteen minutes before you arrived, to be made by the chefs in the kitchen, and ready on the hot table to be delivered as you are seated.
The ability to signal through time using Sag A*'s ergosphere would make it possible to assure galactic emigres they would arrive at their destinations, since they would able to speak with themselves - within the limits of the Novikov self-consistency criteria.
Of course long-duration hibernation experiments spanning 1,000 years, would be a breeze and be capable of communicating their findings to those initially funding the research.
Thus, using laser light sails, solar pumped lasers, and suspended animation, combined with self-replicating machine systems, we have the capacity to send folks across the galaxy - 10,000 people each - around 700,000 stars all within 350 light years of Earth.
We'd first survey the stars within this radius using a telescope positioned at 660 AU from Sol, using the Sun's gravity field as a vast primary lens.
http://www.spaceroutes.com/astrocon/AstroconVTalks/Maccone-AstroconV.pdf
http://www.youtube.com/watch?v=ObvKVe5H8pc
We would then deploy space colonies first to stars 350 light years from Earth at 1/3 light speed, slowing departure speeds so that all space colonies arrive at their destinations at precisely the same galactic time - 1,000 years in the future.
Of course, all those folks, even though spread across a 700 light year region containing 700,000 star systems, using this technique could easily communicate instantly with one another. So, using tele-robotics, a person could visit via virtual presence anyone anywhere a tele-robotic system existed.
Now, what we can do today with radio waves might be done some day by high speed spacecraft. At one gee acceleration to travel 25,900 light years requires 19.755 years of ship time.
http://www.convertalot.com/relativistic_star_ship_calculator.html
The energy for each kg of mass is 1.2 trillion MJ/kg - about 13.3 x the rest mass of the vehicle. This initially is achieved by using solar pumped free electron lasers capable of any frequency up to gamma ray that is focused on a laser light sail in such a way that the frequency of 0.5 micron is maintained relative to the spacecraft, regardless of its speed relative to Earth.
Of course as it approaches Sag A* it navigates to a path through the ergosphere in such a way that it arrives back at its point of departure 39.510 years after it leaves - keeping star time equivalent to ship time - which is maintained totally by convention.
Now, slowing the spacecraft in this case is problematical. It is possible to send a 2-stage light sail, as in the case of conventional light sail star ships, and illuminate the first stage in a way that allows the first stage reflection to slow the second stage. However, doing this over 29,500 light years, without the help of a Sun's gravity lens doesn't seem easily doable.
Of course we could use the Penrose Mechanism to extract from the supermassive black hole itself structured arrays of microscopic black holes which could be engineered to decay to produce a gamma ray or better yet, a neutrino exhaust, to slow the ship at one gee over 29,500 light years, arriving back at starting point at the appropriate time.
Once we have structured arrays of microscopic black holes that we can engineer to decay - and also use to calculate with and store and process information -we can dispense with the laser light sails and solar pumped gamma ray lasers.
http://www.scientificamerican.com/article.cfm?id=black-hole-computers
Neutrino production is favoured especially in small black holes. So, the idea of creating a neutrino rocket, rather than a gamma ray rocket, isn't so far fetched.
http://arxiv.org/pdf/1001.5084.pdf
Of course, once we have a single copy of an engineered black hole array capable of accelerating payloads at high gees, and have demonstrated an ability to tap into the massenergy of Sag A* and send it anywhere in spacetime we like, we have the ability to create very capable star ships to all of humanity - giving everyone the ability to go anywhere any when they like! In fact, by travelling back in time, humanity enters parallel universes, and so, ALL multiverse becomes available.
http://www.scientificamerican.com/article.cfm?id=new-physics-complications-lend-support-to-multiverse-hypothesis
This answers the Fermi Paradox, namely, "Where are they?"
After the atomic bomb was invented it was clear, since Leo Szilard, the inventor of the nuclear fission chain reaction, promoted the use of atomic explosives first and foremost for nuclear pulse rocket technology
The answer is, with sufficiently advanced technology, all species are able not only to traverse all of space, but also all of time. So, if we look at the period of time supermassive black holes remain stable, approximately 1 trillion years, and the number of galaxies, about 176 billion, and the number of ETIs, about 70 million civilizations of about 1 trillion individuals each - we see that even in a single time line - there are very few people per galaxy.
Furthermore, when we add other time lines, we see that the universe is far larger than the people in it.
Which shouldn't be surprising.
NOTE ABOUT THE NUMBER OF ETIs.
Frank Drake estimated the number of ETIs as
Number = Rate x Fraction x Lifetime.
The way to think about this is to think about the number of lightbulbs lit versus their production rate. Say a lightbulb factory produces 100 light bulbs an hour and that they last 1,000 hours. So, there are 100,000 light bulbs lit. If ten percent the light bulbs are red and the remainder white, we can say that 10,000 of the total are red.
Now applying this to ETI we have
N = R* fp ne fl fi fc L
Where
R* is the rate of star formation.
fp is the fraction of stars with planets
ne is the number of planets that are habitable
fl is the fraction of planets that actually have life
fi is the fraction of planets that have intelligent life
fc is the fraction of planets that have communicative intelligence
L is the lifetime of that intelligence.
R* ~ 2 (for the Milky Way galaxy)
fp ~ 1 (based on recent surveys)
ne ~ 2 (based on Jupiter, Mars results)
fl ~ 1 (based on Miller Urey results)
fi ~ 1/1,000 (based on the considerations in NOTE 1)
fc ~ 1/1,000 (based on the considerations in NOTE 2)
L ~ 100 (based on considerations in NOTE 3)
NOTE 1: Life appears to have arisen almost immediately after the conditions for life arose on Earth. This result is suggested by the speed with which the Miller Urey experiment produced amino acids in a reducing atmosphere(hours). However, it took over half the history of life on Earth for multi-celled life to occur. This means it was a very difficult thing to achieve. Brains are not possible with single celled life.
NOTE 2: After multi-celled life appeared, it took half the history of life on Earth for technology to appear. This suggests that brains are as difficult to produce as brains are.
NOTE 3: Technological species grow or die. Those that grow grow far faster than exponential growth. That's because technology accelerates the rate of growth. This is known mathematically as the Dirac Delta function, that achieve infinite - or cosmic - capacity in a finite time. At our present rate of growth we will achieve cosmic capacity by 2040 AD. This is also known as a singularity. If we project our present rate of development back into the past, we can see that our present trend line started sometime 10,000 to 12,000 years ago. While we will likely be around a long time if we survive the singularity, the nature of our existence after we achieve cosmic scale capacity violates the conditions of Drakes original conditions. That is, we are communicative in the sense of Drake for only 10,000 years, and in fact we should reduce this to approximately 100 years since its about that long between the time of discovering radio telescopy (Jansky developed this in the 1930s and 40s) and the cosmic singularity we're discussing.
http://blogs.discovermagazine.com/crux/2012/10/10/how-many-galaxies-are-there-in-the-universe-the-redder-we-look-the-more-we-see/
CALCULATION
N = 2 x 1 x 2 x 1 x 1/1,000 x 1/1,000 x 100 = 4/10,000
per galaxy.
In the 100 million light years of Earth, known as the local super cluster, we have 100,000 galaxies. This would contain 40 to 50 independent civilizations in our local group.
Through the cosmos with 176 billion galaxies there are 70.4 million independent civilizations across the cosmos.
It is likely that given the nature of spacetime and the nature of technological development that the developmental trajectory of a species can be predicted by their history as they approach their singularity and so there may be a profound interest among 40 or 50 civilizations in the local group most affected by the development of a civilization a century or so before singularity is reached.
http://www.startrek.com/watch_episode/z76MVgP06P23