Physicist Sergei Blinnikov of quantization of fields, features of gravity and the problem of registration of gravitons
Quantization - the construction of a quantum version of the classical model, in accordance with the principles of quantum physics . All fields that we know in nature, are quantized. The most evident quanta of the electromagnetic field - photons. For example, the Soviet physicist Pavel Cherenkov naked eye watching them open individual photons of Cherenkov radiation, for which he received the Nobel Prize in 1958. Today, anyone can buy and listen to the clicks Radiometer tougher photons - gamma radiation (10 pieces per minute in a normal situation in Moscow and 300-400 ppm in the plane at an altitude of 10 km).

Gravity - is one of the fields, which also must be quantized, and the quanta of this field is called gravitons. Gravity is largely similar to electromagnetism. For example, electricity is Coulomb's law, which is quite similar to open up to him to Newton's law. But electricity two identical charges repel, and gravity all the "gravitational charges", ie the mass, always attract. Conversely, two parallel current drawn Ampere force, and gravity, in the general theory of relativity, two parallel current repelled.

In general it can be said that gravity is "richer": to describe electromagnetism need four numbers (vector potential), and for more than gravity - is a force tensor. However, you can select a part of it is similar - for example, "gravimagnetic" or "gravitomagnitnuyu." It can be seen in the weak gravitational field of a complete analog of Maxwell's equations in electromagnetism, and quantize. It did back in the 1930s - to quantize both. Some quanta called photons, gravitons other.
However, there is a big "but." Gravity in a weak field is clear and well understood, and in a strong field, which can be black holes and similar objects, it can not be successful quantization. Electric and magnetic fields can be very powerful, but they are not directly affected by the passage of time and, therefore, easily be quantized. Only gravity, they created - for example, electromagnetic waves, that is, photons - affected. A gravity and gravitational waves (strong) should directly influence the curvature of space, and the passage of time that each owner or GLONASS GPS devices used every day in practice, without even knowing about it.

The main difficulty in quantum gravity - that its impact on the future.

Another difficulty - ultraweak gravity. We feel the gravity of the Earth, simply because it a lot of us, and the gravity of a passing truck we do not feel. Electromagnetic waves discovered a long time ago, and gravitational waves due to the weakness of the gravitational interaction is still no. Only indirectly, in the binary pulsar, we see their effect.
There is another remarkable feature of quantization. If the light is weak as Cherenkov, the individual photons seen. And if he is a heavy duty, let the same wavelength of visible light, and coherent, the concept of the photon loses meaning. In a laser light with a very well-defined phase φ, that is, the uncertainty phase Δφ is very small. In quantum electrodynamics, there is a surprising uncertainty relation if N = number of photons, the ΔN is multiplied by Δφ should be the order of unity:
ΔN • Δφ ~ 1
The more accurate the phase lasts, the greater the uncertainty of the number of photons. But if we can not say, in principle, how many pieces of the photons in the wave train, which means that the physical meaning of the concept of the photon disappears, and adequate to describe these waves becomes continuous field of classical language. This is what happens when large N all bosons, which include photons and gravitons.
Unfortunately, because even with the huge N is we have not yet been discovered gravitational waves, we hope to open individual gravitons (N ~ 1) becomes vanishingly small.

The formula of the form ΔN • Δφ ~ 1 lead back in the old textbooks - Heitler W. The Quantum Theory of Radiation. Courier Corporation, 1954 (in Russian translation - W. Heitler quantum theory of radiation, 1956) - with reference to the first work on the Dirac quantization of the electromagnetic field (Dirac PAM Proceedings of the Royal Society. London. (A) 114 (1927), 243 ).

However, after the invention of lasers and masers, which have been producing powerful beams of coherent light, it became clear that such a relationship is not quite correct, because you can not correctly identify the operator of a quantum phase φ.

The correct presentation of the issue can be found in the book of Akhiezer AI, Berestetskiy VB Quantum electrodynamics. M .: Nauka, 1981.
In Section 2.4, "Correlation functions of the electromagnetic field" they lead the operator cosine sine C, and S phase and show that the operators corresponding to the number of photons, and operators of the cosine and sine phase does not commute with each other, so the uncertainty in these quantities are related by:
ΔN • ΔC ~ ΔS, ΔN • ΔS ~ ΔC

This means that the electromagnetic wave can be characterized by a certain number of photons at the same time and a certain phase. Akhiezer and Berestetskiy here refer to two important articles:
R. Glauber Optical coherence and statistics of photons. M .: Mir, 1966

Carruthers, P., Nieto M. Phase and Angle Variables in Quantum Mechanics. Reviews of Modern Physics. Vol. 40 (1968) 411-440.
Especially useful is the last article, where all described in exhaustive detail.