Perimeter had its last Public Lecture of the season this week, with Mario Livio giving some highlights from his book Brilliant Blunders. The lecture should be accessible online, either here or on Perimeter’s YouTube page.
These lectures tend to attract a crowd of curious science-fans. To give them something to do while they’re waiting, a few local researchers walk around with T-shirts that say “Ask me, I’m a scientist!” Sometimes we get questions about the upcoming lecture, but more often people just ask us what they’re curious about.
Long-time readers will know that I find this one of the most fun parts of the job. In particular, there’s a unique challenge in figuring out just why someone asked a question. Often, there’s a hidden misunderstanding they haven’t recognized.
The fun thing about these misunderstandings is that they usually make sense, provided you’re working from the person in question’s sources. They heard a bit of this and a bit of that, and they come to the most reasonable conclusion they can given what’s available. For those of us who have heard a more complete story, this often leads to misunderstandings we would never have thought of, but that in retrospect are completely understandable.
One of the simpler ones I ran into was someone who was confused by people claiming that we were running out of water. How could there be a water shortage, he asked, if the Earth is basically a closed system? Where could the water go?
The answer is that when people are talking about a water shortage, they’re not talking about water itself running out. Rather, they’re talking about a lack of safe drinking water. Maybe the water is polluted, or stuck in the ocean without expensive desalinization. This seems like the sort of thing that would be extremely obvious, but if you just hear people complaining that water is running out without the right context then you might just not end up hearing that part of the story.
A more involved question had to do with time dilation in general relativity. The guy had heard that atomic clocks run faster if you’re higher up, and that this was because time itself runs faster in lower gravity.
Given that, he asked, what happens if someone travels to an area of low gravity and then comes back? If more time has passed for them, then they’d be in the future, so wouldn’t they be at the “wrong time” compared to other people? Would they even be able to interact with them?
This guy’s misunderstanding came from hearing what happens, but not why. While he got that time passes faster in lower gravity, he was still thinking of time as universal: there is some past, and some future, and if time passes faster for one person and slower for another that just means that one person is “skipping ahead” into the other person’s future.
What he was missing was the explanation that time dilation comes from space and time bending. Rather than “skipping ahead”, a person for whom time passes faster just experiences more time getting to the same place, because they’re traveling on a curved path through space-time.
As usual, this is easier to visualize in space than in time. I ended up drawing a picture like this:
Imagine person A and person B live on a circle. If person B stays the same distance from the center while person A goes out further, they can both travel the same angle around the circle and end up in the same place, but A will have traveled further, even ignoring the trips up and down.
What’s completely intuitive in space ends up quite a bit harder to visualize in time. But if you at least know what you’re trying to think about, that there’s bending involved, then it’s easier to avoid this guy’s kind of misunderstanding. Run into the wrong account, though, and even if it’s perfectly correct (this guy had heard some of Hawking’s popularization work on the subject), if it’s not emphasizing the right aspects you can come away with the wrong impression.
Misunderstandings are interesting because they reveal how people learn. They’re windows into different thought processes, into what happens when you only have partial evidence. And because of that, they’re one of the most fascinating parts of science popularization.
4 gravitons 
Spot on observation. Very true.
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Polite cough! Time dilation doesn’t come from space and time bending. Curved spacetime is a curvature of your metric or measurements rather than curved space and curved time. An atomic clock is in essence an microwave optical clock, and there’s no literal time flowing through it. Such a clock runs slower when it’s lower because the speed of light is slower when its lower. I kid ye not, see the Einstein digital papers : http://einsteinpapers.press.princeton.edu/vol7-trans/156 . If you place an array of optical clocks throughout an equatorial slice through the Earth and the surrounding space, then plot the clock rates in a 3D grid, your plot is curved like the Riemann curvature depiction of curved spacetime. But the lower clocks don’t run slower because your plot of clock rates is curved. The don’t run slower because spacetime is curved. They run slower because a concentration of energy in the guise of a massive planet “conditions” the surrounding space, this effect diminishing with distance in a non-linear fashion. Because of this light goes slower when its lower, as do light clocks. Then because of the wave nature of matter, so does everything else. We model all this using curved spacetime, but the map is not the territory.
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“Curved spacetime is a curvature of your metric or measurements rather than curved space and curved time.”
Curved space and curved time are shorthand for curvature of metrics, frequently used in popularizations of science.
“The map is not the territory” doesn’t really apply in discussions of relativity, because there isn’t another way for us to gain access to the territory. Put another way, you can certainly describe a warping of space-time as just a warping of everything else, if you want to. But in practice, the former description is more useful: mathematicians have fairly detailed formalism for describing warped spaces, and that formalism is precisely that which describes general relativity.
So yes, the map is not the territory. But as physicists, our job is to find the best map we can, and in practice this is the one we use. If there were an experiment that distinguished the two, that would be one thing. But in this case, there’s not.
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The trouble is that Wheeler and others drew a new map, and it’s wrong. See the Einstein digital papers: “This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that ’empty space’ in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)…”. Space is inhomogeneous where a gravitational field is, not warped. See Inhomogeneous vacuum: an alternative interpretation of curved spacetime, and talk to John Moffat re section II of this paper.
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First of all, citing Einstein’s papers on this topic is beyond silly. Even if they supported what you think they do, Wheeler and the others were writing after Einstein!
In this case, Einstein used the word inhomogeneous, and the paper you link does too, which is giving you the impression that Einstein is agreeing with that paper. But “inhomogeneous” doesn’t mean “not empty”, it means “different in different directions”, i.e. curved. Einstein is not saying that space is not empty, but that space varies from place to place, which is what we mean when we say space is curved.
Moffat and others (presumably including Ye and Lin) have specific proposals for modifying GR. I’m not going to say either of their proposals have been completely ruled out, though Ye and Lin seem to be conspicuously avoiding more prestigious journals. But in either case, it’s on them to provide a way to distinguish their proposals from the consensus. (In Moffat’s case at least, he’s not just proposing a reinterpretation, his modified gravity has testably different consequences.)
Regardless, my role here is to explain the consensus: the map that we use, and why we use it. If Moffat manages to definitively show some version of modified gravity to be correct, then my explanations will change to suit it. As-is, though, it’s irresponsible to present that sort of proposal as if it were settled science. (Note that when I talk about untested proposals, I use clarifying language: “within string theory, x is true” not simply “x is true”)
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The Moffat reference was merely to do with the speed of light, not his modified gravity. The Ye and Lin reference was just to back up the Einstein quote. Don’t read too much into them. Instead see this Baez article : “Similarly, in general relativity gravity is not really a ‘force’, but just a manifestation of the curvature of spacetime. Note: not the curvature of space, but of spacetime. The distinction is crucial.” Space is inhomogeneous where a gravitational field is, but it isn’t curved. Unfortunately Wheeler, who said “matter tells space how to curve”, created a misunderstanding. You think it’s a consensus, but it isn’t. The strong curvature regime is nothing to do with the gravitational field. And the geon is tragically misnamed. Anyway, like I said, sorry for commenting so much, pleased don’t hesitate to say if you’d prefer me to take it offline etc.
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It’s fine. I’m a little annoyed that you chose to approach this as “you’re wrong” rather than “here is something I’m confused about”, but regardless I’m happy to help.
You’re misunderstanding the Baez article, in particular. Baez is trying to clarify that, if you simply imagine space as curved without taking into account time as well, then you’d think it would have to be much more curved than it actually is. That’s what he’s trying to show with the parabola example, that space isn’t actually curved so completely that a parabola is straight, rather that the curvature of space and time together adds up to make the parabola the shortest path.
This also gives me a clearer idea of what’s confusing you about that Einstein paper: when he says that “space” is inhomogeneous, he’s not trying to draw a distinction between space and time. If you look just a little earlier in the same sentence, he’s talking about both. He’s just using the phrase “empty space” because “empty space-time” doesn’t have the same rhetorical cachet, but he’s still talking about the same thing modern folks are: that the metric is inhomogeneous, able to vary from place to place.
In terms of the Moffat reference, my point was that in his case he’s able to treat the speed of light as non-fixed because he’s working from some very specific proposals for modified gravity that allow him to do that. He’s “done his homework” in some sense, and one really needs that kind of “homework” to make a proposal like that viable.
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With respect X, I’m not at all confused about the Baez article or the Einstein paper. Or about the distinction is crucial. As for Moffat being able to treat the speed of light as non-fixed because he’s working from some very specific proposals, see this: “the curvature of light rays occurs only in spaces where the speed of light is spatially variable”. With that I’m going to stop hogging your comments. Carry on blogging!
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In the spirit of duffieldjohn,
Proof of God’s existence:
1. Einstein wrote, “God does not play dice.”
2. Therefore God exists.
QED
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