In the previous post we have seen the relation between light and gravity and the endeavours taken by Einstein to prove how gravity affects light. We continue ahead to really see how time runs faster in space.
The word “frequency” means number of cycles per second; if the frequency of light goes down as a result of a gravitational red shift, the number of cycles of the wave that pass each point in space per second is reduced. But to measure frequency we need to use a clock to count the seconds. So, if light from the bottom of the conveyor arrives at the top with a lower frequency, we could say either that the light frequency had been reduced, or, equally well, that time at the bottom of the conveyor runs a bit slower than
So, if light from the bottom of the conveyor arrives at the top with a lower frequency, we could say either that the light frequency had been reduced, or, equally well, that time at the bottom of the conveyor runs a bit slower than time at the top. After all, since we can only measure frequency using clocks, a change in frequency is equivalent to a change in clock rates. Isn’t it?
That seems a bit of a cheat, complains our ever-vigilant skeptic. Why can’t we simply say the frequency of light changes with height, and maintain that time is the same at all heights?
Well, suppose we used the cycles of the light wave as the beats of a clock? It would make a perfectly good clock. In that case, the gravitational red shift would amount, directly, to a change in clock rate.
Okay. But what if we use another sort of clock? We don’t have to use a light-wave clock. You can’t claim that time itself changes with height unless all clocks are affected in the same way.
Indeed so. And they are! Here is the reason why. The tick-tocking activity of a clock has some associated energy, and this possesses weight, like all forms of energy (E = me2 again). If you lift a clock to a greater height, you have to do work on it—against its weight, so to speak. The work done appears as gravitational energy stored in the clock; you could get it back by allowing the clock to fall back down. Now, a very small part of the total weight of the clock comes from its internal energy—the tick-tock energy. Therefore, a portion of the extra energy gained by the clock when it is raised up comes as a result of our lifting the tick-tock weight. This portion (tiny though it is) shows up in the guise of extra tick-tock energy, as a result of which the clock ticks a bit faster. So raising a clock makes it run faster!
A careful study reveals that the clock’s rate changes with height in exactly the same way as a light wave or a photon loses frequency as it climbs. Moreover, the effect is independent of the design of the clock. Whatever clock you are interested in (including the human brain), it will run faster up there than down here. And the change in rate is identical for every sort of clock. So, rather than saying, “All clocks run faster up there,” it is better to say, “Time runs faster up there.”
Let’s take stock of the reasoning so far. We have been led to conclude that, because perpetual-motion machines are impossible, time “speeds up” with height. Einstein arrived at the same conclusion from a consideration of accelerating elevators and the Doppler Effect. Both arguments suggest that, the higher up you go, the faster time runs. Apart from mentioning that the effect is tiny, I haven’t given any figures, but, to take one example, a clock on the ground will, after an hour, lose a nanosecond (one-billionth of a second) relative to a clock in space. The effect also implies that time runs slightly faster at the top of a building than at the bottom. Over a lifetime, you could gain a microsecond or so over your high-rise neighbors simply by living on the ground floor.
You might be inclined to think that such tiny temporal distortions are both undetectable and utterly insignificant. In fact, they are neither. Not only can they be measured, but under some circumstances gravitational timewarps can grow enormous and lead to dramatic effects.
You would be right to be skeptical of the foregoing theoretical arguments taken alone. If time really does change with height, it is important to demonstrate this experimentally. Ironically, this third argument was used against Einstein—who had overlooked it himself—in a famous debate with the Danish physicist Niels Bohr. Their encounter took place much later—in 1930—by which time Einstein was an international superstar professor with a Nobel Prize. But Bohr’s intellect was every bit a match for him.
Only time will tell if time travel will be for real or not. Until then much more discoveries related to time travel will continue to be made. If really time runs faster in space this can be used to further explore the limitless boundaries of space and know more about the universe.