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Relativity question

Squeegee Beckenheim

Penultimate Amazing
Squeegee Beckenheim
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Dec 29, 2010
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Okay, this is a simple question for anybody who knows the ins and outs of special relativity, but I'm finding different answers everywhere I look.

Let's assume for the sake of argument that it's possible for a spaceship to travel at lightspeed (or as close to lightspeed as allows calculations of different frames of reference to actually make sense), and let's assume for the sake of argument that we can ignore acceleration and deceleration times.

How long would it take that ship to travel 100 lightyears from the perspective of people on the ship, and from the perspective of people on Earth?
 
The Great Zaganza said:
At light-speed?

no time at all for the people on-board.

For people on earth: 100years.
Click to expand...

We can expand on this a little. Since SR says it's impossible for a massive object to travel at c, we can instead ask a similar but slightly adjusted question: what's the limit on travel experienced by a spaceship traveling 100 lightyears as it approaches c?

The answer is also zero. The closer you get to c, the closer the travel time gets to 0, and you can get arbitrarily close to zero travel time with enough (still sub-c) velocity.

So that gets to the heart of what I think he was after, but we've actually sidestepped the singularity: the ship never actually goes c.
 
I once read a sci-fi book by Poul Anderson, titled 'Tau Zero'. It dealt with the concept that the closer you get to c, the higher the mass of the ship becomes. I think you end up with infinite mass if you reach c. Which cannot happen, of course.
https://en.wikipedia.org/wiki/Tau_Zero
 
jonesdave116 said:
I once read a sci-fi book by Poul Anderson, titled 'Tau Zero'. It dealt with the concept that the closer you get to c, the higher the mass of the ship becomes. I think you end up with infinite mass if you reach c. Which cannot happen, of course.
https://en.wikipedia.org/wiki/Tau_Zero
Click to expand...

Relativistic mass diverges as you approach c, but relativistic mass is dumb, and you shouldn't use it. Rest mass is the only mass that really matters. Many modern relativity texts don't even introduce relativistic mass.

ETA: at extreme relativistic velocities, the CMB from the forward direction would get blue-shifted enough to produce significant radiation pressure on the ship, slowing it down. You can't shield from photons.
 
Last edited:
Ziggurat said:
Relativistic mass diverges as you approach c, but relativistic mass is dumb, and you shouldn't use it. Rest mass is the only mass that really matters. Many modern relativity texts don't even introduce relativistic mass.

ETA: at extreme relativistic velocities, the CMB from the forward direction would get blue-shifted enough to produce significant radiation pressure on the ship, slowing it down. You can't shield from photons.
Click to expand...

It's an old book. That's my excuse, anyway.:)
 
Squeegee Beckenheim said:
How long would it take that ship to travel 100 lightyears from the perspective of people on the ship, and from the perspective of people on Earth?
Click to expand...
We need to answer this question for two different destinations: one that's 100 lightyears away as seen from Earth (X), and one that's 100 lightyears away as seen from the ship (Y).

Y is much farther away than X.

The trip to X takes about 100 years according to the people on Earth. It takes less than that on the ship, but only because the distance for them is compressed. If they're going fast enough to finish in 3 hours of ship-time, the distance was about 3 light-hours. If they're going fast enough to finish in a week, the distance was about a lightweek. If they're going fast enough to finish in 6.2 seconds, the distance was about 6.2 lightseconds.

The trip to Y takes about 100 years on the ship because it's about 100 lightyears away on the ship. But, for people on Earth, it's a lot farther away than that, so it takes a longer time. If its distance as measured from Earth is 400 lightyears, the trip will take about 400 years on Earth. If the distance as measured from Earth is 83 million light-years, the trip will take about 83 million years on Earth. No matter how far away it seems from Earth, we started by defining this point as whatever distance away gets compressed to 100 lightyears for the ship at the ship's speed, so it only takes about 100 years for the ship.

* * *

Keep in mind that when they say that travel at high sub-light speeds reduces the time so much that you can seem to be going faster than light, they're mixing two different points of view: time aboard the ship, and distance as measured on Earth. And that's not really a valid way to look at physics. (In fact, it's perfectly equivalent to using the distance as measured from the ship and the time that passed on Earth... which would give the opposite impression of moving pretty slowly because it's a long time and a short distance. You can't use one point of view for distance and the other for time either way.)
 
Doesn't the distance outside the ship shrink from the perspective of people inside the ship? I'm thinking of the thought experiment of someone with a long ladder running through a short room. From the perspective of someone in the room the ladder shortens so that it's possible to close both doors briefly with the ladder still inside, whereas from the perspective of the person with the ladder the room becomes even shorter and the same action closes each door in turn rather than simultaneously.
 
If you were on earth watching a ship travelling to a destination 100ly away at almost c then it would take 200+ years for the observer on earth to see it arrive at the destination.
For an observer at the destination watching the ship leave earth the journey would take almost no time.
 
alexi_drago said:
If you were on earth watching a ship travelling to a destination 100ly away at almost c then it would take 200+ years for the observer on earth to see it arrive at the destination.
For an observer at the destination watching the ship leave earth the journey would take almost no time.
Click to expand...

Which is why it's important to note that what you see is different from what you "observe" in relativity. Both viewers will observe the same travel time of 100+ years.
 
Squeegee Beckenheim said:
Doesn't the distance outside the ship shrink from the perspective of people inside the ship?
Click to expand...
That is length contraction - the lengths measured by observers in a ship getting arbitrarily close to the speed of light will contract toward zero.
What you then describe is the ladder paradox, which like many paradoxes in SR is resolved:
The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally and therefore undergoing a Lorentz length contraction. As a result, the ladder fits inside a garage which would normally be too small to contain it. On the other hand, from the point of view of an observer moving with the ladder, it is the garage that is moving, so it is the garage which will be contracted to an even smaller size, thus being unable to contain the ladder. This apparent paradox results from the mistaken assumption of absolute simultaneity. The ladder fits into the garage only if both of its ends are simultaneously inside the garage. In relativity, simultaneity is relative to each observer, and so the question of whether the ladder fits inside the garage is relative to each observer, and the paradox is resolved.
Click to expand...
 
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