Just how far away is that star?

[jnorman]

as with many laypersons who have an abiding interest in physics and the nature of reality, i only know enough to generally confuse myself. so if i am asking a senseless question, please tell me the fallacy in my assumptions.

assume that i am going on a short interstellar journey to a nearby star that we measure on Earth to be about 10 LY away. i have a ship that can travel at 0.99999999C.

an observer on Earth will watch my trip to the star and report that it took me about 11 years to reach my destination, and another 11 years to return - a total of about 22 years have passed on the clocks on Earth during my journey. however, due to time dilation, the clock on my ship indicates that only about 2 years have passed during the entire journey.

so, have i traveled faster than the speed of light (ie, gone 20LY in 2 years time), or is the star really not 10 LY distant? am i making some incorrect assumption about time dilation? thanks for any comments that might help me understand this better.

 

[Janus]

While you are traveling at 0.99999999c wtih respect to the Earth, you will measure the distance between the star and the Earth as only being 1 ly. Thus for you, you only had to travel a total distance of 2 ly at 0.99999999c, which took you 2 yrs.

 

[jnorman]

thanks janus - hence the title of my question, so, just how far away is that start in reality? is it only 1LY away from earth, or is it 10LY? or is distance just an illusion? apparently, if you get close enough to C, the distance between galaxies is only a few feet - this is starting to sound crazy.

also, it sounds like faster-than-light travel is not really needed to explore the universe if we can just get close enough to C to make all the so-called vast distances shrink down to almost no distance... of course that does not address the then enormous differences in time passage for those exploring and those who remain at thome awaiting the results of the exploration.

 

[russ_watters]

thanks janus - hence the title of my question, so, just how far away is that start in reality? is it only 1LY away from earth, or is it 10LY? or is distance just an illusion?

Its not an illusion, its just relative. When you get back to earth, you'll find that the distance you traveled isn't the only thing you and a guy on Earth disagree about - you'll also disagree about how long the trip took.

 

[yogi]

The proper distance to the star in the problem you have posed will be measured in the Earth frame - the star and the Earth are not moving relative to one another, so the proper distance is 10 LY. The distance you calculate in the spaceship is based upon the fact that your clock is running at different rate and therefore since d = vt the distance is apparently less because t is less.

 

[BGreene]

absolute spacetime

Motion through space-time is… complementary, so to speak. When you are stationary in space, you move at light speed through time. When you move at light speed (just assume for the sake of it) through space, you are stationary in time. That’s why Einstein said when someone moves at light speed time doesn’t flow for them. So the more we speed through space, at a lesser rate time flows for us. Thus it appears as though it has taken a hell of lot of years for the traveler, to a person watching from earth… since earth’s speed through time is little compared to the traveler’s. The distance to the star cannot be regarded as absolute; the time taken cannot be regarded as absolute, since these observations change from observer to observer. Only the totality of space-time is absolute, or you could say invariable.

 

[Rob Woodside]

Motion through space-time is… complementary, so to speak. When you are stationary in space, you move at light speed through time.

Where on Earth did you get that idea? Time happens, what on Earth could you be moving through? Speed comes from the idea of distance traveled divided by time taken. Time is NOT distance - in spite of welding time and space together to get space-time. Timelike curves are very different than spacelike curves. The signature in the metric tells you the difference!

 

[BGreene]

what metric? minkowski metric of spacetime? refer to Brian Greene's Elegant Universe, pages 47-51...

 

[Rob Woodside]

I saw the Nova program. Don't believe everything you read or see on Nova! Why do believe what he says? I assume that on the pages you refer to he talks about "travelling through time", after all it is just part of the fabric of space-time?

 

[pervect]

Bgreene is just saying that the norm of a 4 velocity is "c". (I usually use geometric units, where the norm of the 4-velocity is one, but in that case c=1 of course).

 

[BGreene]

well cos he's the greatest physicist I've ever come across... I'm awestruck by his explainotary power... you tht's wht he says... cos it's spacetime after all, we do regard time as we treat space... that's wht einstein has said as well. it's one whole jumble, space-time.

 

[BGreene]

directly quoted from the book... "here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed- that of light.

 

[Rob Woodside]

Bgreene is just saying that the norm of a 4 velocity is "c". (I usually use geometric units, where the norm of the 4-velocity is one, but in that case c=1 of course).

Thanks Pervect, I react badly to nonsense. Merry Xmas.

 

[Rob Woodside]

directly quoted from the book... "here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed- that of light.

Thank you for the quote, Caveat Emptor!

 

[yogi]

That quote from Brian Greens book has come up before - it was questioned where Einstein had uttered those words - Hawking and Epstein have made analogous statements and they can be found in their popular books, but I could not find where Einstein had made such a statement - and I think the thread died w/o anyone finding the source.

Whether Einstein said it or not, it is a convenient concept for deriving the velocity transforms graphically.

 

[Rob Woodside]

Thanks Yogi. There's quite a difference between speed and the magnitude of the velocity 4 vector, that by conventions and definition can be normalized to anything. Some may take it as +c, I prefer (for no good reason) to take it as -1.