If you leave now,
you'll get there just about the time it becomes habitable.
If, like us, you're dying to get off this ridiculous little rock, here's some hope* to cling onto. There’s a planetary system slowly forming about 470 light years away from Earth that looks uncannily like our Solar System in its younger days. An image taken by the Atacama Large Millimeter/submillimeter Array (ALMA), an …
LHB is what I recall is the term for the incoming hail of planetary formation debris, and maybe asteroids and comets, the latter of which may have provided the damp layer on our rock that we call the oceans . That might not be a hopeful time at which to visit Earth 2.0, and even if that's over, there's not likely to have been a Great Oxygenation Event [pdf], either. There are many things that have to happen to make an apple pie from scratch.
 A vSauce segment seen on YouTube calculated that if you scaled the Earth down to the size of a basketball, you'd be able to dry it off with a not-rescaled kitchen towel. I don't have a link to hand, sorry.
470 light years might be achievable in a human lifetime when we have a method of propulsion which uses very little fuel.
The idea that we cannot travel more than 1 light year in 1 year is based on the reference frame of an observer on Earth. When you accelerate at 'g'* it only takes a couple of years to be pushing relativistic speeds, and then the distance that you need to travel actually contracts (in the reference frame of the spacecraft).
I haven't made any calculations, but perhaps it would be possible to travel that distance within the lifetime of the pilots, even though us Earthlings would measure the time as thousands of years.
* 'g', the acceleration at the surface of the Earth, is a natural choice because it causes the pilots to feel exactly as though they're standing on Earth and avoids some of the health issues with microgravity. One of the biggest limits on piloted space travel is that a prolonged acceleration of much more than 'g' may not be feasible for health reasons.
One of his juvenile novels (cant remember which one and too lazy to walk to the bookcases) is all about STL interstellar travel, plus some sort of telepathy between twins and - eventually - other relatives.
"Time for the Stars" says a small voice in the corner of my mind
"470 light years might be achievable in a human lifetime when we have a method of propulsion which uses very little fuel."
Yes, this is entirely possible, once you have the necessary propulsion technology.
Time dilation at relativistic velocities (slowing of time relative to a static observer) is exponential at constant acceleration, so once you have a ship that is capable of constant 1G acceleration*, you can reach the nearest star in less than a decade, cross the Milky Way in around a decade, reach the nearest major galaxy (Andromeda, ~2.5 million light years away) in a few decades, and reach the edge of the observable universe within a human lifetime.
These are local ship times, obviously. To anyone not on the ship it would take tens / thousands / millions / billions of years for it to complete those journeys.
*Constant acceleration as experienced by the ship's crew. A static observer would see the ship's acceleration tending towards zero as it approached c (light speed.)
There is a slight problem.
You have to carry enough of whatever fuel you used to slow down at the far end, otherwise you simply pass your destination at near lightspeed.
All that acceleration unavoidably requires energy. A lot of energy. Doing the maths is a bit too complicated for Saturday morning, as it involves integrating the full Einstein equation for energy and mass, but once the ship has any kind of relativistic mass you have to start plugging that into the equation since your destination is roughly stationary with regard to the origin. You can't handwave your way around "to the people on the ship" because what matters is your velocity relative to where you're going.
Unless you can magically get a way round Einstein's equations, the energy requirements will kill you. It's like those theoretical studies of wormholes which mention at the very end (or in a footnote) that unfortunately the energy requirements for any practical size exceed that of the entire universe.
Bussard ramjets are your friend!
The fuel comes for free, and the faster you go the more you get.
Of course, there are minor problemettes: there isn't enough interstellar hydrogen to drive the ramjet; we're not quite sure how to do the necessary hydrogen fusion; and the magnetic fields required to sort out the collection and pinch would turn the pilot inside out... but hey, details. That's just engineering.
All that acceleration unavoidably requires energy. A lot of energy.
Yeah. Even before you reach significantly relativistic speeds, it's nasty.
I did some back-of-the-envelope calculations years ago for my brother, who was working on a medium-hard SF novel at the time. As an upper limit, we assumed the engine could do full mass conversion of its fuel, which was metallic hydrogen. Acceleration of g even well below where I had to take relativistic effects into account turned out to be crazy expensive thanks to the rocket equation (more fuel means more mass means a higher rate of fuel consumption means more fuel...).
There's a reason why SF authors like Bussard ramjets. They save carrying all that fuel.
Saying "you just have to figure out the propulsion" is like saying "it's easy to have really low consumer energy bills, we just have to figure out feasible home fusion reactors". The propulsion is the problem.
Well, that and the fact that any other planet within a reasonable distance is almost certainly to be far less pleasant to us than the least-pleasant places on Earth. Sure, it's a big universe, and if modern cosmology is correct there's a huge number of essentially Earth-identical planets out there. But the vast majority will be outside our Hubble space, so they might as well not exist; and the vast majority of the ones we could even see (if we could make out something that small, which for all but a relatively tiny sphere around Earth we can't) aren't reachable while they're viable. And finding any that do happen to be in our neighborhood at the right point in their development won't be easy.
As others have noted, an Earth-type planet has a lot of crucial ingredients. A rocky planet in the Golidilocks zone with a spinning core (to generate a magnetic field), to start with. Yeah, maybe we could find some like that with water and a reducing atmosphere that could be seeded with cyanobacteria to give it an oxygen-rich atmosphere, if we're patient, and no one has qualms about killing off most of the planet's life, if it has any. I'm not holding my breath.
Coincidentally 1g x 1 year => ~ light speed
365 * 24 * 3600 * 10 = 315 360 000 ie 300000 k/s
The “little fuel” bit leaves me puzzled. Even assuming very high efficiency you need to get your ship’s mass + its fuel to that speed with additional relativistic mass effects (not sure the relation of mass effect to time dilation coefficients). That’s a lot of energy, I think some propose antimatter drives but you still have to produce that antimatter. Then you need to decelerate your way in, more fuel.
Windows will be secure before we can even get to Alpha Centauri, 100x nearer.
The problem is that at any point, to get 1g acceleration relative to your destination, you have to accelerate not the rest mass but the relativistic mass. As the time dilation scales with the relativistic mass factor, to get a large time dilation requires a lot of energy.
I have to say that watching people try to get round the sheer scale of the universe and find a means of interstellar travel is a bit like watching the Conservatives trying to find a way round Northern Ireland, though not as serious.
"The problem is that at any point, to get 1g acceleration relative to your destination, you have to accelerate not the rest mass but the relativistic mass. As the time dilation scales with the relativistic mass factor, to get a large time dilation requires a lot of energy."
As far as I'm aware, that's a popular misconception that comes from the way that special relativity is sometimes explained to undergraduates.
If you (the observer) see a ship flying past at a relativistic velocity, it intuitively appears that it is getting heavier and heavier as its velocity approaches c, because its acceleration reduces despite it firing its engines at full power, while its momentum increases. This is what is sometimes described as relativistic mass.
Which doesn't actually exist, it's just a useful way of getting a concept across.
The ship's momentum = mass x velocity is only true when the observer and the ship have the same relative velocity - the actual value is gamma x m x v (where γ is derived from the difference in velocity between the observer and the ship and equals 1 at non-relativistic speeds), so as the ship's velocity approaches c relative to the observer, the value of γ rises exponentially above 1, and the ship's momentum (energy) can increase without its mass increasing. The γ value explains how (to the static observer) acceleration can be falling while energy input (force) is constant.
I think even Einstein used the phrase relativistic mass in trying to explain special relativity, so it's easy to see why people use it even though it causes confusion.
If a ship starts its journey with a mass of 50 tonnes (sometimes called its rest mass, though its really just its mass), the mass will still be 50 tonnes at 99.99999% of c, so to the crew onboard the acceleration will be Newtonian i.e. the ship's engines are generating a constant force and mass remains constant so they will experience constant acceleration. The crew won't experience the falling acceleration seen by the static observer due to the time dilation they are also experiencing.
So astronomical amounts of energy are not required - all you need is a propulsion system which can provide approximately 10N of force per Kg of ship's mass, and enough fuel to keep it going for a few decades.
That's all you need he said...
"If a ship starts its journey with a mass of 50 tonnes (sometimes called its rest mass, though its really just its mass), the mass will still be 50 tonnes at 99.99999% of c, so to the crew onboard the acceleration will be Newtonian i.e. the ship's engines are generating a constant force and mass remains constant so they will experience constant acceleration. The crew won't experience the falling acceleration seen by the static observer due to the time dilation they are also experiencing."
This as stated leads to the paradox that the ship can exceed the speed of light from the point of view of the crew. That's OK for a photon which from its point of view crosses the universe in zero time, but if we agree with Einstein, nothing with mass can reach or exceed c.
I am willing to be corrected if wrong, but as I see it the mistake you are making is confusing the force on the ship with the acceleration. The crew experience a force of 1g relative to ship because it is pushing them. But their observations of the outside world are relative.
To see what this means assume that the ship travels 470ly. To the crew the journey, due to time dilation, seems to take only a decade. But to the start observer, it takes maybe 500 years (a lot longer in fact if it is being tracked). An observer at the starting point sees the engines fire for a number of years, and if the output is constant she sees the acceleration drop as relativistic speeds are reached. The crew, if you are correct, see the ship accelerate for a much shorter time at constant acceleration and thus use a lot less energy.
Somewhere something is wrong unless we give up on conservation laws.
"This as stated leads to the paradox that the ship can exceed the speed of light from the point of view of the crew. That's OK for a photon which from its point of view crosses the universe in zero time, but if we agree with Einstein, nothing with mass can reach or exceed c."
I'm probably not being very clear (it wouldn't be the first time...)
There's no paradox, as the ship never exceeds the speed of light. A photon pulse fired at the destination at the same time as the ship leaves would beat the ship by a significant amount of observer time, and a smaller amount of ship local time.
To the crew on the ship, an accelerometer based speedometer would indicate a speed greater than c, and if they looked out of the window at the changing position of the stars, they would calculate that they were going faster than c. However, if they fired a photon pulse at their destination, they would see it moving away with a velocity of c; light speed is constant so they would know that they weren't travelling faster than c.
As to the conservation laws - in your example, the ship takes a decade to complete its journey (it doesn't 'seem' to take a decade, it takes that actual period of time in local ship time.) So the amount of energy used will be the power output of the engine multiplied by the number of seconds in a decade. To the observer, that amount of time and energy will be stretched out over 500 years, so there is no discrepancy over the amount of energy required. You have to remember that force and acceleration are time based, and time is relative, so that what the observer and the crew measure will be different due to the different rates of time dilation they are experiencing because of their velocity relative to one another.
i.e. The crew will experience 1G of acceleration when the observer measures a fraction of that amount because it is measured in metres per second squared, and a second as measured by the observer would be 50 times shorter than a second as measured by the crew.
So maybe a similar planetary arrangement has seen in our solar system from afar and they sent astronauts to visit us? Had they arrived 50,000 years ago they might have given up and returned home - if they arrived now they might look around the planet and say, "This ain't going to last" ... looking at what little we know, or care about, history there's good argument that intelligent life self destructs within a hundred thousand years.
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Faster than Light Travel, in a collider somewhere on Earth they accelerated a molecule (was it or a composite particle) to near speed of light before it broke apart.
I determine velocity as the time it takes to move you own distance in space, so if you are in a space craft 100 feet long it would be the time to move 100 feet. An extension of this would be time to move away from your initial position in a straight line (compensating for warp of space).
I think though that to travel in absolute terms at light speed you'd have to be Electro-magnetic radiation (light).
Pushing that much energy slowly or quickly, into a bunch of eager beavers waiting to get a slice of real estate on a new planet would render them into bleeding fizzers, the energy would eventually radiate out in all directions like fireworks.
Whilst ripping along at near light speed, hit a dust particle or dust cloud and particles would rip through the craft.
[I note voyager1 encountered solar system & galactic winds going in opposite directions each about 75% speed of light]
Life on Earth will do me just fine thanks, but feel free to sell every bit of area on the planet to who ever wants to purchase it.