K-PAX: A Scientific Analysis of Interstellar Travel and the Speed of Light

[Livingod]

Let's say you are driving a racecar from one end of a field to the other. Let's say that you can travel at exactly constant velocity for the entire ride. Let's also say that it takes you exactly 1 minute to make it their, when you travel at constant velocity (meaning that your speed and direction remain exactly the same). Now, try traveling to the end, but at a slight angle. It would, logically, take you longer to do so, because your speed is distributed over more than one dimension now (instead of just being straight, you now have to go forward, and a little side-ways).


Now, according to Relativity, our movement is always exactly equal to "c" (the speed of light). However, it is distributed between spatial movements and your movement through time. Meaning that if you speed up in space, you slow down in time (just as when I give more of my speed to going "left" I have less for going "forward").

people, people, people.

Calculate the time required to travel using Mentat's racecar example (above) and the Phythagorean Theorem and you shall get that the time is not "negative time" but it is an imaginary number:

c = speed of light, n = speed of Prot (n > c), t = time

c^2 = n^2 + t^2

t^2 = c^2 - n^2
c^2 < n^2
t^2 < 0
you get that t^2 is a negative number.
t is an imaginary number

 

[BoulderHead]

Say, a movie I've actually seen!

Forget the math, was the man insane or not is all I care to know.

 

[Livingod]

mentat, please, tell me where you got that racecar example, please, I need to know.

boulderhead, i would say that he was not insane. seeing that he can detect UV rays, communicate with animals, and he explains how he got here really good. and unless anywhere in the movie it says that the disabled man knows einstein's special theory of relativity really well, i would say that he is not crazy.

NOT CRAZY

 

[Louis Cypher]

no but u 2 are.

lol

 

[tribdog]

if it takes an infinite amount of energy to accelerate to the speed of light does it take something traveling above c an infinite amount of energy to slow down to the speed of light

 

[Livingod]

yes it does, tribdog...

 

[tribdog]

thank you, livingod
is your name missing a g or a d? Living god or living odd?

 

[Mk]

yes it does, tribdog...

So you are saying that a tachyon with an imaginary value for rest mass would need infinite energy to go down to under the speed of light?

 

[Livingod]

i would think so, yes. well, we may never find out until we make further progress in this area of physics.

tribdog, its "living god", because that is what my name literally means.

 

[curiouschemist]

Why only 2-D?

My question, Livingod, is why only consider the motion in one spatial dimension and the time dimension? What about, say, a rotating disc, which must by definition move through two spatial dimensions? Or an expanding/contracting object (say a collapsing star)? What happens when these approach the speed of light, since their movement is spread out over more than two dimensions, wouldn't that mean you would have to "spread it less?"

This raises my second question, so you're moving 1/3c in the x plane, 1/3c y plane, and 1/3c z plane... how much have you decreased the passage of time? Exact figures aren't necessary, just a concept, and I don't have the answer... I'm just curious and I'm not a relativistic physicist by any means. I'm open to any constructive input on this question as well, not just Livingod's...

 

[voodoomagic]

No, Ploegman. I don't think that that part of K-Pax made any sense. Here is why. He said that, even after harnessing the movement of something that was going faster than the speed of light, it took him a long time to get here. Special Relativity shows that, if something were to go faster than c, time would be backward for that object. "Prot" would have had to have arrived on Earth before he departed K-PAX, because time would be backward.

so, under c time goes "forward", and over it goes "backward" then at c would you not experience any time?

 

[Livingod]

to curiouschemist,


consider every point of the disk by itself. we divide the disk into an infinite set of points. then, for each point, consider every point in time of that point by itself. we take one point, and divide that into infinite different points in time. basically, consider every point in space-time of the disk by itself. each of those points in space-time has a velocity. Without loss of generality, assume the direction of the velocity is the x axis. you have now reduced the three spatial dimension motion of the spinning disk into the one spatial dimension motions of an infinite number of points in space-time. calculate the travel through time of each of those points and re-combine them in the end to see where the disk ends up in time, not that I encourage you to calculate the time travel of an infinite number of points...

 

[Livingod]

to curiouschemist,


consider every point of the disk by itself. we divide the disk into an infinite set of points. then, for each point, consider every point in time of that point by itself. we take one point, and divide that into infinite different points in time. basically, consider every point in space-time of the disk by itself. each of those points in space-time has a velocity. Without loss of generality, assume the direction of the velocity is the x axis. you have now reduced the three spatial dimension motion of the spinning disk into the one spatial dimension motions of an infinite number of points in space-time. calculate the travel through time of each of those points and re-combine them in the end to see where the disk ends up in time, not that I encourage you to calculate the time travel of an infinite number of points...

I love quoting myself...

And I'm going to keep doing this so this thread is seen more.

 

[Livingod]

...

 

[oldunion]

It's a simple postulate of Relativity. If one reaches the speed of light (which one cannot do, but if they did) one stands absolutely still in time. If they exceed the speed of light (which they also cannot do...) they move backward in time.

An analogy, to help explain:

Let's say you are driving a racecar from one end of a field to the other. Let's say that you can travel at exactly constant velocity for the entire ride. Let's also say that it takes you exactly 1 minute to make it their, when you travel at constant velocity (meaning that your speed and direction remain exactly the same). Now, try traveling to the end, but at a slight angle. It would, logically, take you longer to do so, because your speed is distributed over more than one dimension now (instead of just being straight, you now have to go forward, and a little side-ways).

Now, according to Relativity, our movement is always exactly equal to "c" (the speed of light). However, it is distributed between spatial movements and your movement through time. Meaning that if you speed up in space, you slow down in time (just as when I give more of my speed to going "left" I have less for going "forward").

Does this make more sense?

could you explain this analogy further. I see that it takes longer to go from plane A to plane B when the path taken is not 1D linear, but 2D linear in a diagonal vector from plane A to plane B. It now takes longer to go from A to B using the 2D route, but the adjacent 1D route is not slowing down in time or anything.

The shortest distance (besides folding space) between two points is a straight line, but a diagonal line still gets you there. I don't see how your analogy proves anything about a 4th dimenions.

 

[Livingod]

Oldunion, if the racecar goes at an angle, that is, moves in a horizontal dimension, it loses some speed in the forward dimension. Consider the forward dimension as time, and the horizontal dimension as the three spatial dimensions. So basically, if we move in space, we move slower in time, thus everything looks faster to us. And the point of this anology is that if we were to move at the speed of light in space, we wouldn't be moving in time at all, to us, we would be traveling from place to place instantaneously, which is physically impossible, and that's why Einstein said that we can't travel at the speed of light.

 

[JesseM]

It's a simple postulate of Relativity. If one reaches the speed of light (which one cannot do, but if they did) one stands absolutely still in time. If they exceed the speed of light (which they also cannot do...) they move backward in time.

An analogy, to help explain:

Let's say you are driving a racecar from one end of a field to the other. Let's say that you can travel at exactly constant velocity for the entire ride. Let's also say that it takes you exactly 1 minute to make it their, when you travel at constant velocity (meaning that your speed and direction remain exactly the same). Now, try traveling to the end, but at a slight angle. It would, logically, take you longer to do so, because your speed is distributed over more than one dimension now (instead of just being straight, you now have to go forward, and a little side-ways).

Now, according to Relativity, our movement is always exactly equal to "c" (the speed of light). However, it is distributed between spatial movements and your movement through time. Meaning that if you speed up in space, you slow down in time (just as when I give more of my speed to going "left" I have less for going "forward").

Does this make more sense?

Actually, this idea that everything always moves at c through spacetime is not the standard way relativity is understood by physicists, and as far as I know Einstein never thought of it this way--the only physicist I have seen explain relativity this way is Brian Greene, and although there is nothing wrong with the math he uses to justify it, the way he chooses to define the notion of "speed through spacetime" is pretty arbitrary and counterintuitive. This was discussed at length on this thread if you're interested. As for the question of whether tachyons would be going back in time, the answer is that they would appear to be going forwards in time in some reference frames and backwards in time in others, but it is meaningless to ask what things would look like from the tachyon's own point of view, because relativity cannot give a sensible answer to the question of how fast a tachyon's clock would tick relative to our own. For more details, see this thread where the issue of whether tachyons go back in time was discussed in more detail.

 

[Chaos' lil bro Order]

Faster than light travel - Cherenkov Light

It is possible to go faster than light's reduced speed in some mediums. For example, light slows down in water to about C/1.40, or roughly 130,000 miles/second. This occurs because water has a density greater that a vacuum (space as an example). Imagine if you were in a relay race and the baton was light... You are an electron and your running mate is also an electron, but on another atom. Your goal is to pass the baton (light) to your mate (another atoms's electron) as fast as possible, yet no matter how fast you pass the baton, there is a slight lag when you hand it off. This is what happens in water, or any other medium other than a vacuum, for that matter.

However, if there is no running mate in front of you that you have to pass the baton (electron) to, then you can simply throw the baton forward and you the time it would take your running mate to grasp the baton.

In extremely dense materials like diamonds, where the 'index of refraction' is even higher than in water (diamond = ~2.00, vs. water = ~1.40), light slows down by a factor of two, to about 95,000 miles/second.

Noting the above, it IS possible for light to go faster than its local medium(diamond or water) speed limit. For example, light CAN exceed 130,000 miles/second in water, and when it does the equivalent of a sonic boom in air occurs. In other words, a Photonic boom happens and a bluish light called Cherenkov radiation is emitted that you can see with your naked eye.

BUT, light can never exceed the speed limit of the medium of space (the vacuum), meaning, light can NEVER go faster than 186,000 miles/hour.

Some people here have mentioned Tachyon radiation, which can theoretically go faster than light speed in a vacuum. As I do not know about this, I won't comment on it.

Hope that helps a bit.

:)

 

[Livingod]

Well, I really don't think that that will help because Prot travels at around seven times the speed of light, and he travels though vacuum. (It's the only medium between galaxies)