While we have observed the universe expanding since Edwin Hubble published his findings 90 years ago, it was in fact the Friedmann equations produced 10 years earlier that established how it would work within the context of general relativity.

The Universe is expanding at every known point at the same time at the same rate. However, this is only an observable effect over > 10 Mpc of distance (e.g. extra-galactic distances). This is far too large to effect a point particle like a photon no matter how far it travels so I'm afraid your analogy of a rubber sheet is incorrect.

The lengthening of said photon's wavelength comes instead from doppler expansion due to the nature of differing relativistic reference frames.

According to our local reference frame, doppler effects of nearby stars and galaxies are only due to local motion such as Andromeda being blue shifted as it approaches us for our eventual merger. However, as you go further and further out from our galaxy the metric expansion of spacetime begins to dominate the relative motion of all bodies, leading to observing progressively redder and redder light curves. A galaxy billions of light years away is perceived to be moving away from our reference frame at a significant percentage of the speed of light!

However, if you were to change our relativistic reference frame to match a distance galaxy's you would not see its photons "stretched out" but in fact they would look completely unshifted despite having traversed nearly all of spacetime, expanding as it went.

This part I don't get (I am in no way versed in astrophysics).

If I am in a box, and that the box grows 10%, but that at the same time I grow 10%, what has changed?

I mean, if every point in the universe expands at the same rate at the same time, what does it change? Relatively speaking, everything is the same size before and after expanding right?

It feels a bit like expanding a 1 meter line and expanding the meter standard the same rate as the line.

If anyone has an explanation and is willing to spend some time writing it down, I would be most grateful :)

This itches my brain ^^

This scales up to forces in between atoms, molecules, and bits of matter. It's only at the very large scales (larger than galaxies) that all the forces that are holding the stuff together starts getting overwhelmed by the expansion of space and it starts to pull things apart. The expansion is so gentle that even relatively weak gravity can hold galaxy clusters together even as space grows.

In other words: space gets bigger, but matter doesn't. It more or less stays the same size.

If I understand correctly, space is what supports matter? Like a table supports dishes for instance (well, except that space is also "inside" particules) — and so if the table grows, the dishes don't.

I never actually even thought of what "space" means before. I thought that when we talked about space, matter was included in that (in the sense that quarks or whatever is the smallest — known? — particle take some "space" ; they're not points that can't be measured — or are they? ^^').

Anyway, it sparkled back an old interest of mine for astrophysics (well, I read one book from Hubert Reeves when I was a kid — and loved it).

Thanks again :)

(oh, as an added bonus: I guess we have no idea _why_ space is expanding, right? Because, I mean, it's a bit mind boggling...)

Edit: to be a bit clearer; I thought space was just void that "always" existed and extended indefinitely. Like, there was nothing except a small point with all the energy in the universe ; "everywhere" else a bit nothingness. Then, bim, the big bang, and matter was just booming away and making stars and planets and then galaxies and all that was just floating in this void/nothingness that was always there, never changing, still extending indefinitely. And that was why we were saying the universe was expanding — because galaxies were still speeding away from each others due to the big bang ; like an explosion with no friction perpetuing indefinitely. Now I guess I'm really confused about what "space" is...

The weird thing about the Big Bang is that it's really all of space that banged, and to a first approximation, space and time as we know it didn't exist before a singularity at the beginning of the expansion. It's very possible that's wrong (there may have been a "parent universe" or a "big bounce") but to a first approximation it seems to be that there may not have been a "before" the Big Bang.

https://en.m.wikipedia.org/wiki/Expansion_of_the_universe

So fine, but then why would we say that space is expanding, that would seem to imply we know there is some edge of space which is moving away from us, but what evidence do we have that space has such an edge?

Saying that "space is expanding" seems to hold the assumption that space has a (limited) width and height.

This makes me uneasy about your analogy. It’s like saying “relative to space” which is nonsense. Also, why would space limit itself to only expanding outside a physical body?

It is equivalent to asking why a car driving towards me does not turn blue due to doppler shifting. Except even more negligible than that.

Edit: the pearl is made from around bound by electric forces, so you can repeat the same argument for inside the pearl. You can repeat it all the way down until you have to admit that the approximations inherent in the concepts useful to describe the world at distances from nano meters to mega parsec eventually break down.

It doesn't, it's just that the forces within the body (the spring in the analogy) are stronger than the expansion.

The "relative to space" bit is the nonsense part of their analogy, but I'm not sure of a clearer way to describe things than what they did. It's not my field.

The mathematically precise statement is that you are not moving on a geodesic. You are therefore experiencing acceleration (the objects that are not bound and have increasing distance are on geodesics and do not experience acceleration).

But the expansion of space does "stretch" light- or at least, the wavelength gets longer, so it's not not happening.

It can actually end up making things very far away appear to move faster than light away from us, since there's a lot of space in between.

We cannot measure distance to super far away stars directly. Period.

10^-17 m/s is very high speed. Distance to Moon is 0.385E15 mm, and it can be measured at sub-millimeter accuracy, so this effect can be spotted. However, it will violate Conservation of Energy principle: no force applied, but job is done.

0: https://www.youtube.com/watch?v=i6GhsYrU5WQ

You don't have the decency to try to learn the basics but presume to lecture me/expect explanations? Take a course. Show a little humility. Even reading Wikipedia thoroughly would have informed you that it's galaxies, not stars that confirm the expansion of the universe. The expansion (not the acceleration of the expansion) is beyond doubt. Conservation of Energy is not a priory defined for the question at hand because in GR you can not just add the energy at different points in space.

Measuring the perturbation to the moon's trajectory from expansion would require knowing all parameters that enter the trajectory to this accuracy, not just the average distance.

This is all basic if you want to learn, but you seem to have a different agenda...

TLT predicts that value of "Speed of expanse" will be different when measured using different methods or frequencies, and it is: https://en.wikipedia.org/wiki/Hubble%27s_law#Measured_values... .

TLT predicts that there is much more stars, but we cannot see them yet because they are too dim, but more powerful telescopes will be able to pickup them. https://en.wikipedia.org/wiki/Tolman_surface_brightness_test https://www.nasa.gov/feature/goddard/2016/hubble-reveals-obs...

TTL predicts stars and galaxies older than BB (because of no BB), and they are found: https://en.wikipedia.org/wiki/List_of_the_most_distant_astro...

TTL predicts that Cosmic Background Radiation is just radiation of distant objects with Z=1000 .

And so on.

In short, mainstream theories doesn't hold against new data.

Tolman surface brightness test now looks much brighter. ;-)

Can we discuss something easier?

Why you think that photon is immortal? Why we have rule of right hand in EM? Why we see star formations older than BB? WTF is "physical vacuum"? What is waved by gravitational waves? What is happen in linear Sagnac interferometer? How photon is formed (it requires FTL to form)? What happens in double slit experiment? And so on.

Nothing is hidden, but it does take time and persistence.

Photons are not "immortal" they can decay if they have enough energy. Rule of right hand is a convention, could be left hand if you define the sign of charge differently. We don't see star formation older than BB but early universe physics is not easy to understand and there are lots of model uncertainties. Physical vacuum is what remains when no excitations are present. Gravitational waves are ripples in space itself. I don't understand what you mean by photons being formed.

You can not expect the concepts and intuitions that you formed by interacting with the macroscopic world to serve you well when thinking about the microscopic and fundamental. People used to think that you need some type of material aether that carries the waves of light. But that turned out not to be concepts that map well to reality. It took decades to learn to unthink these concepts, there is no shortcut to doing so yourself.

Expanding space doesn't necessarily imply edge of space. What if your universe isn't flat, what if it's a torus? It could hypothetically have a finite volume but no edge.

There's also no reason an infinite universe couldn't have local expansion everywhere.

Think of the changing pressure. If the box is tight and rigid and the pressure outside the box increases, the box will roughly stay the box until the pressure overcomes the the forces between the molecules that build the walls.

Same with space. If you could measure, the increase in the volume of space would put a constant pressure on every molecule to try to rip it from other molecules. The fact that the rate of change of space and the distances between molecules are so small means that it is not evident that it will ever be possible to devise an experiment to show this on very short distances.

We can only see this on very long timescales and between objects that are very far from each other because all other forces on those scales have diminished so much that only then the increase of volume of space can dominate.

It is easier to understand in 2D: Imagine a deflated balloon with two dots drawn on it. When you inflate the balloon, its 2D surface increases, which results in the two points "moving away" from each other, without either of them actually moving. It‘s just that the surface on which they lie grows. This is also the reason why distant galaxies are getting more distant faster than the speed of light: They are not actually moving, but the space in between us and them grows.

Notice that the farther two points on the surface of the balloon are apart, the faster they will appear to be moving away from each other, which is why the effect is unnoticeable over small (in astronomical terms) distances. Gravity pulls things together much faster than space expansion pulls them apart.

Bringing this back to your example: Imagine "blowing up" the box. Things inside it are growing a little bit (but gravity pulls them back together), but everything seems to be moving away from everything else.

That is to say, what is my ruler that is untethered to the surface of the balloon?

Relativity probably doesn’t work this way at all, but if light did actually slow down, would it be perceived by us as light moving at the same speed across a greater distance?

As to the previous question about relative size. If the universe doubled in size, the objects within it such as atoms don’t also double in size. Gravity and the atomic forces don’t change, so eg the size of stable electron orbits or planetary orbits don’t double in size.

It is not the meter that is growing, that's impossible. Instead you must see it as it is, which is that there are more meters continuously appearing in all of space.

Do you mean all particles are moving away from each other? I think the question here was what would it mean for "points" to move? What are points anyway?

Note that the ball has not grown twice its size. The sizes of atoms and molecules have not changed (as they have mechanisms to keep them exactly the size they are, despite space growing). It is only when there are no mechanisms or forces to keep distances between objects fixed, they seem to drift apart very slowly. The question the article addresses, is whether that growth is accelerating or not.

Maybe I'm also confused though

My understanding is that the fundamental forces are strong enough to resist the local expansion of space.

So the box gets bigger but particles do not get ripped apart or themselves expand. Space is expanding. Not matter. The particles occupy the same space and the fundamental forces keep them together. Space just keeps moving and expanding around them.

This (coupled with the fact that, at least currently, the expansion is happening very slowly) is why the expansion isn't observable unless you're looking at a very large scale.

I think it's more a mathematical trick than something deep about the universe. If you tweak the change of the universal "constants" correctly in a universe that doesn't expand, it is equivalent to a universe that expands where the "constants" don't change.

Note that there is some research about the change of the universal constant, but in most models they don't have just the rights values to make the universe look like expanding. https://en.wikipedia.org/wiki/Time-variation_of_fundamental_...

How do we tell the difference between the expansion of space and the dilation of time?

Given that space and time are crudely specking intertwined (spacetime) how do we know that the effect we see -- redshifting -- is due to the spatial expansion at every known "point" and not the temporal expansion (contraction?) at every known moment? Could not the spatial size of the universe be constant and its "clock" be being distorted?

Now, spacetime geometry might be such that there exists space/time decompositions that allow us to attribute the shift to specific physical effects (relative velocity of emitter and absorber in case of special-relativistic Doppler shift, time dilation in case of gravitational shift in Schwarzschild spacetime, spatial expansion in case of cosmological shift in FLRW spacetime), but from the perspective of spacetime geometry, these are just specific instances of a general mechanism that is agnostic to such attributions.

If you can't explain what's in your head in plain English in answer to a question that was asked in plain English then there's not much point in answering.

I'm not getting the impression that you've answered my question, I'm getting the impression that you don't know how to answer my question.

General relativity comes with a generic mechanism to compute frequency shifts. We don't need to try to figure out whether or not the effect is due to time dilation or spatial expansion, we can just do the math. But if we're lucky, we can find a way to split up space and time that allow for such intuitive interpretations. However, that's window dressing, so to speak.

All this assumes that the spacetime in question is already known, but that's how it actually happened historically: Friedmann and Lemaitre derived their solutions by imposing certain symmetries on the problem. From that, you can derive observations like redshift (Lemaitre had already done so by 1927, ie two years before Hubble published his paper), which you then compare to observation in order to fix the parameters of your model, or scrap it if it cannot accomodate observation.

As far as I'm aware, at no point in time did a physicist sit down and think "I wonder, what's the best way to incorporate redshift into my model, time dilation or spatial expansion?".

Now, if there is a failure to understand your answer the reason why lies with me :)

(If it doesn't fit, then it's just wrong.)

I have this odd notion that the universe has stayed the same "size" (since inception) and that the parameters of the universe and the amount of matter/information has changed over time.

The impression we get (from our perspective) is that of an initial singularity, a period of hyper inflation, and then the expansion we have now.

Probably bollocks but I'd like to know why it's bollocks.

Time everywhere is slowing down (speeding up?) Which it's why the expansion of space seems so perfect to neither accelerate nor decelerate.

My gut tells me that the layman's model I have of the universe precludes me from having a handle on why the idea is dumb. I console myself with the knowledge that at least I'm not so dumb that I think the idea is l33t and the whole scientific community are morons. Still, it'd be nice to have an answer.

https://www.youtube.com/watch?v=7UNLgPIiWAg

Unlike math, you can never prove that something is correct and true. You can only prove that reality likely does not fit a given theoretical model to a vanishing probability. The models we have, we only have because they have not been proven to have a vanishingly small likelihood of explaining physical phenomena.

Btw, this is what frustrates everyone about string theory. It's mathematically correct and quite elegant, but extremely difficult to gather any observational data that could prove it unlikely or another theory unlikely compared to it, leaving it in a sort of scientific limbo.

Astrophysics is hard because it is an observational science only. You cannot run your own experiments so you must simply gather as much observational data as possible. It is really, really hard to gather significant data about the universe at the largest scales. The video talked about hundreds of observations, but in a universe with more whole galaxies than grains of sand on earth there are implicitly a huge number of assumptions about how representative any data set is.

The numbers in astrophysics are so mind-meltingly enormous that often unimaginable and unintuitive consequences become regular occurrences.

This new data should obviously not be ignored, but it also shouldn't be interpreted as "disproving" anything. That is journalistic attention grabbing. Rather the results are simply some experimental physicists saying to theoretical ones: "here, look at these interesting new data about important data sources. It reduces our uncertainty about one specific thing. Please incorporate this into your cosmology theories"

No, it's not. The (local) metrics sourced by the Earth, Earth-Moon, Sun, solar system, Milky Way, and the Local Group are not at all like FLRW with or without a cosmological constant, while all those metrics are very much like Kerr or LTB, wherein ordinary matter like gas and dust gradually condenses into a point. Conversely, the metric globally is very much like FLRW with a small positive cosmological constant, and very much unlike a spacetime in which matter condenses into a point.

We can use Israel junctions to knit together "stacks" of regions that are well-approximated by a Kerr or LTB metric, and ultimately knit galaxy cluster sized LTB regions into expanding FLRW, representing the LTB regions as dust particles. This matches observations very well, and is called a "swiss cheese" cosmology, the name arising from how gravitational collapse ultimately creates voids -- holes -- in the otherwise homogeneous diluting dusts.

Kolb and others have a decent overview of how an Einstein-de Sitter-Lemaître-Tolman-Bondi swiss cheese universe works (the paper is in the context of the homogeneous-vs-inhomogeneous+backreacting cosmology debate, which is largely about connecting theory with astrophysical observations of a somewhat lumpy real universe especially in the transition from the matter-dominated era to the dark-energy dominated era) : https://www.osti.gov/biblio/21023997-cosmological-observable... ( PDF https://archive-ouverte.unige.ch/files/downloads/0/0/0/3/6/5... ). There's a good textbook treatment in Harwit's _Astrophysical Concepts_ as well (a preview exists at https://books.google.co.uk/books?id=gZfuBwAAQBAJ&pg=PA516&lp... ), and MTW has a (not very easy) overview of Israel-Darmois junctions in §21.13.

Such swiss cheese models match observations so well that it would be surprising (in a cool way) to find that there is any metric expansion at all in our solar system or in any of the galaxies and galaxy clusters we observe on the sky. We don't see that, though. In particular, one should take into account the evidence for accelerated expansion over the past few decades. Given that, one can consider a "fifth-force" (or nth, given Higgs etc.) representable as a field with a density and gradient, rather than the purely geometrical scaling in \Lambda-CDM. (This is at the root of some quintessence projects.) Results usually involve a lot of dynamics to suppress cosmological shear and other "little rip" effects at the margins of clusters with highly-luminous components, and adding several degrees of freedom that lack other physical support seems a lot worse than accepting an Einstein-de Sitter like swiss cheese geometrical model.

> local reference frame

It has nothing to do with reference frames; the metric tensor focuses matter and light one way or another (cf. Raychaudhuri) and within galaxy clusters practically all matter is focused towards a point in the future, whereas globally the same matter, and all other matter, and light, focus towards a point in the past (and the future focus points within galaxy clusters do not themselves focus together in the future). The only requirement is that the manifold is Lorentzian and time-orientable; you can use any system of coordinates that an arbitrary observer carries around with it, and you only need to do that if you care to describe when in the past or future and/or where relative to an observer the focus points lie.

> ... to match a distant galaxy's ...

How do you propose to do that? I think it's worth it for you to think about that a little: does your conception of a frame in which \lambda_{obsv} = \lambda_{emit} (rather than 1 + z = \frac{\lambda_{obsv}}{\lambda_{emit}}) extend into the distant past and distant future? How accelerated is this z-suppressing frame? In this frame what's the expectation for the wavelength of a CMB photon over time, or for galactic and extragalctic H I lines ?

> doppler expansion due to the nature of differing relativistic reference frames

Kinematical interpretations fall apart really spectacularly at high z, and conveniently we have a probe of (6 > z > 1) in the https://en.wikipedia.org/wiki/Lyman-alpha_forest which is a challenge for constructing a sensible z-suppressing frame of reference.

(See also MTW §29.2)

I disagree: Relativistic frequency shifts (doppler shift, gravitational shift, cosmological shift,...) can all be understood kinematically:

The invariant quantity you have to consider is photon 4-momentum, with energies at time of emission and absorption given by the projections onto the 4-velocities of the respective observers, so it's all about the relative orientation of some vectors, ie kinematics.

If spacetime is flat, photon momentum is constant, so all that matters is the relationship between emitter and observer frame. However, in curved spacetimes, there's no distance parallelism, and photon momentum at time of emission and absorption will be related by parallel transport along the photon geodesic.

In principle, you could even view the process of parallel transport as a series of infinitesimal Doppler shifts, though I would argue that puts emphasis on the wrong thing (the arbitrary frames chosen along the geodesic).

I'm not sure if you are objecting to approaches like the tetrad formalism in your final sentence, or even to gauge freedom itself. There's no reason an observer -- even an always lightlike one -- can't carry around its own system of coordinates. People from ISS astronauts (LVLH vs ECEF/ITRF) to aerobatic pilots (LVLH/LENU to GPS) to pedestrians looking at map apps on their smart phones do that casually all the time, and nobody expects ensembles of objects to move with respect to each other as one swaps sets of coordinates. Setting a new coordinate system every few steps while navigating on foot through a complicated city core is perfectly fine, and so is setting up a new coordinate frame at every infinitesimal step along an affine-parametrized curve traced out by a photon. IMHO that is the core of relativity.

I'm not sure if you are objecting to approaches like the tetrad formalism in your final sentence

The final sentence was just a comment on the pedagogy of deriving cosmological redshift via infinitesimal Doppler shifts. There's nothing wrong with it (sections of the frame bundles and all that jazz if you want to get formal), but to me, this feels like putting things on their head: I consider the Doppler shift a special case of the generic relativistic shift, making it circular to then explain the generic case as a series of infinitesimal Doppler shifts integrated along a photon's worldline.

In general, you can't do that: There's no distance parallelism in curved spacetimes...

Is this not because there is simply more space between things that are farther away and therefore more expanding space? So, more space = more magnitude of expansion?

I know my maths is not very accurate and maybe you can help correct my understanding. It just seems adding up each point that creates even more expanding points would never be a linear function.

Don’t understand the downvoted when I asked for more information and said my maths are probably wrong.

[1] https://calgary.rasc.ca/redshift.htm

Check out the wikipedia page on Hubble's Law [2] for more.

[1] https://arxiv.org/abs/0808.1081 [2] https://en.wikipedia.org/wiki/Hubble%27s_law

As a causal science enthusiast I am lost, how does one change our relativistic reference frame?

Or is it really? What if it's staying perfectly still, and YOU'RE the one moving?

... How could you even tell?

The principle of Relativity is that you cannot tell any difference, for the laws of physics are the same whether you are moving or the galaxy is moving. The theory of Special Relativity describes which mathematical transformations you need to go from one description to the other (in the absence of gravity, which is a General Relativity concern). Philosophically, the way of unifying these involves mixing up Space and Time, in which various observers cannot agree on a single version of things like speeds and time and energy levels, into a unified Spacetime, which they all can agree on.

"Changing your reference frame" simply means picking something different that you consider to be at rest.

Generally speaking an event is "observable" if some signal (usually light) could reach you from that event. It is generally uninteresting that different observers can see different sets of events at different points in their world-line. If you are lightyears apart, the signals will take time to reach you. This is what "spacelike separation" is all about.

But if you just sit around in one spot, signals can reach you from billions of light-years away. A certain event in your history might have been separated by space, but a point in your future may be separated from it in a timelike manner. You can't get away from events by simply going fast, either: the velocity addition makes signals impossible to outrun. What you need is to employ acceleration.

Consider a modified Zeno's paradox: you are 1 light year away from a signal, and begin accelerating. By the time it has covered 0.5ly, you are now 0.75 ly away. Unlike the original paradox, the math on this one works out: it is the acceleration equivalent of a black hole. (Most gravity and acceleration effects are interchangeable like that).

We could draw this out with a Minkowski diagrams, and find some line beyond which events become truly unobservable. We could call this line the "event horizon" (which, after all, is what the term is about in other contexts, too.)

On its face this seems like an extraordinary claim; I can’t think of how to square it with the (fundamental) assumption that the laws of the universe have not changed during its lifetime.

The idea that fundamentally, physical law does not change over time, is either a metaphysical or methodological assumption (or a bit of both), but it is certainly not an empirically-derived result, and it clearly does not rule out manifestations of those fundamental laws changing over time.

>evidence of accelerating expansion is that based on the redshift of nearby objects, we would expect distant objects to have a higher redshift than they actually do.

I think what you mean is "than we'd expect them to."

But maybe there are other standardizable objects. The sense I got from TFA is that there aren't.

[0] There is an explanation of this calibration here: https://aasnova.org/2019/07/26/tldr-the-trgb-gives-us-anothe...

May be a stupid question but wouldn't this apply only if we knew that the universe is uniformly dense? And we only see a tiny portion of it.

Fritz Zwicky proposed the idea in 1929 - didn't work out. In 1933 he 'inferred the existence' of dark matter/energy, after using the averaged speed of a group of galaxies to calculate their mass ... and found they were producing too little light to have that mass. And there it sits a century later. MON Dieu!

https://en.m.wikipedia.org/wiki/Speed_of_light

Scientists have even managed to freeze light for short periods of time.

https://io9.gizmodo.com/scientists-freeze-light-for-an-entir...

https://en.m.wikipedia.org/wiki/Tired_light

However, newer telescopes discovers more stars and galaxies than predicted by theories of expanding universe, thus favors Tired Light Theory. Also, discovery of gravitational waves confirmed that (speed of light in pure vacuum) c≠const, so physical vacuum is not an empty space, thus favoring TLT again.