What does the TIM tell us?
 
Most theories these days are built by postulating what is called a “Lagrangian”, or equivalently, an “action”, and testing the predictions that result. The reason is that these mathematical entities, like Newton’s second law, specify the quantitative results of the theory.
Or do they? The key point of the theory of incomplete measurements is that there is another, big, overlooked part in doing such predictions, which is to understand the measurement processes we are predicting things about. This is totally implicit in all modern theories so far. When general relativity writes a space coordinate as “x”, it does not specify how “x” is measured, because all measurements are deemed equivalent. This is what the theory presented here challenges.
But the most interesting thing is that, by asking the question, and then attempting to answer it, the theory of incomplete measurements can deduce the largest part of the structure of the other theories. All, that is, but precisely the form of the Lagrangian, which is instead borrowed from existing theories.
More specifically, here are a few key results.
General relativity:
  1. The properties usually attributed to space and time are actually properties of electromagnetic interactions.
  2. We can build a space-time “continuum”, but it is built from quantized measurements of space and time.
  3. Under reasonable conditions, laws of physics can be made to agree locally between various measurement processes.
  4. However, this agreement will not in general hold at larger scale. The problem of “dark matter” may be an example of such a divergence.
Quantum mechanics:
  1. Quantum mechanics is the necessary form of a probabilistic theory of measurements.
  2. The theory shows why the wave-function is complex-valued, and gives an indication of what the meaning of its phase is.
  3. The standard way of normalizing the wave-function is incorrect, leading to bogus infinities. The theory suggests a normalization condition that is equivalent in terms of measurement results, but does not diverge.
  4. The quantum measurement problem is essentially eliminated. The mathematical answers like decoherence now answer a different question, which is: “why are there measurements”.
Results?
Monday, November 20, 2006