====== 1. A Tour in Space and Time ======
Can you see the connection between English 'star' and Bangla 'স্থির'? And why do English 'love' and Bangla 'লোভ' sound similar, and how do they relate to 'লুব্ধক', the brightest star in the sky called 'Sirius' in English?

===== - Space-time and energy-matter =====
In the year 2005, [[wp>Einstein]] discovered two surprising facts about the universe we live in when he was only 26 years old. The first was simply that [[wp>space]] ($S$) and [[wp>time]] ($T$) are the same thing:

$$ \text{Space} = \text{Time}. $$

The second is that [[wp>matter]] ($M$) and [[wp>energy]] ($E$) are two forms of the same thing. This was formalized in his famous equation $E=Mc^2$ which we will write in English as

$$ \text{Energy} \equiv \text{Matter}. $$

We measure space using the unit **meter** ('m' in short), time using **second** ('s'), energy using **joule** ('J') or **watt** ('W') and matter using **kilogram** ('kg').

{{:courses:phy100:spacetime.png?nolink|}}

The universe we observe from Earth can be thought of as a spherical ball (shown above) of spacetime filled with energy-matter. Here, space is confined to the surface and time to the radius, but they are connected. We are at the center of the sphere, and we can see a sphere at every radius which is basically the distance of the spherical surface from us. In 1915, Einstein found another surprising fact through his mathematical analysis:

$$ \text{SpaceTime} \sim \text{EnergyMatter}. $$

Space-Time (ST) and Energy-Matter (EM) are intimately related. EM tells ST how to bend, and ST tells EM how to move.

===== - A tour in Space =====

What is space? I am not only talking about 'outer space,' the near-empty space between planets, stars and galaxies, but also about space itself, the thing within and through which matter exists. There is no absolute space, no center. A position in space must be measured with respect to some arbitrary reference, and not just one, but 3 different references.

Take the example of a marker in my hand. If you want to locate this marker, you need 3 reference planes: the floor and two of the walls, let us say the northern and the eastern walls. The wall toward Uttara must be the northern wall (Uttara is toward north from Bashundhara), and if you face this wall the wall toward your right will be the eastern wall.

The marker could be located 6 blocks (a block is a 2-feet tile) from the northern wall and 7 blocks from the eastern wall. But using these two reference planes, you will get a point on the floor only; the marker could be at any height from that point. I am holding the marker over my head around 6 feet from the floor. So we can finally give an exact position of the marker: 12 feet southward from the northern wall, 14 feet westward from the eastern wall and 6 feet above the floor. This is the space we will explore here.

How big can this Space be, and what could be the smallest measurable distance in space? If we could have a God's eye view of space, would space extend to infinity as we zoom out and, conversely, would we encounter zero length-scale as we zoom in? We do not know. But scientists have 'found' an outer and an inner limit to space, the limits beyond which our senses and sciences cannot go yet.

In this module, we will explore the whole of known **Space** from the smallest inner limit to the largest outer limit. If I write 'Space' with an uppercase 'S', it will mean this totality of space. And 'space' with a lowercase 's' will indicate a specific place, a specific location where a material object exists.

Where are we in Space? We are on earth, of course! But I want to emphasize the scale of space (distance) we are familiar with. We have defined 1 meter to be a length in space that is familiar to us. One meter is the average height of a thing we adore: a 4-year-old child.

We will begin from a length of 1 meter, and first go toward smaller things all the way up to the tiniest object found by earthlings so far, and then draw ourselves back to the larger scale, come to the scale of 1 meter, and then start an opposite journey toward large objects all the way up to the size of the whole observable universe.

Before going into this journey, we have to understand how to number things. One, two, three are rather easy. But how do we call things that are trillions of times bigger or smaller? Using **powers of 10**. Below I show different ways of talking about the numbers.

| $10^3$ | Three zeros after 1 | 1,000 | 1 thousand | 1k (kilo) |
| $10^6$ | Six zeros after 1 | 1,000,000 | 1 million | 1M (mega) |
| $10^9$ | Nine zeros after 1 | 1,000,000,000 | 1 billion | 1G (giga) |
| $10^{12}$ | Twelve zeros after 1 | 1,000,000,000,000 | 1 trillion | 1T (tera) |

Similarly, if there is a minus sign before the power of 10, that will mean how many times the number is smaller than one.

| $10^{-3}$ | 1,000 (3 zeros) times smaller than 1 | 1m (milli) |
| $10^{-6}$ | 1 million (6 zeros) times smaller than 1 | 1$\mu$ (micro) |
| $10^{-9}$ | 1 billion (9 zeros) times smaller than 1 | 1n (nano) |
| $10^{-12}$ | 1 trillion (12 zeros) times smaller than 1 | 1p (pico) |

Do not memorize any of these. Just try to 'feel' the numbers if you can and then delve into the journey in space using this webpage: https://scaleofuniverse.com.

Here, you can zoom in to go toward smaller known objects. The size of each object is shown using a negative power of 10. That means it tells you how many times smaller than **1 meter** an object is.

And, you can zoom out in this webpage to go toward bigger objects. Here the size of each object is given in positive powers of 10. So here you see how many times bigger than 1 meter an object is.

I have made the the following video of this journey using this webpage.

{{youtube>USv9Clb1eEo?large}}
\\
A sunflower can be as big as a human. We start from there. I start by zooming in and then come back to the human size of around 1 meter. Then I start going toward big things from 1:45 minutes of the video. I am listing some key timesteps in the video where you can pause for a moment and think (or feel the presence of that layer of reality).

  * 0:43: A [[un:virus]] is almost 1 million times smaller ($10^{-6}$) than 1 meter.
  * 0:52: A molecule of water is almost 1 billion times smaller ($10^{-9}$) than 1 meter.
  * 1:09: The length of [[uni:gamma ray]] wave is almost 1 trillion times smaller ($10^{-12}$) than 1 meter.
  * 2:20: [[un:earth]] is almost 1 million ($10^6$) times bigger than 1 meter. The star [[un:Sirius]] B is almost as small as earth.
  * 3:00: The [[un:sun]] is almost 1 billion times bigger than 1 meter. Basically the sun is a billion meter (or million kilometer) in diameter. Pause and Think.
  * 3:34: The star [[un:Antares]] is almost 1 trillion meter in diameter (a thousand times bigger than the sun).
  * 3:46: The [[un:Orion Nebula]] is almost 1 million times bigger than the star Antares. You have to gather a billion stars like the sun to get to the size of the Great Orion Nebula.
  * 4:08: Our galaxy the Milky Way is almost a thousand times bigger than the Orion Nebula. To get its size in meter, you have to add 21 zeros after one, which is equal to 100 thousand [[un:light-year]]s.
  * 4:20: Our galaxy is part of a group of galaxies called the [[un:Local Group]]. The size of this group is almost 100 times bigger than the size of the Milky Way. Andromeda is the other big galaxy in the group.
  * 4:23: There are even bigger clusters and superclusters of galaxies in the universe.
  * 4:32: In order to get to the size of the whole observable universe, you have to add 27 zeros after 1.

But that is not the end. This is only the portion of the universe we can observe. The universe in reality is much bigger, could be even infinite. We do not know.

Again, do not memorize any of these. All these numbers are used to raise an emotion of space.

===== - Maps of Space =====
==== - Terrestrial sphere ====
The curved surface of the spherical earth (the **terrestrial sphere**) is the space we will start to map first, as an orientation for this course. Since Aristotle described the round shadow of earth on the surface of the moon, no astronomer ever doubted that the earth is round. We have mapped the 2-dimensional surface of this sphere using a **geographic coordinate system** that has two references and two angles of measure: latitude and longitude. See the video first.

{{youtube>oyZW8mfxGSo?large}}
\\
There are two reference circles: the horizontal 'equator' halfway between the north and south poles, and the vertical 'prime meridian' passing through the Royal Observatory Greenwich in the UK. These two perpendicular lines are shown in bold yellow.

Horizontal circles parallel to the equator are called 'circles of latitude' and their distance from the equator is measured in angles (subtended at the center of the earth) called latitude. Angles north of the equator are measured from 0 to +90 deg, and those toward south from 0 to -90 deg. In total latitudes span an angle of 180 deg.

Vertical lines connecting the north and south poles perpendicular to all the circles of latitude are called 'lines of longitude' and they are measured in angles called longitude. Longitude of the prime meridian is 0 deg, those to the east can be from 0 to 180$^\circ$E, and those to west from 0 to 180$^\circ$W. In total the longitudes span an angle of 360 deg.

Dhaka is 90 deg east of UK and 24 deg north of equator. So its approximate location on earth is 90$\circ$E, +24$\circ$ as you see near the end of the video.

Can you see the similarity with the example of the marker? The two references here are like the two walls in the marker example. And the angles here are equivalent to those tile-blocks. Here we do not need the third dimension because we are not interested in measuring heights from the surface.

[[https://astro.unl.edu/naap/motion1/tc_both.html|{{:courses:phy100:lat-long.webp?nolink|}}]]

==== - Celestial sphere ====
{{:courses:phy100:twospheres.png?nolink|}}

We can create a **celestial coordinate system** by projecting the geographic one onto our sky (the **celestial sphere**). The north pole extends to the 'north celestial pole' (NCP), the south to 'south celestial pole' (SCP), the equator projects onto the 'celestial equator' (horizontal green line) and all the gridlines do the same. The celestial sphere is round like the terrestrial sphere because we see equal distances toward all directions and our vision, thus, creates a sphere with us at the center.

On the surface of the celestial sphere, the latitudes are called **declination** (DEC) and the longitudes are called **right ascension** (RA). DEC can be from $-90$ deg to $+90$ degree, below and above the equator, just like the latitudes. But the RAs are measured from a specific point on the equator called the 'March equinox' and the vertical line going through this point (the vertical green line on the figure) is similar to the prime meridian of earth. And the March equinox is kind of like Greenwich. But here, the angles go from 0 to 360 deg, instead of 180W to 180E. Sometimes the 360 degrees are given in hours. Earth rotates by 360 deg in 24 hours; so 24 hours is equivalent to 360 degrees; that means **1 hour = 15 degrees**.

The position of a star on the celestial sphere is given in the figure above as +50$^\circ$, $6$ hours (h).

{{youtube>oRiKLMsaVnQ?large}}
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The video shows more details in 3 parts. First, I show the 3D map of the celestial sphere and the position of a star on the sphere. As I move the star, you see that the RA and DEC change. Here, you also see the two references (green lines) more clearly. In the second part (from 0:58), you see the movement of the celestial sphere as seen from earth. Earth rotates from west to east, so the interior surface of the celestial sphere moves from east to west, rises and sets with everything on it, all the stars. You see rising and setting of the 'Orion constellation' as an example. From any point on earth, we only see half of the celestial sphere, its one hemisphere. Northerners like us see the northern hemisphere.

In the third part (from 2:22), I show how the hemispheres move with time within the frame of the four directions (NEWS) from Dhaka. If you are in a dark location and look toward the northern horizon, you can see the Polaris (ধ্রুবতারা), the star very close to the north celestial pole. As the earth rotates with respect to the axis going through NCP, Polaris remains almost at rest, never rises or sets. All the other stars rotate with respect to the NCP. You see how the sky moves with time during a single day, and from one day to the next on a given time at night.

From 3:33 in the video, I remove the earth from the picture and you see both hemispheres of the sky, albeit not at one glance. You are seeing the interior surface of the celestial sphere. The gridlines clearly show the two poles NCP and SCP and the hazy Milky Way appears as a circular band; normally we see only half of this band at a time, the other half being blocked by the horizons.

[[https://astro.unl.edu/naap/motion1/cec_both.html|{{:courses:phy100:ra-dec.webp?nolink|}}]]

===== - A tour in Time =====
So far we have been talking about space without any reference to time, but it turns out one cannot be observed without the other. We observe things using light, and the speed of light is finite, only 300 thousand (300k) kilometers per second (kmps). My hands are now around 1 foot away from me, and light took 1 nano-second to traverse that 1 foot from my hands to my eyes. So I am seeing my hands as they were 1 nan-second ago. I can never see what they look like NOW.

**The farther you look in space the further you see in time.**

One nano-second is a billion times smaller than 1 second. Some of you are sitting at a distance of 10 feet from me. That means, I am seeing you as you were 10 nano-seconds ago. The light from the bulbs in the classroom was reflected from your body and took 10 nano-seconds to reach my eyes after the reflection. This eternal evasion of the present has not been a problem but a blessing. Because of the finite speed of light we can literally see the past.

In principle, it is possible to observe the whole 14 billion years of history of the universe. Want to see how the universe looked like 25 thousand years ago? The center of our Galaxy is around 25,000 light-years (ly) away from us.

**1 light-year (ly) = the distance light travels in 1 year = 10 trillion km.**

So light took 25 thousand years to reach from the Galactic Center to us. That means When you look at the center of our Galaxy, you go back 25k years in the past. Have a look then.

{{:courses:phy100:milky-way-andromeda.jpg?nolink|}}

Seeing the past is not just **possible**, it is actually the only possibility. We are blind to the present and the future. Our vision is a vision of the past. Light is like a letter sent you in the good old times when there was no fast mode of transportation. Let us say you live in the 19th century and you have written a letter to your loved one in China and it took a month for the letter to reach him. When he reads the letter, he will learn what you were thinking one month ago. He has no way of knowing what happened to you in that one month after writing the letter.

Using light as a letter, we can study the past of our universe and uncover everything about its **14 billion years of history**. If we want to know what the universe looked like 5 billion years ago, we just need to find a galaxy 5 billion light years away and observe it. Want to see the universe when it was just 2 billion years old? Just find a galaxy 12 billion light years away and it will show what it meant to exist in a universe only 2 billion years old. here is a list of galaxies and their distances.

^ Galaxy ^ Distance ^ Light travel time ^
| M 81 | 11.8 Mly ((M: mega / million, G: giga / billion, ly: light years, y: years.)) | 11.8 My |
| NGC 584 | 84 Mly | 84 My |
| NGC 4680 | 363 Mly | 359 My |
| 3C 295 | 6 Gly | 4.8 Gy |
| RD1 | 26 Gly | 12.6 Gy |
| [[https://www.nasa.gov/feature/goddard/2016/hubble-team-breaks-cosmic-distance-record|GN-z11]] | 32 Gly | 13.3 Gy |

Light is literally a letter. A light coming to you from a galaxy will not only tell you how far the galaxy is, but also what the galaxy is made of. This is the method using which we have uncovered the history of the universe as laid out in the timeline below. The events related to earth after 5 billion years ago, of course, were not known using light as letter.

{{:courses:phy100:bigbang-to-now.png?nolink&700}}

Let us list the key events shown above up to the extinction of dinosaurs.

^ Years ago ^ Event ^
| 14 billion | Big bang, beginning of the universe from an unimaginable singularity. |
| 12 billion | Almost all galaxies in the universe formed. |
| 5 billion | Our solar system formed. |
| 4 billion | Age of the oldest rocks found on earth. |
| 3.5 billion | Primordial atmosphere of earth and the signs of first life. |
| 2 billion | Plants begin producing oxygen on earth. |
| 1 billion | Earth's atmosphere takes the present form. |
| 250 million | Our sun began the last revolution around the galactic center. |
| 65 million | Dinosaurs went extinct due to the collision of an asteroid. |

This last event has some astronomical significance; at least if the 'asteroid impact' hypothesis is correct. A 10-km asteroid hit the earth around 65 million years ago. The impact was so violent that it sent a huge amount of rocks into the atmosphere and the earth was shrouded in a dense cloud of dust and mist for almost ten thousand years. During that time, earth was dark due the lack of sunlight. The largest animals went extinct due to their higher demand of food and nutrition, small animals like our dear ancestors survived. Google 'Chicxulub crater' to learn more...

===== - Maps of Time =====
It is not easy to fathom 14 billion years, to feel the immensity of this span of time. So we create 'maps of time' to make things more relatable. We have been making calendars for a long time, maybe 50 thousand years. A map of time squeeze the 14 billion years within the space of a more imaginable duration. I will show you two calendars. First, we will fit the whole 14 billion years within the span of 1 year and see what happened at which date. Second, we will fit the 14 billion years into the span of just 14 years and see what happens.

First, iumagine 14 billion years is equal to 1 year. Then how much would be 1 billion year? A little more than 1 month (a year has 12 months). In this cosmic calendar, big bang happened on 1 January, 12 am, midnight. And the current time is 31 December, 12 am, midnight.

{{https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Cosmic_Calendar.png/1280px-Cosmic_Calendar.png}}

Let us see when the key events of the universe happened in this calendar of imagination.

^ Time ^ Event ^
| 1 January | Big bang |
| May  | Formation of the disk of our galaxy, the Milky Way. |
| September  | Formation of our solar system. |
| October | Algae create oxygen via photosynthesis. |
| 15 December | The most ancient fossils of life. |
| 18 December | Animals with backbone arise. |
| 30 December | Dinosaurs are extinct. |
| 31 December, 11:52 pm | Modern humans evolve in Africa. |
| 31 December, 11:59 pm | Modern humans migrate to the whole world from their African homeland. |
| 1.2 seconds ago | Columbus arrives in America and begins the violent process of destruction of the native American cultures. |

This is still not very easy to fathom. This imaginary calendar is so compressed that a 530-year-old event (Columbus' inhuman invasion of the Americas) is just 1.2 seconds old. So let us now makes the recent events more imaginable by fitting the 14 billion years within the span of 14 years.

In the 14-year cosmic calendar big bang happened just 14 years ago on 1 Jan. And the important events are as follows.

^ Time ago ^ Event ^
| 14 years | Big bang occurs. |
| 13.5 years | First stars and galaxies form. |
| 4.5 years | Sun and the solar system form. |
| 3.7 years | The first living organisms on earth appear. |
| 3.5 years | The first multicellular organisms appear. |
| 3 months | All continents of earth come together to form Pangea. |
| 3 weeks | Dinosaurs go extinct due to a meteor, mammals fill the gap. |
| 2 days | The first hominines appear in Africa. |
| 2 hours | The first humans (//Homo sapiens//) evolve in Africa. |
| 25 minutes  | Humans migrate out of Africa to the whole world. |
| 5 minutes | First agricultural villages are established. |
| 3 minutes | First literate urban civilizations appear. |
| 1 minute | The great civilizations of China, India, Persia and the Mediterranean flourish. |
| 21 seconds | Muslims conquer northern India, Black Death strikes Europe. |
| 15 seconds | A single capitalist world system emerges. |
| 7 seconds | First industrial revolution. |
| 3 seconds | The Thirty-one Years' War (first and second world wars) begins. |
| Last second | Seven billion humans, a walk on the moon, electronic revolution. |

The 1-year calendar and the 14-year calendar aside, we have our own sense of time which seldom correspond to reality. The human psychological time cannot be represented in science, but only in poetry, as Shakespeare did in his famous series of 154 sonnets.

<blockquote><poem>
Devouring Time, blunt thou the lion's paws,
And make the earth devour her own sweet brood;
Pluck the keen teeth from the fierce tiger's jaws,
And burn the long-liv'd Phoenix in her blood;

Make glad and sorry seasons as thou fleets,
And do whate'er thou wilt, swift-footed Time,
To the wide world and all her fading sweets;
But I forbid thee one more heinous crime:

O, carve not with thy hours my love's fair brow,
Nor draw no lines there with thine antique pen!
Him in thy course untainted do allow
For beauty's pattern to succeeding men.

Yet do thy worst, old Time! Despite thy wrong
My love shall in my verse ever live young.</poem>
<cite>William Shakespeare, Sonnet 19</cite>
</blockquote>

This sonnet in particular takes us back to one of the most ancient sense of cosmic time, the devouring Time who gives birth to children and then causes their death. We are all born in time, and it is Time who takes our life. The Greeks (and Romans) imagined that the god Chronos (Saturn) is Time who eats his own children except Zeus (Jupiter), who was saved by his mother. The march of the planets Saturn and Jupiter along the ecliptic was so significant for them. In Indian culture, কাল or মহাকাল is another name for the god Shiva who destroys all his creation periodically.

===== - Science and pseudoscience =====
If you get too depressed contemplating your own death at the hands of Time, think about the amazing achievements of Human Culture in the last one hundred thousand years, and specifically about its scientific achievements, at least for the sake of this course.

This has been possible specially because a significant portion of the society decided to create something called 'science' and separate it from pseudoscience. The two were different but not always opposed to each other. For example, in the ancient and middle ages, astronomers depended on astrology for their livelihood. And the words 'astronomy' and 'astrology' were used interchangeably as you can see in the following poem.

<blockquote><poem>
Not from the stars do I my judgement pluck,
And yet methinks I have astronomy,
But not to tell of good or evil luck,
Of plagues, of dearths, or seasons’ quality;

Nor can I fortune to brief minutes tell,
Pointing to each his thunder, rain, and wind,
Or say with princes if it shall go well
By oft predict that I in heaven find.

But from thine eyes my knowledge I derive,
And, constant stars, in them I read such art
As truth and beauty shall together thrive
If from thyself to store thou wouldst convert:

Or else of thee this I prognosticate,
Thy end is truth’s and beauty’s doom and date.</poem>
<cite>William Shakespeare, Sonnet 14</cite>
</blockquote>

Shakespeare does not care much about 'astrology' (astronomy for him) because he derives his knowledge not from the stars of the sky but from the eyes of his friend. The eyes are 'constant stars' (ধ্রুবতারা) for him.

Eventually astronomy (science) separated itself from astrology (pseudoscience); too bad we lost the rights to use 'logy' as in 'biology' and, instead, had to vie for 'nomy.'  The modern advancements of science would not be possible without a rigorous 'scientific method' which must be followed irrespective of all social and cultural superstitions and prejudices. The method is simple.

**Scientific method:** (1) Theorize a hypothesis consistent with the currently established theories in order to solve a new problem or describe a new natural phenomenon. (2) Devise realizable experiments that would either verify or falsify the hypothesis. (3) If the verification works, keep the hypothesis unchanged until new problems arise. (4) If the verification fails or falsification wins, go back to 1 and repeat the procedure with a new hypothesis.

Sven Ove Hansson, a Swedish philosopher gave an useful definition of science: Science is the **practice** that provides us with the most **reliable** (most warranted) statements that can be made, at the time being, on subject matter covered by the **community** of knowledge disciplines. Can you differentiate astrology (a pseudoscience) from astronomy (a science) using this definition?

{{ :courses:phy100:foursciences.png?nolink |}}

Using this definition, we can unite all branches of science and think of them as branches of a single 'tree of knowledge' as shown above.