How Probability Appears Without Randomness
CSD Primer (Page 2 of 5)
Why probability needs an explanation
In everyday life, probability usually means uncertainty. We roll dice, shuffle cards, or measure noisy systems. In all of these cases, probability reflects either randomness or lack of control.
Quantum mechanics goes further. It treats probability as fundamental. Even with perfect preparation, it tells us only the chances of different outcomes, not which outcome will occur.
CSD asks a simple question:
Is probability truly fundamental, or could it arise from something deeper that is fully determined?
Determinism underneath, statistics on the surface
The starting point of CSD is that, underneath what we observe, physical systems behave in a fully determined way. Given the complete physical situation, there is only one way the system can evolve.
However, we never have access to that complete situation.
Instead, we interact with systems repeatedly under similar conditions and record outcomes. When we do this many times, patterns appear. Some outcomes happen often, others rarely. These patterns are what we call probabilities.
In CSD, probability is not about what nature does. It is about what we can predict when we lack complete information.
Typical behaviour replaces randomness
To understand this, consider a simple idea from classical physics.
If a system moves deterministically but explores its allowed states in a regular way, then over time it spends predictable fractions of time in different regions of its possible behaviour. These fractions do not depend on chance. They depend on the structure of the system.
CSD uses this idea in a general setting:
the underlying motion is deterministic
the system explores its possibilities in a stable way
long-run behaviour becomes predictable
When we repeat an experiment many times, the observed frequencies settle down. Not because of randomness, but because most initial situations behave in the same typical way.
Where probability actually enters
An important point is this:
Probability does not apply to the underlying physical state itself.
At the deepest level, the system is always in one definite physical situation. There is no probability attached to that situation.
Probability enters only when we describe the system using incomplete information. When many different underlying situations look the same to us experimentally, we group them together. We then assign probabilities to the possible outcomes we can observe.
In CSD:
the underlying reality has no probabilities
probabilities describe collections of possibilities we cannot distinguish
This is why probability is called epistemic. It belongs to knowledge, not to reality itself.
Spacetime and events come later
At this stage, it is also important to be clear about what has not yet appeared.
We have not assumed spacetime, particles moving in space, or measurement events happening at particular times. Those ideas belong to how we describe experiments and observations, not to the deepest level of the theory.
Spacetime descriptions emerge later, when certain patterns in the underlying behaviour become stable enough to be treated as events, locations, and records.
Probability does not come from spacetime uncertainty. It comes from limited access to underlying information.
What has been established so far
By the end of this page, only a modest claim has been made:
physical behaviour may be fully determined underneath
repeated experiments show stable statistical patterns
probability describes those patterns, not intrinsic randomness
Nothing specifically quantum has been assumed yet. There are no wavefunctions, no superpositions, and no quantum rules.
The next step is to explain why, when we describe systems using the language of quantum states, those probabilities take the specific form we know from quantum mechanics.
That is where geometry and symmetry enter.