# The theory of relativity and its use in Sci-Fi

This investigation looks in to the different aspects of general and special relativity that has been used in science fiction movies. This report talks about the difficulties and possibilities of travelling at the speed of light (c), the different propulsion systems that could be used and how trecknology has changed the boundaries of physics in Hollywood features. Time travel also features looking at different theories behind it with a number of new ideas.

The Foundations of relativity were set out in detail by Albert Einstein. The ‘special’ version of the theory, which applies to observers in a uniform relative motion, has led to a number of successful conclusions of a variety of effects. Newton’s laws of motion give us a complete description of the behaviour of moving objects at low speeds (speed of objects much less than the speed of light). These laws being thought up in the 17th century, when the classical laws of dynamics where being formulated by other early physicists, these classical laws are themselves subject to a relativity principle.

Einstein’s special theory of relativity gives the motion of particles moving at close to the speed of light. It actually gives the motion of any particle. This does not however prove Newton wrong; his equations are within Einstein’s relativistic equations.

Einstein’s theory of special relativity is based on two assumptions:

1. All inertial (i.e. non-accelerating) frames of reference are equally valid (i.e. any observations or experiments performed will produce equally valid results).

2. The speed of light is constant for all inertial frames of reference.

Given these two statements, Einstein showed how definitions of momentum and energy must be refined and how quantities such as length and time must change from one observer to another in order to get consistent results for physical quantities.

Science fiction has for years tried to incorporate the theories that govern the reality of physics within their programmes, to keep those die hard science fiction fans happy. Science fiction has been subject to cult following for many years and in many countries, although no matter how hard they try there are a number of important facts that seem almost popular to overlook, the main one being travelling at the speed of light. Many programmes have some sort of light propulsion, warp drive and travel to other universes. But can this really be done?

Many physicists all over the world have tried to find out if travelling faster than the speed of light is possible without violating relativity. We do know that is impossible to accelerate forever, because the closer to the speed of light we get the mass tends to infinity this means that there would need to be an infinite amount of energy needed to push us past this speed barrier;

This equation represents what would happen to mass when relativistic speeds are reached. Here, m is the mass, of an object at rest; m’ is the value for the moving reference frame. As you get closer to the speed of light the product at the bottom of the equation gets closer to zero so this means that m’/m tends to infinity. If you were to rearrange this equation so to get the value of m’ the same results are seen.

The increase in mass, however, is best understood not as a change in mass but as a change in the relationship of mass and momentum. Momentum (p) is the product of mass x velocity. Here, p’ is the relativistic momentum and m is the rest mass.

Once again we can see that the momentum this time will tend towards infinity as we reach the speed of light.

Using one of Einstein’s most famous equations E = mc2 we can now see that if the mass does tend towards infinity that an infinite amount of energy will be needed to remain at constant velocity let alone accelerate.

Time dilation is another consequence of travelling at relativistic speed. We’ve all heard about the ‘twin paradox’ if one twin went on a space journey at 99.5% the speed of light and returned in what he judged to be 4 years the other twin with have aged by 40 yrs! These effects cannot be seen with humans, yet it has been tested and seen to occur with particles at the atomic scale. So any sci-fi movie where the astronauts return home after visiting other galaxies after travelling at the speed of light is clearly impossible, if they had been travelling for any length of time they would have probably come back to their grandchildren.

To explain this if you could imagine a spacecraft with a light source perpendicular to the motion;

If there were an observer on the spacecraft and the light travelled 0.6m it would take 2 nanoseconds to travel that distance. By using a simple equation speed = distance/ time the light is travelling speed = 0.6 x 2×10-9 = 3×108 ms-1 this should not come to as a surprise as this is the speed of light. However if the observer then was then stationary with the spacecraft moving past them, they would see the light take this direction:

Now in pre-relativistic (Newtonian) physics, both observers record the same period of time. Consequently, the velocity recorded by the two observers is different: the Earth-bound observer would record a greater velocity for the beam of light.

But taking into account Einstein’s assumption that the speed of light doesn’t change, and is the same for both observers, the distance for the light to travel doesn’t change as it is not in the direction of travel, the time which the light takes obviously changes. Does this then mean there is no such thing as absolute time?

The distance that would have been observed for the light to travel would have been 1m so using the equation time = distance / speed, time = 1 / 3×108 = 3×10-9 s, so we can conclude the clock on the space craft is slower than that when stationary.

This is given by the equation:

If v << c, then the result t’/t is very close to 1. But as v approaches c, t’/t becomes smaller. Time slows down for the observer on the spacecraft as its speed approaches the speed of light!

Another effect of travelling at the speed of light is length contraction. The spaceship in any sci-fi movie will be shortened in the direction of its travel. In similar equations as above of the spacecraft were to travel more than the speed of light the spacecraft would have no dimensions what so ever.

Investigation into star trek technology or ‘treknology’ as it is popularly known on the World Wide Web, I have found some interesting theories on how they believe that travel at the speed of light is possible. Some of the more interesting ones I will discuss now.

An interesting idea is to pull space time into waves; a special modulated gravity emitter pulls space time into waves. Gravity can be used to bend light like is seen around a black hole which is an immense gravitational field, below we can see that the light has been bent in a curved shape by the modulated gravity emitter.

By travelling in a straight line between the waves the distance is much shorter the absolute speed is not necessarily higher than light speed, but because we traverse A to B in much shorter time than a beam of light would do, our effective speed is higher than light. We can also use this to build wormholes but can this kind of drive really be realised because of the huge amount of energy that would be needed to make space time in to waves? It’s all a question of energy if we can find enough than this drive is possible but where can we get it from?

Wormholes

Travelling through worm holes is not an uncommon idea and even the most unscientific person has toyed with the idea while down the local. The common concept is to make the distance between two points shorter so not dissimilar to the idea discussed above. We do not how ever have any worm holes at the macroscopic level. Quantum theory predicts them at the microscopic level although they will not be much bigger than 10 x 10-33, if we can feed it with some kind of energy to stop it collapsing under the huge gravitational forces that it will impose on itself. But there are still some problems: we can’t predict where a wormhole will end. And it is also possible that travelling through a wormhole will take you back in time, causing causality paradoxes and if we can predict where wormholes will end, and if we even know how to create a wormhole to the place where we want to be, we need still very huge amounts of energy.

Subspace

We have this space which is a hypothetical continuum surrounding our universe, the ‘rocket science’ world has labelled it subspace. In star trek this hypothetical space doesn’t limit you to light speed, but we don’t know how to get in to it and most bizarrely even if it exists at all??

Warp drive

The famous star trek warp drive is discussed regularly in the field of physics. It’s powered by a tuned plasma stream from a matter/antimatter reactor.

Injectors feed the plasma into coils at specific times; causing pulses to run the length of the nacelles, front to back. This peristaltic flow should cause the push of nested subspace fields, and moves the ship forward.

The Star Trek Technical Manual says that the fields couple and decouple from each other at velocities near (but less than) c. It could be that the interaction of these fields, combined with the special frame subspace provides, causes the ship as a whole to travel at relativistic speeds. One again we have problems with the amount of energy need to keep us at these warp drive speeds.

The designers of the star ship Enterprise use matter/antimatter annihilation to power these drivers. This may seem the stuff from science fiction but we use it at the moment to study the brain using PET (positron emission tomography) scans.

These use the electrons antiparticle called a positron. It has the exact but opposite charge although same mass, these particles can be considered as mirror images of their corresponding particle. When these two particles collide the annihilate each other, they simply vanish, although the energy is still there and is carried away by gamma radiation. In pet scanners they detect this gamma radiation and use it to create an image of activity in the brain.

Although his is an extremely violent transformation there are some things that do not change, in every annihilation

1. charge is conserved,

2. momentum (linear and angular) is conserved

3. Energy (including rest energy E rest = mc2) is conserved

These conservation laws restrict what can happen: only changes in which all conserved quantities remain the same can occur. But we are unsure whether or not this can actually supply us with enough energy to power this warp speed driver.

The star trek enterprise relies on the emission of these gamma rays as a propulsion system and not using the energy from the gamma radiation to power another engine.

To get from one place to another in science fiction movies the general idea of time travel is a common occurrence, Back to the Future has had a number of popular sequels that involve travelling forward and back in time, but is this a viable idea in reality?

The travel forward in time has already been discussed earlier as this is time dilation and so is some one wanted to go forward in time, they would need to travel at near relativistic speeds for a considerable length of time and then come back to earth they would then come back at a later time than they had judged on the space craft, and as I have said this is due to the time dilation effect, once the individual has gone forward in time is there a way of going back in time, maybe travelling faster than the speed of light? The theory suggests that as the speed of light is reached there is no time then passing through to negative time- from your reference frame. Although this assumes that the speed of light is possible, and as I’ve discussed earlier this is not permitted by the special theory of relativity.

But not necessarily, Einstein’s special theory doesn’t allow but Einstein’s general theory of relativity allows this, so fear not young time travellers! It doesn’t take into account effects of acceleration or the four forces-the strong, electromagnetic, weak, and gravitational forces. This theory states that the fabric of space time itself is not constant, it can be bent and stretched this is what the treknology relied on, while Special Relativity imposes a limit to how fast objects can move in space relative to one another, according to General Relativity, there are no limits on how the space in which the objects are placed can move.

It is this effect that explains how the speeds of distance galaxies, measured by their red shift, this being the Doppler Effect, can be greater than the speed of light. The truth is, these galaxies are actually not moving much at all relative to the Earth, but the space between them is expanding like a balloon, carrying the galaxies with it. With enough expanding space in between the Earth and the observed galaxy, the expansion of space can result in the distance between Earth and the galaxy increasing at a rate greater than c.

All of the theories of moving back in time that I have come across involve some sort of negative energy. The work of one scientist Frank Tipler has stated that the only way to travel back in time is to use negative energy.

But how can you have less than nothing, if you have got less than no energy according to Einstein you have less than no mass.

But you can have a condition of negative energy; in a vacuum there is actually nothing on the macroscopic level there is a sea of electromagnetic waves and particles that are made at one point in time, in pairs and then annihilated shortly after, just as discussed earlier. But if this activity were to be dampened than a condition of negative energy would be created. This is observed near the event horizon of black holes (related to the emission of Hawking radiation), and in laboratories on Earth in the Caasimir Effect.

The Caasimir effect happens when two uncharged plates are held very close together less than a hundred nanometers apart. This restrict the number of particles that can fit between the plates, in terms of quantum mechanics, any particle that can appear between these plates must have a de Broglie wavelength that fits in the gap.

De Broglies relation: wavelength = h/p

Where h is planks constant and p is the momentum.

Any particle that has the wavelength than this separation can form outside the plates although this means there is a bigger pressure outside of the plates and the resulting pressure difference results in the plates being forced together. The space between these plates has shown a property of negative energy; that is to have a pressure less than that of a vacuum.

Other properties of negative energy are having negative mass so this means that the energy must have a reverse gravitational effect, this allows space-time to be bent and the possibility of backwards time travel.

There are however some difficulties firstly negative energy must often be confined to small spaces, now with most methods a lot of energy is used so need to be confined to a small space. The negative energy cannot exist independently, after appearing it will be counteracted by the large amounts of positive energy.

Unfortunately the chances of getting this amount of negative energy before it is ‘neutralised’ by the positive energy is extremely low. Now unfortunately for the moment the only way to travel in time is to star in a Hollywood movie.

The theory of relativity has been subject to expansion by British astronomers, who have tried to extend the theory to include electromagnetic phenomena; The Unified field Theory has tried to link together the Four Known interactions 1.Strong, which is a short range force that holds atomic nuclei together. 2. Electromagnetic 3. Gravitational. 4. Weak, which is responsible for slow nuclear processes e.g. Beta decay. They are believed to have one common factor or unity that will link all four forces that are none to cause all interactions together. There are still breakthroughs happening all the time that are always testing and rendering the theory of relativity.

We have seen a number of aspects of physics that have been clumsily portrayed in the media typical, exaggerated fashion that we have all come to enjoy when we visit the cinema, but who am I to put a stop to this enjoyment, for who knows what the future has to offer in terms of space travel, for years the top minds in the world agreed that the word was flat and the atom was the smallest thing that makes up matter, maybe this is another thing, the media has labelled ‘rocket science’, we can also change.