Virtual Dimension Einstein x Virtual Dimension Yuma Murakushi "Beyond Virtual Time" [Virtual Dimension Talk Project Episode 2, Part 1] How does Einstein view the virtual dimension?

One month had passed since their last conversation. Suguri visited Einstein's study in Princeton once again. Today's topic was singular: as a foundation for Einstein's own research, how did he evaluate the concept of "imaginary dimensions"?

Several old notebooks were stacked on the desk. The spine read, "Kaluza, 1921."

Act I - From Minkowski's ICT

Einstein  Alright, Mr. Yuma. Let's continue from where we left off. I'll start today.

Murakami  I'm looking forward to it!

Einstein  I was turning your Z = D + iD over in my head for a few days. And I felt a strange sense of nostalgia.

Murakami  What do you mean by nostalgia?

Einstein  It's Minkowski. When he formulated four-dimensional spacetime in 1908, he wrote the time axis as ict. c is the speed of light, t is time, and i in front – the imaginary unit.

Murakami  Yes, that's a famous notation.

Einstein  At that time, as a young person, I thought of it as a "convenient calculation trick." Just insert an imaginary number to treat time and space with the same square. That was all there was to it, I thought.

Murakami  But later the notation was changed. In general relativity, the metric tensor was used to eliminate ict.

Einstein  Right. I concluded that the 'i' was not an essential part of it, but rather a matter of choosing coordinates. --However, Yuma, listening to you talk this time, I find myself with no choice but to reconsider my actions from that day, even if just a little.

Murakushi holds his breath.

Murakami  What do you mean?

Einstein  Perhaps at that time, I didn't "erase" i, but rather "expelled it from the physical." In reality, i was saying something about the time axis, but I covered it up with a coordinate transformation.

Murakami  Sir, that is──.

Einstein  Wait. Don't jump to conclusions. I haven't agreed to your sub-dimensional yet. I'm just saying that it might be worth reconsidering Minkowski's ICT from another angle.

Act II: The Fifth Dimension of Calza-Klein

Einstein  I have another job I want to tell you about. Here it is.

He taps the notebook on the desk with his finger.

Einstein  It is a paper that Kaluza wrote in 1921. He claimed that by adding "one more dimension" to my general theory of relativity, gravity and electromagnetism could be derived from a single geometry. Klein later interpreted that fifth dimension as "compactly curled up."

Murakami  It's the Kaluza-Klein theory, isn't it? My understanding is that it became the basis for later string theory.

Einstein  I have been drawn to this work for a long time. My obsession with unified field theory did not fade until my later years. Do you know why?

Murakami  I thought, perhaps presumptuously, that you wanted to re-stitch what was divided into a single geometry.

Einstein  That's right. Gravity and electromagnetism, matter and fields, the observer and the world. I could no longer endure speaking about them in separate languages. That's why I seriously bet on the "unseen axis" of the fifth dimension. —And I failed.

Murakami  The teacher says it was a failure, but without that persistence, modern high-dimensional physics wouldn't exist.

Einstein  That's a kind way of putting it. But, Yuma, I'd like to ask you something here. How does the imaginary dimension iD you speak of differ from Kalza's fifth dimension?

— Lord, straighten your posture. —

Murakami  Kaluza's fifth dimension is an added axis to space. It has a physical extent, even if it is small and curled up. It can be an object of observation.

Einstein  Hmm.

Murakami  My iD is not an addition of space. Rather, it is an axis that stands "outside" of space and time. It is not an axis on which physical quantities are placed, but an axis on which "things that have not yet become physical quantities" are placed.

Einstein  Or is it like a reservoir, before it became physical?

Murakami  It's close. If the teacher's Kaltza-like fifth dimension is "physics that hasn't been seen yet," then my iD is "something that isn't even physics yet."

Einstein  Don't get too metaphysical.

Murakami  Yes. That's why I'm not claiming this is a physical theory. I think it would be more readily accepted by various industries if it were considered a kind of philosophy, a type of thought.

Act III – A Long Dispute with Boer

Einstein  By the way, you know about the Bohr-Einstein debates, right?

Murakami  Of course. The EPR paradox, hidden variables, "God does not play dice." Decades of debate.

Einstein  I maintained until the end that quantum mechanics was incomplete. I simply could not come to terms with the idea that a state is not determined until it is observed. To me, the moon should have been there even when no one was looking.

Murakami  It's a famous metaphor.

Einstein  However, listening to you, I noticed something strange. If your iD is real, then Bohr's and my dispute might have a different outcome.

Murai leans forward.

Murakami  Please tell me.

Einstein  Bohr said, "It's not decided until it's observed." I said, "It's already decided even if it's not observed." We were fighting on the same plane. "However, if we adopt your concept of imaginary dimensions, it becomes this: 'It's already decided on the imaginary dimension side even if it's not observed. It becomes observable the moment it descends to the real dimension.'"

Murakami  Yes.

Einstein  This is a structure that saves both my realism and Bohr's probabilistic theory. At least, logically.

Murakami  Sir, I didn't expect you to say that.

Einstein  Don't misunderstand me. I said "logically." I didn't say I recognized it as physics. As soon as you incorporate concepts that don't come under observation, physics devolves into metaphysics. I'm wary of that.

── A moment of silence. ──

Murakami  Sir. Please allow me to offer just one objection.

Einstein  Here you go.

Murakami  When the professor proposed the quantum hypothesis in 1905, it was also considered a "concept that could not be observed" at the time. No one had ever seen light as particles. It was only when the professor drew the coordinates that it became observable.

Einstein gazes at Murakoshi for a moment. Then he chuckles softly.

Einstein  Tough. Life itself punching me in the face.

Murakami  It is a return of respect and a repayment of kindness.

Einstein I understand.

To be continued in part two.

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