Great job distilling the concepts here — that not everything is relative. It’s just that there are things like length and time (and related concepts like simultaneity) that we once thought we absolute, and it’s hard to wrap one’s head around the fact that they depend on your frame of reference.
Category Archives: Physics
WWLD
(Thought I scheduled this to post last week, but apparently I didn’t)
To Save Drowning People, Ask Yourself “What Would Light Do?”
I’ve seen a discussion of the lifeguard dilemma before, but there’s some added value here. Especially the disavowal of the “dog doing calculus” bit
Tim was impressed enough by Elvis’s trick to write a paper called “Do Dogs Know Calculus?” In it he reassures the reader that “Elvis does not know calculus…In fact,” Tim adds, “he has trouble differentiating even simple polynomials. More seriously, although he does not do the calculations, Elvis’s behavior is an example of the uncanny way in which nature often finds optimal solutions.”
I’m glad to see this, as opposed to the “animal of some sort does calculus” headlines I’ve run across a few times.
Gimme That Old Style Energy Storage
Energy Storage Hits the Rails Out West
It’s an interesting concept. They’ve already built a test system, so I’m going to assume this was thought out and will actually work. Let’s look at the numbers.
Each car carries 230 tons and the hill is roughly 3000 feet high, so if we convert to metric and grab an envelope, mgh is about 2 billion Joules of potential energy per car. The output is designed to be 50 MW, so each car gives 40 seconds of runtime at that power, and that’s assuming 100% efficiency of the regenerative brakes. Obviously we need more than one car.
We can also look at this from a different perspective. In this case the power output is P =Fv (that’s actually a dot product, if you’re scoring at home). The incline is given as 6 to 9 degrees, so one car would have to travel at least 160 m/s for that output (at 9º), but that scales with the number of cars. 160 cars can travel at 1 m/s and give us 50 MW (or 80 cars at 2 m/s, etc.), again, modified by the efficiency of the system. Slow speeds would allow the system to “ramp up” by getting to the target speed quickly and operate safely — I doubt anyone wants these trains running down a hill at tens of meters a second.
One last bit of data is that the track is 6.5 km long. I’m assuming that’s the length in addition to the length of the train itself, i.e. it’s how far the train can go.
Let’s assume the efficiency (e) is 75% and we have n cars.
t= (30s)*n and also t = L/v where L is our effective track length. vn = L/30s = 215 m/s
We also know that en(mg)(sin9º)v = 50 MW, or vn = 200 m/s.
Not bad — the answers are within 10%. (Of course it could mean I made the same underlying error in both estimates, or two that happen to cancel)
The final factor is how long the system runs. More cars going slower extends the time, but runs into a space limit. But 50 cars at 4 m/s goes for ~25 minutes, which is not bad for a gap-stopper.
What Happens Next Will Astound You
Top 10 Physics Findings That Will Tangle Your Brain
zapperz has already covered this; it’s got the usual hits like equating quantum teleportation and Star Trek, but the idea that the slowing of the earth means that time is slowing down is a new one. The mistake it makes is old, though; the slowing is an acceleration. 1.4 ms/day/century means that in another 100 years, all things being equal, the slowdown will be 2.8 ms/day. And that even if the rotation stabilized, if the rate were smaller then the earth would still run slow. It would just do it at a constant rate.
The one that gets me in the list is “stopped light.” The experiment is quite cool — being able to absorb light and then recreate the beam later with all of the information about its coherence and polarization intact — but “stopped light” is hyperbole.
Here Be Dragons That Rarely Interact
Physicists Produce Antineutrino Map Of The World
Physicists know that almost all of [the earth’s internal] heat is generated by the decay of radioactive elements such as potassium-40, thorium-232 and uranium-238. But how are these elements distributed and how much heat does each contribute?
In the next few years, geophysicists hope to get some detailed answers to this question thanks to the emerging science of neutrino geophysics. The radioactive decay inside the Earth produces subatomic particles known as antineutrinos. So an experiment that measures the antineutrinos coming out of the Earth should provide a detailed picture of the distribution of these elements within it.
This isn’t a map made by detection, but by calculation based on reactors. Still pretty cool.
Should You or Shouldn't You?
Should you get your PhD? (in science)
I added the parenthetical in science because I’m not sure how well the advice works well outside of it — it may have less applicability outside of physics. I have quibbles with a few things, as I’m an experimentalist and an atomic physicist, and Ethan is a theorist and is trained as an astrophysicist. There are bound to be some differences, but I think most of it is going to hold up for science PhDs in general.
There are plenty of brilliant people who get them, of course, but there are also plenty of people of average or even below-average intelligence who get them. All a PhD signifies, at the end of the day, is that you did the work necessary to earn a PhD. There are many people who have PhDs who will dispute this, of course. There are plenty of people who are insecure about their lives, too, and base their entire sense of self-worth on their academic achievements and accolades. You probably have met a few of them: they are called jerks.
This was probably the biggest surprise in grad school to me — how much the ratio of intelligence to stubbornness actually was in the student population, vs. the larger value I had naively expected it to be.
By Failure, I Assume You Mean Success
Ask Ethan #29: The Most Famous Failed Science Experiment
So, then, the reasoning went, if light is a wave — albeit, as Maxwell demonstrated in the 1860s, an electromagnetic wave — it, too, must have a medium that it travels through. Although no one could measure this medium, it was given a name: the luminiferous aether.
Sounds like a silly idea now, doesn’t it? But it wasn’t a bad idea at all. In fact, it had all the hallmarks of a great scientific idea, because it not only built upon the science that had been established previously, but this idea made new predictions that were testable!
Ethan does a pretty thorough job of this, as usual, with the possible exception of not fully explaining that the observation of aberration was how scientists knew we couldn’t be at rest with respect to an aether — in their paper, Michelson and Morley specifically mention how their null result refutes Fresnel’s model of aberration (involving partial aether dragging and which was backed by an experiment carried out by Fizeau in 1851).
What I really object to here is the notion that this was somehow a failed experiment. The hypothesis failed, but it was not their hypothesis! While it’s quite likely that Michelson and Morley expected a result that was consistent with us moving through an aether, the more idealized view an experimentalist is supposed to take is to not expect a specific result at all, lest one become biased in gathering and interpreting data. That the experiment was clever and thorough enough to be able to refute an incorrect hypothesis means it was wildly successful, rather than a failure.
Not Sticking the Landing
Physics Fail in Record-Setting Car Jump Attempt
Everything seems to be fine for the first two thirds of the flight. But then the sound of the engine dies and the car starts to rock forward. Those two things are intimately connected.
This is something I noticed in the animated movie The Incredibles, where they got this part right, despite all of the suspension of disbelief required elsewhere in the movie: when the van drops free of the rocket, Mr. Incredible stomps on the gas and the van tilts back, which is at least qualitatively what you’d expect.
A Good Week for Waves Continues
‘Waves’ detected on Titan moon’s lakes
Dr Barnes, from the University of Idaho in Moscow, US, used a mathematical model to investigate whether the features in the image were compatible with waves.
“We think we’ve found the first waves outside the Earth,” he told the meeting.
“What we’re seeing seems to be consistent with waves at just a few locations in Punga Mare [with a slope] of six degrees.”
He said other possibilities, such as a wet mudflat, could not be ruled out.
This Won't Affect the Consumer Price Index
Detection of Waves in Space Buttresses Landmark Theory of Big Bang
Reaching back across 13.8 billion years to the first sliver of cosmic time with telescopes at the South Pole, a team of astronomers led by John M. Kovac of the Harvard-Smithsonian Center for Astrophysics detected ripples in the fabric of space-time — so-called gravitational waves — the signature of a universe being wrenched violently apart when it was roughly a trillionth of a trillionth of a trillionth of a second old. They are the long-sought smoking-gun evidence of inflation, proof, Dr. Kovac and his colleagues say, that Dr. Guth was correct.
I imagine that this will trigger an inflationary period of blog posts and science articles by those who are far more qualified than I to explain the results.