Flow of Time
Do you know that the flow of time is different for each of us?
It all starts with a simple observation: light can only travel at one speed. You might say: so what? Well, it changes everything and, foremost, our understanding of time. Since the dawn of modern humankind, we have been led to believe that the rate with which time passes is universal: two hours in New York are the same as two hours on a transatlantic flight. Not quite! Our work life is based upon the universal flow of time: I have a meeting at 3 pm in the city centre, and I need 30 minutes to go there by cab. Because time seemingly flows at the same rate for all of us, my colleagues and I make it all in time to the meeting. But what if the flow of time is personal? Let’s say that the time flows slower for me in the cab. During my 30 minutes in the taxi, 45 minutes pass in the outside world. Not only would I be late by 15 minutes, but scheduling with a calendar would be utterly useless if time flows differently for each of us. And yet, this is the case!
I will blog about the evidence and roots of the constancy of the speed of light in a forthcoming blog and now focus on the breathtaking consequences.
Something moving with just one speed is in stark contrast to our experience. Let’s consider a train ride: the train moves 30 m/s past bystanders on a platform. A traveller throws a tennis ball inside the train: the ball flies with 5 m/s over the train’s floor. How far does the ball get on the platform in one second? The carriage makes 30 m, and the tennis ball inside makes another 5 m. Hence, the ball gets 35 m far or, in other words, the ball travels 35 m/s.
Let’s now remove the tennis ball of the traveller by a torch. The traveller is sending out a light pulse. It moves with the speed of light inside the carriage. The carriage moves with 30 m/s. Thus, the bystanders would see the pulse move with the speed of light plus 30 m/s. This, however, cannot be since light can only move at one speed! Something is not adding up here.
The solution to this problem is if the carriage is moving with some speed relative to the platform, the flow of time in either environment is different. Let’s understand how we can draw this conclusion simply because light moves with one velocity only.
A rather strange clock consists of two parallel mirrors with some distance d, say 1 metre, apart. We emit a light pulse from the top mirror. It gets reflected by the bottom mirror, and when it is back at the mirror on the top, we say 1 time unit has passed. It would be a rather precise clock since 1 time unit is about 7 nanoseconds.
We have now such a clock on the platform measuring the bystanders’ time. Another clock is inside the railway carriage, moving with 30 m/s to the right. What does a bystander see? First, they notice that the light ray must have a bit of bearing toward the forward direction. Otherwise, the beam would miss the mirror on the floor since the train has moved since the light pulse was emitted. The light pulses for the platform clock and the carriage clock move at the same speed. Remember: there is only one speed for light! The bystander notices that the light pulse inside the carriage must bridge a larger distance to get back to the upper mirror. Since the speed of light has not changed, it will take longer inside the carriage than on the platform. The bystander concludes: a time unit inside the carriage takes longer! The flow of time has slowed down inside the carriage!
Why do we still have clocks, calendars and work schedules in our everyday life?
The first thing to notice is, the vacuum speed of light is enormous for everyday living standards. A cyclist can cycle about 8 metres in a second, and we write for their speed 8 m/s. The figure above shows that light is about 300,000 times faster than we can possibly move on Earth. If we send light around the equator, it will travel 7.5 times around the Earth in one second.
The answer is that the clocks are indeed out of sync, but how much depends on the train's speed in relation to the speed of light. Since we are moving so slowly on Earth compared to light, all our clocks are only out of sync by a tiny amount. Indeed, the clock of a fighter pilot flying for one hour with 933 m/s is just 0.000 000 000 009 seconds behind a clock on the ground. This is good news if we want to stay organised on Earth.
The situation drastically changes should we move with speeds comparable to the speed of light, perhaps on an interstellar space mission. For example, an astronaut travels with 80% of the speed of light and returns to Earth after 30 years on Earth have passed. He left at the age of 20. His twin stays on Earth. When the astronaut returns, his twin has just celebrated their 50th birthday. The astronaut, however, is just 38 years old!
It all hinges on one observation: there is only one speed for light. In a forthcoming blog, I will explain why we think that this is the case. The evidence points to the most famous failed experiment in the history of physics.