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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?

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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.

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    $\begingroup$ wouldn't $c$ remain the same due to general/special relativity? $\endgroup$ Feb 2, 2023 at 21:55
  • $\begingroup$ @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. $\endgroup$
    – Carmeister
    Feb 3, 2023 at 2:11
  • $\begingroup$ 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? $\endgroup$ Feb 3, 2023 at 11:33
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    $\begingroup$ @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.) $\endgroup$
    – wizzwizz4
    Feb 3, 2023 at 14:49
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    $\begingroup$ 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. $\endgroup$
    – Michael
    May 26, 2023 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.

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    $\begingroup$ This does not answer the question: how do we know? It just tells what we know, as if "take it or leave it". $\endgroup$ Feb 3, 2023 at 21:11
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    $\begingroup$ @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)? $\endgroup$ Feb 5, 2023 at 13:08
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    $\begingroup$ @ 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. $\endgroup$ Feb 5, 2023 at 17:33
  • $\begingroup$ @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. $\endgroup$ Feb 6, 2023 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.

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    $\begingroup$ Perhaps light gets faster? Perhaps we will feel the growth, it depends how linear it is $\endgroup$
    – Rabbi Kaii
    Feb 2, 2023 at 21:15
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    $\begingroup$ "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? $\endgroup$ Feb 3, 2023 at 9:05
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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.

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  • $\begingroup$ I think you meant to say, if the expansion affected galaxies then they would get bigger... $\endgroup$ Feb 3, 2023 at 21:21
  • $\begingroup$ 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 $\endgroup$
    – avigil
    Feb 3, 2023 at 23:30
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    $\begingroup$ @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. $\endgroup$ Feb 3, 2023 at 23:38
  • $\begingroup$ Distant galaxies are smaller on average (but not for this reason). $\endgroup$
    – ProfRob
    May 28, 2023 at 8:27
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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."
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    $\begingroup$ 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? $\endgroup$ Feb 3, 2023 at 21:23
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    $\begingroup$ @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. $\endgroup$
    – Sten
    Feb 4, 2023 at 9:22
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    $\begingroup$ @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. $\endgroup$
    – Sten
    Feb 11, 2023 at 1:21
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    $\begingroup$ @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. $\endgroup$
    – Sten
    Feb 11, 2023 at 16:33
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    $\begingroup$ 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. $\endgroup$ May 26, 2023 at 14:58
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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.

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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.

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    $\begingroup$ The consensus is that the Pioneer anomaly was caused by thermal emissions. The paper by Kopeikin mentioned in that press release (available non-paywalled here) is completely wrong and it's pretty shocking to me that it was accepted by Physical Review D. It's the same error as in the paper of Cooperstock et al. mentioned in this answer: he's calculating the gravitational effect of nonexistent matter. $\endgroup$
    – benrg
    Feb 10, 2023 at 8:51
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    $\begingroup$ @benrg The work by Kopeikin was accepted by Phys Rev D for two reasons. First, it underwent very thorough refereeing. Second, Kopeikin is one of the world leading experts on GR. Last, and by no means least, there is no established consensus on the Pioneer anomaly. $\endgroup$ Feb 10, 2023 at 14:32
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    $\begingroup$ @Michael_1812 that's interesting; one can calculate the thrust due to recoil from infrared photons radiated from one side of the spacecraft (the hot side of course) and one can know that this must happen. In other words, it would be a huge puzzle if this deviation was not seen! Related in Space SE: Did New Horizons also demonstrate the "Pioneer Anomaly"? (with images from simulation) and Could radiated heat propel space-craft in outer space? $\endgroup$
    – uhoh
    Feb 16, 2023 at 23:20
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    $\begingroup$ @Michael_1812 and Is the speed of the Voyager probes accurately described by Newton's or Einstein's theories? (yes) So for "there is no established consensus" to be true, I think that you have to include flat-Earthers and conspiracy theorists in your pool of opinions. $\endgroup$
    – uhoh
    Feb 16, 2023 at 23:22
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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.

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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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    $\begingroup$ Why Is there a down votes so that I can improve upon my a answer? $\endgroup$
    – user47732
    Feb 3, 2023 at 15:40
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    $\begingroup$ 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. $\endgroup$
    – pela
    Feb 3, 2023 at 16:37
  • $\begingroup$ Thanks a lot, @pela. I've improved upon my answer $\endgroup$
    – user47732
    Feb 4, 2023 at 6:08

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