From: Chris (Avatar) 10/02/99 14:19:11 Subject: Light, mass, momentum, gravity post id: 743 Light, mass, gravity and momentum Ok, its probably time that someone sorted this one out. 1) The photon has no mass. The argument goes "light has energy and momentum, it responds to gravity, therefore it has mass". Not true. Light does have energy and momentum (see below) but these don't imply mass. In fact what they lead to is relativistic mass (see post on Understanding Mass in Relativity). How do we know the photon is a zero rest mass particle? Well, lets look at some of the consequences if it is not. First and foremost quantum electrodynamics is in trouble - the field theory loses a quality called gauge invariance and becomes non renormalisable if the photon is massive. These two properties are essential to the QED field theory, which is perhaps the most statistically accurate theory yet devised. Secondly the property of charge localisation and conservation is not guaranteed if the photon has non-zero rest mass. Perhaps the best and most testable prediction is that there would be a change in the Coulomb inverse square law for electrostatic fields - a small damping would make it fall off quicker. The behaviour of static magnetic fields is likewise modified. A limit on the photon mass can be obtained through satellite measurements of the Earth's magnetic field. The Charge Composition Explorer spacecraft was used to derive a limit of 6x10^-16 eV with high certainty. Which goes to limit the photon's mass to vanishingly small (at least). 2) Momentum is not an indicator of mass. That light can exert a momentum or pressure on striking a surface was known before the introduction of the photon. Don't let the particle description of the photon fool you into falling back on p = mv as the only definition of momentum. Momentum is related to energy and energy to mass by Einstein's mass energy relation: E^2 = m^2c^4 + p^2c^2 where in this case the mass can be unambiguously defined as a real mass or rest mass, reducing the relationship to E = p c for the massless photon. Using E = mc^2 to base an energy - mass equivalence upon is ambiguous, the mass here is relativistic mass. The correction then would be: E = m c^2 / sqrt( 1 - v^2/c^2) which uses a Lorentz transform (the bit under e=mc^2) to correct a frame variant mass-energy. (you can see how this may be used to derive the full form of Einstein's mass-energy relationship). It follows that there can't be a local mass energy equivalence for the photon. 3) Light and gravity. It has been observed that the gravitational fields of very massive objects (star sized) "bends" light rays which pass by it. The phenomenon, known as gravitational lensing has been recorded and verified. But what is going on here? Does this mean the light has mass to be attracted to gravity? According to general relativity gravity is manifest as disturbances or warping of the topology (or geometry) of space-time. Bodies which can gravitate warp the space-time in their vicinity which changes the path of nearby objects through space-time. Definitions: the path of an object through space-time is called a worldline, the worldline of a photon is called a geodesic. Ok, now here's the crunch: light rays don't actually bend in response to gravitation! The geodesic looks bent in three dimensions, but is actually a straight path through 4D. An analogy may help illustrate: imagine a plane flying overhead in three dimensions. Now suppose its image is directed onto a two dimensional irregular surface - lets say the plane's shadow falls on some hilly ground. Now the plane may fly a straight path above in 3D while its 2D image appears to deviate all over the place! If you were constrained to the 2D surface you would perceive the plane's path to curve. Everything follows naturally determined paths through space-time in this way, light does as well. The other matter is the possible attraction light has for other objects - does this mean it has mass? The answer is no - and comparison with electrical fields will show how this is possible. Given first that we know energy and momentum couple to gravity, the gravitational analogue to electric charge is not mass, it is what we call the energy momentum 4 vector of a particle (bit of a mouthful, but bear with me…). This is merely the energy-momentum relationship in 4D space-time, where mass is defined invariantly. (Remember above we saw that relativistic mass or mass-energy is frame variant). It follows then that the gravitational analogue of current is the energy momentum stress tensor, which shows up in the GR field equations! Not mass. In summary, light and From: Chris (Avatar) 10/02/99 14:25:53 Subject: re: Light, mass, momentum, gravity post id: 745 In summary, light and in particular the light "particle" - the photon - is massless. This much is required by QED, and is demonstrable in measurements of long range electrostatic and magnetostatic field damping. The photon does have energy and momentum which are defined independently of invariant mass. The gravitational behaviour of light is also independent of mass. Hope this helps! Chris From: steve 10/02/99 14:38:14 Subject: re: Light, mass, momentum, gravity post id: 747 Chris, Just love that analogy of the plane's shadow - visually enlightening - and a brilliant piece of work!! So, in summary as you put it, light has no mass - except for relativistic mass, which is not the same thing as 'rest mass' as demonstrated in the several articles you pointed to in your recent posts (which were quite coherent and educative, by the way). Also (continuing the summary), light does not 'bend' around massive objects, it simply follows a straight path that appears curved due to a warping of the space-time reality we inhabit - again, lack of dimensionality on the part of the observer - ie, us on Earth. Does this seem about right? Cheers Steve From: Rowan Crawford 10/02/99 19:46:06 Subject: re: Light, mass, momentum, gravity post id: 772 The plane's shadow analogy was interesting but there's an aspect that puzzles me. In the case of the shadow, once it has passed the hill or valley the shadow returns to it's "normal" position. In other words, the shadow has an average position, but in the case of light around gravity wells the light appears to make a permanent change - once it's passed the gravity well it still continues (in appearence) in the newly changed direction. Is this just me not being able to visualize the shadow in 4D? While on the subject of photons, what does "has no mass" actually mean? Does that mean it's has no size? Isn't a physical thing? Is it one of the many sub-atomic particles or is it something else entirely (and if so, are there other things that fit into the same catagory?)? Cheers, Row. This forum is un-moderated. The views and opinions expressed are those of the individual poster and not the ABC. The ABC reserves the right to remove offensive or inappropriate messages.