[reubenswartz]

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."

[Swizec]

> 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?

[speeder]

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.

[platz]

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

[cygx]

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

[platz]

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. "

[cygx]

Tomayto, tomahto. You can't parametrize a null geodesic by proper time, sure, but I don't see anything particularly wrong with calling the arc 'length'/spacetime interval between events along any particle trajectory a proper time, even when it's 0.

[platz]

actually i'm reading now that photons do not even have their own reference frame simply by definition/axiom. Interesting..

[sscarduzio]

I wish HN had "reddit gold". Thanks for jotting this down for us, super clear and interesting.

[TheOtherHobbes]

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.

[cygx]

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

It's just a colloquial description of the fact that the time interval between two events along a null geodesic is zero.

[meric]

But some believe it's God who does this.

[TimTheTinker]

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.

[e12e]

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?

[TimTheTinker]

There's a lot of difference between "there are some things we cannot know" and "all systems of belief rest on axioms that must be taken on faith".

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.

[tasty_freeze]

> 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.

[TimTheTinker]

Acknowledged. Advocating for a more specific form of theism would require more specific arguments.

[azag0]

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).

[erikpukinskis]

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.

[bramen]

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.

[Koshkin]

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.

[erikpukinskis]

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

[Koshkin]

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.

[neom]

This might help: https://simple.wikipedia.org/wiki/Space-time

[jfjdiriri73737]

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.

Think more Cartesian space than left->right

[colordrops]

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?

[ajross]

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.

[lomnakkus]

Well, you can't reach c unless you're massless.

(Anything with non-zero mass would require infinite energy to reach c.)

[raattgift]

> 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.

[CamperBob2]

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.

[sidlls]

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.

[cyphar]

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.

[platz]

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

[Koshkin]

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

[platz]

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

[platz]

actually i'm reading now that photons do not even have their own reference frame simply by definition/axiom. Interesting..

[raattgift]

> "its own reference frame"

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.

[raattgift]

Sure, you can always choose useless systems of coordinates.

[nileshtrivedi]

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.

[raattgift]

Just about any standard textbook on General Relativity will cover the content of my comment in the first chapter or so.

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.

[SAI_Peregrinus]

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.

[spaceseaman]

You would be interested in this book

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.

[reubenswartz]

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.)

https://smile.amazon.com/dp/B002TJLF7W/

[gnaritas]

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.

[dang]

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.

[gnaritas]

Fine, I think it was simply blunt, not uncivil, but whatever.

[marcosdumay]

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.

[gnaritas]

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.

[smallnamespace]

> 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.

[gnaritas]

> and putting one particular model above all others as the 'correct' is actually discouraging the reader from getting towards the deeper truth.

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.

[cyphar]

> the existence of many valid models and simple mappings between them implies a 'deeper model' at play

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.

[Koshkin]

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.

[raattgift]

> 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.

[ldp01]

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.

[raattgift]

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.

[QAPereo]

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.