KAHIBARO
Table of Contents
Gravity and the Standard Model
The Standard Model is a very successful theory of three of the four known fundamental interactions. It describes electromagnetism, the weak interaction, and the strong interaction. It also describes the known elementary particles that take part in those interactions. But gravity is not included in the Standard Model. This is one of its most important limitations.
Why gravity stands apart
Gravity is familiar because it governs falling objects, planetary motion, stars, and the large scale structure of the universe. Yet at the level of elementary particle physics, gravity is extraordinarily weak compared with the other interactions.
For example, two electrons repel each other electrically far more strongly than they attract each other gravitationally. This means that in most particle physics experiments, gravity is so tiny that it can be ignored.
A simple comparison helps:
| Interaction between two electrons | Depends on | Relative size |
|---|---|---|
| Electric force | electric charge | very large |
| Gravitational force | mass | extremely small |
Using the classical formulas,
$$
F_{\text{electric}} = k \frac{e^2}{r^2}
$$
and
$$
F_{\text{gravity}} = G \frac{m_e^2}{r^2}
$$
the ratio is enormous:
$$
\frac{F_{\text{electric}}}{F_{\text{gravity}}} \sim 10^{42}
$$
So gravity is negligible in ordinary particle collisions, but dominant for planets, stars, and galaxies because large masses add together and gravity is always attractive.
Gravity is not part of the Standard Model. The Standard Model includes only the electromagnetic, weak, and strong interactions.
How gravity is described today
In modern physics, gravity is described by Einstein's general theory of relativity, not by the Standard Model. General relativity says that gravity is not an ordinary force in the same sense as the other interactions. Instead, mass and energy curve spacetime, and objects move in that curved spacetime.
This idea is very different from the Standard Model picture, where interactions are described through quantum fields and exchange particles.
In general relativity, the central relation is Einstein's field equation,
$$
G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}
$$
Very roughly, this says that matter and energy, represented by $T_{\mu\nu}$, determine the curvature of spacetime, represented by $G_{\mu\nu}$.
For beginners, the key point is simple. The Standard Model is a quantum field theory of particles and forces, while gravity is currently described by a classical geometric theory of spacetime.
Why this is a problem
Physics aims for a unified description of nature. Since gravity is one of the four fundamental interactions, leaving it out means the Standard Model cannot be the final theory.
The trouble becomes especially serious in situations where both quantum effects and strong gravity matter at the same time. Examples include the center of black holes and the very early universe shortly after the Big Bang. In such situations, we would need a theory of quantum gravity, a theory that combines quantum mechanics with gravity consistently.
A major limitation of the Standard Model is that it does not provide a quantum theory of gravity.
The graviton idea
By analogy with the photon for electromagnetism, physicists often speak of a hypothetical quantum particle of gravity called the graviton. In a quantum field picture, the graviton would be the carrier of the gravitational interaction.
The expected properties of a graviton are usually taken to be these:
| Property | Expected value |
|---|---|
| Electric charge | 0 |
| Mass | 0 |
| Spin | 2 |
A massless particle would allow gravity to act over long distances, just as the massless photon allows electromagnetism to have infinite range. Spin 2 is linked to the special tensor nature of gravity in relativity.
However, the graviton has not been detected experimentally, and more importantly, a simple quantum field theory of gravitons does not work as neatly as the Standard Model theories do.
Why quantizing gravity is hard
The Standard Model is built using quantum field theory, and its calculations can be handled in a mathematically controlled way. Gravity resists this treatment.
If one tries to quantize gravity in the same straightforward way used for other forces, the calculations produce severe infinities that cannot be removed in the usual renormalization procedure. This means the theory loses predictive power at very high energies.
A useful energy scale here is the Planck scale, built from fundamental constants:
$$
E_{\text{Planck}} = \sqrt{\frac{\hbar c^5}{G}}
$$
Numerically, this is about
$$
E_{\text{Planck}} \sim 10^{19}\ \text{GeV}
$$
This energy is vastly beyond what current particle accelerators can reach. It suggests that quantum gravitational effects become especially important only at extremely high energies or extremely tiny distances.
At ordinary particle physics energies, gravity is usually negligible. At the Planck scale, gravity is expected to become as important as quantum effects, and the Standard Model is no longer enough.
Gravity compared with Standard Model interactions
It is helpful to see the contrast directly.
| Feature | Standard Model interactions | Gravity |
|---|---|---|
| Included in the Standard Model | Yes | No |
| Present theory | Quantum field theory | General relativity |
| Range | strong is short, weak is short, electromagnetic is long | long |
| Source | charges such as electric charge and color charge | mass and energy |
| Mediator | gauge bosons | hypothetical graviton |
| Quantum description confirmed | yes | no complete confirmed theory |
This table shows why gravity is special. It is fundamental, but it does not fit naturally into the same theoretical framework.
Where the conflict appears most clearly
The conflict between gravity and the Standard Model is not obvious in everyday laboratory particle physics. It becomes important in extreme situations.
Near a black hole singularity, matter is compressed so strongly that both quantum physics and gravity should matter together. In the early universe, temperatures and energies were so high that spacetime itself may have required a quantum description. The Standard Model alone cannot fully describe such conditions.
This means that although the Standard Model is excellent for many experiments, it is incomplete as a description of all of nature.
Directions beyond the Standard Model
Because gravity is missing, physicists search for deeper theories. Several approaches have been explored, including string theory and loop quantum gravity. These are attempts to build a consistent quantum theory that includes gravity. At present, none has been experimentally confirmed as the final answer.
The important lesson is not the details of these proposals, but the reason they are needed. A complete fundamental theory must explain gravity together with the other interactions.
A simple picture
A visual contrast can help. In the Standard Model view, particles interact by exchanging force carriers. In gravity, mass and energy curve spacetime.
Final perspective
The absence of gravity from the Standard Model is not a small technical gap. It tells us that the Standard Model is incomplete at the deepest level. It is a powerful theory of elementary particles and three interactions, but not a full theory of nature.
The Standard Model succeeds brilliantly in its own domain, but a complete fundamental theory must also include gravity.