Long live the work of Emma Noether

A wonderful article at arstechnica tells of the work of a woman Jew in the early 20th century. She lived in Germany in the years leading up to WWII. She had to leave, and came to America. Some of her best work is on Einstein‘s General Theory of Relativity.

Science kind of takes some symmetries for granted. For example, you should be able to perform the same experiment a year later and get the same result. Or you should be able to do it in two places and get the same result. But one of the main laws of physics — conservation of energy — seems to be broken by general relativity. It is possible for a machine to emit gravity waves, and gain energy instead of losing it.

This paradox was solved by Emma Noether who’s theorem proves a connection between symmetries and conservation laws.

It turns out that with general relativity, you may get different results depending on where you are when you perform your experiments. Here on earth, the experiments all happen in very similar circumstances. But in a strong gravitational field, the curvature of space is different, and you can get different measurements. This strange effect is predicted by Einstein’s theories, and Neother’s theorem provides the connection.

The Neutron has more mass than the Proton

80 years ago scientists discovered the neutron. The masses of the two nucleons, the neutron and the proton, are so close that in middle school it doesn’t make sense to distinguish the difference. Last week scientists have determined that the neutron is ≈0.14% more massive than the proton. This implies that the down quark is slightly more massive than the up quark.

If the difference is masses were slightly different, our universe would be very different, with not as much hydrogen, not many heavy metals, or more.

Evidence of new phase of matter competing with superconductivity

So, the 3 phases of matter are Solid, Liquid, and Gas. Oh, and Plasma. And if you get it really cold, Bose-Einstein Condensate. And then there’s Pseudogap.

It turns out that pseudogap is one thing that stops things from being superconductive at high temperatures.

In a study they found that

In this latest study, Hashimoto was able to find out exactly what was happening at the moment the material transitioned into a superconducting state. He did this by measuring not only the energies and momenta of the electrons, but the number of electrons coming out of the material with particular energies over a wide range of temperatures, and after the electronic properties of the material had been altered in various ways.

 

He discovered clear, strong evidence that at this crucial transition temperature, the pseudogap and superconductivity are competing for electrons. Theoretical calculations by members of the team were able to reproduce this complex relationship.

Promising new spaceship drive

NASA has recently tested a new type of drive that may be used in future spaceships. The Cannae Drive is unique in that it doesn’t use propellant. Since propellant (fuel) has mass, normal drives need to move the spacecraft and the propellant for future thrust. This leads to needing lots of mass, frequently as much as the payload.

But the Cannae Drive is different. It uses microwaves instead of propellant. By bouncing microwaves in a specially shaped container, they have managed to create a difference in radiation pressure, generating between 30-50 micronewtons. This is a very small amount of thrust. The only energy that is needed is electricity, which is readily available through solar panels.

This technology is in its infancy, and is a long way from being used in spacecraft.

I love this kind of thing because it appears to violate the Law of Conservation of Momentum (simpler). This means that we’re at the edge where our understanding of the way the universe works may be wrong. Our scientific understanding may have to change to account for this effect.

Teaching Newton’s second law

I’ve been teaching Newton’s second law to my 6th graders, and I’m really surprised at how the textbooks try to do the math. When I learned it (back before dirt), I learned f = ma (force is mass times acceleration). Our textbook says a = f/m (acceleration is force divided by mass). But I haven’t seen a textbook use this:

Newton's Second Law

With this, all you do is plug in what you know, and it will show you how to get what you’re missing. For example, if you have force and acceleration, you fill them in, and you have force divided by acceleration. That gives you mass.

You can also think about like this: I want to get the force, so I cover up the f. I’m left with mass times acceleration. Or I want to get acceleration, so I cover up the a. I’m left with f over m.

Now, instead of having to remember 3 formulas (f=ma, m=f/a, a=f/m), I just have to remember this one thing that gives me the 3 formulas. All I really need to remember is that force goes on top (because multiplication is commutative).

 

The Slow Funnel

Usually when you use a funnel the fluid goes through quickly. Even if you’re filtering something you expect it do be done in 10 minutes or so. How about longer? How about over a year? Over a decade? How about almost 100 years?

One of the long running experiments is the Pitch Drop Experiment started at the University of Queensland in 1927. Pitch is another word for bitumen, or asphalt. It’s a very viscous liquid. Water has low viscosity. Honey flows slower, so it has a higher viscosity. Pitch has the somewhat higher viscosity of 2.3 × 1011. That’s 230,000,000,000 times slower than water.

To demonstrate this, in 1927 Thomas Parnell heated a sample of pitch and put it in a sealed funnel. 3 years later he cut the seal on the neck of the funnel to let the pitch start flowing. It took about a decade for the first drop to fall. The 8th drop fell on 28 November 2000. You can see the progress of the next drop in the experiment at this webcam.

This experiment is in the Guinness World Records as the longest continuously running lab experiment. There are other, longer running, experiments, but they have had interruptions.

Update 17 April 2014The 9th drop has collided with the 8th drop. Due to the amount of pitch at the bottom of the beaker, the 9th drop can’t fully detach from the funnel, so they are calling this the official 9th drop (or so I’ve heard). Onward to number 10!

Moving … the new fad diet!

Did you know that how much you weigh in your hometown is different from what you would weigh if you moved somewhere else? Since weight is caused by how much gravity is pulling you down onto whatever surface you’re on right now, it changes depending on where you are. If you’re on the moon, you would weight 1/6th your regular weight, because the moon’s gravity is 1/6th of Earth’s.

But it also changes for different locations on the Earth. You would weigh slightly less on the summit of Mt. Everest, because you’d be further away from most of the Earth’s mass. Or at least, further away from mean sea level, which is closer to where things are normally weighed. It’s even different depending on what city you’re in. If your scale is accurate to more than 2 decimal place, you should calibrate it with a standard mass when you move it far away.

So, if you want to weigh less, you can try going to Denver, CO, where you’ll be over 1 mile above sea level. Since you’re further away from the center of the Earth, you’ll weigh less. Not much less. And your mass will still be the same.

That’s right. Weight and mass are different things. Weight is how much gravity is pulling you down. Mass is how much matter you’re made of. So you’ll weigh less in Denver than New York (or Watchung), but your mass would be the same.

Yes, there is a conversion between them. 1 Kg is 2.2 pounds (really 2.205). And this time we are comparing apples to oranges, because grams is mass, and pounds is weight. I expect that this conversion is only valid at mean sea level at the equator.

All right, mean sea level makes sense, since that’s elevation which we just talked about. Why the equator? Because the Earth isn’t a sphere. It’s really an oblate spheroid. That means that it bulges out a little bit at the equator because of centrifugal force of its spinning. Earth’s equatorial diameter is 7926.385 miles and the polar diameter is 7899.9 miles.

I was inspired to write this post when reading http://what-if.xkcd.com/67/.