# Traveling to Alfa Centauri at 1/2 the speed of light

1. May 29, 2012

### McCartney

Not a physicist or a mathematician, but reading about cosmology whenever I have a chance.

Alfa Centauri is 4.37 light-years away, so I conclude that it takes 4.37 x 2 traveling at 1/2 the speed of light. However, I am assuming that 4.37 x 2 is measured here on Earth. How much time has elapsed for the pilot of the spaceship?

In other words: How do we measure the distance to Alfa Centauri? Because of time dilation I am assuming it takes less time for the pilot to get there. I have heard of length reduction while moving, but i don't see how this applies to the distance to Alfa Centauri.

So the question is:

What is the real distance to Alfa Centauri?

I am confused.

Last edited: May 29, 2012
2. May 29, 2012

### Vorde

There is no 'real' distance. In relativity, everything is, well, relative. We would measure one distance/time, and a pilot onboard a spaceship would measure a totally different number (less time, or alternatively less distance). Both would be completely valid measurements.

3. May 29, 2012

### McCartney

I have a hard time visualizing what you say. I see that the clock in the spaceship is slower, but the pilot cannot tell. One woud think that for the pilot it would take 4.37 x 2 ly to get there. I guess a ly implies both the time and the space. However, if the pilot has to drive the spaceship for 4.37 x 2 ly to get there. The guy monitoring the flight on Earth will have to wait much longer. For the Earth bound person it would seem that Alfa Centauri is farther. Unless, the distance is shorter for the spaceship. I suspect the latter is correct, but cannot put it into words.

In other words, the people on Earth wait for 4.37 x 2 ly for the completion of the trip and the people on the spaceship have to wait less.

4. May 30, 2012

### Drakkith

Staff Emeritus
An observer on the ship would experience time at 0.866 the speed of an observer back on Earth. So the pilot of the ship would experience a local time for the trip to Alpha Centauri of 7.45 years instead of 8.74 years.
Look up Special Relativity on wikipedia to find all the equations to use, or look up a Special Relativity calculator on google (like i did) if you don't want to learn the math.

5. May 30, 2012

### McCartney

OK, thanks.

So according to the Lorentz transformation two different observers will see different time and distance.

Does that mean that space travel will be much shorter than anticipated if traveling real fast?

Obviously it takes less time to get to Alfa Centauri than anticipated.

6. May 30, 2012

### Whovian

One thing to note is that a lot of things are relative. Saying "something's going fast" means nothing, you'd have to say "something's going fast with respect to this other thing." If we have observer A and observer B moving quickly relative to each other (like an observer on Earth and an observer in the spaceship), observer A (on Earth, in this case) observes B's clock as ticking slowly, but observer B observes A's clock as ticking slowly.

But yes, space travel will be shorter than anticipated when traveling quickly with respect to the Earth and the destination. (For simplicity, let's assume the Earth and the destination are in the same frame of reference.)

7. May 30, 2012

### Drakkith

Staff Emeritus
To the person doing the traveling, yes. If you increased your speed to 0.8c it would only take 60% of the time as a person on Earth would experience.

8. May 30, 2012

### Chronos

And this time line does not consider the need for controlled acceleration and decelleration during the journey. Human physiology would greatly constrain how quickly you could reach .5c, then slow back down to zero.

9. May 30, 2012

### McCartney

I believe the acceleration would further slow down the clock. Assuming the acceleration is a form of gravity. Is that correct?

How fast could a spaceship travel in space assuming there is little friction and little pull by gravity?

10. May 30, 2012

### Vorde

Infinitely close to the speed of light, but never at the speed of light.

11. May 30, 2012

### Chronos

It would be the same as for gravitational time dilation. At only a g or so [to accomodate human physiology], the effect would be negligible.

12. May 30, 2012

### McCartney

I am familiar with the concept that the mass becomes larger and supposedly infinite at the speed of light. But, at some point the acceleration needed to to go even faster must be enormous due to the increment in mass.

However, I assume once a respectable speed is reached there is no need for more acceleration to maintain speed due to negligible friction and gravity. So perhaps intergalactic space travel will be cheap (good mileage) in relationship to the enormous distances.

13. May 30, 2012

### Vorde

Friction is practically absent in space, especially in the interstellar void, practically I don't really think friction is ever an issue. The thing is you need ridiculous, ridiculous amounts of energy just to get a sizable object up to a fraction of the speed of light. To accelerate something like a spaceship up to those speeds is still well outside our reach as a civilization.

14. May 31, 2012

### Chronos

I recall having seen a figure of about 4 lbs of antimatter per light year [assuming highly efficient conversion to thrust]. Antimatter is not something you want laying loose in the cargo hold, so JIT generation would be essential.

15. May 31, 2012

### Drakkith

Staff Emeritus
Here's the thing. The amount of fuel and thrust needed to provide 1g of acceleration does NOT change for a person inside the spaceship under acceleration. (Ignoring the loss of mass as fuel is spent and ejected as exhaust from the engines) They will accelerate at a constant 1g until the ship stops accelerating or it runs out of fuel. The "increase" in mass due to high velocity is...not really accurate. Mass is generally considered to be something calculated in the rest frame of an object. Relativistic mass is an outdated term if what I've been told about it is true, and relativistic mass is what is increasing as velocity increases. In the frame of the spaceship no mass is ever gained.

Correct. Once you get up to speed you will travel effectively forever as long as you don't run into anything.

16. May 31, 2012

### SHISHKABOB

or require course corrections >.>

17. May 31, 2012

### twofish-quant

Get rid of it, since it's wrong. There was a popular book in the 1940's that used it to explain relativity, but that's caused more confusion.

The reason you can't travel faster than light is that light always travels at the speed of light. If you shine a flashlight, the light is traveling away from you at speed C. If you run toward the light, it's still traveling away from you at speed C. No matter how hard you try, light is always going away from you at the speed C, so you'll never catch up to the beam of light.

The problem is that physics but biology and sociology. It doesn't take that much fuel to go into interstellar space. So if you don't care how long it takes to get to a star, you'll make it there. However, our bodies self-destruct after about 70 years which imposes a limit.

18. May 31, 2012

### twofish-quant

Maybe, but it looks like something that can be solved with a few hundred years of effort.

Personally, my guess is that "suspended animation" will turn out to be an easier problem than acceleration to 0.5c. Or you could do both. Once you are an ice-cube, then you can accelerate at 1000g without turning into jelly.

19. May 31, 2012

### Ryan_m_b

Staff Emeritus
It really depends on future economics and sociology to determine what is regarded as "cheap" but I doubt anyone will ever think interstellar (never mind intergalactic) space travel would be cheap1!

To accelerate a vehicle with the mass of a space shuttle to 0.5C would take at minimum 22.5ZJ. That would require the perfect harvest and perfect transfer to momentum of all the solar energy hitting Earth for one and a half days! Or to put it in another perspective, all energy produced by human civilisation pumped into this vehicle for ~45 years! And then you have to do that all again to slow it down2.

1The reason I say it wouldn't be considered cheap is because throwing around that kind of energy is damn near apocalyptic. Any civilisation that didn't treat it with a healthy amount of fear isn't going to last long. If we throw in shedloads of handwavium and propose that a future space effort could simply send a small, cheap probe to a large asteroid and have it replicate and reassemble the asteroid into a very thin, Earth sized solar array with a several-hundred-petawatt laser to shine on the vehicles laser sail whilst we might think we've made a gateway to interstellar travel a more careful look would reveal we've made a device capable of snuffing out all life on Earth easily. A nation that attempts this would be regarded by other nations as well as one IRL that tried to stock all its planes with nuclear warheads that detonate if the plane is mildly damaged.

2That was all back of the envelop so take those numbers with a tiny pinch of salt just incase I made a basic mistake (though I don't think I have).

20. May 31, 2012

### Vorde

I've often thought of similar techniques, or the general idea of figuring out how to accelerate the whole body at once to eliminate an acceleration barrier. I think the larger problem in terms of a civilization-wide thing (apart from figuring out where to get the energy), is the acceptance that interstellar (and potentially, even intergalactic) travel will require the fragmentation of our civilization through time.

Traveling long distances would either require suspended animation for long periods of time (which obviously splits up the time of the astronauts and the people at home) or travel at relativistic speeds, which due to time dilation would also split up the timelines of the two parties.

In a way, the best way to insure the survival of our civilization would be interstellar travel.