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Nov
22nd
Tue
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Raphael Bousso: Thinking About the Universe on the Larger Scales

        

“‘The far-reaching questions are things like how do we unify all the laws of nature, how do you do quantum gravity, how do you understand how gravitation and quantum mechanics fit together, how does that fit in with all the other matter and forces that we know?’ That’s a really far-reaching and important question. 

Another far-reaching question is "what does the world look like on the largest scales?" What does the universe look like on the largest scales? How special is the part of the universe that we see?  Are there other possibilities?  Those questions are connected with each other, but in order to try to answer them, we have to try to come up with specific models, with specific ways to think about these questions, with ways to break them down into pieces, and of course, most importantly, with ways to relate them to observation and experiment. 

One important hint that came along on the theoretical side a long time ago was string theory, which wasn’t invented for this sort of deep-sounding questions. It was invented to understand something about the strong force, but then it took on its own life and became this amazing structure that could be explored and which started spitting out these answers to questions that you hadn’t even thought of asking yet, such as quantum gravity.  It started doing quantum gravity for you. (…)

Another hint that helps us break things up and lower the questions down to accessible levels is, of course, observational: what do we see when we look out the window? The one thing that’s really remarkable that we see, and it’s remarkable in the way that the question of why the sky is not bright at night is remarkable, is (it sounds stupid, but when you really think about it, it’s a profound question, and it needs an explanation: “Why isn’t there a star everywhere you look?”)  A similar kind of question is: "Why is the universe so large?"  It’s actually extremely remarkable that the universe is so large, from the viewpoint of fundamental physics.  A lot of amazing things have to happen for the universe to not be incredibly small, and I can go into that. 

One of the things that has to happen is that the energy of empty space has to be very, very small for the universe to be large, and in fact, just by looking out the window and seeing that you can see a few miles out, it’s an experiment that already tells you that the energy of empty space is a ridiculously small number, 0.000 and then dozens of zeros and then a 1.  Just by looking out the window you learn that.  

The funny thing is that when you calculate what the energy of empty space should be using theories you have available, really well-tested stuff that’s been tested in accelerators, like particle theory, the standard model, things that we know work, you use that to estimate the energy of empty space, and you can’t calculate it exactly on the dot. But you can calculate what the size of different contributions is, and they’re absolutely huge. They should be much larger than what you already know it can possibly be, again, not just by factor of 10 or 100, but by a factor of billions, of billions of billions of billions. 

This requires an explanation.  It’s only one of the things that has to go right for the universe to become as large as we see it, but it is one of the most mysterious properties that turned out to be right for the universe to become large, but it needs an explanation.

Funnily enough, because we knew that that number had to be so small, that is the energy of empty space, the weight of empty space, had to be so small, it became the lore within at least a large part of the physics community that it was probably zero for some unknown reason.  And one day we’d wake up and discover why it’s exactly zero. But instead, one day in ‘98 we woke up and discovered that it’s non-zero. One day we woke up in ‘98 and we discovered that cosmologists had done some experiments that looked at how fast the universe has been accelerating at different stages of its life, and they discovered that the universe had started to accelerate its expansion, when we used to think that what it would do is explode at the Big Bang, and then kind of get slower and slower in the way that galaxies expand away from each other.  Instead, it’s like you went off the brakes and stepped on the gas pedal a few billion years ago; the universe is accelerating. That’s exactly what a universe does if the energy of empty space is non-zero and positive, and you could look at how fast its acceleration is happening, and deduce the actual value of this number. In the last 13 years a lot of independent observations have come together to corroborate this conclusion.

It’s still true that the main thing that we needed to explain is why the cosmological constant, or the energy of empty space, isn’t huge. But now we also know that the explanation was definitely not going to be that for some symmetry reason that number is exactly zero. And so we needed an explanation that would tell us why that number is not huge, but also not exactly zero.

The amazing thing is that string theory, which wasn’t invented for this purpose, managed to provide such an explanation, and in my mind this is the first serious contact between observation, experiment on the one side, and string theory on the other. It was always interesting to have a consistent theory of quantum gravity, it’s very hard to write that down in the first place, but it turned out that string theory has exactly the kind of ingredients that make it possible to explain why the energy of empty space has this bizarre, very small, but non-zero value. 

I thought I was going to become a mathematician, and then decided to study physics instead, at the last minute, because I realized that I actually cared about understanding Nature, and not just some abstract, perhaps beautiful, but abstract construct. I went to Cambridge, the one in England, for my PhD. I worked with Stephen Hawking on questions of quantum properties of black holes, and how they might interplay with early universe cosmology.  (…)

Another topic that I started thinking about was trying to understand the small but non-zero value of the cosmological constant, energy of empty space, or as people like to call it, dark energy.  I worked on that subject with Joe Polchinski, at KITP, in Santa Barbara, and we realized that string theory offers a way of understanding this, and I would argue that that is the leading explanation currently of this mysterious problem. (…)

I don’t do experiments in the sense that I would walk into a lab and start connecting wires to something. But it matters tremendously to me that the theory that I work on is supposed to actually explain something about Nature. The problem is that the more highly developed physics becomes, we start asking questions which, for technological reasons, are not in the realm of day-to-day experimental feedback. We can’t ask about quantum gravity and expect at the same time to be getting some analog of the spectroscopic data that in the late 19th century fed the quest for quantum mechanics.  And I think it is a perfectly reasonable reaction to say, “Well, in that case I think that the subject is too risky to work on.”  But I think it’s also a reasonable reaction to say, “Well, but the question, it’s obviously a sensible one.”  It’s clearly important to understand how to reconcile quantum mechanics and general relativity.  They’re both great theories, but they totally contradict each other, and there are many reasons to believe that by understanding each other we will learn very profound things about how Nature works. Now, it could be that we are not smart enough to do this, in particular without constant feedback from experiments, but we could have been pessimistic at so many junctures in the past and we found a way around. 

I don’t think that we’re going to understand a lot about quantum gravity by building more particle accelerators.  We’ll understand a lot of other things, even a few things about quantum gravity, but ratherindirectly. But we’ll look elsewhere, we’ll look at cosmological experiments, we’ll use the universe to tell us about very high energies. We’ll come up with ideas that we can’t even dream about right now.  I’m always in awe of the inventiveness of my experimental colleagues, and I don’t doubt that they will deliver for us eventually. 

It has been said that it’s been a golden age for cosmology in the last 15 years or so, and it’s true.  I was very lucky with timing. When I was a graduate student, the COBE satellite was launched, and started flying and returning data, and that really marked the beginning of an era where cosmology was no longer the sort of subject where there were maybe one or two numbers to measure and people had uncertainties on say how fast the universe expands. They couldn’t even agree on how fast galaxies are moving away from each other.

And from this, we move to a data-rich age where you have unbelievably detailed information about how matter is distributed in the universe, how fast the universe is, not just expanding right now, but the expansion history, how fast it was expanding at earlier times, and so on.  Things were measured that seemed out of reach just a few years earlier, and so indeed it’s no longer possible to look down on cosmology as this sort of hand-waving subject where you can say almost anything and never be in conflict with the data. In fact, a lot of theories have gone down the road of being eliminated by data in the past 15 years or so, and several more are probably going to go down that road pretty soon. (…)

Inflation looks really good.  It’s not like we have a smoking gun confirmation of it, but it has passed so many tests, it could have been ruled out quite a few times by now, that it I would say is looking really interesting right now. 

Inflation comes in many detailed varieties, but it does make a number of rather generic predictions, and unless you work very hard to avoid them, they come with pretty much every inflation model you grab off the shelf. One of those predictions is that the spatial geometry of the universe would be flat.  It should be the kind of geometry that you learn about in high school as opposed to the weird kind of geometry that mathematicians study in university, and that has turned out to be the case. To within a percent precision,  we now know that the universe is spatially flat. Inflation predicts a particular pattern of perturbations in the sky, and again, to the extent that we have the data, and we have very precise data by now, there was plenty of opportunity to rule out that prediction, but inflation still stands.  So there are a number of general predictions that inflation makes which have held up very well, but we’re not yet at a point where we can say, it’s this particular make and model of inflation that is the right one, and not this other one.  We’re zooming in.  Some types of inflation have been ruled out, large classes of models have been ruled out, but we haven’t zoomed in on the one right answer, and that might still take a while, I would expect. 

I was saying that string theory has in a way surprised us by being able to solve a problem that other theories, including some that were invented for that purpose alone, had not been able to address, i.e. the problem of why empty space weighs so little, why is there so little dark energy. The way that string theory does this is very similar to the way that we can explain the enormous variety of that we see when we look at the chair, the table, and the sofa in this room. What are these things? 

They’re basically a few basic ingredients, electrons, quarks, and photons. You’ve got five different particles, and you put them together, and now you’ve got lots and lots of these particle. There are very few fundamental ingredients, but you have many copies of them. You have many quarks, you have many electrons, and when you put them together you have a huge number of possibilities of what you can make.  It’s just like with a big box of Legos, there are lots of different things you can build out of that.  With a big box of quarks and electrons you can build a table if you want, or you can build a chair if you want.  It’s your choice.  And strictly speaking, if I take one atom and I move it over here to a slightly different place on this chair, I’ve built a different object. These objects in technical lingo will be called solutions of a certain theory called the standard model. If I have a block of iron, I move an atom over there, it’s a different solution of the standard model.

The fact that there are innumerably many different solutions of the standard model does not of course mean that the standard model of particle physics (this triumph of human thinking) is somehow unbelievably complicated, or that it’s a theory of anything, or that it has no predictive power, it just means that it is rich enough to accommodate the rich phenomenology we actually see in nature, while at the same time starting from a very simple setup.  There are only certain quarks. There is only one kind of electron.  There are only certain ways you can put them together, and you cannot make arbitrary materials with them.  There are statistical laws that govern how very large numbers of atoms behave, so even though things look like they get incredibly complicated, actually they start simplifying again when you get to really large numbers

In string theory we’re doing a different kind of building of iron blocks. String theory is a theory that wants to live in ten dimensions, nine spatial dimensions and one time. We live in three spatial dimensions and one time, or at least so it seems to us. And this used to be viewed as a little bit of an embarrassment for string theory, not fatal, because it’s actually fairly easy to imagine how some of those spatial dimensions could be curled up into circles so small that they wouldn’t be visible even under our best microscopes.  But it might have seemed nicer if the theory had just matched up directly with observation.

It matches up with observation very nicely when you start realizing that there are many different ways to curl up the six unwanted dimensions. How do you curl them up?  Well, it’s not like they just bend themselves into some random shape.  They get shaped into a small bunch of circles, whatever shape they want to take, depending on what matter there is around. 

Similarly to how the shape of your Lego car depends on how you put the pieces together, the shape of this chair depends on how you put the atoms in it together, the shape of the extra dimensions depends on how you put certain fundamental string theory objects together.  Now, string theory actually is even more rigorous about what kind of fundamental ingredients it allows you to play with than the Lego Company or the standard model.  It allows you to play with fluxes, D-branes, and strings, and these are objects that we didn’t put into the theory, the theory gives them to us and says, “This is what you get to play with.”  But depending on how it warps strings and other objects called D-branes and fluxes in the extra six dimensions, these six dimensions take on a different shape.  In effect, this means that there are many different ways of making a three-dimensional world, just as there are many ways of building a block of iron, or a Lego car, there are many different ways of making a three-plus-one dimensional-seeming world

Of course, none of these worlds are truly three-plus-one dimensional.  If you could build a strong enough accelerator, you could see all these extra dimensions.  If you could build an even better accelerator, you might be able to even manipulate them and make a different three-plus-one dimensional world in your lab.  But naturally you would expect that this happens at energy scales that are currently and probably for a long time inaccessible to us.  But you have to take into account the fact that string theory has this enormous richness in how many different three-plus-one dimensional worlds it can make.

Joe Polchinski and I did an estimate, and we figured that there should be not millions or billions of different ways of making a three-plus-one dimensional world, but ten to the hundreds, maybe ten to the five hundred different ways of doing this. This is interesting for a number of reasons, but the reason that seemed the most important to us is that it implies that string theory can help us understand why the energy of the vacuum is so small.  Because, after all, what we call “the vacuum" is simply a particular three-plus-one dimensional world, what that one looks like when it’s empty. And what that one looks like when it’s empty is basically, it still has all the effects from all this stuff that you have in the extra dimensions, all these choices you have there about what to put. 

For every three-plus-one dimensional world, you expect that in particular the energy of the vacuum is going to be different, the amount of dark energy, or cosmological constant is going to be different.  And so if you have ten to the five hundred ways of making a three-plus-one dimensional world, and some of them just by accident, the energy of the vacuum is going to be incredibly close to zero. 

The other thing that is going to happen is that in about half of these three-plus-one dimensional worlds, the vacuum is going to have positive energy. So even if you don’t start out the universe in the right one, where by “right one” I mean the one that later develops beings like us to observe it, you could start it out in a pretty much random state, another way of making a three-dimensional world.  What would happen is it would grow very fast, because positive vacuum energy needs acceleration, as we observed today in the sky, it will grow very fast, and then by quantum mechanical processes it would decay, and you would see changes in the way that matter is put into these extra dimensions, and locally you would have different three-plus-one dimensional worlds appearing.  (…)

What happens is the universe gets very, very large, all these different vacua, three-dimensional worlds that have positive weight, grow unboundedly, and decay locally, and new vacuole appear that try to eat them up, but they don’t eat them up fast enough. So the parents grow faster than the children can eat them up, and so you make everything.  You fill the universe with these different vacua, these different kinds of regions in which empty space have all sorts of different weights. Then you can ask, “Well, in such a theory, where are the observers going to be?" To just give the most primitive answer to this question, it’s actually very useful to remember the story about the holographic principle. (…)

If you have a lot of vacuum energy, then even though the universe globally grows and grows and grows, if you sit somewhere and look around, there is a horizon around you. The region that’s causally connected, where particles can interact and form structure is inversely related to the amount of vacuumed energy you have.  This is why I said earlier that just by looking out the window and seeing that the universe is large, we know that there has to be very little vacuum energy.  If there’s a lot of vacuum energy, the universe is a tiny little box from the viewpoint of anybody sitting in it. The holographic principle tells you that the amount of information in the tiny little box is proportional to the area of its surface.  If the vacuum energy has this sort of typical value that it has in most of the vacua, that surface allows for only a few bits of informationSo whatever you think observers look like, they probably are a little bit more complicated than a few bits. 

And so you can immediately understand that you don’t expect observers to exist in the typical regions.  They will exist in places where the vacuum energy happens to be unusually small due to accidental cancellations between different ingredients in these extra dimensions, and where, therefore, there is room for a lot of complexity.  And so you have a way of understanding both the existence of regions in the universe somewhere with very small vacuum energy, and also of understanding why we live in those particular rather atypical regions. 

What’s interesting about this is the idea that maybe the universe is a very large multi-verse with different kinds of vacua in it was actually thrown around independently of string theory for some time, in the context of trying to solve this famous cosmological constant problem. But it’s not actually that easy to get it all right. If you just imagine that the vacuum energy got smaller and smaller and smaller as the universe went on, that the vacua are nicely lined up with each one that you decay into having slightly smaller vacuum energy than the previous one, you cannot solve this problem. You can make the vacuum energy small, but you also empty out the universe. You won’t have any matter in it. (…)

I think that the things that haven’t hit Oprah yet, and which are up and coming are questions like, well, if the universe is really accelerating its expansion, then we know that it’s going to get infinitely large, and that things will happen over and over and over. And just simply because if you have infinitely many tries at something, then every possible outcome is going to happen infinitely many times, no matter how unlikely it is.

This is actually something that predates this string theory multiverse that I was talking about. It’s a very robust question in the sense that even if you believe string theory is a bunch of crap, you still have to worry about this problem because it’s based on just observation. You see that the universe is currently expanding in an accelerated way, and unless there’s some kind of conspiracy that’s going to make this go away very quickly, it means that you have to address this problem of infinities. But the problem becomes even more important in the context of the string landscape because it’s very difficult to make any predictions in the landscape if you don’t tame those infinities.

Why?  Because you want to say that seeing this thing in your experiment is more likely than that thing, so that if you see the unlikely thing, you can rule out your theory the way we always like to do physics. But if both things happen infinitely many times, then on what basis are you going to say that one is more likely than the other? You need to get rid of these infinities.  This is called, at least among cosmologists, the measure problem It’s probably a really bad name for it, but it stuck.

That’s where a lot of the action is right now.  That’s where a lot of the technical work is happening, that’s where people are, I think, making progress.  I think we’re ready for Oprah, almost, and I think that’s a question where we’re going to come full circle, we’re going to learn something about the really deep questions, about what is the universe like on the largest scales, how does quantum gravity work in cosmology? I don’t think we can fully solve this measure problem without getting to those questions, but at the same time, the measure problem allows us a very specific way in. It’s a very concrete problem. If you have a proposal, you can test it, you can rule it out, or you can keep testing it if it still works, and by looking at what works, by looking at what doesn’t conflict with observation, by looking at what makes predictions that seem to be in agreement with what we see, we’re actually learning something about the structure of quantum gravity.  

So I think that it’s currently a very fruitful direction. It’s a hard problem, because you don’t have a lot to go by. It’s not like it’s an incremental, tiny little step.  Conceptually it’s a very new and difficult problem. But at the same time it’s not that hard to state, and it’s remarkably difficult to come up with simple guesses for how to solve it that you can’t immediately rule out. And so we’re at least in the lucky situation that there’s a pretty fast filter. You don’t have a lot of proposals out there that have even a chance of working.

The thing that’s really amazing, at least to me, is in the beginning we all came from different directions at this problem, we all had our different prejudices.  Andrei Linde had some ideas, Alan Guth had some ideas, Alex Vilenkin had some ideas.  I thought I was coming in with this radically new idea that we shouldn’t think of the universe as existing on this global scale that no one observer can actually see, that it’s actually important to think about what can happen in the causally connected region to one observer. What can you do in any experiment that doesn’t actually conflict with the laws of physics and require superluminal propagation. We have to ask questions in a way that conform to the laws of physics if we want to get sensible answers. (…)

A lot of things have now happened that didn’t have to happen, a lot of things have happened that give us some confidence that we’re on to something, and at the same time we’re learning something about how to think about the universe on the larger scales.”

Raphael Bousso, theoretical physicist and string theorist. Currently he is a professor at Department of Physics, UC Berkeley, Thinking About the Universe on the Larger Scales, Edge, Oct 24, 2011. (Illustration source)

See also:

The Concept of Laws. The special status of the laws of mathematics and physics
☞ Tim Maudlin, What Happened Before the Big Bang? The New Philosophy of Cosmology, The Atlantic, Jan 2012.
Vlatko Vedral: Decoding Reality: the universe as quantum information
Universe tag on Lapidarium notes
Universe tag on Lapidarium

Apr
8th
Fri
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Interactive 3D model of Solar System Planets and Night Sky

     
                                              (Click image to see interactive 3D model)

"Solar System Scope space traveller will illustrate you real-time celestial positions with planets and constellations moving over the night sky. You can actively change parameters for a better understanding of happenings in our Solar System and the Universe."

See also:
Hubble Telescope Site
HobbySpace - Webguide to space hobbies and activies
Nine Planets - A Multimedia Tour of the Solar System: one star, eight planets, and more
LSST - Large Synoptic Survey Telescope - the widest, fastest, deepest eye of the new digital age

Apr
7th
Thu
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Measuring hell - How Dante’s Inferno Inspired Galileo’s Physics

"This coming fall, Mark Peterson, a physics professor at Mount Holyoke College, will publish a new book where he makes a rather curious argument: Back in 1588, a young Galileo presented two lectures before the Florentine Academy. And there he laid the groundwork for his theoretical physics when he called into question the accepted measurements of Dante’s hell (as depicted in the Inferno, the great epic poem from 1314). Did debates over a poem figure into the unfolding of The Scientific Revolution?” — (Open Culture)

"It seems odd to think that Galileo’s most important ideas might have their roots not in the real world, but in a fictional one. But that’s the argument that Mount Holyoke College physics professor Mark Peterson has been developing for the past several years: specifically, that one of Galileo’s crucial contributions to physics came from measuring the hell of Dante’s Inferno. Or rather, from disproving its measurements.

In 1588, when Galileo was a 24-year-old unknown, a medical school dropout, he was invited to deliver a couple of lectures on Dante’s “Divine Comedy.” Many in Galileo’s audience would have been shocked, even dismayed, to see this young upstart take the stage and start poking holes in what they believed about the poet’s meticulously constructed fantasy world. (…)

What Galileo said, put simply, is that many commonly accepted dimensions did not stand up to mathematical scrutiny. Using complex geometrical analysis, he attacked a leading scholar’s version of the Inferno’s structure, pointing out that his description of the infernal architecture — such as the massive cylinders descending to the center of the Earth — would, in real life, collapse under their own weight. Later, Galileo realized the leading rival theory was wrong, too, and that even the greatest scholars of the time simply didn’t understand how real-world structures worked.

Debating the mechanics of the Inferno might sound like intellectual horseplay, the 16th-century equivalent of MIT cafeteria debates about the viability of “Star Trek” teleporters. But there was more to the lectures than this. The insights Galileo gleaned from analyzing Dante’s measurements in fact anticipated a vital principle of structural engineering. By asserting that you cannot create a giant Lucifer by super-sizing the model of a man — that increasing an object’s magnitude would create a whole new set of structural and material imperatives — Galileo was paving the way for the construction of everything from ocean liners to skyscrapers to Macy’s parade floats. (…)

In this regard, at least as Peterson sees it, Galileo has more in common with today’s quantum theorists, whose work requires mad leaps of logic, than he does with the generations of by-the-numbers physicists he inspired. The world’s first true scientist, the professor tells us, understood that it takes a man of reason to provide the proof, but only a fantasist can truly reimagine the universe.”

—  Text by Chris Wright, Graphic by Javier Zarracina, Measuring hell. Was modern physics born in the Inferno?, The Boston Globe, Jan 9, 2011.

See also: Mark A. Peterson, Galileo’s Discovery of Scaling Laws (pdf), Department of Physics, Mount Holyoke College, South Hadley, Massachusetts

Sep
2nd
Thu
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Stephen Hawking on the universe’s origin

   
Picture: Starry-Eyed Hubble Celebrates 20 Years of Awe and Discovery / NASA Goddard Space Flight Center

“Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going. (…)”

The universe looks more and more like a quantum phenomenon, in which a multitude of histories diverge. This is what Hawking calls top-down cosmology. Space and time fizzle out, so it can’t be said that there is a time before the big bang — just as you can’t say that there is something north of the North Pole. (I’m talking “north,” not “up.”)

Gravity is part of the picture because it helps keep the cosmic balance sheet in line. (…) Because gravity shapes space and time, it allows space-time to be locally stable but globally unstable. On the scale of the entire universe, the positive energy of the matter can be balanced by the negative gravitational energy, and so there is no restriction on the creation of whole universes.”

Hawking says God’s not needed. So?, Cosmic Log on msnbc.com, Sep 2, 2010. See also Stephen Hawking, The Grand Design

Cosmology from the Top Down

“The bottom up approach is more problem in cosmology however, because we do not know what the initial state of the universe was, and we certainly can’t try out different initial states, and see what kinds of universe they produce. (…)

I think the universe may have had an initial de Sitter stage considerably larger than the Planck scale.

I now turn to pre Big Bang scenarios, which are the main alternative to inflation. I shall take them to include the Ekpyrotic and cyclic models, as well as the older pre big bang scenario. The observations of fluctuations in the microwave background, show that there are correlations on scales larger than the horizon size at decoupling. These correlations could be explained if there had been inflation, because the exponential expansion, would have meant that regions that are now widely separated, were once in causal contact with each other. On the other hand, if there were no inflation, the correlations must have been present at the beginning of the expansion of the universe. Presumably, they arose in a previous contracting phase, and somehow survived the singularity, or brane collision. It is not clear if effects can be transmitted through a singularity, or if they will produce the right signature in the microwave background. But even if the answer to both of these questions is yes, the pre big bang scenarios do not answer the central question of cosmology, why is the universe, the way it is. All the pre big bang scenarios can do, is shift the problem of the initial state from 13 point 7 billion years ago, to the infinite past. But a boundary condition is a boundary condition, even if the boundary is at infinity.The present state of the universe, would depend on the boundary condition in the infinite past. The trouble is, there’s no natural boundary condition, like the universe being in its ground state. The universe doesn’t have a ground state. It is unstable, and is either expanding or contracting. The lack of a preferred initial state in the infinite past, means that pre big bang scenarios, are no better at explaining the universe, than supposing that someone wound up the clockwork, and set the universe going at the big bang. (…)

     

                          Picture source: João E. Steiner, The origin of the universe

(…) One of the first acts of my research career, was to show with Roger Penrose, that any reasonable classical cosmological solution, has a singularity in the past. This implies that the origin of the universe, was a quantum event. This means that it should be described by the Feynman sum over histories. The universe doesn’t have just a single history, but every possible history, whether or not they satisfy the field equations. Some people make a great mystery of the multi universe, or the many worlds interpretation of quantum theory, but to me, these are just different expressions of the Feynman path integral. (…)

(…) there is no way one can rule out the final surface, from belonging to a different universe to the initial surface. In fact, because there are so many different possible universes, they will dominate, and the final state will be independent of the initial. It will be given by a path integral over all metrics whose only boundary is the final surface. In other words, it is the so called no boundary quantum state.

If one accepts that the no boundary proposal, is the natural prescription for the quantum state of the universe, one is led to a profoundly different view of cosmology, and the relation between cause and effect. One shouldn’t follow the history of the universe from the bottom up, because that assumes there’s a single history, with a well defined starting point and evolution. Instead, one should trace the histories from the top down, in other words, backwards from the measurement surface, S, at the present time. The histories that contribute to the path integral, don’t have an independent existence, but depend on the amplitude that is being measured. As an example of this, consider the apparent dimension of the universe. The usual idea is that spacetime is a four dimension nearly flat metric, cross a small six or seven dimensional internal manifold. But why aren’t theremore large dimensions. Thy are any dimensions compactified. There are good reasons to think that life is possible only in four dimensions, but most physicists are very reluctant to appeal to the anthropic principle. They would rather believe that there is some mechanism that causes all but four of the dimensions to compactify spontaneously. Alternatively, maybe all dimensions started small, but for some reason, four dimensions expanded, and the rest did not. I’m sorry to disappoint these hopes, but I don’ t think there is a dynamical reason for the universe to appear four dimensional. (…)

We live in a universe that appears four dimensional, so we are interested only in amplitudes for surfaces with three large dimensions. This may sound like the anthropic principle argument that the reason we observe the universe to be four dimensional, is that life is possible only in four dimensions. But the argument here is different, because it doesn’t depend on whether four dimensions, is the only arena for life. Rather it is that the probability distribution over dimensions is irrelevant, because we have already measured that we are in four dimensions. (…)

Many physicists believe that string theory, will uniquely predict the standard model, and the values of its 40 or so parameters. The bottom up picture would be that the universe would begin with some grand unified symmetry, like E8 cross E8. As the universe expanded and cooled, the symmetry would break to the standard model, maybe through intermediate stages. The hope would be that String theory, would predict the pattern of breaking, the mass, couplings and mixing angles. Personally, I find it difficult to believe that the standard model, is the unique prediction of fundamental theory. It is so ugly, and the mixing angles etc, seem accidental, rather than part of a grand design. (…)

In string stroke M theory, low energy particle physics is determined by the internal space. It is well known that M theory has solutions with many different internal spaces. If one builds the history of the universe from the bottom up, there is no reason it should end up with the internal space for the standard model. However, if one asks for the amplitude for a space like surface with a given internal space, one is interested only in those histories which end with that internal space. One therefore has to trace the histories from the top down, backwards from the final surface. (…)

How can one get a non zero amplitude for the present state of the universe, if as I claim, the metrics in the path integral, have no boundary apart from the surface at the present time. I can’t claim to have the definitive answer, but one possibility would be if the four dimensional part of the metric, went back to a de Sitter phase. Such a scenario is realized in trace anomaly driven inflation, for example. In the Lorentzian regime, the de Sitter phase would extend back into the infinite past. It would represent a universe that contracted to a minimum radius, and then expanded again. But as we know, Lorentzian de Sitter can be closed off in the past by half the four sphere. One can interpret this in the bottom up picture, as the spontaneous creation of an inflating universe from nothing. Some pre big bang or Ekpyrotic scenarios, involving collapsing and expanding universes, can probably be formulated in no boundary terms, with an orbifold point. However, this would remove the scale free perturbations which, it is claimed, develop during the collapse, and carry on into the expansion. So again it is a no no for pre big bang and Ekpyrotic universes.

In conclusion, the bottom up approach to cosmology, would be appropriate, if one knew that the universe was set going in a particular way, in either the finite, or infinite past. However, in the absence of such knowledge, it is better to work from the top down, by tracing backwards from the final surface, the histories that contribute to the path integral. This means that the histories of the universe, depend on what is being measured, contrary to the usual idea that the universe has an objective, observer independent, history. The Feynman path integral allows every possible history for the universe, and the observation, selects out the sub class of histories that have the property that is being observed. There are histories in which the universe eternally inflates, or is eleven dimensional, but they do not contribute to the amplitudes we measure. I would call this the selection principle, rather than the anthropic principle because it doesn’t depend on intelligent life. Life may after all be possible in eleven dimensions, but we know we live in four. (…)

We can’ t tell whether the universe was likely to have the values we observe, or whether it was just a lucky chance. However, it is note worthy that the parameters we measure seem to lie in the interior of the anthropically allowed range, rather than at one end. This suggests that the probability distribution is fairly flat, not like the exponential dependence on the density parameter, omega, in the open inflation that Neil Turok and I proposed. In that model, omega would have had the minimum value required to form a single galaxy, which is all that is anthropically necessary. All the other galaxies which we see, are superfluous.

Although the theory can not predict the average values of these quantities, it will predict that there will be spatial variations, like the fluctuations in the microwave background. However the size of these variations, will probably depend on moduli or parameters that we can’ t predict. So even when we understand the ultimate theory, it won’t tell us much about how the universe began. It can not predict the dimension of spacetime, the gauge group, or other parameters of the low energy effective theory. On the other hand, the theory will predict that the total energy density, will be exactly the critical density, though it won’ t determine how this energy is divided between conventional matter, and a cosmological constant, or quintessence. The theory will also predict a nearly scale free spectrum of fluctuations. But it won’t determine the amplitude. So to come back to the question with which I began this talk. Does string theory predict the state of the universe. The answer is that it does not. It allows a vast landscape of possible universes, in which we occupy an anthropically permitted location. But I feel we could have selected a better neighbourhood.”

Stephen Hawking, Cosmology from the Top Down, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, 29 May 2003 (pdf)

See also:

☞ Tim Maudlin, What Happened Before the Big Bang? The New Philosophy of Cosmology, The Atlantic, Jan 2012.

Aug
28th
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The Concept of Laws. The special status of   the laws of mathematics and physics
         
Platonic mathematical world illustrated in Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe, Jonathan Cape Ltd

"We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.”

Plato made it clear that the mathematical propositions – the things that could be regarded as unassailably true – referred not to actual physical objects (like approximate squares, triangles, circles, spheres, and cubes that might be constructed from marks in the sand, or from wood or stone) but to certain idealized entities. He envisaged that these ideal entities inhabited a different world, distinct from the physical world. Today we might refer to this world as the Platonic world of mathematical forms.”

Roger Penrose, The Road to Reality: A Complete Guide to the Laws of the Universe

“There are some, King Gelon, who think that the number of the sands is infinite in multitude; and I mean by sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. Again there are some who, without regarding it as infinite, yet think that no number has been named which is great enough to exceed its multitude. And it is clear that they who hold this view, if they imagined a mass made up of sand in other respects as large as the mass of the earth, including in it all the seas and the hollows of the earth filled up to the height equal to that of the highest mountains, would be many times further still from recognizing that any number could be expressed which exceeded the multitude of the sand so taken. But I will try to show you, by means of geometrical proofs which you will be able to follow, that, of the numbers named by me and given in the work which I sent to Zeuxippus, some exceed not only the number of the mass of sand equal in size to the earth filled up in the way described, but also that of a mass equal in size to the universe.”

Archimedes, The Sand Reckoner

"If we go back to our checker game, the fundamental laws are rules by which the checkers move. Mathematics may be applied in the complex situation to figure out what in given circumstances is a good move to make. But very little mathematics is needed for the simple fundamental character of the basic laws. They can be simple stated in English for checkers."

Richard Feynman, American physicist, Nobel Laureate in Physics (1918-1988), The Character of Physical Law

„The fact that the physical world conforms to mathematical laws led Galileo to make a famous remark. “The great book of nature – he wrote – can be read only by those who know the language in which it was written. And this language is mathematics.” (…)

It is the mathematical aspect that makes possible what physicists mean by the much-musunderstood word theory. Theoretical physics entails writing down equations that capture (or model, as scientists say) the real world of experience in a mathematical world of numbers and algebraic formulas. Then, by manipulating the mathematical symbols, one can work out what will happen in the real world, without actually carrying out the observation. (…) For example, by using Newton’s laws of motion and gravitation, engineers can figure out when a spacecraft launched from Earth will reach Mars. They can also calculate the required mass of fuel, the most favorable orbit, and a host of other factors in advance of the mission. And it works! The mathematical model faithfully describes what actually happens in the real world. (…) How can you possibly know what a ball will do by writing things on a sheet of paper? (…) Why is nature shadowed by a mathematical reality? Why does theoretical physics work?

How Many Laws Are There?

As scientists have probed deeper and deeper into the workings of nature, all sorts of laws have come to light that are not at all obvious from a casual inspection of the world, for example, laws that regulate the internal components of atoms or the structure of stars. The multiplicity of laws raises another challenging question: How long would a complete list of laws be? Would it include ten? twenty? two hundred? Might the list even be infinitely long?

Not all the laws are independent of one another. It wasn’t long after Galileo, Kepler, Newton, and Boyle began discovering laws of physics that scientists found links between them. For example, Newton’s laws of gravitation and motion explain Kepler’s three laws of planetary motion and so are in some sense deeper and more powerful. Newton’s laws of motion also explain Boyle’s law of gases when they are applied in statistical way to a large collection of chaotically moving molecules.

In the four centuries that have passed since the first laws of physics were discovered, more and more have come to light, but more and more links have been spotted too. The laws of magnetism, which in turn explained the laws of light. These interconnections led to a certain amount of confusion about which laws were “primary” and which could be derived from others. Physicists began talking about “fundamental” laws and “secondary” laws, with the implication that the letter were formulated for convenience only. (…) The Great Rule Book of Nature (at least as it is currently understood) would fit comfortably onto a single page. This streamlining and repackaging process – finding links between laws and reducing them to ever more fundamental lawscontinues apace, and it’s tempting to believe that, at rock bottom, there is just a handful of truly fundamental laws, possible even a single superlaw, from which all the other laws derive.

Paul Davies, Cosmic jackpot: why our universe is just right for life, Houghton Mifflin Harcourt, 2007, p. 9-11.

What it is that mathematicians study?

“But, as the mathematician speculates from abstraction (for he contemplates by abstracting all sensible natures, as, for instance, gravity and levity, hardness and its contrary, and besides these, heat and cold, and other sensible contrarieties), but alone leaves quantity and the continuous, of which some pertain to one, others to two, and others to three [dimensions].”

Aristotle, The Metaphysics of Aristotle, translated by Thomas Taylor. London: Davis, Wilks, and Taylor, Chancery-Lane, 1801.

“It is India that gave us the ingenious method of expressing all numbers by means of ten symbols, each symbol receiving a value of position as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit. But its very simplicity and the great ease which it has lent to all computations put our arithmetic in the first rank of useful inventions; and we shall appreciate the grandeur of this achievement the more when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest men produced by antiquity.”

Pierre-Simon Laplace

Since the Renaissance mathematicians have been concerned with the laws of cause and effect. That is, they have sought to employ the mathematical expression of these laws so that for any particular phenomenon there exists a one-to-one relationship between each cause and each effect. Their goal has been to solve the following simple-sounding problem: Given a unique cause, predict the unique effect. Many phenomena are well suited to this type of mathematical analysis, but there are also situations in which this approach fails. When this happens scientists have learned to rephrase the problem in the language of probability. One modern version of this idea can be described as follows: Given a unique cause, predict the most probable effect. A more general version of the problem is: Given the most probable cause, predict the most probable effect. These types of probabilistic problems are now a fundamental part of science, but this is a fairly recent development.”

— John Tabak, Mathematics and the Laws of Nature. Developing the Language of Science , Facts On File, Library of Congress Cataloging in Publication Data, 2004, p. 153.

Does mathematics help explain the physical world or does it actually hinder a grasp of the physical mechanisms that explain the how and why of natural phenomena?

Mathematics – our creation – is stunningly effective in explaining and limiting the physical world, even very elementary mathematics, mere counting. Why should mathematics, this human invention, be so effective, so relevant to nature, so controlling of it? Perhaps the mathematics that we create is forces by nature and that is why it can describe its world. Mathematics is not arbitrary, it was developed to describe our universe (at least that part that actually does) so is able to. And this seems more and more true but more and more incomplete, more and more puzzling.”

— R. Mirman, Our Almost Impossible Universe: Why the Laws of Nature Make the Existence of Humans Extraordinarily Unlikely, iUniverse, 2006

By the time we reach the seventeenth century and the Newtonian revolution in physics, the problem reappears in the context of a change of criteria of explanation and intelligibility. This has been beautifully described in an article by Y. Gingras (2001). Gingras argues that “the use of mathematics in dynamics (as distinct from its use in kinematics) had the effect of transforming the very meaning of the term ‘explanation’ as it was used by philosophers in the seventeenth century”. What Gingras describes, among other things, is how the mathematical treatment of force espoused by Newton and his followers — a treatment that ignored the mechanisms that could explain why and how this force operated—became an accepted standard for explanation during the eighteenth century. After referring to the seventeenth and eighteenth centuries discussions on the mechanical explanation of gravity, he remarks:

This episode shows that the evaluation criteria for what was to count as an acceptable ‘explanation’ (of gravitation in this case) were shifting towards mathematics and away from mechanical explanations. Confronted with a mathematical formulation of a phenomenon for which there was no mechanical explanation, more and more actors chose the former even at the price of not finding the latter. This was something new. For the whole of the seventeenth century and most of the eighteenth, to ‘explain’ a physical phenomenon meant to give a physical mechanism involved in its production….The publication of Newton’s Principia marks the beginning of this shift where mathematical explanations came to be preferred to mechanical explanations when the latter did not conform to calculations. (Gingras 2001, 398)

(…) Another challenge has been raised by Sorin Bangu 2008, who claims that mathematical language is essential to the formulation of the question to be answered (“why is the life cycle period prime?”) and thus that the argument begs the question against the nominalist. The existence of numbers and properties of numbers is already assumed in the acceptance of the statement “the life cycle period is prime”.

A similar objection to any attempt to use mathematical explanations in physics for inferring the existence of the mathematical entities involved in the explanation had already been raised in 1978 by Mark Steiner, who had discarded such arguments with the observation that what needed explanation could not even be described without use of the mathematical language. Thus, the existence of mathematical explanations of empirical phenomena could not be used to infer the existence of mathematical entities, for this very existence was presupposed in the description of the fact to be explained. Indeed, he endorsed a line of argument originating from Willard Van Orman Quine and Nelson Goodman according to which “we cannot say what the world would be like without numbers, because describing any thinkable experience (except for utter emptiness) presupposes their existence.” (1978b, 20)
Explanation in Mathematics, Stanford Encyclopedia of Philosophy

Mathematics: Invented or Discovered?

Mario Livio discusses the complementary processes of mathematical invention and discovery. While we invent some mathematical concepts—such as prime and imaginary numbers—by deciding how to define them, these concepts can lead to a plethora of mathematical discoveries.

Mathematics: Invented or Discovered?, World Science Festival, Jan 14, 2011.

Mario Livio: Platonism vs. Formalism

Platonists believe that there is a universal truth underlying all of mathematics. Formalists believe all of mathematics can be defined by a set of predefined rules. Ever wonder about the deeper significance of these two critical mathematical philosophies? Using thought experiments like the Allegory of the Cave and the Barber’s Paradox Mario Livio, untangles these two didactic ways of viewing the world and the very nature of human knowledge.

Mario Livio (Astrophysicist), Platonism vs. Formalism, World Science Festival, Jan 11, 2011.

[This note will be gradually expanded…]

See also:

The Limits of Understanding - debate between Mario Livio (Astrophysicist), Gregory Chaitin (Mathematician), Rebecca Goldstein (Novelist, Philosopher), Marvin Minsky Cognitive Scientist), Sir Paul Nurse (Nobel Laureate, Medicine), World Science Festival video, Jan 11, 2011.
☞ Cosmologist Paul Davies: Faith in the Mathematical Order, World Science Festival, 2011.04.15
Gerald B. Folland, Speaking with the Natives: Reflections on Mathematical Communication (pdf)
Vlatko Vedral: Decoding Reality: the universe as quantum information
Geoffrey West on Why Cities Keep Growing, Corporations and People Always Die, and Life Gets Faster
Mario Livio, Why Math Works - Is math invented or discovered? A leading astrophysicist suggests that the answer to the millennia-old question is both, Scientific American, August 2, 2011
Greg Chaitin on the limits of Reason (pdf) - Ideas on complexity and randomness originally suggested by Gottfried W. Leibniz in 1686, combined with modern information theory, imply that there can never be a “theory of everything” for all of mathematics.
Steven Weinberg, Symmetry: A ‘Key to Nature’s Secrets’, The New York Review of Books, Oct 27, 2011
☞ Tim Maudlin, What Happened Before the Big Bang? The New Philosophy of Cosmology, The Atlantic, Jan 2012.
Is mathematics invented or discovered?, answers on Quora

Jul
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A walk through the Universe


“Every galaxy we observe today is related to the small perturbations present in the early Universe. The cold spots in the CMB are slightly denser than the surrounding areas and so as the universe evolved gravity's long range attractive forces meant that over densities were inherently unstable. The over densities grew larger and larger until galaxies, clusters, and super clusters formed. Today, astronomers are measuring the result of this growth of structure through galaxy surveys such as as the Sloan Digital Sky Survey. The observed distribution of galaxies is perfectly consistent with the theories.” — (The History of the Universe, The Astronomist, June 30, 2010

This is a fly through the “local” Universe based on the latest Sloan Digital Sky Survey data release (SDSS DR72). This animation corresponds to the redshif range z=0.01-0.1. The far side of the survey (z=0.1) is approx 400 Mpc (1.3 billion light years). The galaxy size is proportional to the physical size of the observed galaxy. Elliptical galaxies are pseudo-volumetric ellipsoids with random ellipticity. — Miguel Aragon, A walk through the Universe

A little context

"It’s been said that astronomy’s a humbling and character-building experience. There is perhaps no better demonstration of the folly of human conceits than the distant image of our tiny world. To me, it underscores our responsibility to deal more kindly with one another and to preserve and cherish the pale blue dot, the only home we’ve ever known." –- Carl Sagan
May
30th
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William Blake, “I Want! I Want!” 1793, Engraving, Butlin 201 40

“By the 1790s, even the most romantically inclined philosophers no longer believed there was a man in the moon. Yet William Blake, with his characteristic combination of unfettered imagination and irrepressible logic, simply surmised that he must have had a very long ladder.

I Want! I Want! is the title of a small etching Blake produced at the height of the French revolutionary terror. A tiny, anonymous figure stands poised on the first rung of a celestial ladder, lodged like a giant toothpick in the smiling crescent moon. It is a devastatingly simple metaphor for the destructive ambition that grows out of humankind’s capacity to dream. The etching is used here as a striking frontispiece for an exhibition in which nine contemporary artists construct their own utopias.”

— Alfred Hickling, I Want! I Want! Northern Gallery, Sunderland, The Guardian, 27 August 2003
May
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A star is born - thanks to supersonic turbulence
Using the largest simulation of supersonic turbulence to date, UC San Diego researchers have shown how fundamental laws of turbulent geophysical flows can also be extended to supersonic turbulence in the interstellar medium of galaxies. This image, stored and analyzed at the San Diego Supercomputer Center at UC San Diego, shows the density field from one snapshot of the simulation, run on 4,096 processors for two weeks and resulting in 25 terabytes of data. The brightest regions in the image represent gas at the highest density, compressed by the action of a complex system of shocks in the turbulent flow. Dense filaments and cores, created in such a way by supersonic turbulent flows, are subject to massive gravitational collapse – and that leads to the birth of stars.— Source: San Diego Supercomputer Center, UC San Diego. Credit: Alexei Kritsuk, Michael Norman, Paolo Padoan, and Rick Wagner, UC San Diego via Imagine of the week, ISGTW (imagine thx scienceisbeauty)

A star is born - thanks to supersonic turbulence

Using the largest simulation of supersonic turbulence to date, UC San Diego researchers have shown how fundamental laws of turbulent geophysical flows can also be extended to supersonic turbulence in the interstellar medium of galaxies. This image, stored and analyzed at the San Diego Supercomputer Center at UC San Diego, shows the density field from one snapshot of the simulation, run on 4,096 processors for two weeks and resulting in 25 terabytes of data. The brightest regions in the image represent gas at the highest density, compressed by the action of a complex system of shocks in the turbulent flow. Dense filaments and cores, created in such a way by supersonic turbulent flows, are subject to massive gravitational collapse – and that leads to the birth of stars.

Source: San Diego Supercomputer Center, UC San Diego. Credit: Alexei Kritsuk, Michael Norman, Paolo Padoan, and Rick Wagner, UC San Diego via Imagine of the week, ISGTW (imagine thx scienceisbeauty)

Apr
26th
Mon
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Starry-Eyed Hubble Celebrates 20 Years of Awe and Discovery, NASA image release April 22, 2010 
This brand new Hubble photo is of a small portion of one of the largest seen star-birth regions in the galaxy, the Carina Nebula. Towers of cool hydrogen laced with dust rise from the wall of the nebula. The scene is reminiscent of Hubble’s classic “Pillars of Creation” photo from 1995, but is even more striking in appearance. The image captures the top of a three-light-year-tall pillar of gas and dust that is being eaten away by the brilliant light from nearby bright stars. The pillar is also being pushed apart from within, as infant stars buried inside it fire off jets of gas that can be seen streaming from towering peaks like arrows sailing through the air. Credit: NASA, ESA, and M. Livio and the Hubble 20th Anniversary Team (STScI) More See also Hubble Site

Starry-Eyed Hubble Celebrates 20 Years of Awe and Discovery, NASA image release April 22, 2010 

This brand new Hubble photo is of a small portion of one of the largest seen star-birth regions in the galaxy, the Carina Nebula. Towers of cool hydrogen laced with dust rise from the wall of the nebula. The scene is reminiscent of Hubble’s classic “Pillars of Creation” photo from 1995, but is even more striking in appearance. The image captures the top of a three-light-year-tall pillar of gas and dust that is being eaten away by the brilliant light from nearby bright stars. The pillar is also being pushed apart from within, as infant stars buried inside it fire off jets of gas that can be seen streaming from towering peaks like arrows sailing through the air. Credit: NASA, ESA, and M. Livio and the Hubble 20th Anniversary Team (STScI) More See also Hubble Site

Mar
21st
Sun
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The Known Universe as mapped through astronomical observations

The Known Universe takes viewers from the Himalayas through our atmosphere and the inky black of space to the afterglow of the Big Bang. Every satellite, moon, planet, star and galaxy is represented to scale and in it’s correct, measured location according to the best scientific research to-date.

Every star, planet, and quasar seen in the film is possible because of the world’s most complete four-dimensional map of the universe, the Digital Universe Atlas that is maintained and updated by astrophysicists at the American Museum of Natural History as the Digital Universe Atlas.

See also: ☞ Three looks at the Earth and the Universe

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NASA SDO EVE maps the Van Allen radiation belts around Earth

The Van Allen radiation belt is a torus of energetic charged particles (plasma) around Earth, which is held in place by Earth’s magnetic field. This field is not uniformly distributed around the Earth. On the sunward side, it is compressed because of the solar wind, while on the other side it is elongated to around three earth radii. This creates a cavity called the Chapman Ferraro Cavity, in which the Van Allen radiation belt resides. It is split into two distinct belts, with energetic electrons forming the outer belt and a combination of protons and electrons creating the inner belt. In addition, the belts contain lesser amounts of other nuclei, such as alpha particles. The Van Allen belts are closely related to the polar aurora where particles strike the upper atmosphere and fluoresce. (More)

Jan
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History of the Universe in a concise picture
The picture above gives a nice description of events happening at the time shortly after the Big Bang.
Quantum gravity epoch This is the first planck time (10-43 s). In the framework of quantummechanics it is meaningless to say anything about this moment. Grand unification epochIn this epoch the Electroweak and strong forces are still behaving as one GUT force. The precise physics of this force are yet unknown, but many theories have been proposed. Electroweak epoch  The strong force has split off because the Universe cooled down due to its expansion. The electromagnetic force and the weak force are still unified. This is where the Standard model of physics rules. Physicist know pretty well what went on. Quarks are still free particles. This ends after 10-10 s. When they form protons, anti-protons and (anti-)neutrons. At some point there should be an assymetry between the physics ruling normal particles and that ruling anti-particles. This would allow particles to survive where anti-particles would do less so. Otherwise they would anihilate eachother and nothing would be left but radiation. It is estimated by the baryon to proton ratio η ∼ 10-10, that one in every 10 miljard protons survived. This process is called baryogenesisRadiation dominated era Radiation was the dominating component in the Universe. The density of radiation dominated the way the Universe expanded. At the end of this era, when the universe is ∼ 1 s old, proton-neutron freeze-out happens and primordeal nucleosynthesis takes place. Matter dominated era  Matter takes over, because it thins out less rapidly (∝ a-3) than radiation (∝ a-4). This is what their equations of state tell you. Matter becomes the dominant factor in expanding the Universe. After 370.000 years the baryon density drops enough to become transparent to electromagnetic radiation (photons). This is the moment photons and baryons decouple, resulting in a seperate photonic gas and a baryonic gas. This photongas is what we still detect as the Cosmic Microwave Background. Lambda dominated era  According to the current theories, the Universe has just (on a cosmological scale) become Lambda dominated. (It is not in the picture because in 1989 they didn’t know about this).— Johan Hidding, On the total amount of non-baryonic dark matter in the Universe More: Exploding Stars, Supernovae illuminate the expanding universe   Infographic: Understanding of Our Universe and It’s Evolution

History of the Universe in a concise picture

The picture above gives a nice description of events happening at the time shortly after the Big Bang.

Quantum gravity epoch
This is the first planck time (10-43 s). In the framework of quantummechanics it is meaningless to say anything about this moment.
Grand unification epoch
In this epoch the Electroweak and strong forces are still behaving as one GUT force. The precise physics of this force are yet unknown, but many theories have been proposed.
Electroweak epoch
The strong force has split off because the Universe cooled down due to its expansion. The electromagnetic force and the weak force are still unified. This is where the Standard model of physics rules. Physicist know pretty well what went on. Quarks are still free particles. This ends after 10-10 s. When they form protons, anti-protons and (anti-)neutrons. At some point there should be an assymetry between the physics ruling normal particles and that ruling anti-particles. This would allow particles to survive where anti-particles would do less so. Otherwise they would anihilate eachother and nothing would be left but radiation. It is estimated by the baryon to proton ratio η ∼ 10-10, that one in every 10 miljard protons survived. This process is called baryogenesis
Radiation dominated era
Radiation was the dominating component in the Universe. The density of radiation dominated the way the Universe expanded. At the end of this era, when the universe is ∼ 1 s old, proton-neutron freeze-out happens and primordeal nucleosynthesis takes place.
Matter dominated era
Matter takes over, because it thins out less rapidly (∝ a-3) than radiation (∝ a-4). This is what their equations of state tell you. Matter becomes the dominant factor in expanding the Universe. After 370.000 years the baryon density drops enough to become transparent to electromagnetic radiation (photons). This is the moment photons and baryons decouple, resulting in a seperate photonic gas and a baryonic gas. This photongas is what we still detect as the Cosmic Microwave Background.
Lambda dominated era
According to the current theories, the Universe has just (on a cosmological scale) become Lambda dominated. (It is not in the picture because in 1989 they didn’t know about this).

— Johan Hidding, On the total amount of non-baryonic dark matter in the Universe
More: Exploding Stars, Supernovae illuminate the expanding universe  
Infographic: Understanding of Our Universe and It’s Evolution
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How did the Universe Emerge out of ‘Nothing’?

Everything existing in the universe is the fruit of chance and necessity. — Diogenes Laertius IX

"What happened immediately before the Big Bang? The answer to this question is important for understanding some observations in astronomy. How can energy be created out of nothing, and how is it continuing to increase as the universe expands? I quoted Seth Lloyd (2006) in Part 7: "Quantum mechanics describes energy in terms of quantum fields, a kind of underlying fabric of the universe, whose weave makes up the elementary particles - photons, electrons, quarks. The energy we see around us, then - in the form of Earth, stars, light, heat - was drawn out of the underlying quantum fields by the expansion of our universe. Gravity is an attractive force that pulls things together… As the universe expands (which it continues to do), gravity sucks energy out of the quantum fields. The energy in the quantum fields is almost always positive, and this positive energy is exactly balanced by the negative energy of gravitational attraction. As the expansion proceeds, more and more positive energy becomes available, in the form of matter and light - compensated for by the negative energy in the attractive force of the gravitational field.”
Apart from quantum-mechanical effects and the gravitational interaction, other dominant factors in the early stages were the immensely high temperatures and pressures. In the beginning it was all radiation, and no matter. And the energy content and the information content were very small. The energy content and the information content built up as the universe expanded and extracted more and more energy out of the underlying quantum fabric of space and time.
According to the current theories, the energy grew very rapidly in the beginning (by a process called inflation), and the amount of information grew less rapidly. Immediately after the Big Bang there was a hot plasma of elementary particles, which expanded and cooled very quickly. In fact, the first structures got formed within a fraction of a second after the explosion. Protons and neutrons were formed from quarks.
One minute after the Big Bang, helium nuclei were formed. Soon, a full 24% of all matter was in the form of helium nuclei. Radiation interacts primarily with ions (rather than atoms).A few tens of thousand of years after the Big Bang, the first electrically neutral matter was formed, when protons and electrons combined to form atoms of hydrogen. This marked the separation of electrically neutral matter from radiation. On further cooling, gravitational effects became more and more important, as electrically neutral atoms could now clump together because of gravitational attraction. This clumping went on to produce galaxies ultimately.
There are gaps in our understanding of how structure arose out of what was a structureless field of radiation in the beginning. In particular, we do not yet know whether there are forms of matter other than what we already know. Even as early as in the 1930s, it was known that gravitational effects in large galactic clusters are much higher than what can be expected from the known amount of matter there. Apparently, there is another, unknown, form of matter that is a full 90% of all matter, as indicated indirectly by the gravitational effects. It is called dark matter because we are unable to observe it; we infer its existence only through its gravitational effects.
Perhaps neutrinos have something to do with this dark matter. Or perhaps some still undiscovered elementary particles, including some very heavy (but unobserved) ones, may be involved. These particles might have got formed in the very hot conditions soon after the Big Bang.
The reasons for the occurrence of the Big Bang are still a puzzle. Another puzzle in modern cosmology is the fact that matter and the cosmic background radiation are distributed quite homogeneously throughout the observable universe. Consider a galaxy that is 5000 million light years away today from our galaxy, namely the Milky Way. When the universe was, say, just one million years old, it (the universe) was only a thousandth of its present size. Therefore at that time the two galaxies must have been 5 million years apart. But since the age of the universe at that time was only one million years, not enough time was available for the two galaxies to have exchanged signals of any kind (assuming that nothing travels faster than the speed of light). There could not have been any kind of communication between the contents of one galaxy and the other. So how did the homogenization of the shock waves associated with the Big Bang occur?
There is general agreement that the emergence of matter from the early radiation field was a kind of symmetry-breaking phase transition. This can be likened to the phase transition from liquid water (which is homogeneous, or translation-invariant) to ice (which is not translation-invariant). The radiation field was translation-invariant, and the appearance of matter broke this translational symmetry. A hypothetical field called the Higgs field has been introduced in cosmology to understand these phenomena. This field breaks the symmetries of the interactions among the elementary particles, and gives the particles their mass.
The Higgs-field theory predicts the existence of a cosmological constant. Such a constant was indeed introduced much earlier by Einstein, and then withdrawn because it amounted to introducing into his theory of gravitation a parameter ‘by hand,’ with no theoretical justification. Einstein’s cosmological constant was intended to provide the repulsive force needed to compensate for the attractive force of long-distance gravity. In other words, if gravity could be switched off, Einstein’s cosmological constant would result in a rapid inflation of the universe. But once it was known that the universe is expanding, it became unnecessary to try to counterbalance the attractive gravitational force.
The Higgs field results in the existence of a new cosmological constant, which turns ‘empty’ space into a space that has an energy content. The problem at present is that the predicted cosmological constant has too large a value for a correct understanding of the observed cosmic evolution. It is believed that perhaps the Higgs cosmological constant had a large value right after the Big Bang, resulting in a violent and very rapid expansion (or inflation) of the universe. At a certain stage of this inflation, a cosmic phase transition occurred, which freed enormous amounts of energy (rather like the release of latent heat when steam condenses to liquid water). In a way, this energy flash or Big Bang marked the actual birth of our cosmos. After this prelude of inflation and cosmic phase transition, the normal (much slower) expansion of the universe set in, and has continued ever since.
During the inflation prelude, the universe grew extremely rapidly from a volume smaller than that of the nucleus of an atom to the size of a tennis ball. If we associate the Big Bang with the moment at the end of the (very quick) inflation episode, certain cosmological mysteries get resolved. When the universe was just the size of a tennis ball, regions that are far apart today could have been in contact then, thus resulting in the observed homogenization of the universe.
This new model of the Big Bang (i.e. a phase transition after the inflation prelude) answers a few additional perplexing questions as well. The model implies that the observable cosmos is a part of a much bigger system. Our Big Bang occurred in a certain region of the cosmos, leaving other regions untouched. More Big Bangs can keep occurring in other regions of the cosmos, opening up the possibility of parallel universes. There is thus a multiverse, rather than a universe.
In a multiverse, Big Bangs occur repeatedly, and each resulting universe has values of fundamental constants that just happen to be what they are. The universe we live in happens to have values of fundamental constants that make our emergence and existence possible. Otherwise we would not have emerged and evolved. This brings us to the much-maligned anthropic principle. The principle states that: The parameters and the laws of physics in our universe can be taken as fixed; it is simply that we humans have appeared in the universe to ask such questions at a time when the conditions were just right for our life. I have not included a discussion of this principle in the present series because it is covered in another article (on biocentrism) on this website, which I coauthored with Ajita Kamal.
Although there is no law saying that the degree of complexity of the universe must always increase, an empirical observation is that it is increasing, and increasing at an exponential rate. There can be some local decreases in complexity (there is even an anthropocentric angle to this issue), but the overall complexity of our universe is increasing. This has been explained in terms of the fact that our universe is expanding, and thus getting a continuous supply of free energy or negentropy (cf. Part 7).
But how long will the universe continue to expand? Did time begin? Will time end? Here are three likely answers given by the noted cosmologist Paul Frampton in a recent (2010) book:
Most likely: The present expansion will end after a finite amount of time, the universe will contract, bounce and repeat the cycle. In this cyclic universe, time had no beginning, and will have no end.
Next most likely: The present expansion will end after a finite time in a Big Rip. Time began in the Big Bang some 13.7 billion years ago, and will end some trillion years in the future.
Least likely: The present expansion will continue for an infinite time. Time began 13.7 billion years ago, and will never end. In his book Prof. Frampton challenges this prevailing ‘conventional wisdom.”
— Vinod K. Wadhawan, Complexity Explained: 17. Epilogue, Nirmukta

How did the Universe Emerge out of ‘Nothing’?

Everything existing in the universe is the fruit of chance and necessity.Diogenes Laertius IX

"What happened immediately before the Big Bang? The answer to this question is important for understanding some observations in astronomy. How can energy be created out of nothing, and how is it continuing to increase as the universe expands? I quoted Seth Lloyd (2006) in Part 7: "Quantum mechanics describes energy in terms of quantum fields, a kind of underlying fabric of the universe, whose weave makes up the elementary particles - photons, electrons, quarks. The energy we see around us, then - in the form of Earth, stars, light, heat - was drawn out of the underlying quantum fields by the expansion of our universe. Gravity is an attractive force that pulls things together… As the universe expands (which it continues to do), gravity sucks energy out of the quantum fields. The energy in the quantum fields is almost always positive, and this positive energy is exactly balanced by the negative energy of gravitational attraction. As the expansion proceeds, more and more positive energy becomes available, in the form of matter and light - compensated for by the negative energy in the attractive force of the gravitational field.”

Apart from quantum-mechanical effects and the gravitational interaction, other dominant factors in the early stages were the immensely high temperatures and pressures. In the beginning it was all radiation, and no matter. And the energy content and the information content were very small. The energy content and the information content built up as the universe expanded and extracted more and more energy out of the underlying quantum fabric of space and time.

According to the current theories, the energy grew very rapidly in the beginning (by a process called inflation), and the amount of information grew less rapidly. Immediately after the Big Bang there was a hot plasma of elementary particles, which expanded and cooled very quickly. In fact, the first structures got formed within a fraction of a second after the explosion. Protons and neutrons were formed from quarks.

One minute after the Big Bang, helium nuclei were formed. Soon, a full 24% of all matter was in the form of helium nuclei. Radiation interacts primarily with ions (rather than atoms).A few tens of thousand of years after the Big Bang, the first electrically neutral matter was formed, when protons and electrons combined to form atoms of hydrogen. This marked the separation of electrically neutral matter from radiation. On further cooling, gravitational effects became more and more important, as electrically neutral atoms could now clump together because of gravitational attraction. This clumping went on to produce galaxies ultimately.

There are gaps in our understanding of how structure arose out of what was a structureless field of radiation in the beginning. In particular, we do not yet know whether there are forms of matter other than what we already know. Even as early as in the 1930s, it was known that gravitational effects in large galactic clusters are much higher than what can be expected from the known amount of matter there. Apparently, there is another, unknown, form of matter that is a full 90% of all matter, as indicated indirectly by the gravitational effects. It is called dark matter because we are unable to observe it; we infer its existence only through its gravitational effects.

Perhaps neutrinos have something to do with this dark matter. Or perhaps some still undiscovered elementary particles, including some very heavy (but unobserved) ones, may be involved. These particles might have got formed in the very hot conditions soon after the Big Bang.

The reasons for the occurrence of the Big Bang are still a puzzle. Another puzzle in modern cosmology is the fact that matter and the cosmic background radiation are distributed quite homogeneously throughout the observable universe. Consider a galaxy that is 5000 million light years away today from our galaxy, namely the Milky Way. When the universe was, say, just one million years old, it (the universe) was only a thousandth of its present size. Therefore at that time the two galaxies must have been 5 million years apart. But since the age of the universe at that time was only one million years, not enough time was available for the two galaxies to have exchanged signals of any kind (assuming that nothing travels faster than the speed of light). There could not have been any kind of communication between the contents of one galaxy and the other. So how did the homogenization of the shock waves associated with the Big Bang occur?

There is general agreement that the emergence of matter from the early radiation field was a kind of symmetry-breaking phase transition. This can be likened to the phase transition from liquid water (which is homogeneous, or translation-invariant) to ice (which is not translation-invariant). The radiation field was translation-invariant, and the appearance of matter broke this translational symmetry. A hypothetical field called the Higgs field has been introduced in cosmology to understand these phenomena. This field breaks the symmetries of the interactions among the elementary particles, and gives the particles their mass.

The Higgs-field theory predicts the existence of a cosmological constant. Such a constant was indeed introduced much earlier by Einstein, and then withdrawn because it amounted to introducing into his theory of gravitation a parameter ‘by hand,’ with no theoretical justification. Einstein’s cosmological constant was intended to provide the repulsive force needed to compensate for the attractive force of long-distance gravity. In other words, if gravity could be switched off, Einstein’s cosmological constant would result in a rapid inflation of the universe. But once it was known that the universe is expanding, it became unnecessary to try to counterbalance the attractive gravitational force.

The Higgs field results in the existence of a new cosmological constant, which turns ‘empty’ space into a space that has an energy content. The problem at present is that the predicted cosmological constant has too large a value for a correct understanding of the observed cosmic evolution. It is believed that perhaps the Higgs cosmological constant had a large value right after the Big Bang, resulting in a violent and very rapid expansion (or inflation) of the universe. At a certain stage of this inflation, a cosmic phase transition occurred, which freed enormous amounts of energy (rather like the release of latent heat when steam condenses to liquid water). In a way, this energy flash or Big Bang marked the actual birth of our cosmos. After this prelude of inflation and cosmic phase transition, the normal (much slower) expansion of the universe set in, and has continued ever since.

During the inflation prelude, the universe grew extremely rapidly from a volume smaller than that of the nucleus of an atom to the size of a tennis ball. If we associate the Big Bang with the moment at the end of the (very quick) inflation episode, certain cosmological mysteries get resolved. When the universe was just the size of a tennis ball, regions that are far apart today could have been in contact then, thus resulting in the observed homogenization of the universe.

This new model of the Big Bang (i.e. a phase transition after the inflation prelude) answers a few additional perplexing questions as well. The model implies that the observable cosmos is a part of a much bigger system. Our Big Bang occurred in a certain region of the cosmos, leaving other regions untouched. More Big Bangs can keep occurring in other regions of the cosmos, opening up the possibility of parallel universes. There is thus a multiverse, rather than a universe.

In a multiverse, Big Bangs occur repeatedly, and each resulting universe has values of fundamental constants that just happen to be what they are. The universe we live in happens to have values of fundamental constants that make our emergence and existence possible. Otherwise we would not have emerged and evolved. This brings us to the much-maligned anthropic principle. The principle states that: The parameters and the laws of physics in our universe can be taken as fixed; it is simply that we humans have appeared in the universe to ask such questions at a time when the conditions were just right for our life. I have not included a discussion of this principle in the present series because it is covered in another article (on biocentrism) on this website, which I coauthored with Ajita Kamal.

Although there is no law saying that the degree of complexity of the universe must always increase, an empirical observation is that it is increasing, and increasing at an exponential rate. There can be some local decreases in complexity (there is even an anthropocentric angle to this issue), but the overall complexity of our universe is increasing. This has been explained in terms of the fact that our universe is expanding, and thus getting a continuous supply of free energy or negentropy (cf. Part 7).

But how long will the universe continue to expand? Did time begin? Will time end? Here are three likely answers given by the noted cosmologist Paul Frampton in a recent (2010) book:

Most likely: The present expansion will end after a finite amount of time, the universe will contract, bounce and repeat the cycle. In this cyclic universe, time had no beginning, and will have no end.

Next most likely: The present expansion will end after a finite time in a Big Rip. Time began in the Big Bang some 13.7 billion years ago, and will end some trillion years in the future.

Least likely: The present expansion will continue for an infinite time. Time began 13.7 billion years ago, and will never end. In his book Prof. Frampton challenges this prevailing ‘conventional wisdom.”

Vinod K. Wadhawan, Complexity Explained: 17. Epilogue, Nirmukta

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