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Alright so I've been thinking a lot about how the universe expands and I've always wondered if we're getting bigger as well. Since everything would be getting larger at an equal rate (tools of measurements, atoms), would it even be possible to discern if we were getting bigger or not?

Landon
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Matter contraction: If everything got twice as big then you are right that rulers etc. would not be able to measure it. However, some physical constants are expressed (partly) in meters, and it would appear that these constants had halved (because the meter stick has doubled).

For example my distance from the centre of the Earth will have doubled, so gravity would get weaker. We would need a new value for $G$. Light would look like it was going slower, so $c$ would seem smaller.

Space expansion: Interestingly, the expansion of the universe is actually connected to the opposite situation. We see that the distance between stars is twice as many meter-sticks than we infer it used to be. The standard explanation (quite reasonably!) is that the distance has indeed doubled. But we could offer the explanation that the distance remained the same, but the meter stick has halved in length. Matter of a fixed size in an expanding universe looks kind of the same as a universe of a fixed size with shrinking matter.

But the shrinking has to come with physical constants changing to compensate, otherwise we would notice.

Dast
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    wouldn't $c$ remain the same due to general/special relativity? – an inconspicuous semicolon Feb 02 '23 at 21:55
  • @blankettripod $c$ (and other physical constants) would remain the same. But the numerical value of $c$, expressed in $m/s$, could change if the length of the meter changed. – Carmeister Feb 03 '23 at 02:11
  • oh i see, that makes more sense, so if 1 meter became 2, $c$ would become $1.5*10^8$ but would still be the same speed, right? – an inconspicuous semicolon Feb 03 '23 at 11:33
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    @blankettripod Yes. But in order to match our current models, either $c$ would have to change, or we'd have to speed up / slow down as we changed size. (Positing that we're growing / shrinking, and all the physical constants are changing in exactly the way that'd prevent us from noticing this, is a more complicated theory than just assuming we're not.) – wizzwizz4 Feb 03 '23 at 14:49
  • I have heard that light speed c is nowadays defined as a fixed value and meter is now defined as variable - as whatever distance that light passes during one second. Not the way around. Is that true? If so, then the length of a meter would change without c value changing. Do I get that right? – Roland Pihlakas Feb 03 '23 at 21:17
  • @RolandPihlakas That new physics-based definition of the International System of Units (SI for short; the acronym is French) assumes the speed of light is constant. There is absolutely no reason to disbelieve this. Given ever improving observations that the speed of light is indeed constant (and that various other physical quantities are constant), the SI community decided about four years ago to use those constants of nature as the basis for a complete revamping of the SI base units. – David Hammen Feb 05 '23 at 13:50
  • @David Hammen The objective of the question is not whether I am disbelieving that speed of light is constant. Instead I am asking what are the consequences of this sort of setup. Is a meter potentially changing its length? Just as with your other response and comment, again I am surprised that you similar theme here "There is absolutely no reason to disbelieve this" - focusing on forcing my beliefs instead of responding to the content of the question. Why? – Roland Pihlakas Feb 05 '23 at 17:38
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    Interestingly enough, I once did a calculation on how much energy would be radiated if all matter in the universe were shrinking, based on the idea that mass would decrease concordantly. It came out to a pretty reasonable value (small enough that we probably wouldn't detect it locally) as well as comparable in total to the estimated dark energy content of the universe. – Michael May 26 '23 at 19:19
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We do not know whether or not we live in a simulation in which our capricious simulation overlords have conspired to hide evidence that we are growing larger. Discounting that possibility, science says we are not growing larger.

The expansion of the universe is something that happens at very large distance scales. At moderate distance scales gravitation overwhelms expansion, at least for now, and will continue to do so for trillions of years in the future. At even smaller scales (e.g., us), electromagnetic interactions overwhelm gravity.

We are not expanding, nor is the Earth, nor is the solar system, nor is the galaxy. Our galaxy is on a headlong course to collide with the Andromeda Galaxy in about five billion years due to gravitation. The expansion of the universe is something that happens on an even larger scale.

David Hammen
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    This does not answer the question: how do we know? It just tells what we know, as if "take it or leave it". – Roland Pihlakas Feb 03 '23 at 21:11
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    @RolandPihlakas It does answer the question as far as I'm concerned. One either accepts that science is more or less correct, which clearly says we're not getting bigger for reasons elaborated in the answer, or one goes to the woo side of pseudoscience that says anything goes. That woo side is impossible to disprove. What if there's some malevolent super-being who has made key observations we make somewhat fictional? What if we're living in a simulation made by capricious super-beings who decided to toy with the simulated minds of their simulated under-beings (e.g., us)? – David Hammen Feb 05 '23 at 13:08
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    @ David Hammen The question explicitly asked "how" do we know, not "what" we know. I other words, OP wanted to understand. This response does not even attempt to answer the "how" question. It could be even argued that believing the "science" without understanding it is closer to pseudoscience than the desire to understand would be. How is one going to learn science if the responses are like "just trust in the science"? I am surprised that you dismissed my concern. – Roland Pihlakas Feb 05 '23 at 17:33
  • @RolandPihlakas The answer is indeed just trust in the science. As my edit says, we do not and cannot know whether we are simulated beings. I prefer to think we are not. Accepted science says the expansion is a very large scale phenomenon while at small scales (groups of galaxies are "small scale"), the interactions we know of completely overwhelm the expansion of space. – David Hammen Feb 06 '23 at 12:33
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Beyond the other answers here, we can measure an upper limit on how fast we're growing. For example, imagine that everything doubled in size. You're right that our rulers would double in size and everything would seems the same size from that perspective.

However, since everything is twice as big, light now needs twice as long to travel the distances that it used to. Every network engineer using fibreoptic cables suddenly sees their latency double. Every GPS unit fails, as the calculation is partially dependent on using the time it takes the signal to travel from the satellite to the device. Radios would fail as the frequency controlled by the electronics would no longer match the wavelength optimized by the antenna (though this wouldn't be quite as prfound if it was truly an exact doubling).

To be more succinct, the speed of light is defined as 299,792,458 meters per second. The length of the meter and the duration of the second are linked by this fundamental definition. If something comes along and changes the meter, then the second is redefined to match. If the duration of a second was changing, it would be pretty noticeable.

rprospero
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    Perhaps light gets faster? Perhaps we will feel the growth, it depends how linear it is – Rabbi Kaii Feb 02 '23 at 21:15
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    "If the duration of a second was changing, it would be pretty noticeable." - why wouldn't our perception of it change to match the actual change? – Karl Knechtel Feb 03 '23 at 09:05
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If the expansion affected things at the scale of stars and galaxies, we would see galaxies get smaller the further away they are. Since that is not the case, we can deduce that the expansion doesn't happen at those scales.

Greg Miller
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  • I think you meant to say, if the expansion affected galaxies then they would get bigger... – Roland Pihlakas Feb 03 '23 at 21:21
  • well another way to say that is that if everything was getting bigger at a constant rate, things that were closer to us would appear to get bigger faster because apparent size has an inverse relationship to distance, which ends up being the same thing – avigil Feb 03 '23 at 23:30
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    @RolandPihlakas they would get smaller the further away they were. Due to the light travel time, we would be seeing them at a time when they had expanded less. – Greg Miller Feb 03 '23 at 23:38
  • Distant galaxies are smaller on average (but not for this reason). – ProfRob May 28 '23 at 08:27
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Space is not expanding, at least not in the way that you are thinking. Expanding space is just a convention that simplifies some of the mathematics in the context of cosmology. The contents of the universe are expanding -- moving apart in a uniform way -- and this process is conveniently described using a coordinate system in which space is taken to expand. But that is just a convention. Expanding space does not have local physical consequences.

This means that the expansion of space does not cause objects to expand. Not only that, it doesn't even supply an expansion force that has to be counteracted by gravity or electromagnetism, as is often mistakenly believed.

Why then is the universe expanding, if not because of the expansion of space? Imagine throwing a ball up into the air at escape velocity. After the ball departs, there is no continued impetus for separation; indeed gravity is pulling the ball back. And yet the ball continues to move away from the Earth due its initial motion alone. It's similar with the universe. Cosmic expansion is a consequence of motion in the initial conditions.

Notes

There is one physical sense in which space might be expanding. If the universe is finite, then its total volume (measured on comoving surfaces) grows. This does not affect local dynamics, though.

Also, dark energy supplies an expansion force. However, this is more clearly viewed as the cause of accelerated expansion than a consequence of it. Also, the force itself is most clearly interpreted as just gravity, since it arises from the equations of general relativity.

Further reading

I also include some choice quotes.

  • A diatribe on expanding space. "This analysis demonstrates that there is no local effect on particle dynamics from the global expansion of the universe: the tendency to separate is a kinematic initial condition, and once this is removed, all memory of the expansion is lost."
  • The kinematic origin of the cosmological redshift. "The tendency [of the Solar System] to expand due to the stretching of space is nonexistent, not merely negligible."
  • On The Relativity of Redshifts: Does Space Really "Expand"? "But if you assume that expanding space is something physical, something like a river carrying distant observers along as the universe expands, the consequence of this when considering the motions of objects in the universe will lead to radically incorrect results."
Sten
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    Since when does the space not expand? Was big bang expansion of space or the particles moving away from each other? I have heard so far that big bang was expansion of space, so did something change later? – Roland Pihlakas Feb 03 '23 at 21:23
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    @RolandPihlakas As Steven Weinberg said, "Cosmologists sometimes talk about expanding space – but they should know better." To be clear, cosmology is a mathematical science, and everyone agrees on the mathematics. There is no question about the mathematical, and hence physical, description of an expanding universe. The only question is how we translate the mathematics into words or pictures. And "expanding space" is a translation that leads to a lot of misconceptions, like the one that led to this question. – Sten Feb 04 '23 at 09:22
  • Dear @Sten, The statement that "The tendency of the Solar System to expand due to the stretching of space is nonexistent" is incorrect. https://www.sciencedaily.com/releases/2012/10/121009161103.htm – Michael_1812 Feb 10 '23 at 14:20
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    @Michael_1812 That paper's conclusion would imply that cosmic expansion affects local dynamics in the Milne universe, which is impossible because the Milne universe is just re-parametrized Minkowski spacetime. The paper is wrong. – Sten Feb 11 '23 at 01:21
  • @Sten The linear FLRW is mathematically equiv to Milne, which is mathematically equiv to a global Minkowski spacetime. However, the global Minkowski time T is not the local Minkowski time, and is not directly observable. We measure the local Minkowski time, (the proper time tau). In Milne, photons have a constant velocity in the global Minkowski spacetime. So, the tau measured by our clocks and the T along light geodesics are not the same. Kopeikin proves that the difference is measurable if our local space is expanding. His result reproduces the Pioneer anomaly, both in magnitude and sign – Michael_1812 Feb 11 '23 at 14:13
  • @Michael_1812 Are you suggesting that changing the way you parametrize spacetime changes the physical behavior of clocks? – Sten Feb 11 '23 at 15:02
  • @Sten On the contrary, I emphasise that there is a difference between the proper time \tau and the coordinate time T. This difference is exploited in Kopeikin's work: his paper is about kinematics of clocks (timelike geodesics) and light particles (null geodesics) in two different metrics - one is globally flat and another one has a conformal factor depending on the time tau in front of the spatial metric. The Milne coordinates and the local coordinates are not identical - they are connected by a non-linear transformation. – Michael_1812 Feb 11 '23 at 16:28
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    @Michael_1812 Milne coordinates don't matter. They are just coordinates. If the article by S. Kopeikin is correct, then the influence of cosmic expansion is expected in special relativity, and that influence could be of any imaginable magnitude, since Minkowski spacetime can be parametrized with Milne coordinates with any expansion rate. – Sten Feb 11 '23 at 16:33
  • @Sten We measure the proper time \tau. Also, please be mindful that global expansion exists in all viable cosmological models, which models look the same in the linear order of approximation with respect to the Hubble constant. Within this approximation, it is impossible to distinguish (mathematically) the Milne model from the FLRW one. To do so, one would have to extend his calculations to the second Hubble order, which Kopeikin did not do, because H^2 terms are too small to be measurable in the Pioneer experiment. – Michael_1812 Feb 11 '23 at 17:20
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    This answer's cited creates a distinction between vacuum energy and the hubble constant/space expansion, who then say "vacuum energy makes things move apart, but that isn't space expansion". That is rather ahistorical; vacuum energy was created as a mechanism to explain space expansion. Saying "the thing that explains X means X does not exist" seems, well, fundamentally wrong. – Yakk - Adam Nevraumont May 26 '23 at 14:58
  • "In the case of vacuum-dominated models, then, the repulsive effects of vacuum energy cause all pairs of particles to separate at large times, whatever their initial kinematics; this behaviour could perhaps legitimately be called ‘expanding space’. Nevertheless, the effect stems from the clear physical cause of vacuum repulsion, and there is no new physical influence that arises purely from the fact that the universe expands. The earlier examples have proved that ‘expanding space’ is in general a dangerously flawed way of thinking about an expanding universe." arXiv:0809.4573 [astro-ph] – Yakk - Adam Nevraumont May 26 '23 at 14:59
  • @Yakk-AdamNevraumont The distinction comes from the mathematics. It's possible to interpret dark energy's repulsion as a consequence of "stretching of space", but that interpretation is (1) only valid for one particular coordinate system and (2) only valid if dark energy is truly a cosmological constant (we don't know that). General covariance is a central principle of general relativity, and the "stretching of space" interpretation of the action of dark energy does not admit a covariant description. – Sten May 26 '23 at 15:22
  • @Yakk-AdamNevraumont Also, dark energy was not created to explain cosmic expansion! Cosmic expansion would happen with or without dark energy. Dark energy was only devised to explain a particular feature in the expansion history. – Sten May 26 '23 at 15:24
  • @Sten how do you explain a redshift of z=5? – Lawnmower Man May 26 '23 at 15:57
  • @LawnmowerMan What's special about $z=5$? Is this a concern about things receding "faster than light"? The answer to such concerns is that those recession rates are not relative velocities. If you were to define the recession rate of your friend in a rocket traveling away from you at near light speed in the same way that we define the recession rate of a cosmologically distant object, you would also conclude that your friend is receding much faster than light. – Sten May 26 '23 at 16:11
  • In fact, there's a special case of the expanding universe solution (the FLRW metric) called the Milne model (mentioned in earlier comments). It's special because it turns out to be exactly equivalent to (a portion of) the flat, static spacetime of special relativity. In spite of this, the model includes features people normally attribute to expanding space, like faster-than-light recession rates. The Milne model is one of the clearest demonstrations that "expanding space" is just a coordinate choice. – Sten May 26 '23 at 16:32
  • @Sten it also requires zero energy density and negative curvature, both of which are incompatible with cosmological observations. Doesn't this put you in the crank corner of physics? – Lawnmower Man May 26 '23 at 18:40
  • @LawnmowerMan What is this strawman? It's an illustrative example, showing how you can faster than light recession with no concept of expanding space. – Sten May 26 '23 at 19:09
  • @Sten ok, then please explain how the observable universe is > 20 gly across but only 13 gy old. You have to reject BB/inflation or size estimates or you have FTL galaxies. Which do you pick? – Lawnmower Man May 26 '23 at 21:10
  • @LawnmowerMan It's essentially time dilation. The key issue is that there is no objective definition of "now" for observers in different places. In cosmology, we choose to define "now" for a distant observer to mean "the same amount of time has elapsed since the Big Bang". But observers receding at relativistic speeds are time dilated. If an observer is receding from us at a relativistic speed, they could cover a distance much greater than 13 billion light years in an "as measured by them" (proper) time span of only 13 billion years. – Sten May 27 '23 at 00:39
  • That's not an exact picture, since (for realistic cosmologies, i.e. not the Milne model) spacetime is globally curved. In such spacetimes, you can't even uniquely define a relative velocity (and hence time dilation factor) for a distant object, so it's more difficult to give an intuitive account for what's happening. Nevertheless, it should remain qualitatively clear that relativistic considerations can explain the observable universe being larger than the age of the universe. – Sten May 27 '23 at 00:51
  • @Sten I think your argument is disingenuous. ΛCDM is the best-supported model and does explicitly include expansion of space. I think the strongest statement you can make is that a Milne-style cosmology might be compatible with observations, if only you can find all the missing antimatter. But pretending that it is the "true description" of reality while ΛCDM is a poorly described alternative is not the least bit justifiable. – Lawnmower Man May 27 '23 at 19:01
  • @LawnmowerMan Regarding "ΛCDM is the best-supported model and does explicitly include expansion of space", the whole point is that this is false. It doesn't matter if you are considering ΛCDM, Milne, de Sitter, Einstein-de Sitter, whatever. The basic fact is that there is no such thing as an objective notion of "expansion of space" within general relativity. Spacetime simply doesn't include properties like dilation and motion. The only objective physical property of a point in spacetime is its (tensor) curvature. – Sten May 27 '23 at 19:35
  • @LawnmowerMan The only reason I brought in Milne is that it is easier to develop an intuition for. It's not special otherwise. – Sten May 27 '23 at 19:42
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If everything is getting bigger at scale, so that there is no possible way to measure it, than we can't measure it. But if there is no way to measure it, there is no influence on anything. And if it has no influence, it doesn't matter, if it does.

Christian
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In a certain sense, we are getting bigger -- where "we" means: the solar system. I am talking about a physical effect, which is so feeble that it took astronomers dozens of years to measure it reliably. This is the so-called Pioneer anomaly.

It turned out that the two Pioneer spacecraft launched in the early 70s have been decelerating anomalously as they were departing the solar system.

Although the topic is still being discussed, the cosmological expansion seems to be the likeliest reason for this anomaly. See, e.g., this press release and a reference therein.

Michael_1812
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In a closed universe, after expanding, the universe contracts. Locally, we are in a closed region called the Local Group, and the Andromeda galaxy is approaching. Now are we expanding to explain the collapse of the Local Group, or are we shrinking to explain large scale expansion? (We are close to stationary with respect to the Virgo Supercluster, just to make it more problematic). Clearly, neither shrinking nor expanding would work to explain all of this.

GR just says that space is subjected to curvature from mass-energy, and free falling motion is always along a geodesic. If you start with particles all moving away from each other, they may continue to do so for a while, but if they have mass then the curvature of space-time slows them down. If the local density is high enough then this material is destined to fall together. But, if there are centrifugal forces or electrical forces, as in the solid Earth, to oppose the fall, then the motion can be stopped.

eshaya
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How would we know:

If the $Rv$ was great enough, to make us expand. Then how would we know (the main question) ? If the $Rv$ was sufficient, We could also observe the latency between radio waves as increasing as in $Rv$ is proportional to the proper distance or $D$ or $Rv ∝ D$ thus as the distance is increasing light would take more time, given by $T=D/v$, also the magnitude of the radio waves would decrease as a consequence of the inverse square law, the frequencies would be more cosmological redshifted.

We would also observe many planets become cthonian type or it would also amount to higher seismic activity.

Why we aren't expanding:

**A cosmological constant ** causes the universe to expand, however sometimes gravity overwhelms the cosmological expansion. However The hubble constant or the speed at which the universe is expanding, is 160 km/s per million-light-years!, why does gravity overwhelm it when the hubble's constant's value is so huge?, it's because gravity is a distant dependent force. So because gravity is distant dependent, the recessional velocity/$Rv$ is decelerated using gravity, so that an object retains some sort of equilibrium.

Many other forces also do the same like Electromagnetic force or the strong force also do someting similar except at smaller scales

If the expansion was greater than just 1 part in a million or 1/1000000 then the baryonic matter would have expanded so much that there wouldn't have any observable baryonic matter left.

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    Why Is there a down votes so that I can improve upon my a answer? –  Feb 03 '23 at 15:40
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    Not my downvote, but you don't really answer the question, namely how we know that we're not expanding. Also, where did you get the 160 km/s/Mlyr? It should be around 21–22 km/s. – pela Feb 03 '23 at 16:37
  • Thanks a lot, @pela. I've improved upon my answer –  Feb 04 '23 at 06:08