Once we achieve the singularity(tm) and upload our consciousness (or get replaced by AI), we can turn down the clock speed on the matrix (say turn 1,000,000 real years into 1 matrix year), and like magic c stops being a practical limitation. Sending message (or travelling) from one side of the galaxy to another would take a 'matrix month' .. turn the clock down even further and you can make galactic communication instantaneous.
No FTL required. We just need to figure out how to use propellant efficiently enough among a few other slightly difficult challenges.
I imagine we could 'live inside' a projected VR world that looks like earth or some other massive online world unless we wanted to go out camping at whatever planet we were orbiting.
Here is a case where two people are brought in more direct contact, which seems to me to hold the door open for future possibilities. It makes it easier to see how two might merge, at least in a rough accidental sort of way.
https://kottke.org/17/11/these-conjoined-twins-can-share-eac...
https://www.nytimes.com/2011/05/29/magazine/could-conjoined-...
Have a good one.
Traveling between galaxies is another matter, however. The distance from the edge of the Milky Way to Andromeda is about 2.5 million light years. That journey would take 55 years ship time or slightly more than 2.5 million years Earth time and Andromeda really isn't that far on the scale of galaxies. Leaving a solar system might still allow some sort of interplanetary trade (in historic items mostly, since they'd be pretty old by the time they got anywhere) but leaving a galaxy means cutting all ties forever.
Don't worry about it. You can travel from the Milky Way to Andromeda and back 1500 times before the sun explodes.
And re looping the galaxy, I'm reminded of Peter Watts' The Freeze-Frame Revolution. Mission time is hundreds of millions of years.
http://nathangeffen.webfactional.com/spacetravel/spacetravel...
The last paragraphs of explanation below are essentially what the wiki editors have done at https://en.wikipedia.org/wiki/Twin_paradox#Difference_in_ela... only without acceleration/deceleration phases, since they aren't helpful in understanding the geometry of the problem. Moreover, I'd like to lead you to the same result more gently than wikipedia-browsing would.
On a flat Euclidean plane, between two points there is a single shortest path. We call that a "straight line", and we can assemble it from line elements which are tiny little steps from the starting point to the ending point. Using Cartesian coordinates (x,y), we can write the line element dS as dS = sqrt(dx^2 + dy^2) -- we do the squaring and take the square root in order to deal with sign differences. We can also write it as dS^2 = dx^2 + dy^2. Dx and dy are tiny steps along the x or y axes, just as dS is the line element: a tiny step along the line.
A plane is a 2-space. Flatness means that the line element above applies everywhere in the plane, even if it goes to infinity in all directions.
On a flat Euclidean 3-space, our line element becomes dS^2 = dx^2 + dy^2 + dz^2. Again, we have a straight line assembled from tiny displacements in one or more of the three spatial dimensions. Flatness, again, means that this line element applies on a line between any two points.
In the 2-space and 3-space cases, the straight line is the uniquely shortest possible line. If we deviate slightly even at one tiny step when building line out of line elements, the line itself is longer.
The form of these line elements are called metrics, and they apply everywhere in each the spaces described above. They have a signature, which can be found by the operators between the coordinates on the right-hand-side of the metric: two + in the 2-space case, three +es in the 3-space case: note that the + in front of the leading term (dx^2) is implicit. Explicitly, we could say dS^2 = +dx^2 + dy^2 + dz^2 Or dS^2 = 0 + dx^2 + dy^2 + dz^2. Because of the squaring and square-rooting, we can alternatively reverse the signs and say dS^2 = -dx^2 - dy^2 - dz^2. We get the same result, but then the signature is three minuses rather than three plusses.
That's space. Now let's consider spacetime.
A Lorentzian spacetime's timelike dimension has the opposite sign. So the Lorentzian extension of a 3-space into a 4-spacetime takes the signature from (+,+,+) to (+,+,+,-) or from (-,-,-) to (-,-,-,+). So in flat spacetime, in Minkowskian coordinates (they're the flat spacetime analogues of Cartesian coordinates (x,y,z) as (x,y,z,t)) we can write the line element as dS^2 = dx^2 + dy^2 + dz^2 - k^dt^2 or as dS^2 = k^2dt^2 - dx^2 - dy^2 - dz^2. "k" here is a constant; it can be set to the value 1, in which case it vanishes. It can be set to a different numerical value, representing a conversion constant between lengths in the spacelike axes and durations in the timelike axis. In our Lorentzian spacetime, the constant is better known as "c".
One thing to observe here is that if "c" is large than the [+/-]c^2dt^2 in the line element dominates.
Say we mark off spatial distances in light-nanoseconds and timelike durations in nanoseconds, so we can make "k" vanish (this is effectively setting c to 1). If your start point is t=0,x=0,y=0,z=0 and your end point is t=onebillion,x=0,y=0,z=0 you've moved one light second into the future and zero light seconds left/right, up/down, or forward/backward. Using (+,-,-,-) sign convention, S is a large number, because we are subtracting nothing from it. However, light travels at one light-nanosecond per nanosecond, so light shining to the left would go from x=0,y=0,z=0,t=0 to t=onebillion,x=onebillion,y=0,z=0. The length of the line is then zero, exactly. Finally, if we have two objects at t=0, one at t=0,x=0,y=0,z=0 and the other at t=0,x=onebillion,y=0,z=0, then when we calculate dS^2 we get negative one billion.
A Lorentzian (one sign difference) metric lets us categorize based on this. For the (+,-,-,-) signature, a positive value for dS^2 is timelike, a zero value is null or light-like (since c relates to the speed of light), and a negative value is space-like.
The absolute value of dS^2 is smallest when dS^2 = 0. Null intervals are thus the "shortest line" through a flat Lorentzian spacetime. Timelike paths are longer.
The origin and rendezvous points in the "twin paradox" or "relativistic galaxy cruiser who comes back", in light years, differ either not at all (or only a small small fraction if we leave/return right near Earth, since the planet moves around a bit in a year). Non-travelling twin is always at or near x=0,y=0,z=0, but moves a full year along t. Most of the path non-traveller's t is changing but the x,y and z are non-changing. Travelling twin, however, moves away from x=0 while moving "left" away and then moves back towards x=0 when moving "right" back. t is changing throughout traveller's trip, of course, but so is x.
We can look at it like this, with non-traveller t,x and traveller t',x': start: t=0,x=0; t'=0,x'=0. In the very next step, measured in very small units (say, light-attoseconds), and with traveller already accelerated to c exactly, we have t=1,x=0; t'=1,x'=1. In the next step, t=2,x=0; t'=2,x'=2. And so forth. The values for dS for these first two steps are non-traveller 1, 2 while traveller is 0, 0. When we integrate all these, non-traveller's total is about 3 * 10^26 (that's about the number of attoseconds in a year) while traveller's total is about zero (or exactly zero if we assume instant turn-around, and rendezvous spatial coordinates are x=0,y=0,z=0).
These totals are path-lengths. Non-traveller's path length is extreme, traveller's is zero. Proper times -- what one's cells, wristwatch, and other clocks one carries at all times reflect -- follows these path lengths. The non-traveller ages a year, the travelling-at-exactly-c traveller does not age at all.
Usually you take the traveller as massive and make it travel at a bit less than c, so that the total path length is timelike but short (rather than lightlike and thus null) compared to the extremal timelike path of the non-traveller. Thus the traveller's proper time does pass a little, but not nearly as much as the non-traveller's. Additionally, the traveller is often cast as accelerating and decelerating gently, so there are periods where the x coordinate is changing slowly with respect to t, and periods where the x coordinate is changing close to how quickly t is changing.
The massive gently-accelerating (and decelerating) traveller is what is described at the wikipedia link way above.
Almost finally, the geometry does not depend on choice of coordinates. One can use arbitrary units to tick off durations the timelike axis, and can choose spatial coordinates that are spherical or cylindrical rather than Cartesian-like. The metric for flat spacetime changes form with a change of coordinates[1], but the resulting path lengths and travel times work out exactly the same.
Finally, the metric of curved spacetime is different from that of flat spacetime; the reason you get time dilation around a black hole is because path lengths change because the line elements have a radial dependency such that the paths of objects moving tangentially past a black hole are shorter the further away from the black hole the tangent lies. Gravitation, then, is geometrical.
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[1] see, for example, below (10.4) at http://ion.uwinnipeg.ca/~vincent/4500.6-001/Cosmology/Spacet...
That's also the first place I saw the (in hindsight obvious) idea that a ship that can accelerate at over 1G can land on (or hover over) a planetary surface. Everyone else seems to have kept the "starships are for outside atmospheres only" trope.
Might make sense to optimize large ships for space only and use smaller vehicles to taxi back and forth from the surface of planets.
Engineering a ship that can land on a planet with gravity and an atmosphere is much bigger challenge than engineering a ship that never does anything besides go into orbit. It makes it much easier to create a really, really, really huge ship. You're not going to build a Death Star that can land on a planet's surface, unless you can come up with some kind of materials that we have no idea about now. So why bother? It's easy enough to make a giant ship for interplanetary travel with smaller shuttles for landing.
I mention this because your comment made me think: Even staying within the solar system, how short would a trip between Earth and Mars have to be to start to pose relativistic problems? I wonder at what point frequent travelers would start aging noticeably more slowly. (If this is dealt with in the books, now I’ll really have to read them.)
A round trip weekly at average distance (just going with 12mins/trip because the details get complicated), 48 weeks a year for 40 years would leave you just over a month younger than those who stay put.
That's going to get uncomfortable, but most people should be able to cope with 2 or 3G acceleration for short periods.
> We just need to figure out how to use propellant efficiently enough among a few other slightly difficult challenges
Both of these sentiments are pretty common misconceptions I've seen on HN. First, if c was infinite, the energy required to accelerate a constant amount would grow quadratically. This alone is a tough problem. Maybe we could "just" solve it. On the other hand, if c was finite, the energy required to accelerate would grow exponentially. This is more than a "slightly difficult" problem.
Regardless, I'm not sure if splitting humanity into many other species is something you want to do. And you still haven't solved any issue with distance communication and different reference planes.
For example, shorter people could probably deal with heavier gravity better.
The universal speed limit dictates how much of the Universe humans (or whatever comes after us) can ever visit, because of the Hubble constant.
A universal speed limit limits the size of a computer that can still have coherent "thoughts".
The theoretical growth rate; in practice this is impossible to keep up due to biological resource limitations.
> The universal speed limit dictates how much of the Universe humans (or whatever comes after us) can ever visit, because of the Hubble constant.
So unless every point in space was an "agar plate for humans", ready to serve us and house our breeding, we'd run into resource limitations far before any theoretical maximum due to finite c and expansion.
The ones we know. Earth-like planets are hard to spot from very far away.
The "life corridor" is certainly very narrow. But I am sure there are at least some places.
Maybe we find a world near a smaller red dwarf, which will last for trillions of years. Maybe we also don't make that planet uninhabitable in a few thousand years, for once.
I don't think it's a coincidence that going on a century of experimentation with entanglement has yet to yield even a theoretical mechanism for transferring information.
https://phys.org/news/2017-07-physicists-transmit-earth-to-s...
Because you need the classical information channel you are still limited by the speed of light and hence cannot transmit information faster than light.
https://phys.org/news/2017-07-physicists-transmit-earth-to-s...
“...quantum teleportation allows faithful transfer of unknown quantum states from one object to another over long distance, without physical travelling of the object itself. Long-distance teleportation has been recognized as a fundamental element in protocols such as large-scale quantum networks and distributed quantum computation. However, the previous teleportation experiments between distant locations were limited to a distance on the order of 100 kilometers...”
The wiki article clarifies: https://en.wikipedia.org/wiki/Quantum_teleportation
The second seems the most likely to me!
This flies in the face of the Equivalence Principle, and requires that light's wavelength shifts due to the relative time where its energy is measured--not because of an equal and opposite gravitational interaction with the masses causing the gravitation.
Perhaps the most nonsensical consequence is the behavior of a particle-antiparticle pair co-accelerating to infinity...unless their eventual merger through relativity (length contraction) and quantum mechanics (tunneling into a merged state) actually explains the mechanism for annihilation.
The only testable prediction I have: Distant galaxies will be "too mature" for their apparant distance in space and time, meaning that the light has aged more than the distances would suggest (time slows in the presence of a gravity well, and would do the opposite for regions of space with inverse curvature--see above, re:inflation and the very start of the Universe).