Is space exploration and possibly colonization of other planets the future of humanity?

@Sharon

It's for sure a big problem. But even if we can't crack faster than light travel, we could still build colony ships: ships that would house generations of humans until we reach a new planet.

@Pikachu The time dilation effect could allow people to make the journey in their own lifetimes. There is also the possibility of "wormholes".

@Sharon [quote] The time dilation effect could allow people to make the journey in their own lifetimes[/quote]

In the lifetime of the traveler, but not the place they left, or the place they're going to. If you travel at the speed of light, or near it, to get somewhere, it's possible that this "somewhere" is no longer there. For example, if I am traveling at 0.99999999999999c, for a year, then the planet I left, is now 730,000 years older, and so is the planet I was headed to. In the meanwhile, I would only be one year older.

@Northwest That's true. I see you also recognize that one needs to travel at near light speeds for time dilation to be significant for this purpose.

Even without that, many of the stars and exoplanets might not be there now anyway. Beteguese, for example, is ready to go super nova any day now but, as it's 640 light years away, it might have blown up already.

@Sharon Alpha Orionis' age and how long it's been since it entered its red supergiant stage, are mostly guess work at this point, embellished by doomsday scenarios, spread by religious doomsday cults.

When it does go supernova, and due to its "close" proximity to us, it will outshine the moon, and will be visible for about 3 months. I would guess, and like everything else related to Alpha Orionis, it's guess work, that it could be anywhere from 50,000 years to 1 million years.

Time dilation accelerates rapidly, as speed approaches c. At 90% c, it's about 2.5X. Speed/Gravitational potential differential, is experienced by ISS Astronauts, whose watches lose about 2.5 seconds per orbital year.

@Northwest [quote]it could be anywhere from 50,000 years to 1 million years.[/quote]
As I said, any day now - in cosmological terms. We can't be much more precise than that.

I'm familiar with the gamma factor and the way it rapidly increase at near light speeds. You give the value at 0.9c At 0.99c it's 7.1 At 0.9999c it's 70.7 and at 0.999999 it's 707.1 The graph slowly rises until it nearly reaches 'c' then becomes nearly vertical.

@Sharon I gave a rough approximation. At 0.9c, it's about 2.294157339

This is only one factor though. There are also, at least, a couple of additional factors: length and mass dilation

@Northwest I hope you don't think I'm arguing against you, I'm not. We are in agreement. My point in giving the value of gamma at other speeds is an attempt to show for others here how steep the graph is at near light speeds.

The relativistic effect on mass is what prevents a massive object being accelerated to the speed of light. At 'c' its mass would be infinite so would have infinite kinetic energy.

The time dilation effect on pion-muon decay is what allows more pions to reach the Earth's surface than we would otherwise expect. I've seen a simple explanation of it somewhere on the 'net but I can't find it now. :(

@Sharon I was clarifying my answer. I initially said it was about 2.5x, but when I later did the math, it came to 2.294157339, which rounds off to 2.3

I mentioned length dilation, because this is the math you use when figuring out how muons reach the Earth's surface. At rest, or applying Newtonian Physics, a muon has no chance of reaching the earth's surface, before it completely decays, but to a muon traveling at 0.9998c, the Earth's atmosphere, is length contracted, allowing it to reach the surface, before it completely decays.

@Northwest I calculated 2.3 too but, when I talk about 50000 - 1000000 years as "any day now", I thought 2.5 was close enough. ;)

The foreshortening of length is from the muon's point of view, by its clock it still decays in 2.2 E-6s but doesn't travel as far as the stationary observer sees it travel. Instead, the observer measures its lifespan as considerably longer.

To keep things simple, consider a particle travelling at 0.87c (gamma = 2) for distance 's' in time 't'. From the particle's point of view, it only travelled half the distance but from a stationary observer's point of view, it travelled the full distance but took twice as long.

I'm not sure I've explained it all that well I'm afraid. :(

@Sharon There are different factors, all influenced by the Gamma Factor, one is time, the other is shape, and the third is mass, and all based on where the observer is. From a muon's perspective, the earth's atmosphere, which is what it needs to traverse, since its birth, following the collusion between a cosmic ray, and the upper atmosphere, is length contracted.

All these factors are relative to each other, and to observers.

@Northwest GR is a fascinating subject, and a lot easier to understand that quantum theory. ;)

@Sharon SR (Gamma factor) and GR will be harmonized with Quantum Mechanics, sooner or later, of that I am certain :-) I still think that Celestial Mechanics, at the Macro level, are as complicated as quantum mechanics.

@Northwest [quote]SR (Gamma factor) and GR will be harmonized with Quantum Mechanics, sooner or later, [/quote]
Or they'll be replaced by a new, all encompassing theory. That's the beauty of science, it's not held back by outdated dogma.