Relativity and space travel - what's the problem?

[billy_boy_999]

it seems to me that relativity (or at least the constant, impassable c) has had a stifling effect on science fiction and on our conceptualizations of space travel...i think the popular notion is that, because nothing can move faster than c, even with very advanced technology most of the galaxy is unreachable...

but this is all bull***t is it not? the speed of light is only impassable from another intertial reference frame...time and mass make the accomodation to maintain the appearance of an unbreachable speed of light...

in other words, it is perfectly possible for a spaceship to cover a distance of 10 light years (as measured from earth) in what he feels is only one year...all he needs is constant acceleration, since there is no drag in space he doesn't have to worry about any 'speed barriers'...in fact, with constant acceleration, his time lengthens and space shrinks, i can't see that there would be any limit to how far in the universe he can travel in a certain amount of time...again, we watch him from Earth and judge that he is taking longer (his clock ticks slower) and our constant and impassable 'c' is maintained...

so then, really the only obstacles that an interstellar traveller faces are a) a source of constant acceleration, and b) the willingness to say a last 'goodbye' to family and relatives as time dilation will mean he travels forward in time relative to the earth...

what is the problem here?

 

[chroot]

As a traveler approaches the speed of light, he will actually measure, by his own watch, that it only takes milliseconds to be anywhere in the universe. In the limit as he approaches the speed of light, it takes zero time to be anywhere. You could say that "time stops" aboard the ship.

The problem, of course, is that it's a one-way ticket. If you came back to Earth, you'd find that it had aged billions of years in the meantime.

- Warren

 

[billy_boy_999]

right, I'm not denying that billions of years is not a big deal, I'm just saying that there is a common misconception that things like settling other star systems, for instance, is distance-prohibitive when in fact it's nothing of the kind...

and, speaking for myself, if i had the chance to gambol around the universe and settle some strange new space colony, i would be willing to say goodbye to everyone i know...and wouldn't it be neat to see what happened to the dear old Earth in 10 billion years anyway?

 

[DW]

right, I'm not denying that billions of years is not a big deal, I'm just saying that there is a common misconception that things like settling other star systems, for instance, is distance-prohibitive when in fact it's nothing of the kind...

and, speaking for myself, if i had the chance to gambol around the universe and settle some strange new space colony, i would be willing to say goodbye to everyone i know...and wouldn't it be neat to see what happened to the dear old Earth in 10 billion years anyway?

I don't know about that. In 10 billion years you'd likely be thrown in a zoo as a lower life form as reckoned by whatever neosapien race dominates the planet if it even still exists as a living planet at that time.

 

[yogi]

Remember also - the traveler does not get the benefit of living longer and enjoying a longer life - when he returns he will have eaten the same number of meals and enjoyed the same amount of time in contemplating physics problems as if he stayed home - his advantage is that he gets to see a lot more of the universe during his 75 year lifetime - it isn't much different than being frozen for a long trip - you don't get much enjoyment in an ice box - but when your thawed out you can explore some new world .

 

[Janus]

right, I'm not denying that billions of years is not a big deal, I'm just saying that there is a common misconception that things like settling other star systems, for instance, is distance-prohibitive when in fact it's nothing of the kind...

and, speaking for myself, if i had the chance to gambol around the universe and settle some strange new space colony, i would be willing to say goodbye to everyone i know...and wouldn't it be neat to see what happened to the dear old Earth in 10 billion years anyway?

But is is distance prohibitive, but not from a time stand point, but an energy one. Before you even can close to that 10 billion years to 1 ratio you would need to use up the equivalent of the Solar system in mass for fuel.

 

[arildno]

But is is distance prohibitive, but not from a time stand point, but an energy one. Before you even can close to that 10 billion years to 1 ratio you would need to use up the equivalent of the Solar system in mass for fuel.

So what?
Since we won't see our folks again, can't we just use'm for fuel along with the rest of the solar system?

 

[billy_boy_999]

janus, you're probably right that it is distance prohibitive at the moment from fuel...but surely appropriate fuels can be developed...cold fusion would be nice, or even more efficient use of solar energy...

 

[russ_watters]

janus, you're probably right that it is distance prohibitive at the moment from fuel...but surely appropriate fuels can be developed...cold fusion would be nice, or even more efficient use of solar energy...

To get even a single digit percentage of C in a spaceship with people on it will require a propulsion system unlike any yet concieved. 1% C is 6.7 million miles an hour or about 380x orbital velocity. Getting a human to Alpha Centuari before he dies (much less return him to earth) would require at least 10% C. Current propulsion technology is a good 3-5 orders of magnitude below what is required for interstellar travel. IMO, no amount of technology will make it possible: there just isn't anything available with the energy required to do it.

 

[arildno]

What about "generation ships"?

 

[Janus]

janus, you're probably right that it is distance prohibitive at the moment from fuel...but surely appropriate fuels can be developed...cold fusion would be nice, or even more efficient use of solar energy...

Even with a fusion drive you would have to burn a mass of approx. 1/5 that of the Moon for every kilogram you would want to deliver at another star system , traveling at only .25c!

 

[billy_boy_999]

Janus said: Even with a fusion drive you would have to burn a mass of approx. 1/5 that of the Moon for every kilogram you would want to deliver at another star system , traveling at only .25c!

if we, on the earth, were watching this spacecraft , then yes, I'm not checking your calculations but since the craft's speed cannot exceed c, apparent time and mass dilation are in effect...

but this mass increase is relative! it doesn't affect the ship as its own inertial reference point...if a ship can maintain a constant acceleration of, say, 9.8m/s^2 then it can continue speeding up in relation to the earth...if relativity holds, then there is no point at which - within the ship's inertial reference frame - acceleration becomes more of a burden...

am i misinterpreting einstein's theory?

 

[chroot]

Maybe you should check his calculations.

- Warren

 

[Nereid]

What about "generation ships"?

Reduces the energy requirement - for propulsion anyway. All sorts of other problems of course, but perhaps more to do with maintaining a stable 'on-board' society.

In addition to the problems to do with a source of propulsion energy for a relativistic interstellar manned ship, there's the small matter of avoiding collisions. While the density of interstellar dust grains is low - at least in our solar neighbourhood - it's not zero; how to protect the ship and inhabitants against a collision with milligram dust grain?

 

[russ_watters]

Even with a fusion drive you would have to burn a mass of approx. 1/5 that of the Moon for every kilogram you would want to deliver at another star system , traveling at only .25c!

Thanks. I soooo hate doing the math myself, I was hoping someone would do it for me..

 

[billy_boy_999]

Janus: Even with a fusion drive you would have to burn a mass of approx. 1/5 that of the Moon for every kilogram you would want to deliver at another star system , traveling at only .25c!

Russ: Thanks. I soooo hate doing the math myself, I was hoping someone would do it for me..

russ and janus - i don't see how these figures apply at all! they have nothing to do with the inertial reference frame of the traveling spaceship...they have to do with our earthbound observers watching that spaceship and using the equivalence of mass and energy and the pliability of time as a spatial dimension to maintain a local, observed constant of c...that's all...

if I've misinterpreted einstein's theory, please tell me how!

nereid has pointed out something i think is more relevant...

Nereid: While the density of interstellar dust grains is low - at least in our solar neighbourhood - it's not zero; how to protect the ship and inhabitants against a collision with milligram dust grain?

first of all, this addresses a fundamental challenge to the philosophical implications of the principle of relativity...the cosmic microwave background radiation issues a similar challenge...if we can make quantitative measurements of increased incidents of exposure to 'cosmic dust' and measurements of motion in relation to the tiny assymetries of the background radiation, then does the principle of relativity hold?

the practical implications to high-speed space travel are even more salient - at very high speeds, say in relation to an earthbound measurement of distance over a spacebound measurement of time giving 10x the speed of light, tiny dust particles (possibly even neutrinos, if they have mass) would become so massive that there would need to be some sort of shield - perhaps this is the technological requirement that is farthest beyond our abilities at the moment...

 

[selfAdjoint]

Yes, you have misinterpreted Einstein. Relativity doesn't give anybody a free ride (well, until you get into wormholes and Alcubierre warps!). Your spaceship has to accelerate up to its speed - in this case c/4. To do that it has to throw mass out the back and rely on Newton's reaction force. There is no other way known to produce acceleration in empty space. No the Lorentz tranformation doesn't give you any help on the mass. This has nothing to do with "fuel" incidentally, it is reaction mass. And to get to c/4 requires a reaction mass of about 1/5 the mass of the moon (according to Janus' calculation, which I haven't checked).

 

[billy_boy_999]

selfAdjoint - thank you for answering me directly...i admit i do not understand your objections...

Your spaceship has to accelerate up to its speed...And to get to c/4 requires a reaction mass of about 1/5 the mass of the moon...

are you telling me that the faster you accelerate, the more proportional mass (in rocket fuel, or whatever) you need to further accelerate? this completely contradicts the principle of relativity! if we could figure out how much more mass we now need to maintain a constant acceleration if we are traveling at high speed we could easily calculate our absolute motion!

the increase in mass is a relative effect! e=mc^2 and time dilation balance the books to maintain both a constant c and an apparently impassable c...

 

[Janus]

selfAdjoint - thank you for answering me directly...i admit i do not understand your objections...



are you telling me that the faster you accelerate, the more proportional mass (in rocket fuel, or whatever) you need to further accelerate? this completely contradicts the principle of relativity! if we could figure out how much more mass we now need to maintain a constant acceleration if we are traveling at high speed we could easily calculate our absolute motion!

the increase in mass is a relative effect! e=mc^2 and time dilation balance the books to maintain both a constant c and an apparently impassable c...

The problem is like this:

Imagine that you have a rocket with A 1 kg payload, and it takes 1 kg of fuel/reaction mass to give it a delta v of 1 m/s. How much fuel would it take to get it up to 2 m/s? 2 kg ? No, more like 3.

To understand why, think about the state of the rocket at the point when it is 1 m/s short of its 2 m/s final velocity. It consists of the 1kg payload and the 1 kg of fuel needed to give the payload that extra 1 m/s of velocity. If it takes 1 kg of fuel to accelerate 1kg 1 m/s, it will take 2 kg of fuel to accelerate the above 2kg up to 1 m/s. giving a total of 3 kg of fuel you need to start with.

To get up to 3 m/s, you need the 3kg of fuel to accelerate the last 2 m/s, and 4 more kg to acclerated this fuel and payload the first 1 m/s. This gives a total of 7 kg of fuel.

Following the same pattern, it takes 15 kg of fuel to reach 4 m/s, 31 for 5 m/s, 63 for 6 m/s, etc. Notice that the fuel usage goes up almost exponentially.

This example gives you a rough idea what you are up against. And that is just 1/2 of the problem. In a situation where you want to deliver a spaceship to another star system for example, you are going to have to slow down when you get there. So you must provide the fuel to accelerate the fuel you are going to use to slow down

Thus, using the 5 m/s figures, It will take 31 kg of fuel to come to rest at the end of your voyage, which means you will have to accelerate 32 kg of mass up to 5 m/s to start. At 31 kg of fuel per kg, this means that you need a total of 992 kg of fuel to deliver 1kg of payload to its destination.

Generally, the higher the velocity of your rocket exhaust, the better this fuel to payload ratio will be.

 

[billy_boy_999]

yes, of course, janus, i perfectly understand the difficulties regarding fuel...but you're not addressing my point about relative speed...suppose we ignore the fuel difficulty, we have a future technology that allows us constant acceleration without fuel, say cold fusion or elf-power, doesn't matter...at what point in our acceleration curve does the energy we need to put into maintain our uniform acceleration become greater than it was? at what point do we need more elves? we don't, if the principle of relativity holds...if ever we found we were going too fast and needed more elves, the elves could say "blimey, we are now going at 7-elf speed" - which is a measure of absolute motion...

i'm saying that if we had a source of propulsion that gave a certain mass (the mass of our spaceship) a constant acceleration there would be no speed limit and no local mass dilation...

 

[selfAdjoint]

i'm saying that if we had a source of propulsion that gave a certain mass (the mass of our spaceship) a constant acceleration there would be no speed limit and no local mass dilation...

That would be a one-way force: F = ma. Violates the conservation of momentum. Elves indeed! It would only work in OZ.

 

[russ_watters]

at what point in our acceleration curve does the energy we need to put into maintain our uniform acceleration become greater than it was? at what point do we need more elves?

The energy you need to put in increases exponentially all the time. The point at which it becomes noticeabe is around 10% C (IIRC). Even using 25% C as the example though, time dilation hasn't given you much back (time hasn't slowed for you all that much).

suppose we ignore the fuel difficulty, we have a future technology that allows us constant acceleration without fuel, say cold fusion or elf-power, doesn't matter...

Its not about technology. Its the laws of physics you're disregarding here. The only way to accelerate a mass is through Newtonian action-reaction (note: that "something" can be light energy, it doesn't have to be mass).

first of all, this addresses a fundamental challenge to the philosophical implications of the principle of relativity...the cosmic microwave background radiation issues a similar challenge...if we can make quantitative measurements of increased incidents of exposure to 'cosmic dust' and measurements of motion in relation to the tiny assymetries of the background radiation, then does the principle of relativity hold?

'Cosmic dust' is a phenomenon local to our section of the galaxy and would only imply a preferred reference frame for calculating trajectories in our galaxy, not a universal preferred reference frame.

The fact that you can calculate a velocity with the respect to the CMB doesn't necessarily imply a preferred frame either: Relativity simply says that the laws of physics work the same in all frames. A preferred frame would be one where the laws of physics worked differently. The main reason people want to overturn Relativity (it seems to me) is they don't like the idea that C is constant, but time is not. The goal of ether theories is to find a frame in which time is constant and C is not. The various tortured permutations of ether theory attempt to show that so far every time we've measured the speed of light, we've measured it in that frame and that by getting outside that frame (with a light speed experiment performed in space for example), we'd see that C really is only constant in the ether.

i'm saying that if we had a source of propulsion that gave a certain mass (the mass of our spaceship) a constant acceleration there would be no speed limit and no local mass dilation...

That seem like the opposite of what relativity says. I'm not sure where you are getting the idea from except maybe f=ma. F=ma quite simply doesn't apply at relativistic speeds. A particle accelerator (for example) accelerates a constant mass particle (an electron carries no fuel) to a high fraction of C in our reference frame and the energy required to accelerate it is easily measurable. From the perspective of the electron, it is also moving at a high fraction of C, but time and space have dilated (the particle accelerator is smaller).

 

[russ_watters]

Ok, here's the one we can give him though: Using something like solar sails or ground-based laser propulsion, you can do Newtonian acceleration without carrying fuel. In that case, the energy is just e=1/2 mv^2. With a velocity of 75 million m/s, that's still a lot of zeros on your energy level.

 

[arildno]

Just a few questions:
1. I have gleaned from popular (non-scientific) sources that "vacuum" should not be regarded as "nothing" from a quantum mechanical perspective but rather as a "seething soup" of particles which do not quite succeed in remaining in stable forms over time, but "pop in and out of existence" (by transforming into other types of particles or something(?))
Is this, scientifically speaking, an unreasonably inaccurate popularization?
2.
I've heard some rave about the possibility of harnessing vacuum energy.
Are there, today, any indications that this type of "harnessing" is in fact, possible, and if so, will this harnessing give a net energy gain for the harvester (a spaceship, for example)?
(If I have to use more energy to extract the energy from the vacuum I want to use as "fuel", this method seems rather futile..)

 

[billy_boy_999]

hi russ, setting aside for a moment your thoughts on CMBR etc.,

The energy you need to put in increases exponentially all the time. The point at which it becomes noticeabe is around 10% C (IIRC). Even using 25% C as the example though, time dilation hasn't given you much back (time hasn't slowed for you all that much).

are we still talking about spaceships here? or are we talking about electrons in particle accelerators? of course if we accelerate a particle we (the observers) are stationary, as is the particle accelerator (in relation to the particle)...as such, the faster that thing goes the more energy we have to put into accelerating it...but this is not the same as what the particle experiences!

From the perspective of the electron, it is also moving at a high fraction of C, but time and space have dilated (the particle accelerator is smaller).

exactly, space and time have changed for the particle, not for us...if that electron is measuring its speed against the speed of light it will measure its speed to be zero, so will everything...but if it measures its speed using the distance we give it for the circumference of the accelerator and using the time it itself measures to cover that distance it can certainly breach the speed of light...

as well, the particle's mass has not increased in its own inertial reference frame...is this wrong? if this is wrong please explain how this doesn't contradict the principle of relativity! (our increased mass is directly proportional to a measurable absolute motion velocity - this is unacceptable!)

 

[sedam37]

There is no problem, because when time "stops" you are dead.

 

[russ_watters]

Just a few questions:
1. Is this, scientifically speaking, an unreasonably inaccurate popularization?

No, you pretty much have it.

I've heard some rave about the possibility of harnessing vacuum energy.
Are there, today, any indications that this type of "harnessing" is in fact, possible, and if so, will this harnessing give a net energy gain for the harvester (a spaceship, for example)?

Vacuum energy is transient and symmetrical and cannot be harnessed, but its a very common concept: The sites you see on harnessing it are perpetual motion hoaxes.

exactly, space and time have changed for the particle, not for us...if that electron is measuring its speed against the speed of light it will measure its speed to be zero, so will everything...but if it measures its speed using the distance we give it for the circumference of the accelerator and using the time it itself measures to cover that distance it can certainly breach the speed of light...

Well sure - if I run 3 miles in 24 minutes on a treadmill, how much distance have I really covered (0 or 3 miles?)? Using time from one frame and distance from another gives a result of >C, but it doesn't really mean anything.

For a spaceship traveling at a high fraction of C, it will measure a relatively short time to get where its going due to time dilation, but it will also measure a relatively short distance between the two points.

 

[billy_boy_999]

Well sure - if I run 3 miles in 24 minutes on a treadmill, how much distance have I really covered (0 or 3 miles?)? Using time from one frame and distance from another gives a result of >C, but it doesn't really mean anything.

Russ, thank you, this is EXACTLY what I've been trying to say...it doesn't mean anything? i think it means everything!

you're now admitting that there is NO speed barrier, you can satisfy your speed barrier by saying that time dilates and space shrinks, fine, true enough...

but using a distance from one frame and a time from another is exactly the point! a spaceship can travel a distance of 10 light years (as measured from earth) in one year (as measured from the spaceship)...that's all I'm saying...as such, the idea that relativity prohibits traveling great distances in reasonable time frames is a popular misconception...

okay?

 

[russ_watters]

Russ, thank you, this is EXACTLY what I've been trying to say...it doesn't mean anything? i think it means everything!

you're now admitting that there is NO speed barrier, you can satisfy your speed barrier by saying that time dilates and space shrinks, fine, true enough...

Do you want to use physics or not? If you use physics, the "speed" you are calculating isn't a speed.

but using a distance from one frame and a time from another is exactly the point! a spaceship can travel a distance of 10 light years (as measured from earth) in one year (as measured from the spaceship)...that's all I'm saying...as such, the idea that relativity prohibits traveling great distances in reasonable time frames is a popular misconception...

okay?

Well sure, as long as you don't keep falling into a very similar misconception about how the concept of speed is defined, we're fine. We weren't in disagreement about that point about the effects of time dilation - but that isn't what you were saying before.

 

[David]

The main reason people want to overturn Relativity (it seems to me) is they don't like the idea that C is constant, but time is not. The goal of ether theories is to find a frame in which time is constant and C is not.

c is not constant and atomic clock rates aren’t either.

Einstein clearly said in his 1911 paper that gravity fields slow down the speed of light. He specifically said:

“If we call the velocity of light at the origin of co-ordinates c', then the velocity of light c at a place with the gravitational potential Φ will be given by the relation c = c’(1 + Φ/c^2)”

These are two different speeds for the speed of light, and this is an Einstein GR equation.

Shapiro proved it with the radar signals he bounced off Venus. They slowed down when they passed the sun on the way back to the earth.

People don’t want to “overturn relativity”, they want people to get relativity right. Too many amateurs haven’t studied enough Einstein papers, and they tend to focus only on his first 1905 paper. But he wrote many others which should be studied before anyone claims to be an “expert” on “relativity”.

 

[billy_boy_999]

Well sure, as long as you don't keep falling into a very similar misconception about how the concept of speed is defined, we're fine. We weren't in disagreement about that point about the effects of time dilation - but that isn't what you were saying before.

russ - this is what i have been saying all along, maybe you have misunderstood what i was trying to say or haven't been following along or maybe i haven't been clear enough...if you go back and read the posts, as well as the title of this thread, you will find that my point has always been that relativity does not bind us to obeying a relative velocity of light, only a local one...in other words, the misconception that you cannot cover a distance of 10 light years in one year is a misreading of relativity...

Do you want to use physics or not? If you use physics, the "speed" you are calculating isn't a speed.

what is "speed"? speed is simply a measure of distance over time...what i was saying is that we can take the distance as measured from Earth and the time as measured from a moving spaceship and get a speed that is much faster than light...this is not some pedantic trick of logic - this is how you would go about measuring speed if you were undertaking such a space flight...you would measure the distance before you took off and measure how long it took you to get there in local time...

relativistic increases in mass due to high speeds do not apply and relativity does not prohibit this sort of space travel...

 

[Doc Al]

... my point has always been that relativity does not bind us to obeying a relative velocity of light, only a local one...in other words, the misconception that you cannot cover a distance of 10 light years in one year is a misreading of relativity...

If all you are saying is that if a ship is moving fast enough (some high fraction of c) with respect to the earth, then that ship can cover 10 earth-measured light years of distance in one ship-measured year, then sure! But don't think for a minute that its speed relative to Earth is now somehow faster than light. (But it doesn't have to be, in order to get the effect you are talking about.)

what is "speed"? speed is simply a measure of distance over time...what i was saying is that we can take the distance as measured from Earth and the time as measured from a moving spaceship and get a speed that is much faster than light...this is not some pedantic trick of logic - this is how you would go about measuring speed if you were undertaking such a space flight...you would measure the distance before you took off and measure how long it took you to get there in local time...

"Speed" is well-defined. It's the distance traveled divided by the time it takes---but both distance and time must be measured in the same frame. If you just mix and match measurements made in different frames, you'll get nonsense.

But, nonetheless, I believe your basic point is correct. If, somehow, you had the energy to get a ship moving fast enough (never greater than the speed of light, mind you!) then the occupants of that ship could traverse galactic distances within their lifetimes. (From the ship's point of view, these galactic distances are now quite small.)

Of course, as has been pointed out here, practical energy considerations make this scenario unlikely.

 

[billy_boy_999]

thanks for conceding the point Doc...

"Speed" is well-defined. It's the distance traveled divided by the time it takes---but both distance and time must be measured in the same frame. If you just mix and match measurements made in different frames, you'll get nonsense.

your definition of "speed" is very specific and of course this is the tacit conventional definition...but really, why do you have to keep insisting this is nonsense? the practical consequence is that you can travel 10 light years in 1 year...

as far as that not being 'faster than light' in a local sense...of course! in a local sense your speed as measured against light is always ZERO!

why are we so married to this pedantic language in insisting that 'nothing can travel faster than light'? it seems like a meaningless mantra to me, and i think it contributes to a popular misapprehension of relativity...(and popular enough to be evidenced on this board as well, it seems)...

your point about practical energy considerations making the scenario unlikely is absolutely valid...THESE considerations are the limits of space travel, NOT relativistic 'speed limits'...

 

[selfAdjoint]

You seem to think you know more about relativity than the others responding to you on this thread. But all I have seen from you is wild assertions and language tricks.

Relativity (the special kind) is derived logically from two postulates:

1. All inertial frames experience the same physics within themselves.
2. All inertial frames experience the same value of the speed of light.

From these one can deduce the Lorentz transformations, and the Lorentz transformations say that it would take an infinite amount of energy to accelerate any mass up to the speed of light, and that the relative speed of two inertial frames cannot exceed the speed of light.

If you have a theory in which these things are false then it isn't relativity; it's something else. And as something else it has to be justified the same way relativity has been, by experiment.

 

[Doc Al]

thanks for conceding the point Doc..

What point did I concede? This is all relativity 101.

your definition of "speed" is very specific and of course this is the tacit conventional definition...but really, why do you have to keep insisting this is nonsense? the practical consequence is that you can travel 10 light years in 1 year...

"My" definition of speed is the only one used in physics. Your definition is a quaint earth-bound one! Imagine you were born in Galaxy X, which just happens to be moving at 0.9c with respect to earth. You would get a kick out of those old-fashioned "earth light years" that they insist on using. Would you insist that they really should be using "Galaxy X" light years instead--the one true unit!

as far as that not being 'faster than light' in a local sense...of course! in a local sense your speed as measured against light is always ZERO!

Huh?

why are we so married to this pedantic language in insisting that 'nothing can travel faster than light'? it seems like a meaningless mantra to me, and i think it contributes to a popular misapprehension of relativity...(and popular enough to be evidenced on this board as well, it seems)...

If you wish to talk about speeds and times and distances then you must define things carefully. If you wish to talk about when the ship will arrive at its destination as measured by Earth clocks, then you'd better measure the speed of that ship properly. It will still take Time = Distance/speed to reach the destination. No one on Earth will say that the ship is traveling faster than c. (Well... apparently some will. )