quantum mechanics

Dismantling Common Sense, Twice

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In my last post I raised a question about the pros and cons of common sense. I left it as a wide-open question, as I was curious to see how readers would react.

Many aspects of common sense affect how we relate to other people, and it’s clear they have considerable value. But the intuitions we have for nature, though sometimes useful, are mostly wrong. These conceptual errors pose obstacles for students who are learning science for the first time.

It’s also interesting that once these students learn first chemistry and then Newtonian-era physics, they gain new intuitions for the natural world, a sort of classical-physics common sense. Much of this newfound common sense also turns out to be wrong: it badly misrepresents how the cosmos really works. This is a difficulty not only for students but also for many adults. If you’ve read about or even taken a class in basic astronomy or physics, it can then be challenging to make sense of twentieth-century physics, where Newtonian intuition can fail badly.

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Why Current Wormhole Research is So Important

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Once we clear away the hype (see the previous posts 1, 2, 3, 4), and realize that no one is doing anything as potentially dangerous as making real wormholes (ones you could actually fall into) in a lab, or studying how to send dogs across the galaxy, we are left with a question. Why bother … Read more

[Not] A Wormhole in a Laboratory

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Well, now…

  • Did physicists create a wormhole in a lab? No.
  • Did physicists create a baby wormhole in a lab? No.
  • Did physicists manage to study quantum gravity in a lab? No.
  • Did physicists simulate a wormhole in a lab? No.
  • Did physicists make a baby step toward simulating a wormhole in a lab? No.
  • Did physicists make a itty-bitty baby step toward simulating an analogue of a wormhole — a “toy model” of a wormhole — in a lab? Maybe.

Don’t get me wrong. What they did is pretty cool! I’d be pretty proud of it, too, had I been involved. Congratulations to the authors of this paper; the methods and the results are novel and thought-provoking.

But the hype in the press? Wildly, spectacularly overblown!

I’ll try, if I have time next week, to explain what they actually did; it’s really quite intricate and complicated to explain all the steps, so it may take a while. But at best, what they did is analogous to trying to learn about the origin of life through some nifty computer simulations of simple biochemistry, or to learning about the fundamental origin of consciousness by running a new type of neural network. It’s not the real thing; it’s not even close to the real thing; it’s barely even a simulation of something-not-close-to-the-real-thing.

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The Size of an Atom: How Scientists First Guessed It’s About Quantum Physics

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Atoms are all about a tenth of a billionth of a meter wide (give or take a factor of 2). What determines an atom’s size? This was on the minds of scientists at the turn of the 20th century. The particle called the “electron” had been discovered, but the rest of an atom was a mystery. Today we’ll look at how scientists realized that quantum physics, an idea which was still very new, plays a central role. (They did this using one of their favorite strategies: “dimensional analysis”, which I described in a recent post.)

Since atoms are electrically neutral, the small and negatively charged electrons in an atom had to be accompanied by something with the same amount of positive charge — what we now call “the nucleus”. Among many imagined visions for what atoms might be like was the 1904 model of J.J. Thompson, in which he imagined the electrons are embedded within a positively-charged sphere the size of the whole atom.

But Thompson’s former student Ernest Rutherford gradually disproved this model in 1909-1911, through experiments that showed the nucleus is tens of thousands of times smaller (in radius) than an atom, despite having most of the atom’s mass.

Once you know that electrons and atomic nuclei are both tiny, there’s an obvious question: why is an atom so much larger than either one? Here’s the logical problem”

  • Negatively charged particles attract positively charged ones. If the nucleus is smaller than the atom, why don’t the electrons find themselves pulled inward, thus shrinking the atom down to the size of that nucleus?
  • Well, the Sun and planets are tiny compared to the solar system as a whole, and gravity is an attractive force. Why aren’t the planets pulled into the Sun? It’s because they’re moving, in orbit. So perhaps the electrons are in orbit around the nucleus, much as planets orbit a star?
  • This analogy doesn’t work. Unlike planets, electrons orbiting a nucleus would be expected to emit ample electromagnetic waves (i.e. light, both visible and invisible), and thereby lose so much energy that they’d spiral into the nucleus in a fraction of a second.

(These statements about the radiated waves from planets and electrons can be understood with very little work, using — you guessed it — dimensional analysis! Maybe I’ll show you that in the comments if I have time.)

So there’s a fundamental problem here.

  • The tiny nucleus, with most of the atom’s mass, must be sitting in the middle of the atom.
  • If the tiny electrons aren’t moving around, they’ll just fall straight into the nucleus.
  • If they are moving around, they’ll radiate light and quickly spiral into the nucleus.

Either way, this would lead us to expect

  • Rnucleus = # Ratom

where # is not too, too far from 1. (This is the most naive of all dimensional analysis arguments: two radii in the same physical system shouldn’t be that different.) This is in contradiction to experiment, which tells us that # is about 1/100,000! So it seems dimensional analysis has failed.

Or is it we who have failed? Are we missing something, which, once included, will restore our confidence in dimensional analysis?

We are missing quantum physics, and in particular Planck’s constant h. When we include h into our dimensional analysis, a new possible size appears in our equations, and this sets the size of an atom. Details below.

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The Amazing Feat of Quantum Tunneling

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Our quantum world has many odd and counter-intuitive features.  One of these is “tunneling” — the ability of objects to pass through walls, escape from traps, and slip under mountains into the next valley.   We don’t encounter this effect in daily life; objects we’re used to are so incredibly unlikely to tunnel from one … Read more

New Attempt at Atomic Article

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It took me over six months, following my article on molecules, to write the sequel, on atoms. These are just two in a series, intended to introduce the structure of matter to novice readers who want to learn what particle physics is about.  Atoms aren’t the main focus; future articles will focus on electrons, on … Read more

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