In principle, yes, time does go faster at the top of a building compared to the bottom.
This is because time will go faster the further you are from Earth’s surface when you compare it to someone who is on the surface of Earth still. This is something that Albert Einstein predicted when he developed his theory of General Relativity. It is an effect called ‘gravitational time dilation’.
A brief explanation of Einstein’s 1915 theory of General Relativity is that what we perceive to be the force of gravity comes from the curvature of space and time. This can be hard to wrap your head around, but in simpler terms, Einstein suggests that space and time are two parts of spacetime, which is curved when gravity comes into play.
Einstein’s theory of General Relatively has been verified by many experiments throughout the years since he developed it. That is why we can comfortably use it to answer the question of whether or not time goes faster at the top of a building compared to the bottom.
If we take the idea of curved spacetime into account and think about how objects with a great mass can create a strong gravitational field, then the answer becomes clearer.
This strong gravitational field around the object curves spacetime, causing time itself to change depending on where you are in the spacetime surrounding the object.
The key word here is ‘relativity’. If a person were to stand on top of the Empire State Building, and one other person to stand on the bottom, both people would experience time going by in the same way, but it is still different.
This is because the person on top of the Empire State does not necessarily know the exact passage of time occurring below them; they are oblivious to the change in spacetime causing the time around them to move slower than that of the person on the ground. If they had a way of seeing each other’s wrist watches, the person on top of the building would see the person on the ground’s watch moving more slowly.
But the person on the ground would see their watch as moving the same ‘normal’ speed of time. Both people would feel like they are experiencing time in the same way but would be experiencing slightly different passages of time.
What Einstein called gravitational time dilation occurs when there is a difference between strengths in gravity of two places. This can be a large or small difference. Even if you do a high jump, you are getting further from the Earth’s surface and therefore occupying a different area with a different level of gravity for a moment.
The gravitational force on you would be weaker. This is not something you would notice significantly, since we are accustomed to walking up flights of stairs and flying in planes etc. But this difference has been detected by machines specifically made to do so, meaning that we know about fluctuations in gravitational force the further from Earth’s surface you are.
If you have ever wanted to know what it is like to time travel (who hasn’t?) then all you need to do is get in the elevator at the bottom of a skyscraper and take it all the way to the top.
Let’s take the Empire State Building as an example again. If the person that was at the top of the building is now in the middle, and the person that was on the ground decides to take the elevator up to the top, something pretty cool happens. The person in the elevator will literally time travel. Yes, it is miniscule.
And yes, it is time travel relative to the person on the middle floor. The way this works is that the person in the lift is getting further and further away from the surface of the Earth, when the person on the middle floor is staying at the same point. Time is gradually getting faster and faster for the person in the elevator, and therefore when they pass the person on the middle floor, they will have travelled through time compared to them.
But, to answer the original question without getting too far ahead of ourselves. Time does go faster for someone stood at the top of a building compared to a person stood on the ground or at the bottom of it. This can be explained by Einstein’s theory of General Relativity and gravitational time dilation.
Where spacetime bends depending on the amount of gravity that is exerted on it by an object of heavy mass, i.e. Earth in this case. Although minute, we can still measure that time does in fact go faster at the top of a building compared to at the bottom, since it is further away from the Earth’s surface.