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Sampling Universe Theory
2. Spatial and temporal resolutions and limits
That is our second analogy : in both Quantum Mechanics and Digital Signal Processing, there is a minimum amount of time and a minimum amount of space, nothing can exist beyond those limits.
 
The main reason for these limits is that the physical universe and the memory of a computer are not infinite. So they have to use quanta, as if there was such a thing as infinitely small values, the physical universe and the computers would have to be infinite, but they can't: there are not enough resources available.
First there is a "real" wave in the physical universe.
 
An electronic chip, the analog to digital converter, is converting this wave into numbers (samples), and there is a minimum number which is called resolution.
 
Samples are created according to a regular rythm, the "sampling frequency", so that there is a minimum amount of time (sampling period).
 
When the amplitude of the wave is inferior to the resolution, it cannot be represented.
Quantum Mechanics
Digital Signal Processing
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Version 2
January 21, 2007
In Digital Signal Processing:
Spatial Grid
Samples, at the intersections
of spatial and temporal grids
Real Wave
Resolution
Time
Sampling Period
Temporal Grid
Space
In Quantum Mechanics:
Where

How do we know it?

The discovery of Planck's limits comes from the study of black body radiations in the last years of the 19th century.

A black body absorbs all light that falls onto it, but does produce thermal radiations such as light.

When measuring the radiations of black bodies, scientists discovered that they were not in agreement with the classical view where electromagnetic waves are continuous phenomena.

The following figure represents the curve predicted by the classical theory of electromagnetism (where light and the universe are continous entities) and the real curves (red / blue / green curves):

The real curves don't agree with the classical view.
 
The only way to explain the experimental graphs was to assume that electromagnetic radiation could propagate only in discrete packets, or quanta.

As a consequence, both time and space are also based on discrete packets, and the sizes of the spatial and temporal packets give us the Planck's time and length.

By extending the analogy, we see that very short events, very high frequencies or very small objects can exist in the upper universe, when they cannot exist in the physical universe.

When the duration of an event is inferior to  the sampling period, it cannot be represented.
Time
Space
All samples have the same value, the real wave is invisible
Space
All samples have the same value, the real wave is invisible
Short event
Short events and small signals and waves cannot be represented in the digital domain, but they can exist in the real world.
Measured curves
That is the curve we should have if the universe was continuous
Time
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