# Why isn't the universe travelling at $c/2$ to the left?

Consider two inertial observers starting from the same spacetime point, one remaining at rest relative to the CMB and one moving at speed $$c/2$$.

According to relativity theory, neither observer has a preferred status - no local experiment would allow you to determine your velocity in an absolute sense.

However the first observer has a preferred status in that he observes the universe as approximately homogeneous and isotropic whilst the second does not.

This situation is often described by saying general relativity is a background independent theory but the background is determined 'dynamically'.

What is this dynamic mechanism which resulted in the first observer having this preferred status? I am just trying to get a handle on whether this is a meaningful question to ask within the current state of mainsteam physics or not. I will accept a simple "No" as an answer, but any justification would be appreciated.

Edit: I am not asking if the existence of a preferred frame contradicts relativity, but rather whether this situation points to a deeper more natural theory of spacetime where we don't have to just say "this is the universe we find ourselves in".

Edit: The two given answers has allowed me to give a more precise statement of this question: "Of the 10 Poincare group degrees of freedom, our universe appears not to have a preferred spatial origin (3, homogeneity) , not to have a preferred spatial direction (3, isotropy) but it does have a preferred temporal origin (1) and a preferred (local) Lorentz boost (3). Can we explain the latter of these?"

• Commented May 14, 2021 at 20:08
• I believe the crux of the argument presented in the above question is that, relativity simply says the laws of physics do not prefer any inertial reference frame over another. The CMB is, in a sense, an extended object which can be measured, but is not by itself a 'fundamental law'. For example, suppose we're floating out in space. You are stationary relative to the Earth, and I am flying by with speed $c/2$. You observe the Earth at rest, whereas I do not. So is your reference frame is 'preferred'? Does this contradict relativity? I hope you see my point. Commented May 14, 2021 at 20:13
• @ArturodonJuan Thanks, I hadn't found that question. Commented May 14, 2021 at 20:59
• Commented May 18, 2021 at 14:42

## 2 Answers

Maybe it's easier to work by analogy with a simpler example.

The laws of physics are invariant under rotations in three dimensions. But you certainly do not experience "up" to be equivalent to "north" and "east," because the Earth's gravity pulls you down. Is there a contradiction? No -- the fundamental laws are invariant, but we live on a planet, and the effective laws we experience on this planet are not invariant under rotations that exchange "east" and "up" (for example).

It's really the same situation in cosmology. The underlying laws are invariant under Lorentz transformations. But the initial conditions of the Universe had a frame at which the matter was (on average) at rest, and so the specific Universe we find ourselves in has a preferred frame.

• Thanks. I wasn't suggesting in my question that the situation was a contradiction of the principle of relativity. I was rather asking why we "find ourselves" in this frame. I take from your answer that this question lies outside current physics and will accept that unless someone has a deeper answer. Commented May 14, 2021 at 20:56
• @isometry I think I see. Then my answer is that, based on the initial conditions, the vast majority of the matter is in the same frame. Once that is the case it would take a huge amount of energy to accelerate a macroscopic amount of matter to a substantial fraction of the speed of light relative to the cosmological frame. Commented May 14, 2021 at 21:05
• Understood. So "based on the initial conditions" is another way of saying "the specific universe we find ourselves in". Commented May 14, 2021 at 21:12
• @isometry Sort of, but I would say it is more specific. It's true that the details of our current universe are buried in the initial conditions, and it's also true that the initial conditions are what break symmetries of the fundamental laws. But we can try to develop a theory of the initial conditions (inflation, the multiverse...). Additionally there's a mathematical statement that's important: even though our universe has a preferred frame because of our initial conditions, the underlying Lorentz symmetry implies that there are other solutions where the initial matter distribution... Commented May 14, 2021 at 22:10
• ...is boosted by an arbitrary amount in an arbitrary direction. So the symmetry relates different solutions with different initial conditions. This is maybe on a deeper level the answer to your question -- there is another possible universe (according to the laws of physics as we understand them) that have the matter distribution traveling at $c/2$ relative to our frame. We just don't live in that one. Commented May 14, 2021 at 22:11

The "preferred reference frame" thing is really about flat spacetime. When ignored, it leads to statements such as "You can't go faster than light because your mass increases with speed, diverging at $$c$$" ["You can't go faster than light because at any speed, you're still rest in your frame, and light moves at $$c$$ in all directions", is better].

Also: "Time slows down for a twin on a spaceship". [In the twin paradox, each twin sees the other's clock ticking slower].

Enter GR and cosmology, at any point, one can define a preferred rest frame that is (roughly) at rest with respect to the CMB. The problem with this as "defining a preferred frame" is that it is local. Every point in the universe has a different velocity (hence: the Hubble constant).

If every galaxy we see had a zero peculiar velocity (including the Milky Way), they would all be "at rest" relative to the CMB, but each would have a velocity relative to the other.

In your example, with one observer moving at $$c/2$$, if he were suitably far away, then both observers could be at rest relative to the CMB.

• Thanks - that gives me something to think about to ask a more precise question. Commented May 14, 2021 at 21:52