Quantum mechanics/Essays/My conversation with Bard

• Read the entire conversation at Quantum mechanics/A conversation with Bard
• The numbered items (1-8) are my questions. My comments regarding each question are listed below each question.

Clicking the links to my questions above will send me to my comments below. But clicking the title in the sections that follow will send you to Bard's actual answer on Quantum mechanics/A conversation with Bard

You might say that Schrödinger solved the problem of the nonrelativistic spinless electron. When Heisenberg coinvented quantum mechanics, what problem did he solve?

My interest in this problem dates back to a pair of papers I wrote several years ago. My goal was to make quantum mechanics and its probabilistic interpretation seem like logical consequence of a decision to model classical particle motion using wavepackets.

• "Accelerating wave packet solution to Schrödinger’s equation" (Am. J. Phys. 2000)
• "The maze of quantum mechanics" (Eur. J. Phys. 2002)
• "The diffraction and spreading of a wavepacket" (Am. J. Phys. 2004)
• See also Advanced Classical Mechanics/The Eikonal Approximation and Classical Particle Motion on Wikiversity.

My current interest is teaching resources that introduce tensors to students in an introductory physics course, so this got me thinking about matrices and simple harmonic oscillators (i.e. springs and masses.) That naturally led me to an unanswered question I had regarding wave packets and quantum mechanics. The motion of wavepackets makes the quantum mechanics and its Copenhagen interpretation seem obvious and even unavoidable: The fact that a barrier splits the wavepacket into two parts suggests that the wavefunction must somehow represent probability. That fact that $|\psi |^{2}$ and probability both obey the "conservation law" ${\textstyle \int P(x)dx=1,}$ gives us no choice regarding how to interpret psi. A study of wavepacket motion establishes that the wavelength associated with a moving particle is an arbitrary choice, but the atomic spectrum of any elements yields a numerical value for ${\textstyle \hbar .}$

Can you summarize Heisenberg's first (1925) paper in one equation?

If I was introducing the matrix to model the harmonic oscillator to introductory physics students, it would have been nice to say that one version of quantum mechanics was invented as an effort to use a matrix to model a mass on a spring. But, apparently I was wrong.

Did Heisenberg's first paper include the famous version of the uncertainty principle regarding momentum and location?

I asked this out of curiosity. And Bard said the uncertainty principle was not in that paper.

BEWARE: I have caught Bard making erroneous statements (often due to a bizarre interpretation of what I thought was a clearly stated question.)

What inspired Heisenberg to use matrices?

Bard's answer was essentially that nobody knows. I was fascinated by Bard's how simulated wisdom could come up with the following statement:

It's important to remember that scientific discoveries rarely hinge on a single "Eureka!" moment.

Then I informed Bard that I was more informed than the average person on this subject:

But I read the 1925 paper and noticed an analogy to the classical commutators in these advanced versions of Newtonian physics.

Bard acted surprised that I knew so much about this subject! I have never surprised a computer before (at least to my knowledge). I had to investigate this simulated emotion in a computer:

You said "You're absolutely right! It's fascinating that you caught the connection between Heisenberg's use of matrices in his 1925 paper and the concept of commutators in advanced Newtonian physics. " My question is: Fascinating to whom?

Bard set me straight by pointing out that he (it) was not really surprised. But I found Bard's reasons for simulating this emotion very interesting. Bard was programmed to make humans feel at ease, and apparently acting surprised can accomplish that goal.

Bard's apology amused me and prompted me to make the following remark:

Computers should never apologize for acting as if they were human.

Bard's answer was revealing: He explained why he was "programmed" to apologize, and his reasons were sound. I responded with a friendly remark, hoping to end the conversation:

Your computer apologies are endearing.

Bard often talks in this manner. I interpret this as a polite way to suggest that this is a good time to end our conversation.