Origin from Nothing - what does it mean?

[Tanelorn]

I read this about the cosmological constant.

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

I am just not seeing where the energy comes from. I am used to seeing energy being used up doing something, in this case expanding space, which I assume is work."In fact adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy, which causes yet more expansion. Likewise, a universe which contracts slightly will continue contracting. However, the cosmological constant remained a subject of theoretical and empirical interest. Empirically, the onslaught of cosmological data in the past decades strongly suggests that our universe has a positive cosmological constant.[1] The explanation of this small but positive value is an outstanding theoretical challenge." My question is then where does vacuum energy come from?

http://en.wikipedia.org/wiki/Vacuum_energy
One contribution to the vacuum energy may be from virtual particles which are thought to be particle pairs that blink into existence and then annihilate in a timespan too short to observe. They are expected to do this everywhere, throughout the Universe.

So are particles and vacuum energy (dark energy?) appearing from nowhere? ie. They were not a part of the Universe until they appeared?

 

[Mordred]

In the earlier models the vacuum energy comes a model that correlated false to true vacuum with the higg's field acting as the barrier. False vacuum being the lowest the vacuum state. The resultant is the development of virtual particle. This model is oft cited as "false vacuum" by Allen Guth.
Think of a piston inside the piston is a pressure region called false vacuum, the outside of the piston is the true vacuum. As you draw the piston the vacuum pressure inside increases. As energy density/volume is equal to pressure where does the energy come from?
The answer to that derives a process of quantum tunneling.

False vacuum has been replaced with numerous other inflationary fields to explain how inflation works. Such as LQC , chaotic eternal inflation, Higg's inflation etc.

However in the: "origin from nothing model" this is essentially the type of process used for the energy source as per se. Further related to false vacuum is Parker's radiation. The two are very similar and much related.

 

[mikiel]

Tanelorn, Post #30:

Since it is not possible to ever have a first cause then the only other alternative is that reality is perpetual with no beginning.

Agreed. Perpetual means eternal, with no beginning or ending (products of linear thinking.)
The only cosmological model that fits this description is the cyclical or oscillating model. The arguments against that model are many, but we are "finding" more matter all the time, so maybe, eventually the expanding cosmos will slow down, hit the 'gravitational net' and reverse to the to begin the "crunch" half of a perpetual "bang/crunch" cycle.
I don't think the entropy argument against perpetual oscillation is a good one, because of the universal law of conservation of energy/matter, i.e., the 'system' is "all there is," so nothing is lost beyond the system as in the entropy model for energy systems.

In this model "origin from nothing" is not an issue, as everything in the cosmos has always existed, perpetually cycling through bangs and crunches.

 

[Tanelorn]

Cyclical models like this are less favored now in preference to heat death.
Since it is not possible to ever arrive at a first cause then our temporally finite universe has to be a part of something much greater. I don't see any logical alternative - except everything from nothing which I find unsatisfactory.

 

[Adrian07]

So you have another piece to the puzzle.

 

[Tanelorn]

No I don't claim to know anything, I am just brainstorming.

 

[mikiel]

Cyclical models like this are less favored now in preference to heat death.
Since it is not possible to ever arrive at a first cause then our temporarily finite universe has to be a part of something much greater. I don't see any logical alternative.

As I said, entropy (your "heat death") is based on energy loss from a finite system into space beyond that system. That does not apply to the universe (literally 'one verse') which is "all there is" (known and unknown.) Nothing is created or destroyed but only changes form.

Your "something much greater" is the universe as defined above... no possible boundary. (What would that be, and what would be beyond it?)

 

[Tanelorn]

Well we are not supposed to speculate here. You could take a look at the recent Smolin thread, but there are other ideas as well.

 

[mikiel]

Well we are not supposed to speculate here. You could take a look at the recent Smolin thread, but there are other ideas as well.

Speculation is theoretical science. Speculative cosmology is the basis of string theory. It speculates eleven 'dimensions' as its synthesis, now callled M-theory... seven metaphysical dimensions beyond 3-d space and time.
Empirical science demands falsifiable theories. Speculative cosmology is legitimate science, not a forbidden realm.

 

[Tanelorn]

I should have said that we are not supposed to discuss things here that are not already in accepted scientific literature, some things of which are admittedly quite speculative.

eg. If I had some idea that the entire universe, from the BB beginning to its end, when all matter and energy exits our spacetime into black holes, works somewhat like a repeated water cycle, where all the matter and energy exists in a kind of ocean or reservoir outside of our normal spacetime, waiting to be energized into another BB, I would not be allowed to say it, unless something like this model had already appeared in a paper.

 

[StateOfTheEqn]

The vector space of Hamiltonians forms a Lie algebra H. If you exponentiate the Lie algebra H you get the emergence of space-time as well as energy-gravity from absolute nothing. There is no t=0 so there is no first instant of time and no first cause.

 

[Tanelorn]

state, that's a pretty impressive idea. How would we go about reproducing this? After all, absolutely nothing at all is required.

 

[StateOfTheEqn]

$exp(\textbf{H})=\textbf{R}^+\times S^3$ where $\textbf{H}$ is the Lie algebra of Quaternion space.

This can be proven as follows:

Let $\textbf{q}=x+y\textbf{i}+z\textbf{j}+w\textbf{k}$

$x$ commutes with $y\textbf{i}+z\textbf{j}+w\textbf{k}$ so:

$exp(x+y\textbf{i}+z\textbf{j}+w\textbf{k}) =exp(x)exp(y\textbf{i}+z\textbf{j}+w\textbf{k})$

$exp(x)exp(y\textbf{i}+z\textbf{j}+w\textbf{k}) =e^xexp\left(\begin{array}{cccc} 0&-y&z&-w\\ y&0&w&z\\ -z&-w&0&y\\ w&-z&-y&0 \end{array}\right)$

Then $exp(\textbf{H})=\textbf{R}^+\times S^3$

The time variable $t=e^x$ acts as a scalar on the rotation group so this represents a universe $S^3$ expanding at the speed of light, at least in the first moments. Notice that $\textbf{R}^+$ excludes $t=0$ so there is no 'first instant' of time and no 'first cause'. Furthermore, $exp(0)=Planck \ Time \times Planck \ Volume$.

Energy comes into existence as the exponential of the Lie sub-algebra $\textbf{R}$

That is, $exp(\textbf{R})=\textbf{R}^+$ and in particulat $exp(0)=1$ where $1$ is the Planck energy. Gravity comes into existence as the dual of energy. That is $0\rightarrow E^2+(*E)^2$

This can best be seen for mass-less particles.

Let $*E=\sqrt{(\textbf{i}p_x)^2+(\textbf{j}p_y)^2+ (\textbf{k}p_z)^2}$ where $\textbf{i}p_x$,$\textbf{j}p_y$, and
$\textbf{k}p_z$ are the momenta. For mass-less particles $-||*E||$ is their gravitational binding energy.

This gives the Lorentz invariant 4-vector $E^2+(*E)^2=E^2-p_x^2-p_y^2-p_z^2=0$

 

[Tanelorn]

State, you didnt really answer my question. Since nothing at all is required, why can't we create another universe out of nothing? Does the fact that there arent more Universes being created all the time disprove the math?

Also the maths I am afraid is well beyond me so I couldn't tell if one of the steps is like the following false proofs that I was told as a youngster:

Consider two non-zero numbers x and y such that
x = y.
Then x2 = xy.
Subtract the same thing from both sides:
x2 - y2 = xy - y2.
Dividing by (x-y), obtain
x + y = y.
Since x = y, we see that
2 y = y.
Thus 2 = 1, since we started with y nonzero.
Subtracting 1 from both sides,

1 = 0

Did I also just prove that a universe can be made out of nothing? :)

 

[timmdeeg]

Well done, using 0/0 is undefined. Perhaps said universe is undefined too.

 

[Naty1]

x = y.
Then x2 = xy.

"does not compute"... x² = xy

 

[Vanadium 50]

This has become silly. Thread closed.