Minime Physics
Special and General Relativity
Introduction
This section explores Albert Einstein’s theories of special relativity and general relativity and is meant to be a respectful but skeptical analysis of the consequences of the theories.
Both versions of relativity predict time will slow in certain circumstances involving motion or gravity. The concept of time dilation has a strong theoretical underpinning and is useful for mathematical calculations; however, the real-world mechanism remains an enigma and there are many critics who are skeptical of the theories or who offer alternative views on the matter. Time dilation can become lost in the day-to-day world of equations, calculations, and focused investigations, but one should not lose sight of the astounding implications for the functioning of the universe, namely that time itself is purported to actually slow down.
Einstein is often thought of as a lone, absent-minded professor who derived these theories out of thin air, out of whole cloth. That notion turns out to be both true and untrue. Yes, he had a wonderful imagination, his creativity was unbound, and he was willing to take risks and pursue unconventional pathways. And yes, his simple thought experiments that provided the basis for special and general relativity were unique and creative.
However, Einstein’s theories were not untethered from data and real-world observations. For example, he acknowledged that special relativity represented a continuation of several centuries of scientific experimentation, observations of nature, and an evolving understanding of how the world worked, including telecommunications, time, and the invariant speed of light. Although special relativity has unusual features, one can track its invention through a line of reasoning and scientific thought that goes back through a few hundred years of progress.
Conversely, this is diametrically opposed to the development of quantum mechanics that was discussed in the previous section, which essentially had no antecedent history, and really did come out of nowhere.
Special Relativity
So, what is special relativity and why is it a big deal?
The slowing of time as predicted by special relativity is one of the most intriguing phenomenon ever produced by science. The theories radically alter our understanding of the universe as well as the perceived capacity of humans to intuitively understand how nature functions at a fundamental level. Depending on one’s perspective, time dilation is either a fascinating and awe-inspiring element of nature, or is a troubling and problematic concept that must be accepted with little or no mechanistic explanation, as shown in the Figure below, a tongue-in-cheek cartoon that emphasizes the universe-altering implications of the phenomenon.
For the purposes of this section, let’s ponder the overall theory, but then focus on just one issue, the slowing of time with movement. There is more to special relativity than we will discuss here, but let’s keep a laser focus on this single issue. Also, we will simplify things a bit so we don’t need to spend an inordinate time on terminology, definitions, and different interpretations of the theory. However, I urge the interested reader to explore the relevant literature available on the website if they wish to obtain the full story.
Let’s jump right to Einstein’s take-home point.
Special relativity proposes that fundamental features of the universe, such as mass and the length of objects are relative depending on your position and movement. If that sounds radical, like we are all living in different universes, that’s because it is radical – in one sense special relativity says that we are all living in different universes.
Moreover, Einstein integrated time into special relativity – which produced one of the most incredible scientific advances in the history of humans. His thought experiments and mathematics showed that time appears to slow down with movement.
Let me say that again – time seems to slow down when we move.
While you are still trying to wrap your head around that one, know that Einstein did not stop there. He also used thought experiments, theory, and mathematics to create a phenomenally interesting but head scratching new concept in nature – space-time. He created a four-dimensional world. Up, down, left, right, front, back, and now time.
x, y, z, and t
Space-time
Like with many uses of mathematics in science, Einstein’s handling of the numbers was tremendously valuable. Four-dimensional equations turn out to be computationally useful for both explaining and predicting natural events. This is a good use of the numbers. Excellent.
Except, what does space-time mean in the real world?
To address the issue, many physicists simply state that we cannot mentally understand the concept of time slowing with movement because it is beyond our human senses. They say we did not evolve as a species at high velocity, instead we are accustomed to a world that travels much slower than the speed of light c, so we never directly observe, interact with, or feel the effects of an elastic, changeable rate of time. Done.
Many will then say the additional new concept of space-time takes this non-intuitive, non-understandability of nature and time to a whole new level, by combining space and time into a four-dimensional world that we can never intuitively understand.
Don’t even try. Full stop.
Special Relativity - Thought Experiment
Let’s examine the issue of time slowing down a little more deeply, to learn how we got here. If you do not already know about special relativity you are going to learn an apparently incredible feature of the universe. The implications of the thought experiment are going to blow your mind. You will know for yourself why it is claimed that time slows down.
Einstein postulated that light traveled at the same speed in all directions whether a light source is moving or not. Even if you are in a fast rocket ship and send away a beam of light it will always move at the speed of light, c.
Ok, fine, light has unique properties. So, what’s the big deal?
Think about looking at a rocket ship that is on a launch pad as shown in the Figure below. Then, the astronaut inside shines a flashlight at a mirror on the ceiling. As shown in the left Panel, the light beam will go from the flashlight up to the mirror, bounce off, and then go down to a detector that will indicate when the light beam arrives.
Using the equation Velocity = Distance/Time (v = d/t), let’s assume the mirror is ten meters above the floor of the rocket ship, thus d = 20 meters. And let’s further say, just for simplicity, that the light beam takes one half second to travel from the flashlight to the detector so t = 0.5 seconds (although we know it would be much less time since light travels so fast).
So, our equation v = d/t becomes c = 20 meters/0.5 seconds; or c = 40 meters/sec.
And we know that c, the speed of light, is always 40 meters/sec since it is invariant and does not change when one is moving. In the Panel on the right of the Figure, let’s consider the same scenario except the rocket ship has taken off and is traveling when the astronaut flashes the light. Now, our equation has changed. The distance the light beam travels is larger since it includes going up and back to the mirror, but also includes the distance added by the rocket ship moving horizontally. So, d is not 20 meters, but is 2000 meters instead. Thus, our equation v = d/t becomes c = 2000 meters/0.5 second. If we solve the equation for c, then the speed of light now equals 4000 meters/sec.
But wait.
That can’t be correct since we know that c must be 40 meters/sec. The speed of light is invariant. It is always the same. Let’s look at our equation again when the ship is moving versus when it is not moving.
Not moving - V = d/t. c = d/t. c = 20 meters/0.5 sec. Thus, light travels at 40 meters per second.
Moving - V = d/t. c = d/t. c = 2000 meters/0.5 sec. Thus, light travels at 4000 meters per second.
We know that c must be identical for both situations. We must make c the same when the rocket ship is moving versus when the ship is not moving. And we know d is 20 meters when not moving and 2000 meters when moving. This leaves us with only one option to keep c identical. We must change t. We must change time. We must make it larger when moving. In other words, we must make time slow down. When moving, t must now be 50 seconds for c to be 40 meters/sec.
V = d/t. c = d/t. c = 2000 meters/50 sec = 40 meters/sec.
Thus, light now travels again at 40 meters/second. But when moving, the time it took for the light beam to travel from the flashlight to the mirror and then to the detector went from half a second to 50 seconds.
In other words, when moving the astronaut in the rocket ship is in slow motion.
Time appears to slow down.
A.k.a. time dilation
Wait a Minute (Or Longer)
Let’s go back to the questions we asked at the beginning of this subsection. What exactly is relativity and why is it important? What’s the significance of invariant c? Specifically, what’s the big deal about special relativity?
Time slows down when you are moving, that’s the big deal.
Ok, time slows down. Wow. That’s a lot to take in. Let’s think about this. Let’s ponder the idea for a while.
This must be a trick, right? It must be an optical illusion or mathematical chicanery. Time cannot slow down, can it? What does that even mean? Do you know? Can you picture it? Can you understand it? Does time really slow down? Do people move in slow motion when they are traveling in a rocket ship?
Hmmm
If so, if this is true, if the mathematics is correct, if the equations are valid, then if you are stopped for speeding just tell the Officer you were going so fast your speedometer slowed down.
Actually, don’t say that
Seriously, don’t
Here’s a cool thing about science. Data rules. And the data are very clear here. Confirmed repeatedly. Confirmed by many different people in many different places.
Clocks slow down when they move fast.
Scientists put very precise atomic clocks on airplanes traveling at a high rate of speed and compared it with clocks here on earth. And the clocks traveling on the planes ran slower than the ones on earth. This is not mathematical chicanery nor an optical illusion. Clocks slow down when they move fast. Even radioactive atoms decay more slowly at high speed. Time really does seem to slow down.
How could that possibly be?
To ease our angst a bit, there is a way we can begin to reach at least a little peace with this notion. As bizarre as the thought of time slowing down is, as difficult as it is to grasp intuitively, we can become more comfortable if we focus on the mathematics. Once we are immersed in the numbers, we can distance ourselves from the real-world implication of the phenomenon.
Don’t need a mechanism
Just need to stay in the mathematics silo
However, there is a cost for escaping exclusively into the numbers. Lost in the equations are the physical implications of the theory. What is happening when we say time slows? What does this mean? How do we intuitively understand this? And, what in the (real) world is space-time? What does that even mean? What is the mechanism behind space and time being woven together?
The numbers alone do not give us answers to these sorts of questions.
But there is an easy way out of this conundrum, one that is even more effective than just slipping into the numbers-only silo, and is more definitive:
“The world is a strange and non-intuitive place, it just is. You will never be able to understand time slowing down. Stop trying. Use the equations to get the answers you need and forget the weirdness of time slowing when you are moving, it’s in the equations and validated by the clocks, so just calculate and move on.”
No explanation needed
Ultimately, nature may indeed turn out to be weird beyond belief – it will be what it will be. But these attitudes do raise a white flag. Why are we so quick to surrender and move on? These are incredible features of the universe. Time slows down when we move – with no known mechanism. And space and time are space-time, woven together, whatever that means.
Why not ponder and discuss these foundational ideas constantly?
For one example see the
Pilot/Shadow wave subsection
General Relativity
Next, Einstein invented his second version of relativity, called general relativity, which is the most widely accepted explanation of gravity today. As with special relativity, there is an extensive body of excellent information that exists on the topic, including books, websites, academic literature, and televisions shows, highlighted in the reference materials for the interested reader.
Einstein invented general relativity in part because special relativity was inadequate and incomplete. The theory only applies to limited conditions of movement and natural phenomena.
And just so you know, special relativity clamps down hard on development of alternative theories. It’s intriguing, but highly limiting, too. Moreover, there are additional interesting but very troubling aspects of special relativity around the optics of simultaneity of events, absolute reference frames, and determining who is in motion relative to who.
But for this section we need to keep things simple and focused so we will consider only the following two concepts of general relativity, curved space, and gravity causing time to slow down.
Einstein was fascinated by the concept of a large mass, a planet or star for example, mysteriously reaching through space and attracting other objects. He wondered, how did this work? What was the mechanism? The explanation Einstein came up with, using thought experiments on acceleration, is that space is curved. It was Einstein’s eureka moment, his happiest thought. Space is warped. The earth and moon are attracted to each other because the mass of each object distorts nearby space, causing objects to follow a curved trajectory.
Think of a bowling ball sitting on a trampoline and creating a depression in the middle of the mat. When you place a marble (the earth) near the bowling ball (the sun) the marble rolls down the depression created by the ball and moves toward it, mimicking the earth moving toward the sun under the influence of gravity, due to warped space. This example helps us understand the concept of warped space a little bit, but the analogy of the trampoline is primarily in two dimensions, not three, and thus still leaves one uneasy as to how this translates into a three-dimensional world. Perhaps one can think of space being stretched by the sun and having less density nearby than unaffected space, thus for example the earth moves from an area of high ‘space density’ to low, but this is theoretical and still difficult to understand in the real world.
Note that Einstein could not initially make the mathematics work for general relativity and gravity. He could not fit his equations on curved space to the real-world data that existed on celestial movement. It was only when he found a somewhat obscure strand of mathematics on curved spaces and geometrical figures that had been published decades earlier that the pieces fit together, the equations matched the data, and general relativity became a viable theory. Today there are wonderful mathematical constructs to describe warped space, from Einstein’s original equations to more recent theorems.
A lesson here is that one needs to be cautious and careful about eliminating new physical theories of the real world because the equations do not initially work. There are many different flavors of mathematics and sometimes it is not immediately apparent how the equations and real world fit together. It may take a while for equations to mature enough to explain experimental data that conflict with a new theory. Or sometimes new mathematics needs to be invented or re-purposed, as with Einstein and general relativity.
The equations Einstein adapted to general relativity are useful and fit experimental data on gravity better than the original mathematics of Newton. Still, though, understanding exactly what stretched space means in the real world, outside the equations, is tremendously difficult for everyone, even today. Of course, one can indeed simply accept warped space as a fundamental feature of the universe, with no further intuitive understanding of what this really means.
However, there is a price to be paid for doing so. The concept of warped space becomes an odd and disconnected aspect of the universe. It just is. Full stop. It’s the end of the story as far as gravity is concerned. There is no unified whole and it does not fit with other aspects of nature, it remains perplexing and unsatisfying, ugly even to some.
But wait, there is more.
We are not done with general relativity. Not quite yet. General relativity also postulates that time slows down, not with movement as in special relativity, but under the influence of a gravitational field.
Gravity causes times to slow down, with no well-defined mechanism, a mystery. The phenomenon comes from the equations and the effect is real and measurable.
Just like with special relativity and time slowing with movement, the phenomenon of gravity causing time to slow was validated using atomic clocks. If I am at the top of a skyscraper and you are on the first floor your watch will run slower than mine.
Why?
For general relativity there really isn’t a good mechanism that explains the phenomenon other than using terms like warped space and space-time, and of course it’s seen in the equations. But the real-world explanation remains mysterious and unsatisfying.
Are there alternative ways to look at gravity and time dilation, to ponder the phenomenon?
For a provocative alternative on time dilation, see the subsection on
Shadow/Pilot Wave Theory