what we see

[michel123456]

O.K. now that we have find a common ground we can start entering the really weird things.

 

In this diagram, each little triangle represent an event.

 

2 triangles next to each other horizontally are not only different events but also 2 different objects. So, horizontally, along the space dimension, 2 triangles are different events corresponding to 2 different objects.

 

Vertically, along the time dimension, we assume that things are different: 2 triangles belonging to the same world line represent 2 different events corresponding to the same object.

 

So there is a clear difference between the horizontal properties (space) and the vertical properties (time)

 

Why?

 

Question: do we have any indication that the small triangles upon a same world line are the same object at different time coordinates? Or, to put it otherwise, could it be possible that the triangles upon a single world line are different objects?

Edited November 17, 2011 by michel123456

[md65536]

That makes the diagram pretty empty isn't it?

I'm having trouble understanding how the WMAP diagram and a 2D diagram of what's observable fit together.

 

Is the WMAP image a representation of the entire universe (of which we don't know the size, right?), or just the observable universe?

What I think is that it is not meant to be either, but rather just a diagram of history, or the history of distance, where the bell-shaped curve is the distance between two completely arbitrary astronomical spatial coordinates???

 

Yes, the diagram is pretty empty, because it's a 2D image of a 4D representation of the universe.

The galaxies and junk in the image are shown at one moment in time... but these don't exist only for a moment of time! Every object in the diagram could be "extruded" along the time dimension to show its history. Every bright object would have a "birth" along the time axis where presumably it formed from less luminous materials, and each would eventually have a "death" where it exploded or evolved into other things.

 

So, everything that's in this diagram can be traced back through time to an earlier part of the diagram. None of the objects that you show outside the light cone should have come from an earlier part of the universe that was outside the light cone. That is, something that's 15 billion LY away and unobservable to us right now, was something else in the past, say 13 billion years ago when it was 13 billion LY away from us and thus visible to us at the moment.* Your "empty diagram" suggests that visible things are blinking in and out of existence, instead of existing for long periods of time and only being observed in single instants.

 

Presumably, the objects on the diagram are placed "illustratively" roughly in the era that they existed as shown. I assume they'd want to be shown in formative parts of their lifetimes, rather than arbitrary times in their lifetime. But all the material that's shown in the diagram exists for the entire length of time in the diagram, in different forms as stars form and explode and reform into new stars etc.

 

 

Smear the diagram horizontally from CMB to WMAP and vice versa, and even though it still only shows a handful of the hundreds of billions of observable galaxies, the diagram will become pretty full.

 

 

 

 

* Note: I have a feeling this statement is wrong, due to my feeble understanding of inflation. A correction from someone who knows GR would be appreciated. Inflation must involve updates to simultaneity?? -- Due to inflation, an event may have been say only 12 B LY away, 13 B years ago local time, and be visible now 13 B LY away, right???

Edited November 18, 2011 by md65536

[Iggy]

O.K. now that we have find a common ground we can start entering the really weird things.

How'd I know you were gonna say that?

 

In this diagram, each little triangle represent an event.

or the local light cone of an event, ok.

 

2 triangles next to each other horizontally are not only different events but also 2 different objects.

Yes.

 

So, horizontally, along the space dimension, 2 triangles are different events corresponding to 2 different objects.

yes, corresponding. The world lines are the collection of events in the history of the objects. Different world lines, different objects.

 

Vertically, along the time dimension, we assume that things are different: 2 triangles belonging to the same world line represent 2 different events corresponding to the same object.

right

 

So there is a clear difference between the horizontal properties (space) and the vertical properties (time)

 

Why?

the properties of space are different from the properties of time because we measure one with a ruler and the other with a clock.

 

Question: do we have any indication that the small triangles upon a same world line are the same object at different time coordinates?

Any indication that objects persist in time is an indication that objects persist along a world line. It's the same thing.

 

Or, to put it otherwise, could it be possible that the triangles upon a single world line are different objects?

No, the center line, for example, is the Milky Way. The top of the center line is the Milky Way today. A bit further down is the Milky Way a billion years ago -- further down, 2 billion years ago -- and so on.

 

If you consider the Milky Way 12 billion years after the big bang to be the same object as the Milky Way 13 billion years after the big bang then it is the same object.

 

The galaxies and junk in the image are shown at one moment in time... but these don't exist only for a moment of time! Every object in the diagram could be "extruded" along the time dimension to show its history...

 

...Smear the diagram horizontally from CMB to WMAP and vice versa, and even though it still only shows a handful of the hundreds of billions of observable galaxies, the diagram will become pretty full.

I think that's spot on.

 

Any event we see out there, like "star shines", has a history and a future. Draw the complete world line for any event on our past light cone and it can't really be an empty diagram.

[md65536]

Question: do we have any indication that the small triangles upon a same world line are the same object at different time coordinates? Or, to put it otherwise, could it be possible that the triangles upon a single world line are different objects?

I'm not caught up in this conversation but...

 

A world line of an object is the path of that object through 4d spacetime.

The world line is defined by its object.

Different objects would each have their own world lines.

 

You could though describe the world line of a molecule, or describe world lines for each of the molecule's atoms and they'd be very close to "the same" world line at macroscopic scale.

 

Where two world lines intersect, you have two objects collocated in spacetime. A collision event might be described that way, where the collision event is essentially on both world lines... the same point could be said to be on both world lines, even though each world line is still associated with its own object.

 

I suppose that some sets of objects can never occupy the same place and time, so their world lines would never touch.

 

 

[Iggy]

That all sounds correct to me.

[michel123456]

Any event we see out there, like "star shines", has a history and a future. Draw the complete world line for any event on our past light cone and it can't really be an empty diagram.

 

You mean that we can fill the diagram with a past and a future that we know must exist but that we cannot see. What I mean with a empty diagram is that the part of the diagram that we can see today is only upon the surface of our past light cone. All the rest is not visible.

 

the properties of space are different from the properties of time because we measure one with a ruler and the other with a clock.

 

If properties of time are so different that properties of space, how is it possible that space for some observer is time for another?

Hum, this last will put this thread on wrong tracks.

 

A world line of an object is the path of that object through 4d spacetime.

The world line is defined by its object.

Different objects would each have their own world lines.

 

O.K.

Here is the concept.

Houston is sending Neil Armstrong to the Moon. Because Neil goes away, he navigates in the past light cone of Houston. As Neil is traveling, he remains in contact with Houston all the time: Neil remains upon the surface of Houston's light cone.

And Houston remains upon Neil's past light cone.

There is no physical way Neil could escape Houston's light cone surface.

At Houston all kind of devices record Neil's adventure.

After a few days, Neil comes back to Earth. At no moment of his journey he went out the surface of Houston's light cone.

Is that correct?

[md65536]

O.K.

Here is the concept.

Houston is sending Neil Armstrong to the Moon. Because Neil goes away, he navigates in the past light cone of Houston. As Neil is traveling, he remains in contact with Houston all the time: Neil remains upon the surface of Houston's light cone.

And Houston remains upon Neil's past light cone.

There is no physical way Neil could escape Houston's light cone surface.

At Houston all kind of devices record Neil's adventure.

After a few days, Neil comes back to Earth. At no moment of his journey he went out the surface of Houston's light cone.

Is that correct?

 

Sounds alright. I think others would be able to improve that description (better than what I could do).

 

I would say: Everything we observe -- every observation -- can be considered an "event", such as "Neil on Earth", "Neil in space at t=5000", "Neil in space at t=5001" etc.

Some of those events can be outside our (Houston's) light cone, such as "Neil on the moon right now", but those same events will be on the past light cone of ours in the near future (about a second in the future in this case). So I would disagree with "he navigates the past light cone of Houston". However, yes, his world line will always intersect with any of our past light cones, so he is always observable.

 

He navigates the spatial realm of Houston's past light cone, but just outside of it in the temporal dimension, as does pretty much everything (according to SR).

 

 

When you say "he", if you mean him as an object extended through the time dimension, then his spacetime location(s) can be described with his world line, which always intersects with Houston's light cone.

If by "he" you mean him existing in different specific single instants (which could be called events), then there will be instants that are on the light cones of Houston's specific instants, and others that are not. The event of him touching down on the surface of the moon is an instant that is only observable in an instant at Houston. But, for any light cone of Houston's, there will be an event corresponding to "Neil intersecting the surface of that light cone".

 

Either way, some "he" is always theoretically observable to Houston.

 

 

There is probably a simpler way to say this than what I wrote.

[MigL]

You guys have drawn a lot of pretty pictures but you haven't proved what I said to be wrong. So I'll repeat...

 

Starting at a certain distance from us ( 23-24 billion light years comes to mind ) everything in the universe is receding from us at light speed or greater because the separation between our galaxies is growing at or faster than the speed of light. The light we would see from these galaxies is red-shifted to infinity ( infinite wavelength, zero frequency, ie no energy left ), so they are in effect invisible to us. This is what defines the observable universe that is causally connected, any galaxy receding at c or greater is causally disconnected and so has no effect on us.

Your premise that there are galaxies at intermediate distances which can be affected by the causally disconnected galaxies and then pass the effect on to us does not make sense because light speed is finite and the distances cumulative. They still add up to the same total distance and the intervening space still expands by the same amount.

There is a limit to the causally connected observable universe, and it is much smaller than the total universe.

[Iggy]

If properties of time are so different that properties of space, how is it possible that space for some observer is time for another?

Hum, this last will put this thread on wrong tracks.

it is precisely because they have different properties that we are able to know what is entirely spatial separation for one is temporal and spatial separation for another. If space and time didn't have different properties then everything would just be one kind of separation. There would be no difference between proper distance and proper time. As it stands, there is.

 

As Neil is traveling, he remains in contact with Houston all the time: Neil remains upon the surface of Houston's light cone.

I'd echo everything Md said.

 

When Neil said "one small step for man..." -- at that instant -- Houston was in his past light cone in the sense that the whole history of Houston was in his past light cone. All of the events that happened in Houston from the moment it was named up to nearly the present instant (1.3 seconds before the present instant) was in his past light cone.

 

If that's what you mean then I agree

 

You guys have drawn a lot of pretty pictures but you haven't proved what I said to be wrong. So I'll repeat...

 

Starting at a certain distance from us ( 23-24 billion light years comes to mind ) everything in the universe is receding from us at light speed or greater because the separation between our galaxies is growing at or faster than the speed of light. The light we would see from these galaxies is red-shifted to infinity ( infinite wavelength, zero frequency, ie no energy left ), so they are in effect invisible to us. This is what defines the observable universe that is causally connected, any galaxy receding at c or greater is causally disconnected and so has no effect on us.

Your premise that there are galaxies at intermediate distances which can be affected by the causally disconnected galaxies and then pass the effect on to us does not make sense because light speed is finite and the distances cumulative. They still add up to the same total distance and the intervening space still expands by the same amount.

There is a limit to the causally connected observable universe, and it is much smaller than the total universe.

We're only talking about things close enough to be observed... nothing outside the visible universe

[md65536]

Starting at a certain distance from us ( 23-24 billion light years comes to mind ) everything in the universe is receding from us at light speed or greater because the separation between our galaxies is growing at or faster than the speed of light. The light we would see from these galaxies is red-shifted to infinity ( infinite wavelength, zero frequency, ie no energy left ), so they are in effect invisible to us. This is what defines the observable universe that is causally connected, any galaxy receding at c or greater is causally disconnected and so has no effect on us.

Your premise that there are galaxies at intermediate distances which can be affected by the causally disconnected galaxies and then pass the effect on to us does not make sense because light speed is finite and the distances cumulative. They still add up to the same total distance and the intervening space still expands by the same amount.

There is a limit to the causally connected observable universe, and it is much smaller than the total universe.

The first part sounds good but is beyond me. It's the reason for the expected "heat death" end of the universe.

 

The second part must be correct. If we can receive a signal from the "intermediate" which has received a signal from the "disconnected", then there must have been time enough to receive a signal from the "disconnected" which means it's not actually causally disconnected.

 

Disclaimer: I'm trying to figure this out as I go and I have no idea about the credibility of the link I quote below.

 

I suppose we can get mixed up on the meaning of "visible universe". I googled to find out the distance to CMB and found this answer: "[...] the today distance to the matter which emitted the light we are now getting as CMB. It says 45.65 billion LY, but you can round that off to 45 or 46.

OK strictly speaking that is not the 'distance to the CMB'. The distance to the CMB is zero, it is all around us. It is radiation and some of it is in this room.

46 billion LY is the distance to the MATTER that emitted the CMB radiation that we are currently receiving.

Technically, 46 billion LY is called the distance to the 'surface of last scattering'." [marcus, http://www.physicsfo...p/t-280981.html]

 

 

 

But now I've confused myself. If the age of the universe is about 14B years, then we cannot see (now) anything beyond 14B LY because it would require more than 14B years for that light to reach us. Therefore I think the causally connected observable universe must be at most 14B LY.

HOWEVER, 14B LY is the spatial distance to the event of the "last scattering" of some material, and that material would have kept traveling away from us. Some of that material may now be say 16B LY away???? and may become visible in a few billion years. Other material may be say 30B LY away and moving away faster than the speed of light so it will never be visible to us. Also, since apparently the rate of expansion is increasing, the 23-34B LY boundary should get closer in the future!

 

I think that this means that the currently observable universe is within 14B LY.

The causally connected universe extending to 23-24B LY is not currently visible, but events within that range can become visible in the future (but, for events around that range, not until the universe is at least 23B years old).

 

 

 

Also... as the age of the universe grows, while the distance to the "causal boundary" or whatever decreases, at some point these two values should be equal. At that point, I think what happens is that the material that gave off the CMB radiation we're then seeing, will quickly be moving away faster than the speed of light???, and the CMB radiation will be the last we'll see of that material! After that point, we should not be able to detect CMB radiation any more.

Edited November 21, 2011 by md65536

[Iggy]

The first part sounds good but is beyond me. It's the reason for the expected "heat death" end of the universe.

 

The second part must be correct. If we can receive a signal from the "intermediate" which has received a signal from the "disconnected", then there must have been time enough to receive a signal from the "disconnected" which means it's not actually causally disconnected.

 

Disclaimer: I'm trying to figure this out as I go and I have no idea about the credibility of the link I quote below.

 

I suppose we can get mixed up on the meaning of "visible universe". I googled to find out the distance to CMB and found this answer: "[...] the today distance to the matter which emitted the light we are now getting as CMB. It says 45.65 billion LY, but you can round that off to 45 or 46.

OK strictly speaking that is not the 'distance to the CMB'. The distance to the CMB is zero, it is all around us. It is radiation and some of it is in this room.

46 billion LY is the distance to the MATTER that emitted the CMB radiation that we are currently receiving.

Technically, 46 billion LY is called the distance to the 'surface of last scattering'." [marcus, http://www.physicsfo...p/t-280981.html]

 

 

 

But now I've confused myself. If the age of the universe is about 14B years, then we cannot see (now) anything beyond 14B LY because it would require more than 14B years for that light to reach us.

The two links I can think on this are the following:

http://www.astro.ucla.edu/~wright/cosmo_02.htm#MD

http://www.astro.ucla.edu/~wright/Dltt_is_Dumb.html

 

There is more than one definition for distance is cosmology. If you go to the cosmology calculator:

 

http://www.astro.ucla.edu/~wright/CosmoCalc.html

 

plug in z=1090 (that's the redshift of the cmb) and hit 'general' on the left it gives the distance to the cmb on the right,

 

The light travel time was 13.665 Gyr.

The comoving radial distance, which goes into Hubble's law, is 13995.7 Mpc or 45.648 Gly.

 

As you suspected, 45.6 Gly is the current distance. The distance, for example, from the milky way to another galaxy which is as old as the milky way. At the time of the CMB the two areas (they weren't galaxies yet) were roughly 42 million lightyears apart. The universe expanded 1091 times over since then so the two areas are currently 45.6 billion years apart. One of the areas turned into the milky way and the other turned into a galaxy at the edge of our visible universe.

 

Because of the acceleration of expansion we will never see that galaxy. The CMB is the last glimpse we got of that mass.

Edited November 21, 2011 by Iggy

[md65536]

http://www.astro.ucl...tt_is_Dumb.html

Quote from the link:

"- Distance is defined as the spatial separation at a common time. It makes no sense to talk about the difference in spatial positions of a distant galaxy seen 9.1 billion years ago and the Milky Way now when galaxies are moving.

- The Universe is homogeneous and isotropic, so it has no edge. Thus there cannot be a maximum distance. Distances greater than speed of light times the age of the Universe are commonplace. But a uniform grid in the Universe shown at left below is very non-uniform when plotted using the light travel time distance"

 

This doesn't make sense to me. What's the point of talking about the distance between the Milky Way and a galaxy that you can only see as it was 9.1 billion years ago? Sure, you can predict its "true distance right now", but that won't have any effect on us whatsoever for over 9 billion years. There is no causal connection between "us, now" and "that galaxy, now".

 

We see it 9.1 billion LY away, as it was when we are seeing it. What's the point of taking something that we observe, and saying "Well it's not actually there, it's moved. And, it's not actually *that*, it's evolved for 9 billion years so it'll probably be quite different (most of its stars will probably die by then anyway)." I don't see how you could consider what you're talking about as being the same thing as what you observe. -- That can be a philosophical issue but I'm just wondering what the practical point of considering the "current" predicted distance to an observed object is.

 

If you were planning on sending a signal to it, then maybe its distance now is relevant.

 

[michel123456]

 

O.K.

Here is the concept.

Houston is sending Neil Armstrong to the Moon. Because Neil goes away, he navigates in the past light cone of Houston. As Neil is traveling, he remains in contact with Houston all the time: Neil remains upon the surface of Houston's light cone.

And Houston remains upon Neil's past light cone.

There is no physical way Neil could escape Houston's light cone surface.

At Houston all kind of devices record Neil's adventure.

After a few days, Neil comes back to Earth. At no moment of his journey he went out the surface of Houston's light cone.

Is that correct?

Sounds alright. I think others would be able to improve that description (better than what I could do).

 

 

If we all agree that everything we observe remains physically upon the surface of the light-cone, and that even our records are about events placed on the surface of our light-cone, how can we gather information about what is not upon the surface of the light-cone?

Let's use Reductio ad absurdum and suppose there is a co-moving object in time, by which means could we discard such an hypothesis ?

[md65536]

If we all agree that everything we observe remains physically upon the surface of the light-cone, and that even our records are about events placed on the surface of our light-cone, how can we gather information about what is not upon the surface of the light-cone?

Let's use Reductio ad absurdum and suppose there is a co-moving object in time, by which means could we discard such an hypothesis ?

 

A specific light cone is relative to an observational frame of reference (the spacetime point that is the apex of the cone being maybe the most important thing, as least in simple examples???).

Events that lie on any specific cone are fixed spacetime points that don't move. Objects move but events don't... only the events remain on the surface of the light cone (whose apex is also a fixed spacetime point, because we're talking about the lightcone of an observer in a single instant), but... the object, extended in time, and described by its world line... is uh...

 

It's not that "an object is fixed to a light cone", it's that its world line always intersects that light cone (for stuff in our spacetime vicinity at least, on the order of billions of years and light years), so there is always an instant where the object (or a past state of the object, one might say) can be observed "on any given light cone".

 

 

 

We can gather information about stuff that's not on the surface of a light cone, because of "physical laws". We can use the current observed state of a system and understand previous states that must have preceded it, and we can predict future states to varying degrees of certainty, because the progression of states follows certain laws.

 

One might say that the observable state of a system contains "memory" of previous events. Things are the way they are due to causal relationships that precede observable events. So if we see a nebula, its current state encodes much information of say the star that created it. We observe systems that have memories, and the observer systems can have memories too, where information can oscillate for long periods of time and intersect with many many many different light cones through time.

 

 

 

I think you might be talking about extending light cones through time, such as describing "Everything that I see in a day". That's not a light cone. A light cone is a 3D surface in a 4D space. If extended through time I think it becomes a 4D volume that is a subspace of the 4d space.

 

Or, there is the 4D volume that is contained by the past light cone of a single observational instant, which includes everything I see now and everything I could have ever seen and everything that causally affected everything I see or could ever have seen. This is also a 4D subspace.

Edited November 21, 2011 by md65536

[MigL]

Sorry my mistake. I remembered a value of about 47GLY but assumed that to be a diameter, so I used a value of 23-24GLY for the radius. You guys are right it should be the higher value for observable universe radius.

 

I'm no expert in the use of light cones, but are they the right tool to use in this case ??

There is a relative acceleration and speed difference between our galaxy and a galaxy at the edge of our observable universe, but it is due to an expansion of the intervening space, not an actual acceleration or velocity. How does that affect their respective light cones ?

And what about galaxies that lie just outside the observable universe ? Relative to us, they are moving faster than c, how would you represent this with a light cone ?

[Iggy]

Quote from the link:

"- Distance is defined as the spatial separation at a common time. It makes no sense to talk about the difference in spatial positions of a distant galaxy seen 9.1 billion years ago and the Milky Way now when galaxies are moving.

- The Universe is homogeneous and isotropic, so it has no edge. Thus there cannot be a maximum distance. Distances greater than speed of light times the age of the Universe are commonplace. But a uniform grid in the Universe shown at left below is very non-uniform when plotted using the light travel time distance"

 

This doesn't make sense to me. What's the point of talking about the distance between the Milky Way and a galaxy that you can only see as it was 9.1 billion years ago?...

 

We see it 9.1 billion LY away, as it was when we are seeing it...

[my bold]

But, we don't see it 9.1 Gly away. If we did then I'd agree the light travel time would be a much more natural unit of distance.

 

The light took 9.1 gigayears to get to us, but the light's speed relative to us wasn't constant during that time so it doesn't translate directly into a distance.

 

Let's say that the galaxy is named Merlin (my cat's name as it happens), and also pretend that Merlin and the Milky Way are at lest 9.1 billion years old. The Milky Way was 5.72 Gly from Merlin 9.1 billion years ago when it emits light towards the Milky Way. In other words, 5.72 billion observers, each with a ruler 1 lightyear long, would fit between the galaxies when the light is emitted (each observer moving with the expansion of the universe -- "comoving observers" they would be called).

 

The light moves at c relative to its nearest observer throughout the trip. 9.1 Gyr later the light arrives in the Milky Way. By the time it arrives each observer would need a ruler 2.415 ly long because the universe has expanded 2.415 times its previous size. The 'proper distance' (as they call it) to Merlin has gone from 5.7 Gly (when light was emitted) to 13.8 Gly (when light was received).

 

At some point in time Merlin had a proper distance of 9.1 Gly from the Milky Way, but it wasn't when the light was emitted or when it was received. It was some point between. I think light travel time is a fine measure of distance (no less correct than redshift, luminosity distance or any other definition of distance in cosmology), it just doesn't mean what a lot of people intuitively think it means.

 

 

If you were planning on sending a signal to it, then maybe its distance now is relevant.

Quiz question for anybody: if a galaxy is currently 18 billion lightyears from us and we send it a message, will it ever be received (assuming the standard model is correct)?

[md65536]

Sorry my mistake. I remembered a value of about 47GLY but assumed that to be a diameter, so I used a value of 23-24GLY for the radius. You guys are right it should be the higher value for observable universe radius.

 

I'm no expert in the use of light cones, but are they the right tool to use in this case ??

There is a relative acceleration and speed difference between our galaxy and a galaxy at the edge of our observable universe, but it is due to an expansion of the intervening space, not an actual acceleration or velocity. How does that affect their respective light cones ?

And what about galaxies that lie just outside the observable universe ? Relative to us, they are moving faster than c, how would you represent this with a light cone ?

 

 

Observable universe:

"In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light (or other signals) from those objects has had time to reach us since the beginning of the cosmological expansion. [...] the current comoving distance to the edge of the observable universe is calculated to be 14.3 billion parsecs (about 46.6 billion light years) [...]

The age of the universe is about 13.75 billion years, but due to the expansion of space we are observing objects that were originally much closer but are now considerably farther away (as defined in terms of cosmological proper distance, which is equal to the comoving distance at the present time) than a static 13.75 billion light-years distance." [http://en.wikipedia.org/wiki/Observable_universe]

 

I started replying to your post, but then I found everything I was writing in the "Misconceptions" section of the above link.

My previous posts have contained misconceptions too!

 

"Distances obtained as the speed of light multiplied by a cosmological time interval have no direct physical significance." -- Sounds like light cones are not the right tool.

 

The wikipedia article should provide some answers. I need to shut up and do some learnin!

 

The light moves at c relative to its nearest observer throughout the trip. 9.1 Gyr later the light arrives in the Milky Way. By the time it arrives each observer would need a ruler 2.415 ly long because the universe has expanded 2.415 times its previous size. The 'proper distance' (as they call it) to Merlin has gone from 5.7 Gly (when light was emitted) to 13.8 Gly (when light was received).

This is where I was confused, thanks.

[Iggy]

"Distances obtained as the speed of light multiplied by a cosmological time interval have no direct physical significance."

Notice the source it gives for that (19)

 

[md65536]

Notice the source it gives for that (19)

 

Well, it made sense when it was on wikipedia.

 

 

Nah, it still doesn't make sense to me but your previous post makes me see where my error is.

 

 

[Iggy]

 

Yeah, thinking about the brightness and frequency of the light is where the train goes off the rails for me.

[JustinW]

This question is a little late. My network server has been down for a few days.

 

md,

But now I've confused myself. If the age of the universe is about 14B years, then we cannot see (now) anything beyond 14B LY because it would require more than 14B years for that light to reach us. Therefore I think the causally connected observable universe must be at most 14B LY.

HOWEVER, 14B LY is the spatial distance to the event of the "last scattering" of some material, and that materialwould have kept traveling away from us. Some of that material may now be say 16B LY away???? and may become visible in a few billion years. Other material may be say 30B LY away and moving away faster than the speed of light so it will never be visible to us. Also, since apparently the rate of expansion is increasing, the 23-34B LY boundary should get closer in the future!

I agree with most of what is being said about the light cone, but the bolded part of the quote struck me as inaccurate. If something that is moving away from us at more than the speed of light projects light toward us, the projected light will still travel toward us at the SOL from the point it was projected. In order for us never to see that light from the object we would have to travel away from the object at more than the SOL.

 

On a smaller note, could we call it a light circle or sphere instead of a cone? Since we do have a 360degree field of view it would be overlapping circles instead of intersecting cones. Right? Probably not impotant. This is just how I've mapped it in my head. The graph just shows all points looking in the same direction. But with a 360degree field of view there would be no up and down or side to side limitations.(just the furthest point of any direction you look) The principle would still be the same though.

[Iggy]

On a smaller note, could we call it a light circle or sphere instead of a cone? Since we do have a 360degree field of view it would be overlapping circles instead of intersecting cones. Right?

With all three spatial dimensions, it would be a 4 dimensional hypercone. One of the axis in the OP represents time and the other represents one of the spatial dimensions.

Here is a fair description of a light cone.

[JustinW]

With all three spatial dimensions, it would be a 4 dimensional hypercone. One of the axis in the OP represents time and the other represents one of the spatial dimensions.

Here is a fair description of a light cone.

Yes, I had figured it would be something to that effect.

[michel123456]

From your link

As we look into space, we are observing our past light cone slicing concentric rings through the hypersurfaces of the past. Each ring on the past light cone represents a spherical plane in 3-D space centered on the observer.

 

Exactly. Each "spherical plane in 3-D space" is the surface of a sphere, and the light cone is in fact an expanding sphere around the observer.

The fact is: each point of the surface of a choosen sphere corresponds to a specific distance and a specific time. If Distance is D1, time is T1, because D1 and T1 are linked by the Speed Of Light.

If you disconnect the two entities, and take a random point D12 at time T578, this point is not visible.

[Iggy]

From your link

As we look into space, we are observing our past light cone slicing concentric rings through the hypersurfaces of the past. Each ring on the past light cone represents a spherical plane in 3-D space centered on the observer.

 

Exactly. Each "spherical plane in 3-D space" is the surface of a sphere, and the light cone is in fact an expanding sphere around the observer.

Agreed -- a past light cone contracts and a future cone expands, but agreed.

The fact is: each point of the surface of a choosen sphere corresponds to a specific distance and a specific time. If Distance is D1, time is T1, because D1 and T1 are linked by the Speed Of Light.

I would draw exactly the same conclusion.

If you disconnect the two entities, and take a random point D12 at time T578, this point is not visible.

Right. We don't hear Neil saying "one small step for man..." It's not on the surface of our current past light cone.