Has it been experimentally proven that energy causes gravity?

Question

I know that under general relativity energy and mass are equivalent under $E=mc^2$. But has it been experimentally proven that energy alone causes gravity, for example, does a nuclear reaction generate gravity independent of the mass of the reactor alone? Is a kugelblitz possible?

Answer 1

The parametrized post-Newtonian (PPN) formalism is a generalized way of exploring gravity theories, including general relativity. In the older "beta-delta" parametrization, three of the parameters ($\beta_1$, $\beta_2$, and $\beta_3$) describe how much gravity is produced by kinetic energy, gravitational energy, and internal energy respectively. In addition, there's another parameter $\beta_4$ that describes how much gravity a given amount of pressure creates; this is important for photons, since photons have a pressure equal to their energy density (up to a factor of $c$.) The case $\beta_1 = \beta_2 = \beta_3 = \beta_4=1$ corresponds to all three types of energy creating the same amount of gravity as conventional mass does, given the conversion factor $E = mc^2$; this is what is predicted by general relativity.

In terms of the other PPN parameters mentioned in that article, we have: $$ \begin{align*} (\beta_1 - 1) &= \frac{\gamma - 1}{2} + \frac{\alpha_3}{4} + \frac{\zeta_1}{4} \\ (\beta_2 - 1) &= - \frac{\beta - 1}{2} + \frac{3 (\gamma - 1)}{2} + \frac{\zeta_2}{2} \\ (\beta_3 - 1) &= \zeta_3 \\ (\beta_4 - 1) &= (\gamma - 1) + \zeta_4 \end{align*} $$ From current observational bounds on gravity (such as the tracking of space probes in the solar system, the perihelion shift of Mercury, the behaviors of pulsars, etc.) these parameters are bounded to around the following orders of magnitude: \begin{align*} |\gamma - 1| &\lesssim 10^{-5} & |\beta - 1| &\lesssim 10^{-4} & \alpha_3 &\lesssim 10^{-20} \\ \zeta_1 &\lesssim 10^{-2} & \zeta_2 &\lesssim 10^{-5} & \zeta_3 &\lesssim 10^{-8} & \zeta_4 \lesssim 10^{-2} \end{align*} So to within an order of magnitude, these parameters suggest that $\beta_1$ and $\beta_4$ are constrained to be equal to 1 to within a few percent. In other words, we're pretty sure that kinetic energy and pressure create the same amount of gravity that mass do to within a few percent. The gravitational effects of gravity itself and of internal energy are even more tightly bounded.

Caveat: I'm playing a bit fast and loose with these bounds. In reality, they were all established via a series of interdependent experiments, and it's possible that the published bounds are interdependent on one another in a way that allows for larger values. Still, this hopefully gives you a feel for how this question has been experimentally addressed.

Answer 2

But has it been experimentally proven that energy alone causes gravity, for example does a nuclear reaction generate gravity independent of the mass of the reactor alone?

Gravity and nuclear reactions cannot be tested in the laboratory, because gravity is a very very weak force. Only by fitting astrophysical observations with models that combine general relativity and quantum mechanics , for the nuclear reactions, one can say that "since the models fit the data, it is the total four vector energy that generates gravity for a star.

Is a kugelblitz possible?

As for kugelblitz , the introduction in wikipedia says it all:

In simpler terms, a kugelblitz is a black hole formed from radiation as opposed to matter. Such a black hole would nonetheless have properties identical to one of equivalent mass and angular momentum began more conventionally, following the no-hair theorem.

Edition after comments:

I found this review whence I copy this:

John Dotty comments:

@PM2Ring The difference in the mass defects of lithium and iron is ~0.3% of the total mass, so 5 significant digits should put a moderately tight limit on any difference between the gravity of matter and the gravity of energy using those elements.

If you measure G with lithium and then G with iron, the difference, if it exists, would be within the experimental errors as given above, imo.