Episode Details

Ever since Albert Einstein published his Special Theory of Relativity in 1905, one equation has been the bane of humans hoping to explore the stars: E=mc². In addition to informing our understanding of gravity, space, and time, this formula implies that traveling at or beyond light speed is impossible. And given how expansive the universe is, this speed limit severely restricts our ability to zip around the cosmos. But while most physics textbooks describe this speed limit, their explanations don’t always tell the whole story.自从 1905 年阿尔伯特·爱因斯坦发表狭义相对论以来，一个方程一直是人类探索恒星的祸根：E=mc²。除了加深我们对重力、空间和时间的理解之外，这个公式还意味着以光速或超光速旅行是不可能的。考虑到宇宙有多么广阔，这个速度限制严重限制了我们绕宇宙飞行的能力。但是，虽然大多数物理教科书都描述了这个速度限制，但他们的解释并不总是能说明全部情况。

In Einstein’s equation, E stands for energy, m for mass, and c for a constant— specifically, the speed of light in a vacuum. C squared is a huge number, which means it requires enormous amounts of energy to move even small amounts of mass close to the speed of light. This relationship is why the only particles that can travel at light speed are those with no mass at all, such as photons.在爱因斯坦方程中，E 代表能量，m 代表质量，c 代表常数，特别是真空中的光速。 C平方是一个巨大的数字，这意味着即使是很小的质量也需要大量的能量才能接近光速。这种关系就是为什么唯一能够以光速传播的粒子是那些完全没有质量的粒子，例如光子。

That’s the short answer for why objects with mass can’t reach or exceed light speed. But to make full use of Einstein's equation, physicists often include one more variable. This gamma represents the Lorentz Factor, which models how an object’s velocity changes the way that object experiences time, length, and other physical properties. Now, when an object’s velocity is a very small percentage of the speed of light, this variable resolves to 1, so it doesn’t impact the equation. However, when an object is moving fast enough, this denominator drops to 0. Since dividing by 0 is impossible, this breaks the equation and makes the variables therein mathematically impossible— hence the unbreakable speed limit.这就是为什么有质量的物体无法达到或超过光速的简短答案。但为了充分利用爱因斯坦方程，物理学家通常会多加入一个变量。该伽马代表洛伦兹因子，它模拟物体的速度如何改变物体经历时间、长度和其他物理属性的方式。现在，当物体的速度只占光速的很小一部分时，该变量解析为 1，因此不会影响方程。然而，当物体移动得足够快时，该分母就会降至 0。由于除以 0 是不可能的，这会破坏方程并使得其中的变量在数学上不可能 - 因此是牢不可破的速度限制。

But what does it actually mean for this math to break down? To answer that, we need to understand the physical system its modeling: spacetime. After Einstein published his theory of special relativity, his mentor Hermann Minkowski realized that— if his student was right— it would mean space and time were not two separate entities, but one connected system. And everything in the universe travels through space and time simultaneously. However, traveling through one of these vectors limits the speed at which we can travel through the other. To picture this, imagine moving north at a fixed speed. You could turn to travel east at the same speed, but moving northeast would mean you move in both directions more slowly. The tradeoffs are the same when we move through spacetime. Since our typical movement through space is so much slower than the speed of light, we mostly perceive moving through time at a relatively steady speed. But if an object managed to move through space at the speed of light, it would no longer move through time. T