How is the universe expanding if the speed of light is finite?

[Phys12]

The universe seems to be expanding since the farther away an object is, the faster it is moving. However, because of the finite speed of light, the farther away we look in distance, the further back in time we look. Does that mean that galaxies were moving faster in the past and are now slowing down? Wouldn't that indicate a shrinking universe, instead of an expanding one?

I'm having trouble imagining this situation. The inflating balloon analogy helps, but not when it comes to thinking about the expansion taking time intro consideration.

 

[kimbyd]

For far-away galaxies, yes, they were receding from us more rapidly when the light that we see was emitted than they are now. But that's not a shrinking universe: they're still moving further away.

For most closer galaxies, the rate of expansion is such that they are now moving away from us faster than they were when the light we're now observing was emitted.

 

[phinds]

The universe seems to be expanding since the farther away an object is, the faster it is moving. However, because of the finite speed of light, the farther away we look in distance, the further back in time we look. Does that mean that galaxies were moving faster in the past and are now slowing down? Wouldn't that indicate a shrinking universe, instead of an expanding one?

I'm having trouble imagining this situation. The inflating balloon analogy helps, but not when it comes to thinking about the expansion taking time intro consideration.

I suggest the link in my signature.

The far away galaxies are RECEDING from us at super-luminal rates but since there is no proper motion involved, there are no speeding tickets issued.

 

[russ_watters]

The universe seems to be expanding since the farther away an object is, the faster it is moving. However, because of the finite speed of light, the farther away we look in distance, the further back in time we look. Does that mean that galaxies were moving faster in the past and are now slowing down? Wouldn't that indicate a shrinking universe, instead of an expanding one?

Expanding is shrinking? That doesn't follow. No, expanding is expanding. And the rate of expansion is unrelated to the fact of expansion. Seeing that the universe is expanding doesn't imply shrinking and doesn't imply speeding up or slowing down. But we measure it to be speeding up over time (slower in the past).

 

[Phys12]

For far-away galaxies, yes, they were receding from us more rapidly when the light that we see was emitted than they are now.

Then how is that an accelerated expansion if the expansion rate is slowing down?

 

[phinds]

Then how is that an accelerated expansion if the expansion rate is slowing down?

It ISN'T slowing down. The rate of acceleration is slowing down (and only very slightly)

 

[kimbyd]

Then how is that an accelerated expansion if the expansion rate is slowing down?

Far-away galaxies were slowing down. Now galaxies are moving away from one another at increasing rates. The accelerated expansion is a recent (in cosmic terms) phenomenon.

This is why nearby galaxies are now receding faster than they were when the light we see was emitted.

Just fyi, the cutoff where the accelerated expansion began is somewhere around roughly $z=0.6$. The light at that redshift has traveled for nearly 6 billion years.

 

[Arman777]

Far-away galaxies were slowing down. Now galaxies are moving away from one another at increasing rates. The accelerated expansion is a recent (in cosmic terms) phenomenon.

This is why nearby galaxies are now receding faster than they were when the light we see was emitted.

Just fyi, the cutoff where the accelerated expansion began is somewhere around roughly $z=0.6$. The light at that redshift has traveled for nearly 6 billion years.

Could you express it in maths please ?

Also there's only solutions for simple models in the universe but not for the our current universe with respect to $H(t)$.

 

[Orodruin]

It ISN'T slowing down. The rate of acceleration is slowing down (and only very slightly)

This is actually not completely accurate. The Hubble parameter (arguably the only thing that can be called a rate of expansion) is decreasing with time. What accelerated expansion means is that the second derivative of the scale factor is positive.

 

[Arman777]

where the accelerated expansion began is somewhere around roughly z=0.6z=0.6z=0.6. The light at that redshift has traveled for nearly 6 billion years.

So If its begin later times, it means that $\ddot {a}(t)<0$ at the beginning and $\dot {a}(t)<0$ but after a time as 6 billion years ago, somewhere $\ddot {a}(t)=0$ so that it can turn to positive.

. What accelerated expansion means is that the second derivative of the scale factor is positive.

Is it because the matter density is getting lower or there's something else ?

 

[Orodruin]

Is it because the matter density is getting lower or there's something else ?

Are you referring to why $\ddot a$ becomes positive? Yes, it is because the density of matter and radiation goes down while that of dark energy stays constant, eventually leading to dark energy dominating the behaviour of the expansion.

 

[Arman777]

Are you referring to why $\ddot a$ becomes positive? Yes, it is because the density of matter and radiation goes down while that of dark energy stays constant, eventually leading to dark energy dominating the behaviour of the expansion.

Well yes I was referring that.

 

[Bandersnatch]

@Arman777 take a look at the equation in Jorrie's post #3 here:
https://www.physicsforums.com/threads/question-pertaining-to-dark-energy.880129/#post-5529823

 

[Arman777]

@Arman777 take a look at the equation in Jorrie's post #3 here:
https://www.physicsforums.com/threads/question-pertaining-to-dark-energy.880129/#post-5529823

Okay thanks a lot. I thought the calculation was wrong but I did it again and I noticed that I forget the square part. So I find that its correct.

 

[kimbyd]

So If its begin later times, it means that $\ddot {a}(t)<0$ at the beginning and $\dot {a}(t)<0$ but after a time as 6 billion years ago, somewhere $\ddot {a}(t)=0$ so that it can turn to positive.

No. At early times, it is true that $\ddot{a}(t) < 0$. But $\dot{a}(t) >0$ has always been true.

Is it because the matter density is getting lower or there's something else ?

I think you already grasped this from the link Bandersnatch posted above, but yes, it's because the matter density has diluted while the cosmological constant remains the same. If you would like to understand why a cosmological constant causes an accelerated expansion, I find this blog post to provide a nice conceptual explanation:
http://www.preposterousuniverse.com...oes-dark-energy-make-the-universe-accelerate/

(He's actually talking more to other people trying to explain the concept, but along the way presents a good explanation of the concept)

 

[Arman777]

No. At early times, it is true that $\ddot{a}(t) < 0$. But $\dot{a}(t) >0$ has always been true.

Yes, Now I am thinking why I wrote such thing. Probably a typo cause it would be stupid to say $\dot {a}(t)<O$.

Also thanks for the link.

 

[Monsterboy]

The far away galaxies are RECEDING from us at super-luminal rates but since there is no proper motion involved, there are no speeding tickets issued.

https://www.quora.com/How-would-Vik...swer/Viktor-T-Toth-1?share=63074d4e&srid=E7fv

What do you say about this answer ?

 

[phinds]

https://www.quora.com/How-would-Vik...swer/Viktor-T-Toth-1?share=63074d4e&srid=E7fv

What do you say about this answer ?

As far as I am aware, he has this right

Because space isn’t a thing. It is not something we can measure. It has no physical reality in general relativity, other than as the playing field in which events take place.

and this wrong

No, it is the distant galaxy that is, physically and measurably, moving away from you. If you measured it in your reference frame (i.e., the reference frame of the Milky Way, to which your sticks are attached) it would have a large amount of kinetic energy and a large amount of momentum. In short: motion.

This last quote implies that there is proper motion between cosmologically distant objects but there is not.

 

[PeterDonis]

This last quote implies that there is proper motion between cosmologically distant objects

No, it doesn't. "Proper motion" in this context means "motion relative to comoving objects at the same location". Comoving objects at different locations are moving relative to each other, but that motion is not "proper motion" in the context of cosmology.

The real problem with that quote is the implicit assumption that you can set up an inertial frame centered on one comoving object, such as the Milky Way, and have it extend far enough to directly measure the motion of some other distant comoving object, like another galaxy millions of light-years away. Inertial frames in a curved spacetime are local.

 

[Monsterboy]

Inertial frames in a curved spacetime are local.

So, the speed limit is only valid locally in the universe and not globally because of curved spacetime ?

I hope you read the whole answer on Quora, how right or wrong is he ? I don't have enough knowledge about this to make a judgement.

 

[Orodruin]

So, the speed limit is only valid locally in the universe and not globally because of curved spacetime ?

There is no global way of uniquely defining relative velocities so to talk about a global speed limit is not a sensible thing to do. However, locally, in a space-time region small enough to ignore curvature and adopting a local Minkowski frame, galaxies further away do move away faster than nearby ones. It should be noted that the local Minkowski frame has a different definition of simultaneity compared to the comoving coordinates usually used in cosmology. See my PF Insight on this issue.

 

[phinds]

No, it doesn't. "Proper motion" in this context means "motion relative to comoving objects at the same location". Comoving objects at different locations are moving relative to each other, but that motion is not "proper motion" in the context of cosmology.

OK, thanks, but he talks about momentum. Isn't that wrong? Receding galaxies do NOT have momentum relative to us, right?

 

[PeterDonis]

he talks about momentum. Isn't that wrong? Receding galaxies do NOT have momentum relative to us, right?

As @Orodruin said, strictly speaking, you can't define "relative velocity" for spatially separated objects in curved spacetime. That means you can't, strictly speaking, define "momentum" for such objects either.

What Toth appears to be doing is implicitly assuming an inertial frame that covers both galaxies--our Milky Way and the distant one. As @Orodruin said, you can do this for a small enough region (small enough that spacetime curvature can be ignored) by setting up a local inertial frame (his insight article on this is worth reading). In such a frame, the distant galaxy does indeed have momentum relative to the Milky Way. However, as I noted before, Toth might not be paying proper attention to the fact that such a frame is only valid over a region of spacetime small enough that spacetime curvature can be ignored.

 

[Orodruin]

As @Orodruin said, you can do this for a small enough region (small enough that spacetime curvature can be ignored) by setting up a local inertial frame (his insight article on this is worth reading).

However, as I noted before, Toth might not be paying proper attention to the fact that such a frame is only valid over a region of spacetime small enough that spacetime curvature can be ignored.

I think it should be pointed out that I wrote that Insight with an A-level audience in mind. I believe many of the finer details will be lost at I level, but of course one can still read it superficially if one accepts a few things as given and return to those later.

 

[graybass]

"There is no global way of uniquely defining relative velocities so to talk about a global speed limit is not a sensible thing to do. However, locally, in a space-time region small enough to ignore curvature and adopting a local Minkowski frame, galaxies further away do move away faster than nearby ones. It should be noted that the local Minkowski frame has a different definition of simultaneity compared to the comoving coordinates usually used in cosmology. See my PF Insight on this issue."

This makes the most common sense to me. Thank You

 

[Vishal Rana]

The universe seems to be expanding since the farther away an object is, the faster it is moving. However, because of the finite speed of light, the farther away we look in distance, the further back in time we look. Does that mean that galaxies were moving faster in the past and are now slowing down? Wouldn't that indicate a shrinking universe, instead of an expanding one?

I'm having trouble imagining this situation. The inflating balloon analogy helps, but not when it comes to thinking about the expansion taking time intro consideration.

My answer would be the universe is expanding still and the expansion rate is getting faster cause of dark energy. Yeah the speed of light is finite and nothing with mass can go at the speed of light but it’s the space in between the masses which is increasing faster than the speed of light. Something along the lines of what I just said, I remember watching a video of Lawrence Krauss saying it. Someone correct me if I’m wrong.

 

[Arman777]

expansion rate is getting faster

Expansion rate is not getting faster

 

[Arman777]

There's actually very simple explanation. Which I wrote on my article "Furthermore, special relativity is not violated, because it refers to the relative speeds of objects passing each other, and cannot be used to compare the relative speeds of distant objects [19]. The reason for this is, that in large cosmic scales space is curved but the theory is “special” in that, it only applies in the special case where the curvature of spacetime due to gravity is negligible"

Reference https://www.physicsforums.com/insights/journey-cosmos-friedmann-equation/

 

[PeterDonis]

Expansion rate is not getting faster

It depends on how you define "expansion rate". The Hubble constant $H$ is decreasing; that is, $\dot{H} < 0$. However, the "rate of acceleration" of the scale factor is positive: $\ddot{a} / a > 0$. Many texts define "expansion is accelerating" to mean the latter, which can be thought of as "expansion rate getting faster". This is a good illustration of why ordinary language is vague and must be used carefully in physics.

 

[Vishal Rana]

Expansion rate is not getting faster

How do u know this? I thought it was accelerating cause of dark energy?

 

[Arman777]

How do u know this? I thought it was accelerating cause of dark energy?

Well Expansion rate can be defined as $H(t)$ where $H(t)=\frac {\dot {a}(t)} {a(t)}$. Now we can write the Friedmann Equation in the form of,

$\frac {H^2} {(H_0)^2}=Ω_ma^{-3}+Ω_Λ$ and Now in here $H$ is Hubble parameter at any time t. $H_0$ Hubble parameter now. $Ω_m$ matter density
$Ω_Λ$ dark energy density and $a$ is the value of the scale factor at that time respeect to the $a(t_0)=1$.

Note: $Ω_m$ and $Ω_Λ$ should be current (Now) values

Now we can re-write the equation as,

$H^2={(H_0)^2}[Ω_ma^{-3}+Ω_Λ]$

take square root and we get,

$H=H_0\sqrt{Ω_ma^{-3}+Ω_Λ}$

Since, $H_0$, $Ω_m$ and $Ω_Λ$ are constant numbers, we can simply think this equation like this,

$H=\sqrt{x^{-3}}$

and I graphed it in desmos and I get,

As PeterDonis Said $\ddot {a}(t)$ is icreasing but it doesn't mean $H(t)$ is also increasing.

 

[graybass]

In layman terms, are we saying that the dark energy is/will eventually expand faster than C but that actual matter of the galaxies can not move faster than C because of common relativity? So this is why the standard model does not work?
Pardon my ignorance.

 

[phinds]

In layman terms, are we saying that the dark energy is/will eventually expand faster than C but that actual matter of the galaxies can not move faster than C because of common relativity? So this is why the standard model does not work?
Pardon my ignorance.

Dark energy does not expand, but I think what you mean to ask is will the effect of dark energy cause expansion faster than C. It ALREADY causes recession velocities faster than c. The objects at the outer regions of our observable universe are already receding from us at about 3c. Recession velocity is not proper motion, so no speeding tickets are issued.