Vector Time Analogy
7778 Thornapple Bayou SE,
© David Barwacz 10/03/2004
http://members.triton.net/daveb
Most people who read my paper (Linear Motion in
Space-Time, the Dirac Matrices,
and Relativistic Quantum Mechanics ) come away a bit perplexed about my treatment
of time. They have trouble accepting that time could be directional, let alone
the cause of all changes we perceive. The following simple analogy should make
these ideas more understandable.
Let’s assume that there is a raft anchored at sea. The water is perfectly calm and a steady wind is blowing. The wind velocity is constant. The direction and speed never change. For the sake of argument, let’s say the wind speed is 10 mph.
On the raft is a trough of calm water. On the windward side of the trough is a small raft which is anchored in the trough.
Both rafts are very well designed and can glide on water friction free. The large raft has a drag device (a board) that can be inserted into the water to slow its speed should it be moving.
A wind powered computer is on the large raft. The clock rate of the computer is directly proportional to the wind speed.
The computer controls some actuators which can release either anchor. It also has sensors from which it can measure the position of the small raft should it move in the trough.
The computer has a wireless connection to a computer on the shore which is operated by a researcher. The researcher has a radar gun with which he can measure the speed of the large raft. He cannot measure the speed of the small raft in the though.
He has been given the task of measuring the speed of the small raft when the large raft is anchored and when it is moving. He is given the distance between position sensors on the trough. He has not been told that the computers clock is proportional to the wind speed.
He remotely programs the computer to release the anchor of the small raft, wait until the raft reaches a constant speed via the sensors and then start a counter. The counter is stopped when the raft reaches the end sensor. From these reading’s he calculates the speed and determines it to be 10 mph.
Now he releases the large raft and set the drag device such that its speed stabilizes at 5 mph. He then runs the computer program again to measure the maximum speed of the small raft.
The computer once again reports 10 mph.
Perplexed by this reading, he does the experiment many times and with different large raft speeds and in every case he gets 10 mph reported back.
In frustration, he buys a boat and oars out to the raft. He then discovers that the computer is wind powered and that its clock rate is proportional to the wind speed. When the large raft moved, the effective wind speed decreased and the computer ran slower and that is what resulted in the 10 mph result each time.
Now, let’s assume that the researcher himself was an android and his internal timer was wind driven but he was not aware of that fact. When he was on the moving raft his own internal clock slowed. From his stand point the small raft would have a velocity of 10 mph regardless of what his radar gun on shore said the speed of the large raft was. He would be entirely perplexed.
Consider time to be like a wind and everything powered by it, everything’s internal clock rate determined by it.
If every change we perceive, all our instruments, our entire biological processes are time driven and the driving force is a vector projection of time onto the axis of motion what do we get?
We get two of the most important concepts in physics: The Lorentz transforms and the Dirac matrices.