# Big bang singularity size

1. Jan 30, 2014

### dheeraj

hello everyone

like the prevailing theory now on how our universe origin has taken is THE BIG BANG.

BUT i am studying in 11th and one of my lecturer told me that our universe when exploded from the big bang singularity it's size was 10^-36 m
any idea on that? like how scientists calculated that value

you can find this at this website http://universevolution.blogspot.in/

2. Jan 30, 2014

### phinds

Such estimates always apply only to the OBSERVABLE universe, not "the universe" (which was of indeterminate size, possible infinite, at the singularity). I've heard estimates ranging from smaller than a proton to the size of a beach ball (and again, this is for the OBSERVABLE universe)

EDIT: I just checked the link and indeed, it says "our universe", which is a VERY sloppy way of saying "observable universe" (OR, the writer doesn't know what he is talking about and really did mean "the universe")

Last edited: Jan 30, 2014
3. Jan 30, 2014

### JesseM

I imagine your lecturer was referring to the Planck length, though it's closer to 10^-35 meters. The Planck length is thought to be about the length scale at which the current best theory of gravity, general relativity, would probably become totally inaccurate and we would need a more accurate theory of quantum gravity to replace it (see my recent post here discussing how the Big Bang can be derived from using general relativity to project the observed expansion of the universe backwards). However, I don't think it's accurate to say that quantum gravity becomes important when the universe is the size of a Planck length--probably it would be more like when the density of the universe was high enough to reach the "Planck density", or Planck mass per Planck volume (Planck length cubed), which would mean the observable universe as a whole could have been significantly larger in size than one Planck length. That's just a rough guess though, quantum gravity effects might start to become important a little before it reached that density, for example I found this page from physicist John Baez which says:
Loop quantum gravity is one attempt to develop a theory of quantum gravity, the other major one being string theory.

Let's do a back-of-the-envelope style rough calculation. According to this, the current density of all forms of mass and energy (and energy can be treated as a form of mass by E=mc^2) is about 0.85 * 10^-26 kg/m^3. The Planck density is around 5*10^96 kg/m^3. So to squeeze the observable universe to the Planck density, you'd have to divide its volume by about 6*10^122. Since the volume of a spherical region is the cube of its radius, we have to take the cube root of this to find how much to divide the radius, or 8*10^40. The radius of the observable universe is thought to be about 47 billion light years which works out to about 4*10^25 meters, so dividing this by 8*10^40 implies the radius of the observable universe would be about 5*10^-16 meters if it was squeezed to the Planck density. That's fairly close to the size of a proton, about 9*10^-16 meters. So the observable universe would have been small, but still many orders of magnitude larger than the Planck length.

Last edited: Jan 30, 2014
4. Jan 30, 2014

### Chronos

Nice job, JesseM. Many people do not understand the science behind approximating the size of the observable universe at the instant of the BB. Partly because it is poorly explained, and partly, IMO, because of fear an attempt to explain it would create more confusion than illumination. Some writers try to force fit the 'initial' size of the universe into a Planck length, which is unrealistic if you assume the total energy content of the universe was the same as it is in the present and the Planck density is the controlling factor. Quantum effects further compound matters. It is unclear how this might impact maximum permissible density, hence initial size of the universe. As a consequence of these kinds of bias, size estimates in the popular press vary. We can safely say it was very much smaller than at present.

5. Jan 31, 2014

### dheeraj

wonderful replies guys...thanks everyone :)

6. Apr 15, 2016

### xAxis

You don't say!