What do we exactly mean by space is expanding?

[Yashbhatt]

I know this question had often been asked on PF but I don't get them. What do mean when we say that space is expanding? I mean that space is no physical entity that can expand. Space is just (apparently) "nothingness". Please solve my confusion.

 

[Mordred]

the increase of space is simply an increase of geometric volume, that volume is filled with the contents of the universe.

You are right that space is not a physical entity, you oft read misnomers that imply that space has some physical property, however space itself does not. It has neither a physical property nor energy in and of itself.

 

[Yashbhatt]

But does it have the space to expand? Like if a balloon(yes, I am using the misleading balloon analogy) is expanding,
it is expanding in space? Then, what is space expanding into?

 

[Mordred]

this is one of the best balloon analogies I've come across, it is written by another forum member Phind's. He covers that question in better detail than I

http://www.phinds.com/balloonanalogy/ : A thorough write up on the balloon analogy used to describe expansion

 

[eltodesukane]

Space expanding is the same thing as matter contracting.
So instead of space expanding, just think matter contracting.
All we can measure is that the ratio galaxy_size/intergalactic_distance is getting smaller.

 

[phinds]

Space expanding is the same thing as matter contracting.

No, it is not. This has been discussed here on the forum many times.

"Expanding space" only happens outside galactic clusters. What would "matter contracting" mean? Why would it be different from "space shrinking"? Space does not expand or shrink and neither does matter. Things on the size of galactic clusters and larger just move farther apart withing the geometric framework that we call "space".

I suggest that you also follow Mordred's advice and read the link in my signature

 

[Yashbhatt]

Consider this example. Let there be two spaceships between Milky Way and some other galaxy. So, if space is expanding, then the two space ships should start moving away from each other even if they are set at a fixed distance from each other and are stationary with respect to each other. Will they move away?

 

[Mordred]

Ok let's assume you have two stationary objects in a non gravitationally bound region. (expansion doesn't affect gravitationally bound objects)

then the answer is yes the volume of space between them will increase. So they will have an increase in distance between them, however they will not have gained any inertia, they will both remain stationary. The distance between them will simply increase. Expansion does not impart inertia

 

[Yashbhatt]

I assume by gravitationally bound you mean strongly bound objects like binary stars, galaxies etc. Otherwise everything is gravitationally bound as there are no limits to gravitational force.

 

[phinds]

I assume by gravitationally bound you mean strongly bound objects like binary stars, galaxies etc. Otherwise everything is gravitationally bound as there are no limits to gravitational force.

No, that's not quite right. Certainly, you are correct in saying that there are no limits to gravitational force, but that does NOT imply that all objects in the universe are gravitationally bound to each other.

The Earth and the moon are gravitationally bound. The Milky Way and the Andromeda Galaxy are gravitationally bound. The Milky Way and the Bullet Cluster are NOT gravitationally bound. I think Your requirement of "strongly" bound is correct if you consider that your definition of what constitutes strongly bound is overly restrictive. Personally, I don't know if "strongly" bound even HAS a solid definition but "gravitationally bound" does ... it means, roughly, things that don't fly apart from each other.

 

[Jorrie]

Ok let's assume you have two stationary objects in a non gravitationally bound region. (expansion doesn't affect gravitationally bound objects)

then the answer is yes the volume of space between them will increase. So they will have an increase in distance between them, however they will not have gained any inertia, they will both remain stationary. The distance between them will simply increase. Expansion does not impart inertia

I think one must be a little careful with this. Yashbhatt asked the question for two objects stationary relative to each other, which could be viewed as the Tethered Galaxy Problem of Tamara Davis et al.

We use the dynamics of a galaxy, set up initially at a constant proper distance from an observer, to derive and illustrate two counter-intuitive general relativistic results. Although the galaxy does gradually join the expansion of the universe (Hubble flow), it does not necessarily recede from us. In particular, in the currently favored cosmological model, which includes a cosmological constant, the galaxy recedes from the observer as it joins the Hubble flow, but in the previously favored cold dark matter model, the galaxy approaches, passes through the observer, and joins the Hubble flow on the opposite side of the sky. We show that this behavior is consistent with the general relativistic idea that space is expanding and is determined by the acceleration of the expansion of the universe -- not a force or drag associated with the expansion itself. We also show that objects at a constant proper distance will have a nonzero redshift; receding galaxies can be blueshifted and approaching galaxies can be redshifted.

According to Mordred's (apparent) definition, one or both of the tethered ships must have had inertia relative to the Hubble flow, which is then diminished as they later joint the Hubble flow. In the epoch of non-acceleration of expansion, the said inertia could even have gone up (as they fall "through" each other), before joining the Hubble flow on the opposite side.

 

[Yashbhatt]

I think one must be a little careful with this. Yashbhatt asked the question for two objects stationary relative to each other, which could be viewed as the Tethered Galaxy Problem of Tamara Davis et al.

I don't understand the last part. Receding objects can show red shift and approaching objects can show blue shift?

 

[Mordred]

I don't understand the last part. Receding objects can show red shift and approaching objects can show blue shift?

yes motion has an influence on observations called Doppler effect. as objects approach there is a shift in frequency in light and sound waves (blueshift) as they recede there is a corresponding redshift

http://en.wikipedia.org/wiki/Doppler_effect

however redshift(blueshift) due to expansion not motion as per se. is called cosmological redshift
this article will explain the three types of redshifts in cosmology usage.

http://cosmology101.wikidot.com/redshift-and-expansion

 

[Jorrie]

I don't understand the last part. Receding objects can show red shift and approaching objects can show blue shift?

They say the opposite of what you say, but qualified for the 'tethered case'. The detail explanation is in section III (p. 5) of the referenced paper. Essentially, a distant galaxy that would presently be "untethered" from our Galaxy could have a huge peculiar velocity towards us, with the resulting Doppler blueshift overwhelming the normal cosmological redshift.

 

[Mordred]

I think one must be a little careful with this. Yashbhatt asked the question for two objects stationary relative to each other, which could be viewed as the Tethered Galaxy Problem of Tamara Davis et al.

actually I didn't even consider the tethered scenario, my main point is no momentum is imparted upon the galaxies due to expansion. in this article its covered by the statement.

"space is expanding and is determined by the acceleration of the expansion of the universe -- not a force or drag associated with the expansion itself"

still its a good point to be aware of the tethered scenarios

by the way Jorrie I tried posting the lightcone calc on the forum recently and it came up as an error what is the latest version link or is version 7 still the latest?

 

[Mordred]

Jorrie off topic is version 7 the latest version of the lightcone calc?

I'm going to test the one off your signature

$${\scriptsize\begin{array}{|c|c|c|c|c|c|}\hline R_{0} (Gly) & R_{\infty} (Gly) & S_{eq} & H_{0} & \Omega_\Lambda & \Omega_m\\ \hline 14.4&17.3&3400&67.9&0.693&0.307\\ \hline \end{array}}$$ $${\scriptsize\begin{array}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline a=1/S&S&T (Gy)&R (Gly)&D_{now} (Gly)&D_{then}(Gly)&D_{hor}(Gly)&V_{now} (c)&V_{then} (c) \\ \hline 0.001&1090.000&0.0004&0.0006&45.332&0.042&0.057&3.15&66.18\\ \hline 0.003&339.773&0.0025&0.0040&44.184&0.130&0.179&3.07&32.87\\ \hline 0.009&105.913&0.0153&0.0235&42.012&0.397&0.552&2.92&16.90\\ \hline 0.030&33.015&0.0902&0.1363&38.052&1.153&1.652&2.64&8.45\\ \hline 0.097&10.291&0.5223&0.7851&30.918&3.004&4.606&2.15&3.83\\ \hline 0.312&3.208&2.9777&4.3736&18.248&5.688&10.827&1.27&1.30\\ \hline 1.000&1.000&13.7872&14.3999&0.000&0.000&16.472&0.00&0.00\\ \hline 3.208&0.312&32.8849&17.1849&11.118&35.666&17.225&0.77&2.08\\ \hline 7.580&0.132&47.7251&17.2911&14.219&107.786&17.291&0.99&6.23\\ \hline 17.911&0.056&62.5981&17.2993&15.536&278.256&17.299&1.08&16.08\\ \hline 42.321&0.024&77.4737&17.2998&16.093&681.061&17.300&1.12&39.37\\ \hline 100.000&0.010&92.3494&17.2999&16.328&1632.838&17.300&1.13&94.38\\ \hline \end{array}}$$

kk its working now

 

[Jorrie]

Jorrie off topic is version 7 the latest version of the lightcone calc?

Yup, we stopped tinkering at version 7. ;)

 

[nuclearhead]

It is an anachronism.

There are two ways to describe an expanding Universe (equally valid in General Relativity due to diffeomorphism).

1) Keep the coordinates of space fixed and the coordinates of particles change with time.
2) Let the space coordinates expand with time so the particles coordinates remain the same.

They are equivalent but in the 2nd example it is easier to talk about "expanding space" while in the first about "galaxies flying away from each other".

When you change coordinates in General Relativity you also change the gravitational fields. (Just like in the coordanates that move with a falling elevator there is no gravity). So in the 2nd one the particles feel no "force" while in the first one they experience a gravitational force between particles. So does space really "expand"? It depends on your coordinate system!

 

[phinds]

1) Keep the coordinates of space fixed and the coordinates of particles change with time.
2) Let the space coordinates expand with time so the particles coordinates remain the same.

They are equivalent but in the 2nd example it is easier to talk about "expanding space" while in the first about "galaxies flying away from each other".

Your item 1 and your statement about it in the next sentence are contradictory. Galaxies flying away from each other IS what we see experimentally but "coordinates of particles change with time" is NOT what we see. Coordinates of GALAXIES (that are not in galactic clusters) change with time relative to each other, yes, but particles, no.

 

[nuclearhead]

Your item 1 and your statement about it in the next sentence are contradictory. Galaxies flying away from each other IS what we see experimentally but "coordinates of particles change with time" is NOT what we see. Coordinates of GALAXIES (that are not in galactic clusters) change with time relative to each other, yes, but particles, no.

I meant "particle" in the mathematical sense of an object with coordinates. As such a galaxy is a "particle". I didn't meant elementary particles. Sorry for the confusion!

 

[Yashbhatt]

Can anyone explain how we deduced that space is expanding? I read that it was something related to the CMB on this site. http://astronomy.stackexchange.com/a/3654/1156(See the comments on mpv's answer).

Can anyone explain the reason in detail?

 

[Drakkith]

Can anyone explain how we deduced that space is expanding? I read that it was something related to the CMB on this site. http://astronomy.stackexchange.com/a/3654/1156(See the comments on mpv's answer).

Can anyone explain the reason in detail?

See here: http://en.wikipedia.org/wiki/Metric_expansion_of_space#Observational_evidence

There are several key things that support expansion. The redshifting of spectral lines from distant galaxies, the CMB, and the isotropic and homogeneous structure of the universe at the largest scales. In addition, expansion is also supported by helping explain the relative abundance of hydrogen and helium in the universe, as the prevailing cosmological model predicts the observed abundance of these elements to good precision.

Put simply, nothing in astronomy makes sense except in the light of universal expansion.

 

[Yashbhatt]

I read something like if it were we moving away instead of space expanding, then there would have been more dipole anisotropies in the CMB but what we observe is that we are almost stationary with respect to the CMB. I think that makes the most sense of all.

 

[kurros]

actually I didn't even consider the tethered scenario, my main point is no momentum is imparted upon the galaxies due to expansion. in this article its covered by the statement.

"space is expanding and is determined by the acceleration of the expansion of the universe -- not a force or drag associated with the expansion itself"

I'm not sure what you are trying to say here. The expansion of space certainly causes galaxies to end up with velocity relative to each other, and therefore momentum.

 

[phinds]

I read something like if it were we moving away instead of space expanding, then there would have been more dipole anisotropies in the CMB but what we observe is that we are almost stationary with respect to the CMB. I think that makes the most sense of all.

I don't really follow what you mean. Moving away from WHAT? We ARE moving away from every galaxy in the universe except for those in the local group, so what is it that we are not moving away from? We have a fairly modest velocity relative to the CMB but so does every galaxy in the universe despite the fact that they are all receding from each other, some faster than c. How does that fit with what you are saying?

 

[phinds]

I'm not sure what you are trying to say here. The expansion of space certainly causes galaxies to end up with velocity relative to each other, and therefore momentum.

No, it does not. Galaxies can be receding from each other faster than c, but there is no momentum involved. Metric expansion doesn't work like that.

 

[kurros]

No, it does not. Galaxies can be receding from each other faster than c, but there is no momentum involved. Metric expansion doesn't work like that.

Ok it is possibly the acceleration of the expansion rather than the expansion itself, analogously to how in the tethered galaxy paper the small galaxy remains at a fixed distance even after un-tethering in the constantly expanding scenario, but it recedes in the accelerating expansion scenario, and approaches in the decelerating expansion scenario.

edit: actually that seems a sensible result after all to me. Naively one would imagine that it was whatever happened in the beginning of the universe which drove the matter of the universe apart from each other, and that constant expansion would therefore correspond to "no extra force applied", while naively the accelerating/decelerating expansion would correspond to some "constant force applied".

 

[Yashbhatt]

I don't really follow what you mean. Moving away from WHAT? We ARE moving away from every galaxy in the universe except for those in the local group, so what is it that we are not moving away from? We have a fairly modest velocity relative to the CMB but so does every galaxy in the universe despite the fact that they are all receding from each other, some faster than c. How does that fit with what you are saying?

See the link which I mentioned.

 

[TumblingDice]

I'm not sure what you are trying to say here. The expansion of space certainly causes galaxies to end up with velocity relative to each other, and therefore momentum.

No, it does not. Galaxies can be receding from each other faster than c, but there is no momentum involved. Metric expansion doesn't work like that.

Perhaps you mean there are no forces that can be measured? Momentum is a relative measurement depending on reference frame. The definition of momentum is based on mass and relative velocity.
http://en.wikipedia.org/wiki/Momentum

Dependence on reference frame Momentum is a measurable quantity, and the measurement depends on the motion of the observer.

What aspect of the term "momentum" does not apply to two observers moving relatively to each other?

 

[phinds]

Perhaps you mean there are no forces that can be measured? Momentum is a relative measurement depending on reference frame. The definition of momentum is based on mass and relative velocity.
http://en.wikipedia.org/wiki/MomentumWhat aspect of the term "momentum" does not apply to two observers moving relatively to each other?

I think metric expansion is counter-intuitive, so I understand your point of view, but here's the thing: If recession were "motion" in the sense you mean, then distant galaxies actually WOULD be traveling faster than light relative to us. Relative motion of galaxies to the Milky Way does exist, but it is very small and it is not what you are talking about. Your definition of momentum is correct but your understanding of proper motion vs metric expansion is not.

The above statement is more me parroting back what I believe I have heard on this forum than it is any direct mathematical understanding of my own, so I'm open to the possibility that I'm wrong about this, but I don't see how. If I am I have no doubt that one of our more knowledgeable members will jump in and very politely slap me upside the head for being a dunce

Just look at the equation of momentum and you'll see what I mean. Are you seriously going to plug a faster-than-light speed into that equation? Again, that would imply ACTUAL PROPER MOTION greater than c and such a thing does not exist. That's why I don't see how I can be wrong about this.

 

[Mordred]

Perhaps you mean there are no forces that can be measured? Momentum is a relative measurement depending on reference frame. The definition of momentum is based on mass and relative velocity.
http://en.wikipedia.org/wiki/MomentumWhat aspect of the term "momentum" does not apply to two observers moving relatively to each other?

in expansion there is no momentum involved, no inertia gets imparted upon the galaxies as they recede from us.

the easiest way to understand this is to think of expansion in terms of a perfect fluid, radiation,and matter (baryonic and non baryonic) contribute to the positive pressure) the cosmological constant (aka dark energy) is the negative pressure contributor. the relations between the positive pressure contributors and negative pressure contributors determine the rate of expansion. The energy-density of a contributor has a corresponding pressure relations or equation of state

http://en.wikipedia.org/wiki/Equation_of_state_(cosmology)

now in terms of pressure, and the precepts of a uniform distribution (homogeneous and isotropic)
the pressure will exert the same amount of force equally upon a large scale structure in all directions. So the large scale structure itself will not move. Instead the volume of space will simply increase.

http://cosmology101.wikidot.com/universe-geometry page 2 is for the FLRW metric in terms of distance measures
http://cosmology101.wikidot.com/geometry-flrw-metric/

as far as the use of the term recessive velocity, well this isn't a velocity as per se. When Hubble first measured the expansion, he never knew the cause of expansion so he used the term recessive velocity. Unfortunately as a consequence were stuck with the term.

Hubble's law= the greater the distance, the greater the recessive velocity

$$v_{recessive}=H_OD$$. as this depends on separation distance and no inertia is involved, a greater than c recessive velocity does not violate GR or the speed of light. If you were to measure a galaxy with a 3c recessive velocity from Earth, and were able to measure that same galaxy from a nearby location to that galaxy you would get a smaller value. So it depends on the location of the observer.

unfortunately I can't slap Phind's this time darn it lol

edit typing error fixed as per Phind's post below

 

[phinds]

in expansion there is momentum involved ...

I think you meant "there is NO momentum involved ... ", yes?

unfortunately I can't slap Phind's this time darn it lol

Oh, goodie !

 

[Mordred]

yes my mistake typing error

 

[kurros]

in expansion there is no momentum involved, no inertia gets imparted upon the galaxies as they recede from us.

I'm still not seeing it. Why, then, in the tethered galaxy scenario, in a universe with accelerating expansion, does the small galaxy recede once untethered? If this is the case then there must be some tension in the tethering cable (if it existed), and therefore force acting on the galaxies.

Also, then, in scenarios where the acceleration accelerates, do we end up with the "big rip", with all matter eventually being ripped apart at the molecule level and even below? This obviously requires some enormous force.

 

[Mordred]

no that isn't how the tethered galaxy scenario works, there is no line of force between us and the tethered galaxy in that paper.

here is some of the key lines in the paper.

"We set up a distant galaxy at a constant distance from us and then allow it to move freely." so this is essentially a mathematical constructed scenario, no force is required in the tethering

"Suppose we separate a small test galaxy from the Hubble flow by tethering it to an observer’s galaxy such that the proper distance between them remains constant. We neglect all practical
considerations of such a tether because we can think of the tethered galaxy as one that has received a peculiar velocity boost toward the observer that exactly matches its recession velocity"
...
" Note that this is an artificial setup; we have had to arrange for the galaxy to be removed out of the Hubble flow in order to apply this zero total velocity condition."

now the question the paper is trying to determine has to do with the question is the rate at which the galaxy will recede once untethered be due to the Hubble flow or a peculiar velocity.

http://en.wikipedia.org/wiki/Peculiar_velocity
"In physical cosmology, the term peculiar velocity (or peculiar motion) refers to the components of a receding galaxy's velocity that cannot be explained by Hubble's law."

"According to Hubble, and as verified by many astronomers, a galaxy is receding from us at a speed proportional to its distance. The relationship between speed and distance would be exact in the absence of other effects."

in other words is there any other influence not due to what is explained by expansion

"Note that the galaxy joins the Hubble flow solely due to the expansion of the universe"

V. SUMMARY
"We have pointed out and interpreted some counter-intuitive results of the general relativistic description of our Universe. We have shown that the unaccelerated expansion of the universe has no effect on whether an untethered galaxy approaches or recedes from us. In a decelerating universe the galaxy approaches us, while in an accelerating universe the galaxy recedes from us. The expansion, however, is responsible for the galaxy joining the Hubble flow, and we have shown that this happens whether the untethered galaxy approaches or recedes from us."


One thing to also be aware of is that the FLRW metric is an exact solution to the Einstein field equations.

how expansion occurs is essentially how I described it in my previous post.

right now the universe is expanding, the most likely fate is the "heat death/big chill" however if the cosmological constant gains in strength enough to overcome the energy-density per m³ of gravity, then its possible the big rip could occur. However the common understanding is that the cosmological constant is constant. (there is some papers that might show an evolving cosmological constant)