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Thread: Red shift dilemma.

  1. #1 Red shift dilemma. 
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    The standard cosmological paradigm is based on Hubble's spectroscopic discoveries of the red sift data suggesting an accelerating expansion of the universe, but isn't there a confounding issue here? While the red shift is an accurate finding, the data itself is increasingly ancient, sometimes billions of years in the past. While closer objects have less of a red shifts, this data is more contemporary. If the most distant objects have actually slowed we would not have the information yet to consider this. Might an accelerating universe be a artifact of increasingly more ancient data, or has this been accounted for somehow in the analysis of the data. If not wouldn't the assumptions of cosmology need radical revision?



    Last edited by Jerryboy; March 29th, 2013 at 08:42 PM.
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    The redshift is not intrinsic, it doesn't come from the object concerned, it is due to what happened to the light between the time it was emitted and the time it was detected.


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    I find this a very interesting question.
    When do we actually receive this light and at what point in the future would we see a change in red shift indicating a slowing down of expansion, if any?
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    When do we actually receive this light and at what point in the future would we see a change in red shift indicating a slowing down of expansion, if any?
    we receive this light when it hits our detectors. to see a change in the acceleration rate we would need to have data points millions of years apart. we can wait or we can look at objects with different distances from us and work from that. the second is what we do and so can say the the rate is increasing.
    Sometimes it is better not knowing than having an answer that may be wrong.
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    I love it when someone says "paradigm."
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    Yes, I understand that we see the red shift when we receive it.
    My question is, if it takes billions of years for light to reach us (so that we can see the red shift), how would we know if the expansion is STILL accelerating or if it is slowing down or if it may already be reversing in direction, which we would see by a blue shift in the light?

    We might have to wait billions of years for that more recent light to reach us from the edge of the universe, no?
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    My question is, if it takes billions of years for light to reach us (so that we can see the red shift), how would we know if the expansion is STILL accelerating or if it is slowing down or if it may already be reversing in direction, which we would see by a blue shift in the light?
    correct, but, WMAP gave us a pretty accurate picture of the overall density of the universe and from that we can determine the geometry. knowing this and the current expansion rate we can be pretty sure that we wont see a diminishing of this rate. so various theories added together lead us to the conclusions we have.
    Sometimes it is better not knowing than having an answer that may be wrong.
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    But Microwaves are also subject to the speed of light constraints. The further away the source the more ancient the data. It is my notion that the most distant objects or data reflects the exuberant speed of inflation nearer to the the early stages of cosmic inflation. Neither microwave or light can give us contemporary data. The WMAP gives us a dataset based on a higher frequency of the spectrum of the electro-magnetic spectrum. But how does it substantiate the continued acceleration of remote objects. I do not think geometry is relevant here since we are talking about a dynamic universe. Geometry is about fixed shapes which space/time will warp according to the relevant forces applied resulting in vectors of inflation. It only stands to reason that the most distant objects seem to recede from us near the speed of light since that was their speed billions of years ago.
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    Geometry undoubtedly plays a role in the "apparent (rate and shape) of expansion".

    CDT (causal dynamic triangulation) may well hold some of the secrets.

    Then a personal favorite of mine, a doughnut shaped universe. This visual seems so elegant and efficient.
    Energy spewing forth from the doughnut hole (singularity) and traveling along the surface of the doughnut, ever faster separating, until passing the horizon (greatest diameter) and beginning to descend back toward the center on the other side of the doughnut ever increasing in density until a critical point is reached within the singularity, and is spewed out in a BB once more, ad infinitum.
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    Quote Originally Posted by Jerryboy View Post
    But Microwaves are also subject to the speed of light constraints. The further away the source the more ancient the data. It is my notion that the most distant objects or data reflects the exuberant speed of inflation nearer to the the early stages of cosmic inflation.
    The most distant objects are from much, much later than the inflationary era. Even the CMB is from something like 370,000 years after the inflationary period. (If there was a period of inflation, of course.)

    But how does it substantiate the continued acceleration of remote objects.
    I don't think it does. The evidence for acceleration comes from a study of the change in the Hubble constant over time (which, as you point out, we are able to do because the more distant galaxies are more ancient). The key point is that it is not just about changing velocities but changing scale factor.

    Geometry is about fixed shapes ...
    Maybe, if you are talking about Euclid's conception of geometry. But we have come a long way over the last 2000 years. The geometry used in GR isn't about fixed shapes.
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    I was wrong about Euclidian geometry, when the effects of gravity is applied to space/time it is a new conception of the universe, but the fact remains whether you consider microwaves or visible light the both are subject to the speed of light delay and the record of evidence of a rapidly expanding universe is billions of years old. You are right about fixed shapes, but the relativistic shape is still in question, be it flat, curved or donut shaped, but light speed of microwaves and visible light are the same. I don't see how the geometry solves the problem.
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    Quote Originally Posted by Jerryboy View Post
    I was wrong about Euclidian geometry, when the effects of gravity is applied to space/time it is a new conception of the universe, but the fact remains whether you consider microwaves or visible light the both are subject to the speed of light delay and the record of evidence of a rapidly expanding universe is billions of years old. You are right about fixed shapes, but the relativistic shape is still in question, be it flat, curved or donut shaped, but light speed of microwaves and visible light are the same. I don't see how the geometry solves the problem.
    I've lost track of what you think the problem is. We have a model for the universe (from GR), and we have a pile of observational data. You put the two together, and you use the model to (try to) go beyond the observed and answer questions like "what is the ultimate fate of the universe" and "where the heck did I put my car keys?"

    This is what is done with all scientific models. The time delay associated with a finite speed of light merely means that some of the data we put into the model originates from long ago. That by itself doesn't pose a problem for the modeling exercise. Indeed, one could argue that having data that spans a large time scale is useful for validating the model itself.
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    The cosmological redshift data comes from across the range of distances from the edge of the observable universe (13.7 billion years ago) to just outside of our local cluster of galaxies (100 million years ago). Because our local cluster of galaxies is bound by gravity, the expansion of the universe is negated by the local gravitational attraction between neighbouring galaxies.

    The cosmological redshift data tells us that the universe was expanding at a decelerating pace for around 8 billion years, but around 5 billion years ago that deceleration turned into an acceleration, so more recently the expansion has been gaining pace again.

    So, unless the universe suddenly and inexplicably put the brakes on the accelerating expansion sometime within the last 100 million years, bringing everything to a sudden halt, I think we can safely assume the universe is still expanding in the absence of any evidence to the contrary.
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    When you say "The cosmological redshift data tells us that the universe was expanding at a decelerating pace for around 8 billion years, but around 5 billion years ago that deceleration turned into an acceleration, so more recently the expansion has been gaining pace again." On what data is this based on. Red shifts and Microwave shifts have not substantiated this idea which is not in evidence. On what assumptions is this based absent observational data? We don't know what the red shift data was at 8 billion years, we only know what it is now. The slice in time we see is millions and billions of years in the past. I am not a cosmologist, but you have not convinced me that we should assume continued cosmic acceleration. Try again. Where is a really cosmologist when you need one!

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    On what data is this based on
    On observations of type Ia supernova and their associated redshifts and distances. The 2011 Nobel Prize in physics was awarded for this.

    Where is a really cosmologist when you need one!
    Well they were in Stockholm, accepting the Nobel Prize for something you say you're not convinced of.
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    Quote Originally Posted by Jerryboy View Post
    When you say "The cosmological redshift data tells us that the universe was expanding at a decelerating pace for around 8 billion years, but around 5 billion years ago that deceleration turned into an acceleration, so more recently the expansion has been gaining pace again." On what data is this based on. Red shifts and Microwave shifts have not substantiated this idea which is not in evidence. On what assumptions is this based absent observational data? We don't know what the red shift data was at 8 billion years, we only know what it is now. The slice in time we see is millions and billions of years in the past. I am not a cosmologist, but you have not convinced me that we should assume continued cosmic acceleration. Try again. Where is a really cosmologist when you need one!
    Okay, well for a start, our cosmology is not based on redshift alone. We also need another piece of data in order to ascertain how distance relates to redshift. There are many ways to do this (research the "cosmic distance ladder"), but a simple example is to use the apparent brightness of a distant object.

    As distance increases, the light that reaches you from a given object will decrease by a certain amount. Imagine a star, or a galaxy, giving off light in all directions. Because the light propagates in all directions you can consider the sum total of all light emitted at a certain time in terms of a sphere whose radius increases with time, where the photons of light form the surface of that sphere. So as the propagating spherical wavefront gets further away from the source, all the photons on that "surface" get further apart from each other. So, the further away you are from the object, the less light will reach you, by an amount that conforms to the inverse square law.

    This is one method by which we can correlate redshifts to distance.

    With this information, we can make predictions for how distances will increase if the universe expands in different ways - if the expansion is decelerating, constant or accelerating, we will see a different relationship between redshift and luminosity across the range of distances.

    If we take the case of constant expansion, and predict what the redshift - luminosity relationship should be, and then we apply it to our observations of distant supernovae (of a type that always have the same intrinsic brightness), we find that those distant supernovae are dimmer than expected. This means they have receded more than would be the case if the universe is expanding at a constant rate, which means the rate of expansion must be accelerating.
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    this is confusing. you say it first slowed down, then sped up again. how you know it's been like this? what shows you that the expansion slowed down until 5 billion years ago?
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    Of course I know about the Ia super nova. And that is a corralate with distance which confirms the red shift. But you miss the point of the question. And no I don't doubt the expansion data or the big bang theory. But what you try to say is that the luminosity of Ia super nova compared to red shift data can provide information on current expansion all from data millions of years old? If the Ia super nova data does not agree with the red sift how does that at the same time confirm the distance and at the same likewise reflect its current actual recession rate millions of years in the future? All of the data from Micro wave, super nova, and red shift data is reaching us at the same time, but all of it millions, and in some cases billions of years old. On what theory or formula can future galactic recession be predicted or derived from current data? I hope it's not the same computers they are using for terrestrial climate change!
    Last edited by Jerryboy; March 31st, 2013 at 10:19 AM.
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    What shows it is the correlation between redshift, distance, and light-travel time, across the distance range.

    What redshift tells us is how much the universe has scaled up since that light was emitted. It is the apparent "stretching" of the wavelength of that light that indicates the change in the scale factor of the universe since that light was emitted.

    Then we need to know how long the light has been travelling for. This can be calculated from the apparent brightness of a distant object - how much the light has been dimmed depends on how long it has been travelling for, after calculating out the dimming due to expansion.

    Then we need to know how distant the object was when the light was emitted. This is found by looking for indicators of the apparent size of the object in question. How large something looks in the sky tells you how far away it was when the light left it, assuming you can estimate the absolute size of the object.

    When we take all that data and try to find the model that best fits it, we find the best fit is a universe that was initially decelerating due to the gravitational attraction between things slowing down the rate at which they recede from each other. But once everything is far enough apart for the gravitational attraction between things to be weak enough, there seems to be something causing the rate at which things separate to increase - we call this dark energy, as we don't know its nature.

    How we know this is by comparing the amount the universe has scaled up since a certain time, with how far away things were from each other at that time, and then doing the same calculation across the range of times since the Big-Bang.
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    Quote Originally Posted by Jerryboy View Post
    If the Ia super nova data does not agree with the red sift how does that at the same time confirm the distance and at the same likewise reflect its current actual recession rate millions of years in the future? All of the data from Micro wave, super nova, and red shift data is reaching us at the same time, but all of it millions, and in some cases billions of years old. On what theory or formula can future galactic recession be predicted or derived from current data? I hope it's not the same computers they are using for terrestrial climate change!
    It is not about the Type Ia SN data agreeing with the redshift, it is about quantifying the redshift to a spatial distance at a given time. And then we correlate the data across all distances and times.
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    I get all of this. But thank you for your thoughtful and nearly complete answers. But I am therefore right in saying that even though we have evidence that the expansion was slower in the past, we are assuming that it will accelerate into the future, even though a current data is exceedingly old. Past behavior based on current data is still billions of years old. But then our data still tells us little about future expansion except that the dark energy seems to be pushing it along. One more set of speculative questions...shouldn't there be a point where expansion itself will dilute even the propulsive effect of dark energy and the rate of acceleration would then slow down? Might it already have reached that point with the most distant objects, and we won't know for millions of years? Can we be certain that the affect of dark energy will continue acceleration no matter how large the universe is, and how spread out dark energy becomes?
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    Mistake!
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    Quote Originally Posted by Jerryboy View Post
    I get all of this. But thank you for your thoughtful and nearly complete answers. But I am therefore right in saying that even though we have evidence that the expansion was slower in the past, we are assuming that it will accelerate into the future, even though a current data is exceedingly old. Past behavior based on current data is still billions of years old.
    We measure cosmological redshifts for objects only 100 million light-years away. And we know the acceleration of the expansion started around 5 billion years ago. So we know the universe was undergoing accelerating expansion until relatively recently. The reason we cannot measure the expansion "now" is because we are within a gravity bound system, where local expansion is not measurable. Where we can theoretically measure the expansion starts beyond a certain distance, so the data will ALWAYS be old. Because redshift increases with distance, the local peculiar motions of galaxies preclude us from measuring a local rate of expansion.

    Quote Originally Posted by Jerryboy View Post
    But then our data still tells us little about future expansion except that the dark energy seems to be pushing it along. One more set of speculative questions...shouldn't there be a point where expansion itself will dilute even the propulsive effect of dark energy and the rate of acceleration would then slow down? Might it already have reached that point with the most distant objects, and we won't know for millions of years? Can we be certain that the affect of dark energy will continue acceleration no matter how large the universe is, and how spread out dark energy becomes?
    You are correct, in that we cannot tell whether the universe will continue to expand forever at an accelerating rate, or whether it will decelerate back towards a constant rate once the effects of dark energy are diluted. We need to be able to study the nature of dark energy over time in order to more accurately predict the end result of expansion.

    But we have measured the flatness of the universe, which means there will never be enough gravity to bring the expansion to a halt. It will expand forever, but the question is by how much?
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    so you have 2 galaxies of size x/distance x/redshift x, and the data shows light took 20000 years to get from galaxy A to galaxy B?
    and then you compare it with 2 other galaxies of the same size, being further away, and it shows light only took 15000 years to reach it? i.e. different stretch of wavelength for the older? galaxies?


    or that it took light, for example, 2 billion years to reach us for the galaxy being further away. and comparing it to a galaxy being closer, the light should have took only 1 billion years to reach us, but measurements show it's 1.3 billion years?
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    It's a bit more complicated than that, curious mind, but your second example is more representative of how it works.
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    Let me restate one more way: Do we know enough about Dark Energy to assume endless expansion or does the indicate the continued expansion of the universe and continuing acceleration, or does the law of squares of distance predict a diminishing application of force even by Dark Energy? Finally does the existence of Dark Matter further confound the final outcome of the universe.
    Last edited by Jerryboy; March 31st, 2013 at 01:12 PM.
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    Speed Freak,

    Finally, someone understood my question and my suspicions where as you explained, while we're pretty sure the universe will continue to expand, the variables of Dark Energy and Dark matter are not yet fully known, so the outcome of the universe is not going to a Big Crunch, but maybe a slower trend to an increasingly empty, cold, dark and wide universe where the stars and galaxies wink out one by one. I feel so much better. Thanks.
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    ok, that's the thing confusing me then.

    we, the blue galaxy, meassure the cmbr in every direction to be the same(red circle). so that's the furthest into past we are able to see, and space expanded slower then. but the same time it's said, that the further away the galaxy, the more expanded space there is.

    so now, if we see the light of a 6 billion ly old galaxy, it means space between that galaxy and us expanded more, while the galaxy is in a region where the expansion of space was slower a the same time?


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    Quote Originally Posted by curious mind View Post
    ok, that's the thing confusing me then.

    we, the blue galaxy, meassure the cmbr in every direction to be the same(red circle). so that's the furthest into past we are able to see, and space expanded slower then. but the same time it's said, that the further away the galaxy, the more expanded space there is.

    so now, if we see the light of a 6 billion ly old galaxy, it means space between that galaxy and us expanded more, while the galaxy is in a region where the expansion of space was slower a the same time?
    Let me try putting the situation slightly differently. Suppose we are looking at two galaxies, one called N that is nearer to us and one called F that is much further. Say the light we are seeing from N left N at tN and the light we are seeing from F left F at tF, both times being measured from the time of the big bang. Then tF < tN , since light had to leave the further galaxy earlier in order to get to us at the same time as the light we are seeing from the nearer galaxy. In that case, space was expanding at a slower rate at tF than it was at tN . However, there is much more space between us and F, so over a given time interval, the total amount of new space generated between us and F is larger than the amount of new space created between us and N. Hence F is going away from us faster and has a larger red-shift. It just doesn't have as large a red-shift as it would have had if the spatial expansion wasn't accelerating.
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    ok, so you meassure light travel time from cmbr to galaxy N and same for galaxy F, then from galaxy N and F to us? which should add up to 13.7 billion lys for each galaxy?

    but it doesn't, i.e. F = +300 mill ly and N = + 150 mill ly?
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    That total would always add up to 13.7 billion years (the age of the universe), but in terms of light-years it all depends whether we are considering where that object was when the light was emitted, which depends on how the universe scaled up previously, or where that object is "now" which depends on how much the universe has scaled up since that light was emitted.

    The important factors are the redshift, which indicates how much the universe has scaled up since the light we see was originally emitted, and the time that light took to reach us, which is subtracted from 13.7 billion years to give us the age of the universe at the time the light was emitted. Then we can look at angular diameter distance, which tells us how much the universe had scaled up previously.

    Then we compare all these factors for objects across the range of distances, to work out the history of the expansion.
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    i've read some more and as i understand it, it's change in redshift/wavelength? i.e. there are 2 supernovae at different distances, 1st maybe 500 mill lys and the 2nd 900 mill lys away. and due to 'The Chandrasekhar limit' it's safe to say that the redshift/wavelength of both to be equal.

    but what we observe is a change in redshift/wavelength from the 2nd white dwarf. and that's what shows us, that that light must have moved away further from the 1st supernova and us while it traveled through space to get to us? i.e. the light was emitted 800 mill ly ago, but it took another 100 mill lys to reach us due to expansion, and that difference of 100 mill lys can be calculated from the change in redshift/wavelength?
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    The redshifts would be different, due to the different distances involved, but the absolute luminosity would be the same, which is why we can use them as standard candles, by comparing their apparent luminosities (how dim they look to be) with their absolute luminosity (how bright they were in their own locale).
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    now i'm lost again. the super nova in a galaxy being further away, will always look dimmer than of one being closer to us. how that aproves for expansion? i mean, that star will turn into a white dwarf just once.
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    A more distant supernova will always be dimmer than a closer one, of course. But the question is to do with how much dimmer it would be, which depends on how much the universe has expanded since that light started its journey.
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    the dimness shows the distance of a galaxy, i got this. but i can't see how it shows expansion. the dimmer light of the galaxy being further away is simply because of more distance.

    But the question is to do with how much dimmer it would be, which depends on how much the universe has expanded since that light started its journey.
    when the light of that super nova reaches us, it is x distance away, means the light is x dimmer than if that super nova happened right in front of us. i'm not getting how it shows the expansion.

    ok,we observe star exploding - light is x dimmer = light is x distance away. the dimness shows the distance of the star at the moment it exploded ... my head hurts.
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    Quote Originally Posted by curious mind View Post
    the dimness shows the distance of a galaxy, i got this. but i can't see how it shows expansion. the dimmer light of the galaxy being further away is simply because of more distance.

    But the question is to do with how much dimmer it would be, which depends on how much the universe has expanded since that light started its journey.
    when the light of that super nova reaches us, it is x distance away, means the light is x dimmer than if that super nova happened right in front of us. i'm not getting how it shows the expansion.

    ok,we observe star exploding - light is x dimmer = light is x distance away. the dimness shows the distance of the star at the moment it exploded ... my head hurts.
    Actually you are almost there. One minor correction to this point: the intensity of the light drops off as 1/x2 , not as 1/x . Still by looking at the brightness, we know the distance d of the galaxy. From the speed of light and d, we know the time t = d / c that the light left the galaxy. From the red-shift, we know the velocity of the galaxy at that time, v(t) . Everything is measured in our frame, so there will be no corrections due to special relativity. There could be corrections due to general relativity, and I am going to assume that they are small.

    We now know v(t) at a number of different times. We graph these numbers and try to fit the graph with the form v(t) = v0 + a t . When we do this, a is not zero.

    I don't know enough to do the last part of the exercise, which is to verify that general relativistic effects due to the acceleration are small enough to ignore or else to take them into account. I'm satisfied that there would have been a general uproar if that process had not been done correctly.
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    I assume that the frequency of the light waves decrease due to the fact that light is a universal constant according to Einstein? Or am I over-complicating things. Obviously it is the doppler effect, but is it just a compressed light wave? And how does einstein come into all of this?
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    Quote Originally Posted by mvb View Post
    Quote Originally Posted by curious mind View Post
    the dimness shows the distance of a galaxy, i got this. but i can't see how it shows expansion. the dimmer light of the galaxy being further away is simply because of more distance.

    But the question is to do with how much dimmer it would be, which depends on how much the universe has expanded since that light started its journey.
    when the light of that super nova reaches us, it is x distance away, means the light is x dimmer than if that super nova happened right in front of us. i'm not getting how it shows the expansion.

    ok,we observe star exploding - light is x dimmer = light is x distance away. the dimness shows the distance of the star at the moment it exploded ... my head hurts.
    Actually you are almost there. One minor correction to this point: the intensity of the light drops off as 1/x2 , not as 1/x . Still by looking at the brightness, we know the distance d of the galaxy. From the speed of light and d, we know the time t = d / c that the light left the galaxy. From the red-shift, we know the velocity of the galaxy at that time, v(t) . Everything is measured in our frame, so there will be no corrections due to special relativity. There could be corrections due to general relativity, and I am going to assume that they are small.

    We now know v(t) at a number of different times. We graph these numbers and try to fit the graph with the form v(t) = v0 + a t . When we do this, a is not zero.

    I don't know enough to do the last part of the exercise, which is to verify that general relativistic effects due to the acceleration are small enough to ignore or else to take them into account. I'm satisfied that there would have been a general uproar if that process had not been done correctly.

    so redshift has to be accounted for, as i said before, and not just dimness? also what does 1/x^2 stand for? 1 = brightness when right in front of you, and /x^2 distance = dimness? how would that look for a super nova?
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  41. #40  
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    Quote Originally Posted by curious mind View Post


    so redshift has to be accounted for, as i said before, and not just dimness? also what does 1/x^2 stand for? 1 = brightness when right in front of you, and /x^2 distance = dimness? how would that look for a super nova?
    Yes, you must know the redshift to know the speed of the galaxy. If the expansion of the universe is not at a constant rate, however, you obviously can't get distance by assuming it is proportional to redshift. You need to have the observed brightness of an object whose intrinsic brightness is known. That brightness must be measured using the emission over a set of wavelengths that are corrected for the redshift, so that, for each object, they correspond to the same set of emissions at the object.

    The 1/x2 is the form of the decrease of apparent brightness with distance. To be specific, if the standard distance for assessing the brightness of an object is x0 and the measurement at that distance is B0 , the measured brightness at a distance x is given by B = B0 (x0/x)2 . This formula is universal and does apply to supernovae as well. The point of using supernovae is that their standard brightness is much greater than any other object whose standard brightness is known.
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    i googled around and found this formular
    d = 10^{(mv-Mv+5)/5}

    and also read that a type 1 super nova always blows off at a peak brightness of -19, that's why it's used as a standard candle for reallyyyyy large distances, i used it with different numbers.

    first i did this
    d = 10^{(-19-(-19)+5)/5}

    d = 10^1

    d = 10p x 3.26

    d = 32.6 lys away

    that means when i measure the observed brightness to be = peak brightness (-19) that star is 32.6 lys away, right?

    then i just plugged in a positive number around the same amount, to have a dimmer observed brightness and, WOW, got this

    d = 10^{(18-(-19)+5)/5}

    d = 10^8.4

    d = 251188643.2p x 3.26

    d = 818874976.7 lys away

    and this

    d = 10^{(22-(-19)+5)/5}

    d = 10^9.2

    d = 1584893192.5p x 3.26

    d = 5166751807.4 lys away

    if i done it correct, and this really shows the distance compared to observed brightness, can (or better yet, how can) i calculate the redshift/expansion between those results, or to see an accelerating universe?

    i'll have to google that B = B0 (x0/x)2 formula later, or can i use the above calculation with it?
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    Quote Originally Posted by curious mind View Post

    if i done it correct, and this really shows the distance compared to observed brightness, can (or better yet, how can) i calculate the redshift/expansion between those results, or to see an accelerating universe?

    i'll have to google that B = B0 (x0/x)2 formula later, or can i use the above calculation with it?
    The formula you have found involves the astronomical system for representing the brightness of an object. It uses a logarithmic expression for brightness in terms of the total energy contained in the light. My expressions used the total energy itself. You can use the formula you have found to get the distance directly, so it is an alternative formula to what you would find by manipulating mine. It will be more convenient for calculations, since most data you will find will be given in astronomical magnitudes.

    The red-shift is a separate measurement and cannot be gotten from any of these formulae. There should be values tabulated somewhere, but I haven't hunted for them. You will also need some details on the "z-value."
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    why is it said that there's an acceleration in the expansion? if it is like this:

    A B C D -> z

    to this:

    A . B . C . D -> . Z

    to this:

    A . . B . . C . . D -> . . Z

    the it expands at a constant velocity. and if everything moves away from everything at the same rate, sounds like it is an outward expansion (spherical).

    wouldn't an accelerating expansion be more like:

    A B C D

    A . B . C . . D

    A . . B . . C . . . D?
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    Quote Originally Posted by curious mind View Post
    why is it said that there's an acceleration in the expansion? if it is like this:

    A B C D -> z

    to this:

    A . B . C . D -> . Z

    to this:

    A . . B . . C . . D -> . . Z

    the it expands at a constant velocity. and if everything moves away from everything at the same rate, sounds like it is an outward expansion (spherical).

    wouldn't an accelerating expansion be more like:

    A B C D

    A . B . C . . D

    A . . B . . C . . . D?
    That looks to me like a nonhomogeneous expansion, with a different rate at different locations. What we have is something like

    t=0: A.B.C.D
    t=1: A..B..C..D
    t=2: A....B....C....D
    ...

    with time moving in equal steps vertically and the expansion being greater per time step as time increases.
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    but the factor is always the same, i.e 1 dot of distance in x time 10 metres diagonal in 10 seconds, 20 metres in 20 seconds. where's the acceleration in this?
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    I don't think that we are understanding each other's diagrams. Let me try this a different way. I'll put up objects a, b, c ... at the same distance apart at t=0:

    x(a, t=0) = 0
    x(b, t=0) = 10
    x(c, t=0) = 20

    Then one time step later, have them move apart uniformly:

    x(a, t=1) = 0
    x(b, t=1) = 20
    x(c, t=1) = 40

    so that what was a difference of 10 units between each is now a difference of 20 units. I want the expansion of space be the same everywhere, so the increase in distance between each adjacent pair of points is the same. Now one time step more:

    x(a, t=2) = 0
    x(b, t=2) = 35
    x(c, t=2) = 70

    The intervals are still uniform in space, but each interval has progressed over time from 10 to 20 to 35. In other words the increase over the first time interval was 10 and over the second was 15, or 50% more. The intervals are accelerating in size with time, but each one is accelerating in the same way.

    It may be worth noting that the distance from a to c remains twice the distance from a to b throughout the process, which requires c to be moving twice as fast as seen from a as b is moving seen from a.
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    that diagram would actually prove deccelerating rather, to make it constant it should be:

    x(a, t=2) = 0
    x(b, t=2) = 40
    x(c, t=2) = 80
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    Quote Originally Posted by curious mind View Post
    that diagram would actually prove deccelerating rather, to make it constant it should be:

    x(a, t=2) = 0
    x(b, t=2) = 40
    x(c, t=2) = 80
    I don't think my set at t=2 would indicate deceleration, but let's see. My sets were

    x(a, t=0) = 0
    x(b, t=0) = 10
    x(c, t=0) = 20

    x(a, t=1) = 0
    x(b, t=1) = 20
    x(c, t=1) = 40

    x(a, t=2) = 0
    x(b, t=2) = 35
    x(c, t=2) = 70

    Choosing the velocity of b to examine, the average velocity between t=0 and t=1 is
    [x(b,t=1) - x(b,t=0)] / [1 - 0], the denominator being the time difference. Thus v= [20-10]/1 = 10 units/sec. Between t=2 and t=1 we get
    [x(b,t=2) - x(b,t=1] / [2 - 1] = [35-20]/1 = 15 units/sec

    So the average velocity has increased from the first interval to the second. You could get similar results for body c.

    As a technical point, I put body "a" at x=0 in all three cases so that the other positions were given in a's inertial frame. This way I have forced va = 0.

    Edit: I think I see now how I was confusing things. I am correcting the times for propagation time of the light coming to "a" from "b" and "c," so that I have positions and times in a single reference frame. In getting the expansion velocities and accelerations, the observations will be in terms of the arrival time of the light at our eyes; this will have to be corrected back to position and time when the light left the object when handling the data. The correction may be a bit complicated to do in that direction.
    Last edited by mvb; April 3rd, 2013 at 09:52 PM.
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    why 2 -1?
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    Quote Originally Posted by curious mind View Post
    why is it said that there's an acceleration in the expansion? if it is like this:

    A B C D -> z

    to this:

    A . B . C . D -> . Z

    to this:

    A . . B . . C . . D -> . . Z

    the it expands at a constant velocity. and if everything moves away from everything at the same rate, sounds like it is an outward expansion (spherical).
    You are correct. That is expansion with a constant scale factor; no acceleration. That is what was thought to be happening until the acceleration was discovered (actually it was generally thought to be decelerating).

    To model accelerating expansion you would need to add 1 dot between every letter in the first step then 1.1 dots in the second step, then 1.2 dots in the third step, etc. In this way the rate of increase in distance between any two points (their apparent velocity) will increase over time.
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    Quote Originally Posted by curious mind View Post
    why 2 -1?
    It comes from t2 - t1 = 2 - 1. I am calculating v = [x(t=2) - x(t=1)] /[ t2 - t1] . Sorry I left that out, the original was several posts back and not so easy to recall at this point.
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