Since there has been a resurgence of interest amongst members about the mechanics of waves, relativity and simultaneity I would like to pose a question.
We are generally familiar with Fourier series and perhaps know that to represent a step function we require the series to reach all the way to infinity.
However there is one more requirement, understood but not normally stated.
All the components must be present at the same time (simultaneously), for the series to sum to the required function.
Now consider an energy density function, such a solution to Schroedingers wave equation for a step function that occurs when an elementary particle appears (is created)
This has components all the way to infinity, which must suddenly come into being and exist simultaneously. (sound familiar?)
Any changes to the state of the particle must change all these components simultaneously.
So
1) How does this happen if light is the limiting speed?
2) How does the infinite series fit into our allegedly finite universe?
We are generally familiar with Fourier series and perhaps know that to represent a step function we require the series to reach all the way to infinity.
However there is one more requirement, understood but not normally stated.
All the components must be present at the same time (simultaneously), for the series to sum to the required function.
Now consider an energy density function, such a solution to Schroedingers wave equation for a step function that occurs when an elementary particle appears (is created)
This has components all the way to infinity, which must suddenly come into being and exist simultaneously. (sound familiar?)
Any changes to the state of the particle must change all these components simultaneously.
So
1) How does this happen if light is the limiting speed?
2) How does the infinite series fit into our allegedly finite universe?