Time

Time is one of the most enigmatic terms one would have trouble describing. Take a breath and try describing it now. What is time?

Most simplistically time is simply a mathematical dimension describing change in the position of objects in space. It is not a physical quantity like matter but a virtual quantity.

But fundamentally time or more accurately the arrow of time points to a direction in which a quantity we call Entropy increases.

Entropy is disorder in the Universe and it is always on the rise. The order does not come back by itself; it is as if the arrow of time prevents it from happening.

There is also constant loss during the process of making order. Even if we spend energy to restore the order there will always be an amount of entropy we could not restore (conservation of energy).

This is a war we cannot win.

It is for Entropy dust disperses, disorder increases and decay starts to prevail in a room if we don’t clean it up regularly by adding more energy. Ultimately all living species borrow this energy from the Sun so that we could restore stuff and experience living.

The reason we have an illusion that there appears to be an eternal order in the Universe is because in our limited part of the Universe and in our pathetically short life span it appears so.

Life (plants and animals) constantly restores order by spending energy they borrow from the Sun. In our short-life span we avoid realisation of distant-past and far future that have no practical implications.

But in reality the fuel of Sun is not endless end it will die in about 5 billion years into the future. That would be the time when the debt of energy borrowed by all living species for the duration of life would be settled. Entropy will win or rather we would pay our debt by turning into dust.

In its ultimate twilight the increase in entropy will slow down, and the Universe will be in its heat-death. No heat to restore anything.

References:

The Temperature of History

Recommended background music: Blade Runner End Title.

A toroidal lamp

I woke up in Istanbul around 6am staring at a toroid shaped lamp hung from the ceiling.

Toroid’s surface has peculiar properties compared to a much simpler shape such as a sphere.

On a spherical surface you may start travelling in any direction and end up where you started. This property is valid for any point on the surface.

A spherical surface is a finite two-dimensional surface with no boundaries. It is a finite surface hence you end up reaching the same point. It has no borders or sharp edges that you may fall off.

As a result a spherical surface is a useful model to study a universe with no boundaries but a finite shape like ours.

A spherical surface has also constant curvature. Nowhere on it there is a point that sits on an area that is more or less curved than any other point on the sphere.

On a toroid on the other hand you may find points across its surface sitting on different curvatures. A point on its outer rim is on a surface with positive curvature, where a point on the inner rim is on a surface with negative curvature.

A simplified modelling can explain this “curvature business” that is the essence of Einstein’s general relativity.

You may construct a toroid by bending a cylinder along axis and joining its ends.

Imagine you make a toroid from a rubber cylinder. You will see that the outer surface of the toroid will stretch, and the inner surface will squash forming wrinkles.

Take a rubble rectangular slab, and on its surface paint little circles with identical diameter placed in equal distance from each other. Form a cylinder from the slab by rolling it so that the circles we drew can be viewed from outside. We should observe that despite introducing a positive curvature, the sizes of circles and the distance between them remain the same. There is no stretching or squashing; the curvature is positive but constant.

In contrast when we form a toroid using a rubber cylinder by bending it along its axis and joining both ends, we should observe that the circles on toroid’s outer surface grow in size and the distance between them increases too. The circles on toroid’s inner surface should shrink in size and the distance between them should become shorter. This is because we have introduced variable curvature changing from positive (stretching) to negative (squashing) from outer to inner rim respectively.

Imagine the toroid represents a certain space-time configuration.

It is possible a light beam to travel from circle A to its neighbour B on the inner surface in shorter time than between neighbouring circles on the outer surface. Space-time is clearly stretched on the outer rim, shrunk on the inner one.

A black hole is like a toroid that its inner hole is infinitely small hence the circles you drew on its inner surface collapse onto each other. There is no way to identify or differentiate those circles from one another, the information about them are sucked by black hole’s event horizon.

It is fascinating to think that there may be oddly shaped universes with multitude of curvatures. A universe that its space-time properties are shaped like a toroid is possible. But other weirder shapes too. Some of them may even have collapsed regions where curvature is transformed in odd directions that we may not easily imagine their shape in our Euclidian minds.

The reason we could visualise and construct a toroid is because we may construct it from Euclidian shapes that we are familiar with such as a cylinder. However we should note that we might not do so if we could not stretch and squash the outer and inner surfaces respectively. You cannot construct a non-Euclidian shape without introducing variable curvature.

A toroid is a non-Euclidian shape whereas a cylinder is a Euclidian one. Our education system has given emphasis on shapes with Euclidian geometry perhaps because there are economical benefits of realising them. Euclidian geometry has given us ability to make useful approximations. We can build pipes by modelling them as cylinders for instance.

However studying non-Euclidian geometry such as toroids, can be crucial in modelling and understanding the cosmos.

Contact Opening Scene Under the Knife

I am reading "Selected Stories of H.G Wells", edited and with an introduction by Ursula K. Le Guin.

The protagonist in the short story "Under the Knife" undergoes a surgery. During the operation he sees himself as being elevated and detached from his body. He then leaves the room, rising up, watching London in bird's eye view, then rapidly flying up over the British Isles, Europe, and so on. He eventually leaves the Earth, crosses the solar system even briefly going through the rings of Saturn as brilliantly depicted by Wells:

":..and then I saw that a bright spot of light, that shone a little to one side of my path, was growing very rapidly larger, and perceived that it was the planet Saturn rushing towards me. Larger and larger it grew, swallowing up the heavens behind it, and hiding every moment a fresh multitude of stars. I perceived its flattened, whirling body, its disc-lite belt, and seven of its satellites. It grew, and grew, till it towered enormous; and then I plunged amid a streaming multitude of clashing stones and dancing dust-particles and gas-eddies, and saw for a moment the mighty triple belt like three concentric arches of moonlight above me, its shadow black on the boiling tumult below.."

When I finished reading the story I couldn't help but think that Wells perhaps became an inspiration to 1997 movie Contact's opening scene (from Carl Sagan's novel of the same name):

Just watch this and make your own mind up:

No wonder they call him, H.G Wells, "The Father of Science Fiction".

The Grand Design

This is a popular science book from renowned physicist Stephen Hawking with a righteous agenda, and that is to take on strong anthropic principle.

Being a popular science book doesn’t mean this is beginner’s stuff nor you need to be a physicist to digest it.

However to get around comfortably you need to have consumed considerable hours digging other popular science books, or surfing Wikipedia on things like special relativity, general relativity, double-slit experiment, quantum physics, string theory, m-theory, and multiverses.

This book ties them up to a big picture and if you are lucky enough to be an open-minded person then you may have your ‘aha’ moment.

And your ‘aha’ moment may as well be the realization that god is not required to create the Universe, your dog, trees, the can of red-kidney beans on the kitchen table and everything else you see or you don’t see around you.

“The strong anthropic principle idea arose because it is not only the peculiar characteristics of our solar system that seem oddly conducive to development of human life but also the characteristics of our entire universe.”

This book challenges the strong anthropic principle with the multiverse idea.

“The multiverse idea is not a notion invented to account for the miracle of fine-tuning. It is a consequence of the no-boundary condition as well as many other theories of modern cosmology. But if it is true, then the strong anthropic principle can be considered effectively equivalent to weak one, putting the fine tunings of physical law on the same footing as the environmental factors, for it means that our cosmic habitat -now the entire observable universe- is only one of many, just as our solar system is one of many. Many people through the ages have attributed to God the beauty and complexity of nature that in their time seemed no scientific explanation. But just as Darwin and Wallace explained how the apparently miraculous design of living forms could appear without intervention by a supreme being, the multiverse concept can explain the fine-tuning of physical law without the need for a benevolent creator who made the universe for our benefit.”

To some these may seem preposterous claims as no one witnessed evidence for multiverses. But our limited observation capacity is precisely the problem here. Multiverse idea is strongly linked to quantum theory. At quantum scales our observation interferes with the history of events selected. According to Feynman, a system has not just one history but every possible history.

“The histories that contribute to the Feynman sum don’t have an independent existence, but depend on what is being measured. We create history by our observation, rather than history creating us.

When one combines the general theory of relativity with quantum theory, the question of what happened before the beginning of the universe is rendered meaningless. The idea that histories should be closed surfaces without boundary is called the no-boundary condition.

We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics...One can also use Feynman’s methods to calculate the quantum possibilities for observations of the universe. If they are applied to the universe as a whole there is no point A (that it all started), so we add up all the histories that satisfy the no-boundary condition and end at the universe we observe today. In this view, the universe appeared spontaneously, starting off in every possible way. Most of these correspond to other universes. ” 

I thoroughly enjoyed reading this book I hope you too. It is exhilarating and full of trademark humor from Stephen Hawking.

Links:

Michael Shermer on Model Dependent Realism

The shape of the universe

More than four decades ago scientists discovered that the universe is suffused with microwave radiation -long wavelength light- that is a cool relic of the sweltering conditions after the big bang. Earlier on, it was stupendously hot, but as the universe evolved and expanded, the radiation steadily diluted and cooled. Today it is just about 2.7 degrees above absolute zero, and its greatest claim of mischief is its contribution of a small fraction of the snow you see on your television set when you disconnect the cable or turn to a station that isn’t broadcasting.

In 1929, Edwin Hubble, using the 100-inch telescope at the Mount Wilson observatory in Pasadena, California, found that the couple of dozen galaxies he could detect were all rushing away. In fact Hubble found that the more distant a galaxy is the faster its recession.

An essential property of cosmic microwave radiation revealed by precision satellite measurements over the last decade is that it is extremely uniform. The temperature of the radiation in one part of the sky differs from that in another part by less than a thousandth of a degree.

So although the universe is evolving since the big bang, on average the evolution must have been nearly identical across the cosmos.

This conclusion is of great consequence because the universe’s uniformity is what allows us to define a concept of time applicable to the universe as a whole. Thus the universe has enough symmetry to allow us to speak of its overall age and its overall evolution through time.

Using two-dimensional analogy for space, there are three types of curvature that are completely symmetric -that is, curvatures in which the view from any location is the same as that from any other. They are (a) positive curvature, which uniformly bloats outward, as on sphere; (b) zero curvature, which does not bloat at all, as on infinite plane; (c) negative curvature, which uniformly shrinks inward, as on a saddle.

Therefore a short list of curvatures -uniformly positive, negative, or zero- exhausts the possible curvatures for space that are consistent with the requirement of symmetry between all locations and in all directions. And that is really stunning. We are talking about the shape of the entire universe. Yet, by invoking the immense power of symmetry, researches have been able to narrow the possibilities sharply.

So if someone was to wake you in the middle of the night from a deep sleep and demand you to tell him the shape of the universe -the overall shape of space- and grant you a mere handful of guesses, you’ll be able to meet his challenge.

- Compiled from 'the fabric of the cosmos' -Brian Greene-