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RE: Scale vs length
The abstract and article don't really give enough information to entirely judge what they're saying here. ...
The abstract, like all abstracts, is terse, but the relevant info is there. The key idea is that the ratio of the two scales is not invariant under a Lorentz transformation. So, by changing the velocity of the oberserver, you can change the ratio of the two scales bringing them more in line with each other. This occurs even though both scales are affected by the transformation individually. If I get the chance, I'll look at the math a little more closely to see if I can explain it a bit better.
The other thing that seems confusing about the descriptions is that they suggest there's a sort of "sweet spot" in the velocity.
Truth be told, I didn't notice anything about a "sweet spot" in the actual paper, only in the PR Focus. But, I might have missed that point. My thought is that there is a competition between length contraction and time dilation, and the "sweet spot" is the point where they are balanced against each other.
These "pay us to see our results" journals are annoying. :(
Unfortunately, that is how the scientific world works. The APS has some of the least expensive journals (in addition to being one of the most respected), though Partially because, they're a not for profit organization. Of course, most of their operations money comes from the publications. I expect to see this article in their Free to Read list soon, though. The most amusing thing about scientific publishing is that most publishers get paid for an article twice, once by the purchaser and once by the author. It costs the author money to get something published.
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Scale vs length
The abstract and article don't really give enough information to entirely judge what they're saying here.
If I'm following it, they've got this simulation in which the individual elements are smallish - around 10cm - and the overall system is fairly large - around 5km. So we've got roughly a million-to-one scale. Simulating a tens or hundreds of millions of elements as they evolve is where all the workload comes from.
The paper proposes to reduce this workload by simulating instead what it looks like to an observer passing by at near relativistic speed, presumably to harness something like the ladder paradox.
So the total 5km length of the system is shortened by the Lorentz contraction by a factor of γ = 1/√(1 - v2/c2) - if v is 90% of c, then the system is a little over 2km. At 99%, it's only about 700m.
The only way that seems relevant is if the "fine" scale (10cm) measurement doesn't change, or at least changes less than the coarse scale. But at least one dimension of its length will be contracted by the exact same amount.
The other thing that seems confusing about the descriptions is that they suggest there's a sort of "sweet spot" in the velocity. I assume that below this "optimal" velocity, you haven't squeezed out the maximum benefit. What might happen above it? The Lorentz equations are all linear in both time and space, I can't imagine how you might start losing the benefits by running it too "fast". To me, this suggests that part of the effect of the relativistic simulation is to discard some of the detail in the simulation. So the "sweet" spot represents a compromise between getting answers quickly and getting an accurate simulation.
These "pay us to see our results" journals are annoying. :(
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