A particle in a three dimensional volume has three degrees of freedom. So degrees of freedom are bestowed by dimension.
If dimension is fundamental, then how does space time scale? Does it scale like 4 dimensions, or does it scale like 4 degrees of freedom?
Time is not a dimension like the 3 dimensions of a volume, instead moving each point in a volume along a time line. If a 4 tuple qualifies as having 4 degrees of freedom but can only very loosely be described as having 4 dimensions, then would that make degrees of freedom more fundamental than dimension.
If space time is related to cosmogenesis, and energy propelled the universe into existence, then would dimension be a physical aspect of the universe consequent on 4 degrees of freedom?
Which came first physically: dimension or degrees of freedom?
One argument is that a particle in 3 dimensional space is induced by those dimensions to have 3 degrees of freedom. Hence, since dimension induces degrees of freedom, dimension is more fundamental than degrees of freedom.
Another argument assumes that cosmological space at all times from cosmogenesis forward comes into existence as a result of pressure that causes the volume of space to expand. Since the 3 dimensional volume of space arises from a fourth degree of freedom arising from energy, or from 4 degrees of freedom that includes one degree of freedom representing time or motion, degrees of freedom as physical phenomenon precedes the 3 dimensions of space.
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