Light does bend under Newtonian gravity, but it bends in a different way that Einstein predicted. Since light is massless, that means Newtons gravity shouldnt cause light to bend, right? Actually, light does bend under Newtonian gravity, but it bends in a different way that Einstein predicted. Guess which model matches reality. The testing the assumption that photons are massless raised a few questions . We know that if photons have mass it would have to be very small. There are theoretical models that allow for photon mass. For very small masses these models look very similar to the ones we use (such as Maxwell’s equations and the constant speed of light), but at larger masses they predict effects we would have seen by now. One of these effects would be seen in the cosmic microwave background. As outlined in a recent paper in Physical Review Letters, journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.021801 the cosmic background wouldn’t match a blackbody curve if the photon had mass. The cosmic background matches a blackbody so perfectly that the photon mass can be no larger than a hundredth the mass of an electron. That’s pretty tiny, but other optical experiments require that the photon have a mass no larger than a trillionth of a trillionth of the mass of an electron. That’s a septillionth of an electron mass. So if the cosmic background puts less of a limit on photon mass than other experiments, what’s the big deal? If the photon has mass, even a septillionth of an electron mass, it is possible that the lightest neutrino has an even smaller mass. We know that neutrinos have mass. briankoberlein/2014/07/07/little-neutral-one/ There are actually three types of neutrinos, and we know the sum of their masses can be no larger than 2 millionths of an electron mass. But we don’t know what their masses actually are. If the lightest neutrino has a mass even smaller than the photon, then it would be possible for photons to decay into neutrinos. That would mean photons wouldn’t last forever. Instead they would have a half life. Based on observation of the cosmic microwave background, the half-life of a photon must be at least three years. That doesn’t seem like a long time, but light travels so fast that time dilation would make them last much longer. In the visible spectrum their effective half-life would be about a quintillion years, or about a billion times longer than the age of the universe. One of the most common was the idea that the gravitational lensing of light must mean that photons have mass. After all, if a star or galaxy can deflect light gravitationally, doesn’t that mean the light is gravitationally attracted to it? If that is the case, doesn’t that mean that light has mass? There are actually several different types of mass. The type that best corresponds to our intuitive understanding is known as inertial mass. Inertial mass is determined by its resistance to acceleration. If you push on objects with a force, an object with less inertial mass will accelerate more than one with more inertial mass. Another type of mass is known as gravitational mass. Gravitational mass is what (in Newton’s gravity) causes the gravitational attraction between objects. When you step on a scale in the morning, you are measuring your gravitational mass. While technically gravitational mass and inertial mass are not the same thing, we generally treat them as the same thing because of the “principle of equivalence”. Experiments have shown that masses all fall at the same rate in a gravitational field, so that means the gravitational and inertial masses must have the same value. This equality between gravitational and inertial mass is called the principle of equivalence. While this was known since at least Galileo’s time, it was Einstein who made the idea central to our understanding of gravity. The third type of mass is known as relativistic mass. This stems from Einstein’s theory of special relativity and the equivalence of mass and energy (the famous E equals m c squared). In that famous equation, E is the energy of a particle, and c is the speed of light. So if you divide the energy of a particle by the speed of light squared, you get a “mass”, known as the relativistic mass of the particle. Now if an object is at rest (relative to you) then the relativistic mass has the same value as the inertial mass. This is sometimes called the “rest mass” of an object. But in general, relativistic mass is not the same thing as inertial or gravitational mass. Unfortunately this point isn’t often made clear, so it leads to a great deal of confusion. When someone says “the mass of an object increases as it approaches the speed of light”, that’s really the relativistic mass. A fast moving object has not only energy due to its rest/inertial mass, but also a kinetic energy due to its motion. The relativistic mass due to its total energy is what increases. Its inertial (and gravitational) mass is unchanged. This is the key difference. Relativistic mass is an apparent mass that depends on how the object is moving relative to you. Inertial and gravitational mass are inherent properties of an object, and don’t depend on your point of view. So what does this have to do with whether photons have mass? Photons have energy, so we can define the relativistic mass of a photon by taking its energy and dividing by the speed of light squared. The energy of a photon depends upon its wavelength. Long wavelength (reddish light) photons have less energy than short wavelength (bluish light) photons. This means photons have different relativistic masses. Photons don’t have “rest mass” or inertial mass. Despite popular news articles about “stopping light”, you can’t hold a photon in place. The “light stopping” experiments are effects of light waves, which is a whole other rabbit hole. You also can’t accelerate light with a force. The speed of a photon is constant, so again, no inertial mass. By the equivalence principle, that also means they have no gravitational mass. At least that is the accepted answer. Maybe for photons, their relativistic mass is their inertial/gravitational mass. How do we know it’s not? Actually, we have an experiment that proves it, and Arthur Eddington first did it in 1919. In 1919 Eddington photographed the positions of stars near the Sun during a total eclipse. He compared those positions to their positions when the Sun wasn’t there, and found that they had appeared to shift away from the sun. This is because the Sun gravitationally deflected the starlight slightly. This bending of light made the stars appear to be in a different direction. Einstein predicted this light bending due to the curvature of space in his theory of general relativity. Thus, Eddington proved that Einstein’s theory was correct. When this story is presented, it’s often said that since photons have no mass Newton’s model predicts light shouldn’t bend. Einstein’s theory predicts light bending, so this proved Einstein right. But actually that isn’t entirely the case. If the relativistic mass of a photon is equated to its inertial and gravitational mass, then Newton’s gravity does predict light bending. The catch is that the amount of bending predicted by Newton’s model is half what Einstein’s model predicted. Eddington actually demonstrated not only that light was gravitationally deflected, but that the amount matched Einstein, and not Newton. So the gravitational lensing we see from stars and galaxies actually demonstrates that photons aren’t being gravitationally attracted in the Newtonian sense. Instead, space is warped by mass of stars and galaxies, and the path of light is warped accordingly. Light really is massless. You can’t bend it like Newton, but you can bend it like Einstein. From lectures Brian Koberleyn Image 1: Albert Einstein with Sir Arthur Eddington Image 2: Einsteins paper introducing General Relativity Lana Duzes photo. Lana Duzes photo.
Posted on: Tue, 05 Aug 2014 03:58:59 +0000
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