Category Archives: Science

Time travel – revisited

After having watched Primer, thoughts began to whirl wildly in my head. The movie made time travel seem so simple and physically possible, yet there were many catches that you will notice only after watching the movie. The movie gets a very clear summary in the following document: “Primer: The Perils and Paradoxes of Restricted Time Travel Narration.” (Spoilers!)

primer-title

Primer’s theory on time travel

According to the theory in Primer, it is possible to time travel back in time but can only be done so by having the machine in which you are travelling ready to accept any material that is sent back. So this will also limit the time you can travel back to, to the moment when you first start the machine. More so, the machine has to have been continuously kept on from the point you want to go back to, to the moment you decide to go back in time. The biggest downside to the Primer theory is the fact that you’ll have to sit in the time machine as long as you want to go back in time.
Imagine wanting to go back seven days in time, you’d have to stay in the machine for a whole week in order to come out of the machine to exactly 7 days back.

Travelling back in time in Primer actually brings you to an alternative or parallel universe, where the paradox of free. This means you’d be able to kill your old self and still exist as your new self in that universe. This eliminates most of the confusing and complex ideas of the chaos theory that accompanies most time traveling theories.

Anomalous and constant energies

Let’s assume it is possible to time travel exactly like in Primer, what happens when you abruptly introduce new energy (the traveller) into a universe? Wouldn’t this cause problems with the constant energy in the universe?

According to physics, all of the energy in the universe existed in some form at the Big Bang. This means that the total energy in the universe has been constant ever since, and always will be consistent. Even though science seems to indicate that the universe is expanding, it is still plausible that the energy is constant.
There are stars, planets, galaxies, globular clusters – everywhere, matter and energy seem to exist, and it’s constantly rushing off in all directions. But for starters, the expansion of the universe does not necessarily increase the total energy – as the universe expands, the distances between stars or galaxies increases. To compensate, the gravitational energy between them decreases.
And more importantly, thermodynamics doesn’t state what value the total energy should have. It could be a huge, but constant, number (this is what’s known as an “open” universe, where the amount of matter/energy in the universe exceeds a certain “cut-off” density: see Density Parameter, Ω). It could be, as most physicists now believe, zero (this is called a “flat” universe, where the matter density in the universe is equal to the cut-off density). It could be negative, even (a “closed” universe, where the amount of matter is less than the cut-off density). It could be anything, but whatever value it is now, it was at the very beginning!

Is it still possible?

So how does introducing “foreign” energy into a constant energy universe play out?

The first and most popular theory is that a universe would just collapse. The introduction of the new energy instantly blows the whole universe off balance, causing physics, time and space to behave differently and all matter would dissolve into a glorious slurry of mixed energy.

Another theory is that introducing new energy would cause a temporary local overload of energy that will distribute in the surrounding space-time, eventually reaching the outer part of the continuum, where it will reflect the disturbance back through the universe. You can see this as dropping a glass of water in a completely filled bathtub, but without it being able to overflow it will keep reflecting the ripples in the water infinitely. These disturbances can be anything – from little vibrations in space to temporary energy disturbances (heat, sound, atomic energy).

The latter theory actually makes it physically possible to introduce new energy in an existing universe, the only problem is that you will probably break a lot of things.

Time travel

So, time travel is possible after all!

No, you’re not going to step inside a time machine to get physically shredded and transported as tiny packages only to be reassembled in another era where you can wreak havoc by just showing the local people of 1542 BC that you have an iPad 2. Though it might sound very alluring for the aspiring evil scientists among us, it still is possible the other way: traveling forward in time.
Yes yes – not quite that exciting as you’d hoped, but very interesting nonetheless!

The law of universal gravitation

We all know Newton’s laws from high school physics class. Still, for most of us, the equations remained highly abstract and we didn’t get the chance to apply them to real life scenarios. Though the equations were basic, some laws are highly applicable to an enormous amount of the universe. With the first law of Newton: Newton's law of universal gravitation we can have a simple planetary orbit system by applying the equation to the bodies [fig a.1].

fig a.1 – A real-time rendered image of two bodies of mass being attracted whilst having their own velocity, sometimes resulting in a spiraling orbit motion. This is a basic simulation of real planetary orbit physics. By applying a gravity field around the bodies, the bodies will attract each other, and keep in an never-ending orbit motion. Click image to restart with different parameters.

The basic principle behind this confirmed idea is that any form of mass – a body – has gravity. You can simply imagine gravity as a force surrounding a body, pulling other bodies to its center. That is the reason we don’t fall off the Earth when we jump!

Newton was convinced that gravity worked instantaniously. For example: if the sun would suddenly evaporate and disappear, the Earth would fall out of orbit immediately and gets hurled into space. This was later proven to be a misconception of how gravity works.

Unification of theories

So now we know that all bodies – or just mass – has its own gravitational well that pulls other bodies towards the center of the body. This theory was the basis for further research on the matter by scientists such as Albert Einstein.

Albert Einstein was working on a theory about light in his early twenties. At the age of 26, he released a paper that proved that the speed of light was the absolute barrier of everything. Yet, light also travels at a certain speed. For example: the time for the rays of light to travel the distance from the sun to the surface of the Earth (150 million kilometers) is approximately 8 minutes. Einstein said that nothing can go faster than light, not even gravity. Yet, Newton’s theory told a different story.
When Einstein noticed this flaw in Newton's law of universal gravitation, he started working on a solution for this problem – in which he succeeded and revolutioninzed the picture of the universe.

Though to understand what Einstein did, we have to take a big jump through time and go back to 1632, when Galileo Galilei came up with the idea of a coordinate system in which objects, where no force at work, are completely still or make a uniform rectilinear motion. So if you’d spill coffee or drop a ball while on an airplane or while sitting on a couch at home, the same laws apply. Even though, in an airplane, you are traveling at 1000km per hour! This effect is called the Galilean invariance.
Einstein unified this theory with Newton's universal gravitation theory to end up with a coordination grid that simplifies the calculations for measuring the amount of deflection of gravity, amongst other physical changes caused by the mass of an object.

After nearly ten years of racking his brain, he found the answer in a new kind of unification. Einstein came to think of the three dimensions of space (length, width and depth) and the single dimension of time, as bound together as a single fabric of space-time.
Like the surface of a trampoline, is warped and stretched by heavy objects like planets or stars [fig b.2]. And it’s this warping or curving of space-time that creates what we feel as gravity. A planet like the Earth is kept in orbit not because the sun reaches out and instantaneously grabs hold of it as of Newton’s theory. Bodies no longer have a force that pulls other bodies towards them. The reason why the Earth orbits the sun is merely because the Earth follows curves in the space-time fabric caused by the sun’s presence.
This theory is named general relativity.

fig b.2 – A symmetric spherical body on a two-dimensional grid that illustrates the space-time universe. body A is surrounded by its gravitational well, defined by an outer ring and a gradient.

You can simply imagine a gravitational well as a ring or more specifically, a funnel surrounding a body [fig b.3] of mass that depicts the curvature of space-time.

fig b.3 – The same scene as fig a.2 illustrated from the side with the forces of the gravitational well of body A applied to the grid. The gravity well shows an exponential distribution (hyperboloid) of the force in this situation, since body A is a symmetric spherical mass. Therefore, there can also be noted that the gravitational force exponentially increases as you get closer to the center of mass of the body, and will theoretically have an endless reach.

So what does time have to do with gravity?

The current state of the general relativity theory also describes the dilation and delay of time, affected by the curvature of space-time.

When general relativity was introduced in 1915, it had no solid empirical foundation (it did not depend on evidence or consequences that are observable by the senses). This lead to a quest for proof, obtainable through experiments and testing.

General relativity at its best

A very good example of general relativity is a natural phenomenon called gravitational redshifting. It describes how light has to “climb” uphill a gravitational well and thereby losing some energy, shifting the light-waves to a lower energetic frequency and longer in wavelength, resulting in the optical color red [fig c.4].

fig c.4 – The gravitational redshift of a light wave as it moves uphill against a gravitational field (caused by the yellow star body C).

The deflection of light caused by bodies with great mass was already foretold by John Michell in 1783 and Pierre-Simon Laplace in 1796, who predicted that some stars could have a gravity force so strong that light would not be able to escape. It was in 1801 that Johann Georg von Soldner calculated the amount of deflection of a light from a distant star, by the sun. He arrived at the Newtonian answer which is half the value predicted by general relativity. All of this early work assumed that light was a particle, a corpuscle with kinetic energy, which was inconsistent with the modern understanding of light waves.

In 1861 when James Clerk Maxwell published his paper, it was clear that light is in fact an electromagnetic wave rather than a particle. Einstein’s theory on light told that light does not simply “slow down” and combined with the fact that light is an electromagnetic wave, it all made sense. One way around this conclusion would be if time itself was altered – if clocks at different points had different rates! This effect is called time dilation.

What about special relativity

When Einstein came up with general relativity, a problem popped up when he faced calculations in the vacuum of space (or, hypothetically far from all gravitational mass). He did not have a reference of time nor space to make his calculations. So special relativity (SR) was his second invention: a way to make space-time calculations based on a “the inertial frame of reference”. This basically means that you will refer to a force that does exist in that space-time field you are doing calculations in, but only to measure differences between the two forces.

This also means that when making calculations in SR, you are excluding every practical cause of errors in measurements or formulas for a better understanding of what is happening.

Being able to make calculations like that gave a lot of new ways for calculating space-time ratios for different velocities. Now imagine two clocks that get shot into outer space to orbit the Earth. Clock A gets launched to orbit Earth with a velocity of almost the speed of light, while clock B gets launched to orbit at the speed of a regular space shuttle [fig d.5].

fig d.5 – Both clocks are launched at 00:00 hours and are measured 00:21, revealing that clock A has spent less time in space due to its high velocity compared to earth and clock B.

After one year, the time on both clocks would be measured and compared to one another. You would see that clock A would be far behind on clock B. This does not mean that clock A is broken, but simply that the speed time would pass depends on how fast the subject is moving. So clock A would have spent less time in space than clock B, even though they both spent a year in outer space. (Yes, the measurement of a year would be also relative, since the Earth is moving at a different velocity too!)

Welcome on board

In theory, time dilation is the key for travelling into the future without spending the same amount of time you normally would, compared to the speed time moves on Earth. You would need a very, very fast vehicle to have a dramatic difference. For example, one year of travel might correspond to ten years at home. A constant 1g acceleration would permit humans to travel through the entire known Universe in one human lifetime. The space travellers could return to Earth billions of years in the future. A scenario based on this idea was presented in the novel Planet of the Apes by Pierre Boulle, which… really didn’t give hope for having a nice welcome home party.

"YOU! Get off my planet!"

Colors

Ever since I’ve been a little kid, I’ve been thinking about our perceptions we get from our senses. Thinking about if other people saw the world as I did. As a kid you often feel misunderstood, because as a child you seem to see things that other people don’t see. And children aren’t taken very seriously anyway, so no one believed me or took note of my perceptions.

Bifocal insect eyes
Bifocal insect eyes

I often thought about what it would be like to see the world through someone else’s eyes. Animals were a big interest area for my young and still evolving curiosity. I imagined to have eyes of an insect, watching the world through hundreds of lenses. What would it look like?

Though, even simpler things excited my imagination. I would often ask if a person saw the things I saw, explaining in great detail how I perceived it – just to know if I could see things other people couldn’t.

Colors are precisely such a thing. I wondered if everyone saw the world in the same way. The same grass that everyone can see might have a different color for every other person. Because when I say the word “green”, your brain will pop-up a color that you call green, which in my brain could be blue – it’s just a name, not the color.

Wavelengths and rainbows

Light Dispersion
Light Dispersion

As we all were taught in school that Sir Isaac Newton found out that a glass prism could split white light apart into it’s consistuent colors. Light consists out of very small particles called photons, and these photons have a “wavelength” that corresponds to a certain color. White light is made out of a spectrum of these wavelengths. Billions of these photons, with different wavelengths our eyes can see, combined make white light.

So light of a single wavelength corresponds to a single color. The brain just translates wavelengths into colors somehow. If you look at a rainbow, it’s the same natural phenomenon. You’ll see all the natural colors that make up white light.

But these are just the “natural” colors. Let me explain…

Mixing colors

natural light spectrum

At school we’ve learned that adding all colors of paint will produce the color black. Since we’re dealing with light, we have to use additive color mixing. It means that if you add up all the colors, you’ll get white.

Adding two colors of light (two wavelengths) will produce a new color. We are going to make a few mixtures to see what colors we can make.

mixing colors 1
Green and red make yellow.
mixing colors 2
Blue and green make cyan.
mixing colors 3
Blue and red make green?

Blue and red make green? That’s not what we really should get! We should get pink. But where is pink in our spectrum? It’s not red, it’s not violet… It’s not on the spectrum at all!

So, a wavelength of a photon does correspond to a certain color – but we can’t produce all colors the eye sees with a single photon wavelength. There are natural or “pure” or “monochromatic” colors (the rainbow colors) and “unreal” colors, only existing in your brain. It means that at least two wavelengths must be mixed to create all the colors the human eye can see, in this example: pink.

Colors in the brain

The rules for creating these “unreal” colors is to mix the “real” or “monochromatic” colors that hit your eye. In the 1920s W. David Wright and John Guild both conducted experiments designed to map how the brain mixed monochomatic light into the millions of colors we experience everyday. They set up a split screen – on one side, they projected a “test” color. On the other side, the subject could mix together three primary colors produced by projectors to match the test color. After a lot of test subjects and a lot of test colors, eventually the CIE 1931 color space was produced.

CIE-1931

This is the CIE 1931 color space; a map of the colors the brain can produce by mixing the monochromatic colors. On the curved border we can see numbers, which correspond to the wavelengths in the spectrum we saw earlier. We can imagine the spectrum bent around the outside of this map – representing “real” colors. The inside represents all the colors our brain produces by mixing – the “unreal” colors.

Now let’s try to mix the colors again!

cie-blue-green-turq
Blue and green make cyan.
cie-red-green-yellow
Green and red make yellow.
cie-blue-red-magenta
Blue and red make pink!

Pink is not on the curved line, thus is it purely a construction of your brain – it does not reflect a wavelength of a single photon.

Color and reality

Firstly, photons with certain wavelengths correspond to specific colors. These are the monochromatic colors. Variations can be made by mixing these colors. However, there are colors the human eye can see that do not have a specific wavelength. These colors are brain-constructed colors. The inner area of the CIE 1931 color space is purely a mixture of monochromatic wavelengths that the mind converts to different colors. It resembles the natural spectrum of light you saw earlier in this post, but is not the same.

The brain calculates these “unreal” colors by averaging the wavelengths of photons, producing a new color that is not based on the natural spectrum of light. It is an example of what philosophers call qualia – a subjective quality of consciousness.

Is color real? Well it’s not yet specifically defined wether it’s real or not… The real thing I learned is that  it is possible for people to see different colors which do not exist. And I know that children might see things that we as adults cannot perceive. I’ll pay more attention to the curious questions of children in the future.