# Gravitational shielding and equivalence principle

I read on wiki that gravitational shielding is considered to be a violation of the equivalence principle. Is that so, How? A conceptual description without lot of mathematics will be helpful.

I am not sure whether the wiki article refers to shielding only by materials, or it also includes mechanisms - e.g a rotating disk. I know rotating disk does not shield gravity, but just to describe what a mechanism could mean.

It goes on to say that any evidence of gravitational shielding would falsify GR, is this true?

It is hard for me to believe because - suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments and phenomena. So, that makes me think gravitational shielding would not invalidate GR.

• This is very close to a duplicate of Is it theoretically possible to shield gravitational fields or waves? though that does not mention the equivalence principle. The answer from Luboš gives an elegant analysis of why gravitational shielding is impossible. – John Rennie Jul 3 '17 at 5:18
• @JohnRennie: Yes, my question involves equivalence principle and GR. Also, I mean shielding by a material, and/or by a mechanism. Say, a rotating disk, I know this is a bad/false example, but just an example to describe what a mechanism could mean. – kpv Jul 3 '17 at 5:25
• @JohnRennie: Also I am not asking whether gravity can be shielded. So, to me the question does not seem to be duplicate. – kpv Jul 3 '17 at 5:31
• "suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments" While trying to keep an open mind, I think this is back-to-front. Because GR has been verified by so many experiments, the chances of demonstrating gravitational shielding are extremely small. It's doesn't mean there cannot possibly be GS, but given the corpus of GR-confirming experiments, it would require most of the predictions of a GR+GS replacement to be very nearly similar to current GR. – TripeHound Jul 3 '17 at 8:00

The Wikipedia article refers to the paper General Theory of Relativity: Will it survive the next decade? by Orfeu Bertolami, Jorge Paramos and Slava G. Turyshev. In that paper gravitational shielding is discussed in section 3.4 on pages 16–17.

Rather than consider specific mechanisms the article discusses the general possibility that matter itself screens gravity, so for example Newton's law for the force between two bodies would be modified to something like:

$$F = \frac{Gm_1m_2}{r^2} \, \exp\left(-h\int \rho(r)dr\right)$$

where $\rho(r)$ is the density of the matter. This idea is due originally to Quirino Majorana (Q. Majorana, Philos. Mag. 39 (1920) 488 - Googling finds many references to the paper but not the paper itself).

Now consider the force between two spherical masses. We can consider these masses as made up from concentric spherical shells, but the mass in each shell would shield the mass inside it. So as the masses increase and their radii increases the gravitational shielding will increase and the ratio of the shielded force to the Newtonian force will decrease. That means the ratio of the gravitational mass to the inertial mass changes as the size increases. The equivalence principle (one of its many forms) states that the ratio of gravitational to inertial mass is constant. Hence the conflict.

For the more general question of whether shielding is possible I refer to the answer from Luboš to Is it theoretically possible to shield gravitational fields or waves? The problem is that shielding generically requires a negative mass/energy and that causes all sorts of stability problems. While this isn't technically a violation of GR most of us believe that negative mass/energy cannot exist.

• I can understand the case of matter shielding would be impossible. How about some mechanism where we can say - If gravitation is shielded, that means the gravitation effect is reduced, not the gravitation mass. Thus reduction in weight is not due to a different mass but due to different strength of gravity because it has been partially shielded? In other words, the mechanism curves space in a way that the effect itself is reduced without effecting gravitational mass. I guess that would not contradict GR. – kpv Jul 3 '17 at 6:15
• @kpv: this is where you need to refer to the question I linked. The type of gravitational shielding you describe would require negative mass. While this isn't a violation of GR allowing negative mass causes all sorts of stability problems. The fact the universe exists suggests that negative mass doesn't exist. – John Rennie Jul 3 '17 at 6:22
• Yes, that is going into what it takes to shield gravity, negative mass per your description. I agree, there would not be negative mass, and so no shielding by that specific mechanism. – kpv Jul 3 '17 at 6:28
• The paper is by Quirino Majorana, Etorre's uncle. – user1803551 Jul 3 '17 at 11:58

I will reply to this part of the question:

It is hard for me to believe because - suppose gravitational shielding is demonstrated somehow, then how GR can be falsified all of a sudden, which has been verified by so many experiments and phenomena. So, that makes me think gravitational shielding would not invalidate GR.

Take Newtonian gravity , which has been verified by many many experiments. When General Relativity, GR was proposed, it includes in its limiting form Newtonian gravity, and does not invalidate it when the effect of GR is small, within measurement errors. All the results of Newtonian gravity are valid in a specific phase space of the variables, within experimental errors.

Take classical mechanics. When quantum mechanics developed for small dimensions the limits are mathematically approached smoothly as the dimensions grow large with h going to zer0.

So it is conceivable that a new gravitational theory would embed GR at the limits of some phase space. General relativity would be invalid at certain values of the variables and would need corrections but the result should join smoothly, as has happened with all validated theories of physics when new theories are proposed to explain new phenomena.

So a theory with gravitational shielding would make sense only if it reproduces, within experimental errors , the successes in the orbits and even GPS corrections using GR, and in addition explains observations not clear using general relativity, for example dark mass and dark energy.

• I agree with your description and also understand it. However, in this case, the wiki article says, it will contradict with GR in principle, not in limit/boundaries. – kpv Jul 3 '17 at 6:31
• principles/laws/ postulates all hold in specific phase space regions. GR will be invalidated in a specific region. If they say over the whole phase space then the proposed theory is invalid, so it must be a bad description of the paper. validation and falsification happens by experiments within certain experimental errors. If within those errors both theories hold there is no falsification statement that can be made. – anna v Jul 3 '17 at 6:51
• @kpv It is conceivable that the equivalence principle does not hold as universally as it is assumed to, and it is conceivable that in cases where it doesn't hold, it could permit GS. But (and this is an enormous "but"), even if the equivalence principle isn't as universal as thought, it has to hold (or its replacement theory has to predict the same results) everywhere where GR-validating experiments have been conducted. This severely limits the "space" in which GS could operate. – TripeHound Jul 3 '17 at 12:48
• @TripeHound; Agree, – kpv Jul 3 '17 at 15:58
• Or to put it another way; just because something is proven wrong, doesn't mean it wasn't less wrong than the things that came before it. – Shufflepants Jul 3 '17 at 17:40

The shielded body would have to have an inertial mass that is different than its gravitational mass, since it is gravitational mass that would get reduced in shielding. The gravitational mass causes weight, the inertial mass resistance to acceleration. The equivalence principle says they are the same (equivalent). Plenty of experiments showing they are, and that shielding doesn't work.

See the wiki article for the equivalence principle at https://en.m.wikipedia.org/wiki/Equivalence_principle. In the wiki article on shielding gravity it describes the measurements and experiments -- see it at https://en.m.wikipedia.org/wiki/Gravitational_shielding.

Yes, that wiki article should be edited to not make it mysterious why shielding invalidates the Equivalence principle, as written it says 'it is considered', not a very scientific statement.

• Can't I say - If gravitation is shielded, that means the gravitation effect is reduced, not the gravitation mass. Thus reduction in weight is not due to a different mass but due to different strength of gravity because it has been partially shielded? – kpv Jul 3 '17 at 5:59
• IGravitation can only be reduced a)masses are reduced, b)distances increase, or c) some strange nonlinearities or effects happen. Since we don't know any cases of c), and you stay at the distance, it's got to be a). The gravitational constant is just a constant to normalize gravitational and inertial mass,if you want to really claim that a universal constant which explains the universe gravity and the solar system gravity can be changed by interposing something, it makes no sense, you'd to say it's a negative mass thing that you interposed. But gravity has nothing like charge. Don't see how. – Bob Bee Jul 3 '17 at 23:54
• I do not believe in existence of negative mass. Also per other comments/answers, looks like negative mass theory is ruled out. – kpv Jul 4 '17 at 9:15
• It's not ruled out and not something to believe. Just a physics questtion where we have no evidence for it, and from theory looks highly unlikely. So, no shielding is likely either – Bob Bee Jul 4 '17 at 16:24

The assertion is simply wrong. The existence of negative mass by itself would not invalidate the equivalence principle, however negative mass next to a positive mass would shield $r^{-2}$ asymptotic gravitational field dependence, and only dipolar $r^{-3}$ and weaker terms would survive.

This proves you can have gravitational shielding and still preserve the equivalence principle. But it requires negative mass

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