csmyth3025

This might just be a matter of semantics. It's the variations of the gravitational field in space that dictate the inertial path of objects. We can't see or touch this field any more than we can see or touch empty space. So, to avoid unnecessary complication, we just say that the inertial movement of objects follow the curvature of space (more precisely, spacetime). As an approximation, if you're in a windowless space capsule orbiting the Earth you don't feel any force acting on you at all (ignoring miniscule tidal effects). For all you know you could be "coasting" along a straight line at a high or low velocity relative to some distant object or you could be sitting still relative to that object. Even though your space capsule is essentially free-falling in a gravitational field (accelerating to an outside observer), you don't notice any such acceleration because free-falling in a uniform gravitational field is equivalent to inertial movement (traveling in a straight line at a uniform speed) when you're immensely far away from any gravitating body. (ref. http://en.wikipedia....vitation_theory ) Chris Edited to correct spelling error

This is an interesting idea. I believe there are six known and postulated bosons: (ref. http://en.wikipedia.org/wiki/Bosons ) If I understand you correctly, all of the photons, gluons, W+/-, and Zo bosons, as well as the postulated but as yet undetected Higgs bosons and Gravitons in the early universe could all have quite comfortably occupied just about any arbitrarily small measurable space. The energy density would be immense, of course. Does our understanding of bosons still hold up at extremely high energy densities? This leaves the various fermions (quarks and leptons) remaining after the inflationary period and subsequent reheating to take up "space" so-to-speak - which was by this stage quite large as I understand it. Conversely, if quarks and leptons are thought to have already been present when the inflationary period began, this might set a lower limit on the "size" of the early universe that our known physics can accomodate. The mental picture I'm developing on this may be entirely off-base, so corrections are welcome. Chris Edited to correct errors in grammer

Is this the part you're having trouble with? (ref. http://en.wikipedia....n_of_velocities ) Chris

A more complete rendering of Sir Arthur Eddington's comment: (ref: Eddington, A.S., "The Nature of the Physical World," [1928], The Gifford Lectures 1927, Cambridge University Press: Cambridge UK, 1933, reprint, pp.74-75. ) The question of whether the concepts of entropy and evolution are compatible or contradictory is probably best addressed in a separate thread. It's one of those "hot button" topics that will no doubt draw more opinions than logical arguments . The "purely scientific" questions of whether the standard cosmological model and/or our current theory of gravity (general relativity) conflict with the second law of thermodynamics is an interesting one. I'm certainly no expert, but I'm thinking that the entropy of a closed system (in this case, the universe) increases over time not only due to the flow of heat from warmer regions to cooler regions, but also due to the flow of mass from areas of higher gravitational potential energy to areas of lower gravitational energy. I'll limit my reply to this observation for now. I'll have to think about this for a while. Perhaps a more knowledgeable member can respond more completely. Chris

(bold added by me) It seems odd that galaxies can be described as being both extremely homogenous and extremely disordered in the same sentence. It sounds a bit self-contradictory. In the context of entropy, though, homgenous and disordered have essentially the same meaning as far as I know. Although the early universe was, indeed, extremely homogenous, it still had fluctuations in its temperature as I mentioned in my previous post. Additionally, the matter in the universe possessed a lot of potential energy that could then be converted into kinetic energy as it clumped together. This is essentially what happened in order to form galaxies, stars, planets and ourselves. Each step in the process that results in a more ordered state (locally) is at the expenditure of energy that is globally less available to do work. Eventually, all the matter in the universe that is gravitationally bound to other matter will clump together and attain a minimal energy state. At the same time, all the kinetic energy released by the clumping of matter - as well as the ambient flux of radiation - will become both more widely dispersed and more evenly distributed. At some point way in the future the unavailability of energy to do work (entropy) will reach its maximum level because: (ref. http://en.wikipedia...._thermodynamics ) Chris Edited to correct mis-statement in the first paragraph.

Indeed, it seems that the proportion of radiation and ultra-relativistic mass (w= 1/3) compared to non-relativitstic mass (w= 0) has and will remain essentially unchanged. Is this correct? Chris

I wasn't quite thinking in terms of dark matter - but, rather, ordinary matter density and energy density. In regard to regular (non-relativistic) mass, I take it that the amount of non-relativistic mass was fixed in the early moments of the big bang and, according to current thinking, has remained and will remain essentially unchanged: (ref. http://en.wikipedia....he_strong_force ) and... (ref. http://en.wikipedia....on_annihilation ) These passages lead me to believe that any interaction involving quarks will not reduce the amount of quark (non-relativistic) mass in the universe. On the other hand, neutrinos - which apparently do have a vanishingly small amount of non-relativistic mass - have been continuously created since the big bang from energetic nuclear reactions such as nuclear fission, nuclear fusion and, notably, stellar collapse: (ref. http://en.wikipedia....trino_emissions ) This train of thought made me wonder if the proportion of non-relativistic mass (w = 0) compared to radiation (w = 1/3) in the universe is gradually increasing. Your response assures me, I believe, that this is not the case since the mass that neutrinos are thought to have is considered ultra-relativistic mass. Indeed, it seems that the proportion of radiation and ultra-relativistic mass (w= 1/3) compared to non-relativitstic mass (w= 0) has and will remain essentially unchanged. Is this correct? Chris Edited to add last paragraph.

I'm not sure that a super massive black hole from another universe is a very practical idea in terms of the science we have or the science we may develop. If it has no observable effect that we can measure from our little corner of the world then it must remain in the realm of philosophical speculation rather than scientific theory. That's not arrogance, it's just the way science works. Theories that are untestable (even indirectly) are just speculation. If they're postulated as a logical consquence of known science, they're called scientific speculation. Chris

(bold added by me for emphasis) I'm not sure you have the idea of entropy quite right concerning the CMB 300,000 years after the big bang and today, 13.7 billion years later. First, no energy has been converted to matter since about one trillionth of a second after the big bang, as far as I know. (ref. http://en.wikipedia....ectroweak_epoch ) Second, the CMB started with a temperature of about 3000o Kelvin 300,000 years after the big bang and there were minute irregularities (anisotropies) in its distribution due, at least in part, to the distribution of matter that was already present: (ref. http://en.wikipedia....mary_anisotropy ) I'm not sure what to make of your last statement (bold added). Although I agree that the entropy ("Unavailability of energy for useful work", to correct your implied definition) of the universe has increased over the last 13.7 billion years, this notion is a odds with your statement that the present distribution of energy is inconsistent. It is the inconsistent distribution of energy that makes energy available for useful work: (ref. http://en.wikipedia...._thermodynamics ) To be sure, since the present average temperature of the CMB is now about 2.73o Kelvin the temperature gradient available for useful work is a lot less than it was 13.7 billion years ago. Chris Edited to correct syntax and spelling errors

As I understand it, neutrinos are leptons (in the same family as electrons). Also, neutrinos are thought by some to be their own antiparticles: (ref. http://en.wikipedia....or_oscillations ) This leads to a curious situation in my mind. If neutrinos are their own antiparticles, then in the very early universe whatever number of neutrinos and (by identity) antineutrinos that existed (were initially created) would have remained relatively unchanged - since there would be no particle annihilation for neutrinos and their antiparticles. Also, since neutrinos are produced in various types of nuclear reactions - but only rarely interact with matter once formed, it seems that over the history of the universe the number of neutrinos must have been steadily increasing and will continue to do so. Does this steadily increasing proportion of neutrinos have any effect on the cosmos in general? I ask this in regard to the calculations that are made concerning the cosmological equation of state: (ref. http://en.wikipedia....tivistic_matter ) I'm not sure if neutrinos are treated as non-relativistic matter or as ultra-relativistic matter. Chris

I haven't read that before about the Higgs boson. Can you provide a reference? Chris

Black holes (even small ones) are not like billiard balls. They can't form a shell of any kind. If there was a way to "fire" black holes towards one location, their mutual gravitation would cause them to coalesce into one (bigger) black hole. Chris

The prolem, of course, is that we have nasty old gravity to deal with. If there is enough of it, it might just force all the stuff in the universe (including photons) to follow giant geodesics that will eventually lead it back to where it started (if the universe is closed). The "shape" of empty space is dictated by the fields that are contained in it. These fields tell all the stuff in the universe how to move. We don't know yet whether all that stuff will go flying off farther and farther forever or whether it will eventually come back around "full circle". As I understand it, our observations so far are leaning more towards the former rather than the latter. Chris

(ref. http://en.wikipedia....Repulsive_force ) Dark energy is just a shorthand way of saying "We don't know what it is, but it's causing the expansion of the universe to accelerate". Since we don't know what dark energy is, we also don't know if there's an endless supply of it or not. Chris

(ref. http://en.wikipedia....ki/Hadron_epoch ) Depending on how you choose to define matter, the hadron epoch was probably the earliest appearence of what we usually think of as matter (Baryons such as protons, neutrons, and their anti-particles; and mesons of various types - which are generally considered force carriers). The Lambda-CDM standard cosmological model is the most widely accepted model of how our universe evolved. It doesn't say anything about conditions earlier than about 10-36 seconds (the inflationary epoch) except that all parts of our observable universe were in causal contact prior to inflation. Because this is a model of our universe, it necessarily includes matter (because we observe matter in our universe). On the other hand, there are solutions to the Einstein Field Equations of General Relativity that permit universes that contain no matter (a de Sitter universe is one such example). These solutions are strictly theoretical since they obviously don't depict the universe we live in today. If the universe continues to expand (which it is expected to do) and the matter in it becomes more spread out, that matter will become more and more insignificant: (ref. http://en.wikipedia....Sitter_universe ) Chris

I think we're both on the same side of the question here. My comments about "fields" and the stress-energy tensor were in response to pantheory's comments ( Posted 19 June 2011 - 12:05 PM): My comments were intended to point out to pantheory that the existence of space-time does not require the existence of matter, but does require the existence of fields - which may or may not include matter as a component of the stress-energy tensor. Chris

I think J.C. MacSwell's reply covers it very well. The popular notion the the early universe "...began from a region smaller than a proton..." places a restriction on initial conditions that the big bang theory itself doesn't. This notion evokes a very specific image in the mind of the reader. As far as I know, the only conditions that the big bang theory requires is that the universe was very hot and dense and that all parts of it that are in our observable universe were in causal contact when the inflationary epoch began (about 10-36 sec. after the initial event). After the inflationary epoch (about 10-32 sec. after the initial event) the universe was many orders of magnitude larger (at least 1026), hot and dense (but less so) and there were parts of it that were no longer in causal contact. One might reason that the volume of our observable universe "...began from a region smaller than a proton..." by "running the clock backward" so-to-speak, but our observable universe doesn't necessarily encompass the entire universe. Our observations indicate that our observable universe is "very nearly flat": (ref. http://en.wikipedia....lem#Measurement ) As far as I know, this observered flatness implies that the entire universe is either very much larger than our observable universe or, perhaps, infinite. (NOTE: I'm not sure about the relationship between flatness and size, though) Chris Edited to add NOTE

I think the question of "field" vs "matter" is answered by the definition given for the stress-energy tensor in the Einstein Field Equations: (ref. http://en.wikipedia....s-energy_tensor ) In Newtonian gravity, mass is the source of the gravitational field. In GR, matter, radiation, and non-gravitational force fields contribute to the stress-energy tensor - which is defined as the source of the gravitational field. The GR view of the gravitational field allows for it to exist even if there is no contributing matter component. Chris

I'm afraid I don't follow your logic: If "There exists no space empty of field" and there are fields which do not require matter in order to exist, why does the existence of space require both a field and matter? This question focuses on the narrow question of whether the laws of physics as we know them allow for such a unverse. There is, of course, the other purely philosophical question of what a universe without matter (and, presumably, without observers) means. Chris (bold added by me for emphasis) As far as I know, the big bang theory postulates that the universe started in a very hot and dense state and evolved from there. The theory postulates no initial conditions for the "beginning entity". People generally assume that this beginning entity must have occupied a finite amount of space and contained a finite amount of energy. That's just how they visualize the big bang and how the media usually depicts the so-called "big bang singularity". The big bang theory places no such restriction on the beginning entity. It could just as easily have been infinite. The inflationary epoch would have quickly expanded the "rest" of the universe beyond our cosmic horizon. Chris

Chris, all of my statements above are related to the above quote by Einstein. Since there is no consensus in cosmology today concerning one definition of space, my opinion accordingly is that space ends where both matter and field end and its definition should not include the possibility of infinite space if neither matter nor field (ZPF) are believed to be infinite in quantity. The idea is that space without matter or field within it, would be meaningless or you might call it undefined -- such as a quantity divided by zero.... The quote you attribute to Einstein does, indeed seem to be a central part of his cosmological viewpoint. I have a copy of the fifteenth edition of Einstein's book "Relativity The Special and the General Theory" (1952, Methuen & Co.) which includes a Note to the Fifteenth Edition authored by Einstein in which he says: In the fifth appendix, however, he clearly states: (page 190) In the fifth appendix Einstein goes into some detail describing the notion of a field and, particularly, a pure gravitational field. We know from the Einstein Field Equations that the stress-energy tensor is the source of the gravitational field: (ref. http://en.wikipedia....s-energy_tensor ) Eistein has sent mixed signals on the question of the role matter plays in space-time. At one time he's said that space-time can't exist without matter and (in 1952, at least) he's also said that "there exists no space empty of field". As I mentioned in my earlier post, there are "vacuum" solutions the the EFE that do not require the presence of matter (the de Sitter universe being one). We can apply the cosmological principle, however, and since there is matter in our observable universe there is no reason to suspect that the rest of the universe is any different. It's important to note that the presence or absence of matter has no bearing on whether the universe is finite or infinite. Chris

Chris, all of my statements above are related to the above quote by Einstein. Since there is no consensus in cosmology today concerning one definition of space, my opinion accordingly is that space ends where both matter and field end and its definition should not include the possibility of infinite space if neither matter nor field (ZPF) are believed to be infinite in quantity. The idea is that space without matter or field within it, would be meaningless or you might call it undefined -- such as a quantity divided by zero. Our last postings crossed paths during my amendment, adding and changing a few sentences. Sorry about that Do you have a reference for that quote? On the subject of this thread: "Where does the Universe end? It must end somewhere!", the title itself states an assumption based on "common sense". Common sense doesn't include training in mathematics, logical deduction and experimental research, though. Science is very rigorous about these. The quote you attributed to Einstein seems to make common sense, but Einstein, as a scientist, also developed the Special Theory of Relativity in 1905. In this theory he proposed that an object's mass would increase and it's dimension along the axis of travel would shorten and its clock would slow down as it's speed relative to a "stationary" observer approached the speed of light. All of these notions seemed contrary to "common sense" at the time, but Einstein backed up his proposals with rigorous mathematics and sound logical deductions based on known science. His theory was able to explain known experimental observation (the null result of the Michelson-Morley experiment) in a mathematically precise way. To those who haven't studied physics and mathematics there are a lot of science concepts that don't seem to "make sense" or are "too complex to understand". This doesn't make them wrong. Most self-proposed alternative theories are based on "common sense" analogies that describe light as "...being like this..." or gravity as "...being like that..." They don't meet the tests of mathematical rigor and predictive ability that real scientific theories must in order to be accepted. Those in this forum who have extensive knowledge about the scientific process and the scientific theories we discuss here will always guage the value of proposed theories against the rigor they know has already been demanded of existing theories like Special and General Relativity and the Lambda-CDM standard cosmological model. They want to see mathematical formulas and observational evidence, not analogies. Chris

Chris, I generally agree with your comments but think that definitions of words are very important... ...I'm not suggesting that a definition of space should include or exclude theoretical volumes of space outside of what will ever be observable, I'm proposing the exclusion of what some propose as an infinite volume, from definitions of space. I'm discussing a definition of space that might answer the primary question of this thread, where does space end. Your question in quotes I think is a valid one but it seems to me like you are saying something like: what difference does it make how the universe started or any other question in cosmology that we could never know? We have evidence of things through observation and our nature as humans is to try to figure it all out so that we can better understand reality... ...so this is my take concerning what I think is a preferable answer. The sentences in your original post #635 that caught my eye were quoted by me as follows: In the first two sentences you used phrases like "..true answer..." and "...correct definition..." Now you're saying that "...this is my take concerning what I think is a preferable answer..." I would have to agree with your current reply "...that definitions of words are very important..." In your third sentence you characterized a universe (or "...volume of space...") that contains no matter as having no value or meaning. Now you're saying "...I'm not suggesting that a definition of space should include or exclude theoretical volumes of space outside of what will ever be observable, I'm proposing the exclusion of what some propose as an infinite volume, from definitions of space...." This current statement conflicts with your former dismissal of a space devoid of matter - a so-called de Sitter space: (ref. http://en.wikipedia....De_Sitter_space ) NOTE: A vacuum solution is a solution of a field equation in which the sources of the field are taken to be identically zero. That is, such field equations are written without matter interaction (i.e.- set to zero). (ref. http://en.wikipedia.org/wiki/Vacuum_solution ) Your current statement also conflicts with itself in that the first part of it says "...I'm not suggesting that a definition of space should include or exclude theoretical volumes of space outside of what will ever be observable..." and the second part of it says "...I'm proposing the exclusion of what some propose as an infinite volume..." Aside from your statement being self-contradictory, your proposal to exclude an infinite universe has no observational or theoretical basis. The universe may be finite or it may be infinite. Either one of these conditions is permitted in the currently accepted Lambda-CDM standard cosmological model. Observationally, the latest data shows that the universe is "flat" within about 2%: (ref. http://en.wikipedia....of_the_Universe ) On a side note, you probably already know that it's generally considered bad forum manners to change words in an existing post that change the meaning of the sentences in which they're contained. If you edit a previous post to correct spelling or math errors (or to add material) it should be noted in the edited post. This will help to avoid confusing those who are just starting to read the last few posts and the replies to those posts. Chris Edited to add NOTE about vacuum solutions

Let me pose your rhetorical question in somewhat different terms. I would be very interested in hearing opinions other than my own. The current observable universe has a (comoving distance) radius of approximately 46 billion light years. Additionally, the farthest (comoving) distance we will ever be able to detect is: (ref. http://en.wikipedia....rvable_universe ) If light - and by implication, any sort of information, signal, or effect - beyond a comoving distance of 62 billion light years can never reach us, does it make any difference at all to our observations what lies beyond? If one defines space to include volumes outside the confines of that which we will ever be able to observe and beyond the effects of which we will ever be able to detect, what would be the value or meaning of such a definition that's unrelated to any knowledge we can possibly have? Chris

There actually is a hypothesis that the universe did, indeed, "pop out of nothing": (ref. http://www.lifesci.s...ibbin/cosmo.htm ) I'm not sure how this works if there is truly "nothing" - that is, are there quantum fluctuations when there is "nothing" (no universe or "singularity" or anything at all)? Chris

In the ill-used ballon analogy people have a hard time understanding that the 2-D balloon surface represents the 3-D universe in which we live. The 2-D surface of a balloon is imbedded in a 3-D world (the one in which we live). The space manifold in which we live isn't imbedded in any sort of higher dimension as far as we know. It may have positive curvature (like a sphere), negative curvature (like a saddle) or just be flat (like a sheet of paper laying on a desk). As DrR points out, this manifold we live in is the whole enchilada. There are no outside dimensions (that we know about) and there is nothing outside of it. Chris