## Balloons and AccelerationsNovember 30, 2008

Posted by lumeno in Uncategorized.

What happens if you tether a helium balloon to the bottom of a closed air-filled cabin and continuously accelerate the cabin to the right at a constant rate?

That’s easy you’d say. If you’re sitting in a car that lurches forward, you’d feel a force backward and be pressed against the seat. So if the cabin accelerates to the right, the balloon should feel a force to the left so that the string inclines backwards, right?

Wrong! Precisely the opposite happens. The string inclines forwards in the direction of acceleration. This little physics surprise is a nice demonstration of…. (drum roll) … THE EQUIVALENCE PRINCIPLE!!!

Well, the equivalence principle is the short answer to the problem, so let’s see it first. The principle states that a uniformly accelerating frame of reference is indistinguishable from an inertial frame in which a uniform gravitational field (opposite to the acceleration) is present. As an illustration, suppose you’re in a rocket which is accelerating upwards (whatever upwards means) far away from any gravitating bodies. Since you’d experience a pseudo-force downwards, you wouldn’t be able to tell (without looking outside) whether you were indeed accelerating upwards or whether you were stationary on the surface of some planet which is exerting a gravitational field on you.

Equivalence Principle

So how does that help with a balloon in a cabin? All you need to do is forget that the cabin is accelerating to the right and replace the acceleration with an extra “gravitational field” to the left. Combined with the original vertical gravitational field, you get a net gravitational field pointing downwards and left (diagonally). Since the balloon aligned opposite to the gravitational field that it “felt” when there was no acceleration, it should align opposite to the new effective gravitational field. Hence, the balloon and string incline towards the right.

You might rightly ask, aren’t things a little more complicated? Isn’t there air inside the cabin that experiences a force too? And whatever happened to the pseudo-force that pushes things backwards? To answer these questions, let’s look at things in some more detail.

Firstly, the air inside the cabin feels the pseudo-force too and behaves as if there is a gravitational field in the horizontal direction as well. How does a gas respond to a gravitational field? Roughly speaking, the air tends to pile at the bottom so you get a gradient of density (and pressure) in the direction of the field.(Precisely, it takes up an exponential distribution which can be approximated to be linear over small distances.) A linear gradient in pressure in a fluid means that an object immersed in it will experience a buoyant force and in the case of an object less dense than the surrounding fluid, the buoyant force dominates and the object floats. This is of course what made the helium balloon rise up in the first place. But now, since you have a pressure gradient horizontally, you get a horizontal buoyant force too. This force dominates over the pseudo-force to the right since the balloon is less dense than air, just as in the case of the vertical force. So the net force is up and to the right.

Interestingly, the relatively involved analysis in the previous paragraph is completely contained in the statement “a helium balloon aligns opposite a gravitational field” which combined with the Equivalence Principle provides a simple answer to this deceptive problem.

More on the equivalence principle soon…

## Relativity of Length ScalesJuly 30, 2008

Posted by tarun in Uncategorized.

A problem given in The Fundamentals of Physics by Resnick and Halliday asks the following question. If someone told you that overnight the size of the Universe, alongwith the size of everything contained inside it, has doubled, then how would you go about verifying it? If you have access only to length measuring devices then clearly this task is impossible, since all that is important here is the relative size of objects, and obviously the length of the standard metre too has doubled. So whoever told you that could not have known it by conducting any experiments involving only lengths. Fortunately there are other physical quantities in our world, such as mass, time, charges of various kinds; and physical constants such as speed of light, Planck’s constant, Newton’s gravitational constant and so on. Clearly, if only the lengths have changed and not the time then a measurement of speed of light should reveal if the assertion is true or not.

Our Universe is indeed expanding and the previous argument suggests that it can’t be that everything in our Universe is expanding, else how could we figure out that there is more room out there today than was tomorrow? In fact, not only our metre rods are not expanding, even more loosely bound objects such as galaxies and clusters of galaxies are not expanding, and have reached a semi-stable configuration where they do not participate in the general expansion of the Universe any more. The usual explanation of an expanding Universe by using an expanding balloon and dots drawn on it works only if the dots are infinitesimal. For instance, if I make a rather largish dot that occupies half the surface on the balloon then as the balloon expands it will still occupy half the available space.

Incidentally, it might seem that we require other forces of nature to produce a non-expanding metre rod; and indeed it is true that a metal rod is held together by electromagnetic forces, and the atoms inside it acquire a fixed physical length through the principles of quantum mechanics (Planck’s constant and so on), but this is not really true. As I mentioned earlier, a galaxy is held together only by gravitational forces, and it too stops expanding after it has become dense enough to oppose the pull of the rest of the matter in the Universe that is trying to pull it apart. So even if there were no other forces but only gravity, the expansion of the Universe can be still figured out by making a simple experiment of comparing lengths using galaxies as a metre rod. If this were not true we would be led to a Universe that expands but there would be no experimental method to discover it. And that would be a bit metaphysical!

## Amoebic PhysicsJuly 24, 2008

Posted by lumeno in Uncategorized.

Imagine for a moment that you were a rather intelligent amoeba. The typical sizes of objects you encounter and interact with (your food) would be of the order of a few micrometers. You would spend your entire life over a period of a few days in a pond of water a few meters across. During this long and meaningful existence of yours, you try to understand this world of yours telling your fellow amoebae that you’re doing physics research. But this proves to be an extremely difficult task because it seems as if though there really aren’t any laws in this world of yours. You are surrounded by constant turmoil and chaos and those important encounters with objects that are essential for your survival are purely by chance – predictability seems to be fundamentally absent from your universe both at short and large time scales. Weird things are constantly bombarding your cell walls drifting you through the pond. On some rare occasions, some unknown mechanism seems to make your part of the universe move amazingly fast through the rest and you end up in a completely different part of the pond, where nothing is the same again.

Although, there isn’t much scope for an Amoebic Institute of Physics, you seem to do pretty well, surviving and reproducing. Evolving gradually, your species tends to adjust to the long-time-scale environment by unconsciously encoding in its genes the physics relevant to its survival – only the physics it experiences.

Human beings share this particular aspect of life with amoeba and with every other living organism. We have an intuition of how things work mostly based on what evolution has encoded in us and partly based on our experiences as we grow up. This “self-taught physics” includes only the physics that emerges at the time, distance and energy scales that we experience. What makes us different from many other life forms is that we are equipped with the capability to consciously recognize this physics as an apparent order and pattern in our experiences, thus enabling us to act based not just on instinct but on rationalization as well. This capability not only has to do with the relative size of our brains (which came to be through the necessity that evolution posed) but also with the fact that our time, distance and energy scales are such that such a recognizable order does exist  to an appreciable extent, something that you wouldn’t have even if you were an intelligent amoeba.

The important next step, is to make the assertion that this order exists not just in the patterns we observe (a ball thrown up always falls back down) but even where we do not observe patterns (the weather, human interactions, miracles) and that these can all be described by simple laws. When we do not observe patterns, we (should) acknowledge that it is not because patterns/laws do not exist but simply because the laws do not apply to human scales of experience and intuition. This humbling acceptance and the realization of human insignificance has been known to pay off as far as discovering physics is concerned (remember Copernicus?).

The assertion of order combined with a desire to understand why the laws can’t be any other way ultimately lead to all of the new physics – through imagination and physical experimentation. One has to realize this distinction between the physics that we experience and the real underlying physics which it emerges from. Physicists call these respectively, classical physics and quantum physics. Classical physics was fairly well established by the beginning of the 20th century. Although it described all of the physics humans experienced, inconsistencies between its different branches crept up and there seemed to be no indication of why the laws were what they were. Today, experiments suggest strongly that we have discovered a complete quantum physics for everything except gravity. This means that we know the real laws of physics (independent of human experience) for all situations where gravity is not exceedingly strong.

There are three major conceptual gaps left today and a strong indication that many of the open problems in fundamental physics are related to these three. The first is the unknown theory of quantum gravity that I already mentioned. The second is an exact understanding of how and when quantum physics becomes classical physics – the Quantum-to-Classical transition which is what I will mostly be talking about in later posts. The third is that irksome question of why the laws of physics are the way they are – something which has come to be known as Anthropic Physics. Or Amoebic Physics, if you’re the intelligent amoeba.

## Physics and The MassesJuly 18, 2008

Posted by lumeno in Uncategorized.

Whenever I’ve tried explaining what I’ve understood of quantum mechanics to non-science-type friends of mine, I begin to lose them somewhere around the mention of “state vectors”. To keep them interested, I’ve had to use words and phrases like “mystery”, “bringing into existence”, “spooky action” and “nobody really knows”. Most popular science books do the same but in the process of doing so, the true essence of the subject is lost and the more vulnerable of the audience goes on to interpret quantum mechanics as some sort of spirituality. This is quite a sad thing.

The problem of physicists trying to reach laymen is only compounded by (most of the) people who call themselves science journalists. There was a recent article in Discover magazine on why no one still understands magnetism which only went to show how its author didn’t. And then there was that unforgettably horrible movie “What the bleep do we know” which was just plain wrong, misleading and had nothing to do with the way physicists understand quantum mechanics.

So before I begin talking about the weird (but strictly non-mystical) world of the quantum, I want to emphasise that the key to understanding it is to enlarge the purview of what you consider to be abstract. Most people who learn physics systematically (high school to graduate school) do it gradually, first passing through easily observable and intuitive concepts (pulleys and ramps), then learning to accept idealisations such as simple pendulums, perfect gases and elliptic orbits (which don’t really exist) and later moving into the abstractions of state vectors and Hilbert spaces.

Idealisations are done because the real world is complex and it would be impossible to study the universe by considering every single detail. This often gives the impression that physicists only deal with spherical chickens in a vacuum as the joke goes. But the point is it works, and we can test it.

The abstraction is unavoidable because the fundamental laws of physics are counter-intuitive and aren’t apparent in everyday experience. You’ll soon see that the picture of matter being composed of little billiard-ball-like particles bouncing off each other is simply wrong. The ultimate constituents of the universe are not tangible; tangibility being an emergent human-centric phenomenon. Nature is most closely described by mathematics and one soon finds that the math is all there is – no waves, spherical particles, moving points or strings and membranes – just the math. How our experience of the universe arises out of this intangible math is, I think, one of the deepest puzzles Nature poses us.

## Why is There Something Rather than Nothing?July 12, 2008

Posted by tarun in Metaphysics.

All physical laws are expressed in terms of differential equations in space and time that require initial data to predict the evolution of whatever system we are considering. In classical physics we have Newton’s laws, Maxwell’s equations and the Newton’s law of gravitation, which are all second order differential equations in time.  At the quantum level we either speak in terms of Schrodinger’s equation – a first order equation in time – or in terms of propagators that propagate wave-functions forward in time. Relativity mixes time and space and makes gravity a theory of geometry of space-time, thus the fundamental equation of general theory of relativity relates geometry of a space-time to its energy-matter content. However, we most often solve it as an initial value problem. After the space-time, along with its geometry has been obtained, it provides the causal structure that everything else in the universe must abide by. The essential point here is that physics deals mainly with cause and effect.  This is built into the scientific method where we pose questions in terms of experiments that lead to certain results that we then explain in terms of laws of physics.

It seems that the question of the prime mover or the first cause (that itself is uncaused) cannot be formulated in terms of the current structure of physical laws. Is that absolutely true? General relativity predicts that most space-times become singular either in past or in the future, especially the one that we are supposed to be living in. In some sense this singularity removes the problem of initial data since all future states lead back to the same singular state. However, the popular thinking is that the singular event that we call the big-bang, cannot be described in terms of classical physics, primarily due to the mathematical singularity that exists at the big-bang that we believe to be unphysical. It is possible that quantum physics will resolve this singularity? What do we hope to find in such a theory? Shall we find that the Universe tunnels into another phase? Would the structure of that phase still be causal? We don’t know the answers to these question yet.

But perhaps causal laws are not the final truths of Nature? The Universe could also very well exist forever in time, but that too would not explain why it is there in the first place. Thus, steady state cosmology, although it avoids the big-bang, is not necessarily philosophically more appealing, though this is usually stated by its proponents. A philosophically satisfactory universe would be the one that creates itself out of nothing, with all the stuff like matter and energy and laws that govern them built into it. Can differential equations describe such a theory? There are differential equations that in certain cases do not necessarily require initial conditions: these are the so called non-linear equations. However, a resolution of this fundamental problem cannot lie in the absence of initial conditions alone but rather in some sort of package that makes our Universe logically imperative. Although, even then we could question why there should be anything like logic that exists separately. Perhaps we haven’t yet developed the language required to understand why there is something rather than nothing!

PS: This post has been reworked from this original post.

## GenesisJuly 11, 2008

Posted by lumeno in Uncategorized.