What is your view on infinity? Here's mine

Originally posted by CLPrime
You're right, it can't be created out of nothing, but there is no "conservation of matter" in the universe. What there is, however, is the Conservation of Energy - there is a fixed amount of energy in the universe, of which matter is one form (Einstein's principle of Mass-Energy Equivalence: familiarly, E = mc^2).

What's totally wild is that in General Relativity this isn't even necessarily true on a global level. There is no global conservation of (total) energy. Noether's theorem says conservation laws arise from symmetries. Usually, in classical (and even quantum) physics conservation of energy comes about because of symmetry in time. In General Relativity, symmetries are defined by Killing Vectors and there is no time-like Killing Vector on a global scale, so the symmetry in time is "undefined".

Basically, the fact that spacetime is curved makes it impossible to define a global conservation of energy.

I also think the Universe is finite, and most physicists agree with that today.

But, there are a lot of ideas out there that have some sort of "infinite" multiverse.

Eternal Inflation is a popular one. Although time started at some finite moment in the past in this model, it will go on to an infinite future, and there will be presumably an infinite amount of what's called "bubble Universes" in the multiverse.

I personally don't buy into many of the multiverse theories.

reply to post by smithjustinb


Humans can't make a true vacuum... and, even if we could, there's no law that says it has to collapse. By definition, "spontaneous collapse" means the collapse happens... well... spontaneously. It doesn't have to. In fact, the zero-point energy of today's vacuum seems to be pretty stable.

reply to post by EthanT


Well... GR involves the conservation of energy, it's just more fluid with the term "conservation". Energy is conserved so long as relativistic effects are taken into account, and, since relativity is, by definition, relative, this means that energy is ultimately conserved... it just has the illusion of not being conserved in differing reference frames.

Originally posted by CLPrime
reply to post by EthanT

 

Well... GR involves the conservation of energy, it's just more fluid with the term "conservation". Energy is conserved so long as relativistic effects are taken into account, and, since relativity is, by definition, relative, this means that energy is ultimately conserved... it just has the illusion of not being conserved in differing reference frames.

edit on 30-6-2011 by CLPrime because: (no reason given)

No, a total energy really isn't conserved in GR and there is also no way to define a total energy to the Universe. It's the fact that you are taking into account General Relativistic effects (i.e. curved spacetime) that brings this "problem" about.

You can still define the covariant derivative of the stress-enery tensor and set it to zero locally, but that's as good as energy conservation gets in General Relativity.

Sean Carrol talks about this in his General Relativity textbook ( as well as Wald ). Carroll has one of the better explanations I have seen on it.

Originally posted by EthanT

Originally posted by CLPrime
reply to post by EthanT

 

Well... GR involves the conservation of energy, it's just more fluid with the term "conservation". Energy is conserved so long as relativistic effects are taken into account, and, since relativity is, by definition, relative, this means that energy is ultimately conserved... it just has the illusion of not being conserved in differing reference frames.

edit on 30-6-2011 by CLPrime because: (no reason given)

No, a total energy really isn't conserved in GR and there is also no way to define a total energy to the Universe. It's the fact that you are taking into account General Relativistic effects (i.e. curved spacetime) that brings this "problem" about.

You can still define the covariant derivative of the stress-enery tensor and set it to zero locally, but that's as good as energy conservation gets in General Relativity.

Sean Carrol talks about this in his General Relativity textbook ( as well as Wald ). Carroll has one of the better explanations I have seen on it.

I should probably mention that you can, with the Komar Integral, define a stationary spacetime within General Relativity and this will have a time-like Killing Vector and therefore global conservation of Energy, but this does not represent the real Universe.

Originally posted by cyberjedi
Think that there is a fixed amount of physical matter in the universe.

Not true. Matter is often converted into energy through nuclear reactions. This results in less matter but more energy.

Originally posted by cyberjedi
i cannot accept the universe being infinite, maybe i should, but my mind can't accept it. My logical part of my brain can't even remotely try to understand/accept it.

I don't think we're meant / capable of understanding the true nature of the universe. Life, maybe yes, the whole existence of reality and what contains it, no.

reply to post by EthanT


As I said, in relativity, energy is conserved so long as there is no change in reference frames. Maybe I'm being more lenient in my definition of "conservation", but, in all instances in relativity, energy is conserved by making appropriate conversions between reference frames.
Also, in GR, we have to redefine "energy" in terms of energy-momentum, being a vector in space-time, as opposed to a simple energy scalar in space. But, when we consider such a redefinition (which we should, if we're talking about GR), then energy (energy-momentum) is still conserved with time within a closed system - and, thus, within the universe, if we assume the universe is closed.

The switch from energy to energy-momentum, and the switch from a Euclidean 3-space to a Riemannian 4-space, hasn't nullified energy conservation. It's just redefined it beyond recognition.

Originally posted by CLPrime
reply to post by EthanT

 

As I said, in relativity, energy is conserved so long as there is no change in reference frames.

I'm not talking about reference frames though. Tensor equations are independent of the reference frame, or coordinate system chosen. A tensor equation true in one coordinate system is true in all coordinate sytems.

So, you can define the covariant derivative of stress-energy tensor (a tensor equation) and set it to zero and conservation of energy is valid locally (regardless of the reference frame, or coordinate system), but that's about as good as it gets.

You cannot do that for a total energy of the Universe, regardless of conversions, or reference frame, or coordinate systems. It is undefined.

Some links so you don't have to take my word for it

Wiki

In general relativity conservation of energy-momentum is expressed with the aid of a stress-energy-momentum pseudotensor. The theory of general relativity leaves open the question of whether there is a conservation of energy for the entire universe.

Here's a more detailed description in a blog by Sean Carroll, a noted expert on GR, who also happens to write my favorite textbook on General Relativity:

Discover Blog - Energy Is Not Conserved

It’s clear that cosmologists have not done a very good job of spreading the word about something that’s been well-understood since at least the 1920′s: energy is not conserved in general relativity. (With caveats to be explained below.)

But, really, I would suggest getting a graduate level textbook such as Wald to see the gory details , or Carrols book which is a borderline graduate textbook, which won't be as gory, but will at least spell out some of the math, which is not in some undergrad texts like Schutz, etc. Also, Carroll's text has a very succinct, clear description on why total energy is undefined and not conserved in GR.

By the way, this doesn't mean total energy is really not conserved and undefined, it just means General Relativity doesn't have a clear way of talking about it. However, with a curved spacetime, it's hard to imagine how you could ever define it.

Originally posted by CLPrime
reply to post by EthanT

 

As I said, in relativity, energy is conserved so long as there is no change in reference frames. Maybe I'm being more lenient in my definition of "conservation", but, in all instances in relativity, energy is conserved by making appropriate conversions between reference frames.
Also, in GR, we have to redefine "energy" in terms of energy-momentum, being a vector in space-time, as opposed to a simple energy scalar in space. But, when we consider such a redefinition (which we should, if we're talking about GR), then energy (energy-momentum) is still conserved with time within a closed system - and, thus, within the universe, if we assume the universe is closed.

I should also mention that all of what you said here is correct, but ONLY in the context of Special Relativity, which is an incomplete picture since it deals with Minkowski space, or a flat spacetime. General Relativity complicated this picture with the addition of curved spacetime.

Anyhow, I always thought it's pretty cool that GR gets fuzzy on this matter. As well as other matters like with relative velocities being undefined within GR, as well. It's pretty trippy stuff

reply to post by EthanT


The first paragraph was specific to SR. The second paragraph was for GR.
Again, you and I seem to be saying the same thing, it's just that I'm being more liberal with conservation. You were saying that energy is not conserved, but, as you just specified, what you're actually saying is that the conservation of energy can't be mathematically defined. However, I'm saying that, just because it cannot be mathematically defined doesn't mean it isn't conserved.

The Killing field is handicapped by the definition of relativity, which refuses to define a global coordinate system. However, given any random origin, the Killing field could be modified to account for the local effects of GR (the curvature of space-time), thus allowing the application of the Killing vector globally to the geometry of the universe. That is, if we knew what the global geometry of the universe is - which, we don't, so the point, so-to-speak, is pointless.

Also, remember who you're talking to I know the material in the textbooks, but I don't bind myself to it, and I will defend the global conservation of energy, given the definitions of GR.

I believe the brain cannot comprehend Infinity beacause of its (ours) finite existence. Imagine if you will that the brain lived forever would finite (as infinity is) become incomprehendable to the brain.

ALS

Originally posted by CLPrime
reply to post by EthanT

 

The first paragraph was specific to SR. The second paragraph was for GR.

The second paragraph is only correct for SR too. SR uses the energy-momentum 4-vector, but GR replaces that for the more complete stress-enery momentum tensor.

4-vectors are the language of SR, but tensors are the language of GR

Originally posted by CLPrime
Also, remember who you're talking to

I know the material in the textbooks, but I don't bind myself to it, and I will defend the global conservation of energy, given the definitions of GR.

No worries, I take some rather unconvential views myself sometimes. Probably the reason we're both on ATS

All I was saying was: Total Energy for the Universe is undefined and not conserved in General Relativity. And, it's not. Maybe some future theory will fill in the gaps and bring total energy conservation fully back to life, but I'm not so sure.

Originally posted by EthanT

The second paragraph is only correct for SR too. SR uses the energy-momentum 4-vector, but GR replaces that for the more complete stress-enery momentum tensor.

4-vectors are the language of SR, but tensors are the language of GR

And I'll tell you why... because my mind has always used tensors and vectors interchangeably. So, when it came to me thinking of GR, I automatically thought of the 4-vector. I knew what I was talking about in my own head, why didn't you?

No worries, I take some rather unconvential views myself sometimes. Probably the reason we're both on ATS

That would be an affirmative.

Originally posted by CLPrime

And I'll tell you why... because my mind has always used tensors and vectors interchangeably. So, when it came to me thinking of GR, I automatically thought of the 4-vector. I knew what I was talking about in my own head, why didn't you?

I knew too, I'm just trying to keep my pyschic powers a secret right now

reply to post by cyberjedi


Hi cyberjedi,

You gotta love infinity discussions! (Even if they do go on forever.... yeah I know!!! l

Here's one for you...

All matter is made of particles yes?

Imagine that all of the particles which make up the matter in our universe/dimension, are actually planets and stars in the next dimension "in", and that the planets and stars in this universe/dimension are the particles from the next dimension "out". (Very simplistic I know!!!)

This pattern of "particles being planets in the next dimension in"
and
"planets being particles in the next dimension out"
could be repeated forever, thus to infinity.
No beginning, no end.

Molecules, or groups of particles, form the systems/galaxies and so on...

So, the true 4th dimension (not time), could simply be scale?

And this theory also suggests an answer to the BIG question about how GOD (Insert name of your own deity here) could possibly be omnipresent and all around us. It's simply a matter of scale!
We can barely see beyond the next few thousand particles, so how can we even begin to comprehend what lies beyond?

Just a bit of fun, but it's quite an interesting angle isn't it?

G

Everyone read this.

www.abovetopsecret.com...

reply to post by cyberjedi

2. Let's say the universe is infinite. Imagine that we went ahead and made 1 very thin string of ALL the physical matter in the universe, and we then stretch it out in a perfect line, one end to another, perfectly straight. So the string is made out of ALL the planets, stars, debree, anything of physical matter in space. We have now taken ALL that exists into the string. Now how long would this very thin string be?

The answer lies in how you formed the basis for your string.

How would you form the basis for your string Universe out of a perfect /absolute vacuum?

First you would have to make the vacuum change some hove.

How would you do that?

The answer lies right there. Because if you have to compress the vacuum you should be able to figure out how long it would take before the energy mass expands to a vacuum again.

The thing is; if you have to compress free space to create the string you need, you have already compressed a distance/volume of free space.

This volume of compressed energy mass from the free space will equal the compressed energy mass of your string universe.


Our universe will not expand for ever. It will only expand until it equals the energy mass needed to form our universe. Our universe is formed by a finite volume of energy mass from free space, not a infinite amount.

reply to post by cyberjedi

What we determine to be finite is based on our ability to measure. Our ability to measure is by way of comparing two or more things to determine a relationship. What is time, distance, volume or weight if not a comparison between things of like quality.

Time is the measure of distance moved through relative motion. Distance is a comparison of things against a standard rule. All things that are finite are measurable. So wouldn't the opposite, infinite, be that which is then beyond measure?

An infinite amount of time is not a quantity but an expression of timelessness, it is all time and it is no time. To claim an infinite amount of distance or an infinite number of things therefore becomes an oxymoron, they do not exist in any measurable quantity.

So, simply put, infinite is beyond measure.
Even if the Universe was ever infinite we created its finitude through observation.