![]() M i=m p follows from geodesic motion in a curved spacetime. The geodesic motion principle does rely on the assumption of an energy condition, but I think the box satisfies every reasonable energy condition. If this changed its inertial mass, then it would either have to accelerate (violating the principle that small test bodies move along geodesics) or not accelerate (violating local conservation of energy-momentum). If they were unequal, then you could have mechanisms inside the box that would convert the energy back and forth between, say, light and mechanical energy. So basically I want to prove that E=m i=m p=m a (in units where c=1).Į=m i follows from geodesic motion and conservation of energy-momentum, when you put the box in a flat spacetime. The claim that its gravitational fields can be parametrized by a scalar mass is consistent with Birkhoff's theorem. In principle this could actually be three different scalars: the inertial mass, active gravitational mass, and passive gravitational mass. Since the box has spherical symmetry, all you can measure about it, by any external observations, is some kind of scalar mass. While I was in the car this morning, I worked out the following somewhat more detailed and rigorous, but still nonmathematical, argument about the exterior field of the spherical box of photons. I think we're agreeing on the exterior results, but the issue of matching the boundary conditions properly had been bothering me, and I think your explanation helps clear that up. That's helped me to understand this better. This is unrealistic, but it saves you from having to account for the work done by expanding the shell. This translates into a measured acceleration of G (2E/c^2) / r^2.īut if you measure the gravity outside the sphere, the tension in the shell will essentially lower the Komar mass of the shell, and you'll only get an increment of E/c^2 from the original gravitational field you had outside the sphere.įor simplicity I'm assuming the shell doesn't expand when you fill it up with the photon gas. The Komar mass formula boils down to integrating rho + 3P for a small sphere, and since 3P = rho for a photon gas, you'd have twice the Komar mass and twice the gravity. You can think of the interior as a "photon gas", so the pressure is any direction is 1/3 the energy density. If you fill the hollow sphere up with light, you would find the light was twice as good as creating a gravitational field than cold matter, due to the pressure terms, as measured by such a probe just inside the surface of the sphere. ![]() If you imagine you had a hollow sphere, symmetry would mean that a probe just inside the surface of the sphere wouldn't be affected by the sphere. Let me outline an experiment in more detail: In particular, you can't find the gravitational field of a pencil beam of light just by simple application of E=mc 2. (This follows from Birkhoff's theorem, which says that all spherically symmetric gravitational fields have the same form.) But in the general case without spherical symmetry, there is no simple algebraic solution you have to solve the Einstein field equations. Remote control battery: 3 * 1.If you could confine a very intense swarm of light rays of total energy E inside a spherical chamber, then GR predicts that you would get the same external field as you would get from a material sphere of mass E/c 2.Body battery: 3.7V 250mah lithium battery.Use time of wall-climbing vehicle on vertical wall or ceiling: 7-10 minutes.Use time of wall-climbing vehicle on the ground: 20-30 minutes.Comes with an instruction guideĪir Hogs Action: We make an array of exciting remote control vehicles including race cars, tanks, boats, planes, rockets, stunt motorcycles, battle robots, hovering spheres & Star Wars shipsĬutting Edge Rc: We’ve got RC vehicles for both indoor & outdoor play, as well as for racing, stunts, all-terrain, flying & hover capabilities! USB Rechargeable: Racecar is easy to recharge with included USB charging cable, so you can power up to race over & over! The controller uses 3 AAA batteries (not included). Led Light Controller: Point the controller’s LED light at any smooth surface within a 1-foot radius of the vehicle & the race car will chase it in any direction you want at super-fast speeds! ![]() ![]() Wall Climbing Race Car: Defy gravity with the Zero Gravity Laser! Using patented wall climber technology, this lightweight Vehicle drives on floors, up walls & even upside down on the ceiling! RC Car Infrared Laser Tracking Wall Ceiling Climbing Stunt Follow Light Drift 360 Rotating Model Electric Anti Gravity Car Toys
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