Statistical Mechanics of Space Travel

http://www.animations.physics.unsw.e...arth_graph.jpg

The gravitational Potential Energy of objects on Earth is given above. The wealth of a population is proportional to the energy use of that population. The distribution of wealth across each individual follows a simple distribution law, based on merit, in a meritocracy;

n = exp(-E/kW)

we also know that the total energy use adds up to a fixed amount

integral(-inf,+inf,f(E),dE) = 1

which when plotted in terms of numbers of individuals at a given rate of energy usage results in a bell shaped distribution curve around a mean, and the number attaining a specific Energy level (E1 relative to the mean E0) given by;

n1 = n0 * exp(-(E1-E0)/kW)

We can calculate also

n1 = n0 * exp(-GMh/kW)

Number of people: 7,057 millions
Number of people who have been in orbit: 533
Number of people who have been on moon: 24

Orbital Velocity: 7.9 km/sec 31.2 MJ/kg 2.65 GJ/person
Escape Velocity: 11.2 km/sec 62.4 MJ/kg 5.30 GJ/person

Post Apollo

n1/n0 = 533/7.057e+9 = exp(-2.65GJ/kW)
kW = -2.65GJ/ln(533/7.057e+9) =0.162

Apollo Era

n1/n0 = 24/7.057e+9 = exp(5.30 GJ/kW)
kW = - 5.30GJ/ln(24/7.057e9) =0.272

We should have seen something like 41,000 people projected into space and of these 2,050 of these landed on the moon. Had we never achieved the rate at which we achieved in Apollo, we would still not have gotten to the moon.

If we attained a 7% growth rate in energy use per person from 1967 through today, and attained a growing efficiency in moving people to space, trending toward 1 ppm of our total energy to placing people beyond Earth...

NOTE: A person who is free of Earth has had 5.3 GJ imparted to them. Humanity today uses 15.5 TW of power. This translates to a rate of 15.5e12/5.3e9 *1e-6*3600 = 10.5 per hour!! -- 87,660 per year leave Earth!

Now, 15.5e12 Watts divided by $72e12 obtains 0.215 W/$

A world that is 9.68x as wealthy as the world is today - around $700 trillion per year - MORE PEOPLE LEAVE EARTH THAN ARE BORN ON IT! (3% per year leave) Thus, population on Earth declines radically! Cutting in half every 18.43 years!

At a 14% economic growth rate we achieve 9.68x today's income level in 17.32 years. Then, we cut population on Earth in half in the next 18.43 years - a total of 35.75 years from today.

There is a similar calculation for 'evaporation' from the solar system as near light speed. Then, a balance of population as the 'detonation' spreads across the cosmos - and achieves a balance with growth rates due to Lorentz contraction and loss of life with flight span over time.

This explains Fermi Paradox.

In an age of rocketry a portion of the energy produced by humanity gets imparted to a number of people in such a way that they 5.3 GJ required to project a person off Earth actually takes place.

By 1975 a total of 24 persons had escaped Earth's gravity out of a total of 3.5 billions. Total energy use in 1975 was about half what it is today, 7..7 trillion watts.

This means 69.4 GJ per person per year is used on average. Taking the number of people who escaped the Earth in 1975 and dividing by the population at that time, and applying the energies involved we have;

n/N = exp(-5.3/(k*69.4))

k = 0.004

Now, just as the number of molecules leaving a liquid increases as the temperature rises, so too do the number of people leaving Earth as the energy per person rises assuming the same efficiency of application.

So, as the energy per person rises, the number of persons attaining escape increases.

Using a 1.5% per year growth in population and 4.0% per year growth in energy per person, we have;

It take 200 years under these conditions for humanity to 'evaporate' into interplanetary space;

YEAR___GJ/person__People Esc___Pop_____Pct OW__Earth Pop

1975 69.4 18 3.5 0.00% 3.5
1980 84.4 586 3.8 0.00% 3.8
1985 102.7 10,471 4.2 0.00% 4.2
1990 125.0 113,823 4.6 0.00% 4.6
1995 152.1 821,911 5.0 0.02% 5.0
2000 185.0 4,240,597 5.5 0.08% 5.5
2005 225.1 16,597,105 6.0 0.28% 6.0
2010 273.9 51,761,763 6.5 0.79% 6.5
2015 333.2 133.94 M 7.1 1.87% 7.0
2020 405.4 297.30 M 7.8 3.81% 7.5
2025 493.2 581.73 M 8.5 6.81% 8.0
2030 600.1 1.03 B 9.3 10.99% 8.3
2035 730.1 1.66 B 10.2 16.29% 8.5
2040 888.2 2.51 B 11.2 22.50% 8.6
2045 1080.7 3.58 B 12.2 29.34% 8.6
2050 1314.8 4.86 B 13.3 36.50% 8.5
2055 1599.7 6.37 B 14.6 43.68% 8.2
2060 1946.2 8.07 B 15.9 50.62% 7.9
2065 2367.9 9.96 B 17.4 57.15% 7.5
2070 2880.9 12.03 B 19.1 63.13% 7.0
2075 3505.0 14.27 B 20.8 68.52% 6.6
2080 4264.4 16.69 B 22.8 73.29% 6.1
2085 5188.3 19.29 B 24.9 77.46% 5.6
2090 6312.4 22.07 B 27.2 81.07% 5.2
2095 7680.0 25.05 B 29.8 84.15% 4.7
2100 9343.9 28.24 B 32.5 86.78% 4.3
2105 11368.2 31.67 B 35.6 89.00% 3.9
2110 13831.2 35.35 B 38.9 90.86% 3.6
2115 16827.8 39.31 B 42.5 92.43% 3.2
2120 20473.6 43.59 B 46.5 93.73% 2.9
2125 24909.2 48.20 B 50.8 94.82% 2.6
2130 30305.9 53.20 B 55.6 95.72% 2.4
2135 36871.8 58.62 B 60.8 96.47% 2.1
2140 44860.1 64.50 B 66.4 97.09% 1.9
2145 54579.2 70.90 B 72.6 97.60% 1.7
2150 66403.9 77.85 B 79.4 98.02% 1.6
2155 80790.5 85.41 B 86.8 98.37% 1.4
2160 98294.1 93.65 B 94.9 98.66% 1.3
2165 119 TJ 102.64 B 103.8 98.90% 1.1
2170 145 TJ 112.44 B 113.5 99.09% 1.0
2175 177 TJ 123.13 B 124.1 99.25% 0.9

The efficiency factor 0.004 is a function of investment in space faring technology. Over time it can be expected to rise as well, allowing more persons to escape Earth with less energy per person.

Since 1975 several things happened simultaneously;

(1) the efficiency factor dropped to roughly half the value;
(2) energy per person had remained largely constant;

as a result, we have not returned to the moon, nor are more people visiting orbit than in the past.

The powers that shouldn't be have taken the decision with the death of JFK that space travel should end as a human activity, and in fact have promoted widely the belief that such travel is merely legend and did not occur at all.

Had this not been the case there would be over 100 million people living off world and by 2060 over half the people alive would be living off world. Also, the number of people living on Earth would peak by 2060 and by 2175 the number of people living on Earth would drop to less than 1 billion!

Now these assumptions are rather modest! That is, the efficiency factor k=0.004 is assumed not to change over a 200 year period despite the fact that technology is likely to improve over this period. Also, energy per person is expected to grow at 4% which is rather modest when one considers the potential of advanced energy systems to grow at double digit rates. Finally I assume population grows at a stead 1.5% per year when rising living standards actually cause a decline (population growth stands at 1.1% today!)

Assuming no drop in reproductive rates, but a 7% growth in energy per person combined with an increase in efficiency factor from k=.004 in 1975 to k=0.010 by 2005 at a rate of increase of .0002 per year for each year over that period and no increase thereafter we have;

YEAR ENERGY PEOPLE OFF W PEOPLE PCT TOT EARTH PEOPLE

1975 69.4 18 3.5 0.00% 3.5
1980 97.3 71342 3.8 0.00% 3.8
1985 136.5 6479047 4.2 0.15% 4.2
1990 191.5 87697127 4.6 1.92% 4.5
1995 268.6 424291411 5.0 8.48% 4.6
2000 376.7 1144911451 5.5 20.94% 4.3
2005 528.3 2191803242 6.0 36.67% 3.8
2010 741.0 3195893694 6.5 48.90% 3.3
2015 1039.2 4290337621 7.1 60.05% 2.9
2020 1457.6 5430006996 7.8 69.52% 2.4
2025 2044.3 6589672506 8.5 77.16% 2.0
2030 2867.3 7761014611 9.3 83.12% 1.6
2035 4021.5 8947425587 10.2 87.65% 1.3
2040 5640.3 10159321141 11.2 91.03% 1.0
2045 7910.9 11410805544 12.2 93.52% 0.8
2050 11095.4 12717630594 13.3 95.34% 0.6
2055 15561.9 14096109079 14.6 96.65% 0.5
2060 21826.3 15562643627 15.9 97.60% 0.4
2065 30612.5 17133616955 17.4 98.28% 0.3
2070 42935.7 18825477622 19.1 98.77% 0.2
2075 60219.5 20654922059 20.8 99.12% 0.2

Here the 'evaporation' occurs much more efficiently, and the population on Earth peaks in 1995 instead of 2060 at 4.6 billions instead of 8.5 billions.. The number of people off world exceeds the number of people on Earth by 2010. By 2040 the number of people drop below 1 billions and by 2055 below 500 millions.

The next energy barrier facing the expansion of humanity is the one related to light speed. Suspended animation is already a solved problem. This means that any vehicle attaining 1/3 light speed or more can be used to travel to nearby star systems. A speed of 100,000 km/sec means that an 85 kg person must achieve a specific energy of 2.125e+17 Joules. This is 40.09 million times larger than the energy needed to escape Earth.

This means at 7% growth rate in energy per person we require 54.6 years to achieve the same evaporation conditions with respect to star travel as we did for interplanetary travel.

Over another 53 years after attaining 1/3 light speed the energy per person in motion is equal to their rest mass energy. Thus, travel beyond this period occurs at near light speed and Lorentz contraction, not suspended animation, is the primary means of time dilation.

So, if we took space travel seriously again, along with development of the human species rather than its containment, we would find the following;

2015 - start of program
2035 - population on Earth peaks
2050 - more people off world than on Earth
2069 - first travel to star system beyond Sol
2070 - fewer than 0.5 billion on Earth
2090 - population around Sol peaks
2105 - more people beyond Sol than around Sol
2122 - Lorentz dilation star travel
2125 - fewer than 0.5 billion around Sol

Beyond this point we have people flying outward from Sol at the speed of light. We have commerce between stars so there is back propagation. However, the frontier expands at the speed of light encompassing ever larger number of stars. This is very similar to an expanding shock wave. Population density drops dramatically.

Now, unlike molecules in a shock wave, the persons aboard the star ships that are the analog to molecules, reproduce as they develop the resources of each star system. They also reproduce in transit. However, reproduction slows due to suspended animation early-on, and to Lorentz dilation later. So, the stationary populations around each star system dominates in the growth of human numbers.

Countering this reproduction is a death rate. This occurs naturally, but for a space faring population death due to star ship accident predominates and scales with range of travel. This has the effect of causing a decrease of population density with range from Sol, halving the population every 200 light years to 800 light years depending on how safe star travel is. In this case 10x safer and 100x safer than, today's air travel based on hours of exposure.

The upshot is that despite very aggressive programs of interplanetary and interstellar development that are in the end highly successful in freeing humanity from the confines of Earth, total population per star system in the end is very low and remains that way, and the span of space falling under the sway of humanity is quite limited within the galaxy.

Even with star travel 1 million times safer than today's air travel since this scales with star time, not dilated time, humans would remain very rare further than 10,000 light years from Sol even under these conditions.

Now, faster than light travel is not known to exist. However, anti-matter exists, and this is also known as time-reversed matter. Real research exists into the possibility of time travel and physicists have studied the potential of navigating large ergospheres of supermassive black holes in a way that allows travel through time. Such abilities circumvent the light barrier since we can travel great distances and then return to the point in space and time that we departed from.

This technology may some day give us mastery over space and time exceeding that described here.

A statistical mechanical analysis of this more advanced form of travel shows that densities drop off even faster under these conditions and the opportunity for growth in human numbers is further reduced.

So, this method of analysis indicates an answer to the Fermi Paradox.

It may be that only insular isolated populations with no interest in space travel would be capable of achieving high deadly population densities as we have seen here.

The current approach of artificially maintaining limited populations that are isolated from space faring technology as a general feature of their culture, seems custom designed to guarantee the die off and extinction of humanity.

On Sunday, October 6, 2013 6:10:34 PM UTC-7, William Mook wrote:
In an age of rocketry a portion of the energy produced by humanity gets imparted to a number of people in such a way that they 5.3 GJ required to project a person off Earth actually takes place.



By 1975 a total of 24 persons had escaped Earth's gravity out of a total of 3.5 billions. Total energy use in 1975 was about half what it is today, 7.7 trillion watts.



This means 69.4 GJ per person per year is used on average. Taking the number of people who escaped the Earth in 1975 and dividing by the population at that time, and applying the energies involved we have;



n/N = exp(-5.3/(k*69.4))



k = 0.004



Now, just as the number of molecules leaving a liquid increases as the temperature rises, so too do the number of people leaving Earth as the energy per person rises assuming the same efficiency of application.



So, as the energy per person rises, the number of persons attaining escape increases.



Using a 1.5% per year growth in population and 4.0% per year growth in energy per person, we have;



It take 200 years under these conditions for humanity to 'evaporate' into interplanetary space;



YEAR___GJ/person__People Esc___Pop_____Pct OW__Earth Pop



1975 69.4 18 3.5 0.00% 3.5

1980 84.4 586 3.8 0.00% 3.8

1985 102.7 10,471 4.2 0.00% 4.2

1990 125.0 113,823 4.6 0.00% 4.6

1995 152.1 821,911 5.0 0.02% 5.0

2000 185.0 4,240,597 5.5 0.08% 5.5

2005 225.1 16,597,105 6.0 0.28% 6.0

2010 273.9 51,761,763 6.5 0.79% 6.5

2015 333.2 133.94 M 7.1 1.87% 7.0

2020 405.4 297.30 M 7.8 3.81% 7.5

2025 493.2 581.73 M 8.5 6.81% 8.0

2030 600.1 1.03 B 9.3 10.99% 8.3

2035 730.1 1.66 B 10.2 16.29% 8.5

2040 888.2 2.51 B 11.2 22.50% 8.6

2045 1080.7 3.58 B 12.2 29.34% 8.6

2050 1314.8 4.86 B 13.3 36.50% 8.5

2055 1599.7 6.37 B 14.6 43.68% 8.2

2060 1946.2 8.07 B 15.9 50.62% 7.9

2065 2367.9 9.96 B 17.4 57.15% 7.5

2070 2880.9 12.03 B 19.1 63.13% 7.0

2075 3505.0 14.27 B 20.8 68.52% 6.6

2080 4264.4 16.69 B 22.8 73.29% 6.1

2085 5188.3 19.29 B 24.9 77.46% 5.6

2090 6312.4 22.07 B 27.2 81.07% 5.2

2095 7680.0 25.05 B 29.8 84.15% 4.7

2100 9343.9 28.24 B 32.5 86.78% 4.3

2105 11368.2 31.67 B 35.6 89.00% 3.9

2110 13831.2 35.35 B 38.9 90.86% 3.6

2115 16827.8 39.31 B 42.5 92.43% 3.2

2120 20473.6 43.59 B 46.5 93.73% 2.9

2125 24909.2 48.20 B 50.8 94.82% 2.6

2130 30305.9 53.20 B 55.6 95.72% 2.4

2135 36871.8 58.62 B 60.8 96.47% 2.1

2140 44860.1 64.50 B 66.4 97.09% 1.9

2145 54579.2 70.90 B 72.6 97.60% 1.7

2150 66403.9 77.85 B 79.4 98.02% 1.6

2155 80790.5 85.41 B 86.8 98.37% 1.4

2160 98294.1 93.65 B 94.9 98.66% 1.3

2165 119 TJ 102.64 B 103.8 98.90% 1.1

2170 145 TJ 112.44 B 113.5 99.09% 1.0

2175 177 TJ 123.13 B 124.1 99.25% 0.9



The efficiency factor 0.004 is a function of investment in space faring technology. Over time it can be expected to rise as well, allowing more persons to escape Earth with less energy per person.



Since 1975 several things happened simultaneously;



(1) the efficiency factor dropped to roughly half the value;

(2) energy per person had remained largely constant;



as a result, we have not returned to the moon, nor are more people visiting orbit than in the past.



The powers that shouldn't be have taken the decision with the death of JFK that space travel should end as a human activity, and in fact have promoted widely the belief that such travel is merely legend and did not occur at all.



Had this not been the case there would be over 100 million people living off world and by 2060 over half the people alive would be living off world. Also, the number of people living on Earth would peak by 2060 and by 2175 the number of people living on Earth would drop to less than 1 billion!



Now these assumptions are rather modest! That is, the efficiency factor k=0.004 is assumed not to change over a 200 year period despite the fact that technology is likely to improve over this period. Also, energy per person is expected to grow at 4% which is rather modest when one considers the potential of advanced energy systems to grow at double digit rates. Finally I assume population grows at a stead 1.5% per year when rising living standards actually cause a decline (population growth stands at 1.1% today!)



Assuming no drop in reproductive rates, but a 7% growth in energy per person combined with an increase in efficiency factor from k=.004 in 1975 to k=0.010 by 2005 at a rate of increase of .0002 per year for each year over that period and no increase thereafter we have;



YEAR ENERGY PEOPLE OFF W PEOPLE PCT TOT EARTH PEOPLE



1975 69.4 18 3.5 0.00% 3.5

1980 97.3 71342 3.8 0.00% 3.8

1985 136.5 6479047 4.2 0.15% 4.2

1990 191.5 87697127 4.6 1.92% 4.5

1995 268.6 424291411 5.0 8.48% 4.6

2000 376.7 1144911451 5.5 20.94% 4.3

2005 528.3 2191803242 6.0 36.67% 3.8

2010 741.0 3195893694 6.5 48.90% 3.3

2015 1039.2 4290337621 7.1 60.05% 2.9

2020 1457.6 5430006996 7.8 69.52% 2.4

2025 2044.3 6589672506 8.5 77.16% 2.0

2030 2867.3 7761014611 9.3 83.12% 1.6

2035 4021.5 8947425587 10.2 87.65% 1.3

2040 5640.3 10159321141 11.2 91.03% 1.0

2045 7910.9 11410805544 12.2 93.52% 0.8

2050 11095.4 12717630594 13.3 95.34% 0.6

2055 15561.9 14096109079 14.6 96.65% 0.5

2060 21826.3 15562643627 15.9 97.60% 0.4

2065 30612.5 17133616955 17.4 98.28% 0.3

2070 42935.7 18825477622 19.1 98.77% 0.2

2075 60219.5 20654922059 20.8 99.12% 0.2



Here the 'evaporation' occurs much more efficiently, and the population on Earth peaks in 1995 instead of 2060 at 4.6 billions instead of 8.5 billions. The number of people off world exceeds the number of people on Earth by 2010. By 2040 the number of people drop below 1 billions and by 2055 below 500 millions.



The next energy barrier facing the expansion of humanity is the one related to light speed. Suspended animation is already a solved problem. This means that any vehicle attaining 1/3 light speed or more can be used to travel to nearby star systems. A speed of 100,000 km/sec means that an 85 kg person must achieve a specific energy of 2.125e+17 Joules. This is 40.09 million times larger than the energy needed to escape Earth.



This means at 7% growth rate in energy per person we require 54.6 years to achieve the same evaporation conditions with respect to star travel as we did for interplanetary travel.



Over another 53 years after attaining 1/3 light speed the energy per person in motion is equal to their rest mass energy. Thus, travel beyond this period occurs at near light speed and Lorentz contraction, not suspended animation, is the primary means of time dilation.



So, if we took space travel seriously again, along with development of the human species rather than its containment, we would find the following;



2015 - start of program

2035 - population on Earth peaks

2050 - more people off world than on Earth

2069 - first travel to star system beyond Sol

2070 - fewer than 0.5 billion on Earth

2090 - population around Sol peaks

2105 - more people beyond Sol than around Sol

2122 - Lorentz dilation star travel

2125 - fewer than 0.5 billion around Sol



Beyond this point we have people flying outward from Sol at the speed of light. We have commerce between stars so there is back propagation. However, the frontier expands at the speed of light encompassing ever larger number of stars. This is very similar to an expanding shock wave. Population density drops dramatically.



Now, unlike molecules in a shock wave, the persons aboard the star ships that are the analog to molecules, reproduce as they develop the resources of each star system. They also reproduce in transit. However, reproduction slows due to suspended animation early-on, and to Lorentz dilation later. So, the stationary populations around each star system dominates in the growth of human numbers.



Countering this reproduction is a death rate. This occurs naturally, but for a space faring population death due to star ship accident predominates and scales with range of travel. This has the effect of causing a decrease of population density with range from Sol, halving the population every 200 light years to 800 light years depending on how safe star travel is. In this case 10x safer and 100x safer than, today's air travel based on hours of exposure.



The upshot is that despite very aggressive programs of interplanetary and interstellar development that are in the end highly successful in freeing humanity from the confines of Earth, total population per star system in the end is very low and remains that way, and the span of space falling under the sway of humanity is quite limited within the galaxy.



Even with star travel 1 million times safer than today's air travel since this scales with star time, not dilated time, humans would remain very rare further than 10,000 light years from Sol even under these conditions.



Now, faster than light travel is not known to exist. However, anti-matter exists, and this is also known as time-reversed matter. Real research exists into the possibility of time travel and physicists have studied the potential of navigating large ergospheres of supermassive black holes in a way that allows travel through time. Such abilities circumvent the light barrier since we can travel great distances and then return to the point in space and time that we departed from.



This technology may some day give us mastery over space and time exceeding that described here.



A statistical mechanical analysis of this more advanced form of travel shows that densities drop off even faster under these conditions and the opportunity for growth in human numbers is further reduced.


So, this method of analysis indicates an answer to the Fermi Paradox.


It may be that only insular isolated populations with no interest in space travel would be capable of achieving high deadly population densities as we have seen here.


The current approach of artificially maintaining limited populations that are isolated from space faring technology as a general feature of their culture, seems custom designed to guarantee the die off and extinction of humanity.

No question that without off-world resources and obviously effective space travel capability, our planet isn't going to be sufficient for accommodating 10+ billion humans, all attempting to live large and individually standing our ground.