Special Relativity VII: Spacetime and Its Importance

Hello, and welcome back to MPC! Last week, we spoke about proper time and proper length. Today, we will be delving into a new and thought-provoking topic: spacetime!

When we describe the world around us, we usually reference two things: space and time. For example, we may say John ran a 1 mile race (space) in 4 minutes (time). However, based on what we know about special relativity, this may seem a little strange. For instance, we spoke about time dilation and length contraction. From these two topics, we determined that the time between two events and the amount of space between two objects are not the same for everyone: measurements of these quantities depend on the motion of the observer.

Who cares? Well, for our everyday purposes, we do not have to worry about time dilation and length contraction too much (see last week’s post). What about a physicist, though? Physicists deal with the very large, the very small, the very fast, the very massive, etc. There is no doubt that physicists must deal with phenomena in which time dilation and length contraction do play an important role! For this reason, when a physicist is talking about space and time measurements, it is important that he/she knows from whose perspective these measurements were made. In other words, if you were to tell a physicist, “John ran a 1 mile race in 4 minutes,” he/she would ask,  “according to who?” If the 1 mile and 4 minutes measurements were made by someone zooming past the race track at 98% of the speed of light, they would have a completely different meaning than if they were made from someone in the stands!

Overall, this whole idea that space and time are relative quantities (meaning that they depend on who measured them / relative to whom they were made) is a little discomforting. If space and time are relative, then what is absolute? What is something that everyone can agree on (when considering the consequences of special relativity)? The answer: spacetime.

Imagine a graph in which we have plotted the sequence of events in your life, from birth to death:

ST1.PNG

Figure 1: The major events of one’s life

**Note: While this picture only includes “major events,” every instance of time in your life can be considered an “event”**

On the graph in Figure 1, each circle is called an event. This name is very fitting, as each circle represents just that: some occurrence, some event. This graph is a good analogy for spacetime, and for now we can just think of spacetime as a collection of all events that have ever and will ever occur:

ST2.PNG

Figure 2: Spacetime as a collection of events

We will be discussing spacetime itself in more detail next week. For now, though, you may still be wondering who cares? Yes, physicists must worry about time dilation and length contraction, and it is therefore useful for them to have something absolute with which they can work. But the average person does not have to worry about time dilation and length contraction, so who cares? Well, just because the average person does not need to “worry” about spacetime does not mean that he/she cannot learn anything interesting from it!

For example, the average person can hear sounds. But what actually is sound? Believe it or not, sound on its own does not exist! What does exist is atoms, and atoms can move in a variety of interesting ways.

Figure 3: Sound at the most fundamental level
(http://28oa9i1t08037ue3m1l0i861.wpengine.netdna-cdn.com/wp-content/uploads/2016/03/red-dot.gif)

In Figure 3, atoms are moving back and forth in a regular motion. Inside of our ears, we actually have “sensors” which can detect this back and forth movement of atoms. These sensors send signals to the brain which the brain will interpret as a sound. If the sensors in your ear sense that the atoms are moving back and forth quickly (moving back and forth with a high frequency), your brain will create a sensation that we associate with hearing a high-pitched sound. If the sensors in your ear sense that the atoms are moving back and forth slowly (moving back and forth with a low frequency), your brain will create a sensation that we associate with hearing a low-pitched sound.

In other words, sound is simply an illusion created by the brain. We have evolved to interpret the movement of atoms as sounds, but we could have just as well evolved to instead interpret the movement of atoms as colors (atoms moving back and forth quickly could have caused us to see flashes of red and atoms moving back and forth slowly could have caused us to see flashes of blue). Sound is not the only thing that is an “illusion”: so is light, temperature, etc.

What does this have to do with spacetime? Well, what if I were to tell you that space and time, like sound, are just illusions. To rephrase this, what if space and time are just our brains way of interpreting some other phenomenon. What phenomenon could this possibly be? The rotation of atoms? No, not that, something much more interesting: spacetime!

Spacetime exists and it is a fundamental feature of our universe. For our purposes, we are thinking of spacetime as a collection of all possible events. You and I are both, right now, ingrained in spacetime, moving from one event to the next. However, we are not necessarily moving from the same events to the same events. We each have our own paths through spacetime, and these are called our worldlines.

ST4.PNG

Figure 4: A representation of a person’s potential wordline

So, spacetime and its events exist, but space and time themselves do not. Rather, what we call space and time are really just our brains interpreting our journeys along our worldlines. Our brains could have interpreted our journeys along our worldlines as sounds or colors (which would have been very strange), but our brain has instead evolved to interpret our spacetime journeys as space and time.

That’s all for this week’s post, but we are just getting started with spacetime. We still have many questions to answer. For instance, if spacetime contains all events, are our futures already determined? Keep in mind that what we have been discussing thus far has all been purely scientific, not philosophical. I hope that from this post and future posts, you will obtain a deeper appreciation for our universe: the fact that our seemingly simple world can have so much hidden complexity is, quite frankly, humbling. Next week, we will be delving into more details about what makes spacetime “absolute” in special relativity. See you then!

 

For more information on the topics discussed today (and a sneak peak into future topics), be sure to check out the following resources:

http://www.ws5.com/spacetime/

https://www.youtube.com/watch?v=YycAzdtUIko

 

(featured image: http://wallpapercave.com/wp/UNgPrON.jpg)

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