# Can we experimentally detect the weight of energy?

1. May 2, 2015

### The_Duck

Has any experiment detected the weight of energy, $1/c^2 \approx 10^{-17}$ kilograms/Joule?

Wikipedia claims that superconducting gravimeters can measure changes in gravitational force of one part in $10^{12}$.

Wikipedia's table of energy densities says some batteries store of order 0.5 MJ/kg. The weight of 0.5 MJ is $5 \times 10^{-12}$ kilograms, so the weight of the stored energy is 5 parts in $10^{12}$ of the total weight. Could a superconducting gravimeter detect the difference in weight between a charged battery and a depleted one?

[I guess we can easily detect the weight of the binding energy of nuclei. But can we change the energy of a single object and detect the resulting change in the object's weight?]

Last edited: May 2, 2015
2. May 2, 2015

Staff Emeritus
It could detect the difference between a planet made of charged batteries and a planet made of uncharged ones.

3. May 2, 2015

### bcrowell

Staff Emeritus
Nuclei undergo nuclear reactions, and we certainly observe in accelerator experiments that mass-energy is conserved in these reactions. The mass we measure in these experiments is the inertial mass. However, if there was not also a corresponding change in gravitational mass, it would mean that nuclear reactions, including nucleosynthesis, violated the equivalence principle. The equivalence principle has been tested to extremely high precision. See http://relativity.livingreviews.org/Articles/lrr-2014-4/ [Broken] .

I believe that if you compare a fresh fuel rod for a nuclear reactor to a spent one, the mass equivalent of the energy change is of a size that would be easily measurable. However, I don't think this is likely to be a clean, high-precision test of SR, since, e.g., neutrons go flying out and take their mass with them, and there are probably other processes such as outgassing. It would be interesting to learn more about this if someone wants to take the time to research it.

Note that virtually all of the mass of ordinary matter comes from the kinetic energy of the quarks and gluons. (Very little comes from the Higgs boson, contrary to popular belief.)

By the way, GR says that it's not just mass and energy that are sources of the gravitational field, but also momentum and pressure. For a description of some experiments that tested this see section 8.1.2 of my GR book: http://lightandmatter.com/genrel/ .

Last edited by a moderator: May 7, 2017
4. May 2, 2015

### The_Duck

My suggestion is to use the battery as the test mass in the gravimeter, which should be slightly more practical than converting the planet to batteries. Superconducting gravimeters measure $mg$ instead of just $g$ so a change in the test mass $m$ should register.

Sure, by measuring the weights of nuclei we already know that energy gravitates as predicted by relativity. I think it would still be a pretty cool demonstration to measure something like the weight of a battery's energy.

Yeah, lots of mass flies off in nuclear reactions which is a problem for this test. But maybe with enough shielding you can keep the decay products inside a little box and weigh the box? I guess you want an isotope that decays via emission of alpha particles with a half-life of order 1 year. For example americium decays with emission of a 5 MeV alpha particle. The fractional mass loss due to relativity from complete decay would be about $2 \times 10^{-5}$. If you can keep the regular mass loss below this fraction maybe you can detect the mass loss due to relativity. Of course the shielding will add dead weight and make the fractional mass loss smaller and harder to detect.

I also thought about chemical fuel, which has ~100x the energy density of batteries. But if even 1 part in $10^9$ of the fuel escapes the apparatus when you burn it that will swamp the signal.

Last edited: May 2, 2015
5. May 3, 2015

Staff Emeritus
Except that gives you the exact same acceleration due to gravity independent of the test mass.

6. May 3, 2015

### The_Duck

Read the next sentence. Superconducting gravimeters are a type of "spring gravimeter" which measure how much the force of gravity stretches a spring with a mass hanging on the end. Increasing this mass increases the force pulling on the spring, so the spring will stretch more. So they can be used to detect a change in mass. You'd be right if we were talking about the sort of gravimeter that literally measures the free-fall acceleration of a test mass.

7. May 3, 2015

### Staff: Mentor

You would need a superconducting test mass that changes its energy content by 10-12. Unfortunately, superconductors are not good in storing energy. Combining both seems to be tricky, because the best scales are significantly worse than 10-12. I'm sure someone will test it as soon as the devices are sensitive enough (the Moriond conference this year had a talk about it, but I don't find it any more).

8. May 4, 2015

### PAllen

There is indirect evidence of the weight of kinetic energy described in the relatively well known paper:

http://arxiv.org/abs/gr-qc/9909014

which argues that re-interpreting existing measurements establishes that a hot brick weighs more than a cold brick.

9. May 5, 2015

### Staff: Mentor

The OP makes me think of a related question. If energy gravitates, can astronomical obvervations of a galaxy see the gravity contribution of the energy internal to its (arbitrary) boundaries?

My guess is no because the gravitation of dark matter wasn't noticed until recent decades. Gravity measures of galaxies are too coarse.

10. May 5, 2015

### Staff: Mentor

Sure.
That's how dark matter got discovered.

11. May 5, 2015

### Staff: Mentor

Yes, but the OP was asking about energy that is not the mc^2 equivalent of rest mass. Is the gravitation of non-rest mass energy big enough to be noticed on a galactic scale?

12. May 5, 2015

### e.bar.goum

Further to the comments about nuclei above - at a storage ring, such as the one at GSI in Germany, you can resolve the difference in mass of nuclei that are in different excited states! Further, with this method, you have single ion sensitivity! For example, the difference in masses between 184gHf and 184mHf - (hafnium-184 in either the ground and a metastable state) is resolvable.

(ETA: and it really is a mass measurement!)

See these slides for more detail.
https://indico.gsi.de/getFile.py/ac...onId=16&resId=0&materialId=slides&confId=2391

13. May 6, 2015

### Staff: Mentor

We don't have a gravity-independent way to determine the total mass or energy in the galaxy, so it is impossible to distinguish between dark matter and other energy forms just based on gravity.
Regular matter is 99% QCD binding energy. Removing the gravitational effect of this binding energy would have a large influence.
For a black hole, those categories don't make sense, but we certainly see its gravitational influence.

14. May 6, 2015

### The_Duck

Oh, cool! Do you remember any details that might help me search for references?

15. May 6, 2015

### Staff: Mentor

It was in some other context, the idea was to measure some phase transition. Could have been superconductivity or something else, not sure. The required precision was ... problematic, especially as the easier "observe some change from anything" seems to be an easier and interesting experiment on its own that has not been done yet.