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?
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
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.
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.
Very trivialized: in some sense, you could say that for light itself, there is no time. In the same sense as there is no space for things that do not move (in space).
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.
I'm not sure about this analogy. You can argue that the apparent motion of the wave crests is an illusion being pieced together by our brains when we see the totality of the elliptical movements of water particles at the surface.
But at the moment when you drop a pebble into a pond, there are definitely parts of the surface which are moving and parts which are not, and the influence of the energy you introduced with the pebble can clearly be seen to spread outward over time.
Granted this doesn't map directly onto electromagnetic waves because the mechanisms involved in wave propagation are different.
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.
According to the classical electrodynamics - it sure does. From the quantum mechanical point of view, it also does - in the sense that we can always measure it (i.e. it is an observable). The "property" in this case is not so much a particular outcome of such measurement as much as the expectation value; actually, I'm afraid that the use of the word "property" in this context can only lead to confusion as it effectively conflates several different things: the (quantum-mechanical) state, the observable, and the particular value observed.
Basically to establish time a measure has to be taken. Either by a human with our units for time, or by interaction with some force or object to establish that "this happened then".
We commonly think of time in the linear time line sense.
It's more accurate to think of it as a big mesh of points of interaction.
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?
It's more a sci-fi way of expressing things, but yes, sort of. Time dilation becomes infinite at c, so massless particles do not "experience" time. This is the reason that photons on a Feynman diagram are traditionally drawn horizontally.
But the black hole part is actually wrong. Time dilation approaches infinity at the event horizon, not the singularity. So to extend your metaphor the interior of a black hole forever exists "beyond time" from our perspective.
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.
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.
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.
Agreed. The level of pedantry when trying to explain a topic doesn't sound like it comes from someone who's internalised the core physics concepts they want to explain. It reminds me of when I was trying to explain from-first-principles classic thermodynamics to a layperson as a second-year student. It didn't go well.
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
We don't use inertial frames of reference in General Relativity because in the presence of real gravity, there are (strictly speaking) none anywhere. [1]
There are however static spacetimes that admit inertial frames of reference. Flat spacetime aka Minkowski spacetime is an example. That is the spacetime of Special Relativity, and in Special Relativity inertial frames of reference are extremely useful. However, the defining feature of flat spacetime is that there is no gravity anywhere in it.
We can talk about coordinate conditions [2] where those generalize a set of activities that pick out a specific choice of coordinates (and consequently an origin for the coordinates), a choice of units, and some other choices that one can freely make.
The photon's "own reference frame" could be specified as for example keeping it at the origin of a set of flat Cartesian coordinates (x=y=z=0=const) and letting it move against the t coordinate. This is unlikely to be useful, and can be made useless with various choices of units. However, one can say conclusively that the photon's spatial coordinate velocity is zero.
However, coordinate velocity isn't physical: it goes away by changing the system of coordinates. For example, in this system, your coordinate velocity is always exactly c. And so is the moon's. And so is the Andromeda galaxy's. But we can see how unphysical that is simply by fixing coordinates with you always at the origin, or the sun always at the origin, and noticing that the only thing moving with a coordinate velocity of c in those systems of coordinates is the photon.
Indeed, in General Relativity comparing velocities is extremely tricky for objects not occupying the same point in spacetime because it is very easy to be misled by what you're being told by the coordinates and the choices "hidden" within them. The usual advice is to avoid such comparisons (cf. Baez [3]).
Nowadays pretty much every relativist will tell you that Special Relativity emerges from General Relativity (the more fundamental theory) as a special case in the limit where gravity is weak, even though historically Special Relativity came first and informed the development of General Relativity. (They'll also probably advise you to calculate using Special Relativity forms of physical formulae where you can do so!)
However, where gravity is non-negligible or where one is tempted to use a broader set of coordinates than e.g. spherical or Cartesian coordinates on a local patch of sufficiently flat spacetime, Special Relativity is simply inappropriate. Intuitions from Special Relativity about how an object moving at exactly light speed (or even extreeeeeeemely close to it over sufficiently long intervals, like with an extragalactic ultra high energy cosmic ray[4]) are likely to be misleading; instead, one should use the toolset of General Relativity.
Unfortunately that toolset requires complicated mathematics. [5]
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[1] We can define locally inertial frames of reference (LIFs), and the Lorentzian structure of spacetime (four dimensions, three of one sign and one of the opposite sign) guarantees that we can do this in many cases, especially in infinitesimally small regions around a point, or in a small region along a geodesic. (I can explain this further if you are very interested, but its fairly technical and grinding it down to something suitable for HN may take some iteration. I don't even have a link to a decent explanation for what e.g. Fermi coordinates are, why they're useful, and how to use them :( so maybe I'd be breaking new ground ;) ). Some LIFs can be more extensive when gravity is sufficiently weak in that region: an Earth-based "laboratory frame" in Special Relativity is really just a LIF without admitting it; particle colliders typically don't really have to consider the influence of the gravity of bodies like the Earth, the Moon, the Sun, and so on, even if one has a view of the ocean (and its tides) out of one of the lab's windows.
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.
It assumes you know or are ready to learn some differential calculus and how to read a formula with an integral but it (maybe a bit steeply) teaches tensors (and some aspects of vectors and scalars) across the first couple of chapters. Carroll provides some (quasi-)samples under the "Lecture Notes" tab, but the book itself has benefited from editing. He also supplies links to alternatives that can be had for free-as-in-beer.
The classic text is "Grativation" by Misner, Thorne, and Wheeler. It's very dense, but very thorough. The other classic is "General Relativity" by Wald. They don't really include the math background though, for that you need texts on multivariable calculus.
Check out "Why Does E=MC^2". (I wish I understood it better. I think some of what raattgift was saying is related to the deeper issues, which the book does raise, and which I paraphrased at a very high level.)
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.
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.
But the way he communicates eliminates ambiguity and allows the conversation to stay on topic. As soon as you try to express things "very simply", the conversation quickly degrades into an almost meaningless argument about things the participants do not (and, worse yet, do not wish to make a serious effort to) understand - which is exactly what we see here.
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:
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.
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.
Thanks. That is an interesting perspective, and I understand it.
I hope you don't mind if I pick up your comment as an invitation to go even more meta than you. :-)
> if you are interested in reaching as many people as possible
I'm not sure I am, even if it's "as many people as possible on HN who open this discussion". I'm guessing that most people who will read down a thread on a topic like this have some interest in it, and probably have a little math, or some search-fu, or perhaps even a little physics, but little exposure to General Relativity (one can earn a Ph.D. in physics without ever having to walk through a comma-goes-to-semicolon exercise let alone deal with exceptions to that procedure, but I'm not writing for e.g. solid state physics Ph.D.s here and hopefully they already know how to look beyond an HN thread or Nature News link if they want to know more about SN-BH or similar stellar collisions).
However, I don't want to alienate people on either side of that -- neither the experts nor the enthusiastic-but-allergic-to-mathematical-physics readers.
> please don't give up
Thank you again. If you have any concrete suggestions (now or in some future thread) about how to help engage the latter group, I'll gladly read them.
However,
> before they have grokked the intuition behind it
the problem is that intuitions like "the shortest path between two points is a straight line" are based on Euclidean geometry, which is probably much more often taught rather than discovered by a student sua sponte, although once taught experimental validation is easy. But in Euclidean (well, Minkowski) spacetime, curved paths are shorter. I think that pretty much nobody would have any chance of discovering that feature of spacetime on her or his own, or intuiting it from planar geometry. However, it's easy enough to teach by explaining what a line element is, and what the line element of Minkowski spacetime is. Once that is absorbed and is familiar enough that reading and drawing spacetime diagrams isn't a chore, then one might expect intuitions like "one can resolve the twin paradox by observing that the travelling twin takes a more-curved path through spacetime than the non-travelling twin". But even there, people sometimes stumble on understanding that that statement is demonstrably true under any choice of coordinates, not just ones which hold the non-travelling twin at the spacelike origin (from which the traveller departs and to which the traveller returns) throughout. And even then, where does one's intuition take one when one or both twins experiences significant real gravity?
One option of course is to shrug off opportunities to try to write into words what one would normally describe using a formula. I'm sure that's not what you're suggesting (but others in this topic seem to).
Another is to give a reply that is neither correct nor detailed but which is at least more correct. Maybe that helps a little, but I doubt it advances anyone's understanding rather than be memorized as a slogan or factoid.
Yet another might be a pointer to a standard textbook. Since they tend to be chunky and expensive (and I can't even guess about availability at a local public library rather than a major reference library open to the general public), I'm not sure that's so helpful either, unless the pointer is to a pirate scan. :-)
Penultimately, this is unpaid pseudonomymous fun. I think ELIx (FSVO x) is a good challenge for the explainer too, especially for extremely abstract topics, otherwise why bother? From this perspective, what's a decent choice for "x" on HN? (We surely can agree that it will be different than "x" on e.g. physics.stackexchange.com; in fact I think that is close to your central point.)
Finally, in comparison to the previous paragraph other models exist, e.g. http://backreaction.blogspot.com/p/talk-to-physicist_27.html - I am reasonably sure Sabine Hossenfelder would be happy to negotiate on publishing a transcript or summary of a conversation on her blog or elsewhere (perhaps even as a comment on HN :) ) and I am even more sure the quality of her or her associates' answers will be better than mine.
That's more or less how you work it out on paper, with the hope that when you add it all up it comes out to c, (usually tuned to "1" or unity), but that isn't necessarily what is physically happening. There isn't some part of us that's compensating temporally, for a lack of spatial velocity, it's just that when you add up the numbers or draw something like a spacetime diagram, it should come out a certain way.
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.
> 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.
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]
[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).
Let's flip the question and ask what happens if we let the value of c depend on the location in spacetime.
Ellis provides a "short checklist of issues that should be satisfactorily handled by" theories that have a value of c that depends on location in spacetime. https://arxiv.org/abs/astro-ph/0703751
The tl;dr version is that relativistic physical theories will need revising because in the face of a location-dependent c, and in particular the problem arises because we necessarily break lengths and durations when c is not everywhere-and-everywhen identical.
More narrowly observables like spectral lines are sensitive to ratios involving the quantity hc which are taken to be constant. Since cosmological redshifting of spectral lines fits in a substantial web of observables related to distance (e.g. angular diameter, surface brightness) we can practically rule out variation in hc to a very high redshift (z > 10).
You might instead be asking what happens if c is the same everywhere but we've settled on a very slightly wrong value of c. The answer is that this will almost be absorbed into our system of units, in particular in various ratios involving hc. If we change the value of c to the slightly improved value, we also probably slightly change things like the fine structure constant and the electron-to-proton mass ratio, which are dimensionless quantities with ratios involving hc. These dimensionless quantities are good checks on the many ways in which we might measure c empirically.
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.
In none of them can information travel faster than light, but that isn't a satisfactory answer, since one half of an entangled pair still has to "know" what happens to the other in order to give the right result from measurements, even though that doesn't let you send information.
In hidden-variable models, you can argue that the experiment outcome is defined "up-front". In the many-worlds model, both sides have both outcomes but the inconsistent ones "cancel out" as they meet, and pilot-wave interpretations are just many-worlds with one configuration picked out as "real".
But in most of the rest, yes, something travels faster than light. That's a common argument against e.g. collapse interpretations.
They entangle next to each other, and they move apart at max the speed of light. you'll have already paid the price for transferring that bit, so to speak.
Information cannot move faster than the speed of light, period.
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.
How would you do that? You can't force the entangled photon at the other end of the channel to measure in any particular way. Once you've measured yours, the other one will measure the same, yes - but you don't know what yours will be until you measure, and the probability is 1/2 either way.
The reason this isn't paradoxical is because expansion doesn't have a speed, and the phrase "X is expanding faster than Y" doesn't have a proper meaning.
And recession velocities have units of distance per time and exceed c at the Hubble sphere.
Such coordinate velocities are largely meaningless, though: The more interesting quantity is the relative velocity as evaluated via parallel transport along the trajectory of the photon you use to observe the receeding object, which goes to c at the cosmic event horizon.