What is 'quantum foam'?
This is an idea that was originally proposed by Nobel physicist John Wheeler back in the early 1960's to describe what space-time 'looks like' at scales of 10^-33 centimeters.
The basic idea is that gravity is a field with many of the same fundamental properties as the other fundamental 'force' fields in Nature. This means that the state of this field is, at some level, uncertain and described by quantum mechanics. Since Einstein's general theory of relativity requires that gravitational fields and space-time be one and the same mathematical objects, this means that space-time itself is also subject to the kinds of uncertainty required by quantum systems. This indeterminacy means that you cannot know with infinite precision BOTH the geometry of space-time, and the rate of change of the space-time geometry, in direct analogy with Heisenberg's Uncertainty Principle for quantum systems.
Wheeler imagined that this indeterminacy for space-time required that at the so-called Planck Scale of 10^-33 centimeters and 10^-43 seconds, space-time has a foaminess to it with sudden changes in its geometry into a wealth of complex shapes and textures. You would have quantum black holes appear at 10^-33 centimeters, then evaporate in 10^-43 seconds. Wormholes would form and dissolve, and later theorists even postulated 'baby universe' production could happen under these conditions.
The problem is that we have no evidence that 1) gravity is a quantum field and 2) that space-time has this type of structure at these scales.
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