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Does the universe have a fixed centre of mass? If it does, doesn't it necessarily mean that every action of ours has to be balanced by a counteraction somewhere in the universe so as to neutralize the disbalance of mass?

Tapi
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5 Answers5

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As far as we know, the universe does not have a centre of mass because it does not have a centre. One of the basic assumptions we use when describing the universe is that, on average, it is the same everywhere. This is called the cosmological principle. While this is only an assumption, the evidence we have from observing the universe suggests that it is true.

This can seem a bit odd if you have the idea that the Big Bang happened at a point and the Big Bang blasted the universe outwards from that point. But the Big Bang did not happen at a point; it happened everywhere in the universe at the same time. For more on this, see Did the Big Bang happen at a point?

It is certainly true that every action of ours has to be balanced by a counteraction because this is just Newton's third law. If I apply a force on you then you apply an equal and opposite force on me, so if we were floating in space our combined centre of mass would not change. So while it does not make sense to ask about the centre of mass of the universe we can ask what happens on a smaller scale, and we find that unless some external force is being applied the centre of mass of a system cannot change.

Jonathon Reinhart
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John Rennie
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  • I have limited knowledge of the topic. The Big Bang did not happen at a point and after reading your answer to that question, all I can understand is that the universe is like bubblegum of a specific volume which keeps expanding and hence the density decreases. So even if during Big Bang, the spacing between any given object is zero, it is considered to be happening everywhere because that(with the zero spacing) is all that was there making it infinite, i.e., without any edge. Correct me if I'm wrong. – Tapi Apr 21 '19 at 13:03
  • @LenaDas yes, that's basically correct. – John Rennie Apr 21 '19 at 13:28
  • The Universe is expanding, which means that the spacing between objects in the universe is increasing, so it'd keep on increasing until it reaches infinite distance? (which it will never reach as the concept of reaching infinity will be broken if it stops expanding at a particular point) (I'm not considering Big Crunch) If it so, wouldn't there be a time when the light from Sun would take millions of years to reach Earth? (considering the state of Earth to be as it is now) – Tapi Apr 21 '19 at 14:44
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    @LenaDas you are correct that the universe is expanding and that means the distances between objects are increasing. However the universe is increasing only on average. Some bits of the universe are shrinking, for example the collapsing dust clouds that create stars, and some are neither shrinking nor expanding, like the Solar System. It is only when we average out all the expanding bits, all the shrinking bits and all the static bits that we end up with the overall average expansion. – John Rennie Apr 21 '19 at 14:49
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    Anyhow, the Solar System is a static part of the universe so the expansion of the universe does not mean the Earth Sun distance is increasing. – John Rennie Apr 21 '19 at 14:50
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    @LenaDas What John said; however, there will be observable effects - at some (very distant) point in the future, it will no longer be possible to observe the galaxies that aren't gravitationally bound. This will probably mean that it would not be possible to observe the expansion of the universe either. Also, we don't know if the universe is infinite or not, and we don't know if there's universe beyond what was "our" Big Bang - all we know is that some 15 billion years ago, everything we have evidence for was in a tiny volume. – Luaan Apr 21 '19 at 15:41
  • How do we observe the expansion of the universe? You said it will "no longer" be possible to observe the galaxies that aren't gravitationally bound. That means we would not be able to see some of the things we can see now. Isn't that an observation; the disappearance of an object from our sight? Doesn't that mean that we're observing things move so far away that we cannot see them anymore? (collision not being a reason here) We sure don't know if there's something beyond the Universe we see because of Big Bang but had it been finite, wouldn't we have found some means to measure it till now? – Tapi Apr 21 '19 at 16:02
  • It is more than just an assumption... Most of the collective knowledge on physics would break down if it turned out untrue... The symmetry of the universe is important stuff. – Stian Apr 21 '19 at 17:36
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    "As far as we know the universe does not have a centre of mass because it does not have a centre." I don't quite understand how this is a reason. – JiK Apr 21 '19 at 21:14
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    I'm inclined to agree with @JiK... What even is a "center" for arbitrary objects? The center of mass is well-defined, but even a volumetric center isn't really meaningful unless you just happen to have, e.g., a sphere... – Him Apr 22 '19 at 15:27
  • "unless some external force is being applied the centre of mass of a system cannot change." The velocity of the center of mass can't change. The position can. – Acccumulation Apr 22 '19 at 16:09
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    @JiK In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous & isotropic when viewed on a large enough scale since the forces are expected to act uniformly throughout the universe. (In the case of a rigid body with uniform density, CM is at the centroid. In classical mechanics, the CM frame is an inertial frame in which the CM of a system is at rest with respect to the origin of the coordinate system) In the case of the Universe, which is expanding, there is no centroid and GR comes into play. – Tapi Apr 22 '19 at 17:03
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The universe is not obeying a classical Newtonian physics, only locally Newton's laws hold. The universe as seen in the standard Big Bang model, obeys General Relativity.

bb

This is a cut in the time dimension and one space dimension. At the line of the present universe, all points were at the beginning of the universe, and there can be no center of mass for the observable universe.

Visualize a balloon that starts inflating from a (0,0,0) point in space. At time t the surface is a sphere, and all points on the sphere were at the beginning (0,0,0). Is there a center of mass for the surface? All points are at the center of mass, because they are balanced by all other points.

The balloon is an analogue of the three dimensional space of the universe. In contrast to the balloon, the theory does not need to embed the universe in a higher dimension so as to start with a four dimensional space point. All points in our three dimensions were at the beginning of the Big Bang.

anna v
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    The universe is 3 dimensional, and so is a balloon. We have no evidence whatsoever for any curvature in some higher dimension. But we do know that the balloon has a centre. – John Duffield Apr 21 '19 at 08:50
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    @JohnDuffield The balloon is a two dimensional analogue embedded in our three dimensional space, to give an intuition of why there is no center to the surface. The general relativity obeying uiniverse is not embedded in a four dimensional space, as far as our modelin goes. The proof of the validity of the model is that it explains the observations up to now. – anna v Apr 21 '19 at 13:59
  • @annav What is meant by "Earliest time visible with light" in the image attached? Does it mean that we've been able to see light coming from a point 380,000 years ago? And that it took light 380000 years to reach us and that any light beyond that has never reached us? – Tapi Apr 21 '19 at 19:38
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    Lena, the times on the X axis, such as 380,000, are time after the origin, not time backward from the present. So that’s about 13 1/2 billion years ago. – prl Apr 21 '19 at 21:57
  • @LenaDas The universe was so dense, that it wasn't opague until that time, so there is no light from before – Christian Apr 22 '19 at 06:49
  • @LenaDas It is all about the couplings. Electromagnetic scatterings happen in the very dense , once it expands so that electromagetic interactions stop being very probable, photons can get out and survive to our time as the cosmic microwave background. For neutrinos decoupling happens much earlier https://en.wikipedia.org/wiki/Neutrino_decoupling (weak interaction scatters) , but it is very hard to get the usefulness of photons, because detecting low energy neutrinos is much harder.https://en.wikipedia.org/wiki/Neutrino_decoupling – anna v Apr 22 '19 at 08:08
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    Maybe we will be luckier with the gravitaitonal decoupling http://www-ucjf.troja.mff.cuni.cz/~iss2017/ISS2017_files/DaniFIGUEROA_GW_Lecture1.pdf and be able to probe the very beginning – anna v Apr 22 '19 at 08:10
  • One thing always bothers me about this picture. As described, it seems to imply that the universe is finite in its space dimensions. But afaik we have no clue on whether it is or not. So the sideways bell shape could be only the evolution of a one dimensional segment of the universe, which might be only a fragment of a larger segment, or of an infinite line, or an arc on an expanding circle if there is a circular spatial dimension, etc.. Actually, a finite segment does usually have a center, but I may miss a point about the geometry of relativity. – babou Sep 29 '20 at 12:26
  • @babou It is the observable universe in the picture – anna v Sep 29 '20 at 13:31
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The universe is often modelled by the FLRW metric with the assumption of homogeneity and isotropy of space. If we for simplicity assume that there is no curvature $k=0$, and even if we pick a global coordinate system for space (which would artificially distinguish an origin, but remember: the universe has no center), then the center of mass is given as

$${\bf R}_{\rm COM} ~=~ \frac{\int_{\mathbb{R}^3} \!d^3{\bf r}~{\bf r}}{\int_{\mathbb{R}^3} \!d^3{\bf r}~1},$$

which is mathematically ill-defined. (A similar negative conclusion is reached in the case of curvature $k=\pm 1$.)

Qmechanic
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  • Could you explain you calculate the center of mass? I thought that our Universe is a compact 3-manifold space embedded in a higher-dimensional space. Wouldn't the integral need to be over the domain of this manifold instead of R^3? 2. Additionally, if the Universe were a 2-dimensional space, for example, embedded in a 3-dimensional space, wouldn't the center of mass exist outside the 2-dimensional space and be clearly defined? I'd love to understand this better, though I'm not well-versed in physics, and definitely quite ignorant when it comes to Special Relativity.
    • – Catriel Dec 11 '23 at 16:43
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    Hi @Catriel. Thanks for the feedback. 1. This answer assumes the simplest FLRW model with $k=0$ where space is $\mathbb{R}^3$, i.e. non-compact. – Qmechanic Dec 12 '23 at 07:29
  • thank you very much for your reply. If I understand your integral, the density is uniform on an infinite universe which would imply infinite number of galaxies. But, if the universe has no curvature, and had finite number of galaxies, there surely be a center of mass. I guess the fact that we can't spot one means that the universe must be curved. Am I missing something? Thanks again. – Catriel Dec 12 '23 at 22:58