The timeframe of the movie is the same as the TV show and is about 2259 (James T Kirk is supposed to have been born in 2233). 250 years into the future.
It has been 43 years since the show was started in 1966.
A consistent 1% per year error in a projection would be off by about a factor of 400% over 250 years.
A projection to Star Trek like future can discard all disaster and extinction scenarios and focus on relatively optimistic views of technological development. An assumption is also that space development will be chosen by society.
Note: This projection forward is not an inevitable outcome. The assumption is that the majority of people continue to work for a better future. There is a constant race and competition between advancing technology and those looking to stop or roll back technology or to bog it down with useless bureaucracy.
A starting framework is to look at some rough estimates in terms of population, economic development, energy production, computer technology and broad technological and scientific developments.
Energy Production, technological productivity and economic size and growth are all tighly interconnected. Economic growth in the developed countries over the last few decades was 90% dependent upon technology like new information technology (effective computer usage in business).
90% of economic growth is determined by productivity gains from technology.
Population growth can be projected fairly accurately out to 2050. If there is large scale colonization of the solar system and the development of mature nanofactory nanotechnology then both the population carrying capacity of the Earth and open up the capacity of the solar system. One assumption could be that population would then not need to slow from what is projected from 2009 to 2050.
Human Population in Billions
As noted a 1% lower annual population growth rate every year would lower the population projection to 22 billion and a 1% higher annual population growth rate would mean a population target of 360 billion in 2260.
As noted energy Production, technological productivity and economic size and growth are all tighly interconnected. What happens in these areas over the next 250 years will greatly determine the level of development that would exist in a Star Trek timeframe. Mexico experienced 1-2% lower annual economic growth than the USA for most of 100 years. This resulted in Mexico having a per capita income that is 4 times lower than the United States. Some African nations have 100 times lower per capita GDP than the United States. Having 2% lower economic growth every year for 200 years would produce that level of difference. The lowest income countries are in Africa and in Asia. Many of the Asian countries are now making progress out of poverty.
This site has considered a mundane singularity where existing technology and technology in today's labs are developed a mature state to boost economic size and development by 100 to 1000 times. This did not include artificial intelligence or mature nanofactory scale nanotechnology or nuclear fusion. By projecting anything beyond 100 years into the future then artificial intelligence, mature nanofactory scale nanotechnology and complete mastery of nuclear fusion should be reasonably assumed to have been fully developed.
Singularity Lite boosting of one to two levels of faster growth was detailed on this site in this article.
Mode Doubling Date Began Doubles Doubles
Grows Time (DT) To Dominate of DT of WP
---------- --------- ----------- ------ -------
Brain size 34M yrs 550M B.C. ? "~16"
Hunters 230K yrs 2000K B.C. 7.2 8.7
Farmers 860 yrs 4700 B.C. 8.1 7.5
?? 58 yrs 1730 3.9 3.2
Industry 15 yrs 1903 1.9 >6.3
Robin Hanson describes how unlimited automation would remove the limitations of human population from the growth equations.
The roadmaps to full human brain emulation would definitely be achieved within 70 years assuming something like Moore's Law increase in computer power.
Massive scale DNA nanotechnology seems to be certain within two decades.
A couple of scenarios for economic growth would then be
1. 3% annual world economic growth after the current recession with no increase at any point for 250 years. This is basically the equivalent of Star Trek Africa. No next levels of development is achieved.
2. 4% annual world economic growth after the current recession and then a shift up to 10% growth with Singularity Lite in 20 years and then 20% economic growth after a AGI, nuclear fusion and mature nanofactory nanotechnology is available in say 50 years
3. 5% annual world economic growth after the current recession and then a shift up to 20% growth with Singularity Lite in 15 years and then 50% economic growth after a AGI, nuclear fusion and mature nanofactory nanotechnology is available in 30 years.
100 Years of growth at the Above Mentioned Growth Rates
3% 18.7 times larger
4% 48 times larger
5% 125 times larger
10% 12528 times larger (China level growth rates of the last 35 years)
20% 69 million times larger (Fast growing company or mutual fund)
30% 191 billion times larger
50% 271,000 trillion times larger
At the sustained levels of 20%, 30% and 50% annual growth the civilization would progress to and exceed Kardashev Level 2, capturing and using all of the energy (or the equivalent) energy of the Sun.
As we have seen even with high growth for many years recessions and depressions can still happen. However, countries like China that are consistently growing at 10% per year seem able to bounce back faster than countries like Japan that are at low levels of growth. Also, any delay in technological progress would be delays for increasingly technologically sophisticated and economically powerful civilizations. Say in 15 years we have zettaflop supercomputers and petaflop portable devices and some fairly advanced nanotechnology, then how long would it take to find some ways to re-architect and continue technological advancement ?
Assuming no faster than light travel, expansion through the Oort comet cloud and then continuing to other solar systems at near light speed (50+% of light speed)would be a simple task for a civilization with that level of economy and energy control. So in 250 years the civilization would have a 100-200 light year in radius sphere of influence and development.
Energy and Computation
In terms of computing development, this site has considered the limits of reversible computing that are currently in development and has looked at the current development of quantum computing. All three scenarios would see a fully mature level of reversible computing and quantum computing.
A likely minimum reversible computing capability for an advanced civilization is 10**29 operations per watt. Plus that civilization definitely could have figured out more tricks to go a lot higher.
If 10**19 operations per second is a likely upper bound to simulate a human mind, then one watt could be used to simulate 10 billion human mind equivalents. This would be simulating all the minds on earth for one watt using reasonably advanced reversible computing.
A watt is one joule of energy per second.
3*10**47 joules per year for the galaxy
31, 556 ,926 seconds per year.
10*40 joules per second for the galaxy. (Note: Wikipedia has this at 10**37 watts which is also joule per second. The Wikipedia estimates are before the adjustments to the size of the Milky Way.)
The number of stars within the 100 to 200 light year radius is about 1 to 10 billion times less than the whole Milky Way Galaxy.
So 10*30 to 10*31 joules per second for the 250 year civilization. 10**59 reversible operations per second for the lower level. The 250 year civilization would have a lower end of 10**40 simulated human mind equivalents.
Without stagnation or decline the development of powerful technologies such as AGI, molecular nanotechnology and nuclear fusion and even mundane technologies of reversible computing and mass produced deep burn nuclear fission results in a very powerful and rich transhuman/posthuman civilization. Commander Data level robotics and AGI and holodecks equivalents would be trivial. Teleportation could be mimicked with high g force acceleration.
Super Telescopes Easily Within 100 Years
World imagers, Hyper telescopes and Magnetically inflated cable structures could be built over the next 20-30 years. Even without molecular nanotechnology we could have telescopes in space that are 1km-10km in size and then arrayed together. We would be able look in detail out hundreds of light years. By in detail, I mean directly imaging continents on earth like planets.
A hypertelescope would have telescopes in formation in space creating interfemetry baselines that are hundreds to millions of kilometers long. The resolution and light gathering capability of space based telescopes for a civilization with mature space capabilities even within our own solar system would be massive.
World Imager proposals discuss formation flying and the use of starshades so that planets can be observed without interference from the star that is near them.
Molecular nanotechnology enhances the above systems and we could have really big telescope arrays 5 years after the first molecular assembler. We would be able to look in detail out tens of thousands of light years. The systems would have advanced metamaterials to provide more precise focusing of light.
Telescope arrays could be placed at several dozen AU (An Astronomical Unit is the mean distance between the Earth and the Sun) and use the Sun as a gravitational lens.
The Sun's minimum focal length is computed to a refined accuracy of 23.5 ± 0.1 AU, just beyond the orbit of Uranus and other lensing points go out to 550 AU