Time Relativity

The Background
I’ve been watching Stephen Hawking’s Into the Universe lately. I highly recommend it, but I also have to give due credit to my friend Jeremy, who spent an hour patiently answering my resulting, increasingly intricate questions about black holes.

Disclaimer #1: Having said that, any misinformation below is entirely my own fault! I purposely insisted on researching this within my limited layperson ability and refused to ask or receive help from several STEM (Science/Tech/Engineering/Math) friends – I wanted to see what I could uncover on my own and just how much the Internet can empower people to learn (though granted part of its power is in enabling people to crowdsource questions). Having said that, Awesome Science People are more than welcome to leave information in the comments.

Disclaimer #2: At a certain point I reached the limits of my ability to find answers. At that point I basically start sharing my attempt to logic out answers, or at least what the right questions might be. It may get a little muddy and I apologize. But again … this was a type of thought experiment for myself, so I figured I’d share it all the way through. I pretty much wrote this post as I researched/logiced, so it’s a pretty accurate run-through of my thought process.

Background, cont’d

In Hawking’s episode on time travel, he explains that an object with a very large mass actually slows down time around itself – and this is reflected in the GPS satellites in our orbit (they are a little bit faster, since they are a bit farther from the Earth – just a tiny bit, too little to really impact us; they gain one-third-of-a-billionth-of-a-second on us each day). It’s also been proven using aircraft flying over the Earth.

When I started doing some additional research for this post, I came to understand that no, time itself doesn’t slow down, but spacetime warps/gets longer and so it takes longer to travel across/through. This doesn’t seem to significantly impact the questions I explore below, but I don’t really want to mislead people.

To synposize while keeping this in layperson-level terms:

  • Objects produce gravity. Your fourth grade science teacher was onto something!
  • Big objects produce more gravity (big meaning “have lots of mass”; “mass” basically meaning “stuff,” as per the definition we used in live demo shows when I worked at a science museum).
  • This gravity makes time slow down a little bit (or, more accurately, it stretches spacetime so that it takes us longer to cross it – imagine if you were running on a track and someone magically expanded your 1-mile track into a 1.25-miler). To put this in literal terms, their gravity “drags on” time in much the way a toddler slows down their mom by dragging on a shirt sleeve.
  • If you could orbit the black hole at the center of our universe (I know, I had no idea, either) you’d experience time slowed to half the “speed” it moves on Earth (because the black hole is really, really, really, really big). Your body would, apparently, also age five years for our ten years on Earth. (I’m sure there will be an anti-aging intergalactic cruise program someday.)
  • The GPS satellites in orbit around Earth experience time a tiny-wee-bit faster than we do here on Earth, because they are slowed down less by the Earth’s mass (the mom is out with friends and the toddler is at home with a babysitter).
  • You wouldn’t be aware of time being slower or faster (despite the oft-cited mantra that Einstein proved that being bored makes time seem to go slower. I don’t know if that’s true, but it’s not relevant to this). Someone hanging out on those GPS satellites would feel like time was passing normally, and if they had a telescope to Earth it would look like we were moving slowly. Similarly, we feel like time is passing normally, but if we had a view up to that person in space, they would appear to us to be moving quickly.
  • Actually, though, you don’t need to go that far up in space. Just 1 km difference in height is all you need. Stick a clock 1 km higher than another, and over a million years it will emit about three more second-ticks than the lower one. So basically, you don’t need a large distance from Earth to decrease the effect of its gravity, but you would need to create a binding will that somehow requires your descendent to go check the clocks a million years later.
  • Time is, in fact, relative. Once you accept this, your head will stop hurting from trying to conceptualize all the above. I also found it helpful to imagine time as a physical object like fabric that gets pulled at by another object’s gravity (hence the toddler analogy). And imagining time as a stretchy fabric that gets pulled on is probably closer to the actual scientific explanation I found after watching Hawking’s episode.

The Question(s)
I volunteered at the DC Health Expo this weekend. I had no idea the Convention Center was so huge! I couldn’t stop wondering if you could gather enough people to produce enough mass to slow down time in a region (say, an ultra-huge Olympic-size stadium or convention center) – and how that would be reflected on all the timepieces (ie, iPhones) linked the the World Clock (or whatever that main clock is called now).

Question 1: Power to the People

So … how much mass would it take to slow down time?

And, to take a tangent – is population control at all relevant to the Earth’s impact on time around it? Would the Earth slow down time less if people and buildings weren’t on it?

For the first question: It turns out, not so much. Hawking had used the Great Pyramid of Giza as an example of an object with enough mass to slow down time – and I couldn’t find a single source that said, “That was just an analogy and not real.” So: the Great Pyramid of Giza has enough mass to slow down time for a small area around itself. The pyramid weighs an estimated 6.5 million tons. One ton equals 2,000 pounds, so – 13 billion pounds.

Okay, maybe that’s not so little.

But let’s say you brought together approximately 16 people of healthy weight – you’d already have about 2,000 pounds right there. So one ton equals approximately 16 people. And 104 million people would give you approximately 6.5 million tons.

According to Google, the US has over three times that population today. Texas alone has 26 million, one-fourth of the number we need.

Tangentially, I wondered if you need the population (the source of mass) to be dense. Texas, of course, has lots of space. So I decided to look at NYC. Population: 8.337 million, living in approximately 305 square miles (obviously, not counting vertical miles). That came out to 0.0000365839 square miles per person. Some of what I read indicated that density might be important – or shape (say …. pyramid-shaped).

Before I go any farther, I hear you asking: But does it have to be a pyramid-amount of mass?

The answer is that I don’t know. This is one of the limitations I ran into trying to do this research on my own online. Which was also part of the experiment of it: to find the limitations of a non-science/math professional doing some research mostly via Google. I found equations, but not ones that I could translate into actual math. So this is a question to throw back out there to Awesome Science People.

At the end of all this research, my conclusions are essentially that it would be far easier to give people a taste of slower time by giving them an apartment in a skyscraper; we just don’t have the structural capacity to bring enough people into a dense enough area to produce the kind of accumulated mass that would significantly slow time in any noticeable way. I do suspect, though, that human population and building structures contribute to the Earth’s mass, in an extremely limited way. I kept trying to frame this idea with word problems like the following:

Person A is on a satellite in space above the Giza Pyramid.

Person B has challenged his best friend to a virtual race using an iPhone app: they will each run 5 km. B is doing his run around the Giza Pyramid.

Person C is up in space, at the same height as Person A, above the Inner Harbor at Baltimore.

Person D, the best friend, has accepted the 5 km challenge. D is doing his run around the Inner Harbor.

So theoretically, if People A and C compare notes, they should notice that Person B (at the Pyramid) appears to be moving more slowly than Person D (at the Inner Harbor) – even though both of them appear to be moving faster than necessary, since A and C are experiencing time more slowly than both B and D.

The problem with this and any word problem I came up with is that time relativity is all about relativity. It’s all about comparing what one person is experiencing to another. You can see why my head started to hurt slightly at this point. Of course B was slower, because he’s by the Giza Pyramid. But comparing the effect of the pyramid on a person to the effect of an area without a pyramid has nothing to do with comparing the mass of the Earth with buildings to the mass of the Earth without buildings on it, because the people you need to be comparing would be – where? Up in space on a satellite, maybe?

And that’s the only way I can think of to prove whether our buildings significantly affect time around the Earth. If we had satellites with finely calibrated clocks specifically stationed over buildings of varying mass – one stationed over the Pyramid of Giza, one over the rainforest, one over the desert, one over the Empire State Building, etc, and then we compared the clocks after a year, five, ten, a thousand years.

Alternatively, if a manageable equation DOES exist for just how much the Earth should slow down time around it, we could compare the “should” answer to the “real” answer – but only if we had a comparison point (that pesky “relativity” part again), which is where I get stuck. Do we even have a concept of “normal” time? Theoretically, does “normal” time exist at all? At this point, I’m pretty sure that it doesn’t.

As for what it means if our buildings do slow time around the Earth further, I’m honestly not sure. Would asteroids slow down when they neared us, or would they just appear to move very very fast to us? Again, I defer to an Awesome Science Person.

Question 2: Technology Gone Mad

If you could theoretically slow down time, would it be reflected on people’s iPhone clocks?

This question led me through a lot of webpages trying to figure out how iPhone clocks work (or rather, how to ask the question so that I could find a relevant answer). As far as I was able to determine, it’s all GPS-based. So this means that to see a slowing in the passage of time on your iPhone, you’d need to create enough mass to impact the GPS satellites in orbit. (This science experiment may be the best reason I’ve ever heard for buying a non-digital watch – it’d be easier.) So again, this leaves us where I left off with Question 1: if we built enough Giza Pyramids, could we slow time down around the Earth?

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