Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bill S on 11/04/2011 18:51:31
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When I first met the idea that light from an object that was moving away from us at superluminal speed would never reach us, it seemed quite reasonable. However, I seem to have developed a problem arising from the fact that light must always be observed as travelling at c, irrespective of any relative movement between emitter and receiver. It goes something like this.
A distant object is moving away, relative to Earth, at superluminal speed. At a given point (say 15 billion l y away, which we will call “point A”) it emits a photon. This photon should reach Earth 15 billion years later.
Assume the emitting object is receding (relative to Earth) at 1.5c. One year later it is at point B, which is 16.5 l y from Earth. There it emits another photon, which should reach Earth after 16.5 years; ie, 1.5 years after the arrival of the photon emitted at point A.
Whatever the speed of recession of the emitting object, any light emitted must, from the viewpoint of Earth, be approaching Earth at c, so it must eventually arrive.
I accept that there must be something wrong with this reasoning, but at the moment I can’t see what it is.
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Assume the emitting object is receding (relative to Earth) at 1.5c.
1.5c? This would be due to the expansion of the universe all along the route between the object and earth rather than it's movement.
The light approaches the earth at c, but it has further to go due to the expansion of the universe.
It will never reach earth.
"While special relativity constrains objects in the universe from moving faster than the speed of light with respect to each other, there is no such theoretical constraint when space itself is expanding. It is thus possible for two very distant objects to be moving away from each other at a speed greater than the speed of light (meaning that one cannot be observed from the other). The size of the observable universe could thus be smaller than the entire universe."
from http://en.wikipedia.org/wiki/Universe_expansion (http://en.wikipedia.org/wiki/Universe_expansion)
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Thanks JML. I had been thinking about the fact that the expansion was due to the increase in the intervening space, and therefore that light had more distance to cover, but I was still stuck on the necessity for an observer on Earth to measure the light as approaching at c, not c - the rate of increase. The only reason I can find why the distant object would not eventually become visible would be if the light had been red shifted away "to nothing". That's not the technical term, but you know what I mean. [:P]
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Imagine that you are on a raft in an infinitely long canal with cross section of 10 m x 10 m. A fish is swimming at a constant speed of 1 m/s. If the fish starts 100 km away from you, it will take 100,000 seconds to reach you. Now suppose you have a water faucet every meter pouring .001 m³/s into the canal. 100,000 faucets pour in enough water to produce a current of 1 m/s. So, if the fish starts 100 km away, it will never get any closer to you.
The speed of light is constant relative to comoving space. That doesn't mean the rate of change of its distance changes at that rate. You need to understand what comoving space is. It is defined by an expanding grid; as space expands new grid lines are added. Suppose you have a measuring chain whose links do not expand. For every 4 x 10^17 links, you have to add one new link every second; otherwise, the expanding space will stretch the individual links and perhaps snap the chain (if it is really long). Each link is stationary relative to comoving space, but the distance between ends of the chain is increasing. The distance is defined as the fixed length of each link times the number of links between two points.
There is a different kind of space (not used by most cosmologists) defined by ideal unstretchable massless measuring tapes which are stationary at the origin of the coordinate system. Consider such a tape extending 4 x 10^23 meters in both directions from the origin. Its ends will be moving 10^6 m/s and accelerating at a rate of 2.5 x 10-12 m/s², relative to comoving space. The acceleration of the tape is real; if it had mass, it would be in tension. The expansion of space, in this type of coordinate system, is equivalent to a parabolic gravity hill centered on the origin. If your tape is much longer than 10^23 meters, you will have to apply the formulas of relativity to determing the motions of its ends relative to comoving space.
Relativity does not apply to the changing distance in comoving coordinates. It is described as "apparent velocity", and not a real velocity.
The different kinds of space are just mathematical analogies to actual physical space.
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MoHei Bill. :)
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Why might light from distant galaxies not reach us?
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My thought is simple,,i think that why we cannot see all objects is that
- when object send something this something has speed/distance curve and object cannot send something to travell endless to space, example light or radiowave
- that is the reason why we see dark space between objects
I think so,,i made image on my idea.
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Other question comes to my mind.
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Related topic ...
"dark night sky paradox." The paradox states that at any angle from the Earth the sight line will end at the surface of a star, so the night sky should be completely white.
http://en.wikipedia.org/wiki/Olbers%27_paradox
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A fish is swimming at a constant speed of 1 m/s. If the fish starts 100 km away from you, it will take 100,000 seconds to reach you. Now suppose you have a water faucet every meter pouring .001 m³/s into the canal. 100,000 faucets pour in enough water to produce a current of 1 m/s. So, if the fish starts 100 km away, it will never get any closer to you.
True, but relativity does not require that you perceive the fish approaching you at 1 m/s, in spite of the current. Would I not be right in thinking that you must see light as approaching you at c, in spite of the expansion of the Universe?
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The speed of light is constant relative to comoving space.
No problem with this, but is it not also constant relative to objects moving in comoving space?
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Very nice explanation Phractality. And yes Bill, you're perfectly correct as I understands it. If light at some 'point' as measured by us would 'spontaneously' slow down in a vacuum Relativity would be out on a thin limb. The idea of lights constant unvarying speed in a vacuum is one of the cornerstones for Relativity as I see it.
So light has to propagate at 'c', no matter (pun ignored:) what happens to that space it is expected to 'propagate' in. As a wave that is explained by red and blueshift, in this case a redshift, but you could also assume a photon propagating, and there my headache starts :)
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And, looking at your other thought, the comoving part should then, as I see it, be expressed in that red/blue shift relative the observer. But depending on how you imagine a possible expansion there are at least two ways to see it. Either as expanded in every point, and now you only need to ponder what such might do to the geometry of a wave, or as 'expanding' only in the 'direction of a waves motion' which seems to be the definition normally used (naively comparing it here)
If it is doing so (space expanding) how the he* does it work?
Does it ignore two dimensions, expanding in one and only relative the objects 'motion/propagation'?
Think about it :) it's like opening a nest of snakes to me.
As I look at a 'expansion' as coming to be 'instantly' in glorious 3D and in every point of space (between galaxies) I find it unnerving to consider the other possibility. Both as it then assume 'one dimension', of those three defining a 'space' (length width and height), to be able to grow ignoring the other two and as it seem to assume that it also must be related to the observer/detector, in this case our 'propagating wave/photons'.
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Logically it is rather easy to show the futility of that 'common' idea of a expansion. You just need to consider that if you turn you head you will see the other end of the universe. and the redshift will be there too, so red shift as such is definitely related to the observer. But if you now teleport to the moon I'm sure you will find the same redshift, coming at you from all directions as you did on Earth, so assuming both statements being true simultaneously, the idea of 'space' only 'expanding in one direction, and furthermore being related to the observer, must be wrong. Here I'm still imagining those waves as the real 'observers', as that is the relation they have before hitting your retina (relative that possible expansion/space), a 'red-shift', no matter from what position you observe it.
Although, I do have a NOT main-stream way of handling it in my 'room time geometries', allowing every 'SpaceTime' a unique existence, with radiation connecting us all into a 'common experience'. That as you from such a perspective (unique room time geometries) might assume that we all are our own 'center' of 'SpaceTime, and so also making it possible for me to ignore the question of how 'space' expands, point-like, growing like a sphere maybe? Or, in just one dimension following the objects 'motion' relative some coordinate system. And as all coordinate systems in fact are artificial, arbitrarily made, relative some common agreement?
That it may work from my point of view is because it doesn't matter in such a universe, as I see it. You can have it both ways and see the exact same thing, I think? I need to ponder that one for a while. It's a weird one :)
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There are some other possibilities too. In the Wheeler–Feynman absorber theory light goes both ways as I understands it, in its interacting with you. Sort of running both forward and backward in time simultaneously in its interaction, and only as defined by your eye observing it. Then you might alternatively assume that a light quanta/wave (any object observable in fact) have some mystical coherence, hindering it from expanding in that possibly 'point-like' 3D expansion I described. Maybe there are more ways to see it too?
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True, but relativity does not require that you perceive the fish approaching you at 1 m/s, in spite of the current. Would I not be right in thinking that you must see light as approaching you at c, in spite of the expansion of the Universe?
The fish would pass rafts along the way at 1 m/s as seen by observers on each raft. In the comoving coordinate system, that is the velocity of the fish for all observers. But the rate of change of the distance from you to the fish would be 1 m/s less the rate of expansion times the distance. It's the way velocity is defined in comoving coordinates. Radial velocity is not equal to the rate of changing radial distance.
In that other kind of space that I mentioned earlier (with non-expanding ideal measuring tapes centered on the origin) radial velocity IS the rate of changing radial distance. But that system is not popular among cosmologists. There is considerable bigotry among cosmologists who believe their favorite kind of space is true, and all others are false.
Another difference between the two kinds of space is this: The rate of expansion seems to be accelerating slightly, but just suppose it is constant in comoving coordinates. If that were so, then in non-expanding coordinates, the rate of expansion of space would be much slower at greater distances. That is because of time dilation. In non-expanding coordinates, the radial velocity is real, so relativity is applicable to it. Clocks moving away from the observer actually run slower (not just slowed by the redshif), so the rate of expansion must be slower, as well. But distant clocks do not run slower in comoving coordinates, so the rate of expansion is approximately constant. (I assume all this was taken into consideration before they concluded that the rate of expansion is actually increasing.)
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Pharacticality?
This comoving system you are discussing, it's relative the Hubble expansion right? I had to look it up as I reread you. In that sort of coordinate system there is no expansion at all relative the observer, as he moves with it, if I got it right (this time:) and as the Hubble constant is approximately about 71 kps/Mpc (kilometers per second, per mega parsec) it doubles for every mega parsec you 'look out' as I understands it?
So the observer in such a coordinate system should then be at rest with this Hubble constant? And so observe a isotropic universe without a 'expansion' and redshift, as I understands it? I will blame it on my English I think, I thought of comoving as frames measuring frames, not as being at rest. Ahem.
But I don't see how to apply it to the reality of a (possibly) expanding universe, as it does it in all directions possible, as measured from any observer? To be 'at rest' in such a system you too would need to 'expand' constantly, and in all directions simultaneously?
Or am I reading it wrongly?
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I prefer to express the Hubble constant in SI units; H₀ ≈ 2.5 x 10^-18/s. That works out to doubling distances in about 9 billion years, and volumes double in about 3 billion years. Comoving objects at a distance of 10^18 meters, move apart at about 2.5 m/s; at 10^24 meters, they move apart at about 2.5 x 10^6 m/s. But the velocity of any two comoving objects relative to one another, in the comoving coordinate system, is zero m/s. That's just the way velocity is defined in the comoving coordinate system.
This comoving system you are discussing, it's relative the Hubble expansion right?
Actually, it is relative to any set of comoving objects. Two objects are comoving if the distance between them is increasing at the rate of the Hubble expansion times the distance. Distant clusters of galaxies are approximately comoving, but there is proper motion within clusters. If there is an ether, and the ether expands at the rate of the Hubble expansion, then objects that are stationary relative to the ether are comoving relative to each other.
So the observer in such a coordinate system should then be at rest with this Hubble constant? And so observe a isotropic universe without a 'expansion' and redshift, as I understands it?
No. The distance between two comoving objects is increasing, but they both have zero velocity relative to coordinate system. The velocity of two objects relative to one another is defined as the vector difference of their velocities relative to the coordinate system; so they have zero velocity relative to one another, even though the distance between them is increasing.
Light is moving directly toward the observer at velocity, c, relative to the comoving coordinates; and the observer's velocity relative to the comoving coordinates is zero. So the light is moving directly toward the observer at velocity, c, even though the distance may be decreasing at a small fraction of c.
But I don't see how to apply it to the reality of a (possibly) expanding universe, as it does it in all directions possible, as measured from any observer? To be 'at rest' in such a system you too would need to 'expand' constantly, and in all directions simultaneously?
The space you occupy is expanding, but you are not. If meter sticks expanded at the same rate as space, we would not observe any expansion. Light years do not expand because meters and seconds are defined in terms of the speed of light. If you had a 3D grid made of interconnected comoving chain links, you would have to keep adding new links to keep them from snapping. The proportional rate of adding new links is independent of the length of each link; it's the same for nano-meters or Giga-lightyears. For every 4 x 10^17 links, you have to add one new link every second (in one dimension). In 3D, you have to add 3 times that many new cubes per second.
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I wasn't thinking of matter as such there, more as an 'ethereal observer' at any point in the expanse between galaxies. And I went from the definition I understood comoving systems to have reading about it.
"While general relativity allows one to formulate the laws of physics using arbitrary coordinates, some coordinate choices are more natural (e.g. they are easier to work with). Comoving coordinates are an example of such a natural coordinate choice. They assign constant spatial coordinate values to observers who perceive the universe as isotropic. Such observers are called "comoving" observers because they move along with the Hubble flow.
A comoving observer is the only observer that will perceive the universe, including the cosmic microwave background radiation, to be isotropic. Non-comoving observers will see regions of the sky systematically blue-shifted or red-shifted. Thus isotropy, particularly isotropy of the cosmic microwave background radiation, defines a special local frame of reference called the comoving frame. The velocity of an observer relative to the local comoving frame is called the peculiar velocity of the observer.
Most large lumps of matter, such as galaxies, are nearly comoving, i.e., their peculiar velocities (due to gravitational attraction) are low.
The comoving time coordinate is the elapsed time since the Big Bang according to a clock of a comoving observer and is a measure of cosmological time. The comoving spatial coordinates tell us where an event occurs while cosmological time tells us when an event occurs. Together, they form a complete coordinate system, giving us both the location and time of an event."
And that's why I couldn't put it in 'practice' thinking of it. Could I assume that it is a way to negate the expansion mathematically? "Two objects are comoving if the distance between them is increasing at the rate of the Hubble expansion times the distance." That one makes perfect sense to me if I assume that.
This one was a little harder :)
"The velocity of two objects relative to one another is defined as the vector difference of their velocities relative to the coordinate system;"
A vector is a direction and a magnitude(speed) right? Then you write "so they have zero velocity relative to one another, even though the distance between them is increasing." Can I assume that to mean, if I now get it right, to mean that if there is no vector difference found/measured between them, they can be described as comoving? Which I then translate to having the same speed and direction, ignoring expansion?
I think I will have to read this after sleeping actually :), it's a different approach to SpaceTime than what I'm used too. It's not that you are unclear, blame it on my thickheadedness :)
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Yor_on,
You seem to be getting it. But comoving coordinates don't negate the expansion, they merely make it isotropic. They do, however, redefine "velocity" so that the velocity associated with the expansion IS negated. The velocity of one object relative to another in comoving coordinates is the difference of their peculiar velocities. This is the velocity to which relativity applies, so there is no length contraction and time dilation associated with the expansion.
The CMB is probably the best choice of comoving system for cosmological purposes. I suspect that reference frame is the reference frame of the ether (but until "quantum teleportation" is proven to be faster than light, the ether remains irrelevant.) For "practical" matters, you might do better to pick a set of three galaxies in the local group which are comoving with the Milky Way Galaxy.
Non-expanding coordinate systems are still valid, but we must be careful not to mix systems, and always be clear which type of space we are talking about. Most people who are new to cosmology have never heard of comoving coordinates. They are still thinking in non-expanding coordinates when they challenge theories that are valid only in comoving coordinates. I speak from personal experience; been there, done that. The problem is not helped by cosmologists who claim that comoving space is the only space; that's just bigotry.
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Yes, I believe I can see somewhat what you're getting at Practicality. I haven't really thought of space that way. It's a intriguing mathematical definition that I will have to look into.
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and always be clear which type of space we are talking about
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Same thought,,there is so many so called proved information that those who dont have thinking this stuff can start to think something which is not space-natural proved thing or proved/non-proved theory, or many dont understand that we cannot known everything, that is also pure nature fact. Also we cannot denied or proved something which is not existing thing. Our mathematics and words are all image of this existing space, this life what we live.
My thought is that;
- we humans are one point of big space and/can observe small area round of that point and must realize few things
-- observe area / whole size
-- observe time / time calculation
-- we look inside that space in the space, in that area
What happend small area dont means automatically that this happend is start or basic of whole area
Also must remember that space is existing thing,,
we exist all individual living naturation,,,
even we dont know how space is born or what is purpose of space or life,,
or do space have lifetime or is it endless.
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Thanks, folks.
This is going to need a lot of thought, and several re-readings!