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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?

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    $\begingroup$ 1. There is no such thing as "energy alone" - a "box of light" isn't "energy", it's a bunch of photons/coherent photon states. 2. Related/possible duplicate: physics.stackexchange.com/q/209919/50583 $\endgroup$
    – ACuriousMind
    Apr 14, 2022 at 18:03
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    $\begingroup$ A nuclear reaction wouldn't "generate" gravity... the energy liberated by a nuclear reactor was always in the nuclei beforehand (i.e. in the mass of the fuel). The prediction is not that the reaction causes "more" gravity but that the reaction doesn't reduce gravity (since all the mass-energy is still there). Good luck keeping the energy output in a box long enough to weigh it, though. (Though doesn't weighing the reactants and products of a nuclear reaction as in one of the linked answers count as addressing gravity?) $\endgroup$
    – HTNW
    Apr 14, 2022 at 18:33
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    $\begingroup$ If you're not asking about $E=mc^2$, I'm not sure what you're asking about. General relativity doesn't claim that "energy causes gravity", it claims that the Einstein field equations tell us how the stress-energy tensor determines the geometry/metric of spacetime. Are you asking about that? $\endgroup$
    – ACuriousMind
    Apr 14, 2022 at 18:39
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    $\begingroup$ Does this answer your question? Does a photon exert a gravitational pull? $\endgroup$
    – user87745
    Apr 14, 2022 at 21:32
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    $\begingroup$ I don't think this is a duplicate of the proposed question. The OP here wants to know whether there has been experimental proof of the gravitational effects of photons (and other energy), not what the theory predicts. $\endgroup$ Apr 15, 2022 at 17:54

2 Answers 2

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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.

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  • $\begingroup$ Now that I have digested your answer, it DOES appear that experiments on the perihelion shift of Mercury have proven that energy causes gravity. In most articles on this, it merely says something like "relativistic effects". But you have broken them down into B1 and B4, the kinetic and pressure energy factors. So if you flung Mercury at near c, then it would have nearly twice the gravity of a non-moving Mercury? Is that correct? $\endgroup$ Apr 17, 2022 at 13:02
  • $\begingroup$ Can you provide citations for these bounds? $\endgroup$
    – Jagerber48
    Sep 21, 2023 at 1:48
  • $\begingroup$ @Jagerber48: The standard reference is Clifford Will, "The Confrontation Between General Relativity and Experiment", Living Reviews in Relativity 17 4 (2014). There's a summary of the parameters in Table 4, which appears to have just been copied into the Wikipedia article I linked. $\endgroup$ Sep 21, 2023 at 11:12
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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:

gvalue

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.

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    $\begingroup$ "Proven" could mean by looking at gravitational lensing, etc, which is how many of these type things are proven. So I get from your answer that it has not been proven yet. I gather it would take the energy of 100,000 suns to create a kugleblitz around the earth. Thanks. $\endgroup$ Apr 14, 2022 at 20:11
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    $\begingroup$ Could be tested in the lab by a Cavendish-type experiment comparing the gravity of materials with different mass defects. Since we attribute mass defect to binding energy, if energy and nucleon mass were to gravitate differently, the experiment should measure different gravitational constants for the different materials. I suppose somebody must have done this, but I don't know. $\endgroup$
    – John Doty
    Apr 14, 2022 at 22:05
  • $\begingroup$ @JohnDoty There have been many experiments trying to verify that inertial & gravitational mass are equal for different substances. Newton himself did numerous experiments using pendulums. IIRC, in the last few decades there have been some experiments looking for the effect you mention, but it's really hard to get decent numbers from Cavendish-type experiments, which is why the value of G is only known to 5 significant figures. $\endgroup$
    – PM 2Ring
    Apr 15, 2022 at 2:56
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    $\begingroup$ and on top of the comment of PM2Ring, there is the minute difference in binding energy between excited and ground level states to be separated in order to say that the experiments asked by the OP were and can be done in lab conditions. $\endgroup$
    – anna v
    Apr 15, 2022 at 5:51
  • $\begingroup$ @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. $\endgroup$
    – John Doty
    Apr 15, 2022 at 20:28

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