What is the fundamental relationship between the speed of light and spacetime in the universe?
This is a straightforward argument to follow, relying on three proven principles of modern science:
1. The right angle triangle and Pythagoras’s theorem. The square of the hypotenuse equals the sum of the squares of the other two sides. Thus, in the case of a triangle with sides of 3, 4 and 5, 3x3 + 4x4 = 5x5, which is 25, being the square of the hypotenuse.
2. e=mc2. This is Einstein’s theory (energy is equivalent to mass multiplied by the speed of light squared) that makes mass and energy interchangeable, so that the sun shines by nuclear fusion, and we can make nuclear bombs by nuclear fission, converting mass into energy to destroy enemy cities.
3. The concept of space-time. Per Einstein’s relativity, time merges into the other three dimensions. In practice, as you speed up, time dilates. This means that the traveller’s minutes take longer to elapse from the view of the stationary observer and distance shortens. One way to look at is to say that as you go faster you get more time and less space. The proportions of space and time in space-time change as you speed up. GPS satellites have to adjust calculations for this.
Einstein’s equation deals with mass that is not moving; however, things in the universe move. If you rest a hammer on a nail, it does not drive the nail into the wood, which it does when it drops on the nail as you swing it. Its velocity confers extra energy. To take account of this, the equation in 2. is expanded. P is a term added to introduce momentum. This is the equation practical scientists generally use.
e2 = (pc) 2 + (mc2) 2
What you will see is that the above equation is the equation for a right angle triangle, with the first term being the hypotenuse and the two terms the other side of equals being the other two sides.
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Height(m c2) 2
Hypotenuse e2
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_____________________Base (pc) 2___________________________
1. Imagine you shorten the (pc) 2 line up to the point where it touches the (mc2) 2 line. Then its value becomes zero, so: e2 = zero + (mc2) 2. This brings you back to the original equation e=mc2, which makes sense, because what you have done is to take away the momentum (P) and are left with stationary mass, the hammer resting on the nail.
2. Now imagine you reduce the height of the (mc2) 2 line to where it touches the (pc) 2 line, so that the (mc2) 2 line becomes zero. Now you have the equation e2 = (pc) 2 + zero. In this case you have taken out mass and are left with just a flat momentum line. And that is exactly what a photon is. It is a massless particle whose energy derives entirely from its speed. This flat line is a pure energy scenario without mass. A photon is light, travelling at the speed of light.
Now we come to the point.
If you start with the (pc) 2 line only, you have no mass, just energy. If you convert some of that energy into mass, then the (mc2) 2 line starts to rise up from the baseline. But the sum of the squares of these two lines has to equal e2, so as the (mc2) 2 line rises the (pc) 2 line has to get shorter.
When the (pc) 2 line gets shorter, it is telling you that there is less momentum. The speed of the mass is dropping away from the speed of light. This is what we know, that mass cannot travel at the speed of light, so as energy converts to mass, speed reduces.
In simple, non-mathematical terms, as energy converts to mass, speed falls away from the speed of light.
Now we come to what this means.
We know that as speed reduces, so time becomes faster (less time if you like) and distances become longer. The exact opposite of the point in 3. above, where we talk about speeding up, not slowing down.
As energy converts to mass, time speeds up and distances increase. At least that is what we see from here (where we are in the universe). We are getting less time proportionately and more space. It would look to us as if the universe is expanding and the galaxies are accelerating away ever faster. This is what cosmologists observe to reach the conclusion: Big Bang.
However, my contention is that the exact opposite is what is happening. Energy is converting to mass and dropping away from the resting state, which we define as the speed of light.
Now comes the really compelling bit.
What this means is that your view of time and space is determined by your position in the energy to mass conversion cycle. If you were to reverse the process, by speeding up and converting mass to energy, then you would find your universe shrinking in terms of distance as time dilates, until you reach the point where there is no distance left, only time. You are at the extreme end of the space-time scale.
This is what it is like to be a photon: there isn’t anywhere.
And now we come to the corollary. This bit is somewhat complex, mathematically, but is not hard to explain.
The equation e2 = (pc) 2 + (mc2) 2 gave rise to a very simple explanation of atomic shells. If you substitute matrices into the squared terms on the right hand side of the equation, you can get rid of the squaring by putting in matrices that multiply to zero, and give calculate the number of electrons permitted in each atomic shell.
The rule is that no electron can share the space of another electron. This is called the exclusion principle. It is the reason why we do not fall through the earth from England to New Zealand today and arrive early. Our electrons are stopped by other electrons. In quantum physics any electron can be anywhere in the universe. It has no definite place, only probabilities, sometimes called probability waves, but they still seem to manage to exclude one another.
However, we have just demonstrated above that space can collapse to nothing at the speed of light. If two electrons cannot be in the same place, then there can only be one electron in the entire universe. Where that electron may later be found is pure probability.
Finally, this hypothesis is provable, and this is for the experimentalists to take up.
If energy is being converted to mass, there will be space bubbles within the universe, with space expanding at different rates. They are likely to be spherical bubbles, but since there can be no ‘space’ between them, as they are ‘space’, they will be forced into other geometric shapes, like the hexagonal tiles on the kitchen floor, to squeeze together.
The borders of these bubbles should be observable. |