What is time? It is what physics has erased, philosophy has protected, and what we are now trying to pinpoint.

"What is time?"

It is one of humanity's oldest questions. And the exploration of this question has proceeded in two diametrically opposed directions since the 20th century.

Physics has dismantled time.

Relativity theory demonstrated that the passage of time varies with location and speed. Time differences can be measured between mountaintops and flat ground. There is no "absolute time" that flows uniformly everywhere in the universe. Furthermore, in modern quantum gravity theory, the time variable itself disappears from the most fundamental equations of the universe. This is as popularized by Rovelli's bestseller, "The Order of Time."

Meanwhile, philosophy has stood the test of time.

Bergson realized that the time measured by clocks is actually spoken in the language of space—the distance on the dial—and called the qualitative flow that expands and contracts within experience "pure duration." Husserl described the internal structure of the "now." When listening to a melody, the sound currently playing is overlaid with the lingering resonance of the immediately preceding note, and the anticipation of the next note encroaches. The "now" is not a point but has thickness.

"Now" cannot be contained in one dimension

A third way, neither elimination nor mystification

Deconstructing physics and a philosophy of preservation.

The two inquiries, with completely different methods and vocabulary, are, however, running into the same wall.

The "now" doesn't fit on the one-dimensional timeline t.

From the perspective of physics, "the present" holds no privileged position in any equation. From the perspective of philosophy, "the present" is too thick to be squeezed into a point without width.

Here, much of the discussion tends to fall into a dichotomy: either elimination, saying "Therefore, time is an illusion," or mystification, saying "Therefore, time cannot be handled by science."

However, there is a third way.

Mathematics once broke the same wall.

Add an orthogonal axis. T = t + it

In the history of mathematics, there was a problem with the exact same form, and its solution.

In the past, numbers were considered to be confined to a one-dimensional number line, and "numbers that equal -1 when squared" were thought not to exist. However, these numbers continued to appear in calculations. The solution was not elimination or mystification, but the addition of an axis perpendicular to the number line. The world of numbers was extended to a two-dimensional complex plane, and imaginary numbers, once scorned as "imaginary numbers," became indispensable for supporting electricity, communications, and quantum mechanics.

Murakushi's fifth thesis, "Imaginary Time," applies this extension to time.

If a one-dimensional temporal description cannot capture the superposition of phases of "now" — the coexistence of what is passing, what is happening, and what is to come — if the description does not close, then add an independent axis to supplement it, only the bare minimum necessary. The paper calls this approach the principle of minimal extension.

That consequence is this formula.

T = t + it

t is the real time axis measured by clocks. it is the imaginary time axis orthogonal to it, and the coexistence of phases at the "present" is first positioned on this axis. The time we experience is always this two-dimensional structure T—complex time—and the clock time t is merely its projection onto one dimension.

The century-long conflict consisted of two components with the same structure.

Not "whether it exists," but "whether it is necessary for the description."

This viewpoint quietly resolves a hundred-year conflict between physics and philosophy.

Physics dismantled the absoluteness of projection time. Philosophy defended the thickness in the 'it' direction. The two were not in contradiction, but rather spoke of different components of the same two-dimensional structure.

Just one point, to be precise. Suguru's fifth paper, "Imaginary Time," does not claim that imaginary time $i\tau$ exists. What is claimed is the structure of the description, which is that a one-dimensional time description does not close on its own and requires an axis orthogonal to $t$ for a complete description.

But, recall that imaginary numbers, once relegated outside the number line, eventually came to be central to the description of the world.

What is time?

What has been thought of as a line, is actually a plane—this is one answer at the present time.

↓Yuma Murakami's Fifth Paper "Imaginary Time - Non-closure of Description and the Principle of Minimal Extension" is here↓

↓ To learn more about imaginary time, check out Λ Meditation now ↓

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