• Question: What does it mean to say that something is massless? Would these massless particles be affected by any gravitational force since it doesn't have any mass? What about its total energy E=mc^2 as m=0, E=0. Is that the case?

    Asked by rajathjackson to Chris, Dave, David, Fiona, Jack on 25 Jun 2013.
    • Photo: Jack Miller

      Jack Miller answered on 25 Jun 2013:

      Hi Rajath,

      A massless object has no mass!

      At the moment, to the limits of our understanding, the only thing that is definitely massless is light. Neutrinos are _almost_ exactly massless, and gravitons (if they exist) are certainly massless as well. I’m only really going to talk about light, as it’s the only thing I know that definitely is massless.

      You’re right in thinking that E=mc^2 doesn’t give the whole story for light. In fact, that equation’s a simplification of the more generally correct E^2=p^2 c^2 + m^2 c^4, which simplifies down to the much more familiar momentum-energy expression for light, E=pc. The best way I found to think of massless particles (or very light particles moving very quickly) is like this: the amount of mass you have basically states a minimum energy you can have, in your own reference frame. You can have lots more energy than that (by moving quickly), but, in your own reference frame, no less.

      Massless particles can therefore have whatever energy they like.

      One of the key realisations Einstein came to in general relativity was that light is affected by gravity, as gravity changes the shape of space, and light travels through space. By changing the shape of space with objects such as black holes, you change the path light takes. The reason this happens is that, it turns out, light always takes the path of least time (for an object moving at the speed of light) and that’s only a straight line under certain geometries. There’s a good video about black holes and the distortions they cause here: http://www.youtube.com/watch?v=3pAnRKD4raY.

      Hope that helps!

      — Jack

    • Photo: David Freeborn

      David Freeborn answered on 25 Jun 2013:

      Ok, this is a good question.

      E=mc^2 is actually only true in a particle’s own rest frame- i.e. from the perspective of the stationary particle. As Jack says, the more general equation is E^2=m^2c^4 +p^2c^2 , where p is the momentum and m is what we call the rest mass- which should be the same in every relativistic frame of reference.

      There are some cool outcomes of this equation. If you have two particles “orbiting” each other, then they have a particular momentum. Then if you move to a frame of reference where the compound particle, composed of the two particles orbiting each other, is itself stationary, you will see it has a much higher mass than the sum of the two particles. This “mass” comes from the orbital kinetic energy of the two particles. This is how most of the mass of the Universe is generated. For example, protons have a much, much higher mass than their constituent quarks, due to the orbital energy of these quarks.

      OK, so what does it mean to be massless? As Jack points out, gravity in general relativity actually changes the shape of space, so it even affects massless objects.
      But mass has two properties: gravitational and inertial. We still have to explain what it means for a particle to have zero inertia.

      Inertia is the property of mass which classically appears in Newton’s F=ma. It does a similar sort of thing in Relativity and Quantum Mechanics. A lower mass says that it takes less force to accelerate the object to higher velocities.

      When we take mass right down to zero, this classical equation breaks down. In turns out that all massless objects are travelling at the speed of light, and that no objects with a mass can ever accelerate to the speed of light. To get them to reach this speed would take infinite energy.

      Why do massless objects travel at the speed of light? Here’s one way to see it, using that equation again:
      E^2 =p^2 c^2 + m^2 c^4
      but m is the rest mass- which should be the same in every frame of reference. Therefore if m = 0 in one frame, it must be the same in every frame.
      Therefore in every frame of reference E = p c
      i.e. the energy is always equal to the momentum (times the speed of light).
      This means that the particle must have the same speed in every frame of reference.
      In relativity, there is only one speed in every frame of reference- this speed is the speed of light.

      I hope that’s clear!

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