In a quantum well diode (QWD) biased with a forward voltage and illuminated with a shorter-wavelength light beam, an interesting phenomenon that the QWD emits and detects light simultaneously occurs, allowing the diode to function as the transmitter and the receiver at the same time. Therefore, only one single QWD can simultaneously unit light emission and detection (Movie 1), wherein both the injection electrons and the liberated electrons are gathered together inside the QWD, and translated into dynamic electronic signals for wireless optical communication. Moreover, the QWD can only detect and modulate higher-energy photon than that emitted by itself due to the irreversibility of spectral emission-detection overlap.

This intriguing physical phenomenon may help us to deeply understand various expressions of the nature. Thus, we start to get a comprehensive understanding of the relations of Energy, Mass, Space and Time from it. First, A body should obey the law of conservation of energy in one coordinate system, wherein time becomes space, and mass and energy are different manifestations of the same body. Suppose we can make one object disappear in a given space-time coordinate system, and a certain amount of energy will be liberated. The law of conservation of energy provides insight in the relations of energy, mass, space and time, wherein time and space are equivalent, and the mass of a body is a measure of its energy. We can arrive at the view that energy equals mass times a constant: 

 Energy=Mass*Constant =>E=m*Constant （1）

E is the energy and m is the mass of a body. The symbol-transformation model is very useful for deducing what will happen in this conversion. The change in the energy is the force times the distance that the force is pushed. It can be derived as:

(Change in Energy)=(Force)*(Distance force acts through)            (2)

Force is the mass of a body times the acceleration a and thus, the formula for the force can be written mathematically this way:

(Force)=(Mass*Acceleration)=>F=m*a               (3)

The velocity is the derivative of distance with respect time and acceleration is the time derivative of the velocity. In this notation we can write (3) as

(Force)=(Mass)*(Distance/(Time*Time))      (4)

Hence, we can arrive at a general description of a body in one coordinate system, which involves Energy, Mass, Space and Time. The basic formula can be written as

(Energy)=(Mass)*((Distance*Distance)/(Time*Time))  =Mass*Constant    (5)

It means that the energy of a body equals its mass times the square of the space with respect to the time in one coordinate system. The ratio of space to time represents the state of the coordinate system, indicating that the energy of the mass of a body varies with the motion of its coordinate system. The result can provide many exciting conclusions:

1, In one coordinate system, the ratio of space to time can be treated as the velocity and should be a constant. When the coordinate system works at the velocity c of light, we can arrive at the equations:

 Energy=Mass*(Velocity)²=mv²=mc²   (6)

Where, E is energy, m is mass and c is the speed of light. The equation is in line with Einstein’s memorable equation. It means that energy equals mass times the square of the velocity of light when mass is converted completely into energy in one coordinate system at the velocity c of light.

2, Time and space are equivalent, and time becomes space. Suppose radiant energy is liberated in the form of photon, we can arrive at that the energy varies inversely as the time. The energy is proportional to the frequency as:

 (Energy)=(Mass)*((Distance*Distance)/(Time*Time))  =Constant/Time=Frequency*Constant  (7)

The equation is like the statement of Planck: the energy of a photon is a constant times frequency. The fundamental physical constant is called Planck’s constant, and one may accurately determine the constant through experimental measurements.

Let’s go back to the simultaneous emission-detection phenomenon of the QWD. We will combine Einstein’s equation, Planck’s equation, irreversible process and energy diagram theory to answer why the device can only shorter-wavelength photon than that emitted by itself. Figure 1 illustrates a schematic energy diagram for a QWD, wherein the energy is plotted vertically and the horizontal lines are for each allowed values of the energy E_0, E₁, E₂, E₃. The energy E₀ in the valence band is the lowest possible condition, and several possible transitions are demonstrated. When we inject current into the diode, the electrons in one of these conduction bands absorb energy to drop to a lower state and radiate energy in the form of light. According to the law of the conservation of energy and Planck’s equation, the frequency of the emitted light is determined by the difference in the energy. For example, the frequency of the light which is liberated in a transition from energy E₃ to energy E₀ is

  ω₃₀=(E₃-E₀)/h     (8)

where the symbol h is the Planck constant, which is the proportionality constant relating a photon’s energy to its frequency. Other possible transitions would be from energy E₃ to energy E₂, energy E₂ to energy E₁ and energy E₁ to energy E₀, which would then define the spectral emission lines. Conversely, the holes absorb photons of the right frequencies to go up from the valence band to different conduction bands when we shine light on the diode. For a reversible process, we can obtain

ω₃₀=ω₀₃=(E₃-E₀)/h     (9) 

In fact, the reversible process is an idealization. According to the second law of thermodynamics, an irreversible process occurs in reality, and the total entropy of the system always increases. Therefore, the holes require higher energy (they will absorb higher-frequency photons) to climb up a potential hill to reach the conduction bands and remain in these states. One can see that this implies that

 ω'₀₃≥ω₃₀=(E₃-E₀)/h     (10)

The equation is an elegant conclusion: the irreversibility between the emission and detection spectra of the QWD occurs, and only higher-energy photons absorbed by the diode can provide enough energy. As a result, at the modulator and the receiver sides of an III-nitride monolithic photonic circuit, one should explore sophisticated techniques to realize a redshift in the responsivity spectra. Consequently, more light photons emitted from the transmitter can be modulated and detected.

Figure 1. Schematic energy diagram for a QWD, showing several possible transitions.

The symbol v is the velocity of radiation. If a body is converted completely into energy at the speed c of light, the liberated energy is mc². It means that a huge energy will be liberated when we convert a tiny amount of matter completely into energy in the form of photon radiation. Also, in an idealized reversible process, we can transcribe photons into a body if we can manipulate an enormous amount of energy at a speed of light. However, the irreversible process often happens. Therefore, in irreversible process, the required energy to convert energy completely into a body can be written as:

E=hω=mc²≤mv²=m*(s/t)²   (11)

Then we can obtain

 h⁄m≤s∙v                                         (12)

The symbols t and s are time and space that force acts through, respectively. In fact, it’s amazing since this equation happens to come out the Heisenberg uncertainty principle. The simple formula that involves the general relations of energy, mass, space and time of a body is a differential manifestation of second law of the thermodynamics. We can thus arrive at the view that the Heisenberg uncertainty principle is a differential manifestation of second law of the thermodynamics.

Simultaneous emission-detection phenomenon of the QWD is an interesting physical behavior, providing great potential for the development of advanced information systems. More importantly, the mechanism is complex behind this phenomenon. To understand it, we can get a new insight in general unification of Energy, Mass, Space and Time, which can help us to deeply understand various expressions of the nature.