Stowaway to the Stars


 

 

 

by Graham Keeler

 


 

 

More about the science behind Stowaway to the Stars

 

 

Hyperspace

Here is the explanation that Larry gave Karen about hyperspace during their underwater journey on Zilon.

‘It turns out that well away from the gravitational fields of stars and planets, outside what we call the hyperspace boundary, space is folded up.  So it’s possible to jump through hyperspace from one fold to another, many parsecs away.  Our spaceships have an enormous thrust compared with the rockets that you are used to.  They can accelerate all the way out to the boundary at, let me see, in Terran units it would be around fifty gee.  So the hundred and fifty thousand kilometres journey only takes about a quarter of an hour.’

‘I once read a magazine article that said that travel to the stars would always be impossible,’ said Karen.  ‘Nothing can travel faster than the speed of light.’

‘Absolutely right,’ Larry replied.  ‘But there’s no law against taking a short-cut through a higher dimension, which is what hyperspace is.  Your Earth scientists are now theorizing about the possibility of higher dimensions.  They’ve already discovered that three-dimensional space is a surface on a higher-dimensional entity called a brane.  The gravitational force appears so weak compared with the other forces like the electromagnetic force and the weak and strong nuclear forces, because it isn’t confined to the brane.

'You can dream up what seem to be paradoxes that hyperspace would cause like making a small jump and then watching yourself in the distance, but then you can do that with mirrors as well.  And you’d be amazed how little it changes the theories Earth people have at present.  It disposes of the theory of the event horizon, because that is based on how long it takes light to get from one place to another.  But there’s no problem with time reversal or anything like that.  If you make a hyperspace jump somewhere, stay a day and then jump back to where you came from, a day has always passed there as well.  Time still only flows forward.’

All this talk about branes left her floundering.  What had it got to do with hyperspace?  Larry was beginning to remind her of one of her teachers, full of enthusiasm for the most obscure topics.

Larry hadn’t yet finished his explanation.  ‘The hyperspace unit uses the gravitational force to jump from one place on the brane to another, but it only works where there isn’t a large gravitational field like you get near a planet or star, outside what we call the hyperspace boundary.  It’s about a hundred and fifty thousand kilometres out from a typical planet.’

Although she didn’t understand all the stuff about higher dimensions and branes, she was getting the general picture.  She remembered something else in the article.

‘But if you can effectively travel faster than light, I thought that it generated paradoxes or time travel or something?’

‘Wow, that was quite a technical article.’

‘Oh, I did not read all the technical stuff.  I just . . .’ she broke off, seeing his broad grin.  ‘Oh, you are teasing me, aren’t you?’

‘No – well, maybe a little bit.  I’m sorry.  The fact is, to achieve time travel you need stations that are far apart, travelling at near-light speeds, and you have to travel between them faster than light.’

‘Hmm, that sounds pretty complicated.’

‘Yes, you have to work hard to achieve time travel.  If you want to understand how it causes time travel you have to make coordinate transformations in space-time for the two stations.’

Karen’s eyes widened.  ‘But you really can do it?’  Who cared whether it meant making coordinate transformations?

‘No, I’m afraid not.  It requires true faster than light travel to break causality and –’

‘I’m sorry,’ interrupted Karen.  ‘What has casualty got to do with it?’

‘I beg your pardon, breaking causality – not casualty – means reversing cause and effect.  In other words, time travel.  Hyperspace travel is not faster than light travel.  It’s travelling in higher dimensions, which include time.  In effect, you travel forward through time as well when you make a hyperspace jump.  Nature is pretty good at stopping the things that break fundamental laws of physics, like perpetual motion machines and time travel.’

That almost made sense, though she still didn’t understand how you got time travel if you could go faster than light.  Another question occurred to her.  ‘How does your hyperspace system know where the stars and planets are?  The planets are spinning round the sun all the time, and I think the stars are moving as well, aren’t they?’

‘That’s a good question.  I don’t know the details of how it all works, and in fact I don’t think anyone fully understands it.  As I said before, the hyperspace technology came from the ancient race that has gone now.  But you’re quite right, the stars are moving.  The whole galaxy is spinning, extremely fast actually, about one thousandth of the speed of light, and that motion is well known.  But on top of that individual stars are jittering about a bit because their gravitational fields interact.  Planets are even more difficult because, as you say, they’re also spinning around a star.

‘The unit has a powerful computer inside that calculates all the movements, and of course all the Union stars and planets are pre-programmed, so for most people it’s not something they ever have to worry about.’

Karen frowned.  ‘What do you do when the planet is not pre-programmed, like Earth?  Or your secret Hideaway planet?’

‘It’s dead easy – the unit is linked to the viewscreen and you simply mark the star on the screen.  The unit picks up the coordinates from that and tracks it for a little while to work out its movement.’

The hyperspace boundary

        The hyperspace boundary is the point where the gravitational field falls to 0.012 Newtons per kilogram, since anything more is too high to enter the higher dimensions of the brane. This field is just over 1% of the field at the surface of the Earth.  For Earth the boundary is 1.8x108 metres, or about 120,000 miles, from the Earth.   By contrast, the Sun’s hyperspace boundary is far further away at about 70 million miles out, putting it just outside the orbit of Venus.

       At the 50g acceleration of Union ships, it takes about 15 minutes to reach Earth's hyperspace boundary, and as Larry explains to Karen below, the final speed is 4.25x105 m/sec or 1.5x106 km/hr.

How FTL travel gives the possibility of time travel

In the section above, Karen said to Larry, ‘I once read a magazine article that said that travel to the stars would always be impossible. Nothing can travel faster than the speed of light.’

This comment was based on the issue that FTL travel breaks causality (the fact that cause must come before effect) - to all intents and purposes giving the possibility of time travel. The reason behind this is difficult to explain simply, but it also requires people travelling at speeds comparable to light speed before they switch to FTL travel. Those speeds do not have to be very close to light speed, which gives rise to other relativistic complications - half light is fine. So let us imagine observer B travelling at half light compared to observer A. (A thinks B is travelling forward at half light, B thinks A is travelling backwards at half light.)

The key building block of relativity is that all inertial (non-accelerating) frames of reference are equivalent, and the velocity of light is the same in all such frames. A result of this is that A and B disagree on the time and position of distant 'events'. This difference can be calculated by Lorentz transformations. It's easy to quote them, for the technical minded they are

x' = Y(x - vt),  t' = Y(t - vx/c2 )

v is the speed of B relative to A, c is the speed of light and Y (really Greek letter gamma) is the factor that gives rise to time dilation and length contraction. Deriving these equations is not simple, but they can be found in any degree-level physics relativity textbook. For our modest half light relative speed, Y is effectively one.

The Lorentz transformations tell us that if a distant event appears to A to occur now, i.e. the light from the event will arrive in x/c seconds, then to B the event seems to have occurred in the past (the light will arrive sooner than he'd expect). If A jumps into his FTL machine and travels to the distant point, the 'event' is his arrival at the point (let's assume his FTL machine has infinite speed, for simplicity). He rapidly accelerates to the same half light speed as B. (If that bothers you, he could instead simply pass the National Lottery results to a third observer, C, travelling at the same speed as B.) Now his departure event is in the future as perceived in this frame of reference. He returns to his starting point in his FTL machine and arrives in the past, where he kills his grandmother, creating an impossible paradox (or C passes the National Lottery results to A before the Lottery is drawn). Either event breaks causality, which seems a very unlikely scenario.

So how do Larry's hyperspace jumps not potentially break causality? As Larry explained to Karen, it's because he does not travel faster than light. Instead he takes a short cut through a higher dimension, where things are different. In fact, if he went through the elaborate rigmarole explained above, he'd arrive a long while after he departed.

Speed

‘How fast does your ship go?’ asked Karen.

Larry laughed.  ‘That’s a meaningless question for a spaceship.  You’re thinking in terms of land and air-based transport, where speed is limited to the point where the drag from air resistance or friction matches the available thrust.  In space there’s no drag, so there’s no limit to the speed you can reach if you can provide thrust indefinitely like our ships can – unlike your chemical rockets on Earth that soon run out of fuel.

‘The question you should ask is how fast can they accelerate.  Your space rockets go at a few gee and only until the fuel runs out.  Our spaceships generate about fifty gee of thrust, which would squash you to a blob of jelly at the back of the seat if it weren’t for the gravity compensators.  So by the time we reach the hyperspace boundary we’re travelling at over one and a half million kilometres an hour.  If you accelerate for long enough you could get close to the speed of light – except that you’d run into relativistic effects.’

The gravity wave drive

Next Karen wanted to know how the gravity wave drive that powered the spaceship worked.

‘Well, that’s a bit more complicated.  The drive taps into the gravity waves associated with the gravitational field from the nearest large body.  It still takes power, of course, that comes from an anti-matter fuel cell the ship has, but basically the ship gets its thrust from the gravity field.  You can always get thrust from a field if you can persuade it to generate a force in the direction you want.  For example, an electric field will push any positive charge or pull a negative charge, so if you could put a large charge on a body it would experience a huge force in a strong electric field.

‘The normal gravity field always attracts, but if you tune in to the gravity waves you can get it to pull, or push, much more powerfully if you get into phase, or more commonly out of phase, with the waves.  And unlike electric fields, gravity fields and the related gravity waves are present around all large bodies like planets and stars.’

‘Or a magnetic field would work as well, I suppose,’ Karen suggested.

But Larry laughed.  ‘What is it with you Earth people and magnetic fields?’ he asked.  ‘A magnetic field is only a convenient way of describing the relativistic correction to an electric field when the charges are in motion.  The only thing in magnetism that matters much is the magnetic moments that are associated with some types of atom.  And no, you can’t get thrust out of a magnetic field.  The force is at right angles to the motion.’

Anti-matter

The Union spaceships use anti-matter fuel capsules for their source of power.  Smaller than the size of a pea, the anti-matter in the capsule stores enough energy for several hundred trips, in the form of a magnetic material suspended in a hard vacuum in a shaped magnetic field.

Formation flying

While it may not be true that any fool can do formation flying, simple formation flying of the sort spitfire pilots used to do on patrol before they contacted an enemy is not fundamentally difficult, because they were flying steady courses, for the most part, at constant velocity. The Red Arrows formation flying is much more demanding because they formate in loops and suchlike where they have centripetal acceleration that might amount to several gee.

When Larry was tailing the spaceliner down to Zilon they were decelerating at fifty gee. A change of just 1% in the deceleration would close the gap between him and the liner in front in a few seconds. As Larry explained to Karen in his analogy, the equivalent would be tailing another racing car about a metre behind it as it braked hard for a corner.

The gravity wave drive

The provision of thrust to produce acceleration of a body is based on Newton’s third law; that every action has an equal and opposite reaction. Or to put it more mathematically, momentum of a complete system is always conserved. So to increase the momentum of a particular body (and hence the velocity, since momentum = mass x velocity), the rest of the system must receive equivalent extra momentum in the opposite direction.

In a car, we simply utilize friction with the road to give the Earth the opposite momentum (but negligible velocity because of its colossal mass). In space it is more difficult because there’s no easy way of pushing against the Earth (or similar massive body, such as the sun).

The conventional way of providing thrust in space is to provide the equal and opposite momentum from mass ejected in the opposite direction to the spacecraft. Chemical rockets use the chemical reaction of a fuel and an oxidant both to generate energy in the form of the superheated gas and to provide the mass blasted away at high velocity and hence high momentum.  Ion drives blast ionized atoms out, the energy of the ions being generated by electrostatic forces.  Even solar sails work the same way, reflecting light photons from the sail (although photons do not have mass, because they travel at the speed of light they have finite momentum).

In principle, force fields are another way of providing thrust in space. Electrostatic fields are strong, but electrical neutrality means that they are almost completely cancelled out. (Magnetic forces are of no use, because the force is perpendicular to the motion of the body). The gravitational field is another possibility, but it is both weak and uncontrollable. The solution that Union physicists discovered was suitable utilization of gravity waves.

In the gravity wave drive, the interaction of the gravity waves with the mass of the spaceship – or to be precise, the mass of the drive unit – provides the thrust force.  The energy still has to be provided, of course, but the Galactic Union has plentiful supplies of energy, thanks to nuclear fusion. In principle, Larry’s spacecraft could have its own nuclear fusion reactor, but with the availability of anti-matter fuel cells, made with the technology provided by the ancients, a much more compact source of energy is now available.

The interference between the gravity waves from nearby massive bodies, such as the sun or the local planet, with gravity waves generated inside the drive, the direction of the thrust being controlled by the relative phase of the waves.

The gravity compensation unit

The gravity compensator, along with the hyperspace drive, was provided by the ancients, and the theory behind it is not comprehensible to humans.

 

 

 


READ MORE ABOUT HOW IT ALL BEGAN

 

Graham Keeler 2012
 
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