Transcription
Einstein, often hailed as "the greatest physicist since Newton," is most famously known for his theory of relativity, which has fundamentally reshaped our understanding of time and space. In this video, we will delve deeply into this theory.
When relativity is mentioned, many people's first thoughts often go to black holes, spacetime distortion, and the speed of light limit – fascinating phenomena filled with science fiction allure. These are frequently highlighted in isolation, becoming the focus of popular science articles. However, this can easily lead us to overlook a more crucial fact: relativity is not a theory born out of pure imagination. Its primary purpose was to resolve a real and serious internal contradiction within physics at the time.
Einstein's theory of relativity can broadly be divided into two stages. Its core concepts are surprisingly simple. The first stage deals with the laws of physics in the absence of acceleration, only when objects are at rest or moving at a constant velocity. This is known as special relativity. The second stage further incorporates gravity, leading to the development of general relativity. In this video, we will first explore the core theories of special relativity, tracing back to the origin of the problem and gradually investigating the physical difficulties Einstein discovered.
As mentioned in previous videos, physicists never overturn existing theories simply for the sake of amusement. The birth of new theories often arises because the old ones encounter problems, perhaps failing to explain new experimental results or exhibiting fundamental contradictions between different theories. Relativity is a prime example of such a situation. Therefore, to truly appreciate Einstein's groundbreaking contributions, we cannot directly start with exotic phenomena like black holes or time dilation. Instead, we must first review the established and successful theories in physics at the end of the 19th century, understand what each achieved, and where their potential conflicts lay. Only by clarifying this background can we fully grasp Einstein's breakthroughs.
We will endeavor to retrace Einstein's thought process from that era. As you witness these contradictions gradually emerge, you will be astonished to find that the seemingly bizarre phenomena in relativity are not conjured out of thin air but are the natural consequences logically and inevitably derived from a few simple assumptions.
To understand all of this deeply, we must return to the world of physics before Einstein. In that era, the two most important frameworks were Newtonian mechanics and Maxwell's electromagnetism. The former dominated our understanding of motion, force, time, and space, while the latter redefined the nature of electricity, magnetism, and light. The problem was that while both were highly successful individually, they contained fundamental contradictions when combined.
Next, let's first examine the picture of the universe that Newtonian mechanics painted. Newton's classical mechanics is the cornerstone of introductory physics. Simply put, Newton's laws state that an object's acceleration is determined by the force acting upon it. The greater the force, the greater the acceleration; the greater the mass, the smaller the acceleration. Similarly, it's easier to accelerate an empty shopping cart than a full one. The sensation of kicking a soccer ball is vastly different from kicking a cannonball. This means that by knowing the force acting on an object, one can predict its state of motion. This seemingly simple principle was a major leap in physics. Previously, people understood the world through abstract concepts like the nature of matter. However, Newtonian mechanics unified the explanation for everything from stones thrown on the ground, cannonballs fired from cannons, to the orbits of celestial bodies, encompassing the laws of motion for all objects on Earth and in the heavens. Consequently, Newtonian mechanics long served as the standard framework for understanding the world.
Newtonian mechanics implicitly contained a concept of absolute time and space. Time was like a clock shared by the entire universe, flowing uniformly. Even if two people were far apart, they could theoretically share the same "now." Su Dongpo certainly believed this, thinking that even if he and his family were spatially distant, they were still in the same moment in time, otherwise, how could they "share the moon across a thousand miles"? Space, on the other hand, was viewed as a vast, fixed, and stationary stage upon which all objects moved. In other words, in Newton's world, "when" and "where" seemed to have ultimate, objective, and unified answers.
However, classical mechanics soon recognized the relativity of spacetime. For example, it's difficult to distinguish whether you are in a stationary train and another train beside you is moving in the opposite direction, or if your train is moving forward and the other is stationary. This is not just a feeling; in fact, all physical laws are exactly the same in a stationary space and in a train moving at a constant velocity. Since the laws are identical, how can one determine who the true mover is?
To summarize at this point, Newtonian mechanics, on one hand, tells us that many laws of motion have a common form in different inertial frames. On the other hand, it still presupposes absolute time and absolute space as background. Newton's achievement was the first great unification in the history of physics. Two hundred years later, another physicist, Maxwell, achieved a comparable feat by integrating electromagnetism into a unified theory. Today, we often refer to Newtonian mechanics and Maxwell's electromagnetism collectively as "classical physics."
Since our goal is to explore the contradictions between the two, the next step is naturally to understand Maxwell's electromagnetism. In the 19th century, electromagnetism became a rapidly developing field on par with mechanics. People gradually learned about the attraction or repulsion between charged objects, the relationship between electric currents and magnets. Technologies like the revolutionary telegraph further increased the importance of electromagnetic research. Physicists thus investigated the laws governing the interactions between charges and currents, and how electricity and magnetism are interconnected.
However, it's important to clarify one point here: electromagnetism primarily deals with electromagnetic forces, such as like charges repelling and opposite charges attracting, and their mechanisms of origin and transmission. As for how an object accelerates and changes its motion after being subjected to a force, that part still belongs to Newtonian mechanics. In other words, Maxwell did not create a new mechanics but focused on "how forces are generated." Before Maxwell, the physics community generally accepted the mechanism of "action at a distance" for force transmission, where object A could exert force directly on object B across space. Newton's law of universal gravitation was like this; the sun and the Earth, though millions of miles apart, are still bound by gravity. Early understandings of electric and magnetic forces also often relied on this framework. The video discussing electromagnetic fields also touched upon this issue of "action at a distance."
However, the core difficulty with action at a distance lies in its inability to explain the role of the intervening space. If a charge or current at a certain location suddenly changes, why is a distant location affected? Does this influence happen instantaneously, or does it take time to propagate? If it takes time, what is its transmission mechanism? If you want to learn more, you can watch the previous video on electromagnetic fields. It was precisely these questions that led Faraday and later Maxwell to understand electromagnetic interactions in a fundamentally different way. They no longer viewed it as action at a distance between objects but focused on the state of space itself. This can be analogized to the surface of water. Previously, it was thought that by patting the water surface here, the distant water surface would immediately jump. The new perspective is that a local disturbance first affects the adjacent water, and then propagates outward layer by layer. In other words, the interaction does not instantaneously span space but is gradually transmitted through the continuous change of states at each point in space. This mechanism is called a "wave" in physics.
Maxwell's major breakthrough was to organize this picture into a complete theory. Electric and magnetic fields are real physical structures in space. They change and propagate outward in the form of waves. The speed of propagation of electromagnetic fields, calculated theoretically, is approximately 300,000 kilometers per second. Wait a minute, we have measured the speed of something else before, and it's almost the same number. That is light.
From this, Maxwell proposed a revolutionary hypothesis: light is essentially an electromagnetic wave. Subsequently, Hertz succeeded in generating and detecting electromagnetic waves. Therefore, by the end of the 19th century, the physics community generally accepted that light is an electromagnetic wave, meaning the propagation of electric and magnetic fields in space.
At this point, let's return to today's topic. What is its connection to Newtonian mechanics? On the surface, Maxwell seems to have merely rewritten the mechanism of force transmission from instantaneous action at a distance to propagation in space as waves. Once we know the source of electromagnetic forces, the subsequent motion of objects can still be handled by Newtonian mechanics. Doesn't that sound good? So, where does the problem lie?
The real crux of the issue is that if light is a wave, and its speed is determined by Maxwell's theory, then according to the intuitive Newtonian concept of velocity addition, observers in different states of motion should measure different speeds of light. For example, if you are running on a train, your speed relative to someone on the platform would be the speed of the train plus your running speed. The real problem is that Maxwell's theory gives a fixed speed of light in a vacuum, while Newtonian velocity addition implies that people in different states of motion should measure different speeds of light. This creates a conflict when put together. This seemingly minor crack would lead to a major problem in physics: to whom is the speed of light relative? This question is the core of the next part of our discussion.
If you were a physicist at the end of the 19th century, facing the question just posed, what would you think? Since Newtonian mechanics always presupposed that there exists an absolute background stage in the universe, and all motion is ultimately relative to this stage, the most natural thought would be to find the background stage for light. Sound waves propagate through air, and water waves propagate through water. So, what do light waves propagate through? Therefore, 19th-century physicists conceived that the universe was filled with an invisible, intangible medium through which light waves propagated. This hypothetical medium was called "aether."
So, is there any way to measure the aether? Assuming the aether itself is stationary, and the speed of light in the aether is c, then if you move at a speed v along the aether, the measured speed of light should be c-v. If you move in the opposite direction, you would measure c+v. This is like the difference in wind speed felt when facing into the wind versus with the wind. We know the Earth revolves around the sun, meaning the Earth cannot be stationary relative to the aether. Theoretically, an "aether wind" should be produced.
Physicists at the time searched for direct evidence of the aether in various ways but found no conclusive results. This continued until the Michelson-Morley experiment in 1887. They thought that since it was difficult to directly measure the aether, they might as well check if the speed of light varied in different directions. However, the speed of light is more than ten thousand times faster than the Earth's orbital speed. How could such a tiny change be measured?
They utilized the phenomenon of light interference. Do you remember the double-slit experiment discussed a few weeks ago? Both experiments observe interference phenomena. Since light is a wave, when two waves overlap, whether they reinforce or cancel each other out depends on whether their positions in the wave cycle align. This state of "alignment" is called phase. For example, crests aligning with crests reinforce, while crests aligning with troughs cancel. Therefore, if two beams of light have slightly different path lengths or travel times, their phases will change when they overlap, and the interference fringes will shift.
Michelson and Morley's design precisely utilized this. They first split a beam of light into two, sent them in mutually perpendicular directions, and then reflected them back to recombine. If the Earth were indeed moving through the aether, the time required for the light beam traveling with the "aether wind" to go back and forth should be slightly different from that of the light beam traveling in the perpendicular direction. This extremely small time difference would manifest as a shift in the interference fringes. Furthermore, if the instrument were rotated, the relative direction of the two light beams and the aether wind would change, and the fringes should also shift accordingly. They originally expected that if the Earth were moving through the aether, the rotation of the instrument would allow them to infer the direction and speed of the aether flow from the shift in interference fringes.
However, no matter how the experimental apparatus was rotated, the interference fringes did not change. In other words, the experiment did not measure a difference in the speed of light in different directions due to "the Earth moving through the aether." This made the concept of aether as the background stage for light highly questionable.
At this point, the entire field of physics found itself in an awkward situation. On one hand, Maxwell's electromagnetism was highly successful, and the understanding of light as an electromagnetic wave was increasingly solidified. On the other hand, Newtonian concepts of absolute time and space, and the intuition of velocity addition, seemed equally robust. If both were correct, it was difficult to explain why the background aether could not be found.
After this, although some physicists attempted to mathematically patch up the aether concept, these patches never managed to present a new physical picture. It wasn't until about 20 years later that a 26-year-old young man broke this deadlock. His theory shocked the world. He was Einstein. In 1905, Einstein published the paper that marked the beginning of special relativity. What question do you think he was most eager to answer at the time? Are time and space relative? Is the speed of light the cosmic limit? Or does the aether truly exist? None of these were the questions he first posed.
Einstein posed a seemingly simple but deeply contradictory question: a magnet and a conductor. Imagine a very simple experiment: a magnet and a metal coil. As long as there is relative motion between the two, a current will be generated in the coil. This is the principle behind generators. However, within the theoretical framework of the late 19th century, the explanation for this phenomenon differed depending on the perspective of observation.
Let's look at the first scenario: the magnet moves, the coil is stationary. A moving magnet changes the magnetic field around it. Classical electromagnetism posits that a changing magnetic field induces an electric field, which then pushes the electrons in the conductor to form a current, similar to the principle of an induction cooker.
Now let's look at the second scenario: the coil moves, the magnet is stationary. In this case, the magnet is stationary, and so is the magnetic field. A non-changing magnetic field naturally cannot generate an electric field. However, the conductor itself is moving through the magnetic field, so the electrons within the conductor are directly pushed by the magnetic force, still forming a current.
Despite the same observed phenomenon – a current in the coil – the old theory attributed the first scenario to electric field force and the second to magnetic field force. To Einstein, this was highly suspicious. According to Newtonian mechanics and Galileo's principle of relativity, physical laws should not depend on whether you subjectively define something as stationary or moving. Just like the train example we discussed earlier, if two reference frames are moving at a constant velocity relative to each other, the laws of nature should be consistent. The fact that the mechanism for generating current shifts from electric field force to magnetic field force simply by changing from a moving magnet to a moving conductor is clearly absurd.
Einstein thus realized that the problem might not lie in the electromagnetic formulas themselves but in something deeper. Perhaps we must abandon the concept of "absolute rest." He then proposed two simple yet profoundly influential postulates.
The first is the principle of relativity: physical laws should be the same in all inertial reference frames, meaning all reference frames that are at rest or moving at a constant linear velocity. This was not an original idea of Einstein's; physicists since Galileo had tended to believe this. He merely extended it consistently to all areas of physics, including electromagnetism.
The second is the truly world-altering principle of the constancy of the speed of light: the speed of light in a vacuum is the same for all observers in inertial reference frames, and it is independent of the motion of the light source itself. This principle directly challenges the Newtonian intuition of velocity addition.
Why did Einstein have this idea? On one hand, the problem of the magnet and conductor mentioned earlier made him doubt that "absolute rest" was a necessary assumption in nature. On the other hand, according to his memoirs, at the age of sixteen, he pondered a question: what would he see if he chased a beam of light? According to the most direct interpretation of Newtonian mechanics, if you were moving at the speed of light, light should appear stationary to you, becoming a non-propagating electromagnetic wave. However, to Einstein, this seemed impossible. In Maxwell's theory, electromagnetic waves are essentially a structure of alternating electric and magnetic fields propagating forward. A "completely stationary light wave" is difficult to conceive. This intuition became the starting point for his reconstruction of spacetime.
So, the question arises: what are the consequences of accepting these two principles? The answer is that time itself must be re-understood. Consider our usual understanding of "the passage of time," which is inseparable from the operation of clocks. For example, when we say one second has passed, it simply means a periodic process has completed once.
Therefore, Einstein's crucial shift can be understood through a simple thought experiment: the light clock. Imagine a very simple clock composed of two parallel mirrors with a photon bouncing up and down between them. The light first bounces from the bottom mirror to the top, and then back to the bottom. We consider this one "tick." If this clock is stationary, and the distance between the two mirrors is L, and the speed of light is c, then the distance light travels for one round trip is 2L. Thus, the time for one tick is .
Now, let's place this light clock on a high-speed train. For people on the train, the photon still simply bounces straight up and down; the ticking rhythm of the clock remains unchanged. However, for someone standing on the ground, the situation is different. Since the clock itself is moving forward, the photon must move forward with the train while bouncing back and forth between the two mirrors. Therefore, from the perspective of the observer on the ground, the path of light becomes a series of diagonal lines, like a sawtooth.
Assuming this clock moves forward at a speed v, since the speed of light is constant, according to the Pythagorean theorem, the time for half a tick is . After simplification, we get:
We can see that for a moving clock,
Thus, we can relate the time of a moving clock to the time of a stationary clock. We usually call the former the Lorentz factor, so finally, we have:
From this, we can see that as the speed v approaches the speed of light c, γ becomes larger. This means that each tick of a moving clock takes longer, so it appears to run slower to an outside observer. From this formula, it is evident that this phenomenon only becomes significant when you approach the speed of light, which is why we hardly notice it in everyday life. This is also the most crucial step in relativity. It does not tell you that time is relative; rather, it tells you what "is not relative" – the speed of light.
If the speed of light is consistent for all observers, then people in different states of motion cannot share the same absolute time. This is a natural theoretical consequence. In other words, time is no longer a pre-set background of the universe but is closely related to the observer's state of motion. This is a revolutionary shift. It no longer presupposes what time is but asks: how do we determine "how much time has passed" and "whether two events are simultaneous"? Starting from these basic measurement problems, it re-establishes the entire concept of spacetime.
So, how does this new theory explain the initial problem of the magnet and conductor? In relativity, electric fields and magnetic fields are actually the same physical quantity, presented in different forms. If you see the magnet moving and the coil stationary, you would say that the changing magnetic field induces an electric field that pushes the electrons. If you switch to the reference frame of the magnet (typo, should be conductor), what originally appeared purely as a magnetic field (typo) would partially transform into an electric field. Therefore, in this reference frame, it is still the electric field that truly pushes the electrons. Einstein pointed out that a pure magnetic field or a pure electric field is itself a relative concept. If you change your state of motion, what originally appeared as just a magnetic field might mix with an electric field, and vice versa. Electric and magnetic fields are integrated by relativity into a single entity called the electromagnetic tensor. This part belongs to advanced topics in relativistic electromagnetism and will not be detailed here.
Even without delving into mathematical details, we can still see an important point: Einstein was not pursuing bizarre relativistic effects but rather seized upon the loopholes in the old theories that could not explain themselves, relentlessly pursuing the issue until he rewrote time and space themselves. Once this new understanding of spacetime was established, it would produce many counter-intuitive results. Due to space limitations, we will share them one by one in the future.
Finally, let's answer a question: Einstein merely stated that the speed of light is constant, so how did it become the cosmic speed limit? What Einstein proposed in 1905 was that the speed of light in a vacuum is the same for all inertial reference frames. This premise naturally makes the speed of light a special boundary. The light clock example just illustrated that a moving clock slows down. Besides time, if you think carefully, space also changes. For example, the length of a wooden stick refers to the distance between its ends at the same moment. In Newtonian mechanics, everyone shares the same time, so the concept of "simultaneity" is taken for granted. However, relativity tells us that different observers have different definitions of "simultaneity." Since this is the case, spatial length will naturally also change.
Let's use a thought experiment to understand this. Suppose there is a stationary wooden stick with length L0. A beam of light is emitted from the tail end of the stick towards the front end and then reflected back to the tail end. For the observer stationary with the stick, this round trip covers twice the length of the stick, so the total time taken is . This is the time in the stick's own reference frame. If the stick moves forward at a speed v, for the observer on the ground, the light needs to catch up with the front end of the moving stick, so the time taken is longer. When the light reflects back from the front end to the tail end, the tail end is moving towards the light, so the return trip time will be shorter. The total time required is . After simplification, we get:
Note that this is the time observed by the ground observer. Considering the time dilation effect deduced from the light clock, for the ground observer, the time required for this "light round trip" is longer than the time measured by the stick itself. It satisfies:
Substituting the result from the stick's own reference frame, we get:
If we solve this equation, we get:
This means that for an object moving at high speed relative to you, you will measure its length along the direction of motion to be shorter than its length when it is at rest. This is called length contraction. It's not that the wooden stick is actually squashed; rather, because the speed of light is constant, it cannot maintain Newtonian absoluteness, and space, being intrinsically linked to time and simultaneity, must also change.
So, why do these changes in spacetime lead to the speed of light becoming an upper limit? Considering the changes in time and space mentioned above, the formula for velocity addition will also be rewritten. Suppose an object's velocity in a certain reference frame is u, and this reference frame itself is moving at a velocity v relative to you. Then, the velocity you measure is no longer the Newtonian u+v. For example, suppose you throw a ball forward on a train. The train's speed relative to the ground is 0.8c, and the ball's speed relative to the train is also 0.8c. According to Newton's view, velocities simply add or subtract, so the speed of the ball seen from the ground would be 1.6c. However, in relativity, applying the velocity addition relationship just derived, we get 0.976c, which is still less than the speed of light c.
Setting aside the mathematics, we can also understand this intuitively. Since the train is moving at high speed, its length (space) is "contracted." Therefore, the distance the ball appears to travel is shorter. From the perspective of people on the ground, the superimposed speed naturally becomes smaller. Even more extreme, if you shine a flashlight forward on a train, the speed of this light seen by people on the ground is precisely equal to the speed of light c. This means that even if you shine a flashlight forward on a train moving at near light speed, the speed of light seen from the ground remains unchanged. This indicates that no matter how velocities are added, none can exceed the speed of light. The speed of light is special not because it happens to be very large, but because it is directly written into the rules of spacetime transformation, becoming the common foundation for all inertial reference frames.
We can also understand why the speed of light cannot be surpassed from another perspective. From the Lorentz factor we saw earlier, as v approaches the speed of light c, γ approaches infinity. In relativity, γ is also related to the energy of an object. When at rest, γ equals 1, representing the object's rest energy. From this, it is evident that as the speed increases, γ increases, and the object's energy growth becomes increasingly rapid. As it approaches the speed of light, the energy requirement will increase exponentially. Accelerating a massive object to the speed of light would require infinite energy. This means that massive objects cannot be accelerated to the speed of light with finite energy.
However, astute viewers may have noticed a problem. What we've discussed so far only concerns things originally below the speed of light being unable to exceed it. Is it possible that there exist particles in the universe that are naturally faster than light? Such hypothetical particles are sometimes called "tachyons." If we extend the relativistic energy relationship to the superluminal range, it leads to peculiar mathematical results. "Tachyons" would require a mass satisfying:
This seems to suggest that for a particle to continuously exceed the speed of light, its mass must be imaginary. However, both "imaginary mass" and "mass squared being negative" have unclear physical meanings. A more serious problem is that if information can be transmitted faster than light, causality would become problematic within the framework of relativity. This is the core reason why Einstein questioned superluminal motion.
There is a famous thought experiment, the grandfather paradox, which highlights this contradiction. In simple terms, if you could go back in time and kill your grandfather, you would not exist. And if you did not exist, you naturally could not go back to kill your grandfather. From a physical perspective, if event A is the cause of event B, for example, the decay of a nucleus releasing a photon is A, and a detector receiving the photon is B. Even in relativity, all observers consistently agree that "A occurs before B." This invariance of temporal order is precisely the foundation upon which physical laws can make predictions.
Superluminal motion would destroy this foundation. Imagine two people, Alice and Bob, moving away from each other at high speed. Alice sends a superluminal message to Bob. From Alice's perspective, Bob will naturally receive the message after some time. When the speed of the message exceeds the speed of light, according to relativity, Bob could receive the message in Alice's past (from Bob's own perspective). If this is the case, Bob could immediately send a superluminal reply to her. According to the same theory, Alice could receive Bob's reply before she even sent the first message. Thus, a paradox arises. Suppose Bob's reply is "do not send the first message." If Alice hears this, she will not send the first message. But if she doesn't send the first message, how would Bob receive it and then warn her not to send it? The entire event falls into an unresolvable causal loop. Therefore, if superluminal messages were possible, physical laws would be unable to define what is cause and what is effect.
Returning to the core conclusion, the speed of light in relativity is not simply a very fast speed. It is more importantly the key to defining time and transforming space. In other words, the speed of light itself is an intrinsic component of the spacetime structure. It is precisely because of this that the speed of light is ubiquitous in relativity. It is not an accidental role but the spacetime stage itself. Relativity never changes how fast an object can travel, but rather our overall understanding of time, space, and causality.
Let's look back at the entire story. Einstein's theory of relativity was not created out of thin air. Its success lies in his precise insight into the real conflicts between old theories. The absolute time concept of Newtonian mechanics and Galileo's law of velocity addition could not coexist with the fixed speed of light implied by Maxwell's electromagnetism. He did not cling to the old worldview but ultimately redefined time and space with the constancy of the speed of light.
In this episode, we have only explored special relativity, focusing on the structure of spacetime under constant velocity motion. Einstein's later innovation, general relativity, not only deals with inertial reference frames but also reinterprets gravity as part of spacetime. That will be another grand chapter. From the story of the birth of relativity, we can see that successful theories do not begin with rich imagination but originate from understanding contradictions. If you want to be the next Einstein, the key is not to be whimsical but to be able to clearly understand the difficulties and conflicts in existing theories. If you can persist in exploration after deeply understanding them, congratulations! The joy of this exploration process is the most precious enjoyment in the world. But if you find it too difficult and choose to give up, it's okay. I am the same. But we can still appreciate these top-tier intellectual achievements together. This is also the original intention of this channel.