# Why is gravity but not EM 'ripples' in spacetime?

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1. Aug 19, 2015

### Finny

Why do we say gravity [GR] is a theory about ‘spacetime curvature’ and gravitational waves are ‘ripples’ but nobody uses such a description for electromagnetic fields? Don't EM waves 'ripple' spacetime?

For example, one might imagine different types of spacetime curvature associated with each phenomena. Don't EM fields ‘ripple’ spacetime as they carry energy, momentum etc? Anything to do with spin?

Wikipedia says:
https://en.wikipedia.org/wiki/Graviton

" If it exists, the graviton is expected to be massless ..... and must be a spin-2 boson. The spin follows from the fact that the source of gravitation is the stress–energy tensor, a second-rank tensor (compared to electromagnetism's spin-1 photon, the source of which is the four-current, a first-rank tensor).

What's so different besides the information each field [or massless quanta] may carry?

2. Aug 19, 2015

### atyy

EM fields ripple spacetime, but gravity is spacetime itself.

3. Aug 19, 2015

### Staff: Mentor

Because you're shopping for a qualitative and non-mathematical description here.... You could reasonably say that EM waves are "ripples" in the electrical and magnetic fields.

4. Aug 19, 2015

### Finny

If there is a mathematical distinction leading to the different descriptions, that's what I am looking to have interpreted. Somebody decided on a distinction.

I don't know if different spin,for example, leads to such a distinction....that would be quantum explanation which would be ok.

Perhaps it's something buried in the tensor formulation of the gravitational field versus the vector formulation of the EM field....identifying that difference would be ok too.

That can't be literally true,can it, because can't spacetime can exist w/o gravity. But the reverse is not true.

5. Aug 19, 2015

### Finny

As I read around looking for clues, in the same wiki article:

"In some descriptions, matter modifies the 'shape' of spacetime itself, and gravity is a result of this shape, an idea which at first glance may appear hard to match with the idea of a force acting between particles.."

This is sort of what my question implies...if gravity 'warps' spacetime one way and EM fields another....

but perhaps my question butts up against this major unknown I hadn't thought about when I posted: [same article]

".....general relativity is said to be background independent. In contrast, the Standard Model is not background independent, with Minkowski space enjoying a special status as the fixed background space-time.[10] A theory of quantum gravity is needed in order to reconcile these differences.[11] Whether this theory should be background independent is an open question.

Anyway, I'll wait until tomorrow before posting more. thanks

6. Aug 19, 2015

### atyy

Is gravity a type of "matter"? Classically, gravity and matter are both fields. So what is so special about gravity that we call it spacetime instead of matter? The funny thing about gravity is that it does not have *localizable* energy, whereas matter has "localizable" energy.

There are ways to assign gravity an "energy". But if gravity has a "local" energy, the local energy cannot be gauge invariant. If it gravity has a gauge invariant energy, that energy cannot be local.

To summarize: gravity is spacetime, not matter, because it has no local gauge-invariant energy.

7. Aug 20, 2015

### Ben Niehoff

You CAN write down a theory in which EM fields are just part of spacetime. It's called Kaluza-Klein theory, after its discoverers. Spacetime becomes 5-dimensional, with an extra compact circle. The U(1) gauge symmetry of EM is realized as the U(1) isometry on this circle. Electric charge is equal to momentum around the circle.

The problem with Kaluza-Klein theory is that, in order to reproduce the mathematics of ordinary GR + EM in 4d, one must impose unnatural constraints on the 5d metric. First of all, one must impose that there is an isometry around the extra circle; that is, the metric does not depend on the circle direction. Second, this extra circle, even with a U(1) isometry, produces not just the electromagnetic field, but also a scalar field called the "dilaton". There is no dilaton in standard 4d GR, so one must impose the constraint that the dilaton is constant.

So essentially, one has an embarrassment of riches. If we take 5d GR and compactify it on a circle, we can get 4d GR + EM, but only if we impose that the circle direction is Killing, and that the dilaton vanishes.

8. Aug 20, 2015

### Staff: Mentor

There is a class of solutions to GR called pp-wave space times. These describe the spacetime in the presence of massless radiation, including light and gravitational waves. There are several specific ones which model specific scenarios you might think of.

9. Aug 20, 2015

### Finny

Thanks to those who replied. I want to do some background reading with those ideas as pointers.

Here is a specific example that seems to make gravitational and EM waves so similar to me:

https://en.wikipedia.org/wiki/Gravitational_wave

"In the example just discussed, we actually assume something special about the {gravitational} wave. We have assumed that the wave is linearly polarized, with a "plus" polarization, written [PLAIN]https://upload.wikimedia.org/math/1/4/4/14494ae6709bc2dd60bbe5141c319024.png. [Broken] Polarization of a gravitational wave is just like polarization of a light wave except that the polarizations of a gravitational wave are at 45 degrees, as opposed to 90 degrees. In particular, if we had a "cross"-polarized gravitational wave, [PLAIN]https://upload.wikimedia.org/math/2/3/8/238e57da3ec3ad4c6fbe5530070fb76f.png, [Broken] the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of circularly polarized waves. Gravitational waves are polarized because of the nature of their sources.

So it seems like the EM and GW could almost be harmonics of each other, yet we describe them so differently.

In fact , an accelerated charge is the source of electromagnetic waves [EM] [with energy, momentum, and so forth] while accelerated mass/energy [not electric charge] is the source of gravitational waves [GW] [with similar energy content].

And of course since EM waves carries energy, they also produce GW.

Interesting they have to be formulated so differently.

Last edited by a moderator: May 7, 2017
10. Aug 20, 2015

### Staff: Mentor

Despite the similarities in the mathematical description of the waves (and these similarities reach much further than just this discussion - the "wave equation" shows up in an amazing number of places - there is an important qualitative difference. Gravity affects all test particles identically, so it's natural to describe gravitation in terms of spacetime curvature which also acts identically on everything (a worldline is or is not a geodesic no matter what's moving on it). Electromagnetism affects test particles differently according to their charge, an effect that is cannot be explained by a natural tendency of all particles to follow a geodesic.

11. Aug 20, 2015

### Finny

turns out there is a recent one that probably has all the insights we can dig up:

The first post by Orodruin sums it up:
"The physical answer to the question would be: "Because this is what happens when masses accelerate according to Einstein's field equations."

You may go further and ask "Why do Einstein's field equations look as they do?", but that is a philosophical question rather than a physical one.

Compare to the generation of electromagnetic radiation, it is produced based on the acceleration of charges and this is described by Maxwell's equations. There is no underlying "why", it is simply how Maxwell's equations work."

Maybe I understood more than I thought.

12. Aug 20, 2015

### Staff: Mentor

Yes. In the pp-wave spacetimes that I mentioned above some of the spacetimes are vacuum solutions, so they represent pure gravitational waves, but others are non vacuum so they represent the GW produced by massless non gravitational radiation.

13. Aug 20, 2015

### Staff: Mentor

Yep... although this effect can usually be neglected, and a good thing too.

14. Aug 21, 2015

### vanhees71

The question may be restated to "why is gravity "geometrized" in GR and not the electromagnetic interaction?"

This idea also came to Weyl in 1918, who wanted to unify electromagnetics and gravity. To this end he realized that this may be possible by something we call "gauging a symmetry" nowadays because of this idea by Weyl. The point is that in the usual Maxwell-Einstein theory, i.e., GR + free electromagnetic fields the electromagnetic equations of motion are invariant under scale transformations, i.e., for a fixed background space time defined by a metric $g_{\mu \nu}$ the action for the electromagnetic fields,
$$A_{\text{em}}=-\frac{1}{4} \int \mathrm{d}^4 q \sqrt{-g} F_{\mu \nu} F^{\mu \nu},$$
is invariant under rescaling the metric to $\tilde{g}_{\mu \nu}=\Omega g_{\mu \nu}$, where $\Omega$ is an arbitrary function of the space-time coordinates.

What now, when we want to make this symmetry to also include gravity. It turned out on the first glance, that this idea leads to the introduction of a vector field and a theory looking quite similar to the usual Einstein-Maxwell system. There's only one important difference: If this idea was realized in Nature, the space-time scales should depend on the "electromagnetic history" of the clocks and rulers used to measure space and time. Since this was not plausible already in 1918 (and it's the more ruled out nowadays, where we have very accurate means of constructing clocks using frequency combs and also measuring distances than 100 years ago), Weyl immediately got something we'd call a "scientific shitstorm". Pauli even lamented that mathematicians should stay away from theoretical physics, which of course is not a good advice, particularly given Weyl's very fruitful work on the mathematical foundations of physics, including the group theoretical understanding of quantum theory.

Nevertheless, this historical case may answer your question: If you geometrize electromagnetism, you predict phenomena which contradict our experience, and that's why such models, although looking promising on the first glance, are most probably ruled out.

Nevertheless Weyl's failed attempt was not completely useless, because indeed the idea of "gauging symmetries" is among the most successful concepts ever invented in theoretical physics. Only, it's not some conformal invariance which is gauged but symmetries like the symmetry under multiplication of the quantum wave function with a phase or more general non-Abelian intrinsic symmetries like the color symmetry of the quark model. The former gauging of the U(1) symmetry indeed leads to the most accurate description electromagnetism by QED (or in the classical case to Maxwell's theory) and the latter to Quantum Chromodynamics, which also very successfully describes the strong interaction.

15. Aug 21, 2015

### Finny

Look here, Vanhees, it was your posts in another thread that got me into this morass:

Those posts got me thinking about this issue. And now you post that crazy Weyl stuff here!. However, that is exactly the sort of thing I was thinking about in laymen's terms. In 'The 'Road to Reality', Roger Penrose explains Weyl's early work [along the lines you posted] and even Einstein's comments to Weyl about it at the time. For anyone interested in more details, it is roughly from pages 444 to 453 or so in 'The Road to Reality'. That's where I left off yesterday trying to answer my own question.

Among other things Penrose points out that the varying histories of clocks and rulers you describe in Weyl's approach resulted from his attempt to encode electromagnetic potential into a bundle connection. In fact Einstein apparently Einstein objected to Weyl's approach and pointed out to him spectral frequencies, for example, would vary with history, would be path dependent. Penrose explains even a particle's mass would depend on it's history. And even crazier, the 'clock paradox' would not only involve different clock readings when clocks were brought back together, but the clocks would be ticking at different rates!

So it seems there is something, indeed, fundamentally distinct between electromagnetic and gravitational potential.

Thanks for your efforts to explain.

16. Aug 21, 2015

### Finny

17. Aug 22, 2015

### pervect

Staff Emeritus
I haven't read this whole thread, but I'll point out one thing about electromagnetism and gravity that is obviously different and not too technical - at least not on the surface. Gravity affects everything, while electromagnetism only affects objects with electric charge.

Even this simple observation turns out to need quite a bit of clarification and nit-picking. For one thing, we're only talking classically. If we wanted to cover the quantum realm, we'd have to properly categorize things like the Casimir force, something I'm not going to attempt in detail as my focus is classical.

The next point is that while uncharged objects don't experience any classical electromagnetic forces and do experience gravitational forces, charged objects experience both. Furthermore, the charge itself can (and does) have gravitational effects. So the conceptual separation is one-way, uncharged objects have gravity and not electromagnetism, while charged objects have both.

The second point is this - when a force affects literally everything, we can regard the force geometrically in a very natural manner, because geometry affects everything. Attempts to treat electromagnetism geometrically do exist - they haven't worked out for the most part, and it's more difficult (for me, at least) to imagine how geometry can affect some objects and not others.

Now, the third point. Gravity in general relativity causes effects other than forces, effects which are widely regarded and described as being geometrical in nature. For some obvious examples, consider gravitational time dilation. Electromagnetic forces do not cause time dilation (except insofar as they may cause additoinal gravitational effects). Time dilation is caused by gravity, and not by electromagnetism. Time dilation does not have a "force-based" explanation, it's a different class of effect.

Other geometrical effects exist in general relativity. The circumference (or surface area) of the space around a massive object can not be expressed as 2*pi*r where r is the radial distance. What's typically done is to define a coordinate "r" that describes a sub-space with a circumferene of 2*pi*r, and a surface area of 4 pi r^2. Given this definition of the r-coordinate, we then observe that the distance between two points is not dr, but a more complex expression, given by the Schwarzschild metric. We can summarize these observations conveniently by saying that the spatial slices of the Schwarzschild geometry are "curved".

To go further into why we say gravity is curvature, we'd need to go into what curvature is. Given that the OP has mentioned the Weyl tensor, I assume they have at least some exposure to the idea of curvature, though from the tone of the question I'm guessing there is still some uncertainity on their part about just what curvature entails. Regardless, I'm not going to attempt much in the way of a serious explanation of just what curvature is. What I will do is point out that GR is fundamentally based on this concept, in that the Riemann tensor is the mathematical description of curvature. Furthermore, the Einstein's field equations relate a tensor derived from the Riemann curvature tensor to a second tensor that describes the distribution of matter (the stress-energy tensor, which describes the distrubtion and density of energy and momentum).

Why the stress-energy tensor is the "right' tensor to describe the distribution of energy-momentum is also something I'm going to gloss over.

Underlying the concept of the stress energy tensor is the notion of why we talk about space-time, rather than space and time. In Newtonian physics, we talked about space, and time, as if they were separate. The origins of why we talk about "space-time" rather than space-time occur in special relativity. I think it would be too much of a digression to try to say why in this point we do this - and this post is already too long. But if it's not an understanding shared by the OP, it might be worth asking about this quesiton in a separate thread if there is some interest.

18. Aug 22, 2015

### Finny

pervect: Thanks for your insights...a nice summary of why we can't fit things together more neatly. As this thread
progressed I realized more and more there is no satisfactory answer to satisfy me since we don't have a 'theory of everything'.

I understand the distinctions you make and have always thought 'too bad we can fit those disparate pieces together in a unified framework'. This thread drove home that point for me again.

I am about to start a new thread in the next five minutes and we'll see what others think about: the "causal fermion system" a possible unifying theory I just saw for the first time yesterday. Maybe its a dud, maybe not.