The Physical Basis of Bodily Damage

2.1. Introduction to Electromagnetic Radiation and Photons

There are three ways that electromagnetic radiation can cause harm within to living bodies. Each effect is particular to a certain range of frequencies₁. Our main exposure to dangerous electromagnetic radiation is from direct sunlight.

Effect	Range	Effects	Disclaimer
Induced voltage gradients and/or electric currents	Low frequencies (0-3 KHz)	Magnetic fields might do weird things to our bodies.	Normal human technologies do not produce frequencies in this range, and, the Earth itself has a magnetic field.
Thermal effects Absorption causes heating	30 MHz - 300 GHz Microwaves	Absorption of energy causes heating, which if enough happens at once, can damage tissue.	Energy has to specifically and intentionally focused to have an effect.
Ionizing effects Molecules are damaged	Ultraviolet light, X-rays, gamma rays	Carcinogenic due to occasionaldna damage.	We are exposed to these from space and from the sun, but not from human technology.

“Extensive scientific testing has been used to measure these effects and to establish safe limits. [...] In the U.S., FCC regulations set limits on permitted exposure for the public at 1/50 the level at which harmful heating effects may occur. Actual exposures are hundreds to thousands of times lower. The photon energy of a cellphone EMF is more than 10 million times weaker than the lowest energy ionizing radiation.”

Lorne Trottier article "EMF and Health: A Growing Hysteria" in Skeptical Inquirer (2009)₁

In order to understand more deeply the fact that damage from these types of radiation is not due to chance but due to near impossibility, more needs to be explained about the nature of radiation and photons. I would rather quote from a suitable expert rather than attempt to explain the physics myself, so, firstly, understand that all forms of electromagnetic radiation is made from photons, which are the fundamental waves/particles that make up all energy:

“All electromagnetic radiation consists of small particles called photons. The energy of a photon is determined by a formula called Planck's law: the energy of the photon increases as the frequency increases. Now consider a photon of yellow light. This has a frequency of some 5x10¹⁴ Hz. The energy of such a photon is approximately 2 electron volts [...]. If there is an increase in the power, only the number of photos increase, not its energy. Thus, a standard yellow sodium lamp with higher power rating provides more light with more photons, but each photon still has exactly the same amount of energy.
A typical cell phone uses a frequency of 1x10⁹ Hz. The frequency used in a household microwave oven is 2.45x10¹². Therefore, the energy of photons in these sources will be lower than that of yellow light by a factor of a thousand for the microwave oven and a million for the cell phone. The frequency of a standard 60 Hz power line will be further lower by a factor of one million. Roughly one million photons in a power line together have the same energy as a single photon in a microwave oven, and a thousand microwave photons have the energy equal to one photon of visible light. [...]
”

Dr Lakshmikumar in Skeptical Inquirer (2009)₂

These photons, which en masse make up electromagnetic radiation, are absorbed by the atoms that make up all biological matter. The frequency of the radiation determines what method of interaction is important.

2.2. Ionizing Radiation: Gamma Radiation, X-rays and Ultraviolet Light

If the frequency of electromagnetic radiation is high enough, photons will have enough energy to ionize atoms, i.e., to interact with electrons or protons and therefore interfere with molecular structure. This becomes possible at a frequency just above that of visible light - ultraviolet light, and includes gamma radiation and x-rays. None of them are produced routinely by human technological gadgets.

• Gamma rays are found in space, and as the result of radioactive decay and nuclear reactors and atom bombs.
• X-rays, like radio waves, pass through most material without any interaction at all, and are unlikely to cause any cellular damage. This is why they are safe to use on patients in hospitals. There is the chance, however, that rare interactions could damage cells or DNA (something that radio waves cannot do), which is why medics (and dentists) who use X-ray equipment frequently have a screen they stand behind to reduce constant exposure.
• What we are exposed to all the time is ultraviolet light. The sun produces this and the Earth's surface is bathed in it. It has a slightly higher frequency (and therefore higher energy per photon) than light, and is absorbed by most substances, including skin. It is one of the most common causes of cancer and skin problems.

2.3. How Radiation Causes Cancer

The way that ionizing photons cause cancer is as follows. DNA is the famous double-helix chemical strand that controls how our cells manufacture proteins. It is a delicate process. DNA is held together by chemical bonds, the same as all other molecules are. High energy photons can knock electrons out of their orbits, or sometimes interact with the nucleus of an atom. To do this, the frequency of the radiation has to be high enough. It can then damage the DNA. If the frequency isn't high enough (mobile phones and radio waves are not), then, the radiation cannot cause ionization no matter how much of the radiation there is. Even when it is absorbed it is rarely cancerous. Most the time, because of the double-helix structure and various cellular mechanisms of DNA monitoring, the damage is repaired. It is very unlikely that photons happen to hit DNA in a cell (a cell is very large compared to the size of the DNA in the nucleus). It is also rare that when a photon hits DNA that it causes any lasting damage. And if a cell goes wrong, it is also rare that this causes the cell to turn into a cancer as most genetically damaged cells are either destroyed or self-destruct (apoptosis).
Because of the negating factors, it requires continued exposure to high doses of appropriate radiation in order for cancers to be caused. The sun, being a massive nuclear reactor (333 thousand times more massive than the Earth), is one such source. Compared to everyday exposure to ultraviolet light from the sun, no everyday human technology poses a comparable risk, and in addition, the frequencies used by telecommunications equipment is simply not high enough to be ionizing, no matter what strength of signal you are exposed to.

2.4. Heating Effects: Microwaves

Ionizing radiation can be dangerous due to the occasional chance of molecular damage to cells. Some other (lower) frequencies of the electromagnetic spectrum are dangerous not because they knock electrons out of orbit, but, because they are absorbed by liquids and cause heating. In a microwave oven, it is generally water that absorbs the emitted photons. The temperature required to do damage to us is generally rather high because in our bodies, liquids are generally full of long and heavy biological molecules that raise the heat capacity of the liquids.