Calculating the Size of the Universe

[denism]

I read that the radius of the universe is around 1.3x10^26 meters but I did not find how this size has been calculated.
Thanks if you can explain to me

 

[phinds]

There are numerous "calculations" of the size of the universe. NONE of them (at least by reputable sources) is THE radius, they are the MINIMUM radius.

No one knows the size of the universe. The Observable universe is some 90 billion light years in diameter and various estimates put the minimum size of the universe as being that much to many orders of magnitude larger. Some believe it is infinite.

 

[denism]

if you prefer: What are the tools used by reputable sources to estimate the minimum radius of universe?

 

[phinds]

if you prefer: What are the tools used by reputable sources to estimate the minimum radius of universe?

It's like religions. There are many of them and they contradict each other so I ignore them all. My own belief is that the universe is likely infinite but I have no facts to back that up so it is just an unfounded personal opinion. It may be finite but unbounded.

 

[bapowell]

denism -- it's important to distinguish between the size of the universe and the size of the observable universe. To which are you referring?

 

[denism]

My question was about the total size, or more precisely: do we have (indirect) evidences that there is really something beyond the Hubble sphere (of radius c/H)

 

[Number Nine]

My question was about the total size, or more precisely: do we have (indirect) evidences that there is really something beyond the Hubble sphere (of radius c/H)

The issue is that there is absolutely no reason to believe that there isn't. Earth is not in a privileged position; the notion that the Universe is perfectly spherical with Earth sitting in the centre (which is what "Hubble sphere = Universe" would imply) has no support, and there is no reason to believe that it is true. The likely topologies of the Universe wouldn't even permit such a thing.

 

[Chronos]

There is plenty beyond the Hubble sphere - all the way to the particle horizon.

 

[denism]

in my mind, the fact that universe size could be within c/H would not mean that we are at its centre if it is closed. If there is no reason to believe that it is true, conversely is there any support that there is plenty beyond. In fact, this belief is only based on the assumption that recessional velocities can exceed light speed but I never saw any observational support to this postulate

 

[phinds]

In fact, this belief is only based on the assumption that recessional velocities can exceed light speed but I never saw any observational support to this postulate

That's not an assumption or a "postulate", it is fact. The galaxies at the edge of our observable universe are receding from us at about 3c.

 

[denism]

thanks
how this fact has been determined?...or indirectly infered?

 

[denism]

I looked at:
http://en.wikipedia.org/wiki/Redshifts

it is stated that for a flat Minkowski space and for light motion in the transverse direction
1+z=1/sqrt(1-(v/c)^2)
from which z is infinite when v=c

 

[bapowell]

But the geometry of the universe isn't Minkowski. Look up cosmological redshift. Try this:http://en.wikipedia.org/wiki/Cosmological_redshift

 

[denism]

thank you very much. It is stated in this site that "For distant galaxies, v (or D) cannot be calculated from z without specifying a detailed model"
Of course, if postulating Vrec=HD and H constant, one easily obtains Vrec > c beyond a certain distance, but this appears purely theoretical to me. I am afraid that there is not a single supporting observation in this story

 

[bapowell]

I am afraid that there is not a single supporting observation in this story

And you say this why? Because wikipedia hasn't presented you with any? It would be wise to delve deeper before making such sweeping, contrarian statements.

What would a single supporting observation look like to you?

 

[denism]

I would be very pleased seeing any supporting data!

I did not want to be contrarian. Considering my poor knowledge in this field, I am sure that data (more convincing than the theoretical extension of Vrec = HD) should exist. This was precisely the purpose of my question

 

[George Jones]

deniism, you should know (given your background) that nothing is ever proved in science. The best we can do is to have theoretical models that are consistent with observations.

Good models of the universe are (perturbed) Friedmann-Robertson-Walker (FRW) spacetimes, and, properly interpreted, the Hubble relationship is predicted by FRW models. Most cosmologist think that there are gigabytes of observational data that support FRW models.

Also. you might be concerned about recessional velocities greater than c, because a law of physics is that "No physical velocity can exceed c."


1) This a property of special relativity, and, as you have already been told, the universe follows general relativity, not special relativity. Special relativity is a local approximation to general relativity. In general relativity, no observer (including those in FRW spacetimes) ever measures the speed of a local particle to be greater than c. This is consistent with both the "no speed greater than c" aspect of special relativity, and the "special relativity is a local approximation in general relativity" aspect of general relativity.

2) The term "velocity" is used in different ways in special and general relativity. The way "velocity" is used in general relativity is something like the way the term "velocity parameter" is used in special relativity, and, even in special relativity, velocity parameters can take on values that are greater than c.

 

[denism]

thank you very much for your kind answer George. In fact, I was not particularly afraid by recession velocities higher than c given that this limit does not apply to space expansion, but I just wondered (for other reasons) if Vrec > c were really observed because H has been proven to be lower than H0 in the past (expansion accelerates)
I have an other question with respect to your answer: I wonder why SR is not sufficient for studying the geometry of expanding universe models, supposed to be isotropic and homogeneous as empty. General relativity deals with gravity?

 

[Chronos]

SR does not take gravity into account. That was the whole point of GR.

 

[denism]

Yes. But precisely, all what I read about universe expansion and horizons, begins with a redefinition of the line element of SR (ds²=(cdt)²+a(t)²dl²)

 

[George Jones]

Yes. But precisely, all what I read about universe expansion and horizons, begins with a redefinition of the line element of SR (ds²=(cdt)²+a(t)²dl²)

I am not sure what you mean. How is this necessarily a redefinition of the line element of SR?

 

[denism]

Indeed I was not clear. I just wanted to say that authors talking about light connection rates in the expanding universe never make use of GR, but only derive their conclusions from the simple relationship cdt=a(t)*dl (note there is a typing error of sign in my previous equation). SR seems to be sufficient. Gravity and GR are generally not involved in the universe model used in these studies.

Furthermore, even SR seems to be not observed: calculations using speed substractions such as c-Vrec, rather resemble to classical mechanics ... even if I understood that Vrec is not a genuine speed.

 

[qraal]

I would be very pleased seeing any supporting data!

I did not want to be contrarian. Considering my poor knowledge in this field, I am sure that data (more convincing than the theoretical extension of Vrec = HD) should exist. This was precisely the purpose of my question

There's no evidence - yet - that there's anything far beyond the present horizon. An infinite flat space-time is just the simplest topology to assume. Alternative theories exist for a range of different space-time structures which are consistent with the data, some of which are finite and some are actually smaller than the current apparent horizon. The problem with assuming the limits of what we currently see are the actual physical limits is the implication we exist in a privileged moment of history - a possibility that needs a theoretical explanation that'd convince other cosmologists or they'll stick to their current assumptions.

The limits of what we can see are about x3 times the current Hubble light-travel-time. A good place to learn about all the different cosmological distances is Professor Ned Wright's Cosmology Tutorial...
Ned Wright's Cosmology Tutorial
...which features a handy Java calculator of all sorts of cosmic parameters. So handy that people have referenced it in their papers.

 

[denism]

Many thanks for these informations

An infinite flat space-time is just the simplest topology to assume. .

does "infinite flat" means euclidean 3D?

 

[bapowell]

does "infinite flat" means euclidean 3D?

"Flat" means Euclidean 3D. It need not be infinite.

 

[denism]

But how do you conceive a finite euclidean 3D space? with a peripheral boundary? looks strange

 

[qraal]

But how do you conceive a finite euclidean 3D space? with a peripheral boundary? looks strange

That requires some tricky topology I'm guessing :-)

 

[bapowell]

That requires some tricky topology I'm guessing :-)

A torus.

 

[denism]

4D torus?

 

[bapowell]

4D torus?

You can think of it that way, yes. The best way to visualize it, though, is as a cube with opposite faces identified (by identified, I mean topologically connected -- for example, a circle is a line segment with the end points identified.)

 

[denism]

I have a naive perception of topology: the number of dimensions of any shape is that of the minimal euclidean space capable of embedding it. Your torus is 4D to me, even for something confined in its surface

the circle is a good example: unidimensional if envisioned from the interior, but in fact genuinely bidimensionnal

 

[George Jones]

Indeed I was not clear. I just wanted to say that authors talking about light connection rates in the expanding universe never make use of GR, but only derive their conclusions from the simple relationship cdt=a(t)*dl (note there is a typing error of sign in my previous equation).

ds^2 = 0 for a lightlike worldline in both special and general relativity.

SR seems to be sufficient. Gravity and GR are generally not involved in the universe model used in these studies.

This is just plain wrong. In order to use the equation in your post above, the dependence of a\left(t\right) on t is needed. This is given by the solution of the differential equation

<br /> \left( \frac{da}{dt} \left(t\right) \right)^2 = H_0^2 \left( \Omega_{m0} a\left(t\right)^{-1} + \Omega_{r0} a\left(t\right)^{-2} + \Omega_{\Lambda 0} a\left(t\right)^2 + 1 - \Omega_{m0} - \Omega_{r0} - \Omega_{\Lambda 0} \right),<br />
where the constants \Omega_{m0}, \Omega_{r0}, \Omega_{\Lambda 0} are the current densities (relative to critical density) of matter, radiation, and dark energy, respectively. This equation comes from Einstein's equation of general relativity, i.e., it come form Einstein's theory of gravity.

Furthermore, even SR seems to be not observed: calculations using speed substractions such as c-Vrec, rather resemble to classical mechanics ... even if I understood that Vrec is not a genuine speed.

With appropriate definitions of time and distance, c - V_rec is true in special relativity, and in the FRW cosmological models of general relativity

 

[denism]

ds^2 = 0 for a lightlike worldline in both special and general relativity.

sure, SR no way contradicts GR

This is just plain wrong. In order to use the equation in your post above, the dependence of a\left(t\right) on t is needed. This is given by the solution of the differential equation

<br /> \left( \frac{da}{dt} \left(t\right) \right)^2 = H_0^2 \left( \Omega_{m0} a\left(t\right)^{-1} + \Omega_{r0} a\left(t\right)^{-2} + \Omega_{\Lambda 0} a\left(t\right)^2 + 1 - \Omega_{m0} - \Omega_{r0} - \Omega_{\Lambda 0} \right),<br />
where the constants \Omega_{m0}, \Omega_{r0}, \Omega_{\Lambda 0} are the current densities (relative to critical density) of matter, radiation, and dark energy, respectively. This equation comes from Einstein's equation of general relativity, i.e., it come form Einstein's theory of gravity.

I disagree with you, the scale factor has first been naturally postulated because of the observation of Hubble. You describe one of the multiple a-posteriori attempts to calculate the expansion rate(s) from the universe constituents: (matter/energy and now the more exotic dark energy). These attempts are very interesting from a physical viewpoint but please do not inverse the string. a(t) did not emerge from matter/energy density calculations but was just postulated a-priori. To my knowledge its time-dependence has not been firmly established yet and it is likely to be underlain by different successive functions in the course of cosmic time

With appropriate definitions of time and distance, c - V_rec is true in special relativity, and in the FRW cosmological models of general relativity

you are certainly right but this typically looks a Newtonian approach in Galilean coordinates: you know the celebrated thought experiment of Einstein, this approach would lead to the absurd conclusion that the speed of light emitted by a lamp in a train, depends on the speed of the train. Ironically, this is erroneous for the train but true for galaxies