Mowgli

Thank you all for your replies, and thanks Martin for referring me to Ashtekar's paper. After reading and thinking about it, I realized what my trouble with the Big Bang theory was. I thought I would summarize my findings here, more for my own benefit than anybody else's. Classical theories (including SR and QM) treat space as continuous nothingness; hence the term space-time continuum. In this view, objects exist in continuous space and interact with each other in continuous time. Although this notion of space time continuum is intuitively appealing, it is, at best, incomplete. Consider, for instance, a spinning body in empty space. It is expected to experience centrifugal force. Now imagine that the body is stationary and the whole space is rotating around it. Will it experience any centrifugal force? It is hard to see why there would be any centrifugal force if space is empty nothingness. GR introduced a paradigm shift by encoding gravity into space-time thereby making it dynamic in nature, rather than empty nothingness. Thus, mass gets enmeshed in space (and time), space becomes synonymous with universe, and the spinning body question becomes easy to answer. Yes, it will experience centrifugal force if it is the universe that is rotating around it because it is equivalent to the body spinning. And, no, it won't, if it is in just empty space. But "empty space" doesn't exist. In the absence of mass, there is no space-time geometry. So, naturally, before the Big Bang (if there was one), there couldn't be any space, nor indeed could there be any "before." Note, however, that the Ashtekar paper doesn't clearly state why there had to be a big bang. The closest it gets is that the necessity of BB arises from the encoding of gravity in space-time in GR. Despite this encoding of gravity and thereby rendering space-time dynamic, GR still treats space-time as a smooth continuum -- a flaw, according to Ashtekar, QG will rectify. Now, if we accept that the universe started out with a big bang (and from a small region), we have to account for quantum effects. Space-time has to be quantized and the only right way to do it would be through quantum gravity. Through QG, we expect to avoid the Big Bang singularity of GR, the same way QM solved the unbounded ground state energy problem in the hydrogen atom. What I described above is what I understand to be the physical arguments behind modern cosmology. The rest is a mathematical edifice built on top of this physical (or indeed philosophical) foundation. If you have no strong views on the philosophical foundation (or if your views are consistent with it), you can accept BB with no difficulty. Unfortunately, I do have differing views. My views revolve around the following questions. (These are links to posts in my blog. If you feel that I'm trying to promote my blog in this forum, please indicate it in this thread and I will cut and paste here.) What is space? Why is the speed of light important in it? Where does the Heisenberg Uncertainty Principle come from? These may sound like useless philosophical musings, but I do have some concrete (and in my opinion, important) results, listed below. These are again links to my blog. Are GRBs and Radio Sources Luminal Booms? (An article published in IJMP-D, which became one of the "Top Accessed Articles" of the journal. ) Light Travel Time Effects and Cosmological Features (Trying to get this one published.) There articles are my efforts to sound like a "boffin" ! There is much more work to be done on this front. But for the next couple of years, with my new book contract and pressures from my quant career, I will not have enough time to study GR and cosmology with the seriousness they deserve. I hope to get back to them once the current phase of spreading myself too thin passes. Then I will be back with more posts, and hopefully with more results. Sorry for the delay in getting back to the thread. I was trying to put together the articles/post linked to here the whole of last week.

Sorry about the delay, got side-tracked with some personal issues. I was working on a reply (as below), but wanted to provide links to a couple of articles, which I may add by editing this post later. Strange that you should recommend Abhay Ashtekar -- he taught me QM during my graduate school years. (Not that it improves my credibility.) I will certainly read the article though. Thanks Martin. I think I got over the 13.7 billion year hurdle -- Swansont pointed out that light travel time might have been included in the calculation, and you pointed out that the singularity could have an infinite extent in space. Though not satisfied with the validity of BB, I can accept these arguments. My main beef is this: what does it mean to say that space-time expands when we cannot clearly articulate what space and time are? One sensible definition of space is that it is a cognitive construct (much like smell or sound) or a representation of our sensory inputs, which is a view readily embraced in philosophy and neuroscience. Attributing a reality to space that it probably doesn't have, and then imagining its asymptotic and singular properties is a bit weird. The perceptual view of space, though it might sound too philosophical to be useful, was behind my last physics paper published in IJMP-D, which suggested models to certain astrophysical observations. I'm trying to get a sequel (looking at cosmological features) published, but no luck so far. The Big Bang theory, to me, looks like a big leap of faith in terms of its agreement with observations. You know, if you have n+1 points in a 2-D space, you can always find an nth degree polynomial that will go through them. But it is a stretch to call it a model/theory explaining the points. Same with BB. Of course, the skepticism of an ex-physicist is no commentary on the validity of a well-accepted theory. But I wonder, do people actually think long and hard before accepting a theory? Or do they just blindly trust their professors and text books? But you are right, I should invest more time to understand what modern cosmology says, although I may not accept it in the end anyways. Hi Martin, Again, apologize for the delay. My blog has fairly poor traffic -- about 30 to 50 hits a day, probably more than half of them from my friends. The best day I had so far was 102 hits. The trouble with the blog is it is not focused, much like its author. I know that I could greatly improve the traffic if I picked just one topic -- say quantitative finance. But that's just not me... I don't think I have any general readership at all in India, and very little in Singapore. Any way, my current tracking program doesn't give any geographic break down. The book is also doing badly, haven't broken even yet. Luckily I have day job that pays well. At least, so far -- you never know with the current financial meltdown. My next book is going to be on quantitative finance. It is a project proposed by a prestigious publisher. I'm looking forward to working on it, but it will limit the amount of time I have to pursue cosmology and philosophy and these debates and so on... Thanks for Ashtekar's paper. Going through it now...

I am a physicist, but I don’t quite understand the Big Bang theory. Let me tell you why. The Big Bang theory says that the whole universe started from a “singularity” — a single point. The first question then is, a single point where? It is not a single point “in space” because the whole space was a single point. The Discovery channel would put it fancifully that “the whole universe could fit in the palm of your hand,” which of course it could not. Your palm would also be a little palm inside the little universe in that single point. The second question is, if the whole universe was inside one point, what about all the points around it? Physicists would advise you not to ask such stupid questions. Don’t feel bad, they have asked me to shut up as well. Some of them may kindly explain that the other points may be parallel universes. Others may say that there are no “other” points. They may point out (as Steven Weinberg does in The Dreams of a Final Theory) that there is nothing more to the north of the North Pole. I consider this analogy more of a semantic argument than a scientific one, but let’s buy this argument for now. The next hurdle is that the singularity is in space-time — not merely in space. So before the Big Bang, there was no time. Sorry, there was no “before!” This is a concept that my five year old son has problems with. Again, the Big Bang cosmologist will point out that things do not necessarily have to continue backwards — you may think that whatever temperature something is at, you can always make it a little colder. But you cannot make it colder than absolute zero. True, true; but is temperature the same as time? Temperature is a measure of hotness, which is an aggregate of molecular speeds. And speed is distance traveled in unit time. Time again. Hmmm…. I am sure it is my lack of imagination or incompleteness of training that is preventing me from understanding and accepting this Big Bang concept. But even after buying the space-time singularity concept, other difficulties persist. Firstly, if the whole universe is at one point at one time, one would naively expect it to make a super-massive black hole from which not even light can escape. Clearly then, the whole universe couldn’t have banged out of that point. But I’m sure there is a perfectly logical explanation why it can, just that I don’t know it yet. May be some of my readers will point it out to me? Second, what’s with dark matter and dark energy? The Big Bang cosmology has to stretch itself a bit with the notion of dark energy to account for the large scale dynamics of the observed universe. Our universe is expanding (or so it appears) at an accelerating rate, which can only be accounted for by assuming that there is an invisible energy pushing the galaxies apart. Within the galaxies themselves, stars are moving around as though there is more mass than we can see. This is the so called dark matter. Although “dark” signifies invisible, to me, it sounds as though we are in the dark about what these beasts are! The third trouble I have is the fact that the Big Bang cosmology violates special relativity (SR). This little concern of mine has been answered in many different ways: One answer is that general relativity “trumps” SR — if there are conflicting predictions or directives from these two theories, I was advised to always trust GR. Besides, SR applies only to local motion, like spaceships whizzing past each other. Non-local events do not have to obey SR. This makes me wonder how events know whether they are local or not. Well, that was bit tongue in cheek. I can kind of buy this argument (based on curvature of space-time perhaps becoming significant at large distances), although the non-scientific nature of local-ness makes me uneasy. (During the inflationary phase in the Big Bang theory, were things local or non-local?) Third answer: In the case of the Big Bang, the space itself is expanding, hence no violation of SR. SR applies to motion through space. (Wonder if I could’ve used that line when I got pulled over on I-81. “Officer, I wasn’t speeding. Just that space in between was expanding a little too fast!”) Speaking of space expanding, it is supposed to be expanding only in between galaxies, not within them, apparently. I’m sure there is a perfectly logical explanation why, probably related to the proximity of masses or whatnot, but I’m not well-versed enough to understand it. In physics, disagreement and skepticism are always due to ignorance. But it is true that I have no idea what they mean when they say the space itself is expanding. If I stood in a region where the space is expanding, would I become bigger and would galaxies look smaller to me? Note that it is necessary for space to expand only between galaxies. If it expanded everywhere, from subatomic to galactic scales, it would look as though nothing changed. Hardly satisfying because the distant galaxies do look as though they are flying off at great speeds. I guess the real question is, what exactly is the difference between space expanding between two galaxies and the two galaxies merely moving away from each other? One concept that I find bizarre is that singularity doesn’t necessarily mean single point in space. It was pointed out to me that the Big Bang could have been a spread out affair — thinking otherwise was merely my misconception, because I got confused by the similarity between the words “singularity” and single. People present the Big Bang theory in physics pretty much like Evolution in biology, implying the same level of infallibility. But I feel that it is disingenuous to do that. To me, it looks as though the theory is so full of patchwork, such a mathematical collage to cook up something that is consistent with GR that it is hard to imagine that it corresponds to anything real (ignoring, for the moment, my favorite question — what is real?) But popular writers have embraced it. For instance, Ray Kurzweil and Richard Dawkins put it as a matter of fact in their books, lending it a credence that it perhaps doesn’t merit. [This post is from a recent entry in my "Unreal Blog." Hope you like it!]

Glad to report that the paper describing this idea has been accepted for publication in IJMP-D. Here is the journal ref: International Journal of Modern Physics D, Vol. 16, No. 6 (2007) 983-1000. Post-print version URL: http://ejournals.wspc.com.sg/ijmpd/16/1606/S0218271807010559.html

The Asian Tsunami two and a half years ago unleashed tremendous amount energy on the coastal regions around the Indian ocean. What do you think would've have happened to this energy if there had been no water to carry it away from the earthquake? I mean, if the earthquake (of the same kind and magnitude) had taken place on land instead of the sea-bed as it did, presumably this energy would've been present. How would it have manifested? As a more violent earthquake? Or a longer one? I picture the earthquake (in cross-section) as a cantilever spring being held down and then released. The spring then transfers the energy to the tsunami in the form of potential energy, as an increase in the water level. As the tsunami radiates out, it is only the potential energy that is transferred; the water doesn't move laterally, only vertically. As it hits the coast, the potential energy is transferred into the kinetic energy of the waves hitting the coast (water moving laterally then). Given the magnitude of the energy transferred from the epicenter, I am speculating what would've happened if there was no mechanism for the transfer. Any thoughts?

Thanks for the article. I read it rather carefully. I see some issues: The lifetimes fitted using two different fitting methods were off by more than 7 sigma, indicating that some systematic errors were not taken into account. The muon decay time is defined from the time the capture in the scintillator rather than the pion decay generating the muon. One could use the stationarity property of exponential distributions to argue that the lifetime measurement is independent of the shifts in the time origin, which would work if the shifts were constant. Is it obvious that the cross section of charged current decay is independent of the presence of dense matter as in the scintillator? Besides, one sentence in the article bothers me: "Following our calibration, we checked that the high voltage supply and discriminator settings were fixed such that the observed count rate agreed to a good approximation with our theoretical prediction for the rate of muon decay events in the cylinder." To me, it sounds like they tweaked the apparatus to match the expected rate. I should check with the author what it really means.

Okay, let's say the decay time of the muon measured in the lab frame is Tm. We would conclude that the decay time in the muon rest frame is a smaller value tm because of SR time dilation. We measure a large number of tm's and take the half life as the muon lifetime, say tau_m. But, if we had taken the distribution of Tm's and fitted an exponential, we would've gotten a larger lifetime, say Tau_m. We then go and look muon decay in a cosmic rays and find that decay time is Dm (say). We argue that the fraction of a muon lasting Dm is too small using a lifetime tau_m and so the decay time must be dilated. But, if we use the larger lifetime Tau_m, the slow atmospheric deay may not look improbable. So, the cyclicity is that while measuring and veryfying the lifetime, we make the SR correction and call it a proof. Of course, if you can measure the decay time of muons that are at rest in our frame, (and get a lifetime equal to tau_m), we could really call it a proof of SR. The point is that muons are never at rest.

I wonder whether there is a trivial explanation for the longevity of high speed muons. The muon lifetime (half-life) is computed assuming that the measured decay time is dilated according to SR time dilation. Thus, the computed half-life is significantly smaller than the measured decay times. When the atmospheric muons in cosmic rays are studied, their half-life is assumed to be this smaller value computed in accordance with SR. When we see that they do reach sea level, we realize that their decay time is much longer than the computed lifetime. In other words, the decay time appears dilated. We then present this as evidence that SR is correct. This cyclic dependency in the “evidence” in favor of SR is not usually highlighted.

To swansont on why I thought 13 b LY implied an age of 26 b years: When you say that there is a galaxy at 13 b LY away, I understand it to mean that 13 billion years ago my time, the galaxy was at the point where I see it now (which is 13 b LY away from me). Knowing that everything started from the same point, it must have taken the galaxy at least 13 b years to get where it was 13 b years ago. So 13+13. I'm sure I must be wrong. To Martin: You are right, I need to learn quite a bit more about cosmology. But a couple of things you mentioned surprise me -- how do we observe stuff that is receding from as FTL? I mean, wouldn't the relativistic Doppler shift formula give imaginary 1+z? And the stuff beyond 14 b LY away - are they "outside" the universe? I will certainly look up and read the authors you mentioned. Thanks.

I was reading http://www.space.com/scienceastronomy/distant_galaxy_040216.html stating that they found a galaxy at about 13 billion light years away. I am trying to figure out what that statement means. To me, it means that 13 billion years ago, this galaxy was where we see it now. Isn't that what 13b LY away means? If so, wouldn't that mean that the universe has to be at least 26 billion years old? I mean, the whole universe started from one singular point; how could this galaxy be where it was 13 billion years ago unless it had at least 13 billion years to get there? (Ignoring the inflationary phase for the moment...) I have heard people explain that the space itself is expanding. What the heck does that mean? Isn't it just a fancier way of saying that the speed of light was smaller some time ago?

Is this an SR or GR effect? Note that the acceleration of each twin can be made constant. Have the twins cross each other at a high speed at a constant linear deceleration. They will cross again each other at the same speed after sometime. During the crossings, their clocks can be compared. Thus you can keep the accelerations of the clocks constant and always directed towards each other. Would that mean that they always run faster (time contraction) rather than slower?

This was posted under the thread "Twin Paradox" earlier. The Twin Paradox is usually explained away by arguing that the traveling twin feels the motion because of his acceleration/deceleration, and therefore ages slower. But what will happen if the twins both accelerate symmetrically? That is, they start from rest from one space point with synchronized clocks, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it seems that when the two clocks are together at the end of the journey, at the same point, and at rest with respect to each other, they have to agree. Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one. In SR, every clock that is in motion with respect to an observer's clock is supposed run slower. Or, the observer's clock is always the fastest. So, for each twin, the other clock must be running slower. However, when they come back together at the end of the journey, they have to agree. This can happen only if each twin sees the other's clock running faster at some point during the journey. What does SR say will happen in this imaginary journey? (Note that the acceleration of each twin can be made constant. Have the twins cross each other at a high speed at a constant linear deceleration. They will cross again each other at the same speed after sometime. During the crossings, their clocks can be compared.)

I guess the question is something like, "Are space and time real?" Well, one way of answering it would be with other questions like, is smell real? Is sound real? Sound is an experience associated with the sensory inputs that our ears receive. It is a congnitive representation of those inputs. There is nothing real about the subjective experience of sound; only the sensory inputs can be thought of as real. Similarly, space is (by and large) a representation of the light inputs to our eyes. Is it real? You be the judge!

I think I didn't say it right. I meant, by symmetry arguments, at the end of the journey when the two clocks are together at the same point at rest with respect to each other, they have to agree. During the journey, each clock is dilated with respect to the other. Since they have to satisfy the boundary condition that there should be no dilation at the end of the journey, when does the time contraction happen?

Right, but what happens if you accelerate both symmetrically? That is to say, they start from rest from one space point, and get back to the same space point at rest by accelerating away from each other for some time and decelerating on the way back. By the symmetry of the problem, it would seem obvious that the clocks should agree, neither would be dilated wrt the other. Then again, during the whole journey, each clock is in motion (accelerated or not) with respect to the other one, and is supposed run slower than the other. So at what point during the journey does time dilation become time contraction?