Gravitational vs. Electromagnetic Waves: What's the Difference?

[accdd]

in a nutshell what are the differences between gravitational and electromagnetic waves?

 

[Dale]

Gravitational waves obey the Einstein Field Equations and electromagnetic waves obey Maxwell’s Equations.

That is the "in a nutshell" difference. If you change your mind and decide that you would like more details for the answer, then please provide more details for the question.

 

[Lord Jestocost]

"Gravitational waves, similarly, are generated by the bulk motion of large masses, and will have wavelengths much longer than the objects themselves. Electromagnetic waves, meanwhile, are typically generated by small movements of charge pairs within objects, and have wavelengths much smaller than the objects themselves."

http://www.tapir.caltech.edu/~teviet/Waves/differences.html

 

[accdd]

Dale, for example:
-I read that gravitational waves have a relationship with the quadripole, while electromagnetic waves have a relationship with the dipole.
-I have read that gravitational waves permanently distort spacetime
-I have read that there are differences related to polarization
-are there phenomena that happen with gravitational waves and do not happen with electromagnetic waves and vice versa?
I am studying relativity from Schutz's book.

 

[berkeman]

Dale, for example:
-I read that gravitational waves have a relationship with the quadripole, while electromagnetic waves have a relationship with the dipole.
-I have read that gravitational waves permanently distort spacetime
-I have read that there are differences related to polarization
-are there phenomena that happen with gravitational waves and do not happen with electromagnetic waves and vice versa?
I am studying relativity from Schutz's book.

So would it be accurate to say that you already know a lot about EM waves and are just now learning about Gravitational waves? Or are you just now learning about both?

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

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

 

[Dale]

I read that gravitational waves have a relationship with the quadripole, while electromagnetic waves have a relationship with the dipole.

Yes, the minimum order of gravitational radiation is quadrupole, and gravitational waves are emitted for a system with a changing quadrupole moment of the sources. For EM it is dipole radiation and changing dipole moments of the sources.

-I have read that gravitational waves permanently distort spacetime

That doesn’t have any relationship to EM waves that I can see, but no, I don’t think that is a correct statement.

I have read that there are differences related to polarization

Yes, EM waves can be horizontally or vertically polarized which are 90 deg apart, but GW can be plus or cross polarized which are 45 deg apart.

 

[PeterDonis]

I read

Where?

-I have read

Where?

-I have read

Where?

 

[accdd]

PeterDonis:
-Here, Feynman lectures on physics vol 2, Baez site "Does gravity travel at the speed of light", introduction to electrodynamics Griffiths
-quanta magazine "gravitational waves should permanently distort space-time"
-introduction to electrodynamics Griffiths (for electromagnetic waves), wikipedia
I know some special relativity and some electrostatics/electrodynamics

 

[PeterDonis]

quanta magazine "gravitational waves should permanently distort space-time"

This is not a valid reference. Do you have a link to an actual peer-reviewed paper?

wikipedia

This is not a valid reference either.

Also, when you are asked for references, in general, you should give links, if the source is available online. (Even the Feynman lectures are available online now, in HTML form.)

 

[Dale]

This is not a valid reference either.

Wikipedia is OK to reference as long as it is consistent with the professional scientific literature. I have certainly referenced it before.

Of course, when one doesn't know the literature then it makes excessive reliance on Wikipedia a little risky.

 

[accdd]

I see. But I am a student, I am not yet able to read a scientific paper. How do I know if a reference is valid?

 

[berkeman]

I see. But I am a student, I am not yet able to read a scientific paper. How do I know if a reference is valid?

You can start with the guidelines listed in the PF Rules link (see INFO at the top of the page):

Acceptable Sources:
Generally, discussion topics should be traceable to standard textbooks or to peer-reviewed scientific literature. Usually, we accept references from journals that are listed in the Thomson/Reuters list (now Clarivate):

https://mjl.clarivate.com/home

Use the search feature to search for journals by words in their titles.

In recent years, there has been an increasing number of "fringe" and Internet-only journals that appear to have lax reviewing standards. We do not generally accept references from such journals. Note that some of these fringe journals are listed in Thomson Reuters. Just because a journal is listed in Thomson Reuters does not mean it is acceptable.

References that appear only on http://www.arxiv.org/ (which is not peer-reviewed) are subject to review by the Mentors. We recognize that in some fields this is the accepted means of professional communication, but in other fields we prefer to wait until formal publication elsewhere. References that appear only on viXra (http://www.vixra.org) are never allowed.

 

[PeterDonis]

I am a student, I am not yet able to read a scientific paper.

Sure you can. You might not be able to follow all of one, but it will still give you a much better basis for asking questions than a pop science article.

 

[PeterDonis]

Wikipedia is OK to reference as long as it is consistent with the professional scientific literature.

Agreed, but in order to assess that, we need to have an actual link to a specific Wikipedia article. In this case we don't, we just have "wikipedia". (And it's listed after Griffiths, which is a much better reference anyway than any Wikipedia article.)

 

[Vanadium 50]

I am not yet able to read a scientific paper.

So you don't even try? That's just sad.

 

[vanhees71]

Just to answer the physical question.

There are many similarities with electromagnetic waves and gravitational waves but also some important differences. One can understand them best when first looking at the weak-field approximation of the gravitational waves, because then we deal with linear equations of motion as in the case of the electromagnetic field.

The discussion in both cases is somewhat complicated by the fact that both the electromagnetic field and the gravitational field are described as a gauge theory. That's a feature of all possible kinds of massless relativistic fields with a "spin" that is $s geq 1$.

Let's start with the electromagnetic waves. It is a massless vector field. The most natural description of a vector field is, not surprisingly, to use a four-vector field $A^{\mu}(x)$. However, as is well known from phenomenology, these so-called "four-potential" is not uniquely defined by the dynamical field equations, which are the Maxwell equations for the electromagnetic field, which is given by the antisymmetric Faraday tensor $F_{\mu \nu}=\partial_{\mu} A_{\nu}-\partial_{\nu} A_{\mu}$, which has 6 independent components, which in a given reference frame are related to the electric and magnetic field components $(\vec{E},\vec{B})$. However, it's more convenient to work further in the 4D formalism: It's immediately clear that with each $A_{\mu}$ for any scalar field $\chi$ also $A_{\mu}'=A_{\mu}+\partial_{\mu} \chi$ describes the same physical situation, because
$$F_{\mu \nu}'=\partial_{\mu} A_{\nu}'-\partial_{\nu} A_{\mu}'=\partial_{\mu} A_{\nu} + \partial_{\mu} \partial_{\nu} \chi -\partial_{\nu} A_{\mu} - \partial_{\nu} \partial_{\mu} \chi = \partial_{\mu} A_{\nu} - \partial_{\nu} A_{\mu} = F_{\mu \nu}.$$
Now with the introduction of the potentials the so-called "homogeneous Maxwell equations" are fulfilled, and we must only fulfill the "inhomogeneous Maxwell equations", which in 4D form read
$$\partial_{\mu} F^{\mu \nu}=j^{\nu},$$
where $j^{\nu}=(\rho,\vec{j})$ is the electromagnetic four-current ($j^{0}=\rho$ the electric-charge density and $\vec{j}$ the current density of the charges). Since we want to study free waves, we set $j^{\nu}=0$. Using the potentials the equation reads
$$\partial_{\mu} \partial^{\mu} A^{\nu} - \partial^{\nu} \partial_{\mu} A^{\mu}=0.$$
Now we have the freedom to impose an arbitrary constraint, because of the gauge freedom. The most convenient constraint, the so-called Lorenz-gauge constraint is
$$\partial_{\mu} A^{\mu}=0,$$
which is manifestly covariant and also decouples the equations for the four vector-field components to
$$\partial_{\mu} \partial^{\mu} A^{\nu}=\Box A^{\nu}=0.$$
This is the wave equation for each of the four components.

Now we consider plane waves propagating in the 3-direction of our reference frame:
$$A^{\mu} = a^{\mu} \exp(-\mathrm{i} k_{\alpha} x^{\alpha})+\text{c.c.}, \quad \vec{k}=(0,0,k^3).$$
Then the wave equation dictates that
$$k^0=|\vec{k}|=k^3 \; \Rightarrow \; k_{\mu} k^{\mu}=0.$$
The gauge constraint further implies that
$$\partial_{\mu} A^{\mu} = -\mathrm{i} k_{\mu} a^{\mu} \exp(-\mathrm{i} k_{\alpha} x^{\alpha}) = 0,$$
i.e.,
$$k^0 a^0-k^3 a^3=0.$$
This means that
$$(a^{\mu})=(a^3,a^1,a^2,a^3).$$
Now our gauge freedom is not yet fully exploited, because in this case of free fields we can use another gauge transformation
$$A_{\mu}'=A_{\mu} +\partial_{\mu} \chi,$$
for any scalar function with $\Box \chi=0$ without destroying the solution of the free wave equation. Using
$$\chi=\chi_0 \exp(-\mathrm{i} k_{\alpha} x^{\alpha})$$
leads to
$$(a^{\prime \mu})=(a^3-\mathrm{i} \chi_0 k^0,a^1,a^2,a^3-\mathrm{i} \chi_0 k^3).$$
Since we can choose $\chi_0$ arbitrary we may set $\mathrm{i} k^0 \chi_0= a^3$, which leads to
$$a^{\prime \mu}=(0,a^1,a^2,0).$$
We have two independent transverse polarizations as expected for em. waves.

The most convenient choice for the two polarization modes is given by the behavior of the field under rotations around $\vec{k}$. As it turns out these are given by $(a^1,a^2)=(1,\pm \mathrm{i})$ which transform under rotations around the 3-axis as $A^{\mu} \rightarrow \exp(\pm \mathrm{i} \varphi) A^{\mu}$, which tells us the we have two field modes corresponding to helicity $\pm 1$.

In the same way one can discuss the linearized free Einstein equations, i.e., one considers a metric
$$g_{\mu \nu}=\eta_{\mu \nu}+h_{\mu \nu},$$
where $h_{\mu \nu}$ is considered as "small", such that one only needs to consider the terms in first order of $h_{\mu \nu}$ and its derivatives in the free Einstein equations (with "free" I mean in a region of spacetime with $T_{\mu \nu}=0$).

In GR the physics doesn't change under arbitary spacetime-coordinate transformations ("general covariance"), i.e., an arbitrary coordinate transformation doesn't change the physics. Here we have to consider "infinitesimal coordinate transformations" only, because we are only interested in cases, where the new $h_{\mu \nu}'$ are "small" as the original ones. Using the usual tensor transformation law
$$g_{\mu \nu}'=g_{\rho \sigma} \frac{\partial x^{\prime \rho}}{\partial x^{\mu}} \frac{\partial x^{\prime \sigma}}{\partial x^{\nu}},$$
implies that the "gauge transformation" for the $h_{\mu \nu}$ gets
$$h_{\mu \nu}'=h_{\mu \nu} + \partial_{\mu} \epsilon_{\nu} + \partial_{\nu} \epsilon_{\mu}$$
with an arbitrary four-vector field $\epsilon_{\mu}$.

It then turns out that you can use an analogous two-step "gauge fixing" procedure as in the electromagnetic case, leading at the end again to the conclusion that there are only 2 independent polarization modes, and again the helicity eigenmodes are the most natural choice. It turns out that the helicity of gravitational waves is 2, which is the one profound difference between em. and gravitational waves as far as this linear-approximation analysis of the gravitational waves is concerned: The em. field is a massless spin-1 (vector) field, the grav. field a massless spin-2 (tensor) field.

You can also investigate the question, how the em. and gravitational waves are generated from their sources (the em. four-current $j^{\mu}$ or the energy-momentum tensor $T^{\mu \nu}$ for the gravitational waves), and you can discuss the multipole expansion in both cases (for the gravitational waves again in the linear approximation), and it turns out that for the em. waves "non-zero modes" (i.e., real waves not static Coulomb fields) there is no contribution from a "monopole source", i.e., you need at least a time-dependent dipole distribution of charges and currents. For the gravitational waves you find out that both the monopole and the dipole sources don't lead to gravitational waves, i.e., you need at least a time-dependent quadrupole moment of energy and momentum.

 

[berkeman]

Just to answer the physical question.

There are many similarities with electromagnetic waves and gravitational waves but also some important differences. One can understand them best when first looking at the weak-field approximation of the gravitational waves, because then we deal with linear equations of motion as in the case of the electromagnetic field.

@vanhees71 -- Would you consider authoring an Insights article based on this post?

 

[vanhees71]

I can do that, but it'll take some time. Today the Summer Semester started :-)...

 

[Frabjous]

I can do that, but it'll take some time. Today the Summer Semester started :-)...

Summer?

 

[robphy]

I can do that, but it'll take some time. Today the Summer Semester started :-)...

Summer?

apparently ends in mid-July...

 

[vanhees71]

In Germany we have "winter semesters" (Oct-Feb) and "summer semesters" (Apr-Jul).