Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: neilep on 29/09/2023 13:47:39
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Hello,
I'm Sheepy how are ewe ? Don't forget, the Earth is flat, men are women and my cat is a pineapple . Thank ewe.
I am probably completely missing the point here (as I do).....but how can we tell the Universe is 13.8B ? if all we can see is the observable with no idea (or is there?) how big the unobservable is, then how can we determine with such relative assurance how old the Uni is ?
As a firm believer in empirical study I went asked Uni.......
(https://lh3.googleusercontent.com/pw/ADCreHftuL3z_DrslVLb8_DjkdAXGj3r1mEna5fvZc_3G4x6PJfMl3Rw5z3P3N5AjneqBMttjmzGHRkmxqhGcQ87NYJGULK5NtoSkMLHcwyaSjN2ZGPIzDQY=w2400)
Me literally asking how old Uni is just moments ago in this non-doctored, bona-fide, 1-1 scale photo.
so, no luck there !!
whajafink ?
HOW CAN WE TELL THE AGE OF THE UNI IF ALL WE CAN SEE IS THE OBSERVABLE ?
Thank ewe
Hugs
Neil
Questioner to a Patois speaking Universe
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I am probably completely missing the point here (as I do).....but how can we tell the Universe is 13.8B ?
Not sure what this 'the observable' is, but the age is determined by looking at distant things like galaxies. The simplest way to do it is to measure the Hubble 'constant'. The further away something is, the faster it appears to be receding. So we've managed to measure the recession rate per megaparsec of distance and it comes to around 70 m/sec/mpc, which, if you cancel like units, is almost exactly 1/1.38 billion years
That assumes constant expansion, so the actual figure takes varying expansion into account, but our current expansion rate is nearly the average over that time.
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I am probably completely missing the point here (as I do).....but how can we tell the Universe is 13.8B ?
Not sure what this 'the observable' is, but the age is determined by looking at distant things like galaxies. The simplest way to do it is to measure the Hubble 'constant'. The further away something is, the faster it appears to be receding. So we've managed to measure the recession rate per megaparsec of distance and it comes to around 70 m/sec/mpc, which, if you cancel like units, is almost exactly 1/1.38 billion years
That assumes constant expansion, so the actual figure takes varying expansion into account, but our current expansion rate is nearly the average over that time.
Thank ewe Halc. From what I understand the Observable Universe is 93 billion light years. It is often said that we have no idea how big the unobservable is because we shall never see it due to the expansion speed being faster than C. So, my instinct then is to ask is how can we tell how old the universe is if all we have is the observable universe to deduce from ?
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From what I understand the Observable Universe is 93 billion light years.
93 G light years in diameter. That's a distance, not an age.
Half that (the radius) is the current distance to the furthest piece of matter/energy that could possibly ever have had a causal influence on us. If ewe were to emit a light pulse at our location in space, I think right as the inflation epoch ended (implausible since the universe wasn't transparent back then, so a light pulse would get anywhere), 46 Gly is how far away that light pulse would be now.
It is often said that we have no idea how big the unobservable is because we shall never see it due to the expansion speed being faster than C.
And that would be something often misstated.
The expansion is faster than C at the Hubble radius, only about 14 BLY away. We see all kinds of stuff that is currently further away than that. The CMB is probably the furthest at about perhaps 45 BLY distant in all directions. Anything further away than that needs to use something other than light to measure, like say gravitational waves or something, and they've yet to invent a GW telescope.
So, my instinct then is to ask is how can we tell how old the universe is if all we have is the observable universe to deduce from ?
Again, simple answer: by noting Hubble's constant, which is the inverse of that age.
Before Hubble's time when it was discovered that galaxies are receding, and at a rate proportional to their distance from us, there was no concept of the universe having a finite age. After the discovery, the age was pretty much known, but there was still no estimate for the size of the observable universe, which isn't a function of its age, but rather of the rate at which expansion is changing, something which wasn't measured until far more recently.
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Usual problem of ambiguity about "the universe". For all practical purposes, it means the observable universe. Only human vanity would presume that there is nothing else, so it is entirely reasonable to assume that there is more in the "entire" universe that we can't observe, and therefore cannot meaningfully ascribe any properties such as age. How old is the unobservable fairy who may or may not be standing behind me? Since it is unobservable, it cannot affect me and its age doesn't matter.
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Usual problem of ambiguity about "the universe". For all practical purposes, it means the observable universe. Only human vanity would presume that there is nothing else, so it is entirely reasonable to assume that there is more in the "entire" universe that we can't observe, and therefore cannot meaningfully ascribe any properties such as age. How old is the unobservable fairy who may or may not be standing behind me? Since it is unobservable, it cannot affect me and its age doesn't matter.
Is it possible to hypothesize that that part of the universe that we cannot observe but yet believe exists was in the past concentrated in a small region that we can now observe (the Cosmic Background Radiation)?
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Hi.
This seems similar to a question you ( @neilep ) posted not too long ago.
https://www.thenakedscientists.com/forum/index.php?topic=86145.0
There may be some fine differences but I'm not too sure what they are. If you're just looking for fresh answers it's possible to add a new post to the end of that thread - that will automatically push the thread to the top of the pile (the newest). I don't think any moderators would mind provided this sort of "bumping up" isn't done too often (and isn't to promote some product you sell or an idea of your own).
In the old thread, @Halc already discussed the method using expansion and the Hubble parameter. @Eternal Student discussed an alternative that is determining the age of stars. I still think those are the two main methods.
For further interest @evan_au presented one issue that doesn't seem to fit well: Some galaxies seem too big and well developed - our models don't suggest they would have developed in 13.8 bn years. There is also an issue just about black holes (the usual Galactic Nucleii) - some of these seem too big to have developed through mergers and acquiring other material in just 13.8 bn years. The size of black holes is something we're now getting a lot of data on from gravitational wave astronomy such as that done at the LIGO site. So, if you want to be controversial, there is some evidence that the universe may be older than 13.8 bn years BUT it's also quite possible that our understanding of how black holes and galaxies develop just needs a bit of adjustment.
Best Wishes.
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Hi.
This seems similar to a question you ( @neilep ) posted not too long ago.
https://www.thenakedscientists.com/forum/index.php?topic=86145.0 (https://www.thenakedscientists.com/forum/index.php?topic=86145.0)
There may be some fine differences but I'm not too sure what they are. If you're just looking for fresh answers it's possible to add a new post to the end of that thread - that will automatically push the thread to the top of the pile (the newest). I don't think any moderators would mind provided this sort of "bumping up" isn't done too often (and isn't to promote some product you sell or an idea of your own).
In the old thread, @Halc already discussed the method using expansion and the Hubble parameter. @Eternal Student discussed an alternative that is determining the age of stars. I still think those are the two main methods.
For further interest @evan_au presented one issue that doesn't seem to fit well: Some galaxies seem too big and well developed - our models don't suggest they would have developed in 13.8 bn years. There is also an issue just about black holes (the usual Galactic Nucleii) - some of these seem too big to have developed through mergers and acquiring other material in just 13.8 bn years. The size of black holes is something we're now getting a lot of data on from gravitational wave astronomy such as that done at the LIGO site. So, if you want to be controversial, there is some evidence that the universe may be older than 13.8 bn years BUT it's also quite possible that our understanding of how black holes and galaxies develop just needs a bit of adjustment.
Best Wishes.
OOPS !!..sorry about that. I didn't realise I already posted the same question. I hope I have not upset the mods ;) ;)
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Thanks to all participants.
So, I figure it's the Observable Universe that is 13.8 Billion years old.
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Yes neilep, you are in the sheep droppings now!
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Hi.
So, I figure it's the Observable Universe that is 13.8 Billion years old.
Like all things there is some yes and no here. It's more no than anything.
If this: The whole universe obeys the same laws of physics as the observable universe.
Then this: The whole Universe is 13.8 bn years old.
Why? @Halc 's idea is the main idea here. General Relativity (GR) seems to be a fairly good model, it has withstood several tests. Provided that model is right, we do not need to be able to see the whole universe. The expansion that we can see around us is sufficient. The only reasonable explanation is that there was a singularity at time t=0 (where all matter, indeed all things, had indistinguishable spatial co-ordinates, or to para-phrase this greatly everything was squashed up all at the same place). We can adjust the parameters of the model (how much matter, radiation, dark energy etc.) and try to get the best match to what we observe now. It turns out we seem to need a certain proportion of these things but more importantly it turns out that with this blend of stuff, 13.8 bn years of time must have elapsed for the expansion to look like it does at the moment.
Similar arguments could be made for estimating the age of the universe by estimating the age of stars. In this situation though it becomes much more important that we assume we (planet earth) are NOT located in an atypical region of space. If, by chance, we were located in a region of unusually young stars (I don't mean just a small pocket of space - I mean an unusual region that stretched out over the entire span of distance we can observe with our telescopes) then, admittedly, the age of the stars in thiis region would not be a good estimate of the age of the universe.
However, when the IF criteria is not met, i.e. if the entire universe does not follow the same laws of physics as our local region, then we just don't know. Someone has already mentioned string theory and the possibility that there are other regions (other universes really) that may have different laws. Keeping it simple and avoiding too much philosophy, let's just say that we will use the term "universe" to describe all that which does follow the laws of physics we have in our local region, anything with different laws is not in our universe. That just makes it easier to finish with a definitive answer. Since we have specifically excluded anything that doesn't follow our laws of physics, the IF criteria is automatically met, the whole universe follows our laws, so we can conclude that the whole universe is approx 13.8 bn years old and we only needed to match the models of GR and cosmology to the bit of space and expansion that we can see in order to deduce that.
I hope that helps.
Best Wishes.
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General Relativity (GR) seems to be a fairly good model, it has withstood several tests. Provided that model is right, we do not need to be able to see the whole universe.
Well, if we're going to go strictly by what relativity says, it posits the entirety of 4D spacetime as 'the universe', and therefore it has no meaningful age at all. What we have is the temporal distance between the spacetime event of the existence of humanity and the spacetime event of the big bang, as expressed by Earth's frame. That's not the age of the universe, it's just the time coordinate of humanity in that frame. For the universe to have an actual age, it would need to be contained by time (presentism), and that's quite a different theory than what relativity says.
As for the 'Earth's frame' bit, one can make the 'current' time as large as you want by picking a different frame. That lets relativity of simultaneity work for you. So say you want to compute the current age of the universe relative to the (inertialish) frame of some galaxy relative to which our galaxy is moving away at say .97c. In that frame, our clocks are dilated by a factor of 4, so the event on that far galaxy simultaneous with humanity here is somewhere around 55 billion years since the big bang.
There are also ways to make 'the age' lower by choosing yet different frames.
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That sure is an interesting concept, Halc. Not saying I understand completely but it sure has stimulated these old neurons-thanks.
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A quick question, Halc: taking your example of a time dilation factor of 4, suppose our galaxy was receding slightly faster, say 1.03c, what becomes of the Lorentz factor? It will now be a complex number. Does this feed through to a complex age?
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A quick question, Halc: taking your example of a time dilation factor of 4, suppose our galaxy was receding slightly faster, say 1.03c, what becomes of the Lorentz factor? It will now be a complex number. Does this feed through to a complex age?
The recession rate of 0.97c was relative to the 'inertialish' frame of the distant place. Under such a frame, recession rates cannot exceed c. The recession rates you see published are rates of increase of proper distance over time, not speeds. They're relative to an expanding frame, and in such frames, recession rates are rapidities, not speeds. (see bottom of post for example) Celerity adds the regular way and has no upper bound. If, relative to this expanding frame, galaxy X is receding from us at .8c and Y (at twice the distance) is receding from X at 0.8c, then Y would be receding from us at 1.6c. The speeds don't add the relativistic way that they do in inertial frames.
Few of the typical rules of physics apply in such a non-inertial frame. Neither energy nor momentum is conserved. Moving objects tend to come to rest. The wavelength of a light pulse grows over time, the energy going down with it. Light does not travel at c except locally.
Relativity of simultaneity still applies, hence if one is considering the 'current age' of the entire universe of points in space well outside our visible universe, given the right choice of frame, one can make, at that distant location, any point in time be simultaneous with us at Earth, hence the distant parts of the universe having no defined age. So they define a preferred frame, which is the frame in which all events on comoving worldlines at similar gravitational potential as us, are simultaneous with each other. This is known as the frame of constant cosmological time (or just cosmological frame), and it is not an inertial one.
Apologies if that got a little complex. I did several edits trying to make it simpler/more clear.
An example of celerity. There is a highway to the next galaxy with little signs every light year like mile posts. In my fast ship, I can measure my celerity by the rate at which they go by. One sign per year is a celerity of c. If I accelerate more, I can see one go by every day, and hence I can cross to the next galaxy before I die with a fast enough ship. The ship is moving at a speed of under c, but a celerity of 365c in this case (not yet fast enough to get to the next galaxy in a lifetime)
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Thanks, Halc, I got all that completely. I was aware of the rapidity/speed effect but asked my question without analysing the scenario rigorously, mea culpa.
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Hi.
I started writing this after post #11 but it got too long and too late so I left it and went to bed. Since then @paul cotter has shown some interest and @Halc has written more. This is hasty re-editing of the reply I was going make but it now seems even more neccessary to say it because I think you ( @Halc ) are at risk of confusing some readers.
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It's always a pleasure to hear from you, @Halc. I'm also fairly sure you won't be too offended if I oppose some of your comments. It's a discussion and I wouldn't bother to spend the time making this argument if I didn't think you would be able to appreciate it.
Well, if we're going to go strictly by what relativity says, it posits the entirety of 4D spacetime as 'the universe', and therefore it has no meaningful age at all.
Yes, that's OK. However, let's not get too hung up on whether we adopt the view of presentism or of a block universe (or something else). The phrasing I used was just more like natural English language and that does tend to utilise a tacit assumption of presentism.
We (Astronomers / Scientists) do impose some common understanding on what we mean by the age of universe. We understand that the 13.8 bn years refers to the use of co-moving co-ordinates. Specifically, the 13.8 billion years is the proper time interval that would be recorded on a planet that remains (or past tense: remained, maybe but I'm trying to avoid implying presentism) at constant (co-moving) spatial co-ordinates while the sclae factor evolves (the universe expands). To paraphrase that, the planet stays still in as much as it possible for anything to stay still in an expanding universe.
One advantage of this understanding is that no planet (or anything) in the universe would find that more than 13.8 bn years of their proper time had elapsed since the big bang. The Robertson-Walker metric (which is what is used in main-stream Cosmology) has the form
dT2 = dt2 - a(t) ds2
with dT being a proper time interval (a differential) while dt and ds are co-ordinate time and space differentials respectively. a(t) is the scale factor (which is some function of co-ordinate time).
The important point is that a co-ordinate space interval is SUBTRACTED from the co-ordinate time interval, much as in flat Minkowski space.
So, if an object follows a path where the spatial co-ordinates vary with t, then something is subtracted from the change in time co-ordinate. To say this another way, it's just like the travelling twins paradox of SR. The longest proper time path between Event A (say the big bang) and Event B (say the planet being at a given position, s0 and at co-ordinate time, t0), will be obtained when that planet had just stayed as still as possible - it must have 0 peculiar velocity relative to the given co-ordinates s,t that appear in the metric. Those co-ordinates are often called co-moving co-ordinates and it's common enough to say that the the planet must be "co-moving with the expansion of space" to obtain this maximal amount of elapsed proper time since the big bang. For an expanding universe, being co-moving is the equivalent of being the "stationary" twin in the twin paradox. A planet that had a non-zero peculiar velocity relative to the co-moving co-ordinates and arrived at the same event (the given position s0 and time t0) would have experienced LESS proper time since the big bang. Such a moving planet is like the twin who did the travelling in the twin paradox, their path through spacetime was different and it had a shorter proper time length.
We don't need to know exactly where we are right now in the co-moving co-ordinates. We are at some event that we can write as (s0, t0) in those co-ordinates. However we do know something about when we are in those co-moving co-ordinates. The cosmological model implies that t0 = 13.8 bn years. It has to be this value (with a conventional understanding of a "year" as a measure of time) for the current expansion rate or Hubble constant to be what we do observe as we look out into space. (Given the cosmological model we do have that is based on GR and especially the Robertson-Walker metric and the Friedmann equations etc.)
If you take the presentism view of things then you would paraphrase that and say that we know that 13.8 bn years of the co-moving co-ordinate time have elapsed since the big bang. (But that's optional, you can assume a block universe or something else if you wish, all we need to agree on is that we are at an event we will write as (s0, t0) in the co-moving co-ordinates). We know that the proper elapsed time along the path taken from big bang to (s0, t0) cannot be more than 13.8 bn years. If we have some peculiar velocity through the universe then our elapsed proper time since the big bang could be less than 13.8 bn years BUT, for certain, it cannot be more. The way you ( @Halc ) have phrased things it looks as if the age of the universe is quite arbitrary and frame dependant but it is not like that, we can make a much more objective statement.
That's not the age of the universe, it's just the time coordinate of humanity in that frame.
We can make an objective, frame independent statement about the maximum proper time that could have elapsed between the big bang and the event where I find myself while I am writing this forum post. That maximum elapsed proper time is 13.8 bn years. It does not matter if you are a human being living on planet earth or a space alien whizzing through space at great speed in a starship who just passed by planet earth while I was writing this forum post. Any being that finds themselves at the event (s0, t0) - which I'll say is at planet earth and at a time the presentism-ists would call "now" will agree that the maximum elapsed proper time from the big bang event to this event (s0, t0) for everyone is 13.8 bn years regardless of the motion or path they may have taken through spacetime to get there.
If we lapse into more informal English Language which does tend to be more aligned with a presentism view of things, then we can just say that every being who finds themselves at (s0, t0) agrees on the maximum age of the universe.
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That's already getting too long, let's just move on to look at one example you mentioned about frame dependance...
As for the 'Earth's frame' bit, one can make the 'current' time as large as you want by picking a different frame. That lets relativity of simultaneity work for you.
No, not quite. For a start there are no global (or universe wide) inertial frames of reference in an expanding universe - nothing that satisfies the conventional criteria of being an inertial frame for Special Relativity. In GR with the Roberston-Walker metric there are only going to be Local Inertial Frames, they are local in spatial terms but also local in the range of time over which they remain valid. None the less we do often approximate the situation and I'll assume that is what you have done. What I have concerns with is that 13.8 bn years is not a small amount of time, it's the entire lifetime of the universe, it is certainly not keeping anything to a local region in the time co-ordinate. As such using SR as an approximation is probably little better than wild speculation.
More generally, I feel sure that the readers could easily be confused by some of your comments. They aren't necessarily wrong, just easily mis-understood - but time is short and this is too long, so let's just look at one statement that is more easily identified as being wrong than right.
So say you want to compute the current age of the universe relative to the (inertialish) frame of some galaxy relative to which our galaxy is moving away at say .97c. In that frame, our clocks are dilated by a factor of 4, so the event on that far galaxy simultaneous with humanity here is somewhere around 55 billion years since the big bang.
I'm sorry but you have trimmed too many corners here and ended up with a statement that is just wrong even in SR. Time dialtion on its own is not the master of disagreements in what would be said to be happening now or simultaneously across the universe.
Consider a frame S and another frame S' which is a standard Lorentz boost from frame S. Specifically assume the origin (s, t) = (0,0) in frame S and the origin (s',t') =(0, 0) coincide at time t=0 (or at t'=0 if you prefer) but frame S' just has some velocity v relative to S. Now it does not matter what that velocity v is and hence what the time dilation factor of frame S relative to S' might be, the origins of the two spacetime frames (s, t) = (0, 0) and (s', t') = (0,0) just do coincide. The appropriate Lorentz transformation takes (s,t) = (0,0) in S ----> (s', t') = (0,0) in S'. So that event will lie along a line of simultaneity for "my time = 0" that a person would draw across a spacetime diagram regardless of whether they are at rest w.r.t. frame S or frame S'. To say this another way, both observers agree that the event (0,0) is happening at "my time =0" or what they might call "now". You can change the value of v, the offset velocity and have a time dilation factor as large as you like and repeat the calculation, it isn't going to matter because there was no physical spatial distance between the origins at time t=0 (or time t'=0).
This is the essence of what is often called "the Andromeda paradox" in SR. It is not the time dilation factor on its own that determines the discrepency in which events in the universe are considered to be happening "now", it is a combination of the time dilation AND ALSO the distance between the two observers that matters. So, in the case of the Andromeda paradox, a human being on earth can make the invasion force from Andromeda have departed 1 week ago or not having been sent yet just by walking slowly in one direction or the other on planet earth. They are walking slowly, the time dilation factor is not important, however the distance between Earth and Andromeda is large. Now, as it happens, Andromeda is moving towards the Milky Way. If it turned out that the Andromedons were only going to invade Earth when Andromeda was in the same place as planet Earth, then the Andromedon paradox stops working. A human being can walk (or run as fast as possible) in one direction or the other on planet earth but it will not change the invasion launch from being in what they consider as the future or the past.
Summary
"The age of the universe" is not arbitrary and changed just by boosting to another frame. We have a very specific understanding of what is meant by the age of the universe and we can make a powerful and objective statement:
We are at co-moving co-ordinate event (s0, t0 ) and we know that t0 = 13.8 bn years. You do not need to assume that this co-moving co-ordinate system is especially important or a way of describing the universe that is more truthful than some other co-ordinate system. However, we can assert that the maximum proper time that could have elapsed (on the path we have taken) since the big bang event is 13.8 bn years. If we have had some peculiar velocity through space then the proper time elapsed since the big bang could be less than 13.8 bn years but it cannot be more.
Best Wishes.
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Hi, ES, you have now gone way over my head with your last post but I do find it fascinating nonetheless. I am not familiar with the Robertson Walker metric but I have heard of it. Although interested in all science, cosmology would be my weakest. I look forward eagerly to further developments.
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It's always a pleasure to hear from you, @Halc. I'm also fairly sure you won't be too offended if I oppose some of your comments.
I cried myself to sleep after first reading all this, it broke my heart so much...
Actually, you've been away and it's good to see you back ES. Hope you also are not offended by my defending my posts.
The phrasing I used was just more like natural English language and that does tend to utilise a tacit assumption of presentism.
Well, yes, we all know what is being asked when asking the current age of the universe. My initial responses replied to that, and only your mention of relativity theory did I balk since it isn't a presentist model.
The Robertson-Walker metric (which is what is used in main-stream Cosmology) has the form
dT2 = dt2 - a(t) ds2
with dT being a proper time interval (a differential) while dt and ds are co-ordinate time and space differentials respectively. a(t) is the scale factor (which is some function of co-ordinate time).
Your answer (the entire post) concentrates very heavily on dT (which indeed has a sort of maximum of 13.8 ) where I was more concentrating on dt (coordinate time), which can be almost anything. I did say coordinate time:That's not the age of the universe, it's just the time coordinate of humanity in that [or some other] frame.
So, if an object follows a path where the spatial co-ordinates vary with t, then something is subtracted from the change in time co-ordinate.
Totally agreeing and I didn't say otherwise. I never said a clock traveling by any path from BB to Earth now would read anything greater than 13.8 BY. I said something else.
The way you have phrased things it looks as if the age of the universe is quite arbitrary and frame dependant but it is not like that, we can make a much more objective statement.
I said that one could take a very remote event whose proper time is say 100 BY and if sufficiently distant, would be space-like separated from us here and now, and thus, given the right choice of frame, our event would be simultaneous with that distant one that at which an age of 100 BY was measured. That's not a proper time of us here, but rather a coordinate time of us here, and one that is considerably larger than 13.8
For a start there are no global (or universe wide) inertial frames of reference in an expanding universe
I carefully avoided a suggestion that there was. The frame in which humanity is in a universe that is 100 BY old is not an inertial one, just some weird asymmetrical frame which puts us simultaneous with some event where there's a clock that has logged a lot more than 14 BY. I also made no reference to SR since SR does not apply to a universe with energy, making it inappropriate to ask a question like what our current coordinate time is.
I know I referenced the sort of frame that is rarely referenced, one which has no neat clean rules and one in which Earth is not at the center, both horrible sins when discussing where we are in the large scope of things. As such, I agree that some readers can become confused by my comments.
I'm sorry but you have trimmed too many corners here and ended up with a statement that is just wrong even in SR.
Again, I am not using SR when making such statements. I did say 'inertialish', but only to mean I've chosen a coordinate system where Earth moves at .97c, at least on average, and thus our clocks are dilated relative to my chosen frame.
Time dialtion on its own is not the master of disagreements in what would be said to be happening now or simultaneously across the universe.
Not sure what you mean by this. Dilation is a coordinate effect, an abstraction. I've chosen such an abstraction such that our event than that of some distant observer measuring an age of 100 BY are simultaneous. Is that so difficult to accept? They're space-like separated events, not time-like, so it should be valid to do this.
Consider a frame S and another frame S' which is a standard Lorentz boost from frame S.
I think 'Lorentz boost' sounds like something that only applies to inertial frames. I don't think it is meaningful to express the speed of my S' in relation to some other non-inertial frame in which Earth is close to stationary.
Specifically assume the origin (s, t) = (0,0) in frame S and the origin (s',t') =(0, 0) coincide at time t=0 (or at t'=0 if you prefer) but frame S' just has some velocity v relative to S. Now it does not matter what that velocity v is and hence what the time dilation factor of frame S relative to S' might be, the origins of the two spacetime frames (s, t) = (0, 0) and (s', t') = (0,0) just do coincide. The appropriate Lorentz transformation takes (s,t) = (0,0) in S ----> (s', t') = (0,0) in S'. So that event will lie along a line of simultaneity for "my time = 0" that a person would draw across a spacetime diagram regardless of whether they are at rest w.r.t. frame S or frame S'. To say this another way, both observers agree that the event (0,0) is happening at "my time =0" or what they might call "now".
Both observer being at the origin, sure. Remember that I put my origin a great distance away, so we're not talking about Earth observers here, just some Earth clock that reads 13.8
This is the essence of what is often called "the Andromeda paradox" in SR. It is not the time dilation factor on its own that determines the discrepency in which events in the universe are considered to be happening "now", it is a combination of the time dilation AND ALSO the distance between the two observers that matters.
I don't think there are observers in the Andromeda paradox because nothing is observed. It is all about what time it is over there relative to some event here. Sure, it is often anchord by a pair of strongly opinionated people passing by each other, but they are totally optional since a frame doesn't require an observer. It's just an abstract method to assigned coordinates to events. The frame I selected assigned time coordinate 100 BY to the event of humanity's existence. Whether there's an observer on that distant planet (or planet there at all) is irrelevant. I selected that distant event as my origin since it, like any other event, is a valid part of the universe.
So, in the case of the Andromeda paradox, a human being on earth can make the invasion force from Andromeda have departed 1 week ago or not having been sent yet just by walking slowly in one direction or the other on planet earth.
That makes it sound causal instead of abstract. Him walking this way or that has no effect at all. It is his abstract choice of frame that puts the departure moment at an abstract time coordinate that higher or lower than the one he assigns to himself. That's also what I am doing: picking a different way to assign coordinates to events, including the event of the existence of humans (at that precision, yes, it is an event, not a duration).
Anyway, yes, I am leveraging the logic of the Andromeda thing, except I picked something vastly further away than Andromeda, so far away that swings of hundreds of billions of years can result from a different abstract frame choice.
Now, as it happens, Andromeda is moving towards the Milky Way.
It is. In terms of peculiar velocity, we're moving away from it, but it's moving faster, catching up. Just FYI, irrelevant to this discussion.
Summary
"The age of the universe" is not arbitrary and changed just by boosting to another frame.
There is definitely a frame implied by the question "how old is the universe". But I disagree with your statement as worded, since an arbitrary frame choice can very much change the answer.
Also implied by the question is that it is asking for the time coordinate of our current event, which is different than literally asking the age of something which includes all times, and thus has no age.
We have a very specific understanding of what is meant by the age of the universe and we can make a powerful and objective statement:
Agree. The additional assumptions are implied. We all know what they are.
However, we can assert that the maximum proper time that could have elapsed (on the path we have taken) since the big bang event is 13.8 bn years.
No disagreement there.
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Hi.
Thanks for spending the time to write a long reply @Halc
There seems to be a lot of agreement and the differences aren't worth worrying about too much.
For what it is worth, I can fully appreciate what you are trying to say about far distant galaxies that have some velocity relative to us and the difficulty of determining simultaneity at spatially separated points etc. However, much of what you have said will remain theoretical or imaginable but will not be testable. It cannot be proved or disproved in any meaningful way. The expansion of space is such that although we can postulate the existance of a galaxy far enough away and moving fast enough that they would put our spacetime location [so that would be the event (s0 , t0 = 13.8 bn years) in co-moving co-ordinates ] along a line of simultaneity with their own time co-ordinate being something like 100 bn years, we simply will not be able to get to that distant galaxy at that local time and check. It's a bit more than just not being able to go there and check, the expansion of space is sufficiently rapid that their future light cone may never intersect our future light cone here on earth. We can certainly draw spacetime diagrams and extend sloping lines of simultaneity as far as we wish and imagine that at some distant galaxy they do have a universe around themselves that reached an age of 100 bn years and they may have the right motion so that they will put a line of simulataneity through that event and through the event (s0, t0) where we are now BUT that may or may not be true and whatever seems to happen at that distant galaxy on the diagram, it should be forever isolated from us and from that part of spacetime that should exist around us in our future.
Anyway, it's getting too philosophical and hurting my head. The statement we've both agreed upon is much more real rather than just abstract and theoretical: The (maximum) proper time from the big bang event to where we are now (here on earth and now) is 13.8 bn years.
Best Wishes.