Time Travel Essay, Research Paper
Basic Introduction to Time Travel
Time and space have fascinated man since the dawn of civilisation. People have spent aeons thinking about these concepts and the ideas behind them. The Greeks, the Romans, the English, all have stared at the heavens and wondered. And not without reason! As the boundaries of physics are pushed back and back it is becoming clear that whoever understands the laws of physics best will be able to travel through time and space, easily gaining a dominant position in the known Universe. Indeed that race which can move from universe to universe will get to control all universes! We must therefore double our efforts to ensure that it is we and not some other race who gains understanding first! Or we will end up playing second fiddle for rest of time!
Pythagoras into Einstein in two easy steps
So where do we start? Well let us start with one of the greatest triumphs of the human mind, the great theorem of Pythagoras, a true pillar of all mathematics and physics. The theorem, which is applicable to right angled triangles in flat Cartesian (Newtonian) space takes the form of:
c^2 = a^2 + b^2
where a, b and c are the lengths of the sides of the triangle.
Next we will jump straight to Einstein’s theory of Relativity which states that neither time, length, or indeed mass remain constant additive quantities when approaching the speed of light c. Our simple ideas of time and space come from the fact the we are so used to living in a three dimensional universe. Einstein showed that this was simply not true and in fact all the “foundational” three laws of Newton have to be fudged by the Lorentz factor
L_f = (1 – v^2/c^2)^-1/2
Elementary Guide to Relativity
There are, however, certain quantities that do remain constant. These constants are related to four-dimensional quantities known as metric tensors. From this Einstein proved that space and time are two aspects of the same thing and that matter and energy are also two aspects of the same thing. From the second of these concepts we get the most famous equation in physics
E = mc^2
Now since time and space are aspects of space-time and we wish to travel through time and not build atom bombs we will leave E=mc^2 for the moment. To illustrate this, look at the extension of Pythagorean theorem for the distance, d, between two points in space:
d^2 = x^2 + y^2 + z^2
where x, y and z are the lengths, or more correctly the difference in the co-ordinates, in each of the three spatial directions. This distance remains constant for fixed displacements of the origin.
In Einstein’s relativity the same equation is modified to remain constant with respect to displacement (and rotation), but not with respect to motion. For a moving object, at least one of the lengths from which the distance, d, is calculated is contracted relative to a stationary observer. The equation now becomes:
d^2 = x^2 + y^2 + z^2 (1-v^2/c^2)^1/2
and this implies that the distances all shrink as one moves faster, so does this mean there are no constant distances left in the universe? The answer is that there are because of Einstein’s revolutionary concept of space-time where time is distance and distance is time! So now
s^2 = x^2 + y^2 + z^2 – ct^2
and this new distance s (remember s stands for Space-time) does indeed remain constant for all who are in relative motion. This distance is said to be a Lorentz transformation invariant and has the same value for all inertial observers. Since the equation mixes time and space up we have to always think in terms of this new concept: space-time!
A Practical Example of Time Travel
What does this have to do with time travel? Imagine an imaginary journey to Andromeda, some 2.2 million light years away. For the time being ignore the problems of propulsion (like they do in all Sci-Fi films!). Firstly, lets assume a Newtonian Universe and we’ll ignore the effects of gravity and friction (not much of this in space anyway). The first problem: how fast do we accelerate? Well, if we could accelerate at an infinite rate we could reach an infinite speed instantly and reach our destination in no time at all! Unfortunately, if we were to do so we would experience infinite acceleration forces and be crushed to an infinitesimally thin film instantly. Not much use. The gravitational field of the Earth of 1g (9.81 m/s per second) is however a comfortable acceleration to subject us to, so lets assume the acceleration of our spaceship will be 1g.
So how long to Andromeda at 1g using Newton’s theory? We will add the condition that we wish to stop when we get there, if only to turn around and come back. The best time we can make is achieved by accelerating for the first half of the journey and decelerating for the second. The total time for the trip can be calculated to be some 2,065 years. Rather a long time really. Consider the same journey in an Einsteinian Universe. We now have a limited maximum speed (the speed of light), which at 1g is reached in 30,000,000 seconds, or a little under 354 days. After we reach this speed, how much longer will it take to reach Andromeda? The answer is no time at all! For the distance to Andromeda will have shrunk to zero for the spacecraft. However to the people back on Earth a considerable length of time would pass: some 2.2 million years.
OK so what’s the catch ???
For practical reasons, such as having no way of navigating in an infinitely thin universe, we would stop just short of the speed of light at the halfway point and reverse engines to come to a halt at Andromeda. The entire trip would have taken a little less than 2 years at a comfortable 1g. The same is true of a trip to anywhere within the Universe. We can get literally anywhere in a little under two years: four for the round trip. The main problem is the ageing of the rest of the universe while we are travelling. The other problem is that the mass of the spacecraft rises greatly as it approaches the speed of light, so an enormous power source would be required.
What about power? For the Newtonian case the power requirement is enormous, even assuming perfect efficiency. The energy required would be 5.1*10^26 Joules for a 10 tonne spaceship. This is rather a lot. NASA’s space shuttles are not really up to it I’m afraid. In the Einsteinian Universe the power is still huge since the mass of the ship rises and becomes so large! And unless you get very close to c the distance to Andromeda will not shrink very much and it will take ages to get there.
Unfortunately there are still a few little problems: the friction associated with such a high speed and of course the dreaded time dilation effects.
Friction: though space is essentially empty, with increasing speed the little matter that there is would become increasingly concentrated. In addition, its relative mass increases, consequently, we would encounter it with ever greater density. Indeed as we approach the speed of light the whole Universe becomes concentrated into an infinitely thin, and consequently infinitely dense, barrier in the direction in which we are travelling. The force of friction would increase accordingly.
And there are even more catches !!!
The second problem of time dilation means that when we return from our trip to Andromeda we would have aged less than 4 years while the Earth has aged around 4.4 million years. One or two changes would have undoubtedly taken place back here on Earth! This would seem to be an insurmountable drawback, and one which will be discussed at some length later.
The idea of travelling from world to world, having strange and exotic adventures with even more strange and exotic creatures, and then dropping back later for the odd chat about old times, is just not on. The old times would be just too old for those left behind to survive the wait! The galaxy is, after all, about 80,000 light years across, and this immediately converts to a minimum travel time of 160,000 Earth years. So travel as we know it is just not possible. Sailing off across the depths of space on five-year missions is all very well, but whose five years? Obviously sub-light travel puts severe restrictions on what we can reasonably expect to do. But what of travel at speeds faster than light?
Faster than light travel offers the hope of a way around these temporal limitations. It is the mechanism by which we can re-establish the absolute time that approximates so well here on Earth. As a literary device there is nothing at all wrong with faster than light travel, but as an accurate depiction of life in an intergalactic culture there are some problems. It is a shame to dispel these illusions, but the universe is as it is. So that about wraps it up for faster than light travel or does it?
Beyond Text-Book Physics !!!
Special relativity tells us that it is impossible for us externally to accelerate a solid object up to the speed of light, because this requires an infinite amount of energy. This is true for a spacecraft, you, or even something as small as an electron. In fact true for anything that has a finite rest mass. For, as we impart energy to an object, its mass increases at an ever-increasing rate and we can never get to the speed of light since mass becomes infinite. To make progress we must move to the physics of general relativity and beyond. It is known that once the density of matter-energy becomes large enough in a region of space-time the laws of quantum mechanics take over and uncertainty becomes the order of the day. This means that we could achieve a quantum tunnelling through the light barrier to reach trans-light velocities. The only way to amass such energy is to play with black holes. More on this elsewhere.
Until now, we have simply been recapping standard textbook physics. It is now that the speculation begins. When a velocity greater than light is introduced into the equations of special relativity we are left with the conclusion that an observer who is travelling faster than the speed of light relative to us is also travelling backwards in time. Equivalently, we are travelling backwards in time relative to him, from the intrinsic symmetry implied by travelling backwards in time. This symmetry further implies that, just as on our side of the light barrier sub-light velocities add to produce sub-light velocities, so to must pseudo-sub-light velocities sum to pseudo-sub-light velocities, for observers on the other side of the barrier
Light is no Barrier !!!
One criticism that springs naturally to mind is why do we not observe such reverse time particles? To answer this, consider two objects, one on either side of the light barrier. We will start with them stationary, and pseudo-stationary, relative to each other. Now can we expect them to be attracted towards one another by the action of gravity, or do objects on opposite sides of the light barrier have a gravitational repulsion? Lets assume it’s an attraction. We would therefore see the particles approach one another, but would an observer on the other side of the barrier see this? As his time runs backwards, he would see the objects move apart. Yet to him it is our time that is running backwards and so he would reason that objects on different sides of the light barrier must have a mutual repulsion. Similarly, if we begin by assuming that such objects repel we will find they attract for the observer on the other side of the light barrier.
We can reason the same way for all forces and, indeed, all interactions in general. Therefore there can be no interaction of any kind between objects on either side of the light barrier. If such objects do exist we have no way of observing them directly. There could be an entire Universe moving backwards in time and we would never know!
We really do have the possibility of travelling faster than light, and as a natural consequence the possibility of travel backwards in time. We even have the possibility of crossing the light barrier with a finite amount of energy in a finite proper time without it taking forever as far as the rest of the Universe is concerned.
The Time Paradox Problem !!!
Once we are on the other side of the light barrier, travelling backwards in time, what do we do then? Well, we could always cross back again. If we time it right we could return at whatever point in history we wish. As we have seen, we can get anywhere within the Universe in a little under two years travelling below the speed of light. By travelling super-light, or more correctly on the other side of the light barrier, we can arrange to arrive back here at any time. With a little planning, we could arrange to return to Earth after the passage of the same Earth time as our proper shipboard time. This is true faster than light travel and with it comes the power of travel in both space and time. With it also comes the possibility of undershooting our departure time, arriving back before we left and even interfering with our own departure. It seems that this is still the only serious objection to time travel.
This is the great time paradox problem.
The evidence for travel in both directions in time exists in special relativity, general relativity and thermodynamics, and generally throughout the physical sciences. Without reverse time travel there are considerable philosophical and theoretical difficulties, such as that posed by Dirac’s multiple infinite negative mass-energy background.
Time travel has been extensively investigated in connection with Schwartzchild wormholes linking different space-time continuums. Alternatively, it has been proposed that in a curved space-time they could link different points in the same continuum. This allows for the possibility of using a wormhole to travel to a previous time in the same Universe, which puts us at liberty to interfere with our personal histories with all the paradoxes that this entails! We will look at this in some detail now.
High Dimensional Thinking
Professor Hawking invokes a cosmic censor, an omnipotent entity that intervenes to prevent the occurrence of a paradox. It operates something like this. If a man goes back in time and attempts to alter his personal history, for example by trying to kill his father then the cosmic censor would have it that the murdered man was not really his father. What if he attempts to commit a form of retrograde suicide by killing his earlier self? Presumably in this kind of situation the cosmic censor takes a more active role, depending on the method employed. If, for example, the time traveller elects to shoot his earlier self, then the gun will misfire or the bullet will simply miss. The cosmic censor, then, ensures that any and every attempt by the time traveller to alter his personal history will be frustrated. However we will now show that the cosmic censor is not required at all and that there is no such thing as a time paradox. After all there is no paradox with travelling in 3 dimensions. The universe doesn’t fall apart if I go to Cambridge and come back again so why should there be a paradox in 4 dimensions. Paradoxes are for the small minded!
Why only four dimensions? Well, there have to be at least four but why not five, or six, or even a hundred. There is no reason whatsoever to limit ourselves to four, and a great deal to be gained by assuming more. This is not a new idea, and scientists have used it to make significant progress towards constructing a fully unified theory of nature. Currently, the most popular candidate is super string theory, which requires ten dimensions. Lets not get too complicated and start by assuming five dimensions. We all live on a three dimensional surface of a multi-spatial dimensional manifold, and to move a whole universe you just have to move from one three dimensional surface to another. The extra dimensions are those that connect the 3D surfaces together. In terms of temporal dimensions we live on a single dimension!! Time appears linear to us. But one can cross over to other lines of time by moving through the 2nd temporal dimension. To do this a double-dimension time machine is required and masses of extra terms have to be added to the equations of Einstein.
How to be rid of the Cosmic Censor…
Now back to the paradox of the Father killed by his son. In five dimensions we can finally lay to rest our paradox as follows. The man travels back in time. In doing so he enters a reverse time, mirror image, of our Universe. When he starts moving forwards in time again, the same direction as ourselves, he is in an alternative Universe. There he is at liberty to kill the man who would have fathered not him, but his alternative in that Universe. There is then no paradox: his father, unmurdered, inhabits an entirely different Universe, some distance in the fifth dimension from the one in which the murder is committed. If there is a cosmic censor, his task now is simply to prevent time travellers getting back to their home Universes.
However, the cosmic censor can be put out of his job completely if we consider certain implications of quantum mechanics. It is possible that all particles may behave as fermions in relation to the temporal dimension, in which case we can refer to them as termions. If a particle is a termion then according to the space-time extension of the Pauli exclusion principle, no two termions with the same quantum numbers can exist in the same universe (strictly speaking the same time frame, which is basically the same thing). So to keep time travellers from getting back to their own Universes and causing no end of mayhem, you have to ensure that when time travel occurs all termion quantum numbers are changed and then the particles that make up the time travellers body cannot occupy the same universe again. If a time traveller ever approached his own universe with termion quantum numbers equal to those of another object in that universe then the Pauli time invariant exclusion force would push him or her through the fifth (or higher) dimension to a different universe, consistent with his or her termion quantum numbers. Even if repeated time travel events occur, the change in termion quantum numbers effectively mask out every universe than you ever come from. Further study will show that termion quantum numbers always change if you travel through the light barrier – we say they are exclusively time variant i.e. always change as opposed to Lorentz invariant quantities.