I think the overpopulation topic is becoming a bit absurd, so let’s talk about the other issue touched upon in that thread, interstellar travel. The process of doing this would be quite tricky and tremendously expensive. If given enough resources, it would probably be feasible. The trouble comes with the following:
We will be referring to this diagram a lot. On the y-axis is the gamma factor, also called the Lorentz factor. It is defined in the following way:
For a spaceship moving away from Earth in an arbitrary vertice of direction when we refer to gamma henceforth, we will be discussing gamma of the spaceship as recorded in the Earth’s frame. There are several key assumptions which we need to consider here. The first and most important is that the destination star system does not move relative to the Earth. This is roughly true.
The trick with travel to faraway systems is that we must get the spaceship gamma in the Earth frame as high as possible because that way the length contraction measured by the spaceship in comparison to the Earth observers will be as high as possible and consequently, as far as the spaceship is concerned, the time taken to travel to the destination will be much less than that recorded by the Earth. However, since we are considering two reference frames, we must be precise about this. If the spaceship travels to a distant planet/star system, then the spaceship is measuring the proper time between the events because as far as the spaceship is concerned, the events “leaving Earth” and “arriving at the new planet” occur at the same point in space. As per the first postulate of special relativity, no inertial frame is more valid than any other and consequently, if the Earth observer states that the spaceship moves away at velocity v, relative to Earth, the spaceship observer is just as correct to say that Earth hurtles away from them at velocity v and the destination travels toward them at velocity v and they themselves have not moved. This is the tricky part not just about Relativity, but mechanics in general. Absolute space is completely meaningless. When we talk about “velocity” all we are saying is that an observer is measuring a certain object in his local coordinate system as changing coordinates over time. In special relativity, it becomes just as meaningless to assert that if the time between events A and B takes time t in reference frame A then it will in reference frame B. The same must consequently hold true for the rod-like distance between points in space. When we say “Betelgeuse is 780 light years away” what we really mean is that if an Earth observer had a giant ruler which started at Earth and ended at Betelgeuse, the Earth observers would state that the distance between the ends was 780 light years. The Earth measures proper length. This cannot be the case for any observer which is moving relative to the Earth frame since that would violate the second principle of special relativity. Consequently when we talk about stellar distances we will be making frame distinguishing from now on.
The reason this is important is because if we could get a spaceship to travel at 0.999c (exactly 0.999c, this is very important since gamma tends to infinity as v tends to c), then the gamma factor will be 22.4. This could be a good thing. If we wanted to travel to a planet that was 500 light years away in the Earth frame, then at 0.999c in the Earth frame, it would take 500.5 years in the Earth frame. However, in the spaceship frame, the destination planet (which is travelling toward them at 0.999c) is not 500 light years away, because the Lorentz factor contracts the rod like distance in their frame (this is important, it is meaningless to talk about space-like separation without reference to frame), as far as the planet is only (500/22.4)=22.3 light years away. Consequently, they state that the journey takes just over 22.3 years. The other way to look at this is from the Earth frame. The spaceship measures proper time, so the Earth measures dilated time. Since we have just stated the proper time interval to be 22.3 years, it follows that the dilated interval is 500.5 years since the Lorentz factor is the transform for both quantities.
So, this would appear to be no problem. If we found a close terrestrial planet at 20 light years away then at 0.999c in the Earth frame, a spaceship could get there in about 10 months as far as they were concerned. This would be good because then we would have to stock fewer provisions on the spaceship and consequently it would be less massive.
This is sort of important because this is where the major limitation comes in. As a consequence of the mass energy equivalence, the gamma factor dilates mass of an object relative to the rest frame of THAT object. The total energy of an object in an arbitrary frame is therefore the sum of the rest energy (intrinsic quantity of the object under discussion) and the kinetic energy (depends on the frame):
Here, m0 is the rest mass. From above, we have mframe= γm0 where gamma is as recorded for that object in the frame under discussion
The total energy recorded in an arbitrary frame of reference in which the speed of the object is recorded to be v is therefore:
Et= γ m0c2
Ek=( γ-1) m0c2
This is where it gets a little tricky. We have a trade off here. We must have a high gamma factor so that the time taken to travel to a distant star is short in the spaceship frame of reference. This in turn implies fewer provisions need to be stocked. But it also implies that the m in the Earth frame is larger and consequently more fuel is required. In non-relativistic analysis, we would start with the rocket equation which is given as follows:
Vrocket (Earth frame) = vexhaust (rocket frame) [ln(mtotal/mempty rocket]
The quantity mempty rocket is the total mass of the rocket when it is unfuelled. It is assumed that all the fuel is used to accelerate the rocket to the maximum velocity (we would obviously have to take into account the fact that the rocket has to decelerate when it reaches the destination). This works because once the rocket reaches a maximum velocity, it no longer needs fuel to continue travelling through frictionless space at this constant velocity, as per Newton’s first law. This still holds in special relativity (not in General, though since objects follow the geosidics of warped space-time). However, every instance of m must be dilated by a factor of gamma in this case. We need to accelerate the rocket to this maximum velocity and it is this acceleration that requires the fuel. This is the hard part. It is very, very difficult to get a rocket accelerated to that close to c because a high gamma factor implies a higher mass in the Earth frame and consequently more energy required to accelerate the rocket. There are several prerequisites which would have to be in place to achieve something like this. First (obviously) the rocket would have to be assembled far above Earth in orbit. No project would be feasible without this. It’s hard enough to accelerate a rocket to 0.999c let alone with escape velocity of a gravitational potential well to cope with.
Also, if we were travelling to very distant stars then once the initial colonizers had travelled sufficiently far they would be more or less isolated entirely. A beginning student of Relativity would say something like “by the time the rocket reaches the new planet, everyone on board has aged very little even if everyone on Earth is dead”. This is in fact completely meaningless. We cannot compare the time coordinate of two events in two frames of reference in Relativity. The start of the sentence above, "by the time" is meaningful only in the reference frame of the spaceship. If the people on Earth sent a light signal back to Earth to say that they had arrived, then even though as far as the observers on the ship were concerned, this journey only took 20 years for a 500 light year (in the Earth frame) journey, the Earth observers will receive the signal 1000 years (in their frame) after they recorded the spaceship leave.
"Physical reality” isn’t some arbitrary demarcation. It is defined in terms of what we can systematically investigate, directly or not, by means of our senses. It is preposterous to assert that the process of systematic scientific reasoning arbitrarily excludes “non-physical explanations” because the very notion of “non-physical explanation” is contradictory.