Space-Time Is Big
To quote Douglas Adams, “Space is big.” And I have no reason to disagree. But as big as space is, space-time is even bigger. Space is peanuts compared to space-time. Think about how hard it is to find your car in a two dimensional parking lot after shopping at the mall. Then think about how hard it is to find your car in a three dimensional parking garage. Factor the dimension of time to your parking garage scenario and it’s safe to say that you’ll be taking the bus home. Time is big. Space is big. Together, they are really really big, and keep getting bigger. It’s easy to see why the Moment** gets the past and the future mixed up. It’s probably the same reason that people often get up and down confused when they fall into the middle of the ocean. It’s big.
In the event you find yourself disoriented in a large body of water while time travelling, follow the bubbles to go up. Bubbles always go up. And follow entropy to move toward the future. Entropy always moves toward the future.
To get an understanding of the magnitude of space-time, let’s take a small piece of the universe and measure it in the spatial units known as cubic centimeters (ccs). This piece of the universe is a box that is 10 cms in length by 10 cms in width by 10 cms in height. The total volume is 1000 cubic centimeters and is constructed of 1000 individual cubic centimeter boxes. An hour from now, the volume will be 1000 ccs. A month from now it will be the same. No matter how far you go into the future, the 3-dimensional volume will be unchanged. You will always have 1000 individual cc units in that box. If I hid a one cc gold ingot, which is currently worth about $40, in one of those boxes, you would have 1 chance in 1000 of finding it in one guess. Take as long as you like. Time, while it exists, has absolutely no effect on the probability in this scenario because you are only searching for the three dimensional coordinates. You and the gold ingot are occupying the same time, so you’ve already found where it is located in time. And if you were allowed to keep on picking boxes until you found it, at one second per box, it would take you less than a half hour to find it. $40 dollars for less than half an hour of effort isn’t bad.
But now, let’s take another piece of the universe and measure it in the time units known as seconds. We will now say that the dimensions of the box are 10 cms x 10 cms x 10 cms x 1 day (86,400 seconds). Let’s hide the gold ingot in the box again. Only this time, you know the exact spatial coordinates. But you don’t know what time it’s going to be there, only that it’s going to occupy a one second unit of time. The probability of you finding that gold ingot in one guess is 1 chance in 86,400. Space, while it exists, has absolutely no effect on the probability in this scenario because you are only searching for the one dimensional coordinate on the time line. And if you were allowed to keep on picking one second increments on the timeline until you found it, at one second per increment, it would take you one day to examine each second. $40 dollars for 24 hours of effort, if it takes that long, isn’t all that great.
Let’s hide the gold ingot in the box again. Only this time, you don’t know any of the space-time coordinates. We will measure this 4 dimensional box in units that we will call cc-seconds (cubic centimeter-seconds). In one second, your 4D box measures 10 cms in length by 10 cms in width by 10 cms in height by 1 second in time, or 1000 cc-seconds. In 10 seconds, your 4D box measures 10 cms by 10 cms by 10 cms by 10 seconds, or 10,000 cc-seconds. In 24 hours, your 4D box measures 86,400,000 cc-seconds. And in one hundred years you have 3,155,760,000,000 cc-seconds. By factoring space and time together, we’ve greatly increased the magnitude of our box. If I were to hide that same gold ingot in the box at specific 4-dimensional coordinates where the time component measured 100 years, you would have 1 chance in 1000 of randomly selecting the correct spatial coordinates times 1 chance in 3,155,760,000 in finding the location on the time axis, leaving less than 1 chance in 3 trillion of randomly finding it in one guess. In order to find the gold ingot, you have to be at the specific 1 cc box at the specific second it arrives. Not one second before or after, and not in the next box over. And if you were to keep on guessing, probability dictates that the gold ingot in the tiny one liter box that you can hold in the palm of your hand, will never be found in your lifetime because the dimension of time has increased the problem to an incredible level. If you spent one second on each of the cc-second boxes looking for the gold ingot, it would take you 100,000 years to examine each and every box - probably not worth it for $40, or whatever the gold may be worth if you should find it.
This is why you would have enormous difficulty finding your car in the 4D parking garage. If you stay in the same time as the car, you’ll find it eventually. But if you leave your car and go to the mall in some type of space-time tram, you have to be back between the time that you parked the car and the time that the car got towed.
Now let’s move on to a larger box. We’ll call it the universe. But the universe is not like a box with a fixed volume, it is like a balloon with an expanding volume. In the beginning, the four dimensions of space-time intersect at almost zero and expand from there. Currently, the radius of the observable universe is estimated at 46.5 billion light years. The age is 13.835 billion years. Using simple arithmetic, we could calculate that the universe has been expanding at an average increase of one light year of radius every 109 days (Yes, space moves faster than light). Unfortunately, you can’t use simple arithmetic to calculate the rate of change of the volume of the universe, because it is expanding at an accelerated rate. Or at least, that’s the current understanding. You may debate the shape, size, age, and rate of change of the universe. Extremely intelligent, highly observant people have come to different conclusions on the subject. But for the purpose of this thought experiment only, the universe is a perfect sphere with a fixed radius of 46.5 billion light years and is 13.835 billion years old. And while it’s usually not done, we will convert these very large convenient units of space and time into very small inconvenient units of space and time.
Quantum physics states that the smallest unit of length in nature is called a Planck Length. It is 1.616199 × 10e-35 meters*. There is nothing smaller. The smallest unit of time is Planck Time. It is 5.39106 x 10e-44 seconds. There is no smaller unit of time. How Max Planck calculated these units is beyond the scope of this written discourse. But Planck units are important in the study of the universe, because the other units of measure are arbitrarily selected. An extraterrestrial super genius might not be able to relate to inches, meters, hours, etc.,but he’ll be able to comprehend Planck units. Planck units of space and time are universal. The universe started at one Planck length in diameter and one Plank time. Prior to that, space-time was zero. In other words, space-time did not exist. So, in reality, there is no prior to the Big Bang.
There are no partial Planck units. Planck units are as small as they are going to get. To give you an idea of how small, a Planck length is about 20 orders of magnitude smaller than a proton’s radius. Or to put it another way, if a marble’s 1 cm radius were a Planck length, then a proton would have a diameter of over 114 light years. This is worth repeating. It’s very significant.
If a marble’s 1 cm radius were a Planck length, then a proton would have a diameter of over 114 light years. Which would mean its radius would be over 57 light years.
There are approximately 6.19 x 10e34 Planck lengths per meter, 5.85 x 10e50 Planck lengths per light year, and the radius of the universe is 2.72 x 10e61 Planck lengths. Based on the radius, we then conclude that the volume of the entire universe is 8.45 x 10e184 cubic Planck lengths.
Like Planck length, Planck time is extremely small. It is the time it takes for a photon to travel one Planck length in a vacuum. In units of time, there are 1.855 x 10e43 Planck time units in one second. At a scale that is more easily understood, a Planck time compared to one second is like one second compared to 588 billion trillion trillion years. This is also worth repeating.
A Planck time compared to one second is like one second compared to 588 billion trillion trillion years. That big number is over 42 trillion trillion times older than the universe.
There are 8.10 x 10e60 Planck time units in 13.835 billion years.
So now we’ve established that space is big, time is really big, space-time is really really big, and the Planck units used to measure space-time are really really really really small.
At this point, we multiply our 3 dimensions of space by our 1 dimension of time and find that our entire universe is 6.84 x 10e245 Planck Space-Time Units, which I like to call Planck Timed.
Then, accounting for the constant expansion of space-time, possible human error in calculating the radius and/or age of the universe, and to make the number easier to manage by the average person, we can safely estimate the measurement of the universe is 7.0 x 10e245 Planck space-time units.
That’s all of space and all of time.
Some people will focus on the 245 and think, “Meh”, and not see the incredible magnitude that it represents. Remember that a one liter box in the palm of your hand became immense when the 4th dimension was added. And it was measured in centimeters and seconds. This is the entire universe. It’s all of space and all of time divided into the smallest units possible. Each, as The Doctor would say, "a slice of real time, frozen." It’s a 7 followed by 245 zeros. Or, if you feel like spelling it out, 700,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000. You’ll never reach that number by counting things. There are not that many things to count. Space-time is big.
*The fonts on this site don't allow the proper display of exponents. Understand that these numbers are positive and negative exponents of 10.
** see The Day of the Doctor
Copyright 2014 Richard Eldridge