Why Quantum States Look the Way They Do
CSD Primer (Page 3 of 5)
From hidden detail to usable descriptions
So far, we have said two things:
the underlying behaviour of a system may be fully determined
probability appears only because we do not have access to all that detail
The next question is unavoidable:
Why do the summaries we use in quantum mechanics take the specific form they do?
Why not some other way of packaging incomplete information?
Quantum states as summaries, not physical waves
In CSD, a quantum state is not a physical object. It is a summary description.
When many different underlying physical situations all look the same from an experimental point of view, we group them together. A quantum state is simply a label for such a group.
What matters about these labels is not what they are made of, but how they relate to each other:
which states can be smoothly transformed into which others
how experimental setups affect them
how different descriptions overlap
Quantum states are therefore best thought of as points in a space of possible descriptions, not as objects evolving in physical space.
Why this space has a special structure
Experiments impose strong constraints on how these descriptions must behave.
In particular:
multiplying a state description by an overall factor does not change anything observable
different experimental settings are related by smooth, reversible changes
no description is privileged before a measurement is chosen
Taken together, these requirements leave very little freedom.
They force the space of quantum state descriptions to have a highly symmetric structure. This structure is the same one used in standard quantum mechanics, but here it is not assumed. It is forced by consistency and symmetry.
The key point is this:
The mathematical shape of the quantum state space is not a choice. It is the simplest structure that allows all experimental descriptions to be treated on equal footing.
Why the familiar probability rule follows
Once the space of quantum states is fixed, probabilities are no longer arbitrary.
If probability reflects how much underlying physical behaviour is compatible with a given description, then probabilities must respect the same symmetries as the descriptions themselves.
That requirement turns out to be extremely restrictive.
There is essentially only one consistent way to assign probabilities that:
treats all equivalent descriptions equally
respects the symmetry between different experimental choices
behaves smoothly under changes of description
This unique assignment is exactly the probability rule used in quantum mechanics.
In CSD, this rule is not postulated. It is the only way to consistently measure “how much” underlying behaviour corresponds to a given description.
What this does not mean
It is important to avoid two common misunderstandings.
First, this does not mean that probability is hiding inside the underlying physical behaviour. The underlying level remains fully determined.
Second, it does not mean that quantum states suddenly become physical objects. They remain descriptions, not things.
Probability arises because we describe a rich underlying reality using a compressed language. The structure of that language fixes how probability must behave.
What has been gained
At this point, three major pieces are in place:
probability arises from limited information, not randomness
quantum states are structured descriptions, not physical waves
the familiar probability rule follows from symmetry, not interpretation
What remains is to explain how change over time and measurement outcomes fit into this picture.
That is the task of the next page: showing how ordinary quantum dynamics and measurement behaviour emerge from the same underlying ideas, without adding new rules.