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MBT says that the speed of light is a constant because space and time come in discrete chunks that are like the pixels of our virtual reality, such that light can only move one pixel of space per one pixel of time.

MBT defines this reality, in part, based on assumptions, constraints and probability. One such assumption is that the speed of light is a constant. It is not unreasonable to conclude that there is a high degree of probability that the assumption is constrained within this reality.

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What would the speed of light be if space/time were continuous? Wouldn't the speed of light have to be infinite? But then how does Einsteinian relativity make the math work by assuming both C and continuous space/time?

The theory supports the notion that space time is continuous; present moments resulting from future probabilistic choices becoming a past database (metaphor alert). It does not assume that the choices travel at the speed of light.