Expansion of space and momentums of galaxies

[Buckethead]

It is my understanding from reading a few threads that remote clusters don't have any "speed" relative to us, they are simply moving away. Does this mean they have no momentum? And if that is true, does that imply that they have no mass (in this context, not in a local context). And if that is true wouldn't that imply that distant galactic clusters can be accelerated without requiring any force? Would that imply that the dark energy causing an acceleration of expansion is really not so much energy as it is simply something that pushes a massless cluster to accelerate? Just some fun Sunday morning musings. Comments welcome.

 

[phinds]

It is my understanding from reading a few threads that remote clusters don't have any "speed" relative to us, they are simply moving away. Does this mean they have no momentum? And if that is true, does that imply that they have no mass (in this context, not in a local context). And if that is true wouldn't that imply that distant galactic clusters can be accelerated without requiring any force? Would that imply that the dark energy causing an acceleration of expansion is really not so much energy as it is simply something that pushes a massless cluster to accelerate? Just some fun Sunday morning musings. Comments welcome.

Mass does not imply momentum, you need speed and speed is frame dependent, so momentum is frame dependent. If you are sitting in a chair right now, do you have momentum relative to the chair or the room you are in or the sidewalk outside? Yet relative to a car driving by, you are moving at a considerable speed and have considerable momentum. Distant galaxies are receding from us, far away ones at recession velocities greater that c. That does not imply they have momentum relative to us.

 

[Nugatory]

It is my understanding from reading a few threads that remote clusters don't have any "speed" relative to us, they are simply moving away.

That's kinda sort of right, but only kinda sort of - as always, the precise statement of what's going on is in the math. The real problem here is that there is no unambiguous way of defining the relative speed of an object at cosmological distances, so no way of drawing unambiguous conclusions about things like momentum that depend on that speed. Therefore:

Does this mean they have no momentum?

No. Thus the chain of "if that is true" questions breaks right at the beginning.

 

[Brage]

I think the context they meant that they don't have any "speed" is to say that it is not that they are receeding further away from us THROUGH space, but rather that the amount of space between us and the clusters is increasing. Therefore photons traveling through this space get "streched" (redshifting from the gravitational effects) and it appears as if the stars are speeding away from us with the resdhift sometimes interpereted incorrectly to be due to a doppler effect. While dark energy is not well understoon, it is certainly an "energy". From General Relativity the energy associated with "dark energy" is positive, however the pressure associated with it is negative. That is to say unlike positive pressure where energy is released from expanding the volume (positive relative to zero), negative pressure implies energy is needed to expand a volume. Therefore as dark energy is a fundamental property of space by expanding space negative energy is "introduced" to the system, which is compensated for by an increase in dark energy (as there now is more space where dark energy can be introduced).

I believe this is all correct but anyone feel free to correct me if I left something out/believe I have interpreted something incorrectly. Of course we don't understand gravity well in a quantized sense, and dark energy even worse. So while we are not sure what dark energy is or really how it does what it does, from our current understanding it definitely has positive energy.

The galaxies definitely have mass, just because something has no momentum does not imply it is masseless, it could merely be stationary as P=mv. I am sure someone will comment that distant galaxies can be interpreted to have velocity from the reference frame at the Earth. However this is not velocity in the conventional sense. Sure you would have to travel over a certain speed to reach the galaxies, but the speed at which you would pass the cluster is the same speed as with you will have left Earth. That is to say you have to travel over a certain speed to overcome the increase in space between you and the distant cluster, however when you have overcome this distance and are right next to the cluster you would have the total speed you gained from traveling away from Earth, and the Earth would seem to be receeding with a greater speed then you obtained from the acceleration of your space ship.

I hope this helps you understand the concept a bit better, it is very complicated and can be difficult to understand, because the properties of all space can differ quite a lot from the properties of a local piece of space.

 

[Buckethead]

Phinds: I mentioned the lack of momentum because of the lack of "speed", yet the cluster still moves away. This led me to think that if the cluster has speed but no momentum, it must not have mass either.
Nugatory: I was kinda sort of thinking that myself. One additional thought that adds to the confusion is that anything without mass must move at the speed of light, so for a galactic cluster to not have overall mass, yet move subluminally has its issues.

 

[Buckethead]

Brage: Yes, this is how I understand it as well, expansion rather than movement. The energy aspect of dark energy though, is this not just something that is assumed because we are seeing an acceleration of galactic clusters and one can't accelerate a mass without energy. Or am I not getting this quite right? If I am, then if we have a cluster that doesn't have mass (again, on the cluster scale, not locally since of course galaxies themselves have mass) is accelerating then it could do so without energy. But again as Nugatory said, speed and movement break down in such a strange context as this.

 

[Drakkith]

The energy aspect of dark energy though, is this not just something that is assumed because we are seeing an acceleration of galactic clusters and one can't accelerate a mass without energy. Or am I not getting this quite right?

Recession velocities between any two objects already increase over time as the objects get further away from each other even before you account for dark energy. If this were "normal" motion this would be labeled as acceleration. However, in this case this isn't acceleration as you normally think about it. Similar to gravity, no force is applied to the objects to cause them to increase their recession velocities. Instead they remain in an inertial frame. The rate of expansion has been decreasing over time thanks to gravity and dark energy simply causes the expansion rate to decrease less quickly than it otherwise would. That is the "accelerating expansion" that's talked about.

If I am, then if we have a cluster that doesn't have mass (again, on the cluster scale, not locally since of course galaxies themselves have mass) is accelerating then it could do so without energy.

This makes no sense. If the galaxies themselves have mass then the galaxy cluster must also have mass. Mass only comes in positive quantities, so you can't add a bunch of massive objects together and wind up with zero mass.

 

[Buckethead]

Recession velocities between any two objects already increase over time as the objects get further away from each other even before you account for dark energy. If this were "normal" motion this would be labeled as acceleration. However, in this case this isn't acceleration as you normally think about it. Similar to gravity, no force is applied to the objects to cause them to increase their recession velocities. Instead they remain in an inertial frame. The rate of expansion has been decreasing over time thanks to gravity and dark energy simply causes the expansion rate to decrease less quickly than it otherwise would. That is the "accelerating expansion" that's talked about.

Thanks for stating that so clearly. Bizarre in any case to see something accelerate without needing a force. Regarding the "accelerating expansion". I thought before the discovery of this it was thought the universe might collapse on itself and after it was thought to expand forever. But you make it sound like in either case the universe will collapse.

This makes no sense. If the galaxies themselves have mass then the galaxy cluster must also have mass. Mass only comes in positive quantities, so you can't add a bunch of massive objects together and wind up with zero mass.

I was thinking along the lines of something like the Alcubierre warp drive hypothesis where inside the "warp bubble" accelerating the ship would require a force because it has mass, but if the entire system is accelerated instead, the system could achieve faster than light travel because the system itself is massless and therefore not subject to relativistic mass increases. It also would not require any substantial force to achieve ftl speeds because of this. In the same vein (and temporarily sidestepping your above comments to correct me) I was thinking that a galactic cluster could be thought of in the same way because it is accelerating relative to us but not experiencing relativistic mass increase therefore it must be massless and this could be explained by thinking of it as being in a spatial bubble like the Acubierre drive although the bubble would simply be the sector of space around the cluster.

 

[phinds]

Thanks for stating that so clearly. Bizarre in any case to see something accelerate without needing a force. Regarding the "accelerating expansion". I thought before the discovery of this it was thought the universe might collapse on itself and after it was thought to expand forever. But you make it sound like in either case the universe will collapse.

It used to be thought that the expansion would either slow down to uniform expansion forever or more likely collapse back in on itself, but after Dark Energy was realized, it became clear that it would never stop expanding. The rate of ACCELERATION is decreasing, but it will keep accelerating in the speed of the expansion, so recession rates just keep getting bigger and bigger. Eventually our local cluster will be the only visible thing in the Observable Universe.

I was thinking along the lines of something like the Alcubierre warp drive hypothesis where inside the "warp bubble" accelerating the ship would require a force because it has mass, but if the entire system is accelerated instead, the system could achieve faster than light travel because the system itself is massless and therefore not subject to relativistic mass increases. It also would not require any substantial force to achieve ftl speeds because of this. In the same vein (and temporarily sidestepping your above comments to correct me) I was thinking that a galactic cluster could be thought of in the same way because it is accelerating relative to us but not experiencing relativistic mass increase therefore it must be massless and this could be explained by thinking of it as being in a spatial bubble like the Acubierre drive although the bubble would simply be the sector of space around the cluster.

I assume you now realize this is all incorrect, and by the way, Alcubierre Drive does not create a massless system as you seem to think. It warps space around a system with mass.

 

[Buckethead]

I assume you now realize this is all incorrect,

To the degree that I understand that as space expands uniformly, objects will accelerate, although I have reservations in that if we just remove the space part and look at the objects, they are indeed accelerating and therefore either are massless or require a force to accelerate. Since they are in fact doing what we observe them to be doing and since we have no force to account for this, in at least a semantic sense, they must be considered to be massless in this context. This might be an odd way to look at this, but I mean really, something accelerates, there is no force...what else can one conclude from this. The space expanding part is the math, but the reality dictates the objects have to be considered to have no mass in order to do this. If not then wouldn't one have to say the execution of space expanding requires a force at each location pushing everything apart. Like they said during the moon shot when Guss Grissems capsule blew it's doors off, "explosive bolts don't just blow" and space doesn't just expand and push massive galaxies apart without a force, that is unless we consider the space around the clusters to form a massless environment in which case I can make sense of it.

..and by the way, Alcubierre Drive does not create a massless system as you seem to think. It warps space around a system with mass.

But then to a stationary observer, the ship would appear to increase in mass as it approached the speed of light. Wouldn't the only way around this be to say the system as a whole is massless?

 

[phinds]

To the degree that I understand that as space expands uniformly, objects will accelerate, although I have reservations in that if we just remove the space part and look at the objects, they are indeed accelerating and therefore either are massless or require a force to accelerate. Since they are in fact doing what we observe them to be doing and since we have no force to account for this, in at least a semantic sense, they must be considered to be massless in this context. This might be an odd way to look at this, but I mean really, something accelerates, there is no force...what else can one conclude from this. The space expanding part is the math, but the reality dictates the objects have to be considered to have no mass in order to do this. If not then wouldn't one have to say the execution of space expanding requires a force at each location pushing everything apart. Like they said during the moon shot when Guss Grissems capsule blew it's doors off, "explosive bolts don't just blow" and space doesn't just expand and push massive galaxies apart without a force, that is unless we consider the space around the clusters to form a massless environment in which case I can make sense of it.
But then to a stationary observer, the ship would appear to increase in mass as it approached the speed of light. Wouldn't the only way around this be to say the system as a whole is massless?

Ah, there's your problem. They are NOT accelerating. If you were to place a single body in space, at a cosmological distance from Earth (say a billion light years) in a way that was co-moving with Earth and then leave it and come back in a billion years, it would no longer be co-moving with Earth, it would be receding at an increasing rate. I know you think this is accelerating, but it is not. If you were to put an accelerometer on that body it would read zero.

 

[Chalnoth]

Recession velocities between any two objects already increase over time as the objects get further away from each other even before you account for dark energy.

I really don't think this is true. The recession velocity between any two objects should decrease monotonically unless the universe has some dark energy (technically, a substance with $w < -1/3$, or a positive cosmological constant).

The recession velocity for objects further away is higher, but any two specific pairs should have a falling recession velocity regardless.

 

[Chalnoth]

But then to a stationary observer, the ship would appear to increase in mass as it approached the speed of light. Wouldn't the only way around this be to say the system as a whole is massless?

Nope. There are no relativistic effects like time dilation or length contraction for a ship using an Alcubierre drive.

Also, physicists generally don't consider mass to be something which changes with velocity any longer. Rather, the mass of a particle is the amount of energy it has at rest (or technically, its energy in the particle's own inertial frame). The interpretation that mass increased with velocity was dropped because it led to quite a few mistakes.

Then there's the problem that the idea that mass increased with velocity stemmed from special relativity, which has a flat space-time. Special relativity simply does not work in curved space-time, such as with an Alcubierre drive or an expanding universe.

 

[Drakkith]

I really don't think this is true. The recession velocity between any two objects should decrease monotonically unless the universe has some dark energy (technically, a substance with $w < -1/3$, or a positive cosmological constant).

The recession velocity for objects further away is higher, but any two specific pairs should have a falling recession velocity regardless.

Alright. Makes sense if the rate of expansion is decreasing fast enough.

 

[Drakkith]

Since they are in fact doing what we observe them to be doing and since we have no force to account for this, in at least a semantic sense, they must be considered to be massless in this context. This might be an odd way to look at this, but I mean really, something accelerates, there is no force...what else can one conclude from this.

The same thing we can conclude from acceleration due to gravity. There's no force there either. An accelerometer in free fall under gravity would register no acceleration (and thus no net force) even though its velocity is changing as viewed from an observer standing on the surface of a nearby planet. It would be silly to conclude that because an accelerometer isn't registering acceleration in this situation that it somehow has no mass.

The space expanding part is the math, but the reality dictates the objects have to be considered to have no mass in order to do this.

No it doesn't. In fact, if you try to consider them as massless then much of physics completely breaks down, including General Relativity, which is the theory that the cosmologist use to explain expansion.