Is the universe older than we think it is?

[James Random]

Is the universe older than we think it is?

Here's my workings. Discuss!

Why is it scientists say that they can see stars that are older than the universe itself?

Well, today I decided to work it out and dust off my physics 101 brain.

Hubble has a very definite way of measuring the expansion of the universe. The equasion is this

V = Hs

V is the speed that a galaxy is rushing away from Hubble itself.
S is the distance to that galaxy from Hubble.
H is a constant of proportionality known as 'Hubble's Constant'.

If the universe were expanding a constant rate, H would be equal to 1 divided by the time the universe has been expanding.

That equasion would look something like this;

H = 1/t (t being time)
T =13.7 (billion).

That would make the universe about 13.7billion years old as scientist currently believe it to be.

However.

But if a galaxy is accelerating away from Hubble at rate A, as scientists say they are. Then hubbles equation becomes A x T which is the speed the galaxy has after T time equals H times a half ATsquared. (A being for acceleration, T being for time).

So

v becomes at

at = H½at²

This is because ½at² is the distance the galaxy is after T.

Observation of a type 1a supernova has demonstrated to us that the universe is indeed expanding at an accelerated rate.

This being the case then H becomes equal to 2 divided by T. (H =2/T) and T suddenly equals 27.4(billion). So, the age of the universe becomes 27.4 Billion years.

Remember this is using cut and dried applied mathematics used by the guys who operate Hubble.

But the figure of 13.7 Billion years isn't just disinformation or an error. It does mean something. When a galaxy gets to be more than 13.7 billion light years away, it would be imposible to see. Because it would be rushing away from us faster than the speed of light. That's what is known as an 'event horizon'. So 13.7 billion years is our (this galaxy's) event horizon based on our position in the universe offset by the position of the most distant galaxy that we can see.

So, while essentially correct in the figure of 13.7 billion. It is not the AGE of the universe, which seems to be automatically twice as long as the event horizon.

[Zer0th]

Plasma cosmology declares a universe without beginning or end.
http://www.bigbangneverhappened.org/

Eric Lerner, apart from looking like a mad scientist should, is well-respected in plasma physics.

[James Random]

Interesting thread. And most of it makes sense too.

You're right. He does look like a mad scientist.

Kudos to him.

[New Wine]

Originally Posted by Zer0th

Plasma cosmology declares a universe without beginning or end.
http://www.bigbangneverhappened.org/

Eric Lerner, apart from looking like a mad scientist should, is well-respected in plasma physics.

Now where have I heard those words before?

[Cartesiantheater]

Originally Posted by James Random

Is the universe older than we think it is?

Here's my workings. Discuss!

Why is it scientists say that they can see stars that are older than the universe itself?

Well, today I decided to work it out and dust off my physics 101 brain.

Hubble has a very definite way of measuring the expansion of the universe. The equasion is this

V = Hs

V is the speed that a galaxy is rushing away from Hubble itself.
S is the distance to that galaxy from Hubble.
H is a constant of proportionality known as 'Hubble's Constant'.

If the universe were expanding a constant rate, H would be equal to 1 divided by the time the universe has been expanding.

That equasion would look something like this;

H = 1/t (t being time)
T =13.7 (billion).

That would make the universe about 13.7billion years old as scientist currently believe it to be.

However.

But if a galaxy is accelerating away from Hubble at rate A, as scientists say they are. Then hubbles equation becomes A x T which is the speed the galaxy has after T time equals H times a half ATsquared. (A being for acceleration, T being for time).

So

v becomes at

at = H½at²

This is because ½at² is the distance the galaxy is after T.

Observation of a type 1a supernova has demonstrated to us that the universe is indeed expanding at an accelerated rate.

This being the case then H becomes equal to 2 divided by T. (H =2/T) and T suddenly equals 27.4(billion). So, the age of the universe becomes 27.4 Billion years.

Remember this is using cut and dried applied mathematics used by the guys who operate Hubble.

But the figure of 13.7 Billion years isn't just disinformation or an error. It does mean something. When a galaxy gets to be more than 13.7 billion light years away, it would be imposible to see. Because it would be rushing away from us faster than the speed of light. That's what is known as an 'event horizon'. So 13.7 billion years is our (this galaxy's) event horizon based on our position in the universe offset by the position of the most distant galaxy that we can see.

So, while essentially correct in the figure of 13.7 billion. It is not the AGE of the universe, which seems to be automatically twice as long as the event horizon.

Time is relative, remember? We define 13.7 billion years based upon our frame of reference; that is, that is a measurement of PROPER time, which means that other observers that weren't in our chosen frame of reference would measure a longer time interval anyway.

Originally Posted by wiki on proper time in an accelerating frame

An accelerated clock will measure a proper time between two events that is shorter than the coordinate time measured by a non-accelerated (inertial) clock between the same events. The twin paradox is an example of this effect.

Also

Hmmm... I will try to derive the result in terms of differential equations and see if it makes sense.

Originally Posted by My differential equation bs

If v= Hs => ds/dt = H s ==>

Then acceleration would be:

d²s/dt² = d/(dt) (Hx) ==> d²s/dt² = H ds/dt

So you have a differential equation:

s'' - Hs' = 0

where H is some function of t, H(t), in units of 1/s, so I'll pick units in which H = 1, which would make H = 1/t, because H is a number in units of 1/seconds. So I'll just call it some number n * (1/t), with n = 1 for these units. (if that isn't legal I should get a wrong result)

s'' - (1/t)s' = 0

So, to solve this use reduction or order:

u = s' , u' = s''

u' - (1/t)u = 0

which is separable:

du/dt = (1/t) u

du/u = dt/t

Integrating:

ln|u| = ln |t| + C

e^ln|u| = e^(ln |t| + C)

u = e^lnt*e^c

u = Ct

The sub. s' back in but chose C = 1:

s' = t

Then again it is separable

ds/dt = t

ds = t dt

Integrate

s = t²/2 + C

s is a distance, so s * (1/t²)*t is an acceleration * t, which is a velocity, so multiplying both sides by at = s/t² * t gives:

v = (½)at²

And this is in units such that H = 1, therefore:

v = H (½)at²

Which looks similar to the result you started with if the first constant of integration is chosen to be 1 and the second is chosen to be 0, with v = at:

at = H (½)at²

Good, good. That seems to be what you had, right?

Originally Posted by James Random

So

v becomes at

at = H½at²

This is because ½at² is the distance the galaxy is after T.

Now the question is, does it make sense to say that the universe has been around for a time of 2t?

Originally Posted by more DE BS

You can solve for t and you get:

at = H½at²

1 = H½t

t = 1/2H

so you have H = 2t

which is what you have above

So, using a differential equation I got what you have...



However, there is a problem with this.

You initially defined H to be 1/t, and 1/t ≠ 2t


This can only mean that the t on the left is not the same as the t on the right, OR the first H is not the same as the second H.

There is another problem. If H = 2t, then it most certainly CANNOT be the same H you started with, because the UNITS no longer match. In the case that H = 2t, the units of H are seconds, but in the case you started with, the units of H are 1/seconds. This is quite a problem.















Now, consider what exactly IS H. H is the average slope of an approximately linear function that arises when the distance of an object (found through luminosity or parallax) is plotted on the x-axis and the velocity of an object (found by redshift) is plotted on the y-axis.

If the universe is accelerating, than what we will have is that all observed heavenly objects have APPROXIMATELY a linear relationship between their distance and velocity, and this only holds so long as distance (or a time parameter) is relatively small (that is, somewhere on or near the order of 13 billion years).




But don't you see the problem here? There is no way to know exactly what the relationship between the ACTUAL function between recessional velocity and distance and the APPROXIMATION of the current Hubble's law and Hubble constant is.

Therefore we CANNOT know for certain that t = 2t₀. In fact, for all we know, t = at₀ where a ≈ 1, because we don't know exactly what rate the universe was expanding at in the past, nor do we know if any acceleration was constant in the past.

In fact, because of the very high density of the early universe, it stands to reason (and in fact is part of some of the major physical models) that gravitational attraction had a damping effect on cosmological expansion. Which means that while an accelerating universe would skew 1/H₀ in the positive direction, the gravitational attraction of the early universe would skew it in the negative direction.



Essentially this means your entirely derivation is invalid because the relation you used to get it:

s = ½ a(Δt)² + v₀Δt + s₀

where v₀ = 0, s₀ = 0

is only applicable when acceleration is uniform, i.e. unchanging.



But clearly in our universe that is not the case. Early in the universe gravitational affects would have affected acceleration, not to mention that inflation models posit a time of immense acceleration that was then slowed. Acceleration in this universe has not always been constant. If acceleration is not constant, you cannot use the equations of uniformly accelerated linear motion.




So, at best all we can know is what the current relationship is between recessional velocity and distance, and from that extrapolate the age of the universe. We CAN however, figure out new values of H₀, and therefore the age of the universe, depending on different models of the universe. Moreover, we can estimate the most likely value, or rather, put lower limit on the age of the universe. Further still, we can take the most reasonable ranges for values of cosmological parameters and obtain a "mean" age for the universe. This is what we have done, and it is why they give the value ~13 billion years. (see Bayesian Statistical analysis of the issue: although this cannot remove uncertainty from measurements, it NORMALIZES uncertainty that arises from the specific model chosen).

http://en.wikipedia.org/wiki/Bayesian_statistics

in use on the issue:

http://www.andrewjaffe.net/blog/science/000181.html

Originally Posted by above link

The alternative, Bayesian, view of probability, is simply that when I state the age of the Universe is 13.6±1 Billion years, it means that I am 67% certain that the value is between 12.6 and 14.6 Billion years. In the early 20th Century, Bruno de Finetti showed that you can further refine exactly what “67% certain” means in terms of odds and wagering: if something is 50% certain, I would give even odds on a bet; if it’s 67% certain I would give 2:1 odds, etc.

So in light of the various models that exist, the age of the universe turns out to be most likely near the generally given value of ~13 billion years.

http://adsabs.harvard.edu/abs/2005IJMPD..14..775C

So we CAN come up with a MOST LIKELY age, and we CAN come up with some limits, especially lower limits (there is no controversy on LOWER limits because a physical object in the universe cannot be older than the universe).



What we CANNOT do however, is use the equations of uniformly accelerated linear motion to derive that H is really = 2t. It is bad physics, because the universe has NOT always been in uniform acceleration with respect to time (because gravitational attraction near the beginning would have resulted in a DECELERATION opposing any intrinsic acceleration, and CURRENTLY that gravitational factor would be lessened on the large scale because matter is so much further apart than it was near the beginning- not to mention any other possible factors affecting acceleration).

[James Random]

Well, I'm only just getting into this sort of stuff, so you'll have to be patient with a noob here

You asked what H is, H is Hubble's Constant, ( H₀ ). It's a constant of proportionality between the galaxy and hubble itself. The math for hubble's constant is usually described as v = H₀D (D is the proportion to a galaxy and V is the galaxy's speed).
I'm sure I don't need to tell you this ^^
H₀D = 83 ± 13 km s-¹ /Mpc. (using Cepheid variables).

I think, anyway.

I took this to mean that H had a steady value of one based on it being a constant. But since the galaxies are accelerating away, this would actually define the value as 2 and not 1.

I dunno. Mebbe im wrong on this one.

[Cartesiantheater]

Originally Posted by James Random

Well, I'm only just getting into this sort of stuff, so you'll have to be patient with a noob here

You asked what H is, H is Hubble's Constant, ( H₀ ). It's a constant of proportionality between the galaxy and hubble itself. The math for hubble's constant is usually described as v = H₀D (D is the proportion to a galaxy and V is the galaxy's speed).
I'm sure I don't need to tell you this ^^
H₀D = 83 ± 13 km s-¹ /Mpc. (using Cepheid variables).

Yeah, but the Hubble Constant is:

#1 in dispute

#2 not really a constant depending on which universe model they are using.


You basic argument was solid. Even your math was right. The only problem is that you used math that you shouldn't have.

It is true that an ever accelerating universe will be older than one that ends in a big crunch from our present perspective. Same with one expanding with constant velocity. Just like you said.

Where you go wrong is in the details, here:

Originally Posted by James Random

I think, anyway.

I took this to mean that H had a steady value of one based on it being a constant. But since the galaxies are accelerating away, this would actually define the value as 2 and not 1.


I dunno. Mebbe im wrong on this one.

The problem is that you are using a formula that is only valid in a uniformly accelerating reference frame. That means the acceleration rate has always been the same. But that is not the case since early in the universe all matter was very close together, and mass warps space-time, therefore there was a deceleration factor, and so acceleration was very likely not constant.




Lastly, and I am by no means knowledgeable about cosmology, but I believe the that the Hubble constant we use, and the various parameters used to estimate the age of the universe, the accepted values, I mean, are kind of a statistical mean of all the competing models.



Again, in words your argument is right. An accelerating universe will be older.

Here is a good pic from wikipedia showing the various models and how they would relate to age:




Notice that the accelerating universe starts at the oldest point in time. So you are CORRECT that an accelerating universe is older. I just don't think your factor of TWICE as old is correct.

Also, you can see that the early universe had a decelerating factor, so it was not constant acceleration, which means you can't use the constant acceleration relationship that you used. (see how the accelerating line has an s-shape to it? That means that the rate of change of the velocity has NOT always been the same; it was negative near the "Now" location, since the slope at the beginning (the velocity) was higher, and then that slope became lower near the "Now" location, and THEN that slope becomes higher and higher after that time- all that means that acceleration has not been uniform. The rate of change of the slope indicates acceleration- that's not explicitly graphed, but it can be inferred by looking at the graph).


EDIT - and when acceleration is NOT uniform, it is NOT the case that:

v = ½ a(Δt)²

[James Random]

I'm with you.

So we are agreed that the universe is accelerating. But we do not agree that the factor of this might be a factor of 2 when applied to Hubble's law. So the question becomes, what is the factor? Impossible to tell?

They say that the age of some of these globular star clusters are at least 2 billion years older than the universe itself. So given a factor of 2 billion we might be able to come up with a new equation?

[Cartesiantheater]

Originally Posted by James Random

I'm with you.

So we are agreed that the universe is accelerating. But we do not agree that the factor of this might be a factor of 2 when applied to Hubble's law. So the question becomes, what is the factor? Impossible to tell?

The factor is currently what they are using, but depending upon the universe model it will either change with time, or there is a slight inaccuracy in the actual figure.

However, the time that "they" use to give the age of the universe is the statistically most likely result of the combined possibilities based upon the various models (whether accelerating forever, big crunch, out with a whimper, etc).

Originally Posted by James Random

They say that the age of some of these globular star clusters are at least 2 billion years older than the universe itself. So given a factor of 2 billion we might be able to come up with a new equation?

Who are "they" and do you have a source of this?

I do know that for a short time in the mid-90s there was some literature about this possibility, but it was resolved by both better data and getting a more accurate value of H₀.

http://www.tim-thompson.com/oldstars.html

Originally Posted by link

The bottom line is that there is not now a conflict between the astrophysically determined ages of the oldest stars, and the cosmologically determined age of the universe. While there was one in 1994 it was predictably short lived. While it made good reading for the popular press, astronomers were already busy trying to find the right solution. The result was that the cosmological age moved up (as H₀ moved down), through the addition of more and better data, and the astrophysical ages moved down, through the addition of more precise techniques and more detailed models. In short, we learned more about the problem, and exercised that knowledge to reach a new conclusion. But I think it is safe to say that the universe is definitely not less than 10 billion years old, and definitely not more than 20 billion years old, if the expanding universe and big bang cosmology is correct.

Originally Posted by more specifically

The Age of globular clusters in light of Hipparcos - Resolving the age problem
by B. Chaboyer, P. Demarque, P.J Kernan & L.M Krauss

Astrophysical Journal 494(1)Part 1: pp96-110 (1998 February 10)

We review five independent techniques that are used to set the distance scale to globular clusters, including subdwarf main-sequence fitting utilizing the recent Hipparcos parallax catalog. These data together all indicate that globular clusters are farther away than previously believed, implying a reduction in age estimates. We now adopt a best-fit value M-epsilon (RR Lyrae stars) = 0.39±0.08 (statistical) at [Fe/H] = - 1.9 with an additional uniform systematic uncertainty of (+ 0.13)(- 0.18). This new distance scale estimate is combined with a detailed numerical Monte Carlo study (previously reported by Chaboyer et al.) designed to assess the uncertainty associated with the theoretical age- turnoff luminosity relationship in order to estimate both the absolute age and uncertainty in age of the oldest globular clusters.

Our best estimate for the mean age of the oldest globular clusters is now 11.5±1.3 Gyr, with a one-sided 95 % confidence level lower limit of 9.5 Gyr. This represents a systematic shift of over 2 sigma compared to our earlier estimate, owing completely to the new distance scale - a shift which we emphasize results not only from the Hipparcos data. This now provides a lower limit on the age of the universe that is consistent with either an open universe or with a flat matter-dominated universe (the latter requiring H0 less than or equal to 67 km s-1 Mpc-1). Our new study also explicitly quantifies how remaining uncertainties in the distance scale and stellar evolution models translate into uncertainties in the derived globular cluster ages. Simple formulae are provided that can be used to update our age estimate as improved determinations for various quantities become available. Formulae are also provided that can be used to derive the age and its uncertainty for a globular cluster, given the absolute magnitude of the turnoff or the point on the subgiant branch 0.05 mag redder than the turnoff.

In other words, after the mid 90s this problem was resolved by getting better data and fixing the model.






Finally, there is a lot more uncertainty in measuring the age of stars than there is in measuring the age of the universe. That means for large uncertainties, you will get a window of age for a star that might go from younger than the universe to older than the universe, but again, this is due to uncertainty in measurement. Since we DON'T have that level of uncertainty in measuring the age of the universe, we can cut off the interval of possible age of a STAR after that interval passes the interval of the possible age of the universe.




http://map.gsfc.nasa.gov/universe/uni_age.html


The reason this is resolved, and it wouldn't be without it, is because of WMAP.




Potential problem:

Originally Posted by link above

The oldest globular clusters contain only stars less massive than 0.7 solar masses. These low mass stars are much dimmer than the Sun. This observation suggests that the oldest globular clusters are between 11 and 18 billion years old. The uncertainty in this estimate is due to the difficulty in determining the exact distance to a globular cluster (hence, an uncertainty in the brightness (and mass) of the stars in the cluster). Another source of uncertainty in this estimate lies in our ignorance of some of the finer details of stellar evolution. Presumably, the universe itself is at least as old as the oldest globular clusters that reside in it.

[...]

In more familiar units, astronomers believe that 1/Ho is between 12 and 14 billion years.

An Age Crisis?

If we compare the two age determinations, there is a potential crisis. If the universe is flat, and dominated by ordinary or dark matter, the age of the universe as inferred from the Hubble constant would be about 9 billion years. The age of the universe would be shorter than the age of oldest stars. This contradiction implies that either 1) our measurement of the Hubble constant is incorrect, 2) the Big Bang theory is incorrect or 3) that we need a form of matter like a cosmological constant that implies an older age for a given observed expansion rate.

Some astronomers believe that this crisis will pass as soon as measurements improve. If the astronomers who have measured the smaller values of the Hubble constant are correct, and if the smaller estimates of globular cluster ages are also correct, then all is well for the Big Bang theory, even without a cosmological constant.

Resolution of problem:

Originally Posted by link above

Measurements by the WMAP satellite can help resolve this crisis. If current ideas about the origin of large-scale structure are correct, then the detailed structure of the cosmic microwave background fluctuations will depend on the current density of the universe, the composition of the universe and its expansion rate. WMAP has been able to determine these parameters with an accuracy of better than than 3% of the critical density. In turn, knowing the composition with this precision, we can estimate the age of the universe to about 1%: 13.7 ± 0.13 billon years!

How does WMAP data enable us to determine the age of the universe is 13.7 billion years, with an uncertainty of 1%? The key to this is that by knowing the composition of matter and energy density in the universe, we can use Einstein's General Relativity to compute how fast the universe has been expanding in the past. With that information, we can turn the clock back and determine when the universe had "zero" size, according to Einstein. The time between then and now is the age of the universe. There is one caveat to keep in mind that affects the certainty of the age determination: we assume that the universe is flat, which is well supported by WMAP and other data. If we relax this assumption within the allowed range, the uncertainty increases to a bit over 2%. However, theorists have long known that a nearly-flat universe is very difficult to produce, whereas inflation naturally predicts a flat universe.

The expansion age measured by WMAP is larger than the oldest globular clusters, so the Big Bang theory has passed an important test using data independent of the type collected by WMAP. If the expansion age measured by WMAP had been smaller than the oldest globular clusters, then there would have been something fundamentally wrong about either the Big Bang theory or the theory of stellar evolution. Either way, astronomers would have needed to rethink many of their cherished ideas. But our current estimate of age fits well with what we know from other kinds of measurements.

So at this point there is no age crisis. That could change though, and we'll have to modify the models more.

[Cartesiantheater]

One thing that I think might help in this situation is to realize that the Hubble constant has been adjusted over time. In that sense it isn't a constant. It depends on some measurement uncertainties, and so it's value is within a range. However, with the advent of the ΛCDM model, the constant has been given a generally accepted value. This occurred in the late 90s, after the age discrepancy was settled (temporarily? Probably).

[James Random]

I'll get back to you when I've done more research.

In the meantime: Do you believe the universe to be flat?

Under the scenario that the universe is finite, then I'd wager that it'd be a big ol' sphere or at least a spheroid shape. Why do I believe this? Well, because most other stuff in the universe is roughly spherical. It's the most energy efficient shape. It's reasonable to assume that the universe is also a sphere