einstein suggested that mass and energy are actually the same thing.
who suggested that mass and energy are actually the same thing?
einstein
there have been several other analyses of negative mass, such as the studies conducted by r. m. price, however none addressed the question of what kind of energy and momentum would be necessary to describe non-singular negative mass. indeed, the schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position. the question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density. the answer is yes, but not with energy and momentum that satisfies the dominant energy condition. this is because if the energy and momentum satisfies the dominant energy condition within a spacetime that is asymptotically flat, which would be the case of smoothing out the singular negative mass schwarzschild solution, then it must satisfy the positive energy theorem, i.e. its adm mass must be positive, which is of course not the case. however, it was noticed by belletête and paranjape that since the positive energy theorem does not apply to asymptotic de sitter spacetime, it would actually be possible to smooth out, with energy–momentum that does satisfy the dominant energy condition, the singularity of the corresponding exact solution of negative mass schwarzschild–de sitter, which is the singular, exact solution of einstein's equations with cosmological constant. in a subsequent article, mbarek and paranjape showed that it is in fact possible to obtain the required deformation through the introduction of the energy–momentum of a perfect fluid.
negative mass
john locke presented a distinction between primary and secondary qualities in "an essay concerning human understanding". for locke, a quality is an idea of a sensation or a perception. locke further asserts that qualities can be divided in two kinds: primary and secondary qualities. primary qualities are intrinsic to an object—a thing or a person—whereas secondary qualities are dependent on the interpretation of the subjective mode and the context of appearance. for example, a shadow is a secondary quality. it requires a certain lighting to be applied to an object. for another example, consider the mass of an object. weight is a secondary quality since, as a measurement of gravitational force, it varies depending on the distance to, and mass of, very massive objects like the earth, as described by newton's law. it could be thought that mass is intrinsic to an object, and thus a primary quality. in the context of relativity, the idea of mass quantifying an amount of matter requires caution. the relativistic mass varies for variously traveling observers; then there is the idea of rest mass or invariant mass (the magnitude of the energy-momentum 4-vector), basically a system's relativistic mass in its own rest frame of reference. (note, however, that aristotle drew a distinction between qualification and quantification; a thing's quality can vary in degree). only an isolated system's invariant mass in relativity is the same as observed in variously traveling observers' rest frames, and conserved in reactions; moreover, a system's heat, including the energy of its massless particles such as photons, contributes to the system's invariant mass (indeed, otherwise even an isolated system's invariant mass would not be conserved in reactions); even a cloud of photons traveling in different directions has, as a whole, a rest frame and a rest energy equivalent to invariant mass. thus, to treat rest mass (and by that stroke, rest energy) as an intrinsic quality distinctive of physical matter raises the question of what is to count as physical matter. little of the invariant mass of a hadron (for example a proton or a neutron) consists in the invariant masses of its component quarks (in a proton, around 1%) apart from their gluon particle fields; most of it consists in the quantum chromodynamics binding energy of the (massless) gluons (see quark#mass).
quality (philosophy)