To Saturn at (nearly) the speed of light

[ghwellsjr]

Yes, it is this that surprises me: how small the Universe is, in theory at least. To be able to cross the Universe, even in theory, in human timescales is quite amazing.

Is the effect a parabolic curve? How close to the speed of light, for example, do you need to get before the foreshortening is significant enough to allow human migration over a range of say, 100 light years in a few years?

The equation for the Lorentz factor, called gamma (γ), as a function of beta (β), which is speed as a fraction of c, is:

γ = 1/√(1-β²)

The inverse of γ is what you want.

At 99%c, 1/γ=14%
At 99.9%c, 1/γ=4%
At 99.99%c, 1/γ=1.4%
At 99.999%c, 1/γ=0.4%
At 99.9999%c, 1/γ=0.14%

I think you can see a pattern here.

 

[ghwellsjr]

If the aim is human migration in human timescales then the effect is exactly the same.

There's never going to be any human migration outside our solar system. Probably not even inside our solar system except on a very small scale, like when we visited the moon 45 years ago. Even if we could overcome the technical difficulties, nobody wants to fund it. Our technical expertise today far surpasses that of 1969, so why haven't we returned to the moon which we know we can do?

 

[JollyOlly]

Baggins101 - you would probably find my book 'A Roller Coaster Ride through Relativity' on Wikibooks of interest.

 

[Baggins101]

There's never going to be any human migration outside our solar system. Probably not even inside our solar system except on a very small scale, like when we visited the moon 45 years ago. Even if we could overcome the technical difficulties, nobody wants to fund it. Our technical expertise today far surpasses that of 1969, so why haven't we returned to the moon which we know we can do?

The Chinese are doing that as we speak, surveying for minerals.

I also suspect the pressure of resources will eventually lead to mass migration, but not in my lifetime.

 

[Baggins101]

Baggins101 - you would probably find my book 'A Roller Coaster Ride through Relativity' on Wikibooks of interest.

Thanks. I'll take a look.

 

[ghwellsjr]

The Chinese are doing that as we speak, surveying for minerals.

I also suspect the pressure of resources will eventually lead to mass migration, but not in my lifetime.

Doing what? Human migration outside the solar system? Human migration inside the solar system? Human migration to the moon?

 

[Baggins101]

Doing what? Human migration outside the solar system? Human migration inside the solar system? Human migration to the moon?

Surveying the moon with a view to establishing a base for the extraction of minerals.

http://mobile.extremetech.com/#/ext...s-its-journey-to-monetize-the-moon-with-video

 

[Dale]

If the aim is human migration in human timescales then the effect is exactly the same.

No. If the aim is human migration in human timescales then FTL is not required. The effect is not exactly the same as FTL, but the exact same effect is simply not needed to accomplish that aim.

 

[ghwellsjr]

Surveying the moon with a view to establishing a base for the extraction of minerals.

http://mobile.extremetech.com/#/ext...s-its-journey-to-monetize-the-moon-with-video

Establishing a mining base on the moon is a far cry from human migration. And if it proves not to be economically advantageous, they won't do it, will they? They haven't actually done it yet, but when we took our rovers to the moon, we had humans driving them. So we know that this kind of thing can be done technically and it doesn't require high speeds that take advantage of Time Dilation, which is what this discussion is all about, isn't it?

 

[Baggins101]

Establishing a mining base on the moon is a far cry from human migration. And if it proves not to be economically advantageous, they won't do it, will they? They haven't actually done it yet, but when we took our rovers to the moon, we had humans driving them. So we know that this kind of thing can be done technically and it doesn't require high speeds that take advantage of Time Dilation, which is what this discussion is all about, isn't it?

Establishing a permanent colony on the moon and mining minerals in industrial quantities is a very different scenario from the US moon landings however the point I was making is that time dilation and the contraction of space make interstellar migration to habitable (terra formable) planets do-able without the need for inter-generational ships.

When I say "do-able" I mean theoretically. I realize there are one or two minor engineering hurdles to overcome (!)

 

[PeterDonis]

I thought parts of the known universe were traveling away from us at faster than the speed of light and will be forever out of reach.

If our current best fit model of the universe is correct, and the universe is in fact dark energy dominated now (and for the foreseeable future), then yes, there are portions of spacetime that are unreachable, even taking relativistic time dilation into account. "Unreachable" here means unreachable even by light rays emitted from Earth.

 

[ghwellsjr]

A quick question I hope:

What would I see from Earth if I sent a rocket to Saturn at nearly the speed of light?

If the rocket travels a million miles at a thousand miles an hour I will see it arrive in 1000 hours.

If the rocket travels at nearing the speed of light I won't see it arrive for.. what? A thousand years because of relativity? ?

Something is rotten in the state of Denmark... since that would require the Earth observer see a rocket arrive sooner the quicker it traveled until it reached a tipping point and started getting there later and later as speed increased...

Help with my head would be gratefully appreciated@

Why do you think that? If the rocket travels a million miles at 186,000 miles a second, relative to Earth, you on Earth will see it take about 5 1/2 seconds to make the trip. (Saturn is actually about 750 million miles from Earth on average, so you on Earth would see the rocket take about 4000 seconds, or about an hour and 7 minutes, to make the trip to Saturn at that speed.)

If it traveled at very close to the speed of light, you would see it arrive after the same amount of time it takes for light to get from Saturn to here. To think this might be a thousand years is just silly. The time it takes light to get here from the sun is 8 minutes and Saturn is about 9 AUs from us so it would take about an hour.

I see Peter beat me to it.

These two responses to Baggins101's question, "What would I see from Earth if I sent a rocket to Saturn at nearly the speed of light?" could be misleading because that is decidedly not what he would actually see from Earth.

Let's assume that Saturn is 4000 light-seconds away from Earth and that the rocket travels at 97% of the speed of light. Here is a spacetime diagram to show the scenario. The Earth is shown in blue and Saturn in red with dots marking off 1000 second-intervals of time. The rocket is shown as the thick black line with only one dot marking it arrival at Saturn and a light signal shown as the thin black line going back to Earth:

Since the rocket travels at 0.97c and it has to travel 4000 light-seconds, it takes 4000/0.97 = 4124 seconds to get there. But gamma at this speed is 4.113 so the clock on the rocket advances by 4124/4.113 = 1002 seconds. The light signal will get back to Earth at 8124 seconds.

The sense which the two previous responders meant when they answered that you would see the rocket arrive in an hour or so is that in the mutual Earth/Saturn rest frame, the rocket arrives in that much time but it takes almost twice that amount of time to actually see it arrive.

In fact, if you shine a light on Saturn, it will take 8000 seconds before you see it. Don't forget that round trip time.

 

[ghwellsjr]

Establishing a permanent colony on the moon and mining minerals in industrial quantities is a very different scenario from the US moon landings however the point I was making is that time dilation and the contraction of space make interstellar migration to habitable (terra formable) planets do-able without the need for inter-generational ships.

When I say "do-able" I mean theoretically. I realize there are one or two minor engineering hurdles to overcome (!)

Establishing a permanent colony on the moon and mining minerals has been proven to be "do-able". It's not just theoretical. We've already mined minerals and brought them back to Earth in small quantities. Doing it in industrial quantities would possibly have one or two minor engineering hurdles but like all industrial processes, they aren't done unless economically profitable (or just feasible if done by a government).

However, your statement that there might be just one or two minor engineering hurdles to overcome for interstellar migration is pure naivety. There are numerous physics hurdles that have been mentioned earlier in this thread that can never be overcome, energy costs for one, getting smashed by particles at high speed being another one.

Furthermore, the idea of migration to another habitable planet is more pure naivety. Planets don't remain habitable for long enough periods of time for us to be able to identify one, presumably many tens of thousand of light-years away and to get there before it has already become uninhabitable, just like the Earth will be in a few more tens of thousands of years. Remember, if we see a planet fifty thousand light years away, we are seeing it as it was fifty thousand years ago and it would take us another fifty thousand years for us to get there by which time it may be uninhabitable.

 

[mfb]

There's never going to be any human migration outside our solar system. Probably not even inside our solar system except on a very small scale, like when we visited the moon 45 years ago. Even if we could overcome the technical difficulties, nobody wants to fund it. Our technical expertise today far surpasses that of 1969, so why haven't we returned to the moon which we know we can do?

And the open sea is a barrier that we cannot pass, in the same way we will never travel faster than a horse can run, or go to space?
It is too expensive today, that does not mean it will stay too expensive forever.

Furthermore, the idea of migration to another habitable planet is more pure naivety. Planets don't remain habitable for long enough periods of time for us to be able to identify one, presumably many tens of thousand of light-years away and to get there before it has already become uninhabitable, just like the Earth will be in a few more tens of thousands of years. Remember, if we see a planet fifty thousand light years away, we are seeing it as it was fifty thousand years ago and it would take us another fifty thousand years for us to get there by which time it may be uninhabitable.

Tens of thousands years? Earth has been habitable for 4 billion years, and will continue to do so for at least ~500 million to 1 billion years (unless we do something horribly wrong), maybe more with our help. Even with our current rockets, a generation ship would be fast enough to reach many earth-sized planets in the habitable zone within negligible time compared to the timescales of habitability.

Establishing a permanent colony on the moon and mining minerals in industrial quantities is a very different scenario from the US moon landings however the point I was making is that time dilation and the contraction of space make interstellar migration to habitable (terra formable) planets do-able without the need for inter-generational ships.

In the same way cryogenics would make this possible.

 

[phinds]

The sense which the two previous responders meant when they answered that you would see the rocket arrive in an hour or so is that in the mutual Earth/Saturn rest frame, the rocket arrives in that much time but it takes almost twice that amount of time to actually see it arrive.

In fact, if you shine a light on Saturn, it will take 8000 seconds before you see it. Don't forget that round trip time.

Very good point. Thanks for clarifying that. We (well, I anyway) do tend to get too loose when we talk about what we "see".

 

[PeterDonis]

uninhabitable, just like the Earth will be in a few more tens of thousands of years.

Why do you think Earth will be uninhabitable in that time frame? The time frame I'm used to seeing is more like a billion years (the time for solar irradiance to increase to the point where the Earth's temperature becomes too hot).

 

[ghwellsjr]

And the open sea is a barrier that we cannot pass, in the same way we will never travel faster than a horse can run, or go to space?
It is too expensive today, that does not mean it will stay too expensive forever.

I didn't say expense would keep us from interstellar travel, I said physics would. That's where Time Dilation would matter. I said inside our solar system, if we could overcome the technical difficulties, expense would be the deciding factor.

Tens of thousands years? Earth has been habitable for 4 billion years, and will continue to do so for at least ~500 million to 1 billion years (unless we do something horribly wrong), maybe more with our help. Even with our current rockets, a generation ship would be fast enough to reach many earth-sized planets in the habitable zone within negligible time compared to the timescales of habitability.

The Earth has not been human habitable for 4 billion years. I'll grant you maybe a significant fraction of 1 billion years but even then, where are these "many earth-sized planets in the habitable zone"? Even one?

 

[PeterDonis]

The Earth has not been human habitable for 4 billion years. I'll grant you maybe a fraction of 1 billion years

That's only because it took a few billion years for plants to evolve and add enough oxygen to the atmosphere for animals to be able to live on land. Now that that's happened, though, it's not going to unhappen, so the Earth will remain human habitable until, as I said, the Sun's output increases enough to drive Earth's temperature too high, which will take about a billion years. So we're talking a total "window" of time of a least a billion years during which an Earth-like planet would be habitable.

Also, a billion years is a *lot* of time to develop technology; technological obstacles that seem very formidable now (such as how to shield an interstellar spacecraft moving at near the speed of light from radiation, or how to propel one by some method, such as a huge laser, that doesn't require it to carry all its fuel and reaction mass on board), will probably seem trivial in much less than a billion years. We've only had spacecraft for a little more than half a century; judging what's possible for humans in the longer term future by what our limitations are now for space travel would be like judging what's possible for humans to do with fire and combustion by watching what our ancestors did with it a million years ago.

where are these "many earth-sized planets in the habitable zone"? Even one?

http://en.wikipedia.org/wiki/List_of_potential_habitable_exoplanets

 

[PeterDonis]

In fact, if you shine a light on Saturn, it will take 8000 seconds before you see it. Don't forget that round trip time.

Yes, good point; the word "see" is ambiguous. Unfortunately there doesn't seem to be better terminology for this in ordinary English; you have to use technical jargon.

 

[Dale]

the point I was making is that time dilation and the contraction of space make interstellar migration to habitable (terra formable) planets do-able without the need for inter-generational ships.

Sure. But that correct point has nothing to do with the incorrect claim that time dilation and length contraction make FTL possible. Just don't "oversell" the effects as FTL and you will be fine.

 

[ghwellsjr]

Yes, good point; the word "see" is ambiguous. Unfortunately there doesn't seem to be better terminology for this in ordinary English; you have to use technical jargon.

I like the word "establish" because it has just the right double-meaning to include the need specify a frame and the need to determine the parameter of interest. Of course, I have no expectation that it will ever supplant the word "see". But if I'm not sure what the questioner means, I assume he means "actually see" and make sure my answer makes that clear or else I will answer both ways as I did in this case. I believe in full disclosure.

 

[PeterDonis]

I like the word "establish" because it has just the right double-meaning to include the need specify a frame and the need to determine the parameter of interest.

+1 from me on this; it's a word that doesn't have other undesirable connotations already, and as you say it gets across the fact that there's more than just direct perception involved.

Of course, I have no expectation that it will ever supplant the word "see".

Unfortunately, I don't think so either. But at least we can try starting a trend here on PF.

if I'm not sure what the questioner means, I assume he means "actually see" and make sure my answer makes that clear or else I will answer both ways as I did in this case. I believe in full disclosure.

This seems to me to be a good policy.

 

[Baggins101]

The Earth has not been human habitable for 4 billion years. I'll grant you maybe a significant fraction of 1 billion years but even then, where are these "many earth-sized planets in the habitable zone"? Even one?

How many planets smaller than Jupiter had been found 5 years ago? How many planets of any description had been found 20 years ago? To dismiss any possibility of future interstellar migration on the basis that we have only found one possible candidate beyond our own to date is disingenuous as it suggests they either don't exist or that we will never be able to detect them.

The point about the window of habitability has already been made: tens of thousands of years are nothing on a geologocal time scale.

Are you American? I ask because the only motivation for branching out into the Universe you consider is financial gain. Our own solar system will be plundered for financial gain but that will never be a major motivation for permanent migration and separation from Earth. Motivations are likely to include wanting to create a better life for your descendents than living on an over-crowded resource poor Earth, and the native human desire to explore. How many people signed up for Mars 1?

Humanity will migrate to the stars, of that I can see little doubt. I suggest, however that it will not happen until the issue of energy has been resolved, possibly through nuclear fusion.

 

[Baggins101]

Sure. But that correct point has nothing to do with the incorrect claim that time dilation and length contraction make FTL possible. Just don't "oversell" the effects as FTL and you will be fine.

I do realize time dilation and length contraction are not the same as ftl travel, however I'm sure that you can see that from my viewpoint, as a traveller intent on a one way trip to settle on a distant planet, the effect is the same as ftl travel: i can get to a planet 100 light years away from the point of view of both Earth and my destination planet, in considerably less than 100 years. That Earth has aged 100 years in that time or that my new planet is 100 years older is of no consequence to me.

 

[PeterDonis]

Our own solar system will be plundered for financial gain but that will never be a major motivation for permanent migration and separation from Earth.

I'm not sure that's necessarily true on a long enough time scale. Suppose, for example, a longer-term future in which we have robotic ships that can travel at near light speed to nearby star systems, mine them, and send the resources back at near light speed. Say that means a ten-year turnaround time for getting resources from the Alpha Centauri system to our solar system. That's not too different from the turnaround time for, say, companies in Europe getting resources from East Asia during the Renaissance. On a long enough time scale, such activities are profitable; so far enough in the future, we can expect our descendants to engage in them.

That's not to say profit will be the only motivation; the other motivations you mention will certainly be present as well. But consider, for example, that there are already private companies talking about mining resources from Mars and the asteroid belt over the next few decades, whereas nobody, as far as I know, thinks we will be able to have significant human habitation in either of those places in that time frame. I think it's very hard to predict which set of motivations will get there first in any particular case.

 

[Dale]

I do realize time dilation and length contraction are not the same as ftl travel, however I'm sure that you can see that from my viewpoint, as a traveller intent on a one way trip to settle on a distant planet, the effect is the same as ftl travel: i can get to a planet 100 light years away from the point of view of both Earth and my destination planet, in considerably less than 100 years. That Earth has aged 100 years in that time or that my new planet is 100 years older is of no consequence to me.

None of that makes it the same effect as FTL travel. Please don't push this issue further.

As a traveller intent on a one way trip it doesn't matter if it is FTL or not, as long as you can live long enough to get there. The fact that you can live long enough in no way makes it FTL. I.e. your purposes or intentions do not change the fact that you never traveled FTL.

 

[PeterDonis]

from my viewpoint, as a traveller intent on a one way trip to settle on a distant planet, the effect is the same as ftl travel: i can get to a planet 100 light years away from the point of view of both Earth and my destination planet, in considerably less than 100 years.

Considerably less than 100 years according to your clock; or perhaps a better way to put it would be, while you age considerably less than 100 years. That makes it clear what "effect" you consider important, without inviting potentially confusing or misleading inferences about FTL travel that, as DaleSpam has pointed out, are not valid.

 

[russ_watters]

No one responded directly this:

...as a traveller intent on a one way trip to settle on a distant planet, the effect is the same as ftl travel: i can get to a planet 100 light years away from the point of view of both Earth and my destination planet, in considerably less than 100 years.

You said that last part wrong, though it may be accidental: from the point of view of observers on both Earth and the destination planet, you did not get there in less than 100 years, you only did that from your point of view.

It would be fair to say that to the traveler there is a similarity with FTL travel in that you can travel to distant places that from your point of view before you left appeared unreachable. But the fact that you can watch light travel and never pass it clearly indicates that you are not traveling FTL. And the duration of the trip from the point of view of the people who watched it (not participated) is clear indicator that it wasn't either.

The fact that you get to in effect skip the distance but not the time means that at best it is half similar to FTL travel.

 

[.Scott]

Are you sure about that? I thought parts of the known universe were traveling away from us at faster than the speed of light and will be forever out of reach.

That's true. There may be parts of the universe that are either behind an event horizon or would move behind that horizon before you reached them. But my main point was only to demonstrate the scale of the known universe - not to actually plan a trip.

 

[mfb]

That's true. There may be parts of the universe that are either behind an event horizon or would move behind that horizon before you reached them. But my main point was only to demonstrate the scale of the known universe - not to actually plan a trip.

Actually, we know those objects exist (assuming the expansion of the universe continues to accelerate according to our models, otherwise there could be no horizon) - we can see them today as very old, and now very far away galaxies. So far away that light from us today will never reach them.