The Mystery of Superluminal Recession Velocities in Cosmology

[jonmtkisco]

Let's conduct a thought experiment involving a galaxy far, far away ("Galaxy FFA") from earth. Galaxy FFA is observed from Earth to be receding at twice the speed of light.

Let's hire very fast (.9c) alien spaceships to simultaneously release 999 test particles equally spaced across the distance between Earth and Galaxy FFA. (We outsource this work to multiple alien space agencies because their home galaxies are located all along the route between Earth and Galaxy FFA, so each spaceship has less distance to fly. This will help us achieve budget savings.) Clocks on the spaceships are pre-coordinated and adjusted for any differences caused by SR time dilation. Radar ranging is used to achieve evenly spaced drops. At the instant of release, all 999 test particles are released at proper rest with respect to Earth and each other, i.e. no proper motion.

At the instant after release, what is the proper speed of the test particle closest to Galaxy FFA, relative to Galaxy FFA?

Jon

 

[poeteye]

I really like the name of your galaxy! It seems you are giving more detail than is required for your thought experiment, however. Also, I am not sure what you mean by "proper speed." And are you asking what are the comparative speeds of particle 999 and galaxy FFA, relative to an Earth observer?

 

[jonmtkisco]

Hi poeteye,
Thanks for asking. Actually my question can be phrased as, "What is the recession speed of particle #999 as seen by an observer on Galaxy FFA?" Particle 999 being the particle located closest to Galaxy FFA.

I included details about the setup of the thought experiment because I want it to be very clear and not confused by peripheral SR quibbles, etc. Also, in case anyone is against free trade, I explained why the space work is outsourced to alien agencies.

EDIT: "Proper speed" simply refers to the change in directly measured distance, per unit of time, as between two objects. This terminology is used to distinguish it from comoving coordinate systems.

Jon

 

[marcus]

Hi poeteye,
Thanks for asking. Actually my question can be phrased as, "What is the recession speed of particle #999 as seen by an observer on Galaxy FFA?" Particle 999 being the particle located closest to Galaxy FFA.
...

Hi Jon,
your thought experiment setup is a familiar one. IIRC Ned Wright uses it to clarify what he means by the distance at the present moment to a certain galaxy (e.g. your FFA).

The idea is you do all this planning in advance so that a large number of collaborators are stretched out evenly in a line, between us and FFA, at the same moment, and they all measure the distance to their nearest neighbor at the same moment (universal CMB time, I guess) and we add up all the little increments.

Ned Wright used that thought experiment setup to help describe comoving distance, because it concretizes the basic idea in it of the real distance at the present moment.

I think to be quite operationally clear about it you would have to specify that all the collaborators are stationary with respect to the CMB. The CMB or hubbleflow gives us a universal idea of being at rest, and also a universal idea of simultaneity. That would help in the conceptual construction.
=====================

To answer your question, I'd say the recession speed between any two neighbors is 0.002 c.

That is, 2 c divided by 1000.

Because the total distance to FFA is expanding at 2c, and the distance has been equally divided into 1000 increments.
=====================

All your statements involving the term "proper speed" and "proper rest" are potentially confusing because you seem to be using those terms in your own special way. Or else I am missing something. "Proper velocity" as usually defined http://scienceworld.wolfram.com/physics/ProperVelocity.html
as in Wolfram or in Wikipedia, is meaningful in the context of special relativity.
But special rel does not apply because in special rel distances do not expand.
There is no such thing as recession speed, in special rel.

Maybe I am missing something. But I make sense of what you say by focusing on what I quoted, and forgetting about anything involving the words "proper".

I hear you clearly when you put the question "what is the recession speed of particle #999 relative to galaxy FFA?" That makes sense, the terminology is not confusing, and the answer I think is 2/1000 of the speed of light.

 

[jonmtkisco]

Hi Marcus,

I think to be quite operationally clear about it you would have to specify that all the collaborators are stationary with respect to the CMB. The CMB or hubbleflow gives us a universal idea of being at rest, and also a universal idea of simultaneity. That would help in the conceptual construction.

I think you are describing a scenario that is quite different from what I intend. Let's assume for the sake of discussion that the Earth is stationary relative to the CMB frame. Of course it's not, as demonstrated by the measured dipole in the CMB.

In this scenario then, only the Earth is at rest in its local CMB rest frame. All 999 particles are at rest in the earth's local CMB rest frame, but not in the particle's own local CMB rest frame. By definition, no two significantly separated particles which are at proper rest relative each other can both at the same time be at rest with respect to their own local CMB frame.

At the instant of release, the test particles are not in proper motion relative to each other and the earth. Instead, the proper distance between them is constant at the first instant. After the first instant, the test particles will begin to see the proper distances between each other decreasing, as per the Shell Theorem. But in this scenario we aren't studying what happens to the test particles at later times, we are observing only the proper speed of particle #999 relative to Galaxy FFA in the first brief instant.

I don't think the concepts of "proper distance" and "proper speed" as I am using them are different from the normal meaning. Proper distance is directly measured radar distance (or physical rulers laid end-to-end). Proper speed is change in radar distance as a function of time.

Jon

 

[jonmtkisco]

I don't want to bog down on the definition of proper distance (if we don't have to). Here is a simple GR description of the term from Taylor & Wheeler, Exploring Black Holes (p 1-4):

[Simultaneous explosions] are perfect for measuring length. Question: How do you measure the length of a rod, whether it is moving or at rest in your frame? Answer: Set off two firecrackers at the two ends at the same time (t=0) in your frame. Then define the rod's length in your frame as the distance s between this pair of explosions.

Special relativity warns us that a different observer passing us in uniform relative motion typically will not agree that the two firecrackers exploded at the same time. That is the bad news... But there is good news: All inertial observers, whatever their state of relative motion, can calculate the distance $$\sigma$$ between explosions as recorded in the frame in which they do occur simultaneously. The new metric is... :

$$\sigma = s^{2} - t^{2}$$

The Greek letter $$\sigma$$ (sigma) labels what we call the proper distance between such events, or more formally, the spacelike spacetime interval ("spacelike" because the space separation s is greater than the time separation t). All free-float observers agree on the value of the proper distance - the proper distance is an invariant. In contrast, the value of t and the value of s between these events typically differ, respectively, as measured in different frames. Proper distance $$\sigma$$ can be used to describe the separation between any pair of events for which s is greater than t. It tells the observer in any frame what the distance $$\sigma$$ is between the events as measured in a frame in which they occur at the same time.

We attach special significance to the length of a rod measured in the frame in which it is at rest. Let firecrackers explode at each end of a rod at the same time in its rest frame. We call the distance between these explosions the proper length of the rod. Any other inertial observer, whatever her state of relative motion, calculates the same value for the proper length of the rod from the equation [above] using her own measurement time t and distance s between these explosions (or indeed between any spacelike pair of events that occur at opposite ends of the rod).

...the units of space and time in equation [above] are the same, such as light-years and years - or meters of distance and meters of light-travel time.

Jon

 

[jonmtkisco]

Another description of measuring proper distance, from Barnes & Francis "Joining the Hubble Flow" (p2 and fn#1):

Throughout this paper, we will use proper distance $$r_{p}$$, which is defined as being the radial $$(d \theta = d \phi = 0)$$ spacetime interval (ds) along a hypersurface of constant cosmic time (dt=0).

Fn #1: A thought experiment for measuring proper distance is as follows: we imagine being at one end of a giant ruler, pointed at a distant object. A volunteer is sent along the ruler to read off the distance to the object. Since the universe is expanding, the volunteer will need to carry a clock that displays cosmic time, and note down the time when the measurement was made. When light rays have carried the volunteer’s result back to us, we will know the proper distance to the object at the time the measurement was made. Samuel (2005) criticises proper distance as “violating the principle that instantaneous non-local measurements cannot be made”. This amounts to criticising a spacelike interval for being a spacelike interval. In any GR metric, length or distance is defined as the spacetime interval along a surface of constant time, and as such can never be known instantaneously. This does not mean, however, that proper distance is unphysical. It only means that it must be reconstructed at a later time from the information in light signals.

Jon

 

[chronon]

There are so many different distance measures in cosmology that to call one of them 'proper' is asking for trouble. In my Cosmological Distances applet I use 6 different ones, and I think that there are a few more besides. The one you mean seems to be 'radar' distance (intuitively you would expect this to be what a rigid rod would measure, but I'm not sure whether there's any theoretical evidence to back this up)

 

[jonmtkisco]

Hi chronon,

There are so many different distance measures in cosmology that to call one of them 'proper' is asking for trouble.

Your applet is interesting. I'm a big fan of graphs!

Surely we can adopt the premise that I didn't make up the name "proper distance". It is widely used in the technical literature, such as the textbook and article examples I cited. I can cite more examples if necessary. I hope I have not diverged at all from the customary usage of terminology.

I definitely agree that "raw" radar distance may not be exactly the same as "ruler" distance; some adjustments may be required. Clock synchronization certainly. Also, redshift of the radar return signal needs to be checked to detect any dopler effect caused by a target and source which are not truly stationary relative to each other at the instant of transmission, reflection and/or reception.

For the purposes of this thread, I hope we can get beyond the terminology. As I said in my posts, we can also use ruler distance instead of of radar distance if you find it clearer.

Maybe it will help if I recast my original question in the simplest way: If we extend a very long rigid ruler from adjacent to Earth (with that end kept stationary relative to earth) such that the far end of the ruler is adjacent to Galaxy FFA for an instant in time, at what proper speed (order of magnitude) will an observer on Galaxy FFA observe the end of the ruler (adjacent to Galaxy FFA) is moving away from her? Please don't worry about how realistic it is to deploy such a ruler.

Jon

 

[dilletante]

Maybe it will help if I recast my original question in the simplest way: If we extend a very long rigid ruler from adjacent to Earth (with that end kept stationary relative to earth) such that the far end of the ruler is adjacent to Galaxy FFA for an instant in time, at what proper speed (order of magnitude) will an observer on Galaxy FFA observe the end of the ruler (adjacent to Galaxy FFA) is moving away from her? Please don't worry about how realistic it is to deploy such a ruler.

Jon

If FFA is receding from Earth at 2c and a rigid ruler is attached to Earth, I would think that FFA would view their end of the ruler as receding at 2c. Can it be otherwise, assuming that the ruler is truly rigid? It would seem that FFA would recede from the Earth and everything attached to it at the same rate, unless the length of the ruler changes.

 

[dilletante]

On the other hand, if the close end of the ruler moved away at 2c it would seem to violate relativity by exceeding light speed in local space. So therefor FFA must view the two ends of the ruler as moving away at different speeds? Hmm, I thought it was rigid!

 

[DaveC426913]

On the other hand, if the close end of the ruler moved away at 2c it would seem to violate relativity by exceeding light speed in local space. So therefor FFA must view the two ends of the ruler as moving away at different speeds? Hmm, I thought it was rigid!

Well, there is no such thing as a rigid ruler, even in theory. The ruler, made of matter, is pliable and will not violate any SR or GR laws.

 

[jonmtkisco]

Hey, I appreciate all of the responses.

Well, there is no such thing as a rigid ruler, even in theory. The ruler, made of matter, is pliable and will not violate any SR or GR laws.

I think that in cosmology thought experiments there is such a thing as a rigid ruler. I don't think we can short-cut the answer here just by assuming that the ruler stretches or shrinks. C'mon folks, let's lay it on the line here !

Perhaps, even if the ruler is not pliable in the normal sense, it will be shorten as a result of a Lorentz transformation, or a series of Lorentz transformations along its length?

Jon

 

[marcus]

Hi Jon,
poeteye in post #2 originally asked you what you meant by "proper speed" or "proper velocity". I don't think you said yet. The term "proper distance" we've all heard used a lot. But "proper velocity" is hard to find with google except in the context of special relativity, which doesn't cut it here. So maybe you could clarify.

You talk about SIMULTANEOUSLY releasing a bunch of test particles. What reference frame what defines simultaneous? You talk about releasing test particles AT REST with respect to the earth, but some of the particles are out near the distant galaxy.

Explain how this is physically possible, since to release a particle out at the galaxy so that it stays a constant distance from Earth would require accelerating it to towards the Earth at twice the speed of light.

By the time the hired rocket ships have gotten out near the galaxy it is physically impossible for them to assume a station which is constant distance from earth. So the thought experiment is unthinkable. It simply breaks.

But in any case it is not so welldefined mathematically since you seem to think you can have a minkowski reference frame (a la special rel) which extends out to a neighborhood of the distant galaxy. Bad fit. local reference frames don't fit the universe at large scale---they only fit a small patch. (Because they are not expanding, mainly.)

At the instant of release, all 999 test particles are released at proper rest with respect to Earth and each other, i.e. no proper motion.

At the instant after release, what is the proper speed of the test particle closest to Galaxy FFA, relative to Galaxy FFA?

Jon

Lot of vagueness here. You start all the spaceships out at their HOME GALAXIES. and yet you say they have coordinated clocks. How do you establish synchronized clocks?

The main thing though is that the thought experiment seems very fragile because it is physically impossible for a hired rocket ship to establish itself at rest with respect to the earth, if it is very distant (like twice Hubble distance), no matter how much fuel it burns.A practical concept of "at rest" is to be at rest with respect to the Hubble flow, or with respect to the Cosmic Microwave Background. That is easy to achieve anywhere in the universe. But that is evidently not what you want here.

Let me know if you think I am missing something, or don't understand what you are driving at

 

[chronon]

Surely we can adopt the premise that I didn't make up the name "proper distance". It is widely used in the technical literature, such as the textbook and article examples I cited. I can cite more examples if necessary. I hope I have not diverged at all from the customary usage of terminology.

Yes, your quotes imply something like radar distance, but I think the term "proper distance" has also been used for comoving distance. I think it's best to avoid the term.

Hey, I appreciate all of the responses.
I think that in cosmology thought experiments there is such a thing as a rigid ruler. I don't think we can short-cut the answer here just by assuming that the ruler stretches or shrinks. C'mon folks, let's lay it on the line here !

It depends. If there is a cosmological constant then such a ruler would be impossible if it exceeded a certain length. Otherwise it's OK.

The main thing though is that the thought experiment seems very fragile because it is physically impossible for a hired rocket ship to establish itself at rest with respect to the earth, if it is very distant (like twice Hubble distance), no matter how much fuel it burns.

I'm sorry but in the case of a non-accelerating universe it is possible to envisage a reference frame such as jonmtkisco suggests. This would either be in terms of rigid bodies, or in terms of radar measurements. In such a frame the FFA galaxy would be seen as moving at a subluminal velocity.

In the case of an accelerating universe, it's more complicated, but it is still possible to envisage such a frame extending beyond the Hubble sphere. The Hubble sphere is not the Cosmological Event Horizon

 

[yuiop]

...
I'm sorry but in the case of a non-accelerating universe it is possible to envisage a reference frame such as jonmtkisco suggests. This would either be in terms of rigid bodies, or in terms of radar measurements. In such a frame the FFA galaxy would be seen as moving at a subluminal velocity.

I think Chronon has an interesting point here. If a rocket passed the Earth heading towards FFA at 0.8c it would not see FFA as redshifted. The rocket moving at 0.8c relative to the Earth locally would effectively be at rest with FFA receding at 2.0c relative to the Earth. Wierd...

Another interesting observation is that if a traveler headed towards FFA at a constant velocity of 0.1c relative to the local CMB, she would eventually get there in the model where FFA is at rest with the local expanding spacetime. If the spacetime was not expanding and FFA was really receding at 0.8c relative to the Earth then the rocket would never catch up with FFA unless it traveled at a minimum of 0.8c relative to the Earth.

 

[marcus]

...At the instant of release, all 999 test particles are released at proper rest with respect to Earth and each other, i.e. no proper motion.

At the instant after release, what is the proper speed of the test particle closest to Galaxy FFA, relative to Galaxy FFA?

Jon

Chronon,

Jon hasn't explicitly said what "proper speed" means, we only have some shared ideas of proper distance and we extrapolate from that. As I understand what it means to be at proper rest, it is physically impossible for something to be twice Hubble distance from earth, at this moment today, and also be at rest with respect to the earth.

Jon wants one of his rocket ships (out there near the distant galaxy) to do that. Maybe you can show me how that could be done---real world rocket ship, real world local coordinates.

Think about an active galactic nucleus (AGN) in a galaxy that is twice Hubble distance away from us (i.e. receding at 2c). Imagine that one of the two jets is pointed right at us and sending particles at us with speed 0.99 c.

Do you think of those particles as not moving with respect to the earth?

 

[dilletante]

Hey, I appreciate all of the responses.

I think that in cosmology thought experiments there is such a thing as a rigid ruler. I don't think we can short-cut the answer here just by assuming that the ruler stretches or shrinks. C'mon folks, let's lay it on the line here !

Perhaps, even if the ruler is not pliable in the normal sense, it will be shorten as a result of a Lorentz transformation, or a series of Lorentz transformations along its length?

Jon

I am a bit confused. It was my understanding that the expansion of space does not affect bound bodies, from previous discussions. Now it seems that it does, if the ruler is long enough?

What if you change the experiment just a bit and build the ruler first, so that the end of it is far far away (FFA). Now you release dust near the Earth end and wait millions of years until the dust expands to the end of the ruler. Will the dust pass the end of the ruler at a relative speed greater than c?

 

[yuiop]

I am a bit confused. It was my understanding that the expansion of space does not affect bound bodies, from previous discussions. Now it seems that it does, if the ruler is long enough?

What if you change the experiment just a bit and build the ruler first, so that the end of it is far far away (FFA). Now you release dust near the Earth end and wait millions of years until the dust expands to the end of the ruler. Will the dust pass the end of the ruler at a relative speed greater than c?

There seems to be an immediate problem, in that as soon as you build the ruler and attach one end to the Earth, the far end of the ruler will be moving at 2c relative to the CMB.

 

[DaveC426913]

I am a bit confused. It was my understanding that the expansion of space does not affect bound bodies, from previous discussions. Now it seems that it does, if the ruler is long enough?

Yes. Any practical bound body operates on a local scale and it will have a molecular cohesion that overpowers expansion. A ruler as long as the one in your experiment is so long that it would not behave like a classically solid object.

 

[DaveC426913]

There seems to be an immediate problem, in that as soon as you build the ruler and attach one end to the Earth, the far end of the ruler will be moving at 2c relative to the CMB.

Maybe, maybe not. The far end of the ruler will not experience any movement of the near end in any less time than the speed of sound through the ruler. It could take billions of years before the far end moves at all.

 

[yuiop]

Maybe, maybe not. The far end of the ruler will not experience any movement of the near end in any less time than the speed of sound through the ruler. It could take billions of years before the far end moves at all.

If you started building the ruler from the Earth end , ready attached to the Earth and assuming you cannot build it faster than the speed of sound, then the movement factor will already be built in. One possible way around this would be to build the ruler in large overlapping sections that slide slowly relative to each during the construction phase and then attempt to weld all the sections together in a carefully timed operation at the last minute.

I wonder if there is a hypothetical limit on how long such a ruler could be? For example any ruler that is longer than the Hubble radius, that is stationary with respect to the local CMB at one end will be moving faster than the speed of light relative to the local CMB at the other end.

 

[chronon]

The trouble with this discussion is that you have to keep saying 'It depends on the value of lambda'. In what follows I'll assume that we're dealing with a model of the universe in which lambda=0. Can I ask future posters to indicate if they are assuming a specific value for lambda.

Chronon,

Jon hasn't explicitly said what "proper speed" means, we only have some shared ideas of proper distance and we extrapolate from that. As I understand what it means to be at proper rest, it is physically impossible for something to be twice Hubble distance from earth, at this moment today, and also be at rest with respect to the earth.

Jon wants one of his rocket ships (out there near the distant galaxy) to do that. Maybe you can show me how that could be done---real world rocket ship, real world local coordinates.

It is possible to construct a coordinate system which is at rest with respect to the earth, although the details might involve a bit of work. It also might be slightly different if it's done in terms of 'rigid' bodies or in terms of light signals.

Think about an active galactic nucleus (AGN) in a galaxy that is twice Hubble distance away from us (i.e. receding at 2c). Imagine that one of the two jets is pointed right at us and sending particles at us with speed 0.99 c.

Do you think of those particles as not moving with respect to the earth?

The 2c is in comoving coordinates. The 0.99c is with respect to the frame of the galaxy. I would say that the particles are moving towards earth. Again, it is possible to do the calculations and see that the jet will be blueshifted and that the particles will eventually reach earth.

I am a bit confused. It was my understanding that the expansion of space does not affect bound bodies, from previous discussions. Now it seems that it does, if the ruler is long enough?

Expansion of space is a myth. A positive value of lambda would affect such a ruler.

What if you change the experiment just a bit and build the ruler first, so that the end of it is far far away (FFA). Now you release dust near the Earth end and wait millions of years until the dust expands to the end of the ruler. Will the dust pass the end of the ruler at a relative speed greater than c?

As I'm assuming lambda=0 there is nothing to cause the dust to expand.

There seems to be an immediate problem, in that as soon as you build the ruler and attach one end to the Earth, the far end of the ruler will be moving at 2c relative to the CMB.

An observer stationary with respect to the CMB would see the end of the ruler moving at less that c.

 

[jonmtkisco]

Hi Marcus,

The term "proper distance" we've all heard used a lot. But "proper velocity" is hard to find with google except in the context of special relativity, which doesn't cut it here. So maybe you could clarify.

Sure, here's a definition in Lewis, Francis et al 7/07 http://arxiv.org/PS_cache/arxiv/pdf/0707/0707.2106v1.pdf" "

A fundamental definition of distance in general relativity is the proper distance, defined as the spatial separation between two points along a hypersurface of constant time. Given the form of the FLRW metric the radial distance from the origin to a coordinate x along a hypersurface of constant t is;

$$D_{p}(t) = a(t) x$$

Taking the derivative with respect to coordinate time [which is synchronous for all comoving observers (fixed x) and is equivalent to their proper time $$\tau$$] we obtain what we will refer to as the proper velocity

$$v_{p} \equiv \frac {d D_{p}}{d\tau} = \frac {d D_{p}}{dt} = \frac{da}{dt} x + a \frac{dx}{dt}$$

For comoving observers with dx/dt = 0 this becomes the well known distance-velocity law.

What reference frame what defines simultaneous?

For simplicity in this exercise let's say the Earth's reference frame. Clocks will be synchronized in advance by radio coordination. This may take a long time, but we have all the time in the world for this exercise. Long-term outsourcing to aliens is really inexpensive because they use cheap plastic robot spaceships.

Explain how this is physically possible, since to release a particle out at the galaxy so that it stays a constant distance from Earth would require accelerating it to towards the Earth at twice the speed of light.

I don't want to get bogged down on this kind of question, it's sort of like asking how can you construct and deploy a bazillion lightyear long ruler. But I think the alien spaceships I hired with .9c speed can reasonably conduct the thought experiment, even if it takes 500 years for some of them to get into position. E.g., half of the spaceships depart from Earth and position themselves at intervals up to almost half of the total distance to Galaxy FFA. The remainder of the spaceships depart a midway galaxy; one positions itself one interval away from the most outbound of the spaceships that originated at earth, and achieves the requisite velocity towards Earth to maintain a fixed proper distance. The other ships depart from the station of this one ship, and within 500 years they can travel and position themselves at the requisite proper distances from that ship. The fact that, for example, ship #999 might appear to require a proper velocity of 2c relative to Galaxy FFA does not seem to me to reflect a deployment problem per se; instead it is simply a microcosm of the whole question, how fast is particle #999 really moving away from Galaxy FFA in a local observer's frame?

But in any case it is not so well defined mathematically since you seem to think you can have a minkowski reference frame (a la special rel) which extends out to a neighborhood of the distant galaxy.

Those are your words not mine. I never said or implied directly that a global Minkowski frame is possible, because I know it is not. I simply asked a question about the local velocity of particle #999 relative to Galaxy FFA. A question to which, by the way, you have not ventured a firm answer based on my facts.

Perhaps one can best answer my question by using the conformal coordinates described in the Lewis & Francis paper and by Chodorowski. As I suggested in my last post referring to the rigid ruler, I think there are a continuous series of Lorentz transformations along the ruler which result in some aggregate amount of length contraction. For the spaceship version, the Lorentz transformations would be discrete at each interval, but should add up to the same aggregate answer.

Chronon, I wanted to mention that I defined Lambda = 0 in this model universe.

Jon

 

[jonmtkisco]

I forgot to mention that the alien robotic spaceships are each only a few times larger than the Planck length and weigh almost nothing. The nanotechnology is astounding. Of course, the massless test particle they carry in the "bomb bay" doesn't take up much space. We may be able to reverse engineer these ships with electron microscopes, but the fabrication techniques are far beyond our current nanotechnology capability. The best feature is that the aliens can manufacture and launch these ships for just two cents (US) each. After 500 years of future inflation, the project still will be affordable but just barely.

The ships are not self-powered. They are powered externally by high-energy particle beams (with dispersion and coherence far superior to our lasers), fired from an existing comprehensive deep space network infrastructure of power stations.

Jon

 

[yuiop]

...
Expansion of space is a myth. A positive value of lambda would affect such a ruler.

Those are strong words, if are suggesting that the universe is not expanding. Do you mean accelerated expansion of the universe is a myth or the idea of spacetime itself expanding and comoving with distant galaxies is a myth?

It seams to me that the old idea of the big bang as an explosion accelerating particles outwards at subluminal velocities relative to a static non expanding spacetime background, is basically consistent with a model that has distant galaxies being dragged along at superluminal velocities by the expansion of spacetime itself, while the distant galaxies remain on average, at rest with the local spacetime.

For example: (assuming Lambda=0)

Redshift
An galaxy receding at 0.8c in static spacetime has the same redshift signature as a galaxy exceding at 2c in comoving spacetime. I can show the maths if anyone needs to see it.

Time
Consider a star in our target galaxy that is destined to go supernova after a given proper time. The supernova event in the galaxy moving away at 0.8c in static spacetime is delayed due to time dilation of motion relative to the static spacetime. The result is that light signalling the supernova event arrives at the same time at the Earth in either model. The supernova event happens earlier in comoving model because there is no time dilation but the light has to travel further and hence the simultaneous arrival times in both models.

Luminosity
This is the basis of how we judge distances. In the static spacetime model, receding galaxies have reduced apparent luminosity due to time dilation, classic doppler shift and relativistic abberation. The total reduction of luminosity due to relativistic effects is proportional to $$1/(z+1)^3$$ for monochromatic light. In the comoving spacetime model there is no time dilation or relatavistic aberration but this is compensated by the actual distance the light travels being greater and due to a spreading out of the light as it travels through expanding spacetime similar to the way the wavelength of a photon is stretched out by the expansion of spacetime. The exact calculation for the luminosity of an object in expanding comoving spatime is more complicated than the Special Relativity calculation but it is worthy of careful investigation.

Supernova period.
If a sn1a type supernova exploded in the milky way, the period of high brightness is thought to last about 1 week. When a supernova event happens in a galaxy receding at 0.8c relative to static spacetime the peroid of high brightness lasts about 2 weeks due to relativistic time dilation factor of 1.6666 and an additional factor due to its motion away from first light to last light. The supernova event appears to last about 2 weeks as measured on Earth in the comoving case, because although their is no time dilation in the comoving model the galaxy moves further during the first to last light period of the supernova event.


Put all the above together and it can be seen that both models predict identical start times, identical durations supernova events with identical redshifts as measured on Earth and it is likely although I have not rigorously proved it, that they will predict the same luminosity. As mentioned before this last point is worthy of careful investigation. If there is a difference in predicted luminosity then we need to check our assumptions before drawing any conclusions from observations based mainly on luminosity.

It may be possible that there are subtle differences between the two models, but we should be clear exactly what they are before rejecting on of them. For example some of the issues raised in this thread about the absurdity of a very long ruler that seems to imply superluminal velocities relative to the long ruler are not an issue in the static spacetime where all motions are subluminal.

An unpowered projectile fired at say 0.2c towards galaxy FFA which is receding at 2c will eventually get there in the comoving model because the projectile is progressively dragged along with the expanding spacetime. In the static spacetime model a projectile fired at 0.2c towards galaxy FFA, which is receding at 0.8c in this model, will never get there. This seems slightly paradoxical and I wonder if anyone here can resolve it?

Another issue is the visible disc size of a galaxy, as measured by the subtended angle, would seem to different in the two models. There does not appear to be a reason why the disc size of the galaxy would appear to be smaller in the static spacetime model where the galaxy is physically nearer to match the apparent disc size of the galaxy, which is physically further away at any given time in the comoving spacetime model. It should be noted that this is a very difficult parameter to measure for high z objects as they appear as single pixels even with the best telescopes.

 

[chronon]

Those are strong words, if are suggesting that the universe is not expanding. Do you mean accelerated expansion of the universe is a myth

No, I'm happy with the universe expanding and the acceleration of the expansion. What I object to is the idea that space is like a sheet of rubber. I find that this is the cause of a much confusion about cosmology and GR

or the idea of spacetime itself expanding and comoving with distant galaxies is a myth?

Careful. Spacetime can't expand since there isn't any time external to it

For example: (assuming Lambda=0)

Redshift
An galaxy receding at 0.8c in static spacetime has the same redshift signature as a galaxy exceding at 2c in comoving spacetime. I can show the maths if anyone needs to see it.

I would have thought that the exact details would depend on the parameters of the universe, but I agree with the principle. I would say that it is best to think of the actual speed of the galaxy as 0.8c

Time
Consider a star in our target galaxy that is destined to go supernova after a given proper time. The supernova event in the galaxy moving away at 0.8c in static spacetime is delayed due to time dilation of motion relative to the static spacetime. The result is that light signalling the supernova event arrives at the same time at the Earth in either model. The supernova event happens earlier in comoving model because there is no time dilation but the light has to travel further and hence the simultaneous arrival times in both models.


Luminosity
This is the basis of how we judge distances. In the static spacetime model, receding galaxies have reduced apparent luminosity due to time dilation, classic doppler shift and relativistic abberation. The total reduction of luminosity due to relativistic effects is proportional to $$1/(z+1)^3$$ for monochromatic light. In the comoving spacetime model there is no time dilation or relatavistic aberration but this is compensated by the actual distance the light travels being greater and due to a spreading out of the light as it travels through expanding spacetime similar to the way the wavelength of a photon is stretched out by the expansion of spacetime. The exact calculation for the luminosity of an object in expanding comoving spatime is more complicated than the Special Relativity calculation but it is worthy of careful investigation.

Supernova period.
If a sn1a type supernova exploded in the milky way, the period of high brightness is thought to last about 1 week. When a supernova event happens in a galaxy receding at 0.8c relative to static spacetime the peroid of high brightness lasts about 2 weeks due to relativistic time dilation factor of 1.6666 and an additional factor due to its motion away from first light to last light. The supernova event appears to last about 2 weeks as measured on Earth in the comoving case, because although their is no time dilation in the comoving model the galaxy moves further during the first to last light period of the supernova event.


Put all the above together and it can be seen that both models predict identical start times, identical durations supernova events with identical redshifts as measured on Earth and it is likely although I have not rigorously proved it, that they will predict the same luminosity. As mentioned before this last point is worthy of careful investigation. If there is a difference in predicted luminosity then we need to check our assumptions before drawing any conclusions from observations based mainly on luminosity.

Yes, the physics turns out to be just the same in either model. In the end the only difference is the choice of coordinate system

It may be possible that there are subtle differences between the two models, but we should be clear exactly what they are before rejecting on of them. For example some of the issues raised in this thread about the absurdity of a very long ruler that seems to imply superluminal velocities relative to the long ruler are not an issue in the static spacetime where all motions are subluminal.

An unpowered projectile fired at say 0.2c towards galaxy FFA which is receding at 2c will eventually get there in the comoving model because the projectile is progressively dragged along with the expanding spacetime. In the static spacetime model a projectile fired at 0.2c towards galaxy FFA, which is receding at 0.8c in this model, will never get there. This seems slightly paradoxical and I wonder if anyone here can resolve it?

This is one of the confusions caused by the rubber sheet model of space. Space doesn't drag anything along, and the projectile will never get to galaxy FFA. Think instead of a galaxy which is moving at 0.2c from earth, so that the projectile is stationary wrt this galaxy. Then assuming positive density of matter and lambda=0, the projectile will start to fall towards it due to gravity

Another issue is the visible disc size of a galaxy, as measured by the subtended angle, would seem to different in the two models. There does not appear to be a reason why the disc size of the galaxy would appear to be smaller in the static spacetime model where the galaxy is physically nearer to match the apparent disc size of the galaxy, which is physically further away at any given time in the comoving spacetime model. It should be noted that this is a very difficult parameter to measure for high z objects as they appear as single pixels even with the best telescopes.

Angular size distance is generally different from either comoving distance or radar distance. (And luminosity distance is different from all three. An then there's light travel time and transverse comoving distance and ...)

 

[Chaos' lil bro Order]

I think the irony of this thought experiment is that you could never coordinate it unless you possessed luperluminal communication, which is impossible. Think about it, you are using 0.9c alien spaceships, to space out 1000 'orbs' from Earth (0c out to 2.0c). How could you ever drop the 999th orb which is nearest the FFA 2.0c galaxy. Travelling at 0.9c you would constantly be chasing a faster car? Am I missing something here? I probably am.

 

[yuiop]

I think the irony of this thought experiment is that you could never coordinate it unless you possessed luperluminal communication, which is impossible. Think about it, you are using 0.9c alien spaceships, to space out 1000 'orbs' from Earth (0c out to 2.0c). How could you ever drop the 999th orb which is nearest the FFA 2.0c galaxy. Travelling at 0.9c you would constantly be chasing a faster car? Am I missing something here? I probably am.

Imagine someone is standing on a conveyor belt that is moving him at 30 mph relative to you. If you run alongside you can not catch up with him. If you get on the conveyor belt you can catch up with him just by walking. The expanding spacetime is like a conveyor belt that galaxy FFA is sitting on. The alien spaceships are also carried along by the spacetime conveyor belt, so they have no difficulty catching up with FFA. From Earth it will look like the spaceships are going faster than 2c as they get nearer FFA.

P.S. It is more like a succession of progressively faster conveyor belts, so there may be a limit to how much of a head start FFA has, that will still allow you to catch up with it. Maybe someone has a formula for that?

P.P.S. The headstart limit is probably the Hubble Horizon.

 

[marcus]

...
Perhaps one can best answer my question by using the conformal coordinates described in the Lewis & Francis paper and by Chodorowski...

The paper Jon cites is
http://arxiv.org/abs/0707.2106
Coordinate Confusion in Conformal Cosmology
Geraint F. Lewis, Matthew J. Francis, Luke A. Barnes, J. Berian James
5 pages, accepted for publication in MNRAS Letters
(Submitted on 13 Jul 2007)

"A straight-forward interpretation of standard Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmologies is that objects move apart due to the expansion of space, and that sufficiently distant galaxies must be receding at velocities exceeding the speed of light. Recently, however, it has been suggested that a simple transformation into conformal coordinates can remove superluminal recession velocities, and hence the concept of the expansion of space should be abandoned. This work demonstrates that such conformal transformations do not eliminate superluminal recession velocities for open or flat matter-only FRLW cosmologies, and all possesses superluminal expansion. Hence, the attack on the concept of the expansion of space based on this is poorly founded. This work concludes by emphasizing that the expansion of space is perfectly valid in the general relativistic framework, however, asking the question of whether space really expands is a futile exercise."

To put this in context, and Wallace can speak authoritatively about this paper if he cares to, the paper seems to be partly aimed at debunking a certain fringe school of thought (which might be represented by the Chodorowski that Jon mentions) according to which
"a simple transformation into conformal coordinates can remove superluminal recession velocities".

We already had a discussion thread here at the forum about an earlier paper by the same authors which discusses the verbal confusion surrounding expressions like "expanding space". I think what was emphasized in that discussion was a general agreement that space is not to be thought of as a substance, like a rubber sheet. In standard cosmology what expands are distances.

If I remember right, it was around that time (a year or two back) that Chodorowski's name came up. Wallace made the mildly skeptical observation that C. had a somewhat patchy track-record of publication. I think C. is something of a maverick and tends to be ignored. I would be happy to be corrected on this by someone who knows more about it, but my first take on the July 2007 paper by Lewis, Francis, Barnes, and James (LFBJ) is that the Chodorowski fringe element was causing confusion by using invalid arguments to contradict accepted views, and so needed to be debunked. If so, then LFBJ are performing a useful and needed service.

I haven't time to check all the details of the story here, and would be grateful if someone who is more familiar with this would set me straight on anything or supply missing detail.

 

[dilletante]

We already had a discussion thread here at the forum about an earlier paper by the same authors which discusses the verbal confusion surrounding expressions like "expanding space". I think what was emphasized in that discussion was a general agreement that space is not to be thought of as a substance, like a rubber sheet. In standard cosmology what expands are distances.

Marcus,

I agree that the general consensus on this forum is that space does not expand, only distances. I remain unconvinced however, since the concept of space (or spacetime) expanding so simply explains superluminal recession velocities. Not to mention that some notable cosmologists seem to buy into the idea of expanding space. To quote Edward Harrison:

"The answer is that galaxies are not moving through space but are moving apart by the
expansion of intergalactic space...

...recession is a result of the expansion of space that obeys the rules of general
relativity, and is not like motion through space that obeys the rules of special relativity.

Those persons who find it difficult to understand that recession is without limit usually
make the mistake of thinking that the receding galaxies are like projectiles shooting away
through space. This is an incorrect view. The correct view is of galaxies more or less at
rest in expanding space."

Edward Harrison, "Cosmology The Science of the Universe", 2nd edition, 2000, page 282

Is Harrison misinformed, or has there been a breakthrough in understanding since he wrote this? He seems pretty darned clear about his view of expansion of space.

 

[marcus]

I think the irony of this thought experiment is that you could never coordinate it unless you possessed luperluminal communication, which is impossible. Think about it, you are using 0.9c alien spaceships, to space out 1000 'orbs' from Earth (0c out to 2.0c). How could you ever drop the 999th orb which is nearest the FFA 2.0c galaxy. Travelling at 0.9c you would constantly be chasing a faster car? Am I missing something here? I probably am.

lil bro,
there are a lot of problems with Jon's proposal. The one thing it doesn't lack is amusing fanciful detail. As a literary exercise it is entertaining.
But a lot of the detail is actually non-essential---it distracts the reader.

Coordinating things is really a side issue, a red-herring so to speak. Jon's setup doesn't need all those spaceships. It only needs one.
He specifies that all the spaceships shall be at rest with respect to the earth. Or all the released particles, if you prefer. Therefore the last spaceship, out near the galaxy, is (like all the others) at earthy rest----its distance from Earth is not increasing.

To see that Jon's setup is physically impossible to realize, all we need to consider is ONE spaceship or particle, which is out there at twice the Hubble distance close to a galaxy receding at 2c, and whose distance from Earth is not increasing.

The ship or particle is out there next to the galaxy.
The distance to the ship is not increasing
The distance to the galaxy is increasing at the rate 2c.

The absurdity becomes clearer, I think, if one gets rid of all the fanciful unnecessary detail and considers a simpler experiment.

At some time in the past, we have sent a message to a galaxy (which then was closer to us but is NOW at twice Hubble distance or about 27 billion LY and receding at speed 2c) asking them to launch a spacehip towards us at speed 2c.

That is what would be necessary, to achieve the key condition Jon requires. If they could do that, then the ship would have zero proper speed with respect to earth. (Zero proper speed relative Earth is what Jon is asking for.)

If you use the simplified, red, version of Jon's proposal, then as far as I can see it gets rid of the problems with coordination that you mentioned.

 

[marcus]

Marcus,

I agree that the general consensus on this forum is that space does not expand, ...

Heh heh. We are having more verbal confusion. I don't think you understand the state of consensus or non-consensus on this forum. Speaking for myself only, I never said "space does not expand"

I said there is verbal confusion around the phrase "expanding space".

My personal solution is simply don't think of space as a substance.

I think of space as a web of geometrical relationships, not as a material. In particular, space consists of distance relationships. We all agree that DISTANCES EXPAND.
So therefore, to my personal way of thinking space expands. That is how I picture it.

When I want to be extra clear in discussion with others, I am careful to say "distances expand".

All this verbal confusion goes away if you just look at the standard mathematical model---the Friedmann equations.

I think Wallace is the local expert on these issues, maybe he will say something pertinent.
From my viewpoint, I don't think I have any disagreement either with you or with the source you quote. Indeed space expands, and space is not a material but a web of distances. Spatial expansion means that largescale distances on average are expanding----around 1/140 of a percent every million years. Additional clarification can be had by considering the CMB rest frame, or Hubble flow, and restricting to objects widely enough separated that they aren't gravitationally bound up with each other.

Let me know if I haven't responded to what was bothering you. In the meantime let me reaffirm: Space expands! In most cases superluminally! Most objects are outside our Hubble sphere, so the distances to them are increasing faster than the speed of light.
And space is not a substance like rubber.

 

[jonmtkisco]

I would be happy to be corrected on this by someone who knows more about it, but my first take on the July 2007 paper by Lewis, Francis, Barnes, and James (LFBJ) is that the Chodorowski fringe element was causing confusion by using invalid arguments to contradict accepted views, and so needed to be debunked. If so, then LFBJ are performing a useful and needed service.

Marcus, I think it is unbecoming of "science advisors" on this forum to write casually dismissive insults about physicists who publish papers just because they test and challenge various aspects of the standard model. Since when did it become the mission of this forum to defend entrenched scientific orthodoxy from the voices of physicists who suggest possible reasons why it is not all cut and dried?

I have no doubt that Chodorowski is more accomplished professionally, smarter and more knowledgeable about physics and cosmology than any of the regular contributers to this forum. The paper you treat so disrespectfully was of course peer reviewed, and in particular was refereed by Tamara Davis of Davis & Lineweaver fame. Surely she wouldn't have agreed to do so if she believed him unqualified.

The Lewis & Francis paper describes Chodorowski's arguments as "forceful" because they respect his physics and math. They adopt approvingly the conformal coordinate calculations he used, and seem to agree with his intermediate conclusions. As far as I can see, their ONLY critisism is their argument that he failed to take into account a tricky clock difference as a final step in reaching his conclusion that recession is not superluminal in conformally flat coordinates.

Finally, although Lewis & Francis argue that expanding space remains a useful teaching tool, they do NOT come down firmly on the side of the argument that space is truly expanding. To wit, the paper's final conclusion:

From all of this, it should be clear that it is futile to ask the question “is space really expanding?”; the standard-FLRW metric and its conformal representation are the same spacetime. No experiment can be formulated to differentiate one personal choice of coordinates from another.

Jon

 

[jonmtkisco]

Hi Marcus,

At some time in the past, we have sent a message to a galaxy (which then was closer to us but is NOW at twice Hubble distance or about 27 billion LY and receding at speed 2c) asking them to launch a spaceship towards us at speed 2c.

I agree that my description of the deployment of the spaceships vastly understated the distances involved. When I wrote that part I was thinking about the speed each ship might need towards Earth rather than the distance from earth. The thought experiment probably is impossible to coordinate centrally as I described it, even with the finest alien technology.

But let's not throw the baby out with the bathwater. Obviously the answer to the GR question I asked is easier to measure at extremely long distances (if a practical means could be found to do so). The effect becomes very small at more manageable distances. Nevertheless, we can consider this problem on the premise that very advanced future technology will be able to measure these effects at distances which are far smaller than anything we can contemplate with current technology.

So rather than amusing ourselves plucking the feathers out of my scenario, why don't we try to think about the substance of the question I asked. Use the rigid ruler variation if you prefer, or come up with a scenario of your own. But let's not pretend that there is no math and physics available to answer my question, or that my question somehow is nonsensical, just because it's difficult to describe a practical measurement arrangement.

Jon