To Saturn at (nearly) the speed of light

[Baggins101]

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@

 

[PeterDonis]

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

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.)

 

[phinds]

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.

 

[Baggins101]

But.. but... but... if a rocket leaves Earth at near the speed of light, wizzes around then returns to Earth with the ship clock showing just an hour has passed, am I wrong in thinking that a lot more than an hour will have passed on Earth clocks??

 

[russ_watters]

But.. but... but... if a rocket leaves Earth at near the speed of light, wizzes around then returns to Earth with the ship clock showing just an hour has passed, am I wrong in thinking that a lot more than an hour will have passed on Earth clocks??

You have it half backwards: no one ever sees anything outvof thevordinaryvon their own clock. So since the rocketv s moving, its clock shows much less time passed, while our clocks show exactly what is expected (2 hrs or so).

 

[Baggins101]

You have it half backwards: no one ever sees anything outvof thevordinaryvon their own clock. So since the rocketv s moving, its clock shows much less time passed, while our clocks show exactly what is expected (2 hrs or so).

Thanks, but this still doesn't make sense. Are you saying that if I am in a rocket traveling at near light speed I will cover the distance to Saturn, according to my on board clock, in less time than it takes light to reach there? I understand that there is a shortening of length with speed as well as a distortion of time but what you seem to be suggesting is that my rocket will travel faster than light since you say my clock will register less than the (arbitrary) two hours those on Earth see me take traveling at (near) light speed.

 

[Baggins101]

I really would appreciate a clear explanation if possible as I am currently debating with a big bang denying, god fearing neanderthal who will be delighted that I have tripped myself up...! He will proclaim this as evidence for his cause (rather than evidence little old me tripped!)

 

[russ_watters]

Thanks, but this still doesn't make sense. Are you saying that if I am in a rocket traveling at near light speed I will cover the distance to Saturn, according to my on board clock, in less time than it takes light to reach there? I understand that there is a shortening of length with speed as well as a distortion of time but what you seem to be suggesting is that my rocket will travel faster than light since you say my clock will register less than the (arbitrary) two hours those on Earth see me take traveling at (near) light speed.

You're still not quite putting the two pieces together: if both the time and distance traveled are observed to be less by the moving observer than by the stationary one, then he doesn't observe his speed to be above light speed.

 

[phinds]

Baggins, this is EXACTLY the "twin paradox" scenario except that it is using shorter (but proportional) times for the trip. Google "twin paradox" and you'll get a complete discussion of this whole thing.

 

[Dale]

Thanks, but this still doesn't make sense. Are you saying that if I am in a rocket traveling at near light speed I will cover the distance to Saturn, according to my on board clock, in less time than it takes light to reach there? I understand that there is a shortening of length with speed as well as a distortion of time but what you seem to be suggesting is that my rocket will travel faster than light since you say my clock will register less than the (arbitrary) two hours those on Earth see me take traveling at (near) light speed.

In the sun's rest frame the distance of closest approach between Earth and saturn is about 1.25E9 km, which corresponds to 4174 light-seconds. If you travel inertially to saturn at .99 c then in the sun's rest frame it will take 4213 s. In your rest frame you will be stationary and saturn will be at a distance of 1.76E8 km and will travel to you in 594 s, which is a speed of .99 c.

 

[PeterDonis]

But.. but... but... if a rocket leaves Earth at near the speed of light, wizzes around then returns to Earth with the ship clock showing just an hour has passed

If the rocket is going to Saturn, then a little more than an hour will have passed on *Earth* clocks when it returns to Earth. Much less time than that will have passed on the rocket's clock (how much less depends on how close to the speed of light it is going; if it travels close enough to the speed of light the time elapsed on the rocket's clock can be as small as you wish).

Are you saying that if I am in a rocket traveling at near light speed I will cover the distance to Saturn, according to my on board clock, in less time than it takes light to reach there?

No. A light beam that is emitted from Earth at the same instant your rocket leaves will reach Saturn before your rocket does. That's an invariant statement; it's true for all observers.

I understand that there is a shortening of length with speed as well as a distortion of time

Yes, and they both change in just the right way to keep the speed of light the same with respect to both Earth and you in the rocket.

• To observers on Earth, the distance between Earth and Saturn is a little more than one light-hour, and it takes light a little more than an hour to reach Saturn, and your rocket a little longer than that.

• To you in the rocket, the distance between Earth and Saturn might be, say, one light-minute, and a light beam that starts from Earth at the same time you do will take one minute to get to Saturn; and you will arrive at Saturn (more precisely, Saturn will arrive at your location, since in your own frame you don't move) in a little longer than a minute--i.e., a little longer than the light takes.

but what you seem to be suggesting is that my rocket will travel faster than light

No.

since you say my clock will register less than the (arbitrary) two hours those on Earth see me take traveling at (near) light speed.

This is true, but it doesn't imply that you are traveling faster than light. See above.

 

[Baggins101]

Baggins, this is EXACTLY the "twin paradox" scenario except that it is using shorter (but proportional) times for the trip. Google "twin paradox" and you'll get a complete discussion of this whole thing.

Thanks. This is interesting since I assumed time dilation was a result of the increase in mass (and therefore the curvature of space) experienced by the rocket as it approaches light speed. I therefore assumed the effect would be similar to a body going over the event horizon of a black hole in that the body would experience no change in the passing of time at this point yet to an observer the body would appear to slow down and almost freeze.

Unless I've misunderstood that too!

The consequence of time dilation, therefore, is that travel to distant solar systems and even galaxies could be achieved in just moments of perceived time for a traveller if speed approached close enough to the speed of light... ??

 

[phinds]

The consequence of time dilation, therefore, is that travel to distant solar systems and even galaxies could be achieved in just moments of perceived time for a traveller if speed approached close enough to the speed of light... ??

Yep. Now if we just COULD travel at those kinds of speeds. Of course we would be totally obliterated by the first speck of space dust that the ship hit, but what's a little matter of death when you love speed?

 

[mfb]

Thanks. This is interesting since I assumed time dilation was a result of the increase in mass (and therefore the curvature of space) experienced by the rocket as it approaches light speed.

Time dilation (as discussed here) is an effect of special relativity. Curved spacetime (and therefore gravity) has nothing to do with it.

Gravitational time dilation works completely different.

The consequence of time dilation, therefore, is that travel to distant solar systems and even galaxies could be achieved in just moments of perceived time for a traveller if speed approached close enough to the speed of light... ??

Yes, assuming you survive the acceleration.
If you have a ship that maintains a constant acceleration of 1g (as seen by the ship), you can easily reach other galaxies within a few decades for you.

 

[Baggins101]

Yep. Now if we just COULD travel at those kinds of speeds. Of course we would be totally obliterated by the first speck of space dust that the ship hit, but what's a little matter of death among when you love speed?

Technicalities. Mere technicalities! I am already packing my suitcase!

So... why all the "you can't travel faster than the speed of light" fuss then? We CAN travel faster than the speed of light if we can travel a hundred light years in a few hours... Admittedly Ford will have to up their game a bit and you wouldn't be able to pop back if you left the oven on but it IS theoretically possible.

 

[mfb]

So... why all the "you can't travel faster than the speed of light" fuss then? We CAN travel faster than the speed of light if we can travel a hundred light years in a few hours...

The distance won't be 100 light years for you.
And the time won't be a few hours for everyone else.

 

[Baggins101]

The distance won't be 100 light years for you.
And the time won't be a few hours for everyone else.

Semantics. I will be sunning myself on a planet a hundred light years from Earth just a few of my hours after waving goodbye. If it looks like a duck and quacks like a duck...

 

[mfb]

There are so many nice beaches here on Earth ;).
And the attempt to get back would be completely pointless - on earth, 200 years passed. 200 years ago, Napoleon still lived and the US declaration of independence was still new. That is the real difference to science-fiction FTL. Every journey would basically "kill" everyone you know just because you rush through the centuries.

 

[phinds]

Technicalities. Mere technicalities! I am already packing my suitcase!

So... why all the "you can't travel faster than the speed of light" fuss then? We CAN travel faster than the speed of light if we can travel a hundred light years in a few hours... Admittedly Ford will have to up their game a bit and you wouldn't be able to pop back if you left the oven on but it IS theoretically possible.

NO ... we are NOT traveling faster than the speed of light. You still aren't getting it, but don't feel bad as this is a confusing concept when you first get onto it.

What's happening is that you are traveling through a different world line than the folks back home, that's all. Nobody is traveling faster than c. According to the folks at home, when you get to your destination, you have been traveling for an ENORMOUS amount of time ... just a bit longer than it would have taken for light to make the same trip.

 

[PeterDonis]

We CAN travel faster than the speed of light if we can travel a hundred light years in a few hours...

No, because the light still gets there faster than you do according to your clock; if it takes you a few hours by your clock, it takes the light less time than that by your clock. And the distance, according to you, is shortened so the light still travels at $c$ according to you--and your destination travels at less than $c$, according to you. So nothing ever moves faster than the speed of light according to any observer.

 

[Dale]

If it looks like a duck and quacks like a duck...

But it doesn't.

Nothing can travel with a speed faster than c in any reference frame. Speed is the distance in one frame divided by the time in the same frame. The distance in one frame divided by the time in another is not speed. It doesn't look like speed (wrong formula) and it doesn't act like speed (wrong behavior). So it isn't speed.

 

[Baggins101]

NO ... we are NOT traveling faster than the speed of light. You still aren't getting it, but don't feel bad as this is a confusing concept when you first get onto it.

What's happening is that you are traveling through a different world line than the folks back home, that's all. Nobody is traveling faster than c. According to the folks at home, when you get to your destination, you have been traveling for an ENORMOUS amount of time ... just a bit longer than it would have taken for light to make the same trip.

Thanks. I do get it though. My point is that it really is irrelevant what happens to space and time while I travel (assuming this is a one way trip!). The end result is the same: me on a planet 100 light years from Earth and me only one day older than when I left. It might be a one way only trip but it is still space travel, for all intents and purposes, at very much faster than the speed of light.

Now I just need to build a rocket with a big, big engine. And get a can for some spare fuel!

Good old Albert!

 

[Baggins101]

But it doesn't.

Nothing can travel with a speed faster than c in any reference frame. Speed is the distance in one frame divided by the time in the same frame. The distance in one frame divided by the speed in another is not speed. It doesn't look like speed (wrong formula) and it doesn't act like speed (wrong behavior). So it isn't speed.

Indeed, you are right. Yet here I am in sandles and shorts a hundred light years from Earth and I only waved goodbye to my boss yesterday. I didn't break any speed limits but the end result is just the same.

Its cheating really. The rules say you can't travel faster than light yet by going fast you shorten space and dilate time and get around the speed limit with the same end result.

Thete are a few technical issues, admittedly, but there might yet be hope for humanity in the centuries ahead.

 

[PeterDonis]

the end result is just the same.

In some ways it is and in some ways it isn't. If you send your boss a message by radio as soon as you arrive a hundred light years from Earth, your boss will be long dead when the message arrives on Earth (since at least two hundred years will have elapsed on Earth between your departure and your message arriving).

 

[phinds]

Thanks. I do get it though. My point is that it really is irrelevant what happens to space and time while I travel (assuming this is a one way trip!). The end result is the same: me on a planet 100 light years from Earth and me only one day older than when I left. It might be a one way only trip but it is still space travel, for all intents and purposes, at very much faster than the speed of light.

Now I just need to build a rocket with a big, big engine. And get a can for some spare fuel!

Good old Albert!

You do not in any practical sense travel faster than c. The point of your destination when you arrive will be older than it was when you started your trip by the amount of time it takes for light to get from Earth to there, not one day older as you seem to think. It is on the same world-line as Earth, which will have also aged by the same amount and if you were to make a return trip at the same speed, both planets would have aged by that much again by the time you get back.

 

[Dale]

Indeed, you are right. Yet here I am in sandles and shorts a hundred light years from Earth and I only waved goodbye to my boss yesterday. I didn't break any speed limits but the end result is just the same.

As PeterDonis mentioned the end result is decidedly not the same.

there might yet be hope for humanity in the centuries ahead.

I certainly agree with that.

 

[.Scott]

The consequence of time dilation, therefore, is that travel to distant solar systems and even galaxies could be achieved in just moments of perceived time for a traveler if speed approached close enough to the speed of light... ??

If you departed the Earth and then traveled in a spacecraft that maintained 1G of acceleration (10M/s^2), then in about 65 years, you could reach any point in the known universe. Actually there would be radiation issues that would destroy the spacecraft - and we won't talk about fuel economy. But it demonstrates that the foreshortening of distances can have a huge effect on the travel time as seen by the traveler.

 

[ghwellsjr]

If you departed the Earth and then traveled in a spacecraft that maintained 1G of acceleration (10M/s^2), then in about 65 years, you could reach any point in the known universe. Actually there would be radiation issues that would destroy the spacecraft - and we won't talk about fuel economy. But it demonstrates that the foreshortening of distances can have a huge effect on the travel time as seen by the traveler.

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.

 

[Baggins101]

If you departed the Earth and then traveled in a spacecraft that maintained 1G of acceleration (10M/s^2), then in about 65 years, you could reach any point in the known universe. Actually there would be radiation issues that would destroy the spacecraft - and we won't talk about fuel economy. But it demonstrates that the foreshortening of distances can have a huge effect on the travel time as seen by the traveler.

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?

 

[Baggins101]

As PeterDonis mentioned the end result is decidedly not the same.

I certainly agree with that.

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

 

[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.