Visual Effects of Near-Light-Speed Travel: Relativistic Optics

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[00:00:05]When most of us see the world around us, we see  it in a myriad of different colors. Eyesight is   the most dominant sense that most humans have. But this light that we can see is just a tiny   fraction of all the electromagnetic waves  present in the universe - the part where   the electromagnetic wave has a frequency  between 4.3x10^14 Hz to 7.5x10^14 Hz.   This spectrum also contains any other imaginable  frequency - for example light that we can’t see,   such as radio waves, microwaves, infrared  light, ultraviolet light, x-rays and gamma rays.  Light is energy in the form of an electromagnetic  waves governed by this simple energy equation,  where E is the energy, h is Planck’s  constant and nu is the frequency,   or how fast the wave oscillates in spacetime. The electromagnetic waves that we can see are   nothing special, as this simple energy  equation states. All the different   wavelengths are basically equivalent, except  for the fact that waves with higher frequencies   are more energetic. In principle that’s it. The speed of all these electromagnetic waves,   however, is special. All light is made  of massless objects called photons.   Photons happen to travel at the  maximum speed allowed in the universe,   as do all massless objects. The universe has set an upper limit to   the speed with which information can flow from one  part of the universe to another. A finite limit   on the rate of information transfer assures  that causation is preserved in the universe.  And that's the speed at which light travels.

[00:01:44]Einstein showed that we live in a relativistic  universe, where the world can look very different as   you approach this maximum speed, and depending on  how fast you move compared to another person. We   don’t see this world because the speeds at which  we travel, say on a car or airplane are very low   compared to this maximum speed. But what would happen if this maximum speed   was closer to the terrestrial speeds that we are  used to, or equivalently what would we see if we   traveled much closer to the speed of light.  Well we would enter a universe that would be   very strange where thing would appear not as they  are when we are standing still. What would we see?

[00:02:28]And why would things appear this  way? That’s coming up right now… You have probably heard an ambulance or fire  truck drive by outside. As it approaches you,   the siren makes a high pitched noise, but after  it passes you, it changes to a low pitched noise.  Why is that? Sound is mediated through the air,   at a finite speed. As the siren sounds, it  sends out a circular wavefront. But because the   emergency vehicle also moves, each wavefront is  sent out from a different position as it’s moving.  This means that the wavefronts get packed  together towards the direction of movement.   This results in a higher frequency wave  – so you hear a higher pitched sound.   Similarly, the wavefronts get further apart  in the opposite direction. This results in a   lower frequency, or lower pitched sound. The sound waves are simply stretched in   the backwards direction and compressed  in the forward direction. The resulting   frequency is higher up front, and lower in  back. This is called the doppler effect.  Even though the source of the noise is not  changing, it sounds different because that   source is moving relative to you, the observer. Something similar happens with light, but on   much larger scales. Because light is a wave just  like sound, it works in a very similar fashion.  But this doppler effect is only noticeable as  the source of the light compared to the observer,   approaches very high speeds. We don’t see it on earth because   our everyday speeds such as driving or flying is a  tiny fraction of the speed of light. But we see it   in cosmos. If we were to look through a powerful  telescope, we would see that most galaxies are   redshifted, thus the wavelength is stretched, just  like when the ambulance is moving away from you.  Similarly, this redshift happens because  the galaxies are moving away from us.   Now, I should mention that while most  galaxies are redshifted, a few are   moving towards as well, that are blue shifted. This is called the relativistic doppler effect,   and it happens thanks to relativity. We don’t notice this at terrestrial   speeds, but what if we could build a superfast  spaceship to travel close to the speed of light?  In this case a lot of interesting things will  happen, as this relativistic doppler effect   will actually start to change how you see the  world compared to person who is not moving!  What would you see? Well, as I mentioned, light is a wave. And our   eyes and brains have evolved to interpret light  waves of certain wavelengths as the colors that   we a familiar with. Thus, if we have a light wave  with a frequency of 4.3x10^14 or a wavelength of   700 nm, then our brain interprets it as red light. But, let’s say you are travelling in a spaceship,   and there is a traffic light in space. Maybe it’s  a very busy strip of space. If you approach it   slowly, you would see the stop light normally. But what if you’re going very fast approaching   it at a significant fraction of  the speed of light, let’s say 20%?   What should you do if you see a yellow light? The correct answer is, stop. Why?  Well, what happens is that if you’re moving  20% the speed of light, the colors you see   would be different than the colors standing  still. The red light from the traffic light will   actually look yellow to you, as you approach it. Your eyes are still the same. The light source   is still the same. But the relativistic  doppler effect changes what you see.  We can calculate exactly what color light  you would see by using this formula:  Where lambda r is the wavelength of light we see,  and lambda s is the wavelength of the traffic   light for someone standing still. Beta is your  velocity divided by the speed of light. Lambda s   would be 700 nm, in this case, which corresponds to  red light. If we plug in the numbers, we find that   lambda r is around 572nm, which corresponds  to yellow light. But since it’s red to the   stationary observer, you should definitely stop. Something even more dangerous would happen   if you approached the traffic light just a  little bit faster - 25% the speed of light.  Lambda r in this case would be 542nm,  which corresponds to green light. So   the red stop light would look like a  green go light!  Now what would happen if we passed  the traffic light at the same 20%   the speed of light? How would the red light  look from the rear window? We can use a similar   formula to figure out the color of the traffic  light we would observe from the back window:  The equation is the same but the signs change. Lambda r in this case would be 857 nm,   which is in the infrared range. So in this case,  we would not see the red light at all, because our   eyes can’t detect infrared light. So the traffic  light would just appear to be non-functional or broken.  In a similar fashion, some of the low energy  infrared light that is naturally present in   the universe, but invisible to the stationary  observer’s eyes, would now appear to be colorful   to the moving observer on the spaceship, because  just like red light shifts to higher frequency   yellow and green, infrared would shift to the  higher frequency visible light spectrum. Likewise,   natural high energy ultraviolet light which is  also invisible to the stationary observer, would   shift to the visible range if we were to view it  from our rear window. So we might see unexpected   objects and colors both in front and in back our  spaceship. Things that were invisible to us before   could now be clearly seen from the spaceship. This doppler effect is however only ONE of the   weird things that would happen as we move  at speeds close to the speed of light.  Another strange effect you would see  looking out of the side window of the   spaceship is what is called relativistic  aberration, or the "searchlight effect."  When looking out of the side window of the  spaceship, you would not only see the colors   distorted, but you would also notice that the  light is bright towards the direction of motion,   and less bright away from the direction of motion. This might initially seem strange, but here’s why   it makes sense. Light intensity is literally  just the number of photons hitting your eyes,   and if you are going very fast forward  then you are racing into more photons.  So naturally as you hit more photons in the  forward direction, things will appear brighter!   On the other hand, behind you, you are racing  away from photons, so things appear dimmer.  But there are even weirder effects that you  would experience because Einstein’s theory   of special relativity shows us that things like length and time are also different for a moving   observer, compared to a stationary one. So moving at 60% the speed of light,   time will slow down for you compared to  a stationary observer, but you will not   experience anything different. From your frame  of reference, time will tick for you on the   space ship just like it does on earth. Moving at 60% the speed of light though,   what is 1 meter for a stationary observer is only  going to be 80 centimeters for the moving observer   according to this equation. This  is called length contraction.  This should mean that at these speeds, you should  start to see objects more squished together.   And this is in fact what’s happening. However,  this is not what you will see. Instead,   what you see is objects curving away  from you, and rotating towards you.  So if you were traveling at relativistic speeds in a car for example, the buildings would rotate slightly and   curve away from you. The reason this happens is  because the photons from the front of the building   are reaching your eyes earlier than the photons  in the back of the building, so you see it curved.   This is an optical illusion. the object in  fact contracted but you don’t see it that way.  This time difference of photons from different  part of the object reaching your eyes also   means that in space, spherical objects like  earth don’t appear squished like a pancake,   even though they are contracted. But they remain  spherical-looking. The only difference is that   at relativistic speeds, they will appear  rotated towards you, so that you begin to   see the side and back of the sphere. This is not  something that would happen at slower speeds.  This is again an optical illusion, because the  reality is that the object is in fact contracted.   You just don’t see it that way. What you will  experience though is that distances are reduced,   so for example, a trip to Proxima  Centauri, the closest star to us,   which is 4.5 light years away,  will only be 3.6 light years away.  The interesting thing is, however, that  even though things would be closer to you,   they would not appear that way. They would  actually look farther away when you viewed them   from your front window. Likewise looking out the  back window things will appear to be a lot closer.  This seems to be a paradox. Shouldn’t things  look closer in the front window since there   is length contraction when moving so fast?  Here’s the simplified explanation for that.  Let’s look at what’s happening on this on this  graph. B is our spaceship. The angle theta   represents the angle of a photon reaching you on  the spaceship. But as the spaceship moves faster,   length contraction in the direction of  motion means that the length on x- axis   becomes shorter, so the angle theta becomes  larger. Another way to put this is that,   you would view the photon from the side  of the ship as being in front of the ship.   In fact, all the light from the side and  even behind the ship would shift forward.  This effect becomes greater and greater  as the ship moves faster and faster,   shifting more and more of the light from the side  and behind the ship to the forward direction.  We can illustrate this with a circle. If you  are in the middle on the spaceship, for the   case where you are not moving, photons reaching  you from all directions would be the same angle.   There is no length contraction in this case. Now as you start moving towards the speed of   light, this changes so that you start  seeing things that are behind you   in your forward view. This means that your field  of view increases in the direction of movement   and decreases behind the spacecraft. And this effect becomes even more pronounced As you get closer to the speed of light.

[00:12:49]This does two things. It make things look crooked or warped, as if you are looking  at things through a wide angle lens on a camera.   And the other thing that happens is  that since the entire field of view   from the side and the back of the ship now shifts to the forward window, in order to fit in the field of view, everything   looks smaller. This causes the optical illusion of things being further away. But you have to remember   that this is only an optical illusion because in  reality, length contraction will have caused things  to be closer to you, contrary to how it appears. Looking forward in the spacecraft would be like   looking through a fisheye lens and looking out in  the back would be like looking into a zoom lens.  The lesson here is that the universe is truly  relativistic. What you see at terrestrial speeds   in your everyday life is nothing like how the  universe would look if you were moving very fast.   Not only would you see different colors,  but things that are invisible to you now,   would become visible. Time, distances, angles  and views would all be different and bizarre.  This calls into question, what is really true?  Is there an objective reality? You may argue   that objective reality is what we would see  with zero movement. But what is zero movement?   Everything on earth and the universe is moving  relative to something else. There may be aliens   living on planets moving very fast around a super  heavy star? Time and light would be different for   them – but they might think of that as their  objective reality. If in the future, we develop   the technology for interstellar travel at close to  the speed of light, then the world I described in   this video would be the objective reality of any  humans born or brought up in those ships. There   is no absolute objective reality in the universe.  What’s really true is that everything is relative.  If the subject of light fascinates you   and you want to learn more, you’re going to love  a course available on Brilliant, today’s sponsor, an interactive stem learning platform.

[00:14:58]It’s called “Waves and Light.” What’s great  about this course is that it walks you through   the science of waves intuitively. For example  you’ll learn how they travel and interact   in things that you are already familiar with, like musical instruments and ropes.  This course is particularly insightful because it  helps you realize that everything you see and hear   is based on information contained in  waves. And Brilliant makes easy to retain   more information because as you study new  concepts you take fun interactive quizzes, And get to truly learn the material by doing it yourself.

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[00:15:46]And if you have a question for me or any of the other viewers, please leave them in the comments section.

[00:15:51]I'll see you in the next video my friend!