# Where is the mass energy of potential energy (such as for the universe?)

As you know, energy has mass via $E=mc^2$. If I understand right, mass must be inside of a particle, and can not just be "free floating." Gravitational potential energy (or what ever its equivalent would be in General Relativity) is the energy an object has when separated from other objects. Where is all this mass? Which object does it reside in of the two? Or does it reside as invisible mass at the midpoint undetectable except for its gravitation? More importantly why about the potential energy between myself and the center of the galaxy. What about all of potential energy of all the objects in the universe with respect to each other. Does the expansion of the universe create it, and if so, from what other energy source?

• @sanchises "In relativity, all of the energy that moves along with an object (that is, all the energy which is present in the object's rest frame) contributes to the total mass of the body, which measures how much it resists acceleration. Each potential and kinetic energy makes a proportional contribution to the mass." en.wikipedia.org/wiki/… Jan 14, 2015 at 23:02
• It seems to reside in the system as a whole, and would be detectable if a force from outside the system tried to accelerate it. Strictly speaking, potential gravitational energy is negative energy, and increases asymptotically to 0 as objects move away from each other. So it is more like a system losing potential energy as its constituents move together. I would love to hear an expert description of what is happening. Jan 14, 2015 at 23:26
• (In case anyone didn't notice, I was subtly suggesting that dark matter is freefloating potential energy, a notion which is most likely patent nonsense.) Jan 14, 2015 at 23:32
• I didn't notice, so you should put this into your question. Jan 14, 2015 at 23:53
• Again, it seems like patent nonsense, especially given that it turns out potential energy is negative. Jan 15, 2015 at 0:00

First, the equation $E=mc^2$does not mean that if there is energy at a point then there must be mass as well. The equations says that having some energy at some point will have the same effect as having mass at that point. In general relativity, there is no such thing as gravitational potential energy. The theory helps us understand gravitation in terms of curvature of space-time. Things move as straight as possible in curved space time in the absence of any force. Any mass curves spacetime so that the straightest possible paths for objects near it accelerate toward it. Even in non relativistic mechanics, potential energy at some point is defined as the work done to move a a mass from infinity to that point. All potential energy does is allow us to better state and understand the work energy theorem in conservative fields, where one can simply say that energy is conserved.
To make it clearer what $E=mc^2$ implies, let's consider an example. Electromagnetic waves are propogated by massless particles called photons. Yet, photons do have their own gravitational fields(very small ones though) because they carry energy. Hope that clears your doubts.
• Technically, it would. That's cause rest mass of any object is less than its moving mass. Though, the $m$in the equation refers to rest mass of particle only. The technically correct equation is $E =m_0c^2 + \frac{1}{2}mv^2$ Jan 15, 2015 at 10:05
• An isolated systems' inertia can't change. $E=mc^2+\frac {mv^2}2$ only relates rest mass and energy. Jan 15, 2015 at 10:10