how can light have momentum with no mass?
Answers
Explanation:
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.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.
this is your answer
Light can have momentum because momentum is not due to rest mass, except in the low velocity, nonrelativistic approximation.
When you write down the Lagrangian of Maxwell’s theory and calculate the canonical momentum, you get a value, even though the electromagnetic field has no rest mass and influences in the field, far from sources, travel at the invariant speed of the theory, c=1/ϵ0μ0−−−−√c=1/ϵ0μ0. (It is the existence of this invariant speed on Maxwell’s theory that conflicted with the Galilean view of the world, and inspired the development of relativity theory.)
In short, you end up with the energy and momentum of light related by E=pcE=pc. That is, the two are proportional to one another. This is, of course, a special case of the dispersion relation E2=(pc)2+(mc2)2E2=(pc)2+(mc2)2, which yields the famous E=mc2E=mc2 for massive particles at rest (p=0p=0). But for light, it’s m=0m=0, so we end up with E=pcE=pc.
And still more generally, light may not have rest mass but it has a nonzero stress-energy-momentum tensor. As such, when you write down Einstein’s field equations for gravity, even in the case of pure light, there is something on the right-hand side of the equation that produces, and responds to, gravity.
But even without that heavy-duty machinery, simply stating that light in a vacuum always travels at the speed of light, that is to say, for light, c2dt2−dr2=0c2dt2−dr2=0 always, already tells us that light travels on the so-called null geodesics of spacetime, so when gravity bends spacetime and the null geodesics become curved, light will follow a corresponding curved trajectory.
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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.