We suggest that the notion of physical time, though thoroughly discussed in special relativity, is not properly reviewed in physical theory after the quantum theory has emerged and up to now. Still quantum phenomena, as we suggest, provide a new insight in how the physical time can in principle be measured. We propose a fundamental idealized procedure of detecting physical time at microscopic level.
We also specially argue that introduced procedure is fully consistent with relativistic theory.

The procedure we introduce was initially designed to apologize for an interpretation of quantum mechanics we suggested [1, 2]. Though highly interested in that interpretation we take for granted that such interpretations are very speculative and suffer from lack of direct experimental evidence. Still the time detecting procedure we introduced there seems to stand in its own. The paper is devoted only to the procedure itself.

We suppose that the very way we use to measure physical time is not properly reflected in current physical theory. The notion of “clock”, seemingly thoroughly discussed in special relativity, still is not rather strictly re-defined after quantum mechanics has emerged, as we argue.

We propose a “fundamental procedure for detecting physical time”, viewing this like an analogy of A. Einstein’s fundamental procedure for synchronizing remote clocks. In other words, we suggest that the very notion of time should in principle be explicitly defined by some fundamental experimental procedure, like we do with “simultaneity” in special relativity.

The procedure we describe is of no questions highly idealized, and thus may (and should) cause many questions. Still we deliberately tried to formulate such a procedure in maximally simplified and clear way.

We suppose that most physicists will agree with us that any highly stable periodic process can serve as clock. Still there exists a detail usually omitted. Say, David Greene in his scientific popular bestseller “Elegant Universe” [3] uses a photon jailed in optical resonator as a simplest clock to demonstrate physical reasons for Lorenz transformations.

But can light in an ideal resonator really serve as a true clock? If the covers of resonator mirrors are ideal, then the oscillations do not dissipate their energy, and never last. Excellent for storing energy, but this makes such a clock absolutely useless. Since the energy does not dissipate, nothing changes, and we simply will know nothing, looking at such clock.

So we suppose that only dissipation in periodic processes let us know that the time goes, and true clocks always use dissipation. Pendulum clock dissipates gravitational energy; hand electronic watch dissipates the energy of electric battery, and so on.

Next, we suppose that since energy is quantized, the dissipation is also quantized. But this inevitably leads to the idea that the physical time itself is quantized. And next, we state that the physical time can in principle be measured only by the number of absorbed quanta of energy, properly normalized for certain configuration of an experiment.

One can raise objection here that energy is not necessary quantized, according to quantum mechanics. Say, definite momentum states

can have arbitrary momentum p. Still we suppose it’s a formal objection. In reality we always detect some observable’s value by ultimately looking at some “arrow”. The arrow’s position is obviously quantized due to atomic structure of the device we use.

So, anyway we deal with quantized, discrete events.

Let us assume some simple, but definite process. Let us determine, what time does it take for a photon to move from its source to its detector. In other words, we shall describe how in principle the time of photon's "flight" is detected, and, thus, which is experimental sense of "speed of light" notion.

The general schematic idea of time detection procedure is at Fig. 1. Exactly in the middle of line between source atom S₁ and detecting atom D₁ there is one more light source S₀, which we call "a button switch".

Let the "button switch" simultaneously radiates 2 light signals in opposite directions. These signals come to the source and to the detector simultaneously (in the referential frames where all sources are at rest). When the signal comes to the source, the latter emits a photon.

Next, the "valve" at right side is opened at the same instant. The valve shadows the detector form laser S₂ light. The laser is adjusted to the frequency of atomic transition. Thus the detector starts getting photons from the laser.

Let us assume that all considered photons have the same energy (wave length). Let us also admit that after each photon absorption we forcedly relax the detecting atom to its lower level (in some way).

Please note, that in principle we are able to distinguish a photon from the laser S₂ from a photon from our atomic source S₁. The reason here is that the detecting atom gets some recoil at absorption of a photon. Though confined by uncertainty relation, we are able to determine, whether momentum recoil is horizontal or vertical. The former case means the photon is from atom S₁, while the latter means that the photon is from laser S₂.

So, in such a way the detector starts counting photons from the laser, which begins simultaneously to the photon departure from the source atom. This counting stops as soon as the detecting atom gets a photon from the source atom. The "flight" time for that photon is the number of photons received from the laser up to now.

In [1] we argue that proposed technique is not tightly connected to detecting atom D₁. The counter of quanta from laser can in principle be placed in arbitrary place.

(a) One can easily see that the proposed experimental scheme causes many questions. Say, we assumed that each emitted photon will be ultimately absorbed. Still in quantum theory we have only probability amplitudes for such absorptions. In other words, the proposed device will measure time only in average.

Other unclear points are, most probably, momentum detecting (recoil direction) and forced relaxation of the detecting atom D₁ to the lower level. We do not describe these operations in detail, while it can be very tricky to accomplish them in such a way not to prevent correct photons counting, i.e. not to spoil the overall idea.

We deliberately omit such details, though some of them can occur to be crucial. Our task was only to reason and speculate which elementary processes can in principle serve for time detecting at microscopic level. This is why we use the term “fundamental time detecting procedure”. It is fundamental indeed since it simply shows, how the time is detected in principle, and, of course, it is idealized procedure.

(b) If one accepts that mentioned unclear details are not crucial or can be in principle solved, then some important conclusions can be made.

1^st, if we admit that normalized (in some way) number of elementary events is fundamentally the only way to detect time, then we must admit, that physical time itself is discrete. And here we get at once that the space is discrete as well, since the very fabric of space-time physically consists of elementary events (like photon absorptions).

It’s important that such discreteness arises at rather large scales, much greater than Planck’s length and time scales, as it is usually discussed.

2^nd, we can derive that the physical time can occur not to be a property of microscopic domain at all. This may sound much unexpected after previous arguments. The reasons are also discussed above. In practice detecting atom D₁ can measure the time only in average. But even if forget of this, the procedure involves laser S₂. Laser is not only a macroscopic object; it is a very special object, which generates highly stable and coherent oscillations of electromagnetic field.

We should note that the idea to use stable laser line as a fundamental way to measure physical time belongs to L. Brillouin [4]. Still L. Brillouin did not sharply point which is the time unit in such a device. Perhaps he implicitly assumed that the oscillations period is a natural time unit. But this implies that some classical oscillator (a dipole) accepts the radiation.

But light absorption is essentially quantized. This is why we argue that it’s better to speak of time quantum rather than time unit.

(ñ) Finally we want to show that though we omit some details, suggested procedure seems to fit basic physical principles. We argue that this procedure is fully consistent with relativistic concepts, i.e., it is Lorenz – covariant.

Figure 2 represents physical reasons for Lorenz transformation of time. Since we suppose that all light quanta from the laser S₂. are absorbed we count the number of emitted quanta. For simplicity we assume that this number is proportional to full light passes inside the laser resonator.

When the clock (all the installation at Fig. 1) rests, the light moves vertically (Fig. 2, (a)), and the oscillation period is

. When the clock moves horizontally with velocity v, the light moves both vertically and horizontally (Fig. 2, (b)). Since the light speed c stays constant in any referential frames, it occurs to be

Comparing two last equations, one easily derives that

. One can see, that oscillating period of moving clock (as seen by resting viewer) enlarges. This means that photons leave the laser more rarely. Thus the moving clock (atom D₁, who catches quanta from laser) shows Lorenz-enlarged time, as it should be expected according to special relativity.