Infinite universe and energy/matter boundaries

[guywithdoubts]

I know that although there are alternatives to this model (such as the torus model) most observations fit with the classic flat infinite universe, which is what I'd like to inquire about.
If I understood properly, it means that the Universe has no boundaries whatsoever and, were it possible, one could travel in any direction indefinitely without ever coming back to the starting point. Now, if there is a finite amount of energy and matter in the Universe, would that mean we could reach a region in spacetime (please ignore faster-than-light travel limitations) where there is no matter and energy? Would this inevitably contradict homogeneity?
I'm assuming there's a finite amount of energy and matter because I can't visualize how infinite amounts would make the law of conservation of energy any meaningful.

Am I missing something very important and/or making a terrible reasoning mistake? By now it should be pretty clear that I'm by no means trained in physics, so I'd really appreciate it if you could keep it in layman's terms. Thank you very much in advance!

 

[phinds]

You are using contradictory suppositions and then getting surprised that there is a contradiction. If you assume an infinite universe, you cannot then assume a finite amount of mass/energy.

The laws of conservation of energy do not apply on cosmological scales.

 

[sadraj]

Please note that no-data from CMB or other Cosmological data at least now ( and may be never) can decide that our universe is open or closed! The inflation theory says : the fraction of curvature density to density of the universe is negligible , but this does not state that the curvature of the universe is positive or negative or even zero.

 

[Chronos]

The idea that energy conservation does not apply in general relativity is widespread, but, not universally agreed upon among physicists. Phil Gibbs, in http://arxiv.org/abs/1304.6728, states "Energy conservation in general relativity is real, exact, non-trivial and important." See also his blog entry dated 6 August 2010 at http://blog.vixra.org/category/energy-conservation/. John Baez, in http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html, responds to the question [Is energy conserved in general relativity?] by saying "In special cases, yes. In general — it depends on what you mean by "energy", and what you mean by "conserved"." pointing that merely defining energy under GR is non-trivial. IMO it is, at best, misleading to unequivocally claim energy is not conserved in GR. I agree with phinds that you cannot assume matter or energy is finite if you assume the universe is infinite.

 

[phinds]

The idea that energy conservation does not apply in general relativity is widespread, but, not universally agreed upon among physicists. Phil Gibbs, in http://arxiv.org/abs/1304.6728, states "Energy conservation in general relativity is real, exact, non-trivial and important." See also his blog entry dated 6 August 2010 at http://blog.vixra.org/category/energy-conservation/. John Baez, in http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html, responds to the question [Is energy conserved in general relativity?] by saying "In special cases, yes. In general — it depends on what you mean by "energy", and what you mean by "conserved"." pointing that merely defining energy under GR is non-trivial. IMO it is, at best, misleading to unequivocally claim energy is not conserved in GR. I agree with phinds that you cannot assume matter or energy is finite if you assume the universe is infinite.

Chronos, thank you for that. I did not realize it was a contentious subject. I was merely parroting (with some limited understanding) what I thought others had agreed on here on this forum.

 

[Chronos]

There is no compelling reason to assume energy conservation in GR any more than there is to the contrary. The easy part comes when you argue things like redshift and dark energy. If you assume energy is not conserved in GR, discussion ends prejudicially with "next question". I've never found that entirely satisfactory.

 

[guywithdoubts]

Thanks for your answers guys, it's of great help. I wasn't aware conservation of energy may not apply on cosmological scales; trying to find information about this subject I came across that very article by Phil Gibbs but it's too technical for me. I've also found other articles debating Phil Gibbs' view but they're far beyond what I could possibly understand.
It remains unclear to me how the size of the universe at its different stages of development could be calculated if infinity is assumed. Does it mean the observable universe?

 

[phinds]

Thanks for your answers guys, it's of great help. I wasn't aware conservation of energy may not apply on cosmological scales; trying to find information about this subject I came across that very article by Phil Gibbs but it's too technical for me. I've also found other articles debating Phil Gibbs' view but they're far beyond what I could possibly understand.
It remains unclear to me how the size of the universe at its different stages of development could be calculated if infinity is assumed. Does it mean the observable universe?

Any statement about the exact (more or less) size of the universe has to mean the observable universe since there is no known way at present (and may never be) to determine the size of the entire universe at ANY point in time.

 

[julcab12]

It remains unclear to me how the size of the universe at its different stages of development could be calculated if infinity is assumed. Does it mean the observable universe?

So far it is darn 99%(BOSS eye) flat still... it’s “more(cross finger)likely” the universe is infinite, extending forever into space and time.

http://arxiv.org/pdf/1312.4877v1.pdf

pg.36

 

[bapowell]

So far it is darn 99%(BOSS eye) flat still... it’s “more(cross finger)likely” the universe is infinite, extending forever into space and time.

In what sense is it "more likely"? We've examined an unknown amount of universe: the extrapolation you wish to perform might be incredibly unfounded.

 

[Chalnoth]

IMO it is, at best, misleading to unequivocally claim energy is not conserved in GR.

I rather strongly disagree. Energy simply is not a conserved quantity in GR. You can recover energy conservation under specific conditions by defining things carefully. But that's not the same as energy conservation.

What is conserved in General Relativity is the stress-energy tensor, which includes energy but also momentum, pressure, and twisting forces. The combination of all of these together is conserved (in a very specific way), but there's no universal way of defining energy such that it is always conserved.

 

[julcab12]

In what sense is it "more likely"? We've examined an unknown amount of universe: the extrapolation you wish to perform might be incredibly unfounded.

What amount. Are we talking observable universe? Their are data's coming from Baryon Oscillation Spectroscopic Survey measuring baryon acoustic oscillations/baryon waves with comparison to PLANCK+BAO+SN. (according to them).

A strong case/consistent towards flat universe/infinite with uncertainty(that's me saying "more (x) likely"). WMAP ((2013)excluding the latest data) favors a flat universe 0.4% margin of error.Pointing towards Universe that is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. They can only conclude that the Universe is much larger than the volume they can directly observe.

http://arxiv.org/abs/1312.4877

"The acoustic features are detected at a significance of over 7σ in both the correlation function and power spectrum. Fitting for the position of the acoustic features measures the distance relative to the sound horizon at the drag epoch, rd, which has a value of rd,fid=149.28Mpc in our fiducial cosmology. We find DV=(1264±25Mpc)(rd/rd,fid) at z=0.32 and DV=(2056±20Mpc)(rd/rd,fid) at z=0.57. At 1.0 per cent, this latter measure is the most precise distance constraint ever obtained from a galaxy survey. Separating the clustering along and transverse to the line-of-sight yields measurements at z=0.57 of DA=(1421±20Mpc)(rd/rd,fid) and H=(96.8±3.4km/s/Mpc)(rd,fid/rd). Our measurements of the distance scale are in good agreement with previous BAO measurements and with the predictions from cosmic microwave background data for a spatially flat cold dark matter model with a cosmological constant."

http://phys.org/news/2014-01-baryon-oscillation-spectroscopic-survey-universe.html

 

[bapowell]

What amount. Are we talking observable universe? Their are data's coming from Baryon Oscillation Spectroscopic Survey measuring baryon acoustic oscillations/baryon waves with comparison to PLANCK+BAO+SN. (according to them).

A strong case/consistent towards flat universe/infinite with uncertainty(that's me saying "more (x) likely"). WMAP ((2013)excluding the latest data) favors a flat universe 0.4% margin of error.Pointing towards Universe that is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. They can only conclude that the Universe is much larger than the volume they can directly observe.

Yes, but all of these observations pertain to the observable universe! We have no grounds for inferring the geometry of those regions of the universe that lie outside the Hubble sphere. Saying that CMB/LSS data favor a flat, infinite universe (or in some vague sense make it "more likely") is just wrong.

 

[Chronos]

The issue I have with an infinite universe is if it is infinite now, it has always been infinite, which implies the universe is also infinitely age. I just can't wrap my head around the idea we reside in a region which happens to be unnaturally young. On the other hand a finite universe is also unsettling with all the edge and what lies beyond questions you get peppered with. Steven Hawking likes the finite, but, unbounded approach. That works for me - even if I don't completely understand what it actually means. I believe the general consensus is the universe [not just the observable part] is really, really big. We don't know how big, and probably never will.

 

[jcsd]

The issue I have with an infinite universe is if it is infinite now, it has always been infinite, which implies the universe is also infinitely age. I just can't wrap my head around the idea we reside in a region which happens to be unnaturally young. On the other hand a finite universe is also unsettling with all the edge and what lies beyond questions you get peppered with. Steven Hawking likes the finite, but, unbounded approach. That works for me - even if I don't completely understand what it actually means. I believe the general consensus is the universe [not just the observable part] is really, really big. We don't know how big, and probably never will.

An infinite Universe doesn't imply it is infinite in age: take for example a flat FLRW Universe, its spatial slices are infinite in extent, but it has a definite starting point.

"Finite, but unbounded" is a term that is usually applied to the closed FLRW Universe whose spatial slices are topologically 3-spheres and thus it has an always-finite (but changing) spatial volume.

 

[phinds]

The issue I have with an infinite universe is if it is infinite now, it has always been infinite ...

Why? What's your reasoning on this? Why should infinite size imply infinite time?

 

[Chronos]

Good question, it just seems reasonable due to the whole spacetime thing. It is believed there is no spacetime without gravity and I assumed, perhaps in error, it would take an infinite amount of time for gravity to span an infinite universe. As usual, the multiverse comes to the rescue. I'm not convinced I'm satisfied with that alternative.

 

[julcab12]

Yes, but all of these observations pertain to the observable universe! We have no grounds for inferring the geometry of those regions of the universe that lie outside the Hubble sphere. Saying that CMB/LSS data favor a flat, infinite universe (or in some vague sense make it "more likely") is just wrong.

Before anything else. I'm not an expert. Just a lurker in this forum trying to understand as much as i can.^^

Here's the thing. We have a positive data showing a 'glimpse' of the geometry(Ob-Universe)with figures of uncertainty(open, closed, flat etc). When i say 'morelikey'(which seems to be the issue here lol). I'm referring to the 'constraint' of the data (PLANCK+BAO(boss)+SN) which is basically showing flatness to be dominant and favorable to the result. BTW What is outside the Hubble sphere?




"Among other cosmic parameters, says White, the BOSS analysis "also provides one of the best-ever determinations of the curvature of space. The answer is, it's not curved much."
Calling a three-dimensional universe "flat" means its shape is well described by the Euclidean i.e straight lines are parallel and triangles add up to 180 degrees. Extraordinary flatness means the universe experienced relatively prolonged inflation, up to a decillionth of a second or more, immediately after the big bang."

"One of the reasons we care is that a flat universe has implications for whether the universe is infinite," says Schlegel. "That means – while we can't say with certainty that it will never come to an end – it's likely the universe extends forever in space and will go on forever in time. Our results are consistent with an infinite universe."

 

[Chalnoth]

"Among other cosmic parameters, says White, the BOSS analysis "also provides one of the best-ever determinations of the curvature of space. The answer is, it's not curved much."
Calling a three-dimensional universe "flat" means its shape is well described by the Euclidean i.e straight lines are parallel and triangles add up to 180 degrees. Extraordinary flatness means the universe experienced relatively prolonged inflation, up to a decillionth of a second or more, immediately after the big bang."

"One of the reasons we care is that a flat universe has implications for whether the universe is infinite," says Schlegel. "That means – while we can't say with certainty that it will never come to an end – it's likely the universe extends forever in space and will go on forever in time. Our results are consistent with an infinite universe."

This is taking the conclusions of the study too far. We have a detection of the universe being flat at a level of about 0.005 (that is, the spatial curvature contribution to total space-time curvature is less than roughly half a percent or so). In order to say that the universe is exactly flat, we would need to improve experimental accuracy enough to add an infinite number of zeroes between the decimal and the 5. Obviously, that cannot ever be done.

That's the first point. The second point is that even if we dramatically improved our measurement of spatial curvature and that measurement remained flat, it would not say that our universe was infinite. It is perfectly possible to have a spatially-flat universe that wraps back on itself, for example (the shape would be a toroid, which is rather like the surface of a donut).

 

[julcab12]

This is taking the conclusions of the study too far. We have a detection of the universe being flat at a level of about 0.005 (that is, the spatial curvature contribution to total space-time curvature is less than roughly half a percent or so). In order to say that the universe is exactly flat, we would need to improve experimental accuracy enough to add an infinite number of zeroes between the decimal and the 5. Obviously, that cannot ever be done.

That's the first point. The second point is that even if we dramatically improved our measurement of spatial curvature and that measurement remained flat, it would not say that our universe was infinite. It is perfectly possible to have a spatially-flat universe that wraps back on itself, for example (the shape would be a toroid, which is rather like the surface of a donut).

I totally understand your point. As for the shape of the Universe, this depends on the overall curvature. The curvature depends on the amount of matter and energy in the Universe (Einstein's equations). The curvature and energy content can thus be estimated using a cosmological model.We can calculate the likelihood of the parameters in the model. Doing this one gets a curvature equal to, or very close to, zero. The analogue of which is a flat, smooth and infinitely extended bedsheet is dependent on shape. The shape (spacetime in GR), is in mathematical terms analogous to the shape of other geometrical objects. However, not necessarily the case for more general cosmological theories, some of which propose so-called topological defects and other geometrical objects which are not so easily visualized.

Much of the confusion is contributed by the extent of unknowns. Beyond these horizons we can never hope to reach, with our current understanding of things. The reason for bringing up this matter of horizons is that making statements about the Universe beyond the horizons (and out to infinity beyond) is on the verge of philosophy. Many exotic ideas exist about the nature of the un-observable Universe. These include multiverse, eternal inflation, local void, and many others.

Again going back. The claim is mostly bounded by positive observation/real datas. When they mentioned infinity it's not meant to be absolute(reachable?). As far as i understand. It could have been uncertain but definitely not unknown since we somehow have real values.^^

 

[phinds]

It is perfectly possible to have a spatially-flat universe that wraps back on itself, for example (the shape would be a toroid, which is rather like the surface of a donut).

I thought that toroidal was just one of many possible shapes for a bounded universe. Are you saying it is the only one?

 

[Chalnoth]

I thought that toroidal was just one of many possible shapes for a bounded universe. Are you saying it is the only one?

I think that's the only shape for a spatially-flat bounded universe.

 

[Chalnoth]

I totally understand your point. As for the shape of the Universe, this depends on the overall curvature.

No, it doesn't. Topology is distinct from curvature. It is entirely possible for a universe to have a closed topology but flat spatial curvature (like a torus).

 

[phinds]

I think that's the only shape for a spatially-flat bounded universe.

OK, thanks.

 

[julcab12]

No, it doesn't. Topology is distinct from curvature. It is entirely possible for a universe to have a closed topology but flat spatial curvature (like a torus).

Right. Curvature has no influence on the shape? I don't see any disconnection between the curvature of space /negative, positive or flat/ and the topology of the Universe /what is its shape = how is it connected/(sort of the same thing). Isn't curvature appears as a natural parameter in the geometrical model of spacetime?

It is entirely possible for a universe to have a closed topology but flat spatial curvature (like a torus).

Right. Euclidean 2-torus

 

[Chalnoth]

Right. Curvature has no influence on the shape? I don't see any disconnection between the curvature of space /negative, positive or flat/ and the topology of the Universe /what is its shape = how is it connected/(sort of the same thing). Isn't curvature appears as a natural parameter in the geometrical model of spacetime?

For any measured spatial curvature, you can come up with a scenario that permits a closed or open topology (provided the topology itself isn't observable, as it isn't in our universe).

Right. Euclidean 2-torus

In this case it would be a 3-torus.

 

[julcab12]

For any measured spatial curvature, you can come up with a scenario that permits a closed or open topology (provided the topology itself isn't observable, as it isn't in our universe).


In this case it would be a 3-torus.

Ah. Ok. Thanks!

 

[jcsd]

Yep one of the postulates of cosmology is that the Universe is homogeneous (on a large scale the same everywhere), this leads us to the conclusion that the geometry of space is homogeneous, leaving 3 possibilities: postively curved spherical geometry, zero curvature flat geometry or negatively curved hyperbolic geometry. However each of these geometries allow an unlimited number of different topologies, some compact (i.e. spatially finite), some non-compact (i.e. spatially infinite).

The problem is that the topology becomes independent of the physics in this case. However if we also postulate that space is isometric (the same in all directions), then the topology will be fixed by the homogeneous geometry (positive curvature leads to a finite Universe whereas zero or negative curvature leads to an infinite Universe). For example a 3-torus fails to be isometric in that you can travel off in a straight line an reach your starting point again, but whether you do reach your starting point and how far you have to travel to do so depends on which direction you go.

 

[Clayjay]

Now, if there is a finite amount of energy and matter in the Univers

Cosmology indicates there does not seem to be a finite amount of energy but instead, because of Dark Energy energy, an increasing energy is appearing out of nowhere called Dark energy or energy from an unknown source.

I'm by no means trained in physics, so I'd really appreciate it if you could keep it in layman's terms. Thank you very much in advance!

Your request for "layman's terms" to me is a request to understand Cosmology without the details. That is not only possible but should be required. The science of Cosmology operates through the logical connection of cause and effect on a cosmological scale. Humans operate on a scale approaching zero in a cosmological context but through the logic of cosmology - logic on a human scale is projected on the cosmos. The logical framework the greek's created that define cosmology are exactly the same today with some terminology changed. What the greek's called the four elements modern physics refers to as four phases of matter. So earth, water, air and fire of the the ancient greeks become solid, liquid, gas and plasma in modern physics. As language evolve words change. An element is now the smallest constituent of matter - the atom. Terms change but the logical framework of cosmology doesn't. Classical physics is based on logic from the greeks with the atom as the smallest constituent. Quantum mechanics goes deeper than atoms by ignoring classical physics prediction that electrons orbits would quickly decay into the nucleus to just claiming electron are stable regardless of classical physics prediction because of experimental results. Classical physics starts with an object the atom while Quantum mechanics starts with a subjective idea that magically electrons have stable orbits. Magically refers to a happening without logical explanation in a classical way. Quantum Mechanics is just as internally self consistent as Classical Physics but the atom turned out not to be solid but instead empty. Logic is internally self consistent so it is the starting conditions that separate Classical Physics and Quantum mechanics. Atoms and quanta are not the same thing in any way but both can be defined experimentally. They seem like dimetric concepts which setup working limits, which is a good thing. That thing is context.

This is reply to your original post. It may be helpful :-)

 

[phinds]

... An element is now the smallest constituent of matter - the atom.

Sounds like you need to brush up on your knowledge of fundamental particles. The atom is not even close to being the smallest constituent of matter. It is made up of protons, neutrons, and electrons, of which only the electron is a fundamental particle. Protons and neutrons are made up of quarks.

 

[guywithdoubts]

Cosmology indicates there does not seem to be a finite amount of energy but instead, because of Dark Energy energy, an increasing energy

Increasing in the sense of its effect on spacetime (that it increases its expansion) or increasing in the sense that it is permanently increasing in "quantity" or value, inherently?

Thank you all for your answers! I think I must read more about topology.

 

[Clayjay]

Sounds like you need to brush up on your knowledge of fundamental particles. The atom is not even close to being the smallest constituent of matter. It is made up of protons, neutrons, and electrons, of which only the electron is a fundamental particle. Protons and neutrons are made up of quarks.

The smallest practical is an atom in classical physics. A subatomic particle is considered a particle-wave. That is not a classical concept but the beginning of quantum mechanics. Context controls meaning. When is a particle not a particle - when it is a quantum particle. Duality is trademark quantum mechanics.

Sounds like you need to bush up or start leaning the formal rules of logic and meaning making as a separate field of study from science. Science is much more understandable when the foundation of science is understood. Science is a context before it has content that expresses knowing or understanding. Knowing the context of science greatly enhances understanding the content of science.

I think we view things from different vantage points but we share data points. Thanks for pointing out particle in a subatomic context. Partial is a term used in both contexts but the idea is different. Reality was solid in a classical way but in a quantum way reality hardly exist at all. The atom is .9999% empty - who knew :-)