Tag: Big Bang cosmology

The universe’s shape and its oldest light

The 3-torus is a strange and wonderful shape. We can’t readily visualise it because it has a complicated structure, but there’s a way. Imagine you’re standing inside a cube in which light is moving from the left face towards the right face. If the two faces are opaque, the right face will absorb the light, say, and that will be that. But say the two faces are not opaque. Instead, if the light passes through the right face and reemerges from the left face — as if it entered a portal and emerged on the other side — you’ll be standing inside a 3-torus.

If you look in front of you or behind you, you’ll see a series of cubes: they’re all the same cube (the one in which you’re standing) illuminated by the light, which is simply flowing in a closed loop through a single cube. In the early 1980s, physicists proposed that our universe could have the shape of a 3-torus at the largest scale. “There’s a hint in the data that if you traveled far and fast in the direction of the constellation Virgo, you’d return to Earth from the opposite direction,” a 2003 The New York Times article quoted cosmologist Max Tegmark as saying. The idea is funky but it’s possible. Scientists believe our universe’s geometry was determined by quantum processes that happened just after the Big Bang, but they’re not yet sure what that geometry really is. For now, the data are not inconsistent with a 3-torus, according to a paper a team of scientists calling themselves the COMPACT collaboration published in April 2024.

Scientists try to determine the shape of the universe just the way you would have standing inside the 3-torus: using light, and what it’s revealing ahead and behind you. Light passing through a 3-torus would be in a closed loop, which means the visual information it encodes should be repeated: that is, you would’ve seen the same cube repeated ad infinitum, sort of (but not exactly) like when you stand between two mirrors and see endless repetition of the space you’re in on either side. Scientists check for similar patterns that are repeated through the universe. They haven’t found such patterns so far — but there’s a catch. The distance light has travelled matters.

Say the cube you’re standing in is 1 km wide. The light will cross this distance in one-trillionth of a second. If it is 777 billion km wide, the light will take a month. And it will take a full year if the cube is 9.5 trillion km wide. We’re talking about whether the universe could be a 3-torus, and the universe was created 13.8 billion years ago. In this time, light can travel a distance of more than 100 sextillion km. If the width of the cube is less than this distance, we might have seen repeating patterns if the universe is shaped like a 3-torus. But if the cube is even wider, the light wouldn’t have finished crossing it even once since the universe was born, therefore no repeating patterns — yet the possibility of the universe being 3-torus-shaped remains. We just need to wait for the light to finish crossing it once.

Since we can learn so much about the universe’s geometry by studying light, and light that’s travelled the longest would be most useful, scientists are very interested in light ‘left over’ from the Big Bang. Yes, this light is still hanging around, and it’s measurably different from all the other light. Scientists call it the cosmic microwave background (CMB), a.k.a. ‘relic radiation’. It’s left over from a cosmic event that happened just 370,000 years after the Big Bang. We need to subtract the distance light could have travelled in this time from the 100 sextillion km figure (I’m tired of looking at zeroes; you can give it a shot if you like) to find the maximum distance the CMB could have travelled.

In its April paper, the COMPACT collaboration considered data about the universe that astrophysicists have collected using ground and space telescopes over the years — including about the CMB — and with that have checked whether the possibility still exists that our universe could be shaped like three types of a 3-torus. The first type is the one I’ve considered in this post, and they’ve concluded (as expected) that if the cube is less wide than the distance light could’ve travelled since the universe was born, our universe can’t be shaped like this particular 3-torus. The reason is that the data astrophysicists have put together doesn’t contain signs of repeating patterns.

(Update, 8.20 pm, June 23, 2024: Here’s a good primer of what these patterns will actually look like, courtesy Nirmal Raj.)

However, the COMPACT team adds, our universe could still be shaped like one of the other two types of 3-tori even if their respective cubes are smaller than the max. distance. This is because these two shapes include twists that will produce two subtly different images of the universe once the light has completed one loop. And according to the COMPACT folks, they can’t yet eliminate the presence of these images in the astrophysics data. The collaboration’s members have written in the April 2024 paper that they intend to find new/better ways to ascertain their hypotheses with CMB data.

Until then, look out for… déjà vu?

A journey through Twitter and time, with the laws of physics

Say you’re in a dark room and there’s a flash. The light travels outward in all directions from the source, and the illumination seems to expand in a sphere. This is a visualisation of how the information contained in light becomes distributed through space.

But even though this is probably what you’d see if you observed the flash with a very high speed camera, it’s not the full picture. The geometry of the sphere captures only the spatial component of the light’s journey. It doesn’t say anything about the time. We can infer that from how fast the sphere expands but that’s not an intrinsic property of the sphere itself.

To solve this problem, let’s assume that we live in a world with two spatial dimensions instead of three (i.e. length and breadth only, no depth). When the flash goes off in this world, the light travels outward in an expanding circle, which is the two-dimensional counterpart of a sphere. At 1 second after the flash, say the circle is 2 cm wide. After 2 seconds, it’s 4 cm wide. After 3 seconds, it’s 8 cm wide. After 4 seconds, it’s 16 cm wide. And so forth.

If you photographed the circles at each of these moments and put the pictures together, you’d see something like this (not to scale):

And if you looked at this stack of circles from under/behind, you’d see what physicists call the light cone.

Credit: Stib/Wikimedia Commons, CC BY-SA 3.0

The cone is nothing but a stack of circles of increasing diameter. The circumference of each circle represents the extent to which the light has spread out in space at that time. So the farther into the future of an event – such as the flash – you go, the wider the light cone will be.

(The reason we assumed we live in a world of two dimensions instead of three should be clearer now. In our three-dimensional reality, the light cone would assume a four-dimensional shape that can be quite difficult to visualise.)

According to the special theory of relativity, all future light cones must be associated with corresponding past light cones, and light always flows from the past to the future.

To understand what this means, it’s important to understand the cones as exclusionary zones. The diameter of the cone at a specific time is the distance across which light has moved in that time. So anything that moves slower – such as a message written on a piece of paper tied to a rock thrown from A to B – will be associated with a narrower cone between A and B. If A and B are so far apart that even light couldn’t have spanned them in the given time, then B is going to be outside the cone emerging from A, in a region officially called elsewhere.

Now, light is just one way to encode information. But since nothing can move faster than at the speed of light, the cones in the diagram above work for all kinds of information, i.e. any other medium will simply be associated with narrower cones but the general principles as depicted in the diagram will hold.

For example, here’s something that happened on Twitter earlier today. I spotted the following tweet at 9.15 am:

When scrolling through the replies, I noticed that one of Air Vistara’s senior employees had responded to the complaint with an apology and an assurance that it would be fixed.

https://twitter.com/TheSanjivKapoor/status/1154223981358018561

Taking this to be an admission of guilt, and to an admission of there actually having been a mistake by proxy, I retweeted the tweet at 9.16 am. However, only a minute later, another account discovered that the label of ‘professor’ didn’t work with the ‘male’ option either, ergo the glitch didn’t have so much to do with the user’s gender as much as the algorithm was just broken. A different account brought this to my attention at 9.30 am.

So here we have two cones of information that can be recast as the cones of causality, intersecting at @rath_shyama’s tweet. The first cone of causality is the set of all events in the tweet’s past whose information contributed to it. The second cone of causality represents all events in whose past the tweet lies, such as @himdaughter’s, the other accounts’ and my tweets.

As it happens, Twitter interferes with this image of causality in a peculiar way (Facebook does, too, but not as conspicuously). @rath_shyama published her tweet at 8.02 am, @himdaughter quote-tweeted her at 8.16 am and I retweeted @himdaughter at 9.16 am. But by 9.30 am, the information cone had expanded enough for me to know that my retweet was possibly mistaken. Let’s designate this last bit of information M.

So if I had un-retweeted @himdaughter’s tweet at, say, 9.31 am, I would effectively have removed an event from the timeline that actually occurred before I could have had the information to act on it (i.e., M). The issue is that Twitter doesn’t record (at least not publicly anyway) the time at which people un-retweet tweets. If it had, then there would have been proof that I acted in the future of M; but since it doesn’t, it will look like I acted in the past of M. Since this is causally impossible, the presumption arises that I had the information about M before others did, which is false.

This serves as an interesting commentary on the nature of history. It is not possible for Twitter’s users to remember historical events on its platform in the right order simply because Twitter is memoryless when it comes to one of the actions it allows. As a journalist, therefore, there is a bit of comfort in thinking about the pre-Twitter era, when all newsworthy events were properly timestamped and archived by the newspapers of record.

However, I can’t let my mind wander too far back, lest I stagger into the birth of the universe, when all that existed was a bunch of particles.

We commonly perceive that time has moved forward because we also observe useful energy becoming useless energy. If nothing aged, if nothing grew weaker or deteriorated in material quality – if there was no wear-and-tear – we should be able to throw away our calendars and pretend all seven days of the week are the same day, repeated over and over.+

Scientists capture this relationship between time and disorderliness in the second law of thermodynamics. This law states that the entropy – the amount of energy that can’t be used to perform work – of a closed system can never decrease. It can either remain stagnant or increase. So time does not exist as an entity in and of itself but only seems to as a measure of the increase in entropy (at a given temperature). We say a system has moved away from a point in its past and towards a point in its future if its entropy has gone up.

However, while this works just fine with macroscopic stuff like matter, things are a bit different with matter’s smallest constituents: the particles. There are no processes in this realm of the quantum whose passage will tell you which way time has passed – at least, there aren’t supposed to be.

There’s a type of particle called the B0 meson. In an experiment whose results were announced in 2012, physicists found unequivocal proof that this particle transformed into another one faster than the inverse process. This discrepancy provides an observer with a way to tell which way time is moving.

The experiment also remains the only occasion till date on which scientists have been able to show that the laws of physics don’t apply the same forward and backward in time. If they did, the forward and backward transformations would have happened at the same rate, and an observer wouldn’t have been able to tell if she was watching the system move into the future or into the past.

But with Twitter, it would seem we’re all clearly aware that we’re moving – inexorably, inevitably – into the future… or is that the past? I don’t know.

+ And if capitalism didn’t exist: in capitalist economies, inequality always seems to increase with time.