We know an object with positive mass cannot be accelerated to the speed of light because this would require an infinite amount of energy. My question is:
Is there anything in the universe that can travel less than the speed of light in a vacuum and yet has no mass?
Is it even possible within our universe's physical laws?
Best Answer
In vacuum, no. Massless particles travel at the speed of light. In relativity, the definition of the (rest) mass of a particle is the energy (divided by $c^2$) of the particle in its rest frame. If something has zero energy in its rest frame, does it really exist? (No.) Massless particles exploit a tricky loophole in this argument because by moving at the speed of light, it is impossible to boost into their rest frame.
In other words: massless particles are only allowed to exist (ie, have a finite amount of energy), despite not having a mass (energy in their rest frame), because they don't have a rest frame. If a particle was massless and traveling less than the speed of light, we could go into its rest frame, find it had no energy at all, and be led to a philosophical conundrum because such an "object" cannot have any effect on the physical world.
However in a medium, particles that are massless in vacuum can travel at a speed different from the speed of light in vacuum. For example, light traveling through glass travels at a speed that is about 1.5 times slower than the speed of light in vacuum; we describe this phenomenon by saying glass has a refractive index of about 1.5. Having said that, one explanation of the refractive index is that the photon acquires an effective mass due to interactions with phonons in the glass, so in a way the refractive index is "an exception that proves the rule" and actually confirms the idea that if something is traveling at less than the speed of light in vacuum, then it has some form of mass.