That’s an interesting twist on Olbers’ paradox, but there are a few flaws in the logic, or rather, the underlying assumptions. First of all, even assuming that space is really, really big (effectively infinite as far as the statistics are concerned), there still has to be a starting point for this technological singularity that gives rise to an superluminal propulsion system. It is possible that no hypothetical civilization has yet reached this point, or even if they’d discovered a working principle, has been able to harness a sufficient power source yet to make it work; we might as well be the first. Another issue is that even if such a system has been developed, assuming a finite speed the civilization can only expand at a linear rate; in an infinite space even a large number of nuclei for this development will only occupy infinitesimal regions; in a finite but vast space the rate of expansion is proportional to the ratio between propagation speed and the size of the universe, multiplied by the number of non-overlapping spheres of exploration. We can’t speak to the odds of developing conceptual intelligence sufficient to do this, but we know that the probability of arbitrarily repeating specific watershed events in our own evolutionary development are very unlikely; we can assume that intelligent life as we would recognize it is likely very sparse. It may also be that some civilization has developed FTL capability and then abandoned it for an entirely different avenue of exploration and self-preservation of species; instead of “going boldly where no Qualarian has gone before” they might have delved into “exploring” the basic medium of space itself or some equally esoteric line of exploration. And its even possible that what you suggest, but their probes are benign, invisible, incredibly vast, or in the case of self-organizing systems made from non-fermionic matter, we may not even notice that they’re around. We do not usually notice bacteria, and they certainly don’t perceive us in any conceptual fashion. Perhaps, as hard sci-fi author Stephen Baxter suggests, cosmic artifacts like The Great Attractor are actually constructs by some universe-dominating species so advanced it considers humanity to be less than a gnat.
The latter, as far as we know. The rate may have varied with time, as well; we can only make tenuous inferences about the past from spectral data, which is a bit like driving the Pacific Coast Highway on a moonless night without headlights.
I knew that, but somehow it never occurred to me that having celestial bodies moving away at a higher velocity the longer away they were was completely at odd with the concept of an uniform expansion rate. I would have been perfectly able to talk about the red shift and then add that the universe was expanding at the speed of light. I’m completely baffled that I’ve been been able to “compartmentalize” what I knew or believed to know in this way.
I always thought that the relative velocities would have the speed of light as an upper limit.
And actually I still don’t understand how say, two galaxies, can move relatively to each other, at a speed higher than c. Why doesn’t this contradict the theory of relativity?
The galaxies may themselves be in an inertial (i.e. unaccelerated) reference frame, but the spacetime between them is expanding. Since the plenum of spacetime is not “stuff” (we don’t actually know what it is; Special and General Relativity just describe its emergent properties, not its inherent makeup) it can expand at any rate one chooses, including at intervals for which the displacement exceeds c.
I still don’t understand. I’m referring to the galaxies themselves, not space. Those that are beyond the “horizon” would be moving away at a speed higher than c relative to us. Why is that not contradicting the theory of relativity?
I think it would be a better idea to start dumping money into the laps of the math people rather than the rocket people. 15 light years is too far away for any fueled craft to ever reach.
The real question is: what if this planet is inhabited by humaniod lifeforms who are infinately advanced and infinately benevolant, beings with intellegence far beyond what we can even conceive of, and yet they taste like bacon? How long before extinction sets in?
Because the galaxies themselves are not in accelerated motion; the space between them is just expanding. General Relativity only places constraints on how much an object can be accelerated within a reference frame or between causally connected reference frames, but its description of the plenum in which they’re embedded is strictly arbitrary.
Consider this: going back to Sam’s balloon analogy, we can place a couple of ants on the surface. The ants can only walk at a maximum rate, s. However, the balloon itself can expand at any rate of inflation (i.e. the rate at which the radius of the balloon increases) we can sustain, irrespective of the walking speed of the ants. So even if the ants aren’t in motion (relative to their individual patches of real estate on the surface of the balloon) they’ll be moving away from one another, and the more distant they are the faster that rate is. If the rate exceeds s, the ants can never meet, no matter how fast they walk toward each other; in fact, they’ll find that if the rate of inflation is even slightly increasing over time, they’ll continue to get further and further away from one another even going at one another at maximum walking speed, and eventually, they’ll each disappear over the others’ horizon, never to meet again. (The last is a bit of a cheat because we’ve asserted that there is no “up” direction in our balloonoverse and therefore no angle to the horizon, but you get the idea.)
The space between galaxies, and therefore the interval over which emitted light must travel, is increasing to the point that light can never catch up. It’s a bit like Zeno’s paradox of Achilles and the tortoise, except it is the space between them that keeps doubling (giving rise to an infinite divergent series) rather than an a geometric infinite halving of distance (which is actually a convergent series, and so not a paradox).
Does that make it as clear as a Halliburton accounting statement?
Yes, but then, doesn’t this apply equally to any kind of deformation of space, like those caused by a massive object or a black hole? If this is the case, shouldn’t we be able in some instances (I don’t know which ones) to observe light (or something else) moving at an apparent speed different from c, or even greater than c?
Or for that matter, if something is moving at light speed somewhere, say on Mars, shouldn’t it look like it’s moving at a speed higher than c because space is expanding?
It’s probably not very clear and/or doesn’t make much sense the way I’m putting it, but if the expansion of the universe/ the deformation of space is irrelevant re. the theory of relativity (or re. any other physical law for that matter) it seems to me that there should be an observable difference between the theoretical behaviour of matter, particles, etc… in a non expanding universe and their observed behaviour in our expanding universe.
I hope you’ll somehow understand what I mean…
True, and you’re right that I’m making some assumptions. One is that the rate at which technology expands operates on a different scale than other processes - that once it begins it rapidly increases until it hits its limits. That might be an unfair assumption, but it seems reasonable given the speed at which we’ve seen our technology grow from nothing to being able to send spaceships out of our solar system, compared to the pace of evolution and star formation/death.
In other words, even if a civilization developed a mere hundred thousand years before us, it would have FTL travel if such a thing were possible. But it’s always possible that the rapid rate of technological expansion is an illusion because we’re currently only in the very steepest part of the curve. Maybe we’ll hit some limits that will hold us close to our current rate of development for a hundred thousand years.
This is a good point - FTL travel isn’t necessarily ‘infinite speed’. I suppose if the best they could do is twice the speed of light then it just produces a ‘travel sphere’ twice the size of the light sphere, which doesn’t really change much.
Cosmologist Max Tegmark of MIT has actually done the calculation for the distance required before you find another Hubble volume identical to ours, given an isotropic universe and a chaotic inflation at the beginning. The number he came up with is 10^(10^118) meters, which is a huge number, but not infinite. If the universe is infinite, an infinite number of identical volumes would exist - and volumes representing every other possible combination of starting conditions and divergences).
But the point is that if the universe is truly infinite, ALL of these will have happened, an infinite number of times. So either the universe is small enough that it’s highly unlikely that any of this happened, or FTL travel is possible, but still slow enough that the probabily of any FTL-capable civilization being close enough to us is still small.
Either way, an infinite universe in which we are still alone in our own hubble volume implies that instantaneous travel is not possible, and the implications of Tegmark’s calculation indicates that if FTL travel is possible, it’s slow enough that a distance like 10^(10^118) meters is still far, far beyond the ability of such craft to travel within maybe a few billion years time (assuming that conditions in the universe did not allow for intelligent life until a few generations of stars had come and gone).
Of course, that number is for an identical hubble volume. The number gets far, far smaller if you consider the volumes which are fairly similar, the ones which aren’t similar at all but lead to the same result (i.e. there are still humanoids, but the configurations of stars and planets and other elements of the universe are completely different)
Nope. Light always moves at c, putting it under acceleration (or apparent acceleration) merely causes a Doppler shift in frequency. (This is a painful and difficult concept for most people to grasp; light is the measuring stick of distance in spacetime because its speed is always invariant in all reference frames.) If the intervening space expands or is stretched, however, the distance that light has to travel is longer, and thus the interval is greater. We can, in fact, see this locally (in our solar system) by gravitational lensing, where light takes a path that is not a straight line in Euclidean space, so it takes a little longer than it ought. When light gets accelerated away from the observer enough that it can no longer keep up, it just redshifts down to unobservability, with a wavelength so vast that it can no longer be measured or interact with anything physical. Bear in mind, too, that we can’t actually “see” light; that is, the only way of detecting a photon is by interacting with it, so it isn’t as if we can follow behind the path of a photon and measure its speed; all we can do is measure when it left its origin and when it got to the terminus (our eyes or instruments), and subtract to get the interval.
We can see real objects travel an interval faster than they should due to the warpage of space, such as the precession of Mercury’s perihelion (this due to the mass and motion of the Sun twisting spacetime around it, called frame dragging), and in extreme cases like a very massive rotating black hole it is possible to plot a timelike course through space in which (from an external observer) the velocity would have to exceed c (again, due to the frame dragging effect of a rotating mass). If you bring the object back around to the same spatial locus, it will appear to have gone backward in time (however, there are limiting conditions which prevent this from being a useful means to violate causality). These are real phenomena, and completely workable within the framework of General Relativity, because spacetime itself has no inertial properties, i.e. it isn’t made of mass or discrete energy.
I could start throwing out metrics and the Einstein Field equations, but the odds are that I’ll just confuse you (and likely myself) further. Perhaps Chronos will drop in and offer a more formal but still intelligible footing for this, it being his area of professional expertise.
spatial locus=fixed point in space relative to the observer’s frame of reference.
An object can take a path that would, along unwarped spacetime, require a velocity in excess of c. The additional speed comes not from inertial movement of the object, but the non-inertial stretching of the space it is traveling within, which doesn’t violate relativity. In the case of a space expanding at every point, this additional velocity would always be directed outward (from the observer’s point of view) and increases linearly with distance, such that the distance between observer and object is increasing; if it exceeds c it is, like an object that falls into a black hole, lost forever, unless Mr. Scott can amp up the dilithium regulator and negify the polarity of the Cochrane field (or whatever the script says this week).
The light emitted from any object always moves and will be measured as moving at exactly c (as long as we stay far enough away that the madness that lies of quantum electrodynamics doesn’t concern us), but if it travels through expanding space it will take longer to get here and will be shifted toward the red end of the spectrum.
All this technical stuff is fascinating, but the OP’s question was, how will humanity react to a habitable world close by?
I predict that as soon as someone develops a practical faster-than-light drive, armies of tourists will start going there. At that point, if history is any guide, most of them will come back complaining about the rudeness of the locals, how shabby the hotels are and how they couldn’t get any of the foods they normally like to eat.
Indeed. They will pay a lot of money to travel a long way, come back complaining about how it wasn’t exactly like home, and then repeat the exercise every year.
pffft Everyone knows that even Alderbarian Phase Shifting Spider-Rats can understand English if you speak it slowly enough. They’re just pretending not to understand Humans because we’re better than them!
I think the main benefit of discovering potentially habitable worlds within reasonably close interstellar distances would be Inspiration. Even if they’re not reachable by any technology we have or can conceive of at this point, they’re a goal post that we can use to inspire new ways of doing things so that we may eventually reach them.
And seriously, we need to work out a very large amount of shit before we bother getting off this rock.
The following is a dramatization and not an actual quote:
Consider it blown. As far as thread hijacks go, Stranger on a Train and you make it really hard to complain.
A minor nitpick though: The dark ages were geographically restricted and progress marched on in other parts of the world (and the learnings were later shared with everyone else). I’m not sure your assumption holds as there seems to always be a dark age going on somewhere.
Back to the OP: If by “close by”, one is to infer that travel has become possible through some incredible breakthrough, then we will react by studying then colonizing it if it is feasible. Then war will eventually break out as the two planets diverge culturally and New Earth gets tired of the arrogance and obnoxiousness of Old Earth. Ships will be sent, and will destroy both planets, at which point the few tens of thousands of people left in space will cry and mourn, then dive into madness and slowly perish without dignity.
If we are still stuck with sub-light speeds, we will make a few token attempts at sending a tiny, unmanned probe there on a one-way trip, largely as a symbolic gesture, then go on with our lives and promptly forget all about it.
The odds of such a probe arriving to destination and transmitting exciting information back would be statistically negligible and the vast time spans would make the whole concept entirely unappealing to a quicklived, impatient species like ours.
I just don’t care about what my great great great great great great great <add more greats here>grandchildren find out. My genes will have become too diluted by then for me or them to care about each other. That’s just the way things are.
