All Things Relative

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Cover Photo Courtesy of NASA Goddard Space Flight Center’s photostream on Flickr

This is the first in a multi-post series on Special Relativity. Also, Rosie and I have started classes at University again this past week, so the posting frequency may drop a little bit. We are in the process of looking for guest authors in our Astro class to help take some of the load off of our shoulders. Even without them though, we will still be doing our best to deliver posts as often as possible, so please hang in there for us!

There are few things stranger than relativity. We have all heard of it, but how many of us actually know what it’s about? We’ve all watched Interstellar and marvelled at the crazy physics going on there, but just how accurate is it? Turns out, quite accurate!

time-management
Source: [Wikimedia Commons]
Did you know that past, present and future have different meanings depending on your reference frame, giving you the power of precognition or prescience? How about the fact that time slows down depending on your velocity or your gravitational acceleration, essentially making something similar to time travel possible? Or that your mass is not necessarily constant (that one shocked me the first time I heard it!).

And just why is it that the speed of light is a universal speed limit? Why can’t we ever approach it or go beyond it? And what happens to you physically as you approach the speed of light? How do atomic bombs work exactly? Where does all that energy come from?

There are so many questions that relativity raises, so many things that we have all probably heard about at some point or another, on Facebook, YouTube, Twitter, The Discovery Channel, National Geographic – but that hardly any of us actually understand.

If you’ve always wanted to understand what is so great about Einstein and his Theories of Relativity, this post is written just for you. No complications. No crazy mathematics. Just straightforward, simple thought experiments that will have you understanding relativistic mechanics in a few short minutes, and explaining it like a pro to your friends.

Note: Relativity is a really BROAD topic. For ease, and since we also haven’t reached the points in our studies where we understand General Relativity very well, we have decided to focus these posts specifically on Special Relativity. Think of it as a ‘Special’ case of General Relativity. It’s still really cool and will give you plenty of insight already into some of the really exciting consequences of relativistic mechanics.

Our Strange and Wondrous Universe

“We on Earth have just awakened to the great oceans of space and time from which we have emerged.” – Carl Sagan

maxresdefaultFor many years, physicists thought they had it all figured out. The universe could always be understood in a few simple laws, and if you didn’t yet know these laws, they could be discovered through careful experimentation. The cosmos was predictable, constant, finite. There were beautiful symmetries everywhere and mathematical occurrences that were too sweet to be mere coincidence. Nature, it seemed, painted in perfect strokes.

How wrong we were!

It was around the early 1900s when classical physics began to unravel and we started observing things that seemed to defy our neat, little laws: electrons were capable of being in two places at once; the light spectra of stars could not be explained by classical theories; the details of the photoelectric effect (wherein electrons are ejected from a surface by a light source) defied the basic requirements of electromagnetism; atoms always seemed to be doing their own thing, virtually impossible to understand with the assumptions of the day.

Basically, classical physics was in major trouble! For the few centuries following Newton, Kepler and Galileo, physicists had climbed the social ranks to be considered some of the greatest minds in all of society and if we couldn’t solve these problems, who could?

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“You thought you had it all figured out! How cute!” Source: [reportage au top]
This catastrophe threatened to destroy all that we had worked so hard to create. If so many experiments could outright contradict our theories, how could we even be sure they were correct? What if everything we thought we knew about the universe was wrong?

And so began the advent of Modern Physics. This is an era of physics which has lasted to this day and is still being refined. A world where ‘common sense’ runs exactly counter to what is true, where the universe is not so clear cut and well-defined.

Arguably, the two greatest achievements of the 20th century have been Quantum Mechanics (not covered here) and Einstein’s Theories of General and Special Relativity. Quantum Mechanics began its revolution in 1900 with Max Planck’s postulates and 1905 with Albert Einstein’s paper on the Photoelectric Effect. The Theory of Special Relativity was originally published in 1905 and the ‘sequel’, General Relativity, followed ten years later in 1915. Together these two theories govern the worlds of the large and the small.

In his paper on Special Relativity, Einstein layed out the groundwork for such phenomena as Relativity of Simultaneity, Time Dilation, Length Contraction and Mass-Energy Equivalence. All of these phenomena have consequences in every day life and the Mass-Energy Equivalence is directly responsible for the atomic bomb.

This first installment will lay out the groundwork for most of these and explain Relativity of Simultaneity. After that, we will give your brain a chance to re-energise before our next post on Time Dilation.

As complicated and bizarre as these concepts will seem once we get into them, they are the direct result of two very simple statements:

  1. The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference) –  essentially the laws of physics are observed to be identical for all observers, provided the observers are not accelerating.
  2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source – the point made about the vacuum is very important! Light can travel at different speeds in different materials, so particles can travel faster than the speed of light through a medium, but, as we will see, nothing can travel faster than light through the vacuum of Outer Space.

Einstein was able to derive his entire theory from what he termed ‘thought experiments’, essentially making deductions about the world by merely trying to imagine how things worked. If that makes you doubt the validity of his theories, it is important to realise that special relativity can also be derived entirely mathematically, with no regard given to what makes sense.

Naturally, we will stick to the thought experiments. Einstein used them, and we want to feel as smart as him don’t we? If it ain’t broke, don’t fix it, and you’ll see it’s a lot easier than it sounds!

Constancy of the Speed of Light

A universal speed limit, so what? Doesn’t seem very hard to grasp.

For many years, physicists tried to define the speed of light in space as constant relative to some medium. They called this medium the ‘aether’. As became obvious through the failed Michelson-Morley Experiment, this aether does not exist. So how do we measure this constant speed then? It must be constant relative to something surely?

And this is where the effects of relativity begin and things start to get interesting. See, if we say for example that the speed of light is always constant relative to something, then that has some interesting implications.

background-bus-light-effect
“Wow, this bus is fast!” Source: [George Hodan]
Let us begin by considering something moving at a much more manageable speed, say a person (in this case, Rosie) walking down the central aisle of a bus, which is in itself driving along the street. Let us say that we measure the speed of the bus to be 10m/s relative to the ground. If we measure Rosie as walking from the back to the front at a speed of 5m/s relative to the bus, at what speed is she moving relative to the ground?

 

Well, the answer seems a bit obvious to us at this point. 15m/s surely. How did we arrive at that answer?

We simply added the two velocities together. We took her velocity relative to the floor of the bus and added to that the velocity of the bus relative to the ground. A velocity relative to one object can be seen as the sum of velocities relative to other objects. We say that velocities are summative.

But what does this mean? How does this have anything to do with light?

Remember that visible light is the means by which we can see the world. And if we are, for example, to consider the speed of light, we start running into intuitive paradoxes.

Consider  a four-way intersection. Assume you are stopped at the intersection and another vehicle (driven by me for example) is approaching from directly opposite you. Lastly, assume you have a friend (Rosie) watching the experiment from either of the other two entrances to the intersection.

If my car opposite you is stationary, and we denote the speed of the light relative to the ground ‘c’ (this is actually the speed of light in a vacuum, but for now we will assume them to be the same), it should be apparent that the light from my car will approach at speed ‘c’.

light-travel
“Here I come!” Source: [alex grichenko]
Now let us pretend that I start driving towards you. At what speed will we now measure the light from my car relative to the ground?

Well, using the summative property of velocities, that light must have a speed ‘c’ + whatever extra speed my car is travelling at. You must then observe the light of my car arriving at you with a speed faster than the speed of light.

And what about Rosie to your left or right? Well, if we assume my car is not getting any closer or further from her, then she must measure the light as having only a speed ‘c’, since there is no apparent contribution from my car to the speed the light travels.

What does this actually mean? Since you measure a speed of light greater than that of Rosie, you will observe my car arriving at your side of the intersection sooner than Rosie observes the same event. Why? Remember, velocity is a measure of how much distance is covered per unit time. This means the light reaches you sooner than it reaches her.

But if this was actually true, Rosie really would observe my car arriving at you long after you have observed it. We know this isn’t the case. In fact, if it were true we would see all sorts of strange things happening around us that just don’t happen. For example, you might perceive a motorcycle swerving to avoid an accident with a truck while a friend may observe the same motorcycle swerving for no apparent reason since they haven’t yet observed the truck arriving.

This suggests to us that this can not be the case. The speed of light can never be expressed as a sum of other relative velocities. In fact, the speed of light is always constant. Regardless of what reference frame we are using. It doesn’t matter if you’re moving or stationary, from the perspective of every observer, all light arrives at you with a constant speed ‘c’.

So how does the world conspire to make this possible, and what consequences does it carry?

Relativity of Simultaneity

Finally! Time Travel! Can you read my palms? Can you bring Elvis back?

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The City of Love. Source: [tpsdave]
Let us begin by examining one of the simpler consequences: the idea that past, present and future are relative, a concept known as relativity of simultaneity.

Imagine that the three of us (you, me and Rosie) are standing in a street in Paris, and two car accidents occur simultaneously in front of us and behind us. In other words, these accidents occur such that the light from both of these incidents arrives at us at the same time. This must imply that both incidents occur at equal distances from us. So far, so good.

Now imagine that Rosie starts walking towards one accident and I walk towards the other. This is where things start to get strange.

If Rosie is moving towards the accident in front of you, that means the distance between her and that accident will be decreasing as she moves i.e. as time passes. Also, since she is now moving away from the accident behind you, that distance will be increasing with time.

Since we know that light has a finite speed, that means it takes time to reach each of us. Therefore, as time passes, the light from each accident has to travel a slightly different distance compared to you in order to reach her, precisely because she is moving.

Since she is moving towards the accident in front of you, she is moving into that light and it reaches her sooner than you. She is also moving away from the accident behind you and in the same direction as the light from behind you. As such, that light takes slightly longer to catch up to her and arrives at her later.

Likewise, the exact reverse can be thought to happen to me. I experience the light from the second accident (behind you) as reaching me soonest while the light from the first accident (in front of you) reaches me second.

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Source: [Meme Binge]
As a result, from Rosie’s perspective, she observes the accident in front of us before you even realise the accident has occurred. To make matters worse, I observe the exact opposite i.e. that the second accident happened first, even though, in our previous experiment in which we all stood still, we all agreed that the two accidents clearly occurred simultaneously!

This tells us that two events that may be observed to be simultaneous to a stationary observer, will not necessarily be observed as simultaneous to a moving observer. The consequence of this is that you can see into the future by looking in the direction of your motion and into the past by looking counter to your motion, something physicists call Relativity of Simultaneity.

None of this means we can influence our futures or past. We can only observe them slightly differently from one another. So no, we can’t bring Elvis back.

Light Cones and Spacetime

“Time is relative.” So that’s what they mean!

This idea of past, present and future is clearly getting a bit fuzzy. There is no way to define an absolute, objective timeline –  your past, present and future are relative to you. Someone else experiences a completely different past, present and future. How can we even have words like ‘past’, ‘present’ and ‘future’ if it all depends on your perspective?

This is why physicists have defined something

481px-World_line
Source: [Wikimedia Commons]
called a light cone, in an attempt to make these things easier to understand.

These light cones are shown in the diagram to right. They are a little difficult to explain so, for simplicity, try to think of your future light cone as being all events that you have not yet observed but will be able to do at your given velocity. Likewise, your past light cone corresponds to all events that you have already observed and that have had some influence on your present.

Why is all of this even relevant? Well, it is possible to visualise this relativity of simultaneity as a kind of warping of spacetime.

(Note: this section is for advanced readers. It takes a slightly mathematical look at relativity of simultaneity. If you couldn’t be bothered – and honestly, who blames you – skip to our quick summary at **)

Spacetime is merely a means of visualising how we move through the cosmos. Normally we are free to move freely in three spatial dimensions or directions (up and down, left and right, and forwards and backwards) as well as being constrained to move forwards through time. A spacetime diagram allows physicists to record your spatial position along the horizontal axis and your temporal (or time) position along the vertical axis.

Think of it as a means of recording your movement through existence. A horizontal movement in the diagram corresponds to a movement through space while a vertical motion corresponds to the passage of time. Towards the end of this blog series, spacetime diagrams will become incredibly useful for tying everything together and making sense of special relativity as a whole.

relativity_of_simultaneity_animation
Source: [Wikimedia Commons]
In the animation on the left, you can see what a spacetime diagram looks like. Consider three events: A, B and C. Suppose these events occur so that a stationary observer records them as being simultaneous or occuring at the same time (when v=0).

The white line that tracks from the bottom of the diagram to the top is called a “plane of simultaneity”. That means that all events along this line are observed to occur at the same time. As the plane of simultaneity moves from the bottom to the top, it is essentially tracking forwards through time i.e. this motion represents time passing.

As the observer accelerates, the direction of their light cones in spacetime changes slightly. To illustrate Relativity of Simultaneity, we can attempt to keep the shape of the light cones visually identical, instead allowing us to see a warping of spacetime itself.

Consider the case where the observer moves towards event C at a speed v=0.3c. Since the observer is moving through space, the shape of the spacetime diagram appears to bend. Suddenly, the plane of continuity moves first through C, then B and lastly through A.

What does this mean? This corresponds to being able to observe the light from C sooner than B and the light from A last as a direct consequence of the finite speed of light. Essentially, C appears to occur before B and before A. Relative to a stationary observer, we can see into the future in the direction of C and into the past in the direction of B. Naturally, the exact reverse is observed when the observer moves towards A (v=-0.5c).

**In summary, A, B and C represent three events in this diagram. The white line (called a “plane of simultaneity”) represents the passage of time. As you move through space, the shape of the diagram changes and the plane of simultaneity no longer passes through A,B and C at the same time, illustrating the effect demonstrated in our ‘Paris’ thought experiment.

This has some really cool effects for space travel.

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“A tiny blue dot set in a sunbeam. That’s Home.” – Carl Sagan. Source: [Wikimedia Commons]
Spaceships essentially see into the future of the universe if they look in the direction of travel and into the past if they look the other way. But why isn’t this effect obvious to us? For example, why did the Voyager spacecraft capture this picture of the Earth and not some primordial proto-Earth?

Remember, in order for these effects to be noticeable, our speeds need to be comparable to the speed of light. Since light travels the distance between the Sun and the Earth in a staggering 8 1/2 minutes and can even go around the Earth more than 7 times in 1 second, the speed of a spacecraft is virtually negligible. If one had sensitive enough instruments calibrated perfectly for such an experiment, we could probably detect it, but in essence, the effect is so small as not to be noticeable in every day life.

Already, in just one blog post, we have explained why the speed of light is constant and have brought into question the idea of definite time itself. Since I am sure by now your brains must be hurting, we’ll leave it there. But we’re only scratching the surface and getting a brief taste of what relativity has to offer us! If you would like to see more, keep an eye out for a future (relatively speaking) blog post on the nature of time itself!

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“My brain hurts!” Source: [Petr Kratochvil]

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