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New research finds that electric vehicles generally produce less non-exhaust emissions compared with gasoline-powered vehicles.

At the end of 2024, astronomers detected an asteroid in the night sky. It was given the designation Y, since it was discovered in the last half of December, and R4 since it was the 117th rock to be found in the last couple of weeks of December, and since it was discovered in 2024, it was assigned the name 2024 YR4. Naturally, once a rock is found, astronomers start keeping track of it, measuring its position to get a handle on its orbit. In this case, the estimated orbit put it at a 1% chance of striking Earth. As more measurements were taken, those odds have more than doubled. As of this writing, it now has a 2.3% chance of striking Earth on December 22, 2032. While you might think this resembles the plot of Don’t Look Up, none of this is too unusual.

You can see this in the image above, which indicates potential trajectory points. The 2.3% odds aren’t simply the chances of a die roll. What it means is that when astronomers run 1,000 orbital simulations based on the data we have, 23 of them impact Earth. The most probable trajectory currently estimates that it will have a close approach of 240,000 km from Earth, which is within the orbit of the Moon but not dangerously close. So while the odds have doubled, astronomers aren’t too worried. When 2024 YR4 had a risk of less than 1%, NASA’s Planetary Defense Coordination Office (PDCO) ranked it a 3 on the Torino scale, meaning we should keep an eye on it. At a 2.3% risk, it is still a 3.

When it comes to tracking asteroids like this, the one thing we are certain of is that early estimates are uncertain. Unlike the orbits of planets, the orbits of asteroids can be remarkably fuzzy. Gravitational tugs from nearby objects can shift them around. In the case of 024 YR4, one big source of uncertainty is Earth itself. In 2028, it will pass within 8 million kilometers of Earth. This is actually when astronomers will be able to make much more precise measurements of its orbit. We will then see whether we need to start making plans. Even if astronomers find out the odds of impact are almost 100%, we still wouldn’t need to panic, for a few reasons.

Comparison of the dimensions of 2024 YR4 and other bodies. Credit: Wikipedia user Sinucep

The first is that we know it’s there. The real risk of asteroids isn’t from the ones slowly approaching Earth from the outer solar system. The bigger risks are ones such as Chelyabinsk which came from the direction of the Sun and caught us by surprise. We still have years to deal with 2024 YR4, and its orbit is such that we would have a good chance of deflecting it. And even if the absolute worst-case scenario were to occur, 2024 YR4 isn’t large enough to cause an extinction event. The absolute nightmare scenario is that it would strike Earth in a heavily populated area. We’d have to evacuate people from the risk zone, but we would have a few years to do that. An impact would be bad, but we could minimize the risk significantly.

Even with all that said, it’s important to keep in mind that early trajectory calculations can vary significantly. The odds may rise significantly again before dropping, but the most likely outcome is that the odds will eventually drop to zero.

If you want to keep tabs on 2024 YR4, check out NASA’s Planetary Defense Page.

The post Yes, the Odds of an Asteroid Striking Earth Have Doubled. No, You Don’t Need to Worry appeared first on Universe Today.

If asteroid 2024 YR4 does smash down on the lunar surface, the explosion might be visible from Earth and would leave a new crater on the near side of the moon

A study showed that chatbots alone outperformed doctors when making nuanced clinical decisions, but when supported by artificial intelligence, doctors performed as well as the chatbots.

Sixth-generation, or 6G, cellular networks are the next step in wireless communication, and electromagnetic terahertz waves are seen as crucial to its development. However, terahertz waves, with their higher frequency and shorter wavelength, are subject to greater interference from electromagnetic noise, making clear and secure transmission a challenge. Researchers have now created an electromagnetic wave absorber for waves between 0.1--1 terahertz (THz). This greatly expands the range of the terahertz frequency which could be commercially used in the future. The ultrathin film is inexpensive, environmentally friendly and can be used outdoors, as it is resistant to heat, water, light and organic solvents.

Sixth-generation, or 6G, cellular networks are the next step in wireless communication, and electromagnetic terahertz waves are seen as crucial to its development. However, terahertz waves, with their higher frequency and shorter wavelength, are subject to greater interference from electromagnetic noise, making clear and secure transmission a challenge. Researchers have now created an electromagnetic wave absorber for waves between 0.1--1 terahertz (THz). This greatly expands the range of the terahertz frequency which could be commercially used in the future. The ultrathin film is inexpensive, environmentally friendly and can be used outdoors, as it is resistant to heat, water, light and organic solvents.

In a breakthrough for the advanced study of gut health, scientists have developed a 3D microscopic version of the human intestines condensed into a small chip about half the size of a five-cent coin. This new cell culturing platform, known as the Gut-Microbiome on a chip (GMoC), provides a realistic in vitro microgut model that allows researchers to examine the interactions of gut microbes and their collective impact on gut health. The chip offers a scalable, reproducible, and efficient method to dissect the roles of gut microbes and their community, which is of key interest for the preventive healthcare and pharmaceuticals industry.

Thanks to their special iridescence and unmatched beauty, pearls have been highly sought after throughout history. Due to their rarity and demand, the development of pearlescent pigments to mimic the natural beauty of a true pearl became inevitable. Here, researchers utilize plate-like particles to create substrate-free pearlescent pigments, a low-cost and straightforward solution to the issue of substrate-based pigments which can be complex and expensive.

Euclid, the European Space Agency's dark Universe detective, has made an astonishing discovery -- right in our cosmic backyard.

Researchers have developed a sustainable catalyst that increases its activity during use while converting carbon dioxide (CO2) into valuable products. This discovery offers a blueprint for designing next-generation electrocatalysts.

In patients with symptoms such as irregular heartbeats, dizziness, or fainting, or in individuals that physicians suspect may have atrial fibrillation, many days of ECGs may be required for diagnosis -- 'long-term ECG recordings'. These recordings must then undergo a time-consuming and human resource-intensive review to identify heart rhythm abnormalities. In a large international study, researchers tested whether an AI model can replace humans in analyzing long-term ECG recordings. The results: 14 times fewer missed diagnoses by the AI.

Artificial Intelligence of Things (AIoT) is becoming immensely popular because of its widespread applications. In a groundbreaking study, researchers present a new AIoT framework called MSF-Net for accurately recognizing human activities using WiFi signals. The framework utilizes a novel approach that combines different signal processing techniques and a deep learning architecture to overcome challenges like environmental interference and achieve high recognition accuracy.

Artificial Intelligence of Things (AIoT) is becoming immensely popular because of its widespread applications. In a groundbreaking study, researchers present a new AIoT framework called MSF-Net for accurately recognizing human activities using WiFi signals. The framework utilizes a novel approach that combines different signal processing techniques and a deep learning architecture to overcome challenges like environmental interference and achieve high recognition accuracy.

Psychologists warn that AI's perceived lack of human experience and genuine understanding may limit its acceptance to make higher-stakes moral decisions.

Researchers have designed an alternative, autonomous observational method to monitor the Arctic's melting ice, which holds promise for improving the autonomy of marine vehicles, aiding in maritime missions, and gaining a deeper understanding of how melting Arctic sea ice affects marine ecosystems. Their conceptual design features a small waterplane area twin hull vessel that acts as a docking and charging station for autonomous underwater vehicles and unmanned aerial vehicles, using solar and turbine energy to enable continuous monitoring.

Although the climate goals set by the Paris Agreement are based on the long-term average temperature, one year of high temperatures might be a sign that the 1.5°C threshold has already been reached

Seismic waves suggest the planet's solid inner core is being pulled out of shape – and it has undergone these changes over just a few decades

Unexpected epochs of stillness that punctuate the cosmic timeline could offer a natural explanation for dark matter and many other unsolved astronomical mysteries

Well, I’ll treat you to one more item about indigenous knowledge in New Zealand, this time when it clashes with modern science! It turns out that the Māori are beefing about there being too many satellites in the sky, and beefing for two reasons. First, this raises the possibility that the night sky might be changed, making it lighter, and that might make celestial navigation more difficult. Not that the Māori rely on that any more (actually, their Polynesian and SE Asian ancestors developed it), but their historical practice from hundreds of years ago might be made more difficult.

Second, the satellites are somehow said to interfere with a Māori ritual in which the steam from cooked food is allowed to float up toward the stars. (The ritual arose to give thanks for a good harvest.)  It is not clear to me how satellites would interfere with that, so you’ll have to ask the Māori.

Click below to read the excerpt from Stuff, a New Zealand news site:

Here’s the beefing about the ceremony (I’ve added translations):

A Māori scientist has warned our skies could become clogged with up to 100,000 satellites in the next five years – threatening thousands of years of Māori knowledge in the process.

The pollution could get so bad that stars seen by Māori ancestors would no longer be visible to the naked eye.

Elon Musk’s Starlink satellites have already interfered with a tuku wairua [food/steam] ceremony during Matariki, when whānau [members of a family group] who have died are released to the stars; while satellite proliferation threatens traditional waka hourua navigation [celestial navigation using double-hulled canoes].

Scientist, and Indigenous astronomy expert Te Kahuratai Moko-Painting is part of Sustainable Space – a group seeking to save Earth’s lower orbit, under 2000km, from uncontrolled development.

Moko-Painting often shows up in similar items, for he’s quite a vociferous activist.

Moko-Painting said about 15,000 satellites have been sent into space since the 1950s – about 7000 of those are still functional, and about 10,000 are still in space.

“Between 2022 when these estimates were made, and 2030, it’s estimated that we’ll have between 60,000 to 100,000 satellites in orbit.”

He said the about-3000 Starlink satellites in orbit were “already causing issues”.

. . . He got involved in the issue after the first Matariki public holiday in 2022, when he joined his wife’s whānau at Waahi Pā in Huntly for the hautapu (feeding the stars with an offering of kai [food].

“And just as we were doing our tuku wairua, just as we were sending on those who had passed on from that year, we had 21 Starlink satellites cutting through, right past the path of Matariki [the Pleiades star cluster.”

Apparently people thought that this was the stars’ response to the ceremony, and was propitious, but Moko-Painting—who admits that Starlink is important in communicating with rural communities—still has a beef:

“And those who knew would just say ‘no, that’s actually this man who loves the technology for launching satellites but makes them far too bright’ … and he does them in this line in an eye-catching kind of way, and that’s completely unregulated.”

I doubt that people will stop launching satellites because it somehow interferes with this ceremony. But wait! There’s more! As I said, there’s a possibility that too many satellites may interfere with celestial navigation, which only a few Māori still practice. But this is only a hypothesis, and hasn’t been shown, mainly because only a few stalwarts still use celestial navigation, and only as a way to keep alive that ancestral skill:

Even in the middle of the Pacific Ocean on a waka hourua, double-hulled waka used for voyaging, the night sky is 10% brighter than it used to be, Moko-Painting said. “So one could argue that 10% of what our tūpuna could see with their eyes while navigating is no longer visible to us.”

Master navigator Jack Thatcher has travelled tens of thousands of kilometres on waka hourua, as a guiding light that keeps his crews alive.

The Pacific covers a third of the planet. Thatcher’s journeys – using only stars, ocean swells and birds as guides – include a 3200km trip from Aotearoa to Rarotonga, which is only 67km wide.

. . . Having 100,000 satellites in orbit might be good for “pinpoint accuracy” all around the world, but those who rely on the stars for guidance won’t know which is a satellite and which isn’t.

“They’ll obliterate most of the patterns that we all depend on to help us find our way.”

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He said the satellites were already being discussed in the voyaging community. Light pollution wasn’t the only problem – “eventually they’ll be rubbish”, Thatcher said.

“We’re entering that zone of global extinction, because we’ve polluted our planet, now we want to pollute our heavens.”

While the technology might be used instead to navigate the oceans, “that’s not the point”, he said.

“Indigenous knowledge is something that is a self-determination thing.”

It’s not clear to me, though, that if the night sky is 10% brighter than before, this would somehow efface or even impede celestial navigation. They give no evidence, but some want to kvetch about it anyway, because it apparently erases the achievements of the Māori’s ancestors (not the Māori themselves):

Māori know who they are because of their ancestors’ achievements. “And now you’re going to take that all away from us.”

The first waka [canoe] in this country used navigation knowledge that ancestors accrued over millennia, Thatcher said – travelling from Southeast Asia to Aotearoa almost 6000 years later.

Essentially, he said, if you can no longer navigate the oceans through the stars “it becomes book knowledge only”.

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“Indigenous identity helps people to be who they are and enables them to be proud of who they are, because of their ancestral knowledge that they still hold on to.”

The whole idea of keeping indigenous knowledge alive was that “we’re not dependent on any technology”.

So Moko-Painting has joined a group of scientists calling for holding back on launching satellites.  The article ends abruptly:

SpaceX, which operates Starlink, did not reply to queries at time of publication.

The problem with all this is that these two problems haven’t been demonstrated. The navigation impediment is a theoretical possibility and won’t be known until people like Thatcher try it.  Since they can still do it successfully, even with all those satellites up there, I think this is not a serious concern. As for the satellites interfering with the smoke rising to the stars, that is pure superstition and doesn’t command concern from any rational person.

This is admittedly a provocative title coming from a particle physicist, and you might think it tongue-in-cheek. But it’s really not.

We live in a cosmos with quantum physics, relativity, gravity, and a bunch of elementary fields, whose ripples we call elementary particles. These elementary “particles” include objects like electrons, photons, quarks, Higgs bosons, etc. Now if, in ordinary conversation in English, we heard the words “elementary” and “particle” used together, we would probably first imagine that elementary particles are tiny balls, shrunk down to infinitesimal size, making them indivisible and thus elementary — i.e., they’re not made from anything smaller because they’re as small as could be. As mere points, they would be objects whose diameter is zero.

But that’s not what they are. They can’t be.

I’ll tell this story in stages. In my last post, I emphasized that after the Newtonian view of the world was overthrown in the early 1900s, there emerged the quantum physics of the 1920s, which did a very good job of explaining atomic physics and a variety of other phenomena. In atomic physics, the electron is indeed viewed as a particle, though with behavior that is quite unfamiliar. The particle no longer travels on a path through physical space, and instead its behavior — where it is, and where it is going — is described probabilistically, using a wave function that exists in the space of possibilities.

But as soon became clear, 1920s quantum physics forbids the very existence of elementary particles.

In 1920s Quantum Physics, True Particles Do Not Exist

To claim that particles do not exist in 1920s quantum physics might seem, at first, absurd, especially to people who took a class on the subject. Indeed, in my own blog post from last week, I said, without any disclaimers, that “1920s quantum physics treats an electron as a particle with position x and momentum p that are never simultaneously definite.” (Recall that momentum is about motion; in pre-quantum physics, the momentum of an object is its mass m times its speed v.) Unless I was lying to you, my statement would seem to imply that the electron is allowed to have definite position x if its momentum p is indefinite, and vice versa. And indeed, that’s what 1920s quantum physics would imply.

To see why this is only half true, we’re going to examine two different perspectives on how 1920s quantum physics views location and motion — position x and momentum p.

1. There is a perfect symmetry between position and momentum (today’s post)
2. There is a profound asymmetry between position and momentum (next post)

Despite all the symmetry, the asymmetry turns out to be essential, and we’ll see (in the next post) that it implies particles of definite momentum can exist, but particles of definite position cannot… not in 1920s quantum physics, anyway.

The Symmetry Between Location and Motion

The idea of a symmetry between location and motion may seem pretty weird at first. After all, isn’t motion the change in something’s location? Obviously the reverse is not generally true: location is not the change in something’s motion! Instead, the change in an object’s motion is called its “acceleration” (a physics word that includes what in English we’d call acceleration, deceleration and turning.) In what sense are location and motion partners?

The Uncertainty Principle of Werner Heisenberg

In a 19th century reformulation of Newton’s laws of motion that was introduced by William Rowan Hamilton — keeping the same predictions, but rewriting the math in a new way — there is a fundamental symmetry between position x and momentum p. This way of looking at things is carried on into quantum physics, where we find it expressed most succinctly through Heisenberg’s uncertainty principle, which specifically tells us that we cannot know a object’s position and momentum simultaneously.

This might sound vague, but Heisenberg made his principle very precise. Let’s express our uncertainty in the object’s position as Δx. (Heisenberg defined this as the average value of x2 minus the squared average value of x. Less technically, it means that if we think the particle is probably at a position x0, an uncertainty of Δx means that the particle has a 95% chance of being found anywhere between x0-2Δx and x0+2Δx.) Let’s similarly express our uncertainty about the object’s momentum (which, again, is naively its speed times its mass) as Δp. Then in 1920s quantum physics, it is always true that

• Δp Δx > h / (4π)

where h is Planck’s constant, the mascot of all things quantum. In other words, if we know our uncertainty on an object’s position Δx, then the uncertainty on its momentum cannot be smaller than a minimum amount:

• Δp > h / (4π Δx) .

Thus, the better we know an object’s position, implying a smaller Δx, the less we can know about the object’s momentum — and vice versa.

This can be taken to extremes:,

• if we knew an object’s motion perfectly — if Δp is zero — then Δx = h / (4π Δp) = infinity, in which case we have no idea where the particle might be
• if we knew an object’s location perfectly — if Δx is zero — then Δp = h / (4π Δx) = infinity, in which case we have no idea where or how fast the particle might be going.

You see everything is perfectly symmetric: the more I know about the object’s location, the less I can know about its motion, and vice versa.

(Note: My knowledge can always be worse. If I’ve done a sloppy measurement, I could be very uncertain about the object’s location and very uncertain about its location. The uncertainty principle contains a greater-than sign (>), not an equals sign. But I can never be very certain about both at the same time.)

An Object with Known Motion

What does it mean for an object to have zero uncertainty in its position or its motion? Quantum physics of the 1920s asserts that any system is described by a wave function that tells us the probability for where we might find it and what it might be doing. So let’s ask: what form must a wave function take to describe a single particle with perfectly known momentum p?

The physical state corresponding to a single particle with perfectly known momentum P0 , which is often denoted |P0>, has a wave function

times an overall constant which we don’t have to care about. Notice the ; this is a complex number at each position x. I’ve plotted the real and imaginary parts of this function in Fig. 1 below. As you see, both the real (red) and imaginary (blue) parts look like a simple wave, of infinite extent and of constant wavelength and height.

Figure 1: In red and blue, the real and imaginary parts of the wave function describing a particle of known momentum (up to an overall constant). In black is the square of the wave function, showing that the particle has equal probability to be at each possible location.

Now, what do we learn from the wave function about where this object is located? The probability for finding the object at a particular position X is given by the absolute value of the wave function squared. Recall that if I have any complex number z = x + i y, then its absolute value squared |z2| equals |x2|+|y2|. Therefore the probability to be at X is proportional to

(again multiplied by an overall constant.) Notice, as shown by the black line in Fig. 1, this is the same no matter what X is, which means the object has an equal probability to be at any location we choose. And so, we have absolutely no idea of where it is; as far as we’re concerned, its position is completely random.

An Object with Known Location

As symmetry requires, we can do the same for a single object with perfectly known position X0. The corresponding physical state, denoted |X0>, has a wave function

again times an overall constant. Physicists call this a “delta function”, but it’s just an infinitely narrow spike of some sort. I’ve plotted something like it in Figure 2, but you should imagine it being infinitely thin and infinitely high, which obviously I can’t actually draw.

This wave function tells us that the probability that the object is at any point other than X0 is equal to zero. You might think the probability of it being at X0 is infinity squared, but the math is clever and the probability that it is at X0 is exactly 1. So if the particle is in the physical state |X0>, we know exactly where it is: it’s at position X0.

Figure 2: The wave function describing a particle of known position (up to an overall constant). The square of the wave function is in black, showing that the particle has zero probability to be anywhere except at the spike. The real and imaginary parts (in red and blue) are mostly covered by the black line.

What do we know about its motion? Well, we saw in Fig. 1 that to know an object’s momentum perfectly, its wave function should be a spread-out, simple wave with a constant wavelength. This giant spike, however, is as different from nice simple waves as it could possibly be. So |X0> is a state in which the momentum of the particle, and thus its motion, is completely unknown. [To prove this vague argument using math, we would use a Fourier transform; we’ll get more insight into this in a later post.]

So we have two functions, as different from each other as they could possibly be,

• Fig. 1 describing an object with a definite momentum and completely unknown position, and
• Fig. 2 describing an object with definite position and completely unknown momentum.

CAUTION: We might be tempted to think: “oh, Fig. 1 is the wave, and Fig. 2 is the particle”. Indeed the pictures make this very tempting! But no. In both cases, we are looking at the shape of a wave function that describes where an object, perhaps a particle, is located. When people talk about an electron being both wave and particle, they’re not simply referring to the relation between momentum states and position states; there’s more to it than that.

CAUTION 2: Do not identify the wave function with the particle it describes!!! It is not true that each particle has its own wave function. Instead, if there were two particles, there would still be only one wave function, describing the pair of particles. See this post and this one for more discussion of this crucial point.

Objects with More or Less Uncertainty

We can gain some additional intuition for this by stepping back from our extreme |P0> and |X0> states, and looking instead at compromise states that lie somewhere between the extremes. In these states, neither p nor x is precisely known, but the uncertainty of one is as small as it can be given the uncertainty of the other. These special states are often called “Gaussian wave packets”, and they are ideal for showing us how Heisenberg’s uncertainty principle plays out.

In Fig. 3 I’ve shown a wave function for a particle whose position is poorly known but whose momentum is better known. This wave function looks like a trimmed version of the |P0> state of Fig. 1, and indeed the momentum of the particle won’t be too far from P0. The position is clearly centered to the right of the vertical axis, but it has a large probability to be on the left side, too. So in this state, Δp is small and Δx is large.

Figure 3: A wave function similar to that of Fig. 1, describing a particle that has an almost definite momentum and a rather uncertain position.

In Fig. 4 I’ve shown a wave function of a wave packet that has the situation reversed: its position is well known and its momentum is not. It looks like a smeared out version of the |X0> state in Fig. 2, and so the particle is most likely located quite close to X0. We can see the wave function shows some wavelike behavior, however, indicating the particle’s momentum isn’t completely unknown; nevertheless, it differs greatly from the simple wave in Fig. 1, so the momentum is pretty uncertain. So here, Δx is small and Δp is large.

Figure 4: A wave function similar to that of Fig. 2, describing a particle that has an almost definite position and a highly uncertain momentum.

In this way we can interpolate however we like between Figs. 1 and 2, getting whatever uncertainty we want on momentum and position as long as they are consistent with Heisenberg’s uncertainty relation.

Wave functions in the space of possible momenta There’s even another more profound, but somewhat more technical, way to see the symmetry in action; click here if you are interested.

As I’ve emphasized recently (and less recently), the wave function of a system exists in the space of possibilities for that system. So far I’ve been expressing this particle’s wave function as a space of possibilities for the particle’s location — in other words, I’ve been writing it, and depicting it in Figs. 1 and 2, as Ψ(x). Doing so makes it more obvious what the probabilities are for where the particle might be located, but to understand what this function means for what the particle’s motion takes some reasoning.

But I could instead (thanks to the symmetry between position and momentum) write the wave function in the space of possibilities for the particle’s motion! In other words, I can take the state |P0>, in which the particle has definite momentum, and write it either as Ψ(x), shown in Fig. 1, or as Ψ(p), shown in Fig. 1a.

Figure 1a: The wave function of Fig. 1, written in the space of possibilities of momenta instead of the space of possibilities of position; i.e., the horizontal axis show the particle’s momentum p, not its position x as is the case in Figs. 1 and 2. This shows the particle’s momentum is definitely known. Compare this with Fig. 2, showing a different wave function in which the particle’s position is definitely known.

Remarkably, Fig. 1a looks just like Fig. 2 — except for one crucial thing. In Fig. 2, the horizontal axis is the particle’s position. In Fig. 1a, however, the horizontal axis is the particle’s momentum — and so while Fig. 2 shows a wave function for a particle with definite position, Fig. 1a shows a wave function for a particle with definite momentum, the same wave function as in Fig. 1.

We can similarly write the wave function of Fig. 2 in the space of possibilities for the particle’s position, and not surprisingly, the resulting Fig. 2a looks just like Fig. 1, except that its horizontal axis represents p, and so in this case we have no idea what the particle’s momentum is — neither the particle’s speed nor its direction.

Fig. 2a: As in Fig. 1a, the wave function in Fig. 2 written in terms of the particle’s momentum p.

The relationship between Fig. 1 and Fig. 1a is that each is the Fourier transform of the other [where the momentum is related to the inverse wavelength of the wave obtained in the transform.] Similarly, Figs. 2 and 2a are each other’s Fourier transforms.

In short, the wave function for the state |P0> (as a function of position) in Fig. 1 looks just like the wave function for the state |X0> (as a function of momentum) in Fig. 2a, and a similar relation holds for Figs. 2 and 1a. Everything is symmetric!

The Symmetry and the Particle…

So, what’s this all got to do with electrons and other elementary particles? Well, if a “particle” is really and truly a particle, an object of infinitesimal size, then we certainly ought to be able to put it, or at least imagine it, in a position state like |X0>, in which its position is clearly X0 with no uncertainty. Otherwise how could we ever even tell if its size is infinitesimal? (This is admittedly a bit glib, but the rough edges to this argument won’t matter in the end.)

That’s where this symmetry inherent in 1920s quantum physics comes in. We do in fact see states of near-definite momentum — of near-definite motion. We can create them pretty easily, for instance in narrow electron beams, where the electrons have been steered by electric and magnetic fields so they have very precisely defined momentum. Making position states is trickier, but it would seem they must exist, thanks to the symmetry of momentum and position.

But they don’t. And that’s thanks to a crucial asymmetry between location and motion that we’ll explore next time.