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?
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.
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.
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.
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.
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.
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."
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.
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.
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.