The Book of Ashes

An alternative definition of time 5:07AM

So now we need to consider an alternative definition of time. One that is independent of speed or temperature.

The first thing to note is that we cannot keep time by via the interactions of particles, as if these particles are bouncing around, moving relative to each other or moving at all, then their movement will be effected by speed in a given direction (as per relativity and our previous discussions). This rules out a lot, all mechanical or digital clocks, in fact anything constructed from matter.

What does it leave us with? A clock constructed from light? Einstein used a "light clock" in his thought experiments, consisting of light bouncing between two mirrors and showed that it would slow down if travelling close to the speed of light.

So what else do we have? First we don't know what speed the Earth is travelling (in the universe), nor what direction. We must assume it is something non zero as we know it is moving around the sun and the solar system is moving around the center of the milky way.

So can we construct a clock from anything that is limited by the speed of light (light included)? First thought would say no, as everything will be effected by movement. Second thoughts (what I call random brainstorming by the subconscious) brings up a few ideas.

1) Can we use the frequency or wavelength of light? We have light of many different frequencies, these can be shifted by speed (think red/blue shift of galaxies approaching or receding from us). So once again we have to ignore all light from all moving matter. Effectively all stars in the nights sky.

2) That leaves the cosmic microwave background radiation (CMBR). This is supposedly left over radiation from when the universe went transparent to light. Since that time (~380,000 years after the big bang) that light has been travelling out to finally reach us. The CMBR is everywhere in the nights sky, pretty much uniform at 2.725K temperature and peaking in the microwave spectrum. There are small fluctuations within it. The question is since this light has been travelling directly towards us since "soon" after the big bang, can we use it to keep track of time?

3) The width of universe may be a good measure of time. However its impossible to "see" this from within the universe as it has taken light the age of the universe to travel half this distance.

#2 has some potential. If we know the initial temperature of the CMBR from when the universe went transparent and the temperature now is known (2.725K) then we can interpolate from then to now to get the absolute time since the big bang. This may now work for a number of reasons. On a day to day basis the temperature change may be too small to be measurable making any kind of time keeping on a day to day basis untenable (e.g. can we determine a measurable difference in temperature over 1 second? Probably not!). We're also assuming that the expansion of the universe (what exactly is meant by this huh) is uniform over time, what we really mean is that the temperature drop is a linear relationship whereas its possible it was not in which case we cannot interpolate. Finally is the universe spinning? And would this effect the CMBR radiating out (e.g. some of its speed goes in the direction of spin)?

So in summary we would probably say that there is some theoretical absolute time that some observer outside of the universe could keep but from within the universe I can see no way to keep track of time without the difficulties we encounter with relativity.

Thought experiment #1 - The twin paradox 5:50AM

It is difficult to understand all the subtleties of Relativity. By this I mean that it goes against our common sense and we have difficulty applying our usual "rules of thumb" to situations (e.g. keeping it all in your head and making sub-conscious gut-feeling decisions on situations). We are best to run through thought experiments using step by step logical analysis to see how different situations behave. A few such thought experiments are analysed below:

Example #1 - The twin paradox:
This is a classic example. Two twins on Earth (the same age) decide to do an experiment. One sets off on a spaceship to Alpha Centauri and back (at close to the speed of light) while the other stays here on Earth. The classic analysis is that the one travelling in the spaceship will age slower than the one on Earth and come back to find his twin years older than he is. The paradox being that according to relativity from the twin's perspective on the spaceship he see's the Earth accelerate away at close to the speed of light and hence should see that his brother ages slower. E.g. there is no preference to either frame of reference.

Lets analyse the situation. First off we have the twin on Earth. He is in a moving frame of reference, the Earth is rotating, its moving around the sun and the sun is part of our solar system which is moving around in the milky way. There may even be further movement to this, but its irrelevant, we can say that we have some non zero speed in relation to some imaginary static point defined as the center of all mass and momentum in the universe. Second the twin on the spaceship moves off at close to the speed of light. His speed is that of his initial frame of reference (the Earth) and then his total speed after that. He is in a frame of reference that is moving faster compared to that of the twin on Earth.

So the next thing to note is that experiments have been done with atomic clocks. Identical clocks (e.g. ones keeping the exact same time to a very high degree of accuracy) have been used instead of the twins. The time keeping is analogous to the twins aging. One clock is kept on Earth, the other flown around the Earth at high speed (high Earth speed, still slow compared to the speed of light). Still there is some small relativistic effect and the clock on the plane "ages" slower than the one on Earth, hence its time keeping is slightly behind its "twin". Note that it is also higher up and so experiences less gravity. So we have shown here that the two frames of reference are not equal. From the clocks perspective on the plane the clock on Earth does not accelerate past it and age slower. Most explanations of this attribute differences to accelerating frames of reference which make one frame of reference different to the other. Of course this explains nothing and I'm pretty sure that if the acceleration could be removed we would still get the same phenomena.

From my previous discussion we would say that one frame of reference (the Earth) is travelling slower than the other (the spaceship) and hence its atoms are freer to move around (as less of their speed is taken up in the direction of travel. Hence time flows faster on Earth than on the spaceship. This makes a few assumptions which go against relativity. Mainly that there are preferred frames of reference, we're comparing this to an absolute frame of reference with zero speed. What we need to do is prove that a frame of reference where all matter is moving with a constant velocity in a given direction (matter can still move backwards/forwards within this movement but on average...) is equivalent to an outside observer's observations. E.g. more specifically that the laws of physics of such a frame of reference as measured by an observer within that frame are equivalent to what Relativity states they should be.

So this makes perfect sense, the frame of reference travelling the fastest will experience the most time dilation (slowing down of time). We just need to prove that there is an absolute frame of reference which we'll look at later.

Thought experiment #2 - A moving system 5:51AM

Thought experiment #2 - A moving system

Second the speed of light is measured to be the same in all frames of reference. This means that even though we (the Earth) are in a moving frame of reference we are still measuring the speed of light correctly. This seems strange until you realise that measurements are dependent on things like time and movement of particles which slow down the faster you go and this exactly compensates for your measurements.

Tangental thought: It also means that light emitted from our sun (from the perspective of another frame of reference) will appear like sound waves on a moving police car, e.g. bunched up on one side and expanded out on the other. E.g. the event of the sun winking out will travel further on one side than the other. This is a little irrelevant as people within our frame of reference do not see this.