# If a child runs on a train at the speed of light, is it too fast?

2020-01-11 | Science Dock original |

Maxwell ’s electromagnetic theory predicts that the speed of light is a fixed value. The Michelson Morey experiment verified that the speed of light is constant from another angle. In 1905, Einstein published the article "On the Electrodynamics of Moving Objects."This is what we call the special theory of relativity later. In this paper, the speed of light is constant, and the speed of light cannot be exceeded.

What is the speed of light that cannot be surpassed?

Simply put, if you want to make an object with a static mass reach the speed of light by accelerating, this is impossible. Even if you consume the energy of the entire universe, you cannot complete the acceleration task. Not only that, all matter, information, energyThe speed of light cannot exceed the speed of light. The speed of light is a limit value. Currently known ones can reach the speed of light: the propagation of gravitational waves, the propagation of electromagnetic waves, and gravitational interactions. The only thing that is considered to exceed the speed of light is the speed of expansion of the universe, But the expansion of the universe is the expansion of space as a whole, and does not conflict with relativity.

So is there a train that reaches the speed of light? Obviously it does not exist, but this does not prevent the answer to this question. We can do a thought experiment, assuming the speed of a train is the speed of light Vc, and a child is moving along the trainRunning in the carriage at a speed of w, is this child faster than the speed of light?

According to the classic Newton theory, in the classic low-speed physical frame, the speed can be simply superimposed, that is, the Galileo transformation, so the child's speed is Vc + w, obviously faster than the speed of light.

but this is not the case, because the train of light speed does not meet the classical low-speed physical framework, so the Galileo transformation in the previous Newton theory cannot be used, and the Lorentz transformation is used instead. The speed is calculated as shown below :

In this formula, no matter how fast the child's speed is, even if the child's speed reaches the speed of light, the result will be less than or equal to the speed of light.

A similar question is: when two people are running in opposite directions, and their speed is 90% of the speed of light, is the relative speed of these two people faster than the speed of light?

Interested friends can put the value into the formula and calculate it. The result is 99.44% of the speed of light, and it does not exceed the speed of light. However, if processed according to the classical low-speed physical framework of Newton theory, the result will be 180%.Speed ​​of light. Why are the two data so different? This is the relativistic effect brought by high-speed moving objects. What exactly is low speed and what is high speed? Generally speaking, 10% below the speed of light is low speed and higher than the speed of light10% is high speed, because the relativistic effect has begun to become apparent at this time, and the effect will become more apparent as the speed increases further.

Art / Science Dock

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