Quantum mechanics and general relativity were the greatest triumphs in physics in the early 20th century. But they are hardly compatible with each other. This difficulty is related to renormalization. Let's discuss what renormalizability is by comparing photons and gravitons. The conclusion is that photons will lead to a renormalizable theory (i.e. a good theory), while gravitons will lead to a theory that cannot be renormalized - which is not a theory at all. Photons respond to charges but are not themselves charged. For example, an electron in a hydrogen atom is charged, and when an electron jumps from one energy level to another, it emits a photon. This is called photon response to charge. Saying that photons themselves are uncharged is the same as saying that light cannot conduct electricity. If it could, we would get electric shocks if we touched something that had been in the sun for a long time. Photons also cannot respond to each other because they only respond to charges.
Gravitons do not respond to charge, but they do respond to mass and energy. Because gravitons also carry energy, they respond to themselves. They can self-gravitate. It doesn't look like this will be a problem, but here's where our trouble comes from.
Quantum mechanics tells us that gravitons are both particles and waves. According to the hypothesis, the particle is a point-like object. The closer we are to a point-like graviton, the stronger the gravitational pull it excites. The gravitational field of a graviton can be understood as the other gravitons it emits. To label all these gravitons, we call the original one the mother graviton. The gravitons emitted by the mother's graviton are the daughter's gravitons. The gravitational field not far from the mother's graviton is very strong. This shows that its daughter graviton has very strong energy and momentum. This can also be seen from the uncertainty principle: the daughter graviton is observed from △x very close to the mother graviton, which means that the uncertainty △p of their momentum is very large, satisfying the relationship △x×△p ≥h/4Π. The problem is that gravitons also respond to momentum. The daughter graviton will also emit gravitons herself. This is how the whole process starts: you can't keep track of the effects of all these gravitons.
On the left in the picture, an electron (e-) can produce virtual particles: photons (y), positrons (e) and more electrons. The cascades of particles multiply slowly enough that we can compute them using renormalization methods. Right: One graviton (h) creates so many virtual gravitons that we can’t compute them using renormalization.
? Something similar actually happens to electrons. If you get very close to an electron and measure its electric field, the electron will be excited and emit photons with high momentum. This may seem like nothing, since we know that photons cannot continue to emit photons. The trouble is, they can break apart, splitting into electrons and positrons, which can then emit more photons. What's amazing is that with electrons and photons, you can actually track all of these particles cascading off each other. We consider the electron and all its descendants as a whole and call it a "dressed" electron. The electron's descendants are called virtual particles in physicists' lingo. Renormalization is a mathematical method for calculating all virtual particles. The spirit of renormalization is that the electron itself may have infinite charge and infinite mass, but once the electron puts on the clothes, it will have finite charge and finite mass.
The trouble with gravitons is that you can't renormalize the cloud of virtual gravitons surrounding them. The theory of general relativity gravity cannot be renormalized. This sounds like an obscure technical question. It is also possible that we have got the question wrong, but this is only a slight possibility. It is slightly more likely that there is a theory called maximum supergravity similar to general relativity that can be renormalized. Bringing quantum mechanics and gravity together encounters a fundamental difficulty.
In string theory, it is assumed that particles are not like points, but rather different modes of vibration of strings. The string is very small, but it has a definite length. This length is very small, only about 10 meters according to common wisdom in string theory. Now, the strings respond to each other like gravitons. You might be worried about a whole set of troubles caused by a cloud of virtual particles, but actually, we have virtual strings, which can get out of hand just like gravitons. This problem does not arise because strings are not points. All the difficulties with gravity arise from electric particles, which we assume are infinitesimally small, like "point particles" as their name suggests. Replacing gravitons with vibrating strings solves the problem of how they interact.
We can explain it this way, when a graviton splits into two, you can determine the moment and location when the split occurs. But when a string splits, it's like a fork in a pipe. At the bifurcation point, the tube wall did not break the smooth Y shape, it fit perfectly, but the shape was a little special. All of this means that the splitting of a string is a gentler event than the splitting of a particle. Physicists say that interactions between strings are inherently "soft" while interactions between particles are inherently "hard." It is this softness that makes string theory more docile than general relativity and easier to handle with quantum mechanics.