Apparent superluminal velocity of galaxies

[scimeister]

I just posted about what is termed "apparent superluminal velocity of galaxies" and gave a website of an article written by Prof-Dr. L. Schatzer, which was said to be not "main stream". My posting was moved because it contained this website that was not considered " main stream" and no discussion was ever developed. Is there any thought about this topic dealing with the possibility of distance galaxies traveling faster than light or "main stream" websites discussing this ideas? Having been an instructor of physics for over forty years, this topic always seems to surface in one form or another.
Thanks,
Doc

 

[pervect]

I'd like to keep this thread here in the GR forum, but avoid ANY discussion of other websites, personalities, etc, and stick strictly to the GR relevant issues.

There have been quite a few papers written about the apparent superluminal velocity of galaxies. One of the papers that explains many of the common misconceptions is the Lineweaver & Davis paper:

http://arxiv.org/abs/astro-ph/0310808

You can check out it's publication history at http://publish.csiro.au/paper/AS03040.htm

to see where it was originally published. (Publications of the Astronomical Society of Australia 21(1) 97 - 109 ).

While the Lineweaver and Davis paper is pretty good, there are a few points that one might wish it did make which it does not make. The first point is that there is no truly general, coordinate independent notion of the relative velocity of two distant objects in GR, including distant galaxies.

For a reference for this point, see http://math.ucr.edu/home/baez/einstein/node2.html

publication history at:
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000073000007000644000001&idtype=cvips&gifs=yes
( American Journal of Physics -- July 2005 -- Volume 73, Issue 7, pp. 644-652)

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.

Thus while cosmologists have a standardized and well-defined meaning for the 'velocity of distant galaxies", their definition is coordinate dependent, and they frequently don't point this fact out. A related point is that the cosmologists standard definitions, while standard in the field, aren't very SR friendly.

For some related points see http://www.astro.ucla.edu/~wright/cosmology_faq.html#FTL

(Which is not peer reviewed in and of itself as far as I know, though Ned Wright is a recognized authority and the author of many peer reviewed papers).

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 .

Ned Wright is much more "up front" about the issue of "many distances", a point which is sometimes unfortunately glossed over.

 

[Ich]

I don't know exactly what you mean, but besides pervect's explanations concerning the meaning of distance in GR, there are simpler "apparent superluminal velocities" that arise when an object (eg a jet) approaches the observer with near light speed. Google brings up some useful links.

 

[Voltage]

Thanks for that pervect.

 

[Wallace]

I'm in the process of writing a couple of papers on this very topic (and related ones) at present. One is awaiting the referee the other is in preparation. I'll post the ArXiv links once they have been finalised.

 

[marcus]

I'm in the process of writing a couple of papers on this very topic (and related ones) at present...

That's welcome news! I am looking forward to seeing them.

 

[Bose]

I just posted about what is termed "apparent superluminal velocity of galaxies" and gave a website of an article written by Prof-Dr. L. Schatzer, which was said to be not "main stream". My posting was moved because it contained this website that was not considered " main stream" and no discussion was ever developed. Is there any thought about this topic dealing with the possibility of distance galaxies traveling faster than light or "main stream" websites discussing this ideas? Having been an instructor of physics for over forty years, this topic always seems to surface in one form or another.
Thanks,
Doc

What is actually happening is that the metric of spacetime between us and the galaxies has changed (the universe has expanded) along the path of the photon from here to there, leading to an increase in the wavelength of the light. As an example of how you can go wrong, naive application of the Doppler formula to the redshift of galaxies implies that some of them are receding faster than light, in apparent contradiction with relativity. The resolution of this apparent paradox is simply that the very notion of their recession should not be taken literally.

 

[Haelfix]

The usual explanation is purely classical, and the Ned Wright FAQ page does a good job explaining it.

Its extremely rare to see a full GR treatment of it (b/c of the coordinate complexities) but it has been done before.

 

[Chaos' lil bro Order]

Pervect gives a very nice answer.

To summarize what is being said. NO OBJECT can itself move with a velocity greater than C. But SPACE CAN expand at a velocity greater than C. So if you think of galaxies as fixed onto the substrate of space, when space expands at velocities greater than C, the galaxies go along for the ride. As Pervect pointed out, any two galaxies separated by a redshift of greater than z =~1.7, their co-moving velocities with respect to one another exceeds C. It is important to note that Relativity, both special and general, set a fundamental limit on particles, not the substrate of space itself. That is where the general confusion arises in physics, as this is often not properly stated.

 

[Bose]

Pervect gives a very nice answer.

To summarize what is being said. NO OBJECT can itself move with a velocity greater than C. But SPACE CAN expand at a velocity greater than C. So if you think of galaxies as fixed onto the substrate of space, when space expands at velocities greater than C, the galaxies go along for the ride. As Pervect pointed out, any two galaxies separated by a redshift of greater than z =~1.7, their co-moving velocities with respect to one another exceeds C. It is important to note that Relativity, both special and general, set a fundamental limit on particles, not the substrate of space itself. That is where the general confusion arises in physics, as this is often not properly stated.

It's similar to the situation gravitational wave pass two pendulum, the distance between them would change but the pendulum do not move per se

 

[dude222]

this is because the speed of light is not constant

Notice in the Lorentz factor, what is important is v/c (the speed normalized by the speed of light). When doing calculations of momentum and energy changes you work with normalized speeds. Take the twin parodox. To resolve it, 2 things are required:
1) That the frequencies seen by the accelerating twin as it encounters photons emitted from sources are the same as those which a nonaccelerating observer sees it encounter.
2) That a consistent interpretation is given for how the accelerating twin experiences the world.
This can be accomplished by assuming the speed of light changes with distance from the accelerating twin (according to the accelerating twin). Note that since velocities are normalized by the speed of light at the location where any interaction occurs, the formulas for energy and momentum exchange work out the same as for the nonaccelerating observer, so these interactions are consistent. The local speed of light at the location is derived to be compatible with condition 1). This way of viewing the world assumes Euclidian geometry. The usual explanation involves curved geometry, which is difficult to explain. If talking in terms of Euclidian Geometry, these galaxies exist in regions with a higher speed of light.

 

[RandallB]

Notice in the Lorentz factor, what is important is v/c (the speed normalized by the speed of light). When doing calculations of momentum and energy changes you work with normalized speeds.

Take the twin parodox. To resolve it, 2 things are required:
1) That the frequencies seen by the accelerating twin as it encounters photons emitted from sources are the same as those which a nonaccelerating observer sees it encounter.
2) That a consistent interpretation is given for how the accelerating twin experiences the world.

This can be accomplished by assuming the speed of light changes with distance from the accelerating twin (according to the accelerating twin). Note that since velocities are normalized by the speed of light at the location where any interaction occurs, the formulas for energy and momentum exchange work out the same as for the nonaccelerating observer, so these interactions are consistent. The local speed of light at the location is derived to be compatible with condition 1). This way of viewing the world assumes Euclidian geometry. The usual explanation involves curved geometry, which is difficult to explain. If talking in terms of Euclidian Geometry, these galaxies exist in regions with a higher speed of light.

First there is no “accelerating twin” or “nonaccelerating observer” in the twin paradox only reference frames moving at different speeds WRT each other.
One frame may be considered “stationary” with an observer, with another second frame “moving” with a traveler. Even if a third frame is used to allow the traveler to transfer to it in order to return to the observer location in SR that is only a TRANSFER to another reference frame which must be done instantly, and CANNOT be used as an acceleration. If you are using acceleration or gravity you are not referring to the twin paradox which only needs and uses SR.

As for light changing speed with distance it should be obvious that it does not need to change speed in order for light in another Galaxy to have a different speed relative to light in our galaxy.
Clearly if Hubble Expansion of space is to add space and distance between us and distant galaxies such that they appear to recede at a superluminal velocity, then obviously the speed of light there relative to our measure here would not be “c”. But that has nothing to do with light changing speeds and everything to do with Hubble expansion.

If your intent is to refute Hubble expansion, I do not think the Twin Paradox or a variable “c” is the tool to use.