Short answer : because you don’t become weightless when you step into a Faraday cage.
This simple answer is already enough to demonstrate that empirically, gravity does not behave the same way electromagnetism does, more specifically, it cannot be shielded in the same manner, and it is still present even if we block out all external electromagnetic influences. However, it is an unfortunate fact that the “electromagnetic gravity” idea is wide-spread in anti-mainstream, anti-relativity, and general pseudoscientific circles, and occasionally even makes an appearance in pop-sci articles around the web. So let us look at the situation in a little bit more detail. There are 11 primary reasons ( in my own way of reckoning ) as to why gravity is not an electromagnetic phenomenon :
Reason 1 : Charge
This is probably one of the most significant and easy to grasp differences between the two interactions : there are two opposing electric charges, but there are no gravitational charges. The difference between matter and anti-matter is not the same as the difference between positive and negative electric charges, because anti-matter has the same gravitational influence as ordinary matter.
Reason 2 : Relative Strength
Gravity is a very weak interaction which becomes apparent only for energy-momentum distributions of significant magnitude; electromagnetism is stronger than gravity, in terms of relative strength, by some 36 orders of magnitude.
Reason 3 : Linearity
Electromagnetism is a linear interaction, i.e. the electromagnetic field is governed by a linear field equation ( Maxwell’s equations ). In contrast, gravity is governed by a non-linear field equation ( Einstein field equation ), and the non-linearity becomes more apparent in the strong field regime. In practical terms that means that electromagnetic fields superimpose linearly, and but do not self-interact; this stands in contrast to gravitational fields, which do not superimpose in this manner, and which can self-interact.
Reason 4 : Sources
The source of the electromagnetic field are electric charges, whereas the source of gravity is more generally anything that has energy-momentum associated with it. This of course includes electromagnetic fields and charges as well, but is not restricted to it. In addition, two like electric charges repel electromagnetically, but they attract gravitationally – a fundamental difference in behavior between the two interactions.
Reason 5 : Radiation Fields
Electromagnetic radiation is dipole radiation, whereas gravitational radiation is quadrupole or higher multipole in nature. The source of electromagnetic radiation is accelerated charges, whereas the source of gravitational radiation is a more general time-varying reduced quadrupole moment.
Reason 6 : Equivalence Principle
Gravity is subject to an equivalence principle, whereas electromagnetism is not. This is probably the most fundamental difference between these two interactions, and this alone is enough to conclusively show that gravity cannot be of electromagnetic origin. Simply and somewhat sloppily put, what this means is that you can locally (!) “eliminate” gravity by placing yourself in a small enough free fall frame; the same is not true for electromagnetism, since in the presence of electric charges, you can never completely eliminate the field, no matter your reference frame or state of relative motion. This also means that to experimentally detect gravity in a motion-independent manner, you need an extended apparatus, whereas an electric or magnetic field can be detected by a single point-like test charge. Lastly, it implies that gravity acts between any two test particles in the exact same manner, regardless of their composition, whereas electromagnetism acts only between electric charges, and then depends on the polarity of those.
Reason 7 : Inverse Square Law
Electromagnetism is always subject to an inverse-square law, regardless of field strength, whereas gravity is not. The inverse square dependency holds to a very good approximation in the weak field regime; that means that for very weak fields and non-relativistic speeds, gravity does indeed appear to “look like” electromagnetism in that regard. However, if you go into a region of strong fields, or move at relativistic speeds, this similarity breaks down rather quickly – the non-linearity of gravity becomes apparent, and it increasingly deviates from a simple inverse square law. Also it should be remarked that just because two interactions are subject to an inverse square law in some domain does not make them identical – thinking that is a logical fallacy. In fact, the inverse-square law is a generic property of anything that propagates linearly in three dimensions, so no conclusions can be drawn about the nature of this “anything”.
Reason 8 : Field Geometry
Any classical radiation field can only be invariant under a rotation of 2π/S, and it has precisely two states of linear polarisation inclined to each other at an angle of (π/2S). Quantum mechanically, such fields are associated with quanta carrying internal angular momentum ( spin ) of magnitude S, and source-couple to tensors of rank-S. These are basic results from elementary field theory.
For electromagnetism, the empirical finding is S=1 – electromagnetism is mediated by photons of spin-1, couples to vector fields ( the electromagnetic vector potential ), and has polarisation states at right angles to each other.
For gravity, the empirical finding is S=2 – it couples to a rank-2 tensor field ( the stress-energy-momentum tensor ), and has polarisation states inclined at an angle of 45 degrees to each other. The graviton, if it exists, would be a massless spin-2 particle.
This is once again a fundamental difference in the nature of the these two interactions – basically, what this implies is that gravity must be a tensor field theory, and can not be a simple force field such as is the case for EM.
Reason 9 : Degrees of Freedom
Electromagnetism has three off-shell degrees of freedom ( the four components of the vector potential – less one due to the fact that it is subject to an arbitrary gauge choice, so only three explicitly appear in the Lagrangian ). Gravity has only two degrees of freedom – the metric is a symmetric tensor in 4D, giving 10 degrees of freedom. The Bianchi identities eliminate four of these, and diffeomorphism invariance eliminates another four, leaving us with two. Again, this is fundamentally different from electromagnetism.
Reason 10 : Individual Photons
A single photon has no electromagnetic field, carries no charge, and does not emit or absorb other photons ( such processes are quantum mechanically forbidden ). Yet, it has a gravitational influence on its surroundings, and it is itself influenced by external gravity. Hence, gravity can evidently not be electromagnetic in nature.
Reason 11 : The Nature of the Interactions
Electromagnetism is a “force” in the classical sense of field theories – you can describe it via a vector force field, which can be quantized using the usual tools of QFT to give a consistent quantum field theory – quantum electrodynamics, or QED, which is mathematically described by a U(1) symmetry group.
The same is not true for gravity – it is not a force, but a geometric property of space-time itself. Attempting to apply the usual tools of QFT to it yields something that has no predictive power, because it contains non-renormalisable infinities. The symmetry group of general relativity is Diff(M), the group of diffeomorphisms on a manifold, and not U(1). The gauge potential of gravity is the rank-3 Lanzcos tensor field, again very different from electromagnetism.
I am sure that by thinking about this a bit longer, one could come up with many more differences between electromagnetism and gravity ( I haven’t even used any mathematics in this yet ! ), but for the purpose of this article, I will leave it at the above 11 points, which I consider to be the most important ones. It should at this point be pretty obvious that gravity being electromagnetic in origin is not a scientifically tenable position. To be more precise, it is a hypothesis that quite simply does not pass the scientific method, since these two interactions are just too fundamentally different in too many respects.
However, them being different does not preclude the possibility that there might be some way to unify the two interactions under a common framework. On a classical level, the most promising attempt in that regard would be Kaluza-Klein gravity – this is a generalisation of GR to five dimensions, where the extra dimension is “curled up” so that it cannot be macroscopically observed. The metric tensor in this theory has 15 functionally independent components – ten for the gravitational metric, four for Maxwell’s equations, as well as one for an additional scalar field ( the dilaton ), which is needed to keep the model self-consistent. The full set of resulting equations is quite complex, but there is no ad-hoc reason to rule the model out on any grounds; while there is no empirical support for it, there is also nothing that empirically contradicts it, other than the continued absence of the scalar field, or any evidence for the additional dimension.
On a quantum level, the most notable attempt at unification is String Theory – simply put, the graviton here is the ground state of the String in the configuration space of all vibrational modes, whereas the photon corresponds to one of the excited states of the String. The situation here is again similar – there is no direct empirical support, but no grounds on which to conclusively rule it out either.