Net Energy of the Universe

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Net Energy of the Universe
Posted by shakinbake22 on Thursday, October 31, 2013 11:08 AM

I have read that cosmologists postulate that if the universe is flat, it must have zero net energy, and conversely if the universe has zero net energy it must be flat. I am wondering how we can make that assumption. I am a biochemist and in my field there are lots of things that are folded in their lowest energy state. Unfolding them, or making them "flat" as it were, requires energy. So how can we know that the universe doesn't have a natural tendency to be "folded" or curved? Can we be sure that relative flatness isn't a result of some non-zero energy counteracting a natural tendency toward curvature?

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Posted by chipdatajeffB on Thursday, October 31, 2013 11:56 AM

The universe is not only stranger than we imagine, it's stranger than we CAN imagine. --- JBS Haldane

Come visit me at Comanche Springs Astronomy Campus (we're on Google Maps) in Texas.

www.3rf.org

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Posted by archimedes on Sunday, December 01, 2013 1:48 AM
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Posted by Primordial on Thursday, December 05, 2013 9:56 AM

Archimedes : Hi! Long time no see.

It would be nice if we could put dark matter into full perspective. it sort of sits on the edge of negative and positive energy, and how it may just be one ( gravitational ) from my understanding. Correct me if I'm wrong or did I missed something.

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Posted by shakinbake22 on Thursday, December 05, 2013 10:09 AM

I understand (sort of) the whole positive and negative energy thing. The heart of my question lies more in how we know what that energy would do to the curvature of the universe. Maybe I'm wrong, but it sounds like the prevailing theory is that flat universe=zero net energy and vice versa. I question how we know that, since "flat" macromolecule actually equals net positive energy. Why coudn't the same sort of thing be applied to the universe?

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Posted by Bullfox on Thursday, December 05, 2013 12:34 PM

What I have wondered is this:  is the universe doing work by expanding?

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Posted by Primordial on Thursday, December 05, 2013 12:56 PM

Bullfox : Hi Good question. In the classical sense ( positive energy), yes; work is to move a mass in the direction of the force vector, but not to include motion perpendicular to the force vector ( a.i. the photon ), however this ( dark energy )is not motion provided by positive energy. You might think of it as an implicit form of work; as a result of an implicit ( or dynamic implicit ) form of energy. Maybe Archimedes or Jeff can set us right.

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Posted by archimedes on Saturday, December 14, 2013 4:14 AM
Analogies are often useful but do not always reveal the entire picture.
Consider a droplet of water falling through empty space.
The arrangement of molecules of water in this droplet is determined by various forces acting upon them.
These forces comprise repulsive forces arising from the positive (kinetic) energies of motion of the molecules, and attractive forces arising from the negative electrical (potential) energies of the molecules, respectively.
The repulsive forces give rise to a positive pressure which tends to push the molecules apart.
The attractive forces, on the other hand, give rise to a negative pressure which tends to pull the molecules together (which, at the surface, gives rise to the phenomenon known as surface tension).
By Newton’s law of action and reaction, these forces must exactly balance each other.
Therefore the net pressure in a droplet of water is given by
Net pressure = positive pressure + negative pressure = 0
Likewise, because the positive and negative pressures derive from the positive (kinetic) and negative (potential) energies, respectively, the positive and negative energies must also balance.
Therefore the net energy of a droplet of water is given by
Net energy = positive kinetic energy + negative potential energy = 0
This result is not meant to be taken literally, because obviously, in trying to simplify the discussion I have deliberately ignored details which are, however, not directly relevant to the principles that I have tried to bring out here; details such as the binding energies of the molecules, the intrinsic mass-energies of the molecules of water and so on.
But despite these obvious defects, I hope you can appreciate the basic principles involved, namely, concepts like conservation of energy, conservation of momentum etc.
There is another principle which I ought to mention: it is based on the second law of thermodynamics, which says, among other things, that particles tend to arrange themselves whenever possible so as to maximize the total entropy.
Put another way, the second law says that, in general, particles will tend to arrange themselves so as to minimize their potential energies.
Now, the surface potential energy of a homogeneous fluid is proportional to the area of the fluid. The smallest possible area for a given volume of fluid is represented by sphere, which is why a droplet of water tends to assume a spherical shape.
 
OK, having explored some of the basic principles involved, let us now apply these principles to the universe at large.
The universe may be broadly described as an isolated collection of particles which are held together by gravitational force.
The forces acting on the particles may be described as being of one or other of two types: namely repulsive forces and attractive forces.
The repulsive forces derive from the positive (kinetic) energies of those particles. In this context the kinetic energy of a particle includes its intrinsic (relativistic) mass-energy and the ordinary energy of motion, which can be lumped together by Einstein’s mass-energy relation E = mc2.
Such forces give rise to a positive pressure which tends to push the particles of matter apart.
The attractive forces on the other hand derive from the negative (potential) gravitational energies of those particles.
Such forces give rise to a negative pressure which tends to pull the particles of matter together.
By Newton’s law of action and reaction, the forces acting on all the particles of matter in the universe must be equal and opposite. If follows that the positive and negative pressure which arise from these forces must balance each other exactly.
And so we have
Net pressure = positive pressure + negative pressure = 0
And because the positive and negative pressures balance exactly, the positive (kinetic) and negative (potential) energies from which those pressures are derived must also balance exactly.
So we have
Net energy = positive (kinetic) energy + negative (gravitational potential) energy = 0
You can see from these fundamental relations based on Newton’s law of action and reaction and the conservation laws, that even though gravity is an extremely weak force at small distances as compared to the other forces, at distances comparable to the observable size of the universe gravity becomes as important as all the other forces combined.
As to the geometry of the universe, one might suppose that the geometry is simply the shape of the universe.
Well, not quite!
As in the case of the droplet of water, the shape of the universe is dictated by the second law of thermodynamics.
That means that the particles of matter in the universe, as you will no doubt have gathered by now, will tend to arrange themselves so as to maximize the entropy and hence minimize the surface (gravitational) potential energy of the universe.
And as you might also have guessed, the most likely shape of the universe is a sphere, because a sphere represents the lowest surface area (at least for an ideal fluid) and hence the lowest surface potential energy, all else being equal of course.
So, if we regard matter in the universe as an ideal fluid, and if the universe really is like the surface of a sphere then the obvious question is: why do we see the universe as being flat?
To see why, consider a photon propagating from a point A on the surface of this hypothetical sphere to a nearby point B on the surface.
We shall assume that this sphere is expanding, since evidently the universe is expanding.
You can see (I hope) that because the sphere is expanding the path traced by the photon will depend not only on the shape and size of the sphere but also on the rate of expansion.
There are three possibilities which we need to consider, which are:

1.       The path traced by the photon is curved inwardly in a direction toward the centre of the sphere. In this case we say that the geometry of the sphere is positively curved.

2.       The path traced by the photon is curved outwardly in a direction away from the centre of the sphere. In this case we say that the geometry of the sphere is negatively curved.

3.       The path traced by the photon is neither curved inwardly nor outwardly but coincides with the straight line passing through point A. In this case we say that the geometry of the sphere is flat.

 

For the purpose of establishing a reference, it might help if we assume that point A is fixed in space and time. It may be helpful also if we imagine a fixed straight line which passes through point A and which is tangential to the surface of the sphere at point A.

 

After a certain time, depending upon the rate of expansion, point B will pass through the fixed line.

 

If the sphere is expanding very slowly the photon will obviously reach point B before point B reaches the line.

 

In that case it is clear that the path traced by the photon will be curved away from the fixed line in the direction toward the centre of the sphere. In other words the geometry of the sphere is positively curved in this case as perceived, for example, by a hypothetical observer at point B.

 

If, on the other hand the sphere is expanding very quickly, point B will already have passed through the fixed line before the photon reaches point B.

 

In that case the path traced by the photon will be curved  in the direction pointing away from the centre of the sphere, so in this case the geometry is negatively curved.

 

It is not hard to see, I think, that between these two extremes there is a critical value for the rate of expansion such that the photon traces a perfectly straight line. 

 

Therefore if the universe is expanding at the critical rate then the geometry ought to be flat, assuming of course that the arguments I have presented here are right.

 

In 1951 by an astronomer by the name of William McCrea showed mathematically that the critical rate of expansion for a flat geometry is one which increases exponentially with time.

 

Also, according to theory, an empty universe (known as a de Sitter universe) is both flat and expands exponentially with time.

 

[A possible definition of an empty universe is that the net energy density of such a universe is zero.]

 

On the basis of the foregoing I would suggest that a good test for whether or not the net energy density of the universe is zero is to measure both the geometry of the universe and the rate of expansion. If the geometry is flat and if the universe is expanding at an exponentially accelerating rate then I would argue that the net energy density of the universe must be zero

 

Consider the evidence:

 

Since 1998 astronomers have discovered increasing evidence that the universe is geometrically flat and, what is particularly noteworthy, that the universe is expanding at an accelerating, exponential rate.

 

I think the evidence speaks for itself.

 

I hope this helps

 

 

[PS: Primordial & Bullfox:  Hi

 

Years ago when I began studying cosmology, a couple of major assumptions in the standard model of cosmology were that the universe is expanding adiabatically and that the expansion is isentropic (constant entropy).

 

In these models, we treated the expansion as boundary work, which altered the kinetic energy component of the universe but did not change the total energy. Neither did it change the total entropy of the universe because, in the absence of heat transfer, boundary work is a thermodynamically reversible process, which means that there is no net increase or decrease in total entropy.

 

We justified these assumptions on the basis that for an isentropic, adiabatically expanding universe, in which the only energy transfers of energy derived from boundary work, and provided that there were no other (irreversible) changes taking place, the temperature of the universe should vary precisely in inverse proportion to the scale factor (a measure of the relative expansion of the universe).

 

The available evidence at the time seemed to support those assumptions. Specifically, the evidence consisted of temperature of the cosmic microwave background, and measurements of cosmological red shift of light from distant stars and galaxies, which was always regarded as a measures of scale factor. In particular, the measurements of cosmic red shifts seemed to be consistent with observations of time dilation, which are exemplified by the stretched out luminosity-time curves of exploding stars.

 

As you can entropy of the universe does not depend upon energy, or temperature alone; it depends upon the scale factor as well, which in very rough terms can be translated into volume.

 

To illustrate with a very ordinary example: if we partition a chamber and fill half the chamber with a gas and leave the other half empty then the entropy of the gas in the filled half is relatively low (it is less than it otherwise might be) because the molecules of gas are crowded together, which restricts the number of available energy levels to the molecules. That number is a measure of the entropy of the gas.

 

If now we suddenly remove the partition then the gas will rapidly diffuse to fill the entire chamber. The molecules are not restricted so much as before, so there are more available energy states to the molecules and so the entropy is greater. There is no net change in total energy of the molecules, or of their temperature; only a change in the volume of the gas and the increase in entropy reflects that change.

 

However, if the partition is replaced by a piston and the gas is allowed to do work on the piston, by pushing a weight against the force of gravity, then, under ideal conditions (no friction, etc.), there would be no change in entropy. But the temperature of the gas would drop, reflecting the increase in volume, which means that the molecules have less energy than they started with and so despite the increase in volume there is no change to the number of energy states available to those molecules.

 

With the foregoing in mind, an isentropic expansion is consistent with the idea that the expansion is associated with boundary work.

 

As I intimated earlier, the evidence based on the CMB and the red-shift-time dilation relation seemed very strong evidence that the expansion of the universe is isentropic;

 

A related argument in support of that proposition is based on the fact that light from distant stars and galaxies is red shifted implies that the kinetic energies of distant stars and galaxies are diminished.which we attribute of the expansion of the universe. On face value, that what would appear to be a violation of the law of conservation of energy.

 

But if we suppose that the expansion results from boundary work, then the apparent loss in kinetic energy can be explained by a corresponding gain in potential energy, and so there is no violation of conservation of energy.

 

Following the discovery that the expansion of the universe is accelerating, there has been a lot of discussion as to whether the entropy of the universe is increasing and if the universe should expand forever will the entropy increase to infinity.

 

On the basis of the foregoing I would argue that the total entropy is not increasing at all, despite any perceived appearances to the contrary.

 

Of course it can be argued that evidence for increasing entropy can be seen everywhere:  stars are dying, as are plants and animals, decay seems to be a universal phenomenon; clear evidence one might argue that entropy is increasing.

 

Drop a teacup onto a hard floor and what happens?  Most likely the teacup will shatter into a thousand pieces. We never see the pieces spontaneously recombining —evidence of the second law of thermodynamics prediction that entropy can increase but can never decrease.

 

But appearances can be deceiving.

 

The association between entropy and second law of thermodynamics goes way back to the early days of the steam engine but of course a great deal of our understanding has changed with the development of quantum theory. But the basic idea that entropy is not a conserved quantity according to the classical interpretaton of the second law does not seem to have changed.

 

The problem as I see it with the classical interpretation of entropy is that entropy is related to information.

 

Increasing entropy implies increasing information. So if the entropy of the universe is increasing then so is information. Where is that information coming from?

 

Or consider a black hole, which grows by matter falling into the black hole. Matter falling into a black hole carries information so the black hole grows bigger, as evidenced by an increase in the area of the black hole.

 

But black holes also can lose mass as well as gain mass by Hawking radiation. When a black hole radiates away all its mass where does the information go?

 

Personally, I am of the opinion that deep down at some fundamental level entropy is a conserved quantity, like energy and momentum, but most people don’t see it that way, I guess.

 

But that’s science!

 

Cheers

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Posted by Primordial on Saturday, December 14, 2013 9:25 AM

Archimedes : Excellent, especially the suggested possibility for the dynamics of entropy and information. Thank you, for your professional out line. I'll keep.

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Posted by Bullfox on Saturday, December 14, 2013 9:47 AM

Mr. A & Mr.. P,

How many ways can the universe. Be empty?

Mr. B.

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Posted by shakinbake22 on Saturday, December 14, 2013 9:51 AM

Wow, what a thorough answer! That's a lot to chew on. I'll have to work on that for a while, but it helps, especially the part where you talk about how it would have to be flat AND expanding exponentially. I think that might have been the key I was missing. At any rate, thanks for not just sending me to a website that I could have googled myself. Your answer helps.

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Posted by archimedes on Saturday, December 14, 2013 4:30 PM
Bullfox: I would suggest: an infinite number of ways. Regards, A.
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Posted by Primordial on Sunday, December 15, 2013 1:11 PM

Bullfox : It depends on if you are an optimist or a pessimist, if an optimist; it could be many, if a pessimist, it's none. Ha!  Thanks Mr. B.

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Posted by archimedes on Sunday, December 15, 2013 9:46 PM
To be serious, it depends upon the mathematical properties of zero and infinity, respectively.
Because, in a very, very, rough sense, infinity can be thought of as the inverse of zero, a universe having infinite energy arguably is the equivalent of a universe having zero energy.
We tend to think of the vacuum of empty space as having zero energy because the vacuum of space is, by definition, space devoid of all matter, and because matter without energyis contrary to our everyday experiences.
But if the energy of the vacuum were infinite there is no way I know of that we could tell that the energy is not zero.
The reason is that zero and infinity share similar mathematical properties which we can think of as symmetry properties.
For example, you can add zero to itself as many times as you like and the result would always be the same.
And you can add any number you like to the infinite set of numberse and the set of numbers of does not change.
No other number, and no finite set of numbers, have these symmetry properties.
The point I am trying to make is that the symmetry properties of zero and infinity in the mathematical sense translate into the symmetry properties of a zero energy or infinite energy universe in the physical sense.
Hence a particle, for example, can move through a field of infinite energy or through a field of zero energy, and it would make no difference from the point of view of the particle since motion of the particle does not affect the symmetry of this field as seen by the particle.
It is not the same for particle moving through a nonzero, finite energy field. Such a particle would feel a drag because of asymmetry arising in the field, as seen by the particle, due to the motion of the particle.
I know this doesn't fully answer the question which has been asked, and I apologize for that, but I hope that this necessarily brief explanation will at least go part way in clearing up any possible misconceptions.
Regards
A.
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Posted by Primordial on Monday, March 03, 2014 9:16 AM

Archimedes : I agree with the idea of a zero energy prospect for the universe, with the addition of information supportive of energy in its various occurances. I also agree with Mr. Einstein's equation, which equates energy to mass with information inclusive, which in my way of looking the equation indicates all mass can be converted into energy ( a.g. photons ) and information supportive of that energy. With these concepts, let us examine, the matter anti-matter problem. If all matter could be converted into photons then I would suggest the matter anti-matter is perfectly balanced because as we know the product which remains after a matter and anti-matter annihilation, is the photon ( energy with supportive information ), I suggest the primary difference is all of the information necessary to establish a substance which we regard as matter and all its interactions, relative to energy in its purest form as a perfect conservative balance. The important thing to consider is, can both of these objects exist in equal proportions in such a configuration as that which we might observe as a matter anti-matter universe, I would say, no, that information was not available at the bigbang so give us the information rich matter universe which was available. Just my opinion.

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Posted by Bullfox on Monday, March 03, 2014 1:07 PM

It depends on what you mean by empty.  If you have a completly static space time and no hidden varibles and no vacuum energy, why then I suppose there is only one way it can be empty.  If you add vacuum energy and figure out a way to count the energy states then you have an infinite number of ways the universe can be empty, if you want to call that empty.

But hold on now.  If you took one of those energy states, added gravity and allowed space time to expand and contract,  then you have created a potential for an energy gradiant and pretty soon you could have lots of astronomers, but you are never going to have an infinite number of astronomers.

I do not believe that what we, as intelligent observers, perceive as reality is infinite, and not just because of our limitations of perception.  I do not believe that anything we describe as real can be infinite.   However, I am willing to admit that in some mathmatical  sense the underlying space time vacuum energy may be infinite in its possible number of configurations.  But somehow in the process of becoming real the infinities are cancelled out.  Probably, reality can arise from only a small subset of all possible vacuum configurations.  However, that is just my personal belief.

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Posted by Primordial on Monday, March 03, 2014 4:30 PM

Mr. Bullfox : That's great thinking. I like that. So possibilities can only have real, but limited permutations to an observer in a universe or is that true for the whole universe(?)., I'll have to think about that one.Thank you, I'll keep that. You guys are good. Thank you. Just an opinion.

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