Tuesday, 5 May 2015

The Law of Instantaneous Interstellar Travel

The Mayflower and Kapetyn-b
In the mid 23rd century, mankind discovered a new fundamental law of physics: The Law of Instantaneous Interstellar Travel. This led to a flurry of activity, leading to the development of Interstellar Spaceship Travel a mere 27 years later. Every school child knows the story of the first instantaneous interstellar mission, the rescue mission to Kapteyn-b.
150 years to the day after the robot colony had been founded on Kapteyn-b, the first instantaneous interstellar mission carrying the second group of human colonists arrived and re-occupied the ruined settlement. In one of the most celebrated stories of human endeavour, they successfully reactivated the robotic shuttle and Captain Iain M. Banks piloted it into orbit and docked with the inactive Mayflower, overrode the glitching flight computer which had kept it stuck in orbit for 98 years, and successfully performed a manual landing. The original colonists had been asleep for 127 years, nearly 100 years longer than originally planned. "One cool move by me, one giant leap for sentient beings" the Caption famously tweeted.
The Law of Instantaneous Interstellar Travel
An object can instantaneously jump between one point in space and any other point in space, so long as its velocity relative to the CMB (Cosmic Microwave Background) is within 1/adm km/s, where m is the mass of the object, d is the distance between the two points, and a is the Asimov constant. The power required to initiate the jump is given by cd2m GW, where c is the Clarke constant.
Practial Issues for the Interstellar Traveller
Unfortunately, as all modern space tourists know, “Instantaneous Intersteller Travel” is not quite so instantaneous in practice!Firstly you have to accelerate to be almost stationary relative to the CMB, which on Earth is approx. 360 km/s; this means you have to accelerate at 1G in the direction of Leo for approximately 10 hours.Further, since the power required is proportional to the distance squared, interstellar travel is performed as a series of short jumps, with one hour's recalibration between each jump, hence it takes around 1 day to travel each light year.Finally, you have to decelerate at the further end.Hence the total journey time is roughly 1 day + 1 day / light year.Fortunately the direction of approach and departure from any given planet are in opposite directions and are the same for all destinations, hence collisions between accelerating/decelerating spaceships is not a risk.

Isn't FTL Travel Impossible?
Everyone knows that Relativity says that FTL (faster than light) travel would lead to travelling backwards in time, which is impossible, hence faster than light travel isn't possible.

That is true.

However, instantaneous travel might be possible...

Let us consider the paradox:

The FTL Paradox
Imagine that you take off from the earth in a spaceship and fly away from earth at high velocity. Relativity says that your perception of time passing on the earth is altered. Time now appears to run slower on the earth. After two hours of flight, only one hour appears to have passed on earth. Thus if you could travel instantaneously back to the earth, you would arrive one hour after you left. But similarly back on the earth, time on your spaceship appears to be running slower, and only half an hour appears to have passed on the spaceship, so if you now instantaneously travel back to the spaceship, you would arrive only half an hour after it had left the earth. That is, you would have arrived before you left.

The Age of The Universe
This paradox reveals that the concept of “now” is not a constant across the universe – it depends upon your reference frame. If you can travel instantaneously in one reference frame, and then again in a different frame, you could then travel backwards through time.

Thus we have seen that the age of the earth, in fact the age of the Universe, depends upon the observer. It should depend upon which galaxy you’re observing the universe from. So how can scientists talk of measuring the age of the Universe?

Cosmic Microwave Background 
The universe is expanding, hence all of the galaxies in the universe are accelerating away from all of the other galaxies due to the expansion of the universe. What is very surprising is that almost all of the relative velocity of all of the other galaxies in the universe compared to us is due to the expansion of the universe.
The CMB (Cosmic Microwave Background radiation), the “thermal radiation left over from the Big Bang”, provides a universal frame of reference throughout the universe: it is expanding, but relative to it every galaxy in the universe is almost stationary. If we measure the CMB we find that we are moving relative to it at approx. 360 km/s, or only 0.1% of the speed of light. Hence the age of the universe is the same, no matter which galaxy or star system you measure it from.

To quote NASA:
The largest reference frame we know about is that of the cosmic background radiation itself...the fireball light left over from the Big Bang. It samples a scale of the universe over 15 billion light years in radius. If you have no 'peculiar' speed relative to this frame, your galaxy is exactly partaking of the expansion of the universe with no additional local speed added to it. The NASA Cosmic Background Explorer confirmed many previous measurements of the motion of our earth's speed and found that it has a peculiar speed of 360 +/- 20 kilometers/sec in the direction of the constellations Leo and Crater.
CMB as a Univeral Frame of Reference
Now imagine that this cosmic microwave background radiation is the single canonical universal frame of reference for the universe, and that “now” throughout the universe means “now” as perceived by an observer in this particular frame of reference.

In this system, instantaneous interstellar travel between the spaceship and the earth takes you from “now” on the Spaceship to “now” on the earth, and vice-versa, where “now” is measured by the CMB. Since this earth is moving slowly enough against the CMB to ignore relativistic effects, the traveller was two hours on the spaceship before they jump, which to observers on the earth didn't occur until 4 hours after the ship left, so they find themselves back on earth four hours after they left. They jump back to the spaceship and find themselves back at the same moment they left.

There is no paradox*.

Bending The Laws Of Relativity
But haven't we just broken the Laws of Relativity?
The general principle of relativity states
All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics.
The principle has to be bent to say:
All systems of reference are equivalent with respect to the formulation of the fundamental laws of physics except for the Law of Instantaneous Interstellar Travel.
The principle can be bend this much and not break.

In one of the largest ironies in human history, this precise scenario was first discussed in the 21st century by Science Fiction aficionados, but was mistaken for the ravings of nay-saying flat earthers, and dismissed out of hand.

*Note that this only works for instantaneous travel – FTL travel still leads to a paradox!

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