Question about upper energy limits.

[flashprogram]

Is there a limit to the amount of energy that can be located in a fixed volume of space?
e.g. like there is for matter where a black hole occurs past a certain threshold.

 

[LostConjugate]

There is something called the Principle of maximum entropy. If there is a maximum amount of data that can be stored in a unit space then there must be a maximum amount of energy.

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

I am not real familiar with the subject.

 

[mathman]

What do mean by "energy". Usually energy is discussed in terms of photons, which can't be fixed - moving at the speed of light.

 

[flashprogram]

What do mean by "energy". Usually energy is discussed in terms of photons, which can't be fixed - moving at the speed of light.

My question is with regards to the idea that all that eventually became the whole universe was once located in a volume far far smaller than the nucleus of an atom. Since I know it wasn't matter, I assume we're dealing with energy of some sort.

 

[espen180]

My question is with regards to the idea that all that eventually became the whole universe was once located in a volume far far smaller than the nucleus of an atom. Since I know it wasn't matter, I assume we're dealing with energy of some sort.

This is a common misconseption. Nowadays, most cosmologists agree that the universe was not concentrated in a finite volume the the beginning. Rather, it was infinitely big and very dense, and evolved to an even bigger but less dense state.

 

[LostConjugate]

This is a common misconseption. Nowadays, most cosmologists agree that the universe was not concentrated in a finite volume the the beginning. Rather, it was infinitely big and very dense, and evolved to an even bigger but less dense state.

What's bigger than infinite?

 

[espen180]

What's bigger than infinite?

You tell me.

Still, for all intents and purposes, the universe is infinitely large today, but still continues to expand. Why should this state be favored over that one?

Personally I see expansion from infinity to a larger infinity much more reasonable that expansion from finite to infinite.

If I can find a reference to what I said in my previous post I will supply it.

 

[flashprogram]

So that means the following statements are wrong, or must be interpreted in a special way, no?

Inflationary Big Bang cosmology let's us journey to a time 10^-35 seconds after the Big Bang when all that we can see today was crushed into a region of space about 10^-28 centimeters across, or about 100 trillion times smaller than the nucleus of an atom. Once again, we see no evidence that some force was available to prevent the universe from having been even smaller...
The point is that all current versions of Big Bang theory imply that the universe emerged from a very dense hot initial state, and that what we see as the entire visible universe today, out to 15 billion light years, was long ago crushed into a region smaller than a modern atom. -http://www.astronomycafe.net/qadir/q1326.html"

In a fraction of a second, the Universe grew from smaller than a single atom to bigger than a galaxy. And it kept on growing at a fantastic rate. It is still expanding today.-http://www.esa.int/esaKIDSen/SEMSZ5WJD1E_OurUniverse_0.html"

Similar statements have been voiced in various documentaries.

 

[espen180]

Those sources seem to give a very simplified explanation. Especially the first.

A good way to visualize the expansion of the universe is that the metric of space is increasing with time. http://en.wikipedia.org/wiki/Metric_expansion_of_space

The universe really does not get bigger, expanding into new areas. The above link treats the expansion in a much more sophisticated manner than the links you provided.

For a detailed mathematical analysis, see http://en.wikipedia.org/wiki/Friedmann-Lemaître-Robertson-Walker_metric

 

[Orion1]

planck epoch...

Is there a limit to the amount of energy that can be located in a fixed volume of space?

Your question is really, what was the energy density of the Universe during the Planck epoch?

The total energy of the Universe at Planck epoch:
$$E_t = \frac{4 \pi c^5 M_{\odot}}{3 \Omega_s^2 H_0^3} \left(\frac{dN_s}{dV_s} \right)$$

The total volume of the Universe at Planck epoch (Planck sphere volume):
$$V_p = \frac{4 \pi}{3} \left( \frac{\hbar G}{c^3} \right)^{\frac{3}{2}}$$

$$\rho_E \left( t_p \right) = \frac{E_t}{V_p} = \frac{c^5 M_{\odot}}{\Omega_s^2 H_0^3} \left( \frac{c^3}{\hbar G} \right)^{\frac{3}{2}} \left(\frac{dN_s}{dV_s} \right)$$

Maximum energy density limit of the known Universe at Planck epoch:
$$\boxed{\rho_E \left( t_p \right) = \frac{c^5 M_{\odot}}{\Omega_s^2 H_0^3} \left( \frac{c^3}{\hbar G} \right)^{\frac{3}{2}} \left(\frac{dN_s}{dV_s} \right)}$$

This is the maximum energy density limit of the known Universe in absence of quantum gravitation.

To my knowledge, the metric expansion of space has no effect on fundamental physical constants.

Reference:
http://en.wikipedia.org/wiki/Planck_epoch"
http://en.wikipedia.org/wiki/Planck_units"
http://en.wikipedia.org/wiki/Universe#Size.2C_age.2C_contents.2C_structure.2C_and_laws"
https://www.physicsforums.com/showpost.php?p=2127529&postcount=7"

 

[espen180]

The total volume of the Universe at Planck epoch (Planck sphere volume):
$$V_p = \frac{4 \pi}{3} \left( \frac{\hbar G}{c^3} \right)^{\frac{3}{2}}$$

This equals the volume which light can "fill" during one Planck time. That is just the size of the visible universe from anyone point. It doesn't mean there was nothing outside that sphere. As far as I could see, none of the sources you listed support this.

 

[flashprogram]

My understanding of expansion is like that on the provided link, similar to the surface of a balloon expanding eventually there is more space, though you're not expanding into 'something'. Which would suggest that if the universe was somehow cooled early on and had the matter it has today in the amount of space it had available early on, it would have collapsed into a black hole.

 

[Orion1]

This equals the volume which light can "fill" during one Planck time. That is just the size of the visible universe from anyone point. It doesn't mean there was nothing outside that sphere. As far as I could see, none of the sources you listed support this.

In physical cosmology, cosmic inflation, cosmological inflation or just inflation is the theorized exponential_expansion of the universe at the end of the grand unification epoch, 10−36 seconds after the Big Bang, driven by a negative-pressure vacuum energy density. The term "inflation" is also used to refer to the hypothesis that inflation occurred, to the theory of inflation, or to the inflationary epoch. The inflationary hypothesis was proposed by American physicist Alan Guth in 1980.

As a direct consequence of this expansion, all of the observable universe originated in a small causally connected region.

Nothing existed beyond the Planck radius during the Planck epoch, not even metric space-time, because that would violate causality. Any mathematical cognitive conception beyond the Planck radius during the Planck epoch can only be described as an absolute void, completely devoid of any space-time and energy and any laws of physics and the rendition of any of these concepts in this region as absolutely meaningless.

Metric space-time was probably generated during the Planck epoch and space-time metric expansion did not exceed luminous velocity until after the Grand unification epoch when symmetry breaking occurred and resulted in a phase transition and a negative-pressure vacuum energy density, and potentially the generation of a cloud of highly quantized virtual particles at this point which behaved as a simple harmonic oscillator.

Reference:
http://en.wikipedia.org/wiki/Planck_epoch"
http://en.wikipedia.org/wiki/Grand_unification_epoch"
http://en.wikipedia.org/wiki/Cosmic_inflation"
http://en.wikipedia.org/wiki/Inflationary_epoch"
http://en.wikipedia.org/wiki/Causality_%28physics%29"
http://en.wikipedia.org/wiki/Vacuum_energy"
http://en.wikipedia.org/wiki/Quantum_field_theory"
http://en.wikipedia.org/wiki/Virtual_particle"