Einstein’s equations collapse at the speed of light

Einstein’s special theory of relativity predicts some crazy phenomena, none of which is less intuitive than the idea that moving clocks tick slower than stationary ones. As clocks approach the speed of light, they tick more and more slowly and come closer and closer to standstill.

So this raises an interesting question: since fast-moving objects experience time more slowly, and the speed of light is the ultimate speed limit, does light “experience” time? There are many answers given in online physics chat forums. But what is the truth?

At first glance, the idea that light doesn’t experience time seems kind of silly. Finally, we see light coming from the sun to the earth. We can even estimate how long it will take. (About eight minutes.) So it seems pretty obvious that light experiences time. But this is the time We Experience. What does light experience?

Answering this question is a bit tricky. Physics is an experimental science, and the definitive way to answer questions is to conduct experiments. We could design an experiment where a clock is attached to a photon. The only problem with this idea is that it’s completely impossible. After all, only objects without mass (like photons of light) can travel at the speed of light, and objects with mass must travel more slowly. Clocks certainly have mass, so no clock can run along the light to allow us to conduct the experiment.

The Power of Limits

Since we are forbidden from the ultimate experiment, we must turn to theoretical considerations. What do Einstein’s equations tell us?

This is where the story gets a little more complicated. Einstein’s time-related equations apply to objects traveling at zero velocity up to (but not including) the speed of light. They decay at the exact speed of light. Therefore, these equations don’t apply to light itself—only to objects traveling slower than light.

If we can’t run an experiment and our equations don’t apply to the speed of light, are we stuck? Well, to a certain extent, yes. On the other hand, while Einstein’s equations don’t hold for 100% the speed of light, there’s nothing stopping us from asking the same question for objects moving at 99.999999% the speed of light. And if you want to throw in some more nines, go ahead; the equations work fine.

So let’s use the bounds approach, which is often used in mathematics classes. If you can’t solve a problem exactly for a certain value of a parameter, you can use other values ​​of that parameter and ask what happens when you get close to the desired value. Very often the trend you see tells you what will happen when you hit the forbidden level.

We can use this approach here. What happens if you take an object with mass and move it faster and faster? How does this object experience time?

Approaching the speed of light

We’re on a much firmer footing here. Scientists have been conducting this experiment for decades. We can take subatomic particles and accelerate them to very high speeds – speeds very close to the speed of light. In addition, these particles have their own clock. We can use these tiny clocks to study what happens when we make them go faster and faster.

How does this work? As an example, consider a subatomic particle called a pion. Pions are something like low-mass protons. They are also unstable, decaying into 28×10-9 seconds. This life was measured with incredible precision. If you had a pion and hypothetically accelerated it to the speed of light, which is about 300,000 km/s (186,000 mi/s), it should travel a little over 8 meters (27 feet) before decaying. But that’s in a universe where all clocks tick the same way – that is, a stationary human clock and a moving “pion clock” tick at the same rate. But they don’t.

When scientists create pions that travel at 99.99% the speed of light, they find that they travel about 600 meters (1920 feet) before decaying. This can only happen when fast-moving pions experience time more slowly than stationary ones.

Incidentally, 99.99% of the speed of light is not the record for particle accelerators. Scientists can accelerate subatomic particles to much faster speeds. The record was achieved at a particle accelerator in Europe, where electrons were accelerated to a staggering 99.9999999987% of the speed of light. In this incredible environment, Einstein’s equations still worked perfectly. At these speeds, a hypothetical clock accompanying the electrons would tick just over 200,000 times slower than a clock near a stationary electron.

Given the effectiveness of Einstein’s equations and the fact that the only limit to the speed of an electron is the speed of light, we can see that the closer we accelerate a clock to the speed of light, the slower it ticks. If it could reach the speed of light, the clock would stop.

No time or space

What does that mean? From the perspective of a photon, it can traverse the entire universe without ever experiencing time. Billions and billions of light-years can pass in far less than the blink of an eye.

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there is more While the subject of this article is the passage of time experienced by a photon of light, relativity also tells us how space is experienced. As objects move faster, the universe shrinks in the direction they are moving. Using the techniques described here, we can also see that the universe has shrunk to zero size for one photon. Billions of light-years are disappearing, meaning that from the photon’s point of view, it coexists everywhere in its path.

The theory of relativity is certainly a non-intuitive theory and makes some very bizarre predictions. Perhaps most bizarre of all, however, light experiences neither time nor space, since it exists in all places and at all times simultaneously. This crazy-sounding result reminds us that the laws that govern the universe are weird and wonderful – and it gives us a lot to think about.

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