swell ... wave

Someone had fun writing that headline.

No doubt they will "crest" just before the announcement :-). And opinions will "undulate" over whether or not they are valid results.

Perhaps we just need more drama in science classes to be more inclusive, "Will this acid change the Ph level of the solution? Or will its buffering protect it? Find out after the break ..."

As a non-science person who occasionally watches PBS documentaries, could this have any implications for Hawking radiation?

My understanding is that black hole mergers are not expected to have any optical-wavelength emissions, whereas neutron star mergers should have emissions across the electromagnetic spectrum. Is that distinction part of the excitement here?

Mostly but also because we haven’t “heard” the waves caused by a Neutron star interaction before. So experimentally we still have to confirm that they cause GWs.

Which would be surprising if they didn't produce GW

Of course they produce gravitational waves! The main point of curiosity is likely that unlike black holes, that are "hairless" entities of pure curvature, neutron stars are complex objects with multiple, variable layers... and consequentially (I presume) the gravitational waves occasioned by their merger would both carry more information about the objects' composition and likely be more complicated (as well as less powerful at any given distance).

I'm just guessing though.

The matter and light radiated away from black hole (BH) mergers will all come from the accretion discs of each BH. The accretion discs of the BH masses for which LIGO (and Virgo) is most sensitive will generally be fairly sparse, so the emissions will generally be fairly dim.

For a pair of similar-mass neutron stars (NS) that merge into a BH, you can treat region of spacetime close to the merger as being filled with extremely dense accretion discs. The density of matter leads very bright emissions, and the available geodesics produce radiation that will escape to infinity rather than being quickly absorbed close to the source (including within the dense matter around the newly formed BH as it settles into an accretion disc). The picture is slightly different where the NS masses are highly unequal.

The Max Planck Institute for Gravitational Physics at Potsdam Germany has done many numerical simulations of NS mergers. NASA's animated one [1] where the NS are of substantially different masses:

https://www.youtube.com/watch?v=vw2sLcyV7Vc

Systems of mass that are barbell-shaped (a pair of heavy masses connected via an arbitrarily thin bar; for orbiting stars and BHs we take the limit as the bar goes to zero volume and zero mass) will radiate gravitational waves when they are spun about an axis on an axis perpendicular to the bar. These spinning NSes will be radiating gravitational waves with increasing amplitude, and these radiated GWs remove angular momentum from the rotating system, allowing the NSes to move closer to each other. By the start of the video, the GW radiation being emitted should eventually be detectable by instruments at enormous distances; that radiation has allowed the two NSes to reach a critical proximity.

At this point the smaller NS disintegrates under tidal stress and its additional mass-energy-momentum that then begins falling onto the larger NS causes the larger NS to collapse into a BH. A large proportion of the smaller NS remains in the region near the new BH and is swept up into an accretion structure alsong with s small proportion of the larger NS that did not get trapped behind the horizon. The accretion structure is briefly very bright, especially in gamma rays, as the matter from the smaller neutron star self-collides until it is entrained into a dense disc. Those early gammas will be visible at enormous distances (e.g. we can pick up extragalactic NS mergers with sky-scanning instruments searching for gamma ray bursts [2]).

By comparison, the smaller of a pair of mass-mismatched black holes cannot disintegrate (everything is stuck within each BH's horizon), and the larger of the pair is likely to have a sparser accretion disc, so the amount of disc-disc collision will be relatively low. The reshaping of the accretion material around the merged BHs may be driven principally by the dynamical spacetime around the BH, with only occasional collisions. While such collisions can be arbitrarily energetic (at the point where their geodesics intersect bits of matter may be moving ultrarelativistically with respect to each other), there are unlikely to be enough such emissions to be reliably detectable at large distances.

- --

[1] https://arxiv.org/abs/1001.3074

[2] There is a timing-coincidence argument about a short gamma ray burst detected in this way and a detection by LIGO & Virgo that is circulating around the rumour mill. Peter Coles blogged some detail https://telescoper.wordpress.com/2017/08/23/ligo-leaks-and-n... This may be an NS-BH merger, in which the picture is again somewhat different, and depends on the density of the BH's accretion disc both in terms of its matter content and in terms of the momentum (e.g. if the NS and BH are counter-rotating, collisions will be more frequent and more energetic).

This might be a naive question, but I'd like to clear it out.

Do gravitational waves travel at the speed of light?

I know the theory says nothing can travel faster than light. I also know that photons can be seen as quanta or as waves. So my guess is that gravitational waves travel at most, at the speed of light.

But do they? or do they travel slower? faster? Is there a doppler effect for GWs?

I ask because I would think ripples in the space-time fabric itself might be a bit different than light waves or other more studied phenomena.

Can anyone point me in the right direction?

The most popular theories say that yes, they do travel at the speed of light. Only a coincident detection of a gravitational wave and an electromagnetic counterpart would confirm this (such as from a binary neutron star coalescence; the binary black holes seen so far by LIGO didn't emit any visible EM as far as we know).

Would even a binary neutron star coalescence give us the information we'd need to answer this? Interstellar space is not actually empty. It contains a low density plasma, and so the speed of light in it is slightly slower than the speed of light in a vacuum.

I have no idea if that plasma would also slow down gravity waves, but even if it does it wouldn't necessarily be the same amount [1].

Maybe from the differences in arrival time of light at different frequencies we could figure out enough about the intervening plasma to figure out when the light would have arrived if the space had been empty, and check if that is when the gravity waves arrived?

[1] Edit: I have done some Googling. Gravity waves would not be slowed down by the interstellar plasma. The slowdown of light through a medium depends on the existence of positive and negative charges in the medium that can form dipoles in response to the passing electromagnetic wave. For gravity all the "charges" are positive so there is no dipole formation.

We could build a second detector, sync their clocks, separate them, and measure the speed directly.

Check out LIGO episode of PBS SpaceTime youtube channel. Some very informative explanitions about gravity waves are given there.

+1 for PBS SpaceTime, easily one of the best channels on YouTube. Gravitational wave episodes:

https://www.youtube.com/watch?v=1Tstyqz2g7o

https://www.youtube.com/watch?v=gw-i_VKd6Wo

https://www.youtube.com/watch?v=eJ2RNBAFLj0

The speed of light is sometimes referred to as the speed of causality, and it seems like it's more of a fundamental speed limit on the propagation of events or information through space.

IIRC, everything moves through spacetime at c. Things with mass like people, planets, etc, move through the time portion as well as the space portion. As you go faster through space, you travel less through time, though at non- relativistic speeds you don't notice (GPS satellites do have to account for this). Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light."

Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space, so we say they travel at the "speed of light."

This part comfuses me. If they don't travel in time, how do they have a speed? Light is a type of electromagnetic wave right? And it takes many years to travel to us from a nearby star.

If we can measure or calculate the time it takes for light from some place to reach us, does that not imply traveling through time?

Think about a wave on a lake. It may appear to be moving in time. The water particles certainly move up and down. But if nothing is in it's "path" is the wave really moving? It's actually just there, the wave undulates and that creates the perception of motion, but really the thing you see moving is just a visual effect on the surface of a field the size of the entire lake. A field which is not moving at all.

Photons are similar. You see the peak of the wave moving around, but the wave itself is everywhere and eternal... until other forces get involved anyway.

This picture is incorrect: the electromagnetic wave has a mechanical momentum in the direction of its propagation, which means that something is moving in that direction.

Does it have momentum before we measure it? I thought momentum was a property of the collapse event, not a property of the wave?

Another way to think about it, is how time effects the object itself.

Photons are completely immutable, while they travel they don't change at all, if a photon was a "smergsboard" it would remain "smergsboard" during the whole trip.

One of the most interesting ways I saw explaining this, is imagine 'spacetime' as a cartesian space.

You have 4 axis, X, Y, Z and time.

EVERYTHING has speed of 'c', so you use trigonometry and rotations to figure the values, light, that have a speed of 'c' in the 3 space axis, then obviously have speed of '0' in time axis.

----

Now, one interesting application of that knowledge is how they figured the speed of neutrinos... As I just wrote, if something is travelling at speed of light, it is 'frozen', never changing...

But 10 years or so ago people figured that neutrinos change mid-flight, there are 3 (or more... people are unsure yet) 'flavors' of neutrinos, and during tests people noticed that even if you make a machine that generates only one specific flavor, what reaches on the other side is not necessarily that flavor, meaning they changed mid-flight...

But if they change, then they have some speed in 'time', this means then that the speed in space must be smaller than light.

Right now there are couple experiments where people are trying to use the changes in neutrinos to calculate their speed in 'time', and then by elimination figure their speed in space. I find it quite interesting, how people can use math to figure physics when our instruments aren't precise enough.

photons don't freeze in time in their own reference frame, and one doesnt get to priviledge any particular reference frame including those that are different from the photon's

The (proper) time interval between any two points along a null geodesic is zero. I see nothing wrong with calling photons frozen in time.

no,the "Spacetime Interval" along a null geodesic is 0, but a null geodesic "does not have a Proper Time associated with it". Undefined is not the same as 0. "For lightlike paths, there exists no concept of proper time and it is undefined as the spacetime interval is identically zero. "

It's fine to be confused, because the idea that "photons don't experience time" is physically meaningless.

If you plug c into the Lorentz transformation you get an infinity, which doesn't tell you anything particularly useful.

There's no physical way to accelerate to light speed, so it's meaningless to make assertions about how the "experience" of travelling at light speed would be different to the (presumably simpler) experience of travelling at < c.

The problem is that relativity is a classical theory, and it says nothing about the underlying physical processes of photon creation/destruction and propagation.

Maybe one day a Theory of Quantum Gravity will fix that problem and provide a detailed low-level picture of what actually happens when things move through spacetime. But we're not going to get there for a while.

In the meantime, we'll carry on using concepts like "position" and "time" without really understanding the mechanisms that generate them.

And if that sounds obvious, it really isn't. It's astounding that the universe knows where everything is and where it's going. Not only does it somehow keep track of all those changing spacetime relationships within a self-consistent system, but it also generates the counterintuitive geometry described by relativity.

How does it do that? No one knows.

But some believe it's God who does this.

This sounds a lot like the common "God of the gaps" argument that Hitchens and others describe, in which a deity or deities are supposedly invoked to explain what we do not yet understand.

Yet it is fascinating that (1) any system of thought (including science itself) must rely on axioms; (2) by Godël's incompleteness theorem, no system of thought can prove its own axioms; and (3) thus it would seem that faith is inescapably required to believe in anything at all.

When evaluating world views, perhaps the best metric is to evaluate which of them requires the least faith.

For my part, when considering the known universe's mere existence, atheism seems to require a lot more faith than theism.

Another way to look at it, is a requirement to accept uncertainty - the existence of unknowns - or indeed "unknowables".

To each their own - but I don't see "There are some things we cannot describe in our system of knowledge" as a particularly strong proof for the existence of God.

Perhaps some of us have been imbued with an unhealthy and naive lust for certainty, in part by an education system that put an emphasis on right and wrong answers rather than on the quest for better questions?

atheism seems to require a lot more faith than theism.

There is a world of difference between thinking something caused our universe to exist and perhaps giving it the name "god", and believing in a specific god or specific claims about any god.

everything moves through spacetime at c

No. Everything has its own worldline through spacetime, and between two events at point p and q on a worldline through a given spacetime we can measure the interval dS between p and q. When we normalize the interval against a set of coordinates and a chosen metric signature (here +++-) we can have three types of interval: dS^2 = 0 is lightlike, dS^2 > 0 is spacetlike and dS^2 < 0 is timelike.

A concrete example using the Minkowski metric for a set of Cartesian coordinates dS^2 = dx^2 + dy^2 + dz^2 - cdt^2. If we have a test object that always remains at the (x=0,y=0,z=0) origin of the coordinates then as the "t" coordinate increases with the passage of time, -cdt^2 is the only nonzero component of dS^2. From t=0 to t=10000 (where t is in, say, seconds) is perfectly timelike interval. However, any way we vary x, y, and z, (measuring the coordinate distances in, say, light-seconds) if the changes are small compared to the constant factor c, we will have a timelike interval. Light itself, conversely, follows a lightlike interval. If we restrict a beam of light to move only on the x axis, then we have (in (light-)seconds and seconds) x=c, t=1; x=2c, t=2; x=3c, t=3; and so forth; the -c factor cancels out the change in x at each step, so dS^2 = 0.

But bear in mind here that the Minkowski metric is just one of many known exact solutions to the Einstein Field Equations, and there are many many many known approximate solutions. Moreover, we are free to use arbitrary coordinates. The Minkowski metric looks different in spherical polar coordinates, for example. We are also free to use arbitrary units. We can even use the metric signature (-,-,-,+) if we like. However, when we take all of these into account, we're left with the same distinction based on the interval: they're either lightlike, timelike, or spacelike.

A lightlike worldline is one in which intervals on the worldline are always light-like; a timelike worldine is one in which intervals on the worldline are always spacelike.

We have strong evidence and stronger theoretical reasoning to expect that massless objects will always have lightlike worldlines (and that light itself is massless) while massive objects will always have timelike worldlines.

So:

Electromagnetic waves have no mass, they don't travel in time, so the entire portion of their travel takes place in space

No, they have lightlike worldlines. An interval between any two points on the wave's worldline will be lightlike. This generally means that changes in the spacelike coordinates will exactly match the change in the timelike coordinate multiplied by the constant factor c. However, under most reasonable choices of coordinates, the "t" coordinate will certainly vary from point to point along its worldline.

However, one has free choice to decide which axis is timelike or spacelike, and different choices may seem like the natural ones to different observers.

In order to cope with these sets of choices we write down the laws of physics in a generally covariant manner. This has been one of the greatest successes of relativity; any proposed theory that cannot be written down in generally covariant form is almost certainly unphysical in some way.

Lastly, the value of "c" is determined empirically, and will vary depending on one's choice of units. Relativists will often use a system of units in which c is set to unity (c=1), for example, in order to simplify the form of equations.

(GPS satellites do have to account for this)

The theory side of GPS relies upon covariance matrices.

Can you recommend a book/resource that explains this from first principles and introduces the math involved as well? The books I've read either exclude math altogether or if they don't, they assume that reader already knows and understands all the math that is required for this.

That's a rather impenetrable, buzzword-laden way of saying exactly the same thing as the grandparent post: everything moves through spacetime at c, which is a velocity expressed as a 4-vector of constant length. Increase one component and the others have to decrease to maintain the length.

Put all your velocity into the time component and you can't move in space. Conversely, if you put all of your velocity into the spatial components, you will freeze in time like a photon.

photons don't freeze in time in their own reference frame, and one doesnt get to priviledge any particular reference frame including those that are different from the photon's

At what velocity a photon moves "in its own reference frame"?

exactly, my point being whether one can say the photon is frozen in time or not is relative

It's not buzzwords, it's jargon. Speaking as a physicist, here, it also reeks of someone trying to show off GR101 skills.

It's like a CS guy responding to "hashtables are O(1) lookup" with a wall-of-pedantry about different implementations, complete with complexity analysis by evaluation of recursion equations and whatnot.

You are terrible at explaining things and are correcting someone who actually explained it much better than you, even if he is technically incorrect. Your jargon laden overly verbose response is wildly out of place in correcting a simple layman level description of something. It's not appropriate to respond to a simple metaphor by slinging general relativity equations, you've probably instantly turned off anyone reading this from your position and at the end of the day you aren't really saying anything different, you're just trying to sound smart. If you are saying something differently, you've utterly failed to communicate it in any reasonable way.

slinging general relativity equations

I'm sorry this instantly turned you off.

The only equation in my comment is the Minkowski metric which is the metric for Special Relativity, and should be familiar to everyone who has done any SR at all.

Moreover, it's just a a generalization of the Euclidean metric as follows:

The Euclidean interval for

  spatial
  dimension equation for Cartesian coordinates in flat space
  0         dS^2 = 0
  1         dS^2 = dx^2
  2         dS^2 = dx^2 + dy^2
  3         dS^2 = dx^2 + dy^2 + dz^2

What we do differently in spacetime is add in a term with the opposite sign:

  (mostly-plusses, flat spacetime)
  spacetime
  dimension equation for Cartesian coordinates 
  2         dS^2 = dx^2 - cdt^2
  3         dS^2 = dx^2 + dy^2 - cdt^2
  4         dS^2 = dx^2 + dy^2 + dz^2 - cdt^2

Which shouldn't really scare anyone who has done Euclidean geometry.

The interesting difference is this: in Euclidean space, straight paths are shorter than curved paths, but in flat spacetime, it is curved paths that are shorter.

If you prefer wikipedia, https://en.wikipedia.org/wiki/Spacetime#Spacetime_interval which you can edit, or perhaps you can add to the Spacetime page on the simple English wikipedia.

gnaritas is being pretty hard on you and shouldn't resort to ad-hominem, e.g. saying you are terrible at x. I think you obviously care a lot about this topic and actually have a lot to offer.

I will offer a perspective on this exchange...

I think people who have survived many-many math based courses often have an immediate and aggressive response to diving into the minutae of a quantitative topic before they have grokked the intuition behind it. This is a defence mechanism built up from hours and hours of wasted time in lectures where the topic has moved on before the student/s have really developed the basics and are ready for the detailed stuff.

Hours and hours of wasted life.

When a person with this defence mechanism sees a noobie about to fall into the same horrible cycle, this will trigger some aggression. For example: downvoting your post- they are trying to protect the noobs.

So if you are interested in reaching as many people as possible, please don't give up. I think your teaching effectiveness could be improved by finding ways to engage people at their (lower) level of understanding and trying to help then incrementally improve their mental models.

If I get the GP correctly (IANAP and everything), he is pointing that General Relativity works equally well with many different descriptions of space-time.

The one where everything always move at c, and only the direction of movement changes is one among many possible (and indistinguishable) descriptions, and not a very useful one.

If he understood how to communicate with people at all, he'd have simply said what you just did. He's also mistaken, it is an extremely useful one because it makes a complex topic clear in a way that explains why C can't be exceeded. All models are wrong, that model is useful because it can be expressed very simply, it doesn't matter that it's not the only valid way to see things.

it doesn't matter that it's not the only valid way to see things.

It certainly does though -- the existence of many valid models and simple mappings between them implies a 'deeper model' at play, and putting one particular model above all others as the 'correct' is actually discouraging the reader from getting towards the deeper truth.

If you say 'the sun is stationary and the planets revolve around it' is the only valid description of the solar system, you would be wrong, and you're also making it harder for a person to understand relativity down the line.

Could you please just restrain yourself from commenting uncivilly like this on HN? I'd really, really like not to have to go through this again.

So if you reach the speed of light does that mean you'll reach the end of the universe, being that time stops for you and speeds up for everything else? Speaking of which, is a black hole just a window into the end of the universe?

Would you know if (the observable effect of) quantum entanglement is expected to travel faster than the speed of causality?

It is that question that does not have much meaning.

If you observe one of a pair of entangled particles, you will see one of its possible values. Entanglement only means anything when you compare it's value with its pair's value, and that comparison is limited to the speed of light.

So, yes, in a sense quantum entanglement is free of all the causality issues brought by GR. But it does not really exist until the pair can communicate.

So why not communicate via quantum entanglement? Kind of like FTL TCP.

Also, yes, gravitational waves travel at c.

(Caution: Pedantry ahead.)

Gravitational waves are believed to travel at C, the theory says they should travel at C, and we're slowly narrowing in on C in measurements, but our ability to measure gravity waves is poor enough that we aren't yet quite sure.

Which is one thing this observation would fix, assuming it's real.

General Relativity (GR) is a metric theory of gravitation, with one metric to which everything couples.

In GR gravitational waves (GW) have lightlike worldlines. Consequently, a source emitting both electromagnetic and gravitational radiation will have its GWs and EMWs (or more generally its optical image and the direction in which things indicating its gravitational influence point) line up. This has been well-tested observationally, for example by watching the deflection of light from distant objects (like quasars) around Jupiter (whose mass, orbit, and distance from us are all very well characterized).

However, one can write down a bimetric theory of gravitation with different couplings. It's possible to write down a bimetric theory in which gravitational waves move more slowly or more quickly than electromagnetic waves.

It was fairly popular some years to take this kind of approach to solve some cosmological problems relating to the homogeneity within the horizon [1]. These were often cast as "variable speed of light", for aesthetic reasons fixing the speed of the gravitational interaction. However, it is perfectly reasonable to call the same models "variable speed of gravitational radiation" fixing the speed of light, as one has many freedoms with respect to coordinate conditions in General Relativity.

The problem is that these "variable speed of gravitational radiation" theories do not match observations of the galaxy-filled parts of the universe that we can see, and also does not match what we see in the Cosmic Microwave Background. (Some bimetric models fail to match the results of laboratory-scale physics experiments too.) Viable bimetric theories thus have the second metric decay in the very very early universe, such that in the galaxy-filled epoch the speeds of light and gravitational radiation are identical, and physics becomes (outside of the very early universe) indistinguishable from their "standard" single-metric General Relativity based generally covariant formulations. Such decaying-bimetric theories usually are designed to do away with cosmic inflation, but it becomes difficult to distinguish between cosmic inflation and viable bimetric-decay models because the observables eventually have to become identical, and the time at which they can differ gets pushed back further as we develop observatories which can resolve objects at ever higher redshifts, or as we can get better data on the anisotropies of the CMB.

we're slowly narrowing in on C in measurements

We should determine c empirically, but we have already done so to exquisite precision.

However, we can also fix c to some exact value (e.g. the CODATA value, or 1) and be mindful of the side effects of doing so. This is, by far, the most common approach; you will be hard-pressed to find any formulation of a physical law which introduces uncertainty into the value of c, although it's certainly doable.

The fixed CODATA value is extremely good. The relative uncertainty in the speed of light is principally driven by the uncertainties in interferometry, which at the time of the 1983 redefinition of the metre was less than 0.1 part per billion (and is now less than a part per trillion, and so for all practical purposes is unimportant at scales of the observable universe).

Finally, one should note that in a general curved spacetime, while the constant factor "c" arises everywhere, it can only be taken as a speed when comparing two objects that co-occupy exactly the same infinitesimal point in spacetime. Comparing the speeds of distant objects is something that one should avoid in General Relativity. However, everywhere in every spacetime, in vacuum conditions one should find the same "c" as the upper limit of relative speeds of objects just as they enter, co-occupy, and exit the same point.

- --

[1] https://www.wikiwand.com/en/Horizon_problem

What are the side effects of fixing the value of c?

We should determine c empirically, but we have already done so to exquisite precision.

As interesting as that is, what I meant we're narrowing down is the speed of gravity -- that is, that it's almost certainly equal to C. Not that we're narrowing down C itself, it's way more convenient to define that as 1.

Since you're here, though... the horizon problem. I can kind of understand the logic that makes it a problem, but...

If you have the same initial conditions everywhere, and the same laws of physics, wouldn't you expect everything we can see of the universe to look similar even if there hasn't been any communication?

That seems like an obvious implication of having deterministic physics, and sure, "same initial conditions" is a big assumption -- but I never see this hypothesis offered.

more convenient to define that as 1

Yes indeed. :-)

... I never see this hypothesis offered.

The tl;dr is that that hypothesis is a (subjectively) boring and (less subjectively) non-Copernican answer.

I'll expand on this.

Let's just accept arguendo that the laws of physics are everywhere the same and in particular that gravitation matched General Relativity from well before photon decoupling to the end of recombination.

You can indeed then take the position that the initial conditions of a hot big bang were extremely finely tuned, with overdensities at photon decoupling (and thus reflected in our CMB) being exactly encoded in the initial values.

However, the trend is to explore mechanisms that allow for much higher (Boltzmann) entropy in the early universe with overdensities evolving from fluctuations.

ETA, I'll steal a line from slide 6 at [1] : "don't explain low entropy by positing even lower entropy".

This trend has been productive in the sense that it has produced several progressive research programmes amenable to empirical tests.

For example, cosmic inflation (eta: in part by allowing the particle horizon and the Hubble horizon to be very different) allows for a much wider set of initial conditions (some with much higher entropy than is implied by maximally finely tuned initial conditions) that could produce our CMB and ultimately galaxies. Cosmic inflation in the broadest sense has produced a number successful predictions, so work is certain to continue.

Pragmatism, aesthetics, philosophy aside, I have trouble imagining in detail what observatories we would have constructed had late 1990s cosmologists simply pursued a programme of discovering the details of values surfaces at progressively earlier times, with the goal of simply discovering the initial conditions eventually, all without doing much theoretical speculating about what as yet unexplored early values surfaces might contain. What would have succeeded BOOMERANG? Instead, that sort of speculating raises all sorts of interesting questions about the behaviour of matter at extremely high densities and temperatures, how those behaviours might be encoded in a CMB that was not strictly fixed at the hot big bang, and what alternatives to the hot big bang (e.g. a big bounce cf. slides 7- @ [1]) could lead to our galaxy-filled sky.

So you practically hit the nail on the head in recognizing that assumptions about initial conditions is crucial to whether one sees the horizon problem as a problem in the first place. If you don't care about complaints about the apparent non-genericity of the initial conditions, there's no problem; likewise, if you are pretty sure that initial conditions can be highly generic yet lead to the universe we see, then there's also no problem. This is fertile ground for philosophers (and historians) of science. [2]

- --

[1] http://www.preposterousuniverse.com/blog/2017/01/25/what-hap...

[2] A quick search leads to Casey McCoy (University of Edinburgh)'s http://jamesowenweatherall.com/wp-content/uploads/2014/10/Wh... section 3 (edit: notably from the bottom half of p 15 where he has some pleasantly difficult questions in parentheses) and the second half of p 18.

I'm with the first one, then. I consider the Kolomogorov complexity of the laws of physics to be important, and initial conditions to be part of said laws, but I don't think it adds much complexity to posit that the initial conditions are very, very simple (and thus low-entropy).

we're slowly narrowing in on C in measurements

Interesting... I thought that c = 299,792,458 m/s exactly. So what are we are actually measuring here? The meter and/or the second?

I believe the OP meant that they're narrowing in on being confident that gravitational waves travel at C, not narrowing in on a more precise value of C.

That said, if we do obtain a more precise value of C, the definition that changes is the meter. The second is defined in terms of energy states of a caesium atom.

But the universe itself is expanding faster than the speed of light, [1] :)

[1] http://curious.astro.cornell.edu/about-us/104-the-universe/c...

Speed of light has units of distance per time. Expansion rate has units of (distance per time) per distance.

For more info on why this statement makes little sense, see Sean Carroll's post here: http://www.preposterousuniverse.com/blog/2015/10/13/the-univ...

These PBS Spacetime episodes should help:

The Speed of Light is NOT About Light - https://www.youtube.com/watch?v=msVuCEs8Ydo

Is Quantum Tunneling Faster than Light? - https://www.youtube.com/watch?v=-IfmgyXs7z8

The Quantum Experiment that Broke Reality - https://www.youtube.com/watch?v=RlXdsyctD50

Pilot Wave Theory and Quantum Realism - https://www.youtube.com/watch?v=RlXdsyctD50

The Future of Gravitational Waves - https://www.youtube.com/watch?v=eJ2RNBAFLj0

Thank you for this. You linked to the youtube videos but I watch the PBS app on my Roku all the time and it's horrible at recommending what I should watch.

"Watched 'City in the Sky' [a 3-part series about airports and planes]? You'll love Downtown Abbey or The Great British Baking Show!"

I'm always looking for some actual good/educational shows on there, and there's so many great hidden gems, but they're all... hidden.

Your intuition is correct and the question of the speed of gravitational waves is pretty complicated. The usual treatment of gravitational waves is done by linearization of some non-linear equations. This is a very good approximation for the propagation of gravitational waves since they disturb the space-time only very slightly (for example, the mirrors in the interferometry experiment at LIGO get displaced by a tenth of a nucleus of a hydrogen atom, during the passage of a gravitational wave).

In this linear approximation the gravitational waves are governed by the same wave equation as for electromagnetism (only the spin part is different since the spins of the gravitons and photons are different). Since in the linear approximation we recover the Lorentz symmetry, then the linearized wave equation has to be Lorentz invariant. Then, one can apply results from the representation theory of the Lorentz or Poincare groups; there are two major types of representations: massless and massive. They differ in striking ways when it comes to spin and when it comes to propagation, for example massless particles travel at the speed of light. If you want to have a massive graviton then you need to get the mass somehow from your theory. Einstein's theory predicts a massless graviton, which by the argument above has to travel at the speed of light. We still don't know experimentally if the graviton is massless (but last time I looked at the Particle Data Book there was an upper bound on the mass which was very small).

Now, coming back to why your question is complicated. Remember that in Einstein's theory space-time itself is dynamical. Now suppose you follow the propagation of a gravitational wave. Since this takes some time, we need to take into account the fact that the shape of the space-time itself has changed in the meantime. In such dynamical situations it becomes complicated to even define what the speed of propagation between two points is. One way this becomes important is in cosmological situations. For example, the expansion of the universe stretches the distances and this allows us for example to see further that the distance you obtain multiplying the speed of light by the age of the universe. This being said, you can define the speed locally by studying propagation for very short distances and times and this will be a constant. However, you need to remember that the global situation is more complicated.

Normally, the scientific community is pretty careful about not revealing results before they're fully baked (press notwithstanding). Seeing how that control has broken down for this incident, is it correct to infer that astronomers have pretty much lost their minds over the possibility of capturing a neutron star merger?

Edit: calm down, people, I'm excited too.

While I would have a trouble imagining a quantum of the space-time curvature (the graviton), it is not hard to see that the changes in the curvature could propagate in the form of waves. So, while yes, an experimental discovery of these waves is an important event in history of science, I am left curious as to whether it adds anything to our present understanding of Nature...

Someday could we ride these waves to Interstellar travel?