What do we exactly mean by space is expanding?

[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)

 

[phinds]

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.

Yes, I can see that you still don't get it. The force of "dark energy" is staggeringly small in anything like a local effect. If you could magically draw parking space lines in intergalactic space it would be 20BILLION years before they moved far enough apart to park a second car. Such a small effect would have no effect on even a thin rope.

As for things smaller than galactic clusters, dark energy is so weak that it has absolutely no effect at all. It's like an ant pushing on the foundation of a house. It isn't that the ant make such a tiny effect as to be unnoticible, it's that the ant has absolutely no effect at all. It's like you trying to pick up a freight train. Lots of effort, no result, and dark energy is WAY weaker than you are or even than an ant is.

Where dark energy has a huge effect is over many millions and more of light years, and it is cumulative, so the farther away from each other things already are, the more effect it has on their relative position.

 

[kurros]

Yes, I can see that you still don't get it. The force of "dark energy" is staggeringly small in anything like a local effect. If you could magically draw parking space lines in intergalactic space it would be 20BILLION years before they moved far enough apart to park a second car. Such a small effect would have no effect on even a thin rope.

"Small" does not mean "non-existent", so I don't know why you are telling me this. I am aware that the effect is small. Yet your language suggests that yes, a force does exist.

As for things smaller than galactic clusters, dark energy is so weak that it has absolutely no effect at all. It's like an ant pushing on the foundation of a house. It isn't that the ant make such a tiny effect as to be unnoticible, it's that the ant has absolutely no effect at all. It's like you trying to pick up a freight train. Lots of effort, no result, and dark energy is WAY weaker than you are or even than an ant is.

Where dark energy has a huge effect is over many millions and more of light years, and it is cumulative, so the farther away from each other things already are, the more effect it has on their relative position.

This is a thought experiment so distance is irrelevant. Presumably if we make the tether large enough then there will indeed be some size at which a measurable tension in it exists.

 

[Mordred]

dark energy isn't a force and the tethered galaxy is a constructed scenario

however pressure: is the ratio of force to the area over which that force is distributed.
if you want to look at it in terms of forces then the pressure term describes what your asking

 

[kurros]

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

" 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."

This just establishes that the initial tension in the tether is zero. If the smaller galaxy is going to then recede if the tether is removed, I do not see how you can think that there will not ever be any tension in the tether.

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.

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"

I am not questioning any of that. I am talking about what happens to the tether while it is still attached.

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)

Sure, but the point is that even with constant acceleration of the expansion, there is effectively a tiny force acting to pull all matter apart from each other. It is completely immeasurable on the scale of metres of course, but on intergalactic(-cluster) scales this force is extremely large, and will definitely overcome the strength of any tether that you try to use to attach galaxy clusters to each other (unless they are gravitationally bound, in which case they effectively already have an extremely strong tether between them).

 

[Mordred]

OK were talking outside that paper why not replace the word tether with gravity? or the strong force?

the point is the cosmological constant's energy-density influence is not strong enough to overcome gravity and the strong force. Not per m³. The cosmological constant is roughly (and this is an older calculation 6.62*10^-10 joules per m³.

it is so small per cubic meter that its effects can only be measured on extremely large scales. There is always the possibility of an influence too small to measure, but for all practical purposes the influence is non existent at present. for gravitationally bound objects or molecules

Just as gravities influence is essentially non existent or unable to measure at the microscopic level (ie particle to particle interactions)

 

[kurros]

OK were talking outside that paper why not replace the word tether with gravity? or the strong force?

Well I though you were making some strange argument related to the nature of gravity so I chose not to go there, and the strong force is obviously acting on scales far too small to be relevant. The magic tether is a good example because it is at the right scale for intuition, and isn't gravity.

We could go further, and attach our magic tether to two massive objects in vastly separated galaxies. I am quite certain a tension will exist in this tether, and we can therefore, in principle, use it to extract energy out of the cosmological constant, effectively. We can attach one end of the tether to a reel and use it to turn a generator as it unwinds. Of course we need to keep making more magic tether so this cannot work forever, but it does work for as long as we have more tether.

the point is the cosmological constant's energy-density influence is not strong enough to overcome gravity and the strong force. Not per m³. The cosmological constant is roughly (and this is an older calculation 6.62*10^-10 joules per m³.

it is so small per cubic meter that its effects can only be measured on extremely large scales.

Sure. But it is a truly vast amount of energy on those large scales. 1 AU is around 15*10^10 m, so in a cube with side length of only the Earth's orbital radius we already have a few joules.

 

[Mordred]

yes but it is its localized strength of influence in terms of ripping galaxies apart internally, that is the big rip scenario or the start of it. We already know in the vast regions of space the cosmological constant has measurable influence. In order to rip individual galaxies apart its strength of influence would significantly need to increase. In terms of the volume inhabited by those galaxies

in other words it is the energy-density per region that matters not the total energy

 

[kurros]

yes but it is its localized strength of influence in terms of ripping galaxies apart internally, that is the big rip scenario or the start of it. We already know in the vast regions of space the cosmological constant has measurable influence. In order to rip individual galaxies apart its strength of influence would significantly need to increase. In terms of the volume inhabited by those galaxies

in other words it is the energy-density per region that matters not the total energy

Sure. I only brought up the big rip to demonstrate that there is a real force with real physical effects that was acting here. This same force is present even with small and constant cosmological constant. And it therefore is valid to think of this force as "pushing" galaxies apart from each other, i.e. imparting momentum to them.

Yes, there are crazy relativistic effects occurring, so that we cannot directly compare their relative velocities and conclude that some of them are moving superluminally relative to each other, but they ARE being "pushed around" by the cosmological constant, at least in a certain sense.

 

[Mordred]

sure there is nothing wrong in that thinking as long as you keep it in terms of relative energy-densities in a specific volume.. the term force however should be replaced by the term pressure. Just to avoid confusion. Other wise people may mistakenly think your referring to the cosmological constant as a force, when their are only 4 forces.

 

[Mordred]

imparting momentum to them.

now here is the other picky part, and its picky in terms of physics terminology and mathematics

momentum " is the product of the mass and velocity of an object."

which means they follow the laws of motion

First law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.
Second law: F = ma. The vector sum of the forces F on an object is equal to the mass m of that object multiplied by the acceleration vector a of the object.
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

however the cosmological constants pressure influence is upon the regions between the large scale structures (extragalactic space)

the cosmological constant doesn't exert enough force on a galaxy directly to move it, so f=ma does not describe why it is receding due to expansion.

physics terminology describes specific relations

hence expansion is simply described as the increase in geometric volume.

 

[kurros]

Sure, it does not make sense to think of it via pure classical mechanics. But if we go back to the tethering scenario, if we attach other tether to one galaxy, and then fly across the universe and attach the other end to some other galaxy, then the momentum transfer required to halt these galaxies relative to each other is truly enormous. If we then decouple the tether, the galaxies will be dragged apart again due to the cosmological constant, and it will again take an enormous momentum transfer to halt them. So it surely seems valid to me to say that they are gaining momentum relative to each other. Perhaps it takes some tethering scenario to define what we mean by this, but I think it definitely means something.

 

[Mordred]

my point is simply proper terminology avoids confusion, and it saves time when your asking a specific question. You wouldn't want to have to explain your terminology usage each time you ask a question

 

[timmdeeg]

Sure, but the point is that even with constant acceleration of the expansion, there is effectively a tiny force acting to pull all matter apart from each other.

That is correct. The force you are talking about is called tidal force. It means the radial stretching of a body falling towards a mass (Schwarzschild metric) and similarly the stretching of a long rope in the accelerated expanding FRW universe. Generally tidal forces are due to the relative acceleration of two neighbouring geodesics. In GR the tidal force is described by the Riemann curvature tensor.