Disclaimer: machine translated by DeepL which may contain errors.
About Time
Katsuaki Asano (Professor, Institute for Cosmic Ray Research)
I’d like to write about time as the mood strikes me. All physical quantities can be expressed as a combination of three units: time, length, and energy. The essence of physics as a discipline lies in describing the evolution of physical quantities over time, and time is treated as a special concept distinct from space.
When I write this, people working in relativity or particle physics often tell me, “Using a unit system where the speed of light c = 1 allows us to treat time and space equally, which is both beautiful and convenient,” making me—who always uses c in the equations of my papers—feel rather pathetic.
However, I dislike this unit system. First, what does “c = 1” mean in the context above? It means that, for example, when using centimeters (cm) as the unit of length, the time it takes for light to travel 1 cm can be expressed in the same unit of cm. The key point is that the speed of light is constant and unchanging.
As can be seen from the famous equation E=mc², energy and mass are expressed in the same unit. Those who belong to this school of thought further define ħ—Planck’s constant h divided by 2π—as 1. This is called the natural unit system, and as a result, all physical quantities can be expressed solely in units of energy.For us, who base our discussions on observational data, treating time and energy as one and the same is extremely inconvenient.In any case, time is clearly different from space. It moves in only one direction and cannot be reversed. Physics is governed by the law of causality, which cannot be reduced to geometry alone. There is a certain poignancy to this—giving the concept of time special treatment and assigning it its own unit is an expression of our affection for it.
The current definition of the unit of time, the second, in the International System of Units (SI) is as follows: the electromagnetic wave that excites a cesium atom with an atomic mass of 133 oscillates 9,192,631,770 times per second. We measure time by counting the number of oscillations of this electromagnetic wave.This means the wave oscillates approximately 9 times in 1 nanosecond (10⁻⁹ seconds). By defining the distance light travels in one second as 299,792,458,000 cm, the unit of length is also established. Here, the speed of light is a completely fixed value—a defined value.In 2018, the units of energy and mass were also defined by setting Planck’s constant h—represented by a 9-digit number—as the defining value. As a theoretical physicist, I would have preferred to use ħ as the defining value (since pi is an irrational number), but it cannot be helped.Looking at it this way, the definition of time alone feels somewhat artificial—or, one can’t help but think, “cesium, huh?” If the gravitational constant G could be defined as a defined value, we could define the unit of time most elegantly; unfortunately, however, the gravitational constant is a physical constant with poor measurement accuracy, making it unreliable as a standard.
The clock tower in Bern, Switzerland. While living in Bern, Einstein published his theory of special relativity, which states that the passage of time varies depending on the observer.In the universe, astronomical phenomena occur across a wide range of time scales, from nanoseconds to 10 billion years. Sometimes, a single celestial object is observed simultaneously by a ground-based radio telescope and a satellite-based X-ray telescope. If the distances of the two telescopes from the object differ by 100 meters, the arrival times of the radiation will differ by about 300 nanoseconds.To achieve high temporal precision, it is necessary not only to carefully synchronize the clocks of the two telescopes but also to account for the position of the satellite—which orbits the Earth once every 90 minutes—as well as the effects of the Earth’s rotation and revolution, and differences in how clocks run due to variations in gravity.
Gravitational waves—ripples in spacetime—emitted by supermassive black hole binaries outside the Milky Way cause the arrival times of periodic radio pulses from pulsars within the Milky Way to shift by tens of nanoseconds.Efforts are underway to detect gravitational waves by conducting long-term observations of numerous pulsars over a 10-year timescale and confirming these minute changes. Considering the time corrections described above, it is clear that this is an extremely delicate experiment. On the other hand, it is also difficult to detect variations in celestial bodies on timescales of hundreds or thousands of years—timescales that extend beyond a human lifetime. There is an interesting recent example of this.A distant celestial object has been detected as multiple images due to gravitational lensing. Since the light travels along different paths for each image, we are effectively observing the same celestial object at different points in time simultaneously. Using such observations, it is possible to detect long-term variations spanning approximately 100 years. I hope you find it interesting that the keyword “gravity” appears so frequently when discussing time.
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