Universal Central Observer: Doubling Speed of Light Separation

[cdux]

If Galaxy A drifts apart from Galaxy B with twice the speed of light then how could a Galaxy C next to Galaxy A drift apart from Galaxy A at a similar speed?

edit: PS. Wouldn't that need some kind of "universal central observer" to limit Galaxy A from Galaxy C to not drift apart by more than 2*c?

 

[Drakkith]

Head over to the Cosmology subforum and read some of the FAQ's there. I believe one of them should answer your question. If not, look up the Balloon Analogy.

 

[cdux]

It's the same question for points on the balloon.

 

[Naty1]

Not as we currently calculate standard cosmological 'observations'. The 'drift' of two galaxies has nothing to do with the drift of either relative to another galaxy.Can objects move away from us faster than the speed of light?

Again, this is a question that depends on which of the many distance definitions one uses. However, if we assume that the distance of an object at time t is the distance from our position at time t to the object's position at time t measured by a set of observers moving with the expansion of the Universe, and all making their observations when they see the Universe as having age t, then the velocity (change in D per change in t) can definitely be larger than the speed of light. This is not a contradiction of special relativity because this distance is not the same as the spatial distance used in SR, and the age of the Universe is not the same as the time used in SR. In the special case of the empty Universe, where one can show the model in both special relativistic and cosmological coordinates, the velocity defined by change in cosmological distance per unit cosmic time is given by v = c ln(1+z), where z is the redshift, which clearly goes to infinity as the redshift goes to infinity, and is larger than c for z > 1.718. For the critical density Universe, this velocity is given by v = 2c[1-(1+z)-0.5] which is larger than c for z > 3 .

For the concordance model based on CMB data and the acceleration of the expansion measured using supernovae, a flat Universe with OmegaM = 0.27, the velocity is greater than c for z > 1.407.

http://www.astro.ucla.edu/~wright/cosmolog.htm

 

[Trenton]

One of the common omissions when people are learning about GR is the notion that space itself moves - and that the velocity of space is not limited to c. That limit only applies to entities traveling through space. The space around a dense object is falling into the object at the Newtonian escape velocity. This infall is due to the contraction of space due to the presense of the mass. As the space near the mass contracts more space comes into take it's place. Without this process, a black hole would never become 'black'.

The big bang is the inverse of this process and the space is expanding and this expansion is also not limited to c. It is quite possible for a line of objects all to be moving away from their adjacent objects faster than than c even if that means they can't observe them.

 

[Drakkith]

Does GR even describe space as "moving"?

 

[Trenton]

As I understand it yes. It is counter-intuative in the extreme but space and time are said to fall into a black hole. Likewise a spinning black hole drags time and space around with it. All of this would be nonsense unless space itself could move. Indeed if this were not part of GR then a black hole could never be black or indeed have an event horizon. A photon originating inside the EH would, if traveling away from the singularity, escape albeit with massive redshift - because light cannot be slowed and the EH is at a finite distance.

But the photon cannot escape because although it is moving outward at c, that is only relative to space. At the EH space is moving inwards at c and so the photon stays at the EH. Further in space is moving inwards at greater than c and this drags the photon back to the singularity.

 

[Drakkith]

I don't think that's how GR labels it. I don't have much experience with GR, but I believe the metric is just describing how space is curved, not that it moves at all. You can't have a frame relative to space, only relative to another object.

 

[arindamsinha]

I don't think that's how GR labels it. I don't have much experience with GR, but I believe the metric is just describing how space is curved, not that it moves at all. You can't have a frame relative to space, only relative to another object.

As far as faraway galaxies receding from us at c in all directions, I understand there is no "movement" of space, but "expansion" of space. It is the velocity of expansion of space that is not limited to c by GR. So perhaps this is a terminology issue.

 

[Drakkith]

As far as faraway galaxies receding from us at c in all directions, I understand there is no "movement" of space, but "expansion" of space. It is the velocity of expansion of space that is not limited to c by GR. So perhaps this is a terminology issue.

Yes, the popular explanation is that the galaxies are being dragged along with space. However I don't know how accurate that terminology is.

 

[Naty1]

Another explanation from a standard reference for these forums:

Are galaxies really moving away from us or is space just expanding?
This depends on how you measure things, or your choice of coordinates. In one view, the spatial positions of galaxies are changing, and this causes the redshift. In another view, the galaxies are at fixed coordinates, but the distance between fixed points increases with time, and this causes the redshift. General relativity explains how to transform from one view to the other, and the observable effects like the redshift are the same in both views. Part 3 of the tutorial shows space-time diagrams for the Universe drawn in both ways.

In the absence of the cosmological constant, an object released at rest with respect to us does not then fly away from us to join the Hubble flow. Instead, it falls toward us, and then joins the Hubble flow on the other side of the sky, as discussed by Davis, Lineweaver & Webb (2003, AJP, 71, 358). In what are arguably the most reasonable coordinates, the cosmic time t and the distance D(t) measured entirely at the cosmic time t, the acceleration is given by g = -GM(r<D)/D2 where M(r<D) is the mass contained within radius D. This gives g = -(4*pi/3)*G*(rho(t)+3P(t)/c2)*D(t). The 3P/c2 term is a general relativistic correction to the otherwise Newtonian dynamics. Galaxies all move under the influence of this acceleration and their initial position and velocity. In other words, F = ma and gravity provides the force. Nothing extra or weird is needed.

http://www.astro.ucla.edu/~wright/cosmology_faq.html#MX

 

[Naty1]

Here is an explanation of distance changes from phinds...this BALLOON ANALOGY
was developed among a dozen or so members of these forums in looooong thread.

www.phinds.com/balloonanalogy

FORTH: NO STRETCHING The surface of the balloon "stretches" and this leads to weird discussions of the "stretching" of space or the "expansion" of space. To further UN-simplify the balloon analogy, what you REALLY need to think of is the construct described in "THIRD" directly above, BUT ... take away the actual balloon material and just think of things happening to the pennies as though the balloon WAS there (so as to maintain the pennies' motion in the analogy). In other words, what cosmology REALLY says is not that space stretches or expands but rather just simply that gravitationally bound systems keep getting farther away from each other. It is DISTANCE that is changing, not space. This is another of those things that are badly served by the balloon analogy. There is of course, in some sense, "more" of something in between galactic clusters as the distance increases, but just what it is that there is "more" of gets to be a theological/philosophical discussion that gets WAY beyond the balloon analogy. I refer you to 'Metric Expansion of Space'

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

intro paragraph:

The metric expansion of space is the increase of the distance between two distant parts of the universe with time. It is an intrinsic expansion whereby the scale of space itself is changed. That is, a metric expansion is defined by an increase in distance between parts of the universe even without those parts "moving" anywhere. This is not the same as any usual concept of motion, or any kind of expansion of objects "outward" into other "preexisting" space, or any kind of explosion of matter which is commonly experienced on earth.

 

[Naty1]

Further in the metric expansion discussion in Wikipedia is this:

In expanding space, proper distances are dynamical quantities which change with time. An easy way to correct for this is to use comoving coordinates which remove this feature and allow for a characterization of the universe as a whole without having to characterize the physics associated with metric expansion. In comoving coordinates, the distances between all objects are fixed and the instantaneous dynamics of matter and light are determined by the normal physics of gravity and electromagnetic radiation. Any time-evolution however must be accounted for by taking into account the Hubble law expansion in the appropriate equations.

So a MAJOR concept in cosmology, based on the fact that distance/time, even energy, in GR have no global meaning, is that coordinates determine the result of your measure. The reason 'space expands' has become so popular is that HUBBLE utilized 'proper distance' in his v = HD relationship...This is the one where at the Hubble radius, we see distant objects receding at velocity c.

Here is a more precise explanation from someone in another discussion:

The so called 'physical' distance in cosmology doesn't have the status of invariance (independence of coordinate systems) like the line element ds^2 because the 'physical' distance is a coordinate quantity.

This reference is to curved spacetime in cosmology versus line element distance in flat space. distances in GR are different than in SR. In GR the distance you measure depends on the curve you choose...
edit: Different observes utilize different curves and get different measures.

 

[Naty1]

found it:
the ultimate discussion of expanding space in these forums:

https://www.physicsforums.com/showthread.php?t=162727&highlight=current+flow&page=2

It's long and confusing at times, but worth your time. Wallace who posts there
is a practicing cosmologist...

a few insights:

Locally, nothing moves faster than light. Even the most distant observers measure light at 'c' locally.
In introductory physics, "expansion", say of a heated rod, is measured relative to a practical invariant standard, say an invar. measuring tape in an instant of time.. In cosmology, "expansion", refers to something altogether more strange and unfamiliar to practical ordinary life: a change in a metric coefficient a(t) in the expression...

[In cosmology, we have to choose which 'invariant' to use as a basis for our calculations; having chosen, we can't observe them all! An implication of this is that 'increasing distances' are NOT well represented in the balloon analogy!]

I did not begin to understand such measurements until I studied these diagrams:
http://en.wikipedia.org/wiki/Metric..._two_points_measured_if_space_is_expanding.3F

Be sure to click on the illustrations to enlarge them...

 

[Naty1]

Does GR even describe space as "moving"?

As I understand it yes. It is counter-intuative in the extreme but space and time are said to fall into a black hole. Likewise a spinning black hole drags time and space around with it. All of this would be nonsense unless space itself could move.,,,,Indeed if this were not part of GR then a black hole could never be black or indeed have an event horizon. ...But the photon cannot escape because although it is moving outward at c, that is only relative to space. At the EH space is moving inwards at c and so the photon stays at the EH. Further in space is moving inwards at greater than c and this drags the photon back to the singularity.

Most of that reply is not correct.

While in a novice sense, some consider space itself as 'expanding' I don't think any scientist nor anyone in these forums would agree it 'moves'. That a spinning black hole' drags space and time' is a reference to frame dragging, not any motion. It's an effect our our artifical [theoretical] overlay frame. Read about it in Wikipedia and note the reference to linear frame dragging: do you also think a moving particle 'drags space and time with it?'...or is it curvature that changes??
http://en.wikipedia.org/wiki/Frame_draggingBlack hole characteristics do NOT involve 'space moving'. That is not part of SR, GR nor cosmological understanding. Any observed photon motion is relative to the observer! Space is NOT moving inwards at C at the event horizon. The only thing that moves at c at the horizon are PHOTONS. Inside the horizon, space is NOT moving towards the singularity at c! What prevents a photon from escaping is gravitational spacetime curvature.

Check this:

In Fabric of the Cosmos, Brian Greene says in a footnote (Chapter 12, #7,Page 527)

"...It's somewhat of misnomer to speak of the "center" of a black hole as if it were a place in space...Just as you can't resist going from one second to the next in time, you can't resist being pulled to the black holes "center" once you've crossed the event horizon...Thus rather than thinking of the black holes center as a location in space it is better to think of it as a location in time...it may be true that its ...where spacetime comes to an end...if we had equations that don't break down deep inside a black hole we might gain important insights into the nature of time..."An observer freely falling from a distance outside a black hole [or a particle], never exceeds c and is in fact unaware when she passes the event horizon: nothing happens there except that in passing, the observer loses causal connection with the outside universe. And from a distant observer's perspective, 'time stops' at the horizon so the infalling local observer APPEARS to hang there forever...to future infinity. But that, too, is a coordinate effect, NOT a physical one.

JesseM explained elsewhere:

Keep in mind that there's no coordinate-independent way to define the amount of time dilation for a clock at various distances from the horizon--what we're talking about is the rate a clock is ticking relative to coordinate time, so even if that rate approaches zero in Schwarzschild coordinates which are the most common ones to use for a nonrotating black hole, in a different coordinate system like Kruskal-Szekeres coordinates it wouldn't approach zero at the horizon at all.

Once again, different COORDINATES change everything!So the basic rule to remember is that in GR, curved spacetime, distance, velocity,acceleration and even energy are ill defined. Different [coordinate] observers 'see' [predict] different things...even at different times [non simultaneity] and these effects are magnified in cosmology because of the vast expanses we try to describe.

Hope all this helps...it sure took me several years to digest what little I know.

 

[Naty1]

I believe the metric is just describing how space is curved, not that it moves at all..

This is basically correct. The metric provides one aspect of curvature...and is a distance measure, the metric is a distance measure in curved spacetime. Here are some conventions associated with it which I posted in another discussion trying to develop a summary explanation of why its not like a simple ruler:

The FLRW metric [distance measure] is an exact solution to the EFE but only approximates our universe because it assumes the universe is homogeneous and isotropic;
how you measure things, your choice of coordinates, the model chosen, all affect your answers. Since FLRW is the 'standard [cosmological] model', listing a few conventions within the model to illustrate its UNIQUE characteristics could be helpful: being at rest with respect to Hubble flow is what defines the universal cosmological time parameter utilized; Superluminal velocities at great distances are are result of the FLRW model metric , those FLRW distances ARE great circles and space geodesics on the balloon model especially when you think of the balloon surface as a time of radius ‘r’ [approximating a constant, fixed cosmological time, the FLRW metric starts after the initial inflationary epoch; the LCDM is a 'fine-tuned version' of the general FLRW model where the parameters are chosen to get the best possible fit to our universe, the most common distance measure, comoving distance defines the chosen connecting curve to be a curve of constant cosmological time; operationally, comoving distances cannot be directly measured by a single earth-bound observer, etc,etc.

 

[Drakkith]

Thanks Naty!

 

[Trenton]

Whoever mention terminology has the key point. Katy1 states that I am incorrect and that space does not move. Curvature of space is the explanation. I have never been truly happy with either concept but for me space moving is the lesser of two evils. The presence of a mass does cause space around the mass to contract so that a given coordinate would move toward the mass would it not? And how can frame dragging occur without space moving? If sapce is not falling into a black hole can someone give a good description of what curved space might mean in geometric terms to put me out of my misery!

I am intruiged that the singularity is located in time rather than position and that the laws of physics break down. The equations break down because a term is missing. Singularity is a math term and a true physical singularity with one or more meaningful values being infinite cannot exist. There are quantum mechanical limits that we have yet to understand and only when we do can we complete the equations!

As for the 'singularity' (for want of a better term) not being at the center, why not? It is accepted that once a body (neutron star) has a radius equal to the EH it must collapse - no matter how much pressure nutonium could withstand. The reason why is that for the star not to collase matter must remain at the EH and this (with the space infalling at the escape velocity which is c) would require the matter to be traveling through space at c. But whatever causes the collapse, collapse of a spherical object means the matter all moves inward. And unless someone cares to redefine geometry all matter moving inwards means everything is going to end up in the center!

 

[Naty1]

Hi Trenton: I provided a number of reputable sources to help you better communicate in these forums. You ARE free to maintain 'space moves' but I'll not be responding again as you repeat this. And it will hamper your communication and further understanding.

for me space moving is the lesser of two evils. The presence of a mass does cause space around the mass to contract so that a given coordinate would move toward the mass would it not? And how can frame dragging occur without space moving? If sapce is not falling into a black hole can someone give a good description of what curved space might mean in geometric terms to put me out of my misery!

I explained 'frame dragging' is NOT dependent on 'space moving' any more than is linear frame dragging. I hope you read the sources so you at least understand mainstream insights from people with a lot more experience and understanding than I.

We all have some misery! Curved space and TIME is not something we can visualize.

Curved spacetime IS the geometric explanation of gravity. For a large black hole, most of the curvature, that is the distortion of spacetime, is time not space. The tidal gravity outside such a large black hole horizon is small while the time dilation is unbounded as seen from afar..time APPEARS to diverge but does not locally.

Perhaps you could consider time versus space. Perhaps thinking about special relativity might help? Consider time dilation and length contraction, distortions of time and space in flat spacetime...no tidal gravity. Does space have to move there for you too?? I am not looking for you to defend, just asking you THINK about it. If no movement is necessary in SR, why in GR??

And except for a negative sign in relativity, space and time are treated alike. Why do you like space moving but not time? Shouldn't you treat them on an equal footing. Time curves too! good luck.

 

[Trenton]

I shall certainly read further material as I am keen to get to the bottom of these terms. I am not encouraged by your statement that curved space and time is not something we can visualize. The whole ojective for me is to envisage what happens to space and time in the vacinity of mass - which I continue to believe is possible. After all einstein came up with a set of equations to describe these things and I don't see how he could have done this without a very clear idea of what he though was going on.

I am very happy with the SR concepts of the lorentz contraction applied both to time and to space. And I am very happy with the GR concept that gravity is the result of mass 'curving' spacetime for want of a better word. It is for me, a far more intuative explanation of gravity than gravitons.

And I do not like the idea of space moving either although I should have made clear that it is both space and time (Minkowsky spacetime) that was moving! It is a slick way of arriving at results and certainly, the time dilation at a stationary point in a gravitational well (eg a man stading on the Earth's surface) is the same value as for an object moving through space at the escape velocity at the staionary point - but this is all it is, a slick trick (unless space does move). I also take your point that since movement of space is nessesary in SR it should not be nessesary in GR. The trouble is I have never come across a decent explanation of the term curvature.

 

[cdux]

I am not encouraged by your statement that curved space and time is not something we can visualize.

If I'm not mistaken even your favorite GR visualization of spacetime curvature is an approximation that does not fully describe the mathematics, and it reminds me of physicists admitting they don't understand quantum mechanics beyond their understanding of the math. My basic understanding of the concept of visualization in sciences in general is that if something goes beyond the 4 dimensions in the "middle-cosm" has to be understood via math or via crude approximations on those 4 (uncurved) dimensions. I've been hearing of visualizations of the type of multidimentional manifolds and the more I think of it the more it seems unfathmable and the more I suspect it's wishful thinking for full 4 dimensional understanding. In fact, some popular notions sound almost embarrassing, such as the popularized notion that extra dimensions in string theory are "small dimensions like looking at an ant on a flag pole but then zooming in on it". What does that even mean? If my vision is good I may not have to zoom into notice the extra dimensions. Notions such as that look at the end of the day non-sensical or at best crude approximations.