Spacetime

In 1905 Einstein showed that space and time are two parts of a unity: spacetime. In our ordinary life, however, we treat space and time differently, measuring one in meters and the other in seconds. They look so distinct in our experience that it seems obvious to measure them in different ways.

If, however, we accept the Einstein’s conclusion about spacetime, we must deal with space and time on an equal footing. So let’s do it!

How much space is 1 hour of space? What about 2 meters of time? Even if hard to grasp in the beginning, these questions are completely reasonable. There is, in fact, a conversion factor between space and time that physicists use to call c and it’s approximately equal to 299,792,458 meters per second.

Wait a minute, is that the speed of light?

Yes. Actually, there’s no particular reason to call it the speed of light, it may be called the speed of graviton as well. As a matter of fact, it’s the speed at which travels every massless particle.

Keeping in mind this new idea we can see that 1 hour of space is the space that light travels in 1 hour (the space traveled by light in one year is probably more familiar to us and we call it one light-year). Similarly 2 meters of time is the time that takes light to travel 2 meters.

This however doesn’t resolve our whole problem, since we’re still left with human-invented units like seconds and meters upon which the universe surely can’t be founded on. To create a description that works independently of the units we must, finally, use the same units for space and time. In this way we have that light travels at 1 meter per meter (that is, each meter of time light travels 1 meter of space), or 1 second per second, or 1 inch per inch etc. In this description the units cancels out and the factor c, the speed of light, has simply value 1. It becomes evident, then, as just a unitless factor of conversion between space and time.

Sources:

• Spacetime Physics by J.A. Wheeler & E.F. Taylor
• http://en.wikipedia.org/wiki/Spacetime

The Big Bang

The Big Bang is a beautiful theory which is an effort to understand where the universe came from. Some of the most fundamental questions concerning our origins, such as that of the elements, can be explained with the Big Bang theory. But just where did everything come from? What existed before the Big Bang? Where did space come from? And what caused the Big Bang? Well, the simple answer is: We don’t know.

We know the universe is expanding; it’s accelerating, actually. This means that yesterday, the universe was a little bit smaller than it is today. A month ago, it was even smaller. A year ago, smaller still. Turning the clock backwards, the universe seems to be getting smaller, the galaxies closer together. If we go further enough back in time, the universe was so small that everything was contained in a point of space and time. Everything that exists today; you, me, the Earth, our Galaxy, everything came from this point.

Approximately 14.6 billion years ago, the Universe was created and it was very hot. Radiation (simply photons) dominated the early universe which cooled down as it expanded. Analysis of the CMB data suggests that the universe is a perfect blackbody; a higher blackbody temperature means typical photons have higher energies. In the early universe, these photons were so energetic that they produced matter-antimatter particles copiously seemingly out of “nothing” which can be explained using Einstein’s E=mc² formula (see this post.) The early universe was constantly creating matter and antimatter which quickly annihilated; this is the Particle Era. The universe was bubbling with matter, the prerequisite for everything in our Universe. Since our Universe is made of matter, and not antimatter, a baryonic asymmetry is proposed to be the origin of our matter dominated Universe.

Once the mean photon energy drops below ~1MeV, nuclei may be formed. This is the nuclear binding energy and thus, the Nucleosynthesis Era. During the Nucleosynthesis Era, the universe is one big nuclear reactor. This era sets the primordial chemical composition of the universe: 76% Hydrogen and 24% Helium.

The Nucleosynthesis Era is followed by the Era of Nuclei. Photon energies are at this point beyond the electron binding energy (~1eV). This era of the universe is foggy since photons are continuously being scattered by nuclei. At the very special moment during which photon energies drop below the electron binding energy, electrons may then bind to nuclei to form the first atoms - the fog is lifted. The Universe, during the era of atoms, becomes transparent. Photons are no longer being continuously scattered and they are suddenly released. This release of photons during the Era of Atoms is the origin of the Cosmic Microwave Background and is a significant use of study. Recall that beyond the CMB, before stable atoms are made, the universe is still foggy. It is for this reason that we cannot see beyond this point in the universe.

Not only can we not see past this point in the universe, but we cannot (yet) study what is happening at the moment of the Big Bang. There are no mathematical tools that can be used at the moment of the Big Bang, and thus, we cannot study what happened before the Big Bang. The current laws of physics seem to break down at the singularity in the beginning of the Universe, similar to what happens when we attempt to understand what happens inside a black hole. What caused the Big Bang is still a mystery, and there is still a lot left to discover, but we have achieved a lot in our understanding. The origin of our species, of the stars in the sky, of the elements that compose our Universe, can all be explained with this elegant theory.

When we say that the universe is flat, what does that really mean? The possible topologies of space-time are: open, flat and closed. A useful parameter when talking about the curvature of the universe is the density parameter given by omega (Ω) where Ω = Ωm + Ωrel + ΩΛ. The first term is the mass density given by ordinary, baryonic matter. The second term is the equivalent mass density of relativistic particles made up of electromagnetic energy and neutrinos. The last term is the effective mass of the universe dominated by dark energy (the cosmological constant.) The density parameter of the universe is given by the density divided by the critical density to result in a flat universe. If the density in the universe is exactly equal to the required density to inhabit a flat universe, Ω will be equal to 1. Current measurements give that Ω = 1.005 +/- 0.0007. Our universe is nearly flat! This can be seen using the Cosmic Microwave Background using a simple relationship.

Since the fluctuations in the CMB data are standard rulers, the curvature of the universe will determine the angular size of the fluctuations and thus the apparent size of the fluctuations will suggest the curvature of the universe. In an open universe, the curvature of space-time will distort light such that the fluctuations will seem smaller than they really are. On the contrary, in an open universe, the fluctuations will seem larger than they really are. In complete accordance with simulations of a flat universe, the fluctuations of the CMB data signify a flat universe: the universe has nearly exactly the critical density to result in a flat universe.

If the universe is expanding, does that mean that I am getting bigger?

No. The electromagnetic forces that are holding you together are stronger than the expansion of the universe. This means that while the universe is expanding, you are not. Furthermore, while the space between galaxies is expanding, the galaxies themselves are not getting bigger; likewise with clusters of galaxies like the Local Group and even superclusters. The Virgo Cluster, for example, is ~100 million light years across and is marginally gravitationally bound. The attractive forces within the supercluster is slowed down by the expansion of the universe by approximately 20%.

Why is everyone leaving us? Does this mean that we are in the center of the universe?

It looks like everything is moving away from us because the universe is expanding! A useful tool to always keep in mind is the Cosmological Principle. This is commonly stated as ‘Viewed on a sufficiently large scale, the properties of the Universe are the same for all observers.’ This useful tool can be applied to the expanding universe. Since all observers in the universe (meaning your position in the universe will not affect one’s observations) will see the same expansion, everyone will see galaxies moving away from them! Following this, it seems like everyone would believe that they are at the center of the universe, but this can’t be. Every point in space is moving away from every other point in space; there is no unique center to the universe.

Is space expanding, or just galaxies moving apart in space?

Spacetime is constantly being created as the universe expands. With this expansion, galaxies seem to be moving away from us, but astronomers have a technique to test if galaxies are really moving. For the moment, imagine a really large sphere centered on our galaxy perhaps containing a few hundred galaxies. The galaxies along the surface of the sphere have two types of motion: random motion due to their own movement and motion due to the expansion of the universe. When each galaxy along the surface of the sphere is analyzed, they all have almost the same motion: the motion shared among each of these galaxies is due to the expansion of the universe and the motion that diverges from the motion which is caused by the expansion is random motion. It has been found that a significant proportion of the motion is due to the expansion of the universe and very little motion is random when we take into consideration galaxies at large distances. Thus, we can conclude that the motion of galaxies is indeed due to the expansion: the space between galaxies is moving, the galaxies are not receding in a classical sense. Going back to our tool, the Cosmological Principle, if the galaxies were indeed moving away from us, turning back time, the galaxies would be approaching a specific place in space and time where the Big Bang happened. This would violate the notion of a homogeneous and isotropic universe which would lead to the Big Bang happening in a particular place (ie: a special place in the Universe.) Since this cannot be the case, we can easily conclude that galaxies must not be receding away from us but rather that they appear to be.

Can recession velocity be greater than the speed of light?

Astronomers commonly probe the depths of space that reveal redshifts larger than one (z>1) which suggests that these observed objects are receding at greater speeds than that of light. Since nothing can move faster than light, we immediately know that these galaxies are not receding away from us with speeds greater than the speed of light. But if they seem to be moving away from us faster than the speed of light, what does this mean? The space itself is expanding faster than the speed of light! Recall that redshift is just the stretching of photons during their journey to our detectors. While the photons were on their journeys through space, space itself expanded faster than light which stretched these photons significantly to make the galaxies appear to be receding faster than light. Remember, nothing can move faster than light: except the expansion of space itself.

Where in space did the Big Bang happen?

Everywhere! And nowhere! To say that the Big Bang happened in a particular place in the universe would again violate the Cosmological Principle and the notion that there is no special place in the universe. Furthermore, the Big Bang created space, so to ask the question of where it happened is meaningless because prior to the creation of the universe, there was no space! The Big Bang was the creation of space and time whose spatial location in the universe has no meaning.

Are there any other questions you would like to see answered?

The beauty of the world can be revealed through scientific methods, but unless people have experienced the beauty and awe inspiring characteristics of science, they will be unaware of how much they are capable of learning in an effort to understand the world and ultimately, the universe. In high school, I was uninterested in my academics, let alone a pursuit into the unknown. Part of me wishes that I had someone to guide me into the direction I am going now, so let’s be that person to guide even just one person into the right direction. Let’s make a difference.

Here is the above poster regarding the transit of Venus and safety precautions in English, and for those interested, in French, Spanish and Chinese. Also included are grade nine science worksheets and grade twelve science worksheets to investigate the 2012 transit of Venus. Additionally, here you can purchase eclipse glasses to view the transit of Venus; they are cheap and can be bought in bulk!

Within the next few days, I will be making an appearance at my old high school to visit the science teachers with printed posters, and a list for students who would like to purchase eclipse glasses for one dollar. Along with this, I will have the above student worksheets printed for the classrooms; since I can’t expect the teachers to take up classroom time, I will simply ask them to hand them out for those interested in doing them in their personal time. I will also be talking to my management at my workplace to ask if I can have a printed copy of the above mentioned poster to hopefully get some people interested.

The world requires people like us to make an effort to give people insight into how wonderful the world us. So make a difference with me! Print some posters; stick them in hallways, in bathrooms, outside, in schools etc. and get people interested! Even one poster will make a difference. If you’re really passionate, then print some student worksheets, ask around if people want to order glasses, and get people interested.

The universe is a wonderful place, don’t you think people deserve to know?

E = mc²

Probably the most famous equation in all of physics. The energy of a particle is given by it’s mass times the square of the speed of light.

But is it correct?

Actually, it isn’t! The full equation, that comes out naturally from the postulates of special relativity, is:

The p term is called momentum. It is proportional to the velocity in space, so that the greater the speed of an object the greater it’s momentum. Also we can think about energy as the time counterpart of the momentum.

If we allow the particle to be at rest it will have zero speed, so zero momentum, and we can see that the full equation turns back into the more familiar one, that is in fact only valid for particles at rest.

The equation helped explain many mysteries at the time. When Ernest Rutherford discovered the radioactive decay, for example, where the energy of the radioactive process came from was an open question. Using Einstein’s equation we see that for radioactivity to take place the object must drop in mass.

The mass-energy equivalence, as the equation is called, has remained incredibly successful in explaining our universe since Einstein’s discovered it and today it runs our GPS system and allow the most advanced particle accelerators, such as the LHC, to run their experiments.

Sources:

• Spacetime Physics by J.A. Wheeler & E.F. Taylor
• E=mc² is wrong? - Sixty Simbols

Unexplained Mysteries of the Universe: From the present to the Big Bang

Astronomy and cosmology have come a long way in pursuing an understanding of the cosmos; peering into the depths of stars, the vastness of space and the wonders of time, we believe we understand a lot about the cosmos but there remain significant questions unanswered. Let’s start where we’re familiar. Home.

Planet formation: We’ve been living on this spaceship of a rock for about 200,000 years now and embarrassingly, we’re still not sure just how it got here. Astronomers believe that as interstellar gas cools and begins to collapse onto itself, a large disk forms around the protostar. It is in this disk that planetesimals are believed to form but there remain a couple issues. As these planetesimals orbit through the interstellar gas, drag (or friction, a physicist’s worst enemy) should cause these potential planets to lose energy and eventually fall into their host star. Furthermore, as these planetesimals acquire enough mass and become the size of large pebbles, electromagnetic forces can no longer account for their increasing size. The problem is that gravity, at this stage, is just not strong enough to cause these rocks to become any larger. It is not until they are in the range of a kilometer or so that gravity has a significant contribution to their increasing size. So how planets have grown larger than pebbles and survived the gravitational tug of its host star, we just don’t know.

Stellar formation: The nuclear processes that occur within the cores of stars are understood to quite a degree of detail but how it all started isn’t so clear. For interstellar gas to become the first stages of a star, the gas must be cooled to only a few degrees Kelvin above absolute zero (this is colder than any natural environment on Earth.) What astronomers believe is required to cause this cooling is carbon monoxide; without it, interstellar gas would not cool enough to collapse onto itself to begin the first stages of stellar evolution.  We believe almost all “metals,” including carbon, were created in the interiors of stars, which means in the early Universe, there was no carbon. No carbon, no carbon monoxide. No carbon monoxide, no… stars? Without carbon monoxide in the early Universe, how did the first stars form? Your guess is as good as theirs.

Structure formation: In the early universe, there were slight disturbances in the temperature and mass distribution which is shown in the Cosmic Background Radiation (CBR.) In the radiation era, strong coupling between radiation and matter stopped these non-uniformities from growing by a process called damping. Since photons were strongly coupled to matter, as the photons diffused from higher to lower concentrations, they dragged the matter along with them to maintain equilibrium. Photon damping seems to play an important role in the structure of the Universe, but not if the Universe if dark matter dominated. Since dark matter is believed to be collisionless, (see here,) dark matter candidates would travel larger distances and contribute significant collisionless damping, thus smoothing out these non-uniformities more than photon damping. If the Universe is baryonic matter dominated, photon damping would allow for small scale structures to form first, such as galaxies, whereas if the Universe is dark matter dominated, large scale structures such as superclusters could form first since the smaller non-uniformities would be quickly smoothed out. So what came first; the galaxy or the supercluster?

The Big Bang

The Horizon Problem: Out of the large number of solutions for Einstein’s equation, only one of them happen to be that of a homogeneous and isotropic universe. If this is the only universe, why did it choose such a special condition? Furthermore, how does the universe know that it is homogenous and isotropic? Measurements of the CBR by COBE shows that the universe must be isotropic by more than one part in 10^5. The Universe is so large that turning back time, light did not have time to travel across the entirety of space to “communicate” this information; the Universe thus did not have time to become so uniform. In models based on the Friedmann equations, any two objects that are currently separated by approximately 1 angular degree should not have been in causal contact with one another. To visualize this, the full moon is one half of a degree across. The standard Big Bang model does not explain why the Universe seems to have almost perfect isotropy nor homogeneity.

The Flatness Problem: The universe consists of a mass density of approximately 0.3 (the Universe consists of 30% mass and 70% energy.) This condition allows for the Universe to be almost perfectly geometrically flat, which is quite a special condition. If the Universe were not flat, chances are, life would not exist. But for the Universe to be near perfectly flat currently, the early Universe would have had to be flat to within 1/10^15! The Universe would have had to begun at almost complete unity for the Universe to be nearly flat now. Out of all the possible initial conditions, why did the Universe begin with such a special condition of almost perfect flatness to allow us to ask the question?

The Structure Problem: Closely related to the horizon problem (stated above,) the Universe began with non-uniformities that allowed for structures of all scales to look the same. Spiral galaxies, clusters of galaxies, even the voids all look quite the same. Why aren’t there spiral galaxies in one section of the sky, and ellipticals in another? Why did similar non-uniformities arise in causally disconnected areas to create such seemingly connected structures? Why does anything exist at all?

These issues only scratch the surface of the unexplainables of our Universe, but they drive our curiosity to understand these cosmos and remind us how truly incomprehensible this place really is.

Sources: Foundations of Modern Cosmology: Hawley, Holcomb