The Koch curve does not look the same if you scale in arbitrarily, only if you do it in powers of 3. This is different from a percolation cluster or a self-avoiding walk, which statistically look the same on arbitrary scales. This is related to the latter having a *local* scale symmetry.
Interesting article, but the definition of scale invariance may need to be more precisely articulated. There are reasons to believe that the actual "zoom law" in the universe is not necessarily the simple multiplicative law Howard Georgi used ("A scale transformation multiplies all dimensional quantities by a rescaling factor raised to the mass dimension" on page 2 of hep-ph/0703260). Laurent Nottale is probably the first person who explored that in depth with his scale relativity, and he ran into a lot of difficult and interesting problems doing so. Notably when one of his students discovered that this broke Leibnitz's rule.
7:17 AM, September 21, 2007
Thomas D said...
The main objection to unparticles, as a theoretical idea, is that they don't seem to solve any problem in particle theory. The Standard Model on its own has enough problems and unexplained features. To consider physics Beyond the Standard Model, one should have a reasonable expectation that the new physics throws some light on them, rather than being just something else added on.
It's the 'Who ordered that?' syndrome, except the supererogatory bit comes from theory not experiment.
There is a claim (Delgado et al 0707.4309) that a Higgs-unparticle connection can help with some problems of the electroweak breaking sector. If this is true, it might justify attention being paid to some particular models.
One worrying feature of many unparticle preprints is that they cite every single previous preprint or article on unparticles, whether they are relevant to the topic of the paper or not. Essentially the authors decided to search the arxiv for 'unparticle' and then cut and paste the whole resulting list of references regardless of what the papers actually say.
For example from Hannestad et al 0708.1404:
Unparticle phenomenology has been investigated in a large number of recent papers [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].
Steen's paper is about the supernova SN1987A. But he cites (among three dozen others) Mohanta and Giri arXiv:0707.1234 which is on a totally unrelated aspect of particle physics. None of the original results or formulas of the one paper are any use to the other. The only reason for such (to be frank) unscientific citation is back-scratching: the habit is mutually beneficial for the citees and therefore highly addictive.
It is a pyramid scheme. The result of this citation habit is massive inflation, and subsequent devaluation, of reference lists. They become useless either as a help for the reader to find relevant previous work or as an index of the usefulness of a paper ('topcite' etc). Gratuitous citation is certainly not confined to the unparticle sector, but it makes a particularly blatant and depressing case study.
Please don't think I picked out Steen on purpose. I have nothing against him personally or against his work! But his was the first paper I noticed which had such a long and mostly irrelevant list of references. Look at 0709.2583 - their reference [10] extends over three pages. It is an insult to the reader.
7:39 AM, September 21, 2007
Anonymous said...
More importantly, the unparticle stuff is a case study in how to launch a bandwagon. Write a paper that allows people to re-do calculations using techniques with which they are already familiar. Don't ask anyone to learn anything new. Georgi has made a career out of this kind of thing.
In evolutionary theory, one has become familiar with the idea that the success of really primitive organisms is determined almost entirely by their ability to reproduce en masse. Georgi would have dominated the pre-Cambrian era.
Thanks for the clarification on scale invariance. I admit I've been very brief with that. Maybe somewhat too brief.
Hi Thomas D,
Yes, that is exactly what I mean. The problem with that citation scheme is that it's crucial to act fast, because those who follow will cite those who came earlier. I doubt everybody has read all the papers he cited, as well as I doubt all of the papers cited are actually relevant for his/her work. It's a perfect example for what I mean with degeneration of secondary criteria - here, the citation index and working on fashionable topics (see e.g. previous post or S+D III).
Thanks for pointing out 0707.4309, that would be interesting indeed. See, it might very well be that it turns out this is the way to go, and I am not specifically against it or anything. I just have to say I find this development of how to chose a research topic very worrisome, and this rapid increase of papers on the subject is really amazing.
Best,
B.
PS: Regarding eye-insulting reference lists, I vaguely recall there used to be a LaTex style that converted [N,N+1,N+2,....M] into [N-M], whatever happened to that?
Whether Georgi is interesting can be empirically determined. His big problem is visible emergence from a vast inertial background of business as usual.
http://scitation.aip.org/prl/covers/99_12.jsp "...these yield a new combined limit (blue ellipse) in good agreement with the standard model (black star)."
Unless I'm blind, it is in poor agreement. There is an observed offset outside the Standard Model - as though the vacuum had a small chiral bias. But there cannot be such, so there Officially isn't.
Anonymous: Oh really? Maybe what you mean is that anyone could do what Georgi has done? So why don't you do it then, huh?
This is like what people used to say about electronic music. "Oh, but they're just pressing some buttons to create music. That's not difficult." But of course people who said that didn't actually create anything themselves.
Bee: there's the cite package (\usepackage{cite}), but it doesn't work with arxiv because they hyperlink the citations so you can click on each one. Thus the long lists.
4:15 PM, September 21, 2007
Anonymous said...
you can also use \usepackage[sort&compress]{natbib} to prevent arXiv from hyperlinking the citations see http://arxiv.org/help/faq/mistakes#nohypertex
Dear Bee, This is an off-topic question. Is it true that all that we know about dark matter/dark energy is derived from observations in the context of a theory of gravity (GR or its Newtonian approximation where applicable)?
I am not perfectly sure I understand your question. What do you mean with "observations in the context of a theory"? We have a whole number of observations, i.e. data. These can be described very good by using GR (the concordance model) with two additional terms that do not correspond to baryonic matter. What is so far lacking though is any microscopic explanation for these things. As I keep pointing out, this does then not necessarily mean there is actually a 'substance' that is 'vacuum energy', but it could as well mean that some other modification can be formulated 'as if' GR had this additional term. That is not to say that I could point to any attractive realization of this. A similar thing holds for dark matter, though here things look somewhat better, direct searches are running, and the microscopic properties can actually play a role for structure formation. If that is what you mean, then I would say yes, it is true. Best,
What I mean is that observations - of type I supernovae or of galactic rotation curves or of astronomical lensing or CMBR - are all interpreted within the context of General Relativity and the models spawned from it and therefrom we deduce the existence of stuff that isn't described by the Standard Model.
Most likely, we will be able add terms to the Standard Model to cover dark matter; but a faint possibility exists that dark matter/energy lie on the gravity side of the quantum gravity mystery.
Sure, in principle you can push the terms from one side to the other, i.e. it could be a modification of GR. There are people working on that as well. Let me see... for example
Extended Theories of Gravity and their Cosmological and Astrophysical Applications Capozziello and Francaviglia arXiv: 0706.1146
Abstract: We show that the origin of the dark matter and dark energy problems originates in the assumption of standard Einstein gravity that Newton's constant is fundamental. We discuss an alternate, conformal invariant, metric theory of gravity in which Newton's constant is induced dynamically, with the global induced one which is effective for cosmology being altogether weaker than the local induced one needed for the solar system. We find that in the theory dark matter is no longer needed, and that the accelerating universe data can be fitted without fine-tuning using a cosmological constant as large as particle physics suggests. In the conformal theory then it is not the cosmological constant which is quenched but rather the amount of gravity that it produces.
(I missed that talk, so don't ask me what he said)
Also
Cosmic Acceleration and Modified Gravity Author: Mark Trodden astro-ph/0607510
Abstract: I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing extensions to GR, illustrate these with two specific examples, and discuss the resulting observational and theoretical obstacles.
If the dark stuff stems from the gravity side, then a microscopic explanation might just be the wrong thing to look for. I can't say I favor either approach, I personally think it's something completely different. Also, one should be very careful about what the data actually says. I.e. what people usually do is they know the observed data can be fitted with LambdaCDM and the parameters are soandso. Then they go an try to find a theory that has a Lambda and/or CDM. Instead, it might be that a theory does not give directly rise to such terms, but still explains the observation. That is to say, I am not sure it's good to channel explanations through LambdaCDM. (Yes, one would think there should then be a formulation that looks similar to LambdaCDM, at least in some limit, but this might not be completely apparent.)
Does that help? Best,
B.
12:27 PM, September 23, 2007
Thomas D said...
I don't blame Georgi either ... it's not as if he needs a few hundred extra citations, he's just having fun. It's not his fault that people are hanging around until the LHC turns on.
I remember seeing his paper 'The Flavor Problem' from 1986 - 3 journal pages with not a single equation, but people still work on the flavor problem, it's a real and difficult one, and the paper has over 50 citations.
Back to the present, since there is a continuous infinity of field theory models, most of which can be coupled to the SM, there is a continuous infinity of papers that can be written about signals and bounds on them. We urgently need a selection criterion!
I suppose the criterion that applies to unparticles is their detectability due to the phase space (or 'spectral density') looking like a non-integer number of (free) particles.
But Neubert has a nice preprint (0708.0036) where he shows that interacting particles - for example in jets - can generically have a spectral density which looks quite similar to the unparticle one, for some typical parameter choices. The key word here is 'Sudakov resummation'. (Neubert has a monster reference list too, alas.)
Davoudiasl has just got his paper on cosmological / astrophysical bounds (0705.3636) accepted in PRL, and between him and Hannestad et al. and Neubert there is rather little space left for colliders to see any unparticles.
The exception is apparently if scale invariance is significantly broken by coupling to the Higgs, so that there is a relatively large mass gap. Whether the sector then still deserves to be called unparticles is debatable.
When we see an iceberg, we know we are only seeing the TIP of the iceberg above the water
We know about 9/10s is below We can speculate or guesstimate its mass, density & volume, but we can never be quite sure what is below the water or its shape, just from what we observe above.
After all there could be a submarine (or asteroid) trapped in the frozen ice below.
Hi Bee, not sure if you've gone in a circular argument with nothing conclusive.
If things behave differently at the quantum level and known physics breaks down at the planck scale - then there must be a different between the things that are large (galaxies, blackholes) and the things subatomic or microstate ... albeit the large proceeds from the small, the small is altered by the large.
I mean breaking things down to its constituent state, does not necessarily tell us the origins of the universe, but rather its constituent parts. Does mass precede gravity or viceversa.
5:38 AM, September 26, 2007
Late March, I saw a paper on the arXiv with the strange title 'Unparticle Physics' by Howard Georgi (hep-ph/0703260, Phys. Rev. Lett. 98:221601, 2007). The idea outlined there is that our world could contain fields that have very unusual properties - properties that no particle field could have. Georgi's paper is based on a scenario that goes back to Banks and Zaks in 1982 (Nucl. Phys. B 196:189, 1982) which investigates a class of scale invariant fields later termed 'BZ fields'. In the low energy limit, these could couple to the fields of the standard model with fairly unusual coupling of fractional dimension. Since their interaction with the known Standard Model particles could possibly be very weak, they might have gone unnoticed so far.
Scale invariance means roughly speaking a theory is the same no matter how close one looks. This typically is not the case with things we observe, but theoretically a possibility that is compelling because of its simplicity that is the very absence of such a scale. A nice example for scale invariance is e.g. the Koch curve (pictured to the right), where one can zoom in arbitrarily and the structures just repeat. In contrast to this, if we zoom in on things around us, structures change considerably, from Quarks to Quasars. [Image] The presence of such unusual fields would, because they can not be understood as particles, lead to phenomenological consequences different from all other expectations. E.g. cross-sections would display an energy dependence that could not be explained with theories so far considered. This could be observable even if one had only a missing energy signal.
I did not really look into the details of Georgi's proposal, but I have to say the paper is pretty much ingenious. It's a very original work that outlines a scenario with a couple of well made arguments, points out the interesting phenomenology and ends with a list of further possibly interesting things to examine. It's a paper whose destiny it is to become a top-cite.
One month later, there was a follow up paper "Another Odd Thing About Unparticle Physics" (Howard Georgi, arXiv: 0704.2457) about the propagator of the Unparticle fields. After this, there started a steady flow of further investigations of the properties of such fields and their phenomenology for particle physics, astrophysics,cosmology, CP violation, lepton flavor violation, muon decay, or neutrino oscillations, Unparticle fields became supersymmetric, colored, got deconstructed and topped off - just to give a very incomplete list [1]. The number of papers with Unparticle in the title up to now is March: 1April: 3 May: 15 June: 7 July: 16 August: 12 September: so far 7 The Unparticles are a theoretical possibility that has observable consequences, a splendid example for physics beyond the standard model, and an excellent playground. One can set bounds on the model from the absence of evidence in observations made so far, which will occupy people for some more while. On the other hand there is not the slightest indication that these things actually exist. Unlike e.g. supersymmetry, extra dimensions or GUT models, which attract a lot of people because of their multi-faceted motivations, there is to my knowledge no motivation for Unparticles besides the mere possibility of such a scenario. Reasons to work on the topic then sound like "Recently there has been much interest in the possible existence of ..." or "The possibility of a non-trivial scale invariant sector [...] was advocated by Georgi...". A very similar peak of interest followed on the proposal of extra dimensional models in 98 and 99 (for more details see here).
Here we have the visionary standing on the sea-shore, whilst the great ocean of truth lies all undiscovered before him [2]. A mission is planned to sail into the far distance, ready to leave the harbor in May 2008. The visionary points towards infinity and says: "It could be there is a civilization in the West. But it might be different from all we've imagined so far. Maybe they live on the bottom of sea, and what we will see of their cities are the tops of their skyscrapers."
Six months later, people have made detailed drawings of the undersea creatures, they have tried to find out how they would move, how they would live, how they would make love (and of course they would wear Levi's). And we would know their skyscrapers couldn't be too high because otherwise we had already seen them. And their music couldn't be too loud because otherwise we had already heard them. And their sex life couldn't be too wild because otherwise there was a lot of troubled water.
It kind of makes me wonder who's going to pick up the pebbles left behind.
[1] I apologize profoundly, but I did not read all of these papers, so please don't ask me for the details. For a more complete list, see here. [2] "I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me." ~ Isaac Newton, In Brewster, Memoirs of Newton (1855), vol II, Ch. 27
posted by Sabine Hossenfelder at 9:37 PM on Sep 20, 2007
"Unparticles"
16 Comments -
This comment has been removed by the author.
9:46 PM, September 20, 2007
The Koch curve does not look the same if you scale in arbitrarily, only if you do it in powers of 3. This is different from a percolation cluster or a self-avoiding walk, which statistically look the same on arbitrary scales. This is related to the latter having a *local* scale symmetry.
2:06 AM, September 21, 2007
Interesting article, but the definition of scale invariance may need to be more precisely articulated. There are reasons to believe that the actual "zoom law" in the universe is not necessarily the simple multiplicative law Howard Georgi used ("A scale transformation multiplies all dimensional quantities by a rescaling factor raised to the mass dimension" on page 2 of hep-ph/0703260). Laurent Nottale is probably the first person who explored that in depth with his scale relativity, and he ran into a lot of difficult and interesting problems doing so. Notably when one of his students discovered that this broke Leibnitz's rule.
7:17 AM, September 21, 2007
The main objection to unparticles, as a theoretical idea, is that they don't seem to solve any problem in particle theory. The Standard Model on its own has enough problems and unexplained features. To consider physics Beyond the Standard Model, one should have a reasonable expectation that the new physics throws some light on them, rather than being just something else added on.
It's the 'Who ordered that?' syndrome, except the supererogatory bit comes from theory not experiment.
There is a claim (Delgado et al 0707.4309) that a Higgs-unparticle connection can help with some problems of the electroweak breaking sector. If this is true, it might justify attention being paid to some particular models.
One worrying feature of many unparticle preprints is that they cite every single previous preprint or article on unparticles, whether they are relevant to the topic of the paper or not. Essentially the authors decided to search the arxiv for 'unparticle' and then cut and paste the whole resulting list of references regardless of what the papers actually say.
For example from Hannestad et al 0708.1404:
Unparticle phenomenology has been
investigated in a large number of recent papers [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].
Steen's paper is about the supernova SN1987A. But he cites (among three dozen others) Mohanta and Giri arXiv:0707.1234 which is on a totally unrelated aspect of particle physics. None of the original results or formulas of the one paper are any use to the other. The only reason for such (to be frank) unscientific citation is back-scratching: the habit is mutually beneficial for the citees and therefore highly addictive.
It is a pyramid scheme. The result of this citation habit is massive inflation, and subsequent devaluation, of reference lists. They become useless either as a help for the reader to find relevant previous work or as an index of the usefulness of a paper ('topcite' etc). Gratuitous citation is certainly not confined to the unparticle sector, but it makes a particularly blatant and depressing case study.
Please don't think I picked out Steen on purpose. I have nothing against him personally or against his work! But his was the first paper I noticed which had such a long and mostly irrelevant list of references. Look at 0709.2583 - their reference [10] extends over three pages. It is an insult to the reader.
7:39 AM, September 21, 2007
More importantly, the unparticle stuff is a case study in how to launch a bandwagon. Write a paper that allows people to re-do calculations using techniques with which they are already familiar. Don't ask anyone to learn anything new. Georgi has made a career out of this kind of thing.
In evolutionary theory, one has become familiar with the idea that the success of really primitive organisms is determined almost entirely by their ability to reproduce en masse. Georgi would have dominated the pre-Cambrian era.
8:00 AM, September 21, 2007
Hi Thomas L., Hi Christophe:
Thanks for the clarification on scale invariance. I admit I've been very brief with that. Maybe somewhat too brief.
Hi Thomas D,
Yes, that is exactly what I mean. The problem with that citation scheme is that it's crucial to act fast, because those who follow will cite those who came earlier. I doubt everybody has read all the papers he cited, as well as I doubt all of the papers cited are actually relevant for his/her work. It's a perfect example for what I mean with degeneration of secondary criteria - here, the citation index and working on fashionable topics (see e.g. previous post or S+D III).
Thanks for pointing out 0707.4309, that would be interesting indeed. See, it might very well be that it turns out this is the way to go, and I am not specifically against it or anything. I just have to say I find this development of how to chose a research topic very worrisome, and this rapid increase of papers on the subject is really amazing.
Best,
B.
PS: Regarding eye-insulting reference lists, I vaguely recall there used to be a LaTex style that converted [N,N+1,N+2,....M] into [N-M], whatever happened to that?
8:35 AM, September 21, 2007
Whether Georgi is interesting can be empirically determined. His big problem is visible emergence from a vast inertial background of business as usual.
http://scitation.aip.org/prl/covers/99_12.jsp
"...these yield a new combined limit (blue ellipse) in good agreement with the standard model (black star)."
Unless I'm blind, it is in poor agreement. There is an observed offset outside the Standard Model - as though the vacuum had a small chiral bias. But there cannot be such, so there Officially isn't.
3:16 PM, September 21, 2007
Anonymous: Oh really? Maybe what you mean is that anyone could do what Georgi has done? So why don't you do it then, huh?
This is like what people used to say about electronic music. "Oh, but they're just pressing some buttons to create music. That's not difficult." But of course people who said that didn't actually create anything themselves.
Bee: there's the cite package (\usepackage{cite}), but it doesn't work with arxiv because they hyperlink the citations so you can click on each one. Thus the long lists.
4:15 PM, September 21, 2007
you can also use
\usepackage[sort&compress]{natbib}
to prevent arXiv from hyperlinking the citations see
http://arxiv.org/help/faq/mistakes#nohypertex
9:44 PM, September 21, 2007
Dear Bee,
This is an off-topic question. Is it true that all that we know about dark matter/dark energy is derived from observations in the context of a theory of gravity (GR or its Newtonian approximation where applicable)?
10:11 AM, September 23, 2007
Hi Arun:
I am not perfectly sure I understand your question. What do you mean with "observations in the context of a theory"? We have a whole number of observations, i.e. data. These can be described very good by using GR (the concordance model) with two additional terms that do not correspond to baryonic matter. What is so far lacking though is any microscopic explanation for these things. As I keep pointing out, this does then not necessarily mean there is actually a 'substance' that is 'vacuum energy', but it could as well mean that some other modification can be formulated 'as if' GR had this additional term. That is not to say that I could point to any attractive realization of this. A similar thing holds for dark matter, though here things look somewhat better, direct searches are running, and the microscopic properties can actually play a role for structure formation. If that is what you mean, then I would say yes, it is true. Best,
B.
10:56 AM, September 23, 2007
Dear Bee,
What I mean is that observations - of type I supernovae or of galactic rotation curves or of astronomical lensing or CMBR - are all interpreted within the context of General Relativity and the models spawned from it and therefrom we deduce the existence of stuff that isn't described by the Standard Model.
Most likely, we will be able add terms to the Standard Model to cover dark matter; but a faint possibility exists that dark matter/energy lie on the gravity side of the quantum gravity mystery.
11:06 AM, September 23, 2007
Hi Arun,
Sure, in principle you can push the terms from one side to the other, i.e. it could be a modification of GR. There are people working on that as well. Let me see... for example
Extended Theories of Gravity and their Cosmological and Astrophysical Applications
Capozziello and Francaviglia
arXiv: 0706.1146
or
Dark matter and dark energy - Fact or fiction?
Speaker: Philip Mannheim
Abstract: We show that the origin of the dark matter and dark energy problems originates in the assumption of standard Einstein gravity that Newton's constant is fundamental. We discuss an alternate, conformal invariant, metric theory of gravity in which Newton's constant is induced dynamically, with the global induced one which is effective for cosmology being altogether weaker than the local induced one needed for the solar system. We find that in the theory dark matter is no longer needed, and that the accelerating universe data can be fitted without fine-tuning using a cosmological constant as large as particle physics suggests. In the conformal theory then it is not the cosmological constant which is quenched but rather the amount of gravity that it produces.
(I missed that talk, so don't ask me what he said)
Also
Cosmic Acceleration and Modified Gravity
Author: Mark Trodden
astro-ph/0607510
Abstract: I briefly discuss some attempts to construct a consistent modification to General Relativity (GR) that might explain the observed late-time acceleration of the universe and provide an alternative to dark energy. I mention the issues facing extensions to GR, illustrate these with two specific examples, and discuss the resulting observational and theoretical obstacles.
If the dark stuff stems from the gravity side, then a microscopic explanation might just be the wrong thing to look for. I can't say I favor either approach, I personally think it's something completely different. Also, one should be very careful about what the data actually says. I.e. what people usually do is they know the observed data can be fitted with LambdaCDM and the parameters are soandso. Then they go an try to find a theory that has a Lambda and/or CDM. Instead, it might be that a theory does not give directly rise to such terms, but still explains the observation. That is to say, I am not sure it's good to channel explanations through LambdaCDM. (Yes, one would think there should then be a formulation that looks similar to LambdaCDM, at least in some limit, but this might not be completely apparent.)
Does that help? Best,
B.
12:27 PM, September 23, 2007
I don't blame Georgi either ... it's not as if he needs a few hundred extra citations, he's just having fun. It's not his fault that people are hanging around until the LHC turns on.
I remember seeing his paper 'The Flavor Problem' from 1986 - 3 journal pages with not a single equation, but people still work on the flavor problem, it's a real and difficult one, and the paper has over 50 citations.
Back to the present, since there is a continuous infinity of field theory models, most of which can be coupled to the SM, there is a continuous infinity of papers that can be written about signals and bounds on them. We urgently need a selection criterion!
I suppose the criterion that applies to unparticles is their detectability due to the phase space (or 'spectral density') looking like a non-integer number of (free) particles.
But Neubert has a nice preprint (0708.0036) where he shows that interacting particles - for example in jets - can generically have a spectral density which looks quite similar to the unparticle one, for some typical parameter choices. The key word here is 'Sudakov resummation'. (Neubert has a monster reference list too, alas.)
Davoudiasl has just got his paper on cosmological / astrophysical bounds (0705.3636) accepted in PRL, and between him and Hannestad et al. and Neubert there is rather little space left for colliders to see any unparticles.
The exception is apparently if scale invariance is significantly broken by coupling to the Higgs, so that there is a relatively large mass gap. Whether the sector then still deserves to be called unparticles is debatable.
6:58 AM, September 24, 2007
When we see an iceberg, we know we are only seeing the TIP of the iceberg above the water
We know about 9/10s is below
We can speculate or guesstimate its mass, density & volume, but we can never be quite sure what is below the water or its shape, just from what we observe above.
After all there could be a submarine (or asteroid) trapped in the frozen ice below.
5:31 AM, September 26, 2007
Hi Bee, not sure if you've gone in a circular argument with nothing conclusive.
If things behave differently at the quantum level and known physics breaks down at the planck scale - then there must be a different between the things that are large (galaxies, blackholes) and the things subatomic or microstate ... albeit the large proceeds from the small, the small is altered by the large.
I mean breaking things down to its constituent state, does not necessarily tell us the origins of the universe, but rather its constituent parts. Does mass precede gravity or viceversa.
5:38 AM, September 26, 2007