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I was reading Dirac's "The Principles of Quantum Mechanics" and on page 7 he makes the following statement:

"Like the fundamental concepts (proximity, identity) which everyone must learn on his arrival into the world, the newer concepts of physics can be mastered only by familiarity with their properties and uses."

I take "identity" to mean the vague collection of concepts such as "identity functions/operators", "identities between equations" etc.

But I cannot form any reasonable notion of what "proximity" could mean, even vaguely. My best is "how close things are" and that means almost nothing in this context.

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You are thinking much too advanced. By identity and proximity Dirac means the most elementary facts of nature. Every baby learns these facts during the first few months in life.

Identity

The objects in nature have a persistent identity.

Examples in baby life:

  • This red ball I'm holding with my hand now is the same thing which I see in front of me.
  • This ball I'm holding now is the same which I was playing with some minutes ago.
  • This ball continues to exist even when my mom takes it away and I cannot see it anymore.

Proximity

Objects nearby have a greater effect than objects further away.

Example in baby life:

  • I can feel this ball only when I touch it. When it is further away I can't feel it, but I can still see it.
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No one learns about “identity functions/operators” or “identities between equations” on their arrival into the world (i.e., as an infant), so this could not possibly be what Dirac meant by “identity”.

Dirac is using the terms “identity” and “proximity” in their most obvious everyday meanings. An infant learns to identify Mommy and Daddy as unique, persistent, and separate entities. They have “identities” which even an infant can perceive. Similarly, an infant learns proximity or closeness through feelings such as “I like it when Mommy holds me close” vs. “I don’t like being alone in my crib with nobody around to hear me cry”.

The key clause that indicates Dirac is not talking abstract physics here is “which everyone must learn on his arrival into the world”. I think he is simply saying that you cannot master physics until you have become completely familiar with it, as familiar with physics as an infant is familiar with family.

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