The Expanding Universe: Calculating Real-Time Distances of Objects

[hsbrown]

Hello, All,

I hope I am not out of line here, this is the only cosmology forum I could find to ask a few questions...

I am considering developing a piece of software that can produce a 3D model of cataloged objects, by querying something like NED or SIMBAD, and generating this as a real time model. In other words, representing all objects where they actually are in relation to one other at a given moment, not where we are able to observe them. Maybe even try and overlay their observed positions for effect. Maybe try to play with gravity, I dunno.

However, I am having trouble locating how published distances are arrived at, and am making certain lay assumptions that may or may not be accurate. For one thing, I am assuming that the published distances of objects are calculated using the speed of light, and do not take into account the expansion of the universe...

If I input the distance of an object, and take into account the red shift that is observed, can I say with any certainty that that object's current position relative to other objects (i.e. the sun) is anything?

For example (and grins), if the (albeit short lived) published/observed distance of an object from Earth is 1 light second (300,000km), and the red shift of that object tells me that it is moving away from me at the rate of 300,000km/s then if I calculate the "actual" distance of the object for rendering purposes, would 600,000km be accurate (assuming I calculated it within a second, duh)?

Assuming that the explanation for red-shift is not EM wave propogation (and it does not play any role in the red shift):rofl: , but that it is actually a function of the objects motion, this gets confusing over greater distances when the rate of expansion of the universe is not a constant, but is either accelerating or deccelerating.

My quandary:

If one observes an object with a distance of d, and observes the red shift, applies the formula to calculate how far the object has moved away from me in the time between now and however many years, months, days, hours, seconds, etc... have passed since the light that I am observing has left the object, I would be able to calculate the actual distance of the object that I am observing, right?

Well, not really. If the object has sped up over time I have to use the red shift of progressively nearer objects (this of course assumes that the rate of expansion at any given moment in time is uniform throughout the cosmos) to calculate how much the acceleration of the object has increased over time (and the distance it is from the point of observation now), i.e if the universe is accelerating, there should be a more pronounced observable effect on red shift for nearer objects than more distant, right? The faster an object is moving away from you, the more the spectra will shift toward the red end, right?

Well, but then aren't I riding a proverbial snowball down a hill? Each progressively nearer object should have a less pronounced shift, but the shift in the spectra as I am observing it is as it was x millenia ago, and so on and so forth...

Color me confused! How can the actual real-time distance of any object be calculated when everything we can observe about it actually happened aeons ago? Including the speed at which we observe it to be moving away from us?

It doesn't really seem as though an accurate expansion rate of the universe weighted over time could be calculated or extrapolated, given that we have no way to observe how fast it is expanding right now, but only the rate as it was expanding when the nearest object to the point of observation was when the observable radiation emitted from it left the object! (say that three times fast)

Somebody must have puzzled these calculations out somewhere and have a formula for it...

Thanks

 

[chroot]

You seem to have a few misconceptions about the so-called "Hubble flow."

To a first approximation, the velocity of an object with respect to us is given by Hubble's law:

$v = H_0 d$

This is linear. Hubble's constant $H_0$ defines the rate of the expansion of the universe. Its current value is around 70 km/s per megaparsec of distance. If the universe's expansion is accelerating, then Hubble's "constant" is actually growing with time.

The redshift is simply another way to express velocity, and thus, by Hubble's law, distance.

$z = \frac{{\Delta \lambda }} {\lambda } = \sqrt {\frac{{1 + {v \mathord{\left/ {\vphantom {v c}} \right. \kern-\nulldelimiterspace} c}}} {{1 - {v \mathord{\left/ {\vphantom {v c}} \right. \kern-\nulldelimiterspace} c}}}} - 1$

If you're trying to imagine what the objects are doing now, rather than as we see them now, you're headed down a slippery slope, indeed. There is no universal concept of now. In other words, every observation must be made by some realistic observer, and no realistic observer can see every object in the universe at the same time. One of the conclusions of the special theory of relativity, in fact, is that every observer has his own personal notion of now, and his notion of now is not necessarily related to anyone else's.

You're going to have to settle for plotting your objects at the positions they appear for some realistic observer.

I'm also going to note that your example,

For example (and grins), if the (albeit short lived) published/observed distance of an object from Earth is 1 light second (300,000km), and the red shift of that object tells me that it is moving away from me at the rate of 300,000km/s then if I calculate the "actual" distance of the object for rendering purposes, would 600,000km be accurate (assuming I calculated it within a second, duh)?

is unrealistic, because a) it implies an enormous Hubble constant, b) it implies that the object is receding from the observer at the speed of light, and is thus actually on the boundary of being invisible to the observer. If the universe's expansion is accelerating, it will momentarily become invisible to the observer.

Keep in mind that, with realistic values of Hubble's constant, the distances to very distant objects are changing relatively little. If an object is 10 billion light years away, for example, what does another half a light-year per year matter?

- Warren

 

[kmarinas86]

For example (and grins), if the (albeit short lived) published/observed distance of an object from Earth is 1 light second (300,000km), and the red shift of that object tells me that it is moving away from me at the rate of 300,000km/s then if I calculate the "actual" distance of the object for rendering purposes, would 600,000km be accurate (assuming I calculated it within a second, duh)?

As long as this object is a photon at moving at 300,000 km/s. But I don't know of any photons giving off mini photons without a atomic nucleus or some other object/field acting like a braking mechanism, so this would not be possible.

Assuming that the explanation for red-shift is not EM wave propogation (and it does not play any role in the red shift):rofl: , but that it is actually a function of the objects motion, this gets confusing over greater distances when the rate of expansion of the universe is not a constant, but is either accelerating or deccelerating.

Doppler redshift depends on the instantaneous velocity. By plotting the the change in doppler shift over time, you can pick out the change in velocity. That same goes with any "acoustic" doppler as well.

My quandary:

If one observes an object with a distance of d, and observes the red shift, applies the formula to calculate how far the object has moved away from me in the time between now and however many years, months, days, hours, seconds, etc... have passed since the light that I am observing has left the object, I would be able to calculate the actual distance of the object that I am observing, right?

No. The speed of sound and speed of light are both finite. In the same way with the speed of sound, where there is delay, the same is true for light. The redshifted light that has not reached you yet will give you information that would otherwise not be known. All of a sudden, it could go the opposite direction, and you wouldn't know it because the signs of that change in velocity haven't reached you yet.

Well, not really. If the object has sped up over time I have to use the red shift of progressively nearer objects (this of course assumes that the rate of expansion at any given moment in time is uniform throughout the cosmos) to calculate how much the acceleration of the object has increased over time (and the distance it is from the point of observation now), i.e if the universe is accelerating, there should be a more pronounced observable effect on red shift for nearer objects than more distant, right?

The "more pronounced" effect is due to the greatest redshift, which is case for farther objects in the expanding, accelerating universe.

The faster an object is moving away from you, the more the spectra will shift toward the red end, right?

Yes.

Well, but then aren't I riding a proverbial snowball down a hill? Each progressively nearer object should have a less pronounced shift, but the shift in the spectra as I am observing it is as it was x millenia ago, and so on and so forth...

Yes. But validity of the notion of "x millenia ago", depends on the optics of the environment outside the solarsystem.

Color me confused! How can the actual real-time distance of any object be calculated when everything we can observe about it actually happened aeons ago?

Ya can't do it. You can guess, but the greater the delay, the less you can rely on it.

Including the speed at which we observe it to be moving away from us?

Yes.

It doesn't really seem as though an accurate expansion rate of the universe weighted over time could be calculated or extrapolated, given that we have no way to observe how fast it is expanding right now, but only the rate as it was expanding when the nearest object to the point of observation was when the observable radiation emitted from it left the object! (say that three times fast)

We obviously don't see the acceleration of Andromeda as it was 10 billion years ago, and we certianly don't see the acceleration of the furthest galaxies as they are right now.

Somebody must have puzzled these calculations out somewhere and have a formula for it...

Yes they have. Calculations, and reality, if that.

Thanks

No problemo.

 

[chroot]

As long as this object is a photon at moving at 300,000 km/s. But I don't know of any photons giving of mini photons without a atomic nucleus or some other object/field acting like a braking mechanism, so this would not be possible.

It is perfectly consistent for an object to be receding from us at a velocity equal to or greater than the speed of light, if space itself is expanding between the object and the observer; this is not a violation of special relativity.

I ask that you sit out discussions for which you are unprepared to contribute.

- Warren

 

[kmarinas86]

It is perfectly consistent for an object to be receding from us at a velocity equal to or greater than the speed of light, if space itself is expanding between the object and the observer; this is not a violation of special relativity.

Of course not. It's a matter language really though. It is said that a mass cannot travel at the speed of light, and of course, if this is with respect to the space itself, then the limit is imposed. But if it is with respect to the previous state of that space, then that's where your statement comes in.

I ask that you sit out discussions for which you are unprepared to contribute.

Then I will prepare to contribute.

 

[chroot]

Of course not. It's a matter language really though.

No, it really isn't.

- Warren

 

[hsbrown]

Hi, all,

Sorry, just a little clarification...

Okay, so no subjective observer can see the universe as a whole at one moment in time, or that is to say, from the perspective of another "subject" millions or so light years away. Which in and of itself would seem to make this a fool's game, eh? I can make predictions (read: guesses) regarding the relative positions of objects based only on subjective observation from my observers point of view (and could never account for anything that altered the objects path in the "past"; the time between when the light left and "now"). Any quasi-real time model, would always be from the standpoint of the subject, and would be unable to account for an infinite number of variables, but might make a unique conversation piece.

Although, eventually one would think that complex enough mathematics could eventually produce a theory that, while only explaining what we observe from our collective/subjective point of view (like dark matter; we can infer it's existence based on what we observe, but no one has ever actually seen it. Or stars that appear to wobble imply the existence of a mass orbiting it.), if the same laws apply (singular events excepted) throughout this particular universe one could use our point of view to apply those theories to another point of view. It would just depend on the accuracy of information that is applied to that point of view... I would think, but I digress.

In essence, what you are saying is that I should be able to take the Hubble constant, or my subjective view of it, and given its observed value over time (by making observations of object near and distant), I could extrapolate its apparent value over time? i.e (and this is rudimentary, and only an example) if I have information regarding the apparent value of the Hubble constant based on observation of Andromeda (2.2 million light years) and Abell 1835 IR1916 (13.23 billion) whose distances I would assume have been calculated by standard candle or something similar, one could approximate their actual distance from the subject which should be significantly greater than the distances referenced, as well as infer the value of the Hubble constant in any direction before or after (assuming that no unpredictable changes occurred to it, that acceleration is a gradient over time, not sudden and jerky)?

But hmmm... This would seem to have an impact on the approximate age of the universe. If something is 13.23 billion light years away, then it would seem to indicate that the two objects could not have been at the same place (the "big bang") any less than n years ago (sort of the inverse of Hubbles law, rewind the distance and apply the velocity backwards accounting for the acceleration), which would seemingly be significantly greater than the currently accepted age of the universe... You couldn't really pinpoint anything (like exactly when they were at the same "place", or where that place might be), but one would think you could say with some certainty that the universe had to be at least so many years old. It would also at some point place the Hubble constant at 0, which may or may not correlate with that age.

Ah the joys of a lack of understanding, I r a programmer.

One thing confuses me though. Bear with me! If more distant objects have the greatest redshift, and the speed of light is finite, then that would seem to mean that more distant objects appear to be moving away from us at a faster rate than nearer objects. Which in turn would seem to indicate to me that objects closer to us, and therefore observed as they were at a moment in time significantly closer to "now" (ouch, not sure how to express that, other than to put it in quotes) are moving away at a slower rate, then wouldn't that indicate that the expansion of the universe is actually slowing down?

Well, I guess more than one thing confuses me...

If red shift is more of an optical illusion (so to speak) and is not related to the "point in time" that the light left the object, but is related to the point in time the light arrived at its "destination" (current accepted value of 70 for the Hubble constant), than wouldn't it appear to be the same for all objects we could observe?

The long and short of it is, lacking understanding, can I apply Hubble's law to any observed object in the universe (given the ongoing refinements of the constant, but applying the currently accepted value), and thus calculate a "best guess" regarding an objects subjective "actual" distance from the subject, apply whatever other physical laws there may be accepted programmatically, and have a somewhat workable "thing"?

If it were somewhat workable, although nowhere near all of the objects in the universe are known, and very few (relatively) are cataloged, it would still be a nice toy to play around with...

 

[chroot]

Okay, so no subjective observer can see the universe as a whole at one moment in time

Correct. In fact, there's no such thing as a universal "moment" that observers across the universe could even agree to.

Although, eventually one would think that complex enough mathematics could eventually produce a theory that, while only explaining what we observe from our collective/subjective point of view... to apply those theories to another point of view.

Well, it's fundamentally impossible for us to know what's happening in Andromeda until 2.2 million years have elapsed and its light has reached us. We can't say anything at all about it "now," and it's not because we lack mathematical sophistication.

If you make the tacit assumption that the objects themselves do not change with time, but only move, then yes, you should be able to "translate" the view at one location to a view at any other location by simply applying the Lorentz transform. You have the coordinates in one frame of reference, so you can translate those coordinates into any other frame of reference. This is a good question, though, and one that I would need to ponder a bit.

The most important conclusion of your program should be that, no matter where you place your hypothetical observer, the universe appears much the same -- everything appears to be moving away from every observer, with the same Hubble relationship.

I have information regarding the apparent value of the Hubble constant based on observation of Andromeda (2.2 million light years) and Abell 1835 IR1916 (13.23 billion) whose distances I would assume have been calculated by standard candle or something similar

Hubble's constant was originally derived by statistics. Obviously, you can't determine the expansion of the universe by looking at only one object, because each individual object has its own "proper motion," a deviation from the average Hubble flow, caused by gravitational interactions and so on.

In fact, distances are usually not determined by "standard candle," but are instead calculated directly from redshift. The redshift-to-distance conversion requires Hubble's constant, so you can see that it's a circular sort of argument.

Let me explain a bit about the so-called "distance ladder" employed by astrophysicists to measure distances.

The closest objects, like the Moon and nearby planets, can actually be ranged with radar. You bounce pulses of EM radiation off of them, and time how long the echos take to return.

For nearby stars, you can use parallax. When you look at a nearby star's apparent position relative to much more distant background stars, you'll notice it varies over a 12-month period as the Earth moves around the Sun. You can use the magnitude of the variation to measure distance. The more a star appears to move, the closer it is.

For nearby galaxies, you can use Cepheid variable stars, which change in brightness over time. Cepheids have a distinct and well-studied relationship between luminosity (power output) and period of variation. Since the period is not affected by distance, you can measure the period and calculate the luminosity. Next, you can compare the luminosity to the power you receive from the star with your telescope, and determine the distance.

At this point, you begin calibrating the redshift. You can use the galaxies with known distances (due to Cepheids) to determine Hubble's constant, which you can then use to measure distances to much, much more distant things.

It's a "ladder" in the sense that each step depends upon the last. In fact, if we were to discover that Cepheids don't work exactly as we thought they did, we'd have to update every catalog yet made; Hubble's constant would be shown to not be what we thought it was.

There are also more "high-tech" ways to measure Hubble's constant, and satellite experiments like WMAP have succeeded in measuring many of our universe's parameters to great precision by studying the cosmic microwave background radiation.

The bottom line, though, is this: the distances quoted for very distant objects like quasars are calculated by redshift alone, with the assumption that Hubble's constant is already known accurately.

But hmmm... This would seem to have an impact on the approximate age of the universe. If something is 13.23 billion light years away, then it would seem to indicate that the two objects could not have been at the same place (the "big bang") any less than n years ago (sort of the inverse of Hubbles law, rewind the distance and apply the velocity backwards accounting for the acceleration), which would seemingly be significantly greater than the currently accepted age of the universe...

Some of the early calculations of the age of the universe were, in fact, made by the method you propose -- by rewinding the Hubble flow and determining when everything was in the same spot.

I'll note that the currently accepted age of the universe is 13.7 billion years (per WMAP). I'll also note that we can see objects much further than 13.7 billion light years away, because the Universe was much smaller in the past, and it didn't take as long for their early light to reach us. In fact, if you do the calculus, you'll find that the so-called "particle horizon," the furthest distance we can physically see, is about 46 billion light years.

One thing confuses me though. Bear with me! If more distant objects have the greatest redshift, and the speed of light is finite, then that would seem to mean that more distant objects appear to be moving away from us at a faster rate than nearer objects.

Correct so far.

Which in turn would seem to indicate to me that objects closer to us, and therefore observed as they were at a moment in time significantly closer to "now" (ouch, not sure how to express that, other than to put it in quotes) are moving away at a slower rate, then wouldn't that indicate that the expansion of the universe is actually slowing down?

I don't see how your conclusion follows from your premise. The velocities of objects depend linearly on their distances. If the same parameter applies equally to both nearby and more distant objects, it would imply that the expansion has been constant.

If red shift is more of an optical illusion (so to speak) and is not related to the "point in time" that the light left the object, but is related to the point in time the light arrived at its "destination" (current accepted value of 70 for the Hubble constant), than wouldn't it appear to be the same for all objects we could observe?

It isn't a function of the observer. It's a function of the expansion of space between the emitter and the observer. As space expands between the emitter and the observer, the photons lose energy and appear (to any observer who wishes to observe them) as redshifted.

The long and short of it is, lacking understanding, can I apply Hubble's law to any observed object in the universe (given the ongoing refinements of the constant, but applying the currently accepted value), and thus calculate a "best guess" regarding an objects subjective "actual" distance from the subject, apply whatever other physical laws there may be accepted programmatically, and have a somewhat workable "thing"?

I believe so, yes.

If it were somewhat workable, although nowhere near all of the objects in the universe are known, and very few (relatively) are cataloged, it would still be a nice toy to play around with...

It sounds like a neat project. You'd probably be able to visually demonstrate a number of the conclusions of modern cosmology.

The only problem I see is that we can only see objects in a 46 billion light-year radius, and we've only catalogued a tiny fraction of the closest such objects. The most interesting "translation" you could make would be one that places the observer close to the edge of our known universe -- but it would also be the most boring, because we know nothing at all about most of that observers's sky.

- Warren

 

[hsbrown]

Just a quick one re: conclusion follows premise...

My thought was that if we are looking at an object 13 billion years back in time, and it appears to be receding away from us (based on red shift) faster than an object 2 million years back in time, then I thought that to mean that 13 billion years ago, the universe was expanding faster that it was 2 million years ago, hence that it is slowing.

I have no sort of transcended beyond the project and been bitten by an inexplicable desire to understand... Cosmosis?

Thanks, chroot!

 

[chroot]

hsbrown,

I think your last conclusion is based on the (very common) misconception that space is expanding from some specific point, i.e. that the universe has a 'center' from which everything is expanding.

This is not true, of course; space is expanding everywhere, at the same rate. Every observer thus sees every other object as moving away, and with a (now famous) linear dependence of velocity on distance.

The most popular analogy is that of a rising loaf of raisin bread. If each raisin is a galaxy, an observer on any raisin will always see all the other raisins moving away. You can calculate (relatively simply) the velocity each raisin will see the other raisins moving. You'll find it's linear with distance.

And isn't cosmosis what you get when you drink the water in Mexico?

- Warren