Gravity is very important - and the non-scientist is never really concerned with it - just taking this 'force' for granted. It turns out that the force keeping us on this very planet, also keeping the planet's in their galactic centers of rotation, is the real democratization of time, because the rotation of these planets bring with them their own set of hours in a day. First of all, what is gravity all about? We need to understand some geometry first. Is the universe flat or curved?
Back in the days of Christopher Columbas, they had believed that the earth was flat. It's not really hard to imagine that these earlier humans had thought this. After all, just look around you... You don't see a spherical reality... but rather a flat land, with the odd mountain or hill here and there. Obviously we know better today. The first time we saw earth in all it's spherical glory, was when we where able to leave the planet itself. Mind you, the earth is more an oval shape, than being perfectly spherical.
What do we say about space? Is it a flat surface, or is it a curved surface?
The question was tackled by the world-famous Albert Einstein, developed in his General and Special Relativity papers. Einstein’s general papers describe the nature of gravity as being a distortion of space and time. His papers, coupled with mathematical pillars, say's that whenever there is a distortion in space and time, there needed to be the presence of matter.
The classical way students and non-students are told to visualize such distortions, is by imagining a stretchy sheet, in which someone rolls a bowling ball upon it. The sheet itself becomes heavy around the parameter of where the bowling ball rolls. This indentation caused by the weight of the ball in the sheet is analogous to the distortions found around a large piece of matter. The earth for instance, causes a spacetime distortion, and is equivalent to gravity itself. Thus, matter distorts space and warps time. We say it bends both space and warps time, simply because space and time are according to the modern interpretation of relativity as being two sides of the same coin. We call this naturally a continuum as spacetime. This meant that both space and time are inseparable.
Einstein had problems with the current view of the geometry of the universe. At the time, the insights into spacetime geometry were influenced heavily on Euclidean and Pythagorean spacetime, describing the universe in flat dimensions. It was probably Einstein’s realization at his high school, learning about geometry, that it had later occurred to him that spacetime no longer needed to be flat. His mind was on curves.
A curved space was quite difficult for even the mainstream scientists at the time to visualize, simply because it defeated all logic. Intuitive thinking be cast aside, because in a curved space, the shortest distance between two points was no longer a straight line. It was a curved path! Strange this isn't it? It is strange because when we move from one side of the street to another, we tend to move in a straight line. The measure of a shortest path in a flat space follows what is called 'geodesics.' But in Einstein’s space, the surface was rippled with 'imaginary mountains.' I use a mountain here to describe space, (not because mountains exist in space obviously), but because i am going to ask, 'When you come to the foot of a mountain, which is the fastest path to get to the other side?'
A little thought would indicate, that instead of traveling over the mountain in a straight line, the quickest path would be to travel around the base, wouldn't it? Thus, this analogy describes space; curved lines are the quickest routes to any other point. In fact, travel far and fast in enough in Einstein’s space, and you will end up exactly where you had started! This isn't the only relativistic puzzle that evidently arises from introducing curvature in spacetime: a new notion for gravity takes a twist. It turns out that a curve in time and space was the equivalent to gravity!
Einstein was aware, that by introducing spacetime curvature, gravity could be more easily accounted for, rather than a flat spacetime arena. In fact, he may have been inspired by the curvature of the planet, and how it itself produces it's own gravitational pull. But like any source of gravity, it could be cancelled out, provided you traveled fast and far enough. To break free of the earth's gravitational pull, you need to accomplish what is called, 'the escape velocity.' To leave earth, you need a constant speed of around 25,000 miles per hour. Consider astronauts. They circle the earth in a state of 'free fall' - and they are not influenced by gravity at all.
Einstein figured that if you are in an elevator that is accelerating upwards, the elevator would push up against you. This is of course, the force of the elevators mass, pushing you up against the force of the earth’s gravitational field trying to pull you back down. This small analogy proved something. When the elevator moved upward, the force of the platform was pushing up against the mass of your body, turned out to be like the force of gravity keeping us all on this green planet! Thus, he was able to calculate that acceleration was the same thing as curvature: With this clearly in mind, knowing that gravity was the same thing as curvature, he was able to surmise that acceleration too was equivalent to gravity.
More arises from the curvature of space. It turns out that the curve of space, also curves into time... and thus time is effected by gravity... We call such effects, 'time warps,' in physics, and it may surprise you that gravity warps time in such a way, the proverbial wall on the clock will slow down, or speed up, depending on the gravitational field! And what may equally surprise you, we have already measured the presence of time warps.
The effects of time warps where first measured in 1959 by physicists R. V. Pound and G. A. Rebka at Harvard University. Their experiment was relatively easy. They set up a clock in the basement of Harvard, and another (around 70 feet) above in the buildings penthouse. Then, the two physicists figured out how to send time signals from the basement, to the penthouse. It turns out, that the signal would carry a very small time interval, which would inexorably match the clock rate in the basement; and to their surprise, the interval would not match up to the time in the penthouse...
One must respect however, that the shift in time was very small indeed: Nevertheless, the clock in the basement had a slowed down! This proved the gravitational shift to be correct, and also showed that the clock on the wall will tick slower in a strong gravitational field.
The special papers are a little harder to understand - it isn't easy when talking about relative affects. It describes what one observer sees moving at a constant speed past another observer. It shows that the equations describing mechanical and optical phenomena when seen by an observer moving relative were not the same as an observer at rest. The special papers highlight that time is not fixed, and that a space leg can be represented against a time leg. If the space leg is found to be longer than the time leg, we say that the observer is experiencing normal time.
If the space leg is exactly the same value as the time leg, we say that the observer experiences absolutely no time at all. If the space leg is shorter than the time leg, then the observer finds herself moving backwards through time. The space leg is a real leg. However, the time leg isn't. This is what we call an 'imaginary leg,' on the spacetime triangle. This might seem strange, this ''imaginal stuff''. For physicists to understand imaginary concepts, we needed to bring in ''complex numbers'' - and don't be deterred by the name - they are relatively easy to understand.
Some particles might even travel throughout spacetime when the time leg is longer than the space leg. These fast chaps are called Tachyons. These particles are made of a strange substance called ‘’imaginary mass.’’
Is the neutrino a tachyon?
Dr. Cramer quite rightly reminds us that tachyons could quite very well be a particle we already know of in physics; the neutrino... about a billion of these pass through our body in just under one second.
We have all heard of the hypothetical particles called tachyons. They have a rest mass M that also has an imaginary value (M2<0). It turns out that (E=gM), the observable mass-energy of these light weight particles, becomes ''real'' and ''positive''.
If a particle was able to defy the light-speed barrier so that v was greater than c (v>c), then both g and E would become imaginary quantities, because ß would be larger than 1 and (1 - ß2) would be negative.
When using imaginary concepts, we must use complex numbers... nothing too complex about them, so don't be scared off! We need the calculus in concepts that are imaginary - not quite existing in the realms of the real - but are ''real'' nonetheless... we use it when calculating the imaginary dimension of time, and even concepts beyond ''c'' - imaginary mass.
To understand this better, we must consider the pyhagorean theorem.Complex numbers deal with square roots. Now, you might remember square roots from high school. A number that is multiplied by itself produces the square root - thus, the square root of 4 is (2 x 2). The square root of 9 is (3 x 3). The square root of 16 is (4 x 4), ect. Note however, that the square root of 1, is (1 x 1).
Complex numbers move into the negatives; thus, it helps mathematicians work out the improbable square root of -1, for instance, which is 'i' x 'i' = -1. The 'i' stands for ''impossible'', and it helps us in calculating numbers that are not in the real world. Another example is the square root of 4, which is (i2) 2 = -4. Quantum Physics and Relativity would be impossibility, without complex numbers, and so would our ability to calculate time as an imaginary dimension of space.
In geometry at school, one will eventually learn the Pythagorean theorem. As you will probably know, the theorem applies to length of the right sides of a right triangle.
It is a simple formula, and it tells us that if one was to work of the angles on the sides of the triangle, the sums of two of those angles will equal the sum of the remanding value angle. We say that the third angle is the one raised on the hypotenuse. The formula is:
(a2+b2=c2)
The sides of the triangle are similar based to how we work out the lengths of space and time. Because time is a universal invariant, we say that the imaginary time dimension is an invariant relationship.
Now, it has come to light (mind the pun) on the mass of the electron neutrino (Ve), because it is a leading "dark matter" candidate... and we don't know the physical properties of dark matter. We have some examples of what some dark matter might be like, such as the axion particle which travels through material objects!
We can create neutrinos from the decay of tritium. The basic underlining rule is through the relativistic relation between energy and momentum;
E2 = p2 + M2
... and we find out that it is mass squared that works out the neutrino mass from tritium decay... but this mass squared can be seen in light of either a positive result or a negative result, and if it is a tachyon, containing a very light weight amount of imaginary matter of about i × 12 eV, there is the big problem that nothing fruitful will arise out of this... because the theorists do not believe its qualities would be observable or known.
