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
"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.
"Neutron star": https://en.wikipedia.org/wiki/Neutron_star
Thanks a lot!
I'll have to check them out and study up a bunch of stuff it seems.
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?
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.
(Δs)2 = 0
It is wrong to then equate this to some sort of proper time Δτ, find that
Δτ = 0
for a photon, and thus conclude that photons always "experience" zero proper time. No. Remember that Δτ is defined as the
time difference between two events as measured by an observer (i.e., an inertial frame) that actually travels between the events. Photons
have no reference frames! So the definition of Δτ doesn't apply to null paths.But as I was alluding to with my 'tomayto, tomahto' remark, this is a question of semantics, and we're not really arguing about physics, but labels.
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.
It's just a colloquial description of the fact that the time interval between two events along a null geodesic is zero.
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.
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?
To me, the latter is an encouragement to rationally evaluate existing belief systems against each other, since it reduces all of them to a level playing field. From there, one can apply a simple twofold truth test to each system: correspondence to reality and internal consistency.
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.
2. God is not part of this universe.
3. God, having been the cause of this universe, can be described as all powerful - at least in the same way Big Bang was powerful.
4. God is outside of time.
The above requires no faith at all - to me it's obvious God described in points 1-4 is true.
Now the following requires a degree of faith:
5. God is one, indivisible, at least in the same way a quantum (by definition) is indivisible.
6. God, rather than having zero consciousness, is completely conscious, having equal or more consciousness than all the consciousness in this universe.
If God is all powerful by definition of having caused the universe then I find it harder to believe the specific claim that God in fact, is not conscious, even less than a starfish. And when we are talking about God, it's more likely to be all or nothing, so my specific claim is that God is completely conscious, and being outside of time, all-knowing.
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.
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.
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.
Think more Cartesian space than left->right
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.
(Anything with non-zero mass would require infinite energy to reach 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.
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 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.
For the same patch of spacetime with "a photon" in it, different observers can calculate different photon numbers and different photon energies.[2] That is to say that these properties are not always conserved under a change of systems of coordinates (trivially, when we have two observers with different observables, we can fix a coordinate system's origin on either of them, but that doesn't make either "right"). Indeed, the properties of the photon that survives such changes are: they locally move at c, they have no intrinsic mass, but they do have momentum (and thus contribute to the stress-energy-momentum tensor).
The intrinsic mass is the same as the rest mass (a quantity that remains the same in all frames of reference related by Lorentz transformations). The intrinsic masslessness of photons is required for the gauge invariance of the Feynman amplitudes of QED or the Standard Model. More detailed explanation would involve a trip through an explanation of the Ward identity[1] which gets even harder when curved spacetime is in play.
I'm sure you've already discovered that the topic of photons' frames of reference comes up a lot in much harder-science forums than HN, and hopefully you've found a decent treatment of that on e.g. physics.stackexchange.com or physicsforums.com. If you find a decent link, maybe someone (and probably I) would appreciate it if you attach it to this thread because it is likely to come up again someday. :-)
- --
[1] https://www.wikiwand.com/en/Ward%E2%80%93Takahashi_identity
[2] redshifting is the clearest case of photon energy change, and can arise from uniform relativistic motion, relative acceleration, metric expansion, or real gravitation. Extremely relatively accelerated observers will disagree on particle counts generally, with the Unruh effect serving as a partial formalization.
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]
- --
[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.
[2] https://www.wikiwand.com/en/Coordinate_conditions goes pretty deep on this
[3] http://math.ucr.edu/home/baez/einstein/node2.html third paragraph
[4] https://www.wikiwand.com/en/Ultra-high-energy_cosmic_ray
[5] where one is dealing with generalized matter (light and massive particles, etc) in general curved spacetime, one might want to take the initial values approach in http://fanfreluche.math.univ-tours.fr/notes/geroch/geroch_no... (or if you like) ch. 27. onwards of https://books.google.co.uk/books?id=NOJ9AgAAQBAJ&printsec=fr... but also in more recent work -- Special Relativity is essentially a framework which has done all this heavy lifting for the user.
I like Carroll's [ https://www.preposterousuniverse.com/spacetimeandgeometry/ ] and indeed, you get to deal with intervals and worldlines in chapter 1.
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.
https://en.wikipedia.org/wiki/The_Road_to_Reality
It is quite long and dense but explains the math from first princples like you want.
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.
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.
No one is putting a particular model above all others, one model is simply being used to explain the relationship between C and time, it's not incorrect just because other models are also valid as long as they all explain the same relationship between C and time.
Not necessarily. You can have completely different formulations of the same physics. Lagrangian, Hamiltonian, and Newtonian dynamics are different models of classical motion. Does that imply there's a "deeper model" of classical motion? I wouldn't say so.
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
(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
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.
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.
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.
If you don't care about that, then I think that we should agree that nobody profits by you or I replying to one another's HN comments in future.
I think your comment is too long and too technical, but it's correct and explain why the original comment is wrong. So I upvoted it.
The problem is that is too long and too technical, so the main ideas are lost and many people prefer some wrong handwaving.
Some recommendations:
* Try to keep the answer shorter. Link to the Wikipedia article if possible. Perhaps ignore part of the original comment to make the reply shorter.
* Try to avoid too much technical jargon. This is a technical forum. You can assume everyone has Calculus 101 and Algebra 101, and a few more elementary courses, but nobody has advanced knowledge of all the topics.
It's difficult to explain in simple words why I don't like the original comment. The answer is strangely in one of your other comments.
> "Sure, you can always choose useless systems of coordinates."
It's too short! I'd try to add some details: The problem with "everything moves through spacetime at c" is that you must "sum" the squares of distance "x" in the laboratory reference frame and the time in the reference frame of the moving spaceship "s" (and fix the units, sorry). So you get a nice property that is valid if you use properties that are measure in different reference frames. But 99.99% of the time, life it's much better if you don't mix measurements in different reference frames.
[My version still needs a lot of fixes, fix the units, perhaps replace "reference frame" with "astronaut", add at least a formula, ... I guest that with 1 or 2 more hours I can fix it, but this is a deeply nested thread that nobody will read and I have to go to eat ... https://xkcd.com/386/ ]
I read it.
> too technical
Too technical for the comment or too technical for HN period?
> Link to the Wikipedia article if possible
I do link to things that go into further detail in many of my comments.
However, I think the relevant (English-language) wikipedia articles for this thread are bound to be much longer and more technical. The simple English wikipedia versions, to the extent they even exist, are generally not worth linking to.
Do you think it would have been right to simply drop https://www.wikiwand.com/en/Line_element#/General_spacetime as the bulk of the content of my original disliked-by-you comment?
> I'd try to add some details
The details were already in the replied-to message that people seem to either like or dislike. :-)
> I guest that with 1 or 2 more hours I can fix it
FWIW, I only took a few minutes. Is it likely that anyone would spend an hour or two on any HN comment (especially a down-thread one) as opposed to a blog posting, article or comment elsewhere?
Indeed some of my original motivation is exactly https://xkcd.com/386/ however the point wasn't just to be right, but also to try to advance someone's (not necessarily the original writer's) understanding of a line element and that line elements are meaningful (and in particular typically nonzero) for light.
https://www.sciencealert.com/watch-why-the-speed-of-light-is...
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.
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.
- --
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.
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]
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[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.
If you have no problem with an infinite history of ever lower entropy, then luckily observations to date do not contradict this sort of cosmology, and under time-reversal the "movie" showing the universe crunching into an ever more orderly state forever isn't very shocking other than we arrange our lives with the movie playing the other way, sweeping up broken shards of glass rather than catching rising stemware. Maybe conscious life somewhere else in our Hubble volume arranges their lives in that way, though, unbreaking and unmaking their artefacts and thinking our way of doing things is strange.
Some other questions for you: how far does this cosmology's future grow? Do we get infinite entropy in the infinite future? If we don't have an infinite future, why do we have an infinite ever-more-orderly past? If we have an infinite future, do you suppress fluctuations? Do you wholly suppress Poincaré recurrence? How would you distinguish us here as us here now from a recurrence? Are we a recurrence? etc.
These questions do not seem as amenable to testing with current technology as questions arising from other cosmologies.
One point, at least. I see no reason why a theory being difficult to test should count even slightly against the probability of its being true. Sure, it's inconvenient -- and there's something to be said for focusing on ideas that can be tested -- but since when was nature ever constrained to convenience?
As to your other questions...
I'm not sure where the 'infinite past' comes from. There's a single slice of space-time that needs to be constrained; everything else can flow from there, in both directions. If it's a low-entropy constraint then causality would naturally flow away from that slice. The two sides should be mirrors of each other, though.
As to the far future... that's harder.
- My intuition is that, when you're trying to guess at which of many possible universes you actually live in, the amount of "runtime" the theoretical universe spends on computing you (that is, some form of life, at least) should matter. But that's problematic, since it seems to predict higher complexity of the physical laws in exchange for a universe that's denser with life, and it's not what we see.
- More realistically, perhaps, the big rip might be a thing. Recurrence could fail to happen because the far future doesn't allow for structures complex enough to have thoughts, not even by random chance.
I prefer to punt on the question, though. I don't know enough to have an informed opinion.
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.
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?
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.
Information cannot move faster than the speed of light, period.
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.
[1] http://curious.astro.cornell.edu/about-us/104-the-universe/c...
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...
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.
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.
I'm no physicist, but couldn't lack of matter in some region otherwise filled with particles play the part of "virtual" negative matter?
https://www.youtube.com/watch?v=1Tstyqz2g7o
Another great channel is looking Glass Universe - https://youtu.be/r0plv_nIzsQ
And Udiprod doesn't have a habit of making physics vids, but this is my all time favorite physics videos on YouTube which explains quantum waves better than anything else I've seen - https://youtu.be/p7bzE1E5PMY
But I also know that the Alcubierre Drive have some weird implications, such as the inner of the ship is causally disconnected from the space wrap, basically you can't control it from the inside.
Anyways, I'm curious if the gravitational waves are "space waves", in that case it wouldn't have limit, as space can move at any speed.
It took me a while to read them all and not sure I do understand them all.
It's amazing how complicated can physics stuff get. I'll be sure to check all the linked resources.
Thanks again!
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.
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?