# I Is a photon simply a vibration of the spacetime lattice?

#### Curiousphy

Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude, and the electron that creates it plucks a single lattice string rather than a bunch? Therefore it has no mass and travels differently through spacetime than massed entities, and it bends when the spacetime lattice bends near massive bodies...

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#### Drakkith

Staff Emeritus
2018 Award
Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude
No. Spacetime is not a lattice. A lattice is broadly defined as a repeated arrangement of something, such as atoms in a metallic lattice or a repeated arrangement of points in group theory. Spacetime is continuous and is not composed of repeated structures like a lattice is.

Photons are fully described by Quantum Electrodynamics, and no evidence has yet arisen suggesting it is inaccurate or incorrect. QED also cannot be combined with General Relativity at this time.

#### Ibix

No. For a start there is no "spacetime lattice". Spacetime is modelled as a smooth manifold.

A photon is an excited state of the electromagnetic field. A gravitational wave is part of spacetime, which you can view as a travelling wave. Light and gravitational waves are very different in a great many ways - notably one is a vector wave and the other a tensor wave.

They travel at the same speed (to the best of our knowledge) because $c$ is more or less the only available defined speed.

#### Curiousphy

So perhaps the use of the word "lattice" is incorrect or imprecise, but the generation of propagating EM waves also involves moving electrons in alternating directions, and it correlates with how electrons release photons during a state change. It is consistent how electrons can impart spatial ripples that propagate out at c. If spacetime consisted of anything, it would seem like electrons had the ability to cause a propagating vibration along an invisible spacetime "string" in the direction of the propagation. How do we rule out the possibility that spacetime itself was the medium for the energy propagation and that itself was vibrating?

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#### Orodruin

Staff Emeritus
Homework Helper
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2018 Award
Electromagnetism is sourced by the electromagnetic current, gravitational effects are sourced by the stress-energy tensor. They are completely different concepts. Comparing things that they do share in common just using words is not going to change that.

#### Ibix

How do we rule out the possibility that spacetime itself was the medium for the energy propagation and that itself was vibrating?
One of Einstein's key realisations was that you can model gravity as spacetime curvature because everything reacts the same way to gravitational fields. The same cannot be said of electromagnetic fields - particle paths curve one way or the other or not at all depending on their charge. That makes it extremely difficult to view electromagnetic phenomena as anything like gravitational ones.

I believe there have been attempts to include fields other than gravity in the structure of spacetime (Kaluza-Klein theory for example). I don't think they were ever really successful.

#### FactChecker

Gold Member
2018 Award
Gravity waves distort spacetime but light, or any electromagnetic wave, does not.

#### Dale

Mentor
How do we rule out the possibility that spacetime itself was the medium for the energy propagation and that itself was vibrating?
Easy. Waves that cause vibrations in spacetime as a medium are called gravitational waves. They are both theoretically and observationally distinct from electromagnetic waves.

Edit: @FactChecker for the win!

#### Ibix

Gravity waves distort spacetime but light, or any electromagnetic wave, does not.
Nitpick: gravity waves are a kind of surface wave on water. Gravitational waves are what you mean.

Less nitpicky, electromagnetic waves have a non-zero energy density, so do lead to spacetime curvature. I believe the relevant class of solutions are called pp-wave spacetimes and don't generally include gravitational waves, but know little beyond that. Given the actual energy densities of practical EM waves, this is entirely irrelevant to anybody except theorists. The difference with gravitational waves is that they don't cause spacetime curvature, they are spacetime curvature.

#### FactChecker

Gold Member
2018 Award
Is a photon simply a propagating vibration of the spacetime lattice similar to gravitational waves but at a different wavelength and amplitude,
You might be interested in this description of how gravity waves were detected. https://www.ligo.caltech.edu/WA/page/ligo-gw-interferometer
If light did anything like this, it would be detected all the time. Furthermore, the theoretical basis does not hint at any spacetime vibrations.

#### FactChecker

Gold Member
2018 Award
Nitpick: gravity waves are a kind of surface wave on water. Gravitational waves are what you mean.

Less nitpicky, electromagnetic waves have a non-zero energy density, so do lead to spacetime curvature. I believe the relevant class of solutions are called pp-wave spacetimes and don't generally include gravitational waves, but know little beyond that. Given the actual energy densities of practical EM waves, this is entirely irrelevant to anybody except theorists. The difference with gravitational waves is that they don't cause spacetime curvature, they are spacetime curvature.
I stand corrected.

#### Ibix

One more point about the difference between electromagnetic and gravitational waves. A plane electromagnetic wave normally incident on a ring of electrons will displace the ring bodily up and down, while a gravitational wave will deform the ring into an ellipse (or make it oscillate between two perpendicular ellipses, more precisely). The electromagnetic wave and its effects are symmetric under 360° rotation, while the gravitational wave and its effects are symmetric under 180° rotation. This reflects differences in the way the electromagnetic and gravitational fields work which impose different constraints on what sources and waves can look like.

#### WWGD

Gold Member
No. For a start there is no "spacetime lattice". Spacetime is modelled as a smooth manifold.

A photon is an excited state of the electromagnetic field. A gravitational wave is part of spacetime, which you can view as a travelling wave. Light and gravitational waves are very different in a great many ways - notably one is a vector wave and the other a tensor wave.

They travel at the same speed (to the best of our knowledge) because $c$ is more or less the only available defined speed.
Vectors and tensors are equivalen/isomorphict when there is a metric; any relationship between the two in this respect?

#### Dale

Mentor
Vectors and tensors are equivalen/isomorphict when there is a metric; any relationship between the two in this respect?
In this context "vector" means "rank 1 tensor" and "tensor" means "rank 2 tensor"

#### WWGD

Gold Member
In this context "vector" means "rank 1 tensor" and "tensor" means "rank 2 tensor"
Thanks, I mean, are light and gravitational waves dual to each other under this equivalence? EDIT: Apologies if I am derailing the thread, I can ask this as a stand-alone if that is best.

#### DaveE

So perhaps the use of the word "lattice" is incorrect or imprecise...
Precision matters in formulating a question that will produce answers that satisfy your underlying curiosity.
This is one of the key things that distinguishes popular science from real science.

#### Dale

Mentor
Thanks, I mean, are light and gravitational waves dual to each other under this equivalence? EDIT: Apologies if I am derailing the thread, I can ask this as a stand-alone if that is best.
No. Rank 1 and rank 2 tensors are not dual to each other. Covariant tensors are dual to contravariant tensors of the same rank.

#### Ibix

Thanks, I mean, are light and gravitational waves dual to each other under this equivalence? EDIT: Apologies if I am derailing the thread, I can ask this as a stand-alone if that is best.
Not as far as I know. Gravity, including gravitational waves, is the metric, while the electromagnetic field is a field on top of spacetime.

#### Ibix

No. Rank 1 and rank 2 tensors are not dual to each other. Covariant tensors are dual to contravariant tensors of the same rank.
I think we probably are getting off topic, but there are dualities such as the Hodge dual that relate tensors of different ranks. The Hodge dual of a rank $k$ tensor is of rank $n-k$, where $n$ is the dimension of the space - four, in GR. And, in my (limited) understanding, it's just mathematical playing around in the same sense as index raising and lowering. Potentially very useful, yes, but taking the dual (any dual) of a vector does not change the physics. An electromagnetic wave still moves the ring of charges I was talking about bodily up and down, whether you describe the electric field as a vector or as its dual (Hodge or otherwise).

#### pervect

Staff Emeritus
Thanks, I mean, are light and gravitational waves dual to each other under this equivalence? EDIT: Apologies if I am derailing the thread, I can ask this as a stand-alone if that is best.

There are several tensors involved, I would point to the rank 2 Faraday tensor, and it's dual, the rank 2 Maxwell tensor, as the source of electromagnetic radiation in flat space-time in a 4-tensor treatment. Components of these tensors include the electric and mangetic fields, which satisfy the wave equation. See for instance <<wiki link>>.

You'll note that components of this rank 2 Faraday tensor are the electric and magnetic fields. In the 4-tensor treatment of electromagnetism, which I would call the "realtivistic" treatment, the electric and magnetic fields are not rank 1 tensors (vectors) themselves. This may not be familiar, unfortunately - a detailed explanation of the 4-tensor treatment is beyond the scope of what I want to write, though learning about the Faraday tensor, which I've linked to, would be the first step.

For gravitational waves, what satisfies the wave equation is the metric tensor. This is something completely different than either the Faraday or Maxwell tensors.

These are the most important tensors, but there are a bunch more that one might wish to use. For gravitation, one can derive the rank 4 Riemann tensor from the metric tensor, from the rank 4 Riemann tensor one can derive the rank 2 Ricci tensor and the rank 2 Einstein tensor, which gives Einstein's field equations $G_{\mu \nu} = 8 \pi T_{\mu \nu}$. Here $G_{\mu \nu}$ is the Einsten tensor, $T_{\mu \nu}$ is the stress-energy tensor.

The electromagnetic contribution to the total stress-energy tensor, the "electromagnetic stress-energy tensor", can be computed from the Faraday tensor, see for instance <<yet another wiki link>>.

So, electromagnetic fields (incuding electromagnetic waves) have a stress-energy tensor (computable from the Faraday tensor) which is an incomplete part of the total stress energy tensor $T_{\mu\nu}$ in Einstein's field equations.

Einstein's field equations themselves involve $G_{\mu \nu}$, the Einstein tensor, computed from the metric tensor $g_{\mu \nu}$, and the stress-energy tensor $T_{\mu \nu}$. The stress-energy tensor is not very intuitive, but it's the key element as being the "source of gravity", replacing the idea of "mass" as the source of gravity in Newtonian theory.

#### Curiousphy

One more point about the difference between electromagnetic and gravitational waves. A plane electromagnetic wave normally incident on a ring of electrons will displace the ring bodily up and down, while a gravitational wave will deform the ring into an ellipse (or make it oscillate between two perpendicular ellipses, more precisely). The electromagnetic wave and its effects are symmetric under 360° rotation, while the gravitational wave and its effects are symmetric under 180° rotation. This reflects differences in the way the electromagnetic and gravitational fields work which impose different constraints on what sources and waves can look like.
Could this be because gravitational waves are longitudinal while EM waves are transverse?

#### PeterDonis

Mentor
Could this be because gravitational waves are longitudinal
No, because they aren't, they're transverse.

#### Ibix

Could this be because gravitational waves are longitudinal while EM waves are transverse?
No. Longitudinal waves would bodily displace the ring of electrons backwards and forwards. Gravitational waves are transverse tensor waves - the gravitational field won't support longitudinal waves or transverse vector waves (at least in vanilla GR, and I believe most variants that allowed other kinds of wave were ruled out with some certainty by analysis of the LIGO detections). The electromagnetic field, in contrast, won't support longitudinal waves or transverse tensor waves.

And there's still the fact that a gravitational wave will stretch-and-squish a ring of free-floating anythings in the same way. But an electromagnetic wave will displace negative charges up and down, positive charges down and up, and neutral objects not at all. Electromagnetic and gravitational waves really cannot be different kinds of the same thing, except in the very broad sense that they are both waves.

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#### Curiousphy

OK, thank you all. You've convinced me that EM waves and gravitational waves are different; however, many questions remain... for example, do EM waves and/or matter displace spacetime, or are they manifestations of the properties of spacetime itself? (in other words, are they in it, or part of it? I guess they could be in it but not "displace" it, too, in a "superposed" manner) if they are "in" it, can they theoretically exist outside of it?

#### Dale

Mentor
It feels like these questions are just pure speculation. As far as I know there is no standard meaning for the term “displace spacetime”.

Usually when scientists speak of a quantity we first think of either a way to measure it or to calculate it from other measurable quantities. We give it a name afterwards. So when you say “displace spacetime” can you describe the measurement you could use to determine the amount of spacetime displacement or the formula you would use to calculate it?

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