# Why doesn't light carry momentum?

Category: Physics
Published: June 11, 2013

By: Christopher S. Baird, author of The Top 50 Science Questions with Surprising Answers and physics professor at West Texas A&M University

Light does carry momentum. Momentum can be thought of as an object's ability to push another object due to its motion. Classically, momentum is defined as the mass of the object times the velocity of the object, p = mv. Since light has no mass, you may be tempted to say that light has no momentum. Additionally, everyday experiences may seem to confirm that light has no momentum (sunlight does not knock over soda bottles like baseballs do). However, light does indeed carry momentum in the form of energy. In fact, for photons (the smallest bits of light), the energy E and momentum p are related by the simple equation E = pc, where c is the speed of light. The momentum that light carries is so small that we don't notice it in everyday life. We do not get knocked over when we turn on light bulbs, and the light from candles does not make the curtains sway. But the momentum of light is large enough to be measurable, and can in fact be used in certain applications. For instance, laser cooling machines shoot a sample from all directions with laser light in order to use the laser light's momentum to slow down the atoms in the sample, thereby cooling it. In optical traps, also called optical tweezers, the momentum of the light is used to trap and manipulate small objects. Solar sails on space probes catch sunlight and use its momentum to propel the probe forward.

Light carries momentum and can therefore push objects. This concept is crucial to the operation of solar sails, such as shown in this artistic rendering. Public Domain Image, source: NASA.

Interestingly, light always travels at the same speed in vacuum, and can't go any slower in vacuum. Unlike a baseball, light loses momentum by lowering its frequency rather than by lowering its speed. The fact that light carries momentum has profound effects on particle interactions because of the law of conservation of momentum. For instance, if an electron and a positron fly at each other from opposite directions with equal speeds, their total momentum is zero. After the particles annihilate each other and convert their mass totally to energy, they must turn into something that has zero total momentum. A single photon would not do, as it carries momentum. But two photons traveling in opposite directions would add up to zero total momentum (because they are traveling in opposite directions). For this reason, electron-positron annihilation events always create two photons traveling in opposite directions, and not just one. This fact is used in medical positron emission tomography (PET) scans to image human tissue. The patient is given a radioactive drink. When the radioactive chemicals decay in the body, they emit positrons. Each positron annihilates an electron in the patient's body, creating two photons traveling in opposite directions. The machine detects these two photons, and can use their direction and timing to pinpoint where they were created and where the drink is therefore congregating.