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Today’s Jesus and Mo strip, called “whip,” came with the note, “You shouldn’t flip tables, Jesus.” It’s about as scathing an indictment of Islamism that I’ve seen in this strip. Mo, of course, is as clueless as ever.

Got clear skies this weekend? If clouds cooperate, observers in the North Atlantic and surrounding regions may witness a rare spectacle: a partial solar eclipse. This is the second eclipse of 2025, and bookends the first eclipse season of the year. The season started with March 14th total lunar eclipse. Depending where you are observing from, this is a shallow to a deep partial, ‘almost’ total solar eclipse.

Reader Mark Otten sent in some lovely photos taken by his wife Dianne. Mark’s (or Dianne’s) IDs are indented, and you can enlarge the photos by clicking on them.

These photos were taken by Dianne over the last 3 years in various locations in the greater Cincinnati, Ohio area.

Great blue heron (Ardea herodias) in a rock divide between two constructed ponds.

Female northern flicker (Colaptes auratus) showing the brightly-colored underside of the tail feathers typical of the eastern “yellow-shafted” form:

Spotted sandpiper (Actitis macularius):

Yellow-billed cuckoo (Coccyzus americanus):

In July, 2023 a limpkin (Aramus guarauna), normally resident in Florida, the Caribbean, and Central and South America, showed up at a county park in the northern suburbs of Cincinnati.  It stayed around for about 2 weeks causing quite a stir among local birders.  Limpkins feed mostly on freshwater snails and mussels:

This female killdeer (Charadrius vociferus) and her mate used an existing ring of rocks along the margin of a walking path to make their nest.  Her four eggs are visible directly below her:

A killdeer chick a few days after hatching:

Male American kestrel (Falco sparverius):

The same kestrel a few minutes later with a grasshopper meal:

In 1979 there were only 4 confirmed nesting pairs of bald eagles (Haliaeetus leucocephalus) in Ohio, all of them along Lake Erie. Eagles have since become a familiar sight in many locations.  A 2020 survey by the Ohio Department of Natural Resources recorded more than 700 eagle nests throughout the state.  This one, and its mate, have been nesting in a county park (about 11 miles north of downtown Cincinnati) for the last several years:

A family of red foxes (Vulpes vulpes) denned under the porch of a nearby church in 2022.  We were able to observe and photograph the adults and pups over several evenings.

One of the adult foxes with a light snack.  I’m not sure of the species, maybe a mockingbird:

There were at least 4 pups.  These 3 were playing in the lawn in front of the church:

We first observed this piebald white-tailed deer (Odocoileus virginianus) fawn in June, 2023 but were not able to get a good photo until late July.  The fawn was observed off and on until November, 2023.  We have not seen it since:

Piebald white-tailed deer fawn and (presumably) its sibling”

The focus is all on the Moon at the moment as we strive to establish a permanent lunar base. At the south polar region there are permanently shadowed craters protecting pockets of water ice. Korea’s Pathfinder Lunar Orbiter (KPLO) has been capturing images of these craters using its ShadowCam instrument. Now, using that data, planetary scientists are using a machine learning algorithm to identify over a billion impact craters in the region, deep inside the shadowed craters and each is at least 16 metres in diameter.

In my last post and the previous one, I put one or two particles in various sorts of quantum superpositions, and claimed that some cases display quantum interference and some do not. Today we’ll start looking at these examples in detail to see why interference does or does not occur. We’ll also encounter a difficulty asking where the interference occurs — a difficulty which will lead us eventually to deeper understanding.

First, a lightning review of interference for one particle. Take a single particle in a superposition that gives it equal probability of being right of center and moving to the left OR being left of center and moving to the right. Its wave function is given in Fig. 1.

Figure 1: The wave function of a single particle in a superposition of moving left from the right OR moving right from the left. The black curve represents the absolute-value-squared of the wave function, which gives the probability of finding the particle at that location. Red and blue curves show the wave function’s real and imaginary parts.

Then, at the moment and location where the two peaks in the wave function cross, a strong interference effect is observed, the same sort as is seen in the famous double slit-experiment.

Figure 2: A closeup of the interference pattern that occurs at the moment when the two peaks in Fig. 1 perfectly overlap. An animation is shown here.

The simplest way to analyze this is to approach it as a 19th century physicist might have done. In this pre-quantum version of the problem, shown in Fig. 3, the particle has a definite location and speed (and no wave function), with

• a 50 percent chance of being left of center and moving right, and
• a 50 percent chance of being right of center and moving left.

Figure 3: A pre-quantum view of Fig. 1, showing a single particle with equal probability of moving right or moving left. The particle will reach x=0 in both possibilities at the same time, but in pre-quantum physics, nothing special happens then.

Nothing interesting, in either possibility, happens when the particle reaches the center. Either it reaches the center from the left and keeps on going OR it reaches the center from the right and keeps on going. There is certainly no collision, and, in pre-quantum physics, there is also no interference effect.

Still, something abstractly interesting happens there. Before the particle reaches the center, the top and bottom of Fig. 3 are different. But just when the particle is at x=0, the two possibilities in the superposition describe the same object in the same place. In a sense, the two possibilities meet. In the corresponding quantum problem, this is the precise moment where the quantum interference effect is largest. That is a clue.

Two Particles, Two Orderings

So now let’s look in Fig. 4 at the example that I gave as a puzzle, a sort of doubling of the single particle example in Fig. 1.

Figure 4: Two particles in a superposition of moving left or moving right — a sort of doubling of Fig. 3.

Here we have two particles moving from left to right OR from right to left, with 50% probability for each of the two possibilities. I haven’t drawn the corresponding quantum wave function for this yet, but I will in a moment.

We might think something interesting would happen when particle 1 reaches x=0 in both possibilities (Fig. 5a), just as something interesting happens when the particle in Figs. 1-3 reaches x=0 in both of its possibilities. But in fact, there is no interference. Nor does anything interesting happen when the blue particle at the top and the orange particle at the bottom arrive at x=1 (Fig. 5b). Similarly, no interference happens when particle 2 reaches x=0 in both possibilities (Fig. 5c). These “events” are really non-events, as far as quantum physics is concerned. Why is this?

Figure 5a: After the two particles in Fig. 4 have moved slightly, the blue particle is at the same point in both halves of the superposition. Yet in the quantum version of this picture, no interference occurs. Figure 5b: As in Fig. 5a, but slightly later; again no interference occurs. Figure 5c: As in Fig. 5a; yet again there is no quantum interference. The Puzzle’s Puzzling Lack of Interference

To understand why interference never occurs in this case, we have to look at the system’s wave function and how it evolves with time.

Before we start, let’s make sure we avoid a couple of misconceptions:

• First, we don’t have two wave functions (one for each particle);
• Second, the wave function is not defined on physical space (the x axis).

Instead we have a single wave function Ψ(x1,x2), defined on the space of possibilities, which has an x1-axis, (which I will draw horizontal), giving the position of particle 1 (the blue one), and an x2 axis (which I will draw vertical) giving the position of particle 2 (the orange one). The square of the wave function’s absolute value at a specific possibility (x1,x2) tells us the probability of simultaneously finding particle 1 at position x1 and particle 2 at position x2.

In Fig. 6, I have shown the absolute-value-squared of the initial wave function, corresponding to Fig. 4.

Figure 6: Graph of the squared absolute value of the initial wave function, |Ψ(x1,x2)|2, corresponding to Fig. 4. The function is shown dark where it is large and white where it is very small. The two peaks are located at (x1,x2)=(-1,-3) and at (x1,x2)=(+1,+3).

In the first possibility in Fig. 4, we have x1=-1 and x2=-3. One peak of the wave function is located at that position, at lower left in Fig. 6. The other peak of Fig. 6, corresponding to the second possibility in Fig. 4, is located at the position x1=+1 and x2=+3, exactly opposite the first peak.

Fig. 7 now shows the exact solution to the Schrodinger equation, which shows how the wave function of Fig. 6 evolves with time.

Figure 7: How the wave function starting from Fig. 6 evolves over time; there is no interference.

What do we see? The two peaks move generally toward each other, but they miss. They never overlap, so they cannot interfere. This is what makes this case different from Fig. 1; the wave function’s peaks in Fig. 1 do meet, and that is why they interfere.

Why, conceptually speaking, do the two peaks miss? We can understand this using the pre-quantum method, drawing the system not in physical space, as in Fig. 4, but in the space of possibilities. The top possibility in Fig. 4 first puts the system at the star in Fig. 8a, moving up and to the right over time. Because the two particles have equal speeds, every change in x1 is matched with an equal change in x2, which means the star moves on a line whose slope is 1 (i.e. it makes a 45 degree angle to the horizontal.) Similarly, the bottom possibility puts the system at the star in Fig. 8b, moving down and to the left.

Figure 8a: In the space of possibilities, the pre-quantum system in the top possibility of Fig. 4 is initially located at the star, and changes with time by moving along the arrow. Figure 8b: Same as Fig. 8a, but for the bottom possibility in Fig. 4.

If the two stars ever did find themselves at the same point, then what is happening in the first possibility would be exactly the same as what is happening in the second possibility. In other words, the two possibilities would cross paths. But this does not happen here; the paths of the stars do not intersect, reflecting the fact that the top possibility and bottom possibility in Fig. 4 never look the same at any time.

Quantum physics combines these two pre-quantum possibilities into the single wave function of Fig. 7. The two peaks follow the arrows of Figs. 8a and 8b, and so they never overlap.

The three (non-)events shown in Figs. 5a-5c above correspond to the following:

• At the time of Fig. 5a, the two peaks in Fig. 7 are on the same vertical line (they have the same x1)
• At the time of Fig. 5b, the two peaks are aligned along the diagonal from lower right to upper left.
• At the time of Fig. 5c, the two peaks are on the same horizontal line (they have the same x2).

The Flipped Order

Let’s now compare this with the next example I gave you in my previous post. It is much like Fig. 4, except that in the second possibility we switch the two particles.

Figure 9: As in Fig. 4, except with the two particles switching places in the bottom part of the superposition.

This case does have interference. How can we see this?

The top possibility is unaltered, and so Fig. 10a is the same as Fig. 8a. But in Fig. 10b, things have changed; the star that was at x1=+1 and x2=+3 in Fig. 8b is now moved to the point x1=+3 and x2=+1. The corresponding arrow, however, still points in the same direction, since the particles’ motions are the same as before (toward more negative x1 and x2.)

Figure 10a: Same as Fig. 8a, except with the point (x1,x2)=(+1,-1) circled. Figure 10b: A new version of Fig. 8b with particles 1 and 2 having switched places. The system now reaches the circled point (x1,x2)=(+1,-1) at the same moment that it does in Fig.10a.

Now the two arrows do cross paths, and the stars meet at the circled location. At that moment, the pre-quantum system appears in physical space as shown in Fig. 11.

Fig. 11: Quantum interference occurs when, in the pre-quantum analogue, the two possibilities put all their particles in the same place.

In both possibilities, the two particles are in the same locations. And so, in the quantum wave function, the two peaks will cross paths and overlap one another, causing interference. The exact wave function is shown in Fig. 12, and its peaks move just like the stars in Fig. 10a-10b, resulting in a striking interference pattern.

Figure 12: The wave function corresponding to Figs. 9-11, showing interference when the peaks overlap. Profound Lessons

What are the lessons that we can draw from this pair of examples?

First, quantum interference occurs in the space of possibilities, not in physical space. It has effects that can be observed in physical space, but we will not be able to visualize or comprehend the interference effect completely using only physical space, whose coordinate in this case is simply x. If we try, we will lose some of its essence. The full effect is only understandable using the space of possibilities, here two-dimensional and spanned by x1 and x2. (In somewhat the same way, we cannot learn the full three-dimensional layout of a room having only a photograph; some information about the room can be inferred, but some part is inevitably lost.)

Second, starting from a pre-quantum point of view, we see that quantum interference is expected when the pre-quantum paths of two or more possibilities intersect. As an exercise, go back to the last post where I gave you multiple examples. In every case with interference, this intersection happens: there is a moment where the top possibility looks exactly like the bottom possibility, as in Fig. 11.

Third, quantum interference is generally not about a particle interfering with itself — or at least, if we try to use that language, we can’t explain when interference does and doesn’t happen. At best, we might say that the system of two particles is interfering with itself — or fails to interfere with itself — based on its peaks, their motions and their potential intersections in the space of possibilities. When the system consists of only one particle, it’s easy to confuse these two notions, because the system interfering looks the same as the particle interfering. More generally, it is very easy to be misled when the space of possibilities has the same number of dimensions as the relevant physical space. But with two or more particles, this confusion is eliminated. For significant interference to occur, at least two possibilities in a superposition must align perfectly, with each and every particle in matching locations. Whether this is possible or not depends on the superposition’s details.

How Do We Observe the Interference?

But now let’s raise the following question. When there is interference, “where” is it? We can see where it is in the space of possibilities; it’s clear as day in Fig. 12. But you and I live in physical space. If quantum interference is really about interfering waves, just like those of water or sound, then the interference pattern should be located somewhere, shouldn’t it? Where is it?

Well, here’s something to think about. The double-slit-like interference pattern in Fig. 2, for one particle in a superposition, produces a real, observable effect just like that of the double-slit experiment. In Fig. 12 we see a similar case at the moment where wave function’s two peaks overlap. How can we observe this interference effect?

An obvious first guess is to measure the position of one of the particles. The result of doing so for particle 1, and repeating the whole experiment many times (just as we always do for the double-slit experiment) is shown in Fig. 13.

Figure 13: If we measure the position of particle 1 at the moment of maximum interference in Fig. 12, and repeat the experiment many times, we will see random dots centered near x=+1, with no interference pattern. (Each new measurement is an orange dot; previous measurements are blue dots.)

There are no interference peaks and valleys at all, in contrast to the case of Fig. 1, which we examined here (in that post’s Fig. 8). Particle 1 always shows up near x1=+1, which is its location where the two peaks intersect (see Figs. 10-12). No interesting structure within or around that peak is observed.

Not surprisingly, if we do the same thing for particle 2, we find the same sort of thing. No interference features appear; there’s just a blob near its pre-quantum location in Fig. 11, x2=-1.

And yet, the quantum interference is plain to see in Fig. 12. If we can’t observe it by measuring either particle’s position, what other options do we have? Where — if anywhere — will we find it? Is it actually observable, or is it just an abstraction?

If you are already tired of hearing about RFK Jr. being the Secretary of Health and Human Services (HHS), buckle in. I get it – it can be exhausting. Don’t we already know everything we need to about what a medical crank he is? While SBM will not neglect the many topics that we cover, we certainly consider it a high priority […]

The post David Geier Hired to Study Vaccines and Autism first appeared on Science-Based Medicine.

Masaki Kashiwara has won the 2025 Abel prize, seen by some as the Nobel of mathematics, for his contributions to algebraic analysis and representation theory

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Interferometers, devices that can modulate aspects of light, play the important role of modulating and switching light signals in fiber-optic communications networks and are frequently used for gas sensing and optical computing. Now, applied physicists have invented a new type of interferometer that allows precise control of light's frequency, intensity and mode in one compact package.

A species of houndshark called Mustelus lenticulatus makes sharp clicking noises when handled. Until now, sharks as a group were thought to be universally quiet

Women with premenstrual syndrome reported big improvements in their symptoms after taking placebo pills, despite knowing they did not contain any active ingredients

What happens when you mix clouds of gas and dust, strong outflows, and energetic shock waves at the core of the Milky Way Galaxy? Space tornadoes. At least, that's how researchers using the Atacama Large Millimeter Array in Chile to study the galaxy's heart described what they found.

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The James Webb Space Telescope has given us a view of the earliest moments of galaxy formation in the Universe. It's also revealed a few surprises. One of these is the appearance of small, highly redshifted objects nicknamed "little red dots (LRDs)." We aren't entirely sure what they are, but a new study points to an answer.