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New research shows that Sat Nav systems are helping keep older drivers on the roads for longer. The study reveals that over 65s with a poorer sense of direction rely more on help from GPS navigation systems such as Sat Nav or smartphone maps. Those using GPS tended to drive more frequently -- suggesting that the technology helps older people maintain driving independence.

To the uninitiated, astronomers' interest in ancient black holes might seem like an obsession. Why spend so much time, energy, and resources looking back billions of years just to detect the nearly undetectable? They do it because ancient black holes hold unique clues to understanding the modern Universe.

Ancient humans living in what is now Ukraine 400,000 years ago may have practised or taught tool-making techniques using mammoth tusks, a softer material than bone

A widely used artificial sweetener increases brain activity in regions involved in appetite, suggesting it makes people hungrier

As everyone knows, I adhere to the gametic definition of sex, in which individuals are classified as male or female (or, as in hermaphroditic plants, both sexes in one individual) based on whether their bodies are set up to produce small, mobile gametes (the “males”) or large, immobile gametes (the “females”).  I’ve explained why I adhere to this definition, because it is not only universal in animals and vascular plants, but also because the difference between males and females in investment in gametes, which leads in general to females having a greater overall investment in reproduction, explains a lot of puzzles in evolution. One of them is why sexual selection creates males and females who are often so different in color, size, weaponry, and so on. Just remember: universality and utility.

Here’s a more formal definition given by Colin Wright write in his new post on his website, Reality’s Last Stand.

In biology, the definition of male and female has never been arbitrary or culturally relative. It is grounded in the concept of anisogamy: the existence of two distinct types of gametes—sperm and ova. This fundamental reproductive asymmetry defines the two sexes across all sexually reproducing anisogamous species. An individual that has the function to produce small, motile gametes (sperm) is male; one that has the function to produce large, immobile gametes (ova) is female. This is not a social construct or a philosophical preference—it is a basic principle of evolutionary biology, established long before today’s cultural debates.

Now of course this definition wasn’t pulled out of thin air: it is an a posteriori conclusion about how nature is set up. It is a truth that all animals and vascular plants have only two sexes, male and female, though in some species, as I said, individuals can be of both sexes. (And some individuals, like clownfish, can change their gametic sex.) But there is no third sex, no matter how hard the ideologues squeal about seahorses, clownfish, and hyenas. There is no third type of gamete in any species.  In fact, the opposition to the binary nature of sex by gender ideologues have led some of them to argue that the gametic definition of sex is a recent confection sneakily devised by “transphobic” biologists who want to shoehorn all people (and animals and plants, apparently) into two categories. Colin wrote the piece below to show that this claim is false. The gametic definition has been around for about 140 years.

Click on the screenshot below to read the piece (Colin’s bolding).

Now I make no claim that the gametic definition of sex is universal among evolutionary biologists, much less all biologists. I haven’t taken a poll! But the biologists I’ve encountered in my own field almost universally adhere to that definition. At any rate, Colin goes way back in the past to show a passel of biologists (I know many of the more recent ones) who adhere to and have presented the gametic definition of sex. As Colin says:

The historical and scientific record is clear: from the 19th century to the present day, biologists, medical professionals, philosophers of science, and evolutionary theorists have used gamete type as the defining criterion for sex. This document compiles citations from that record, providing a reference point for students, scientists, educators, and anyone interested in understanding what “male” and “female” mean in biological terms.

These citations span more than a century of scientific literature, showing that the gamete-based definition of sex is not a recent invention or a reactionary response, but a longstanding, fundamental biological principle. While sex roles and secondary sex characteristics can vary, the definition of the sexes does not: male and female are reproductive categories rooted in the type of gamete an individual has the function to produce.

This document is a work in progress. If you are aware of additional scholarly references—especially historical ones—that clearly depict the gametic definition of sex, please share them in the comments so I can continue to expand and improve this resource. I encourage readers to bookmark this page and return to it often as a reference in conversations, research, and advocacy.]]

I think I sent him the Futuyma reference (not below), but I can’t remember. At any rate, you can read them all yourself, but I’ll put up five of them spaced apart, starting with the first one in 1888. These are from Colin’s piece:

1888 – Charles Sedgwick Minot. “Sex,” in A Reference Handbook of the Medical Sciences Embracing the Entire Range of Scientific and Practical Medicine and Allied Science, Vol. 6, Alfred H. Buck (ed.) (New York: William Wood and Company), 436-438

As evolution continued hermaphroditism was replaced by a new differentiation, in consequence of which the individuals of a species were, some, capable of producing ova only; others of producing spermatozoa only. Individuals of the former kind we call females, of the latter males, and they are said to have sex.

1929 – Horatio Hackett Newman. Outlines of General Zoölogy (New York, The Macmillan Company), p. 448.

Any individual, then, is sexual if it produces gametes—ova or spermatozoa, or their equivalents. Thus we would be justified in calling any individual that produces ova a female, and one that produces spermatozoa a male. One that produces both kinds of gametes is a male-female or, more technically, a HERMAPHRODITE. Thus we may say that the PRIMARY SEXUAL CHARACTERS of individuals are the ova or the spermatozoa, and that maleness or femaleness is determined by the possession of one or other of these two types of gametes.

A ringer: Simone de Beauvoir!

1949 – de Beauvoir, Simone. The Second Sex, translated by H.M. Parshley (New York: Vintage Books), 39

In the vast majority of species male and female individuals co-operate in reproduction. They are defined primarily as male and female by the gametes which they produce—sperms and eggs respectively.

2013 – Roughgarden, Joan. Evolution’s Rainbow: Diversity, Gender, and Sexuality in Nature and People. University of California Press. [Note: Roughgarden is a trans-identifying male]

To a biologist, “male” means making small gametes and “female” means making large gametes. Period! By definition, the smaller of the two gametes is called a sperm, and the larger an egg. Beyond gamete size, biologists don’t recognize any other universal difference between male and female.

2021 – Bhargava, Aditi, et al. “Considering sex as a biological variable in basic and clinical studies: an endocrine society scientific statement.” Endocrine Reviews 42.3: 219-258.

The classical biological definition of the 2 sexes is that females have ovaries and make larger female gametes (eggs), whereas males have testes and make smaller male gametes (sperm); the 2 gametes fertilize to form the zygote, which has the potential to become a new individual. The advantage of this simple definition is first that it can be applied universally to any species of sexually reproducing organism. Second, it is a bedrock concept of evolution, because selection of traits may differ in the 2 sexes. Thirdly, the definition can be extended to the ovaries and testes, and in this way the categories—female and male—can be applied also to individuals who have gonads but do not make gametes.

So much for those chowderheads who say that, using the gametic definition, neither a pre-puberty human, a postmenopausal woman, or a sterile person can be male or female. If you see this argument, you know you’re dealing with someone who’s intellectually dishonest.

Again, this is not a vote to see how many biologists (or feminists!) would define biological sex. It is meant, as Colin said, to show that the gametic definition of sex has been around for well over a hundred years.

Overheating batteries are a serious risk, in the worst cases leading to fires and explosion. A team has now developed a simple, cost-effective method to test the safety of lithium-ion batteries, which opens up opportunities for research into new and safer batteries for the future. The researchers created an intentionally unstable battery which is more sensitive to changes that could cause overheating. The battery is one-fiftieth the size of conventional batteries, so is less resource intensive and tests can be carried out in a smaller lab environment.

A genomic study of hydrogen-producing bacteria has revealed entirely new gene clusters capable of producing large volumes of hydrogen.

Scientists have developed an AI-powered fluid simulation model that significantly reduces computation time while maintaining accuracy. Their approach could aid offshore power generation, ship design and ocean monitoring.

A unique carbon capture technology could offer a more cost-effective way to remove carbon dioxide (CO2) from the air and turn it into clean, synthetic fuel.

Imagine a world where industrial waste isn't just reduced, it's turned into something useful. This kind of circular economy is already in the works for carbon. Now, researchers in energy, environmental & chemical engineering at Washington University in St. Louis have developed a promising pathway to convert harmful nitric oxide, a key component of acid rain, into valuable nitric acid, which is used in everyday applications from fertilizer production to metal processing. The new approach converts nitrogen waste into valuable chemical product.

A new method to recycle wind turbine blades without using harsh chemicals resulted in the recovery of high-strength glass fibers and resins that allowed researchers to re-purpose the materials to create stronger plastics. The innovation provides a simple and environmentally friendly way to recycle wind turbine blades to create useful products.

A solar wind event from 2017 that hit Jupiter and compressed its magnetosphere created a hot region spanning half Jupiter's circumference.

Researchers have expanded the potential of carbon capture technology that plucks CO2 directly from the air by demonstrating that there are multiple suitable and abundant materials that can facilitate direct air capture. Researchers present new, lower-cost materials to facilitate moisture-swing to catch and then release CO2 depending on the local air's moisture content, calling it 'one of the most promising approaches for CO2 capture.'

The same dirt that clings to astronauts' boots may one day keep their lights on. Researchers created solar cells made out of simulated Moon dust. The cells convert sunlight into energy efficiently, withstand radiation damage, and mitigate the need for transporting heavy materials into space, offering a potential solution to one of space exploration's biggest challenges: reliable energy sources.

The same dirt that clings to astronauts' boots may one day keep their lights on. Researchers created solar cells made out of simulated Moon dust. The cells convert sunlight into energy efficiently, withstand radiation damage, and mitigate the need for transporting heavy materials into space, offering a potential solution to one of space exploration's biggest challenges: reliable energy sources.

An innovative proposal would be a first for planetary exploration. Turns out, it’s as tough to drop inward into the inner solar system, as it is to head outward. The problem stems from losing momentum from a launch starting point on Earth. It can take missions several years and planetary flybys before capture and arrival in orbit around Mercury or Venus. Now, a new proposal would see a mission make the trip, using innovative and fuel efficient means.

Researchers used a synthetic version of moon dust to build working solar panels, which could eventually be created within – and used to power – a moon base of the future

Several months ago I reported, based on articles from sources like New York Magazine, that Pamala Paul, heterodox New York Times columnist, was leaving the paper’s op-ed section, and the paper altogether. I was upset to hear that, for although she didn’t toe the paper’s “progressive” line, her columns were thoughtful and liberal.  Here’s the New York Magazine article (click headline to read):

The article was a bit ambiguous, as it implied that Paul’s ideas, which ran contrary to the NYT’s progressive op-ed aura, were the cause of her getting the pink slip. But the NYT also denied that. From the piece above:

Paul is admired by some of her colleagues for her willingness to buck liberal-left conventional wisdom. She has written a defense of J.K. Rowling and scrutinized the MeToo movement for overreach, while a recent column criticized the American Historical Society’s vote to condemn the ongoing “scholasticide” in Gaza. But others have said she does little more than produce rage bait, with what one Times staffer referred to as “intellectually lazy” positions. “It is a rarity inside the Times for someone to manage to make enemies on every desk they touch; Pamela is indeed a rarity,” one newsroom employee said. “She should have spent time making allies if she was going to be as divisive a figure as she was internally. But she didn’t put the time in there, or at least did not have the interest.”

I’m told, however, that Opinion’s decision to part ways with her is not because of her ideological positions. [Opinion editor Kathleen] Kingsbury said, “We don’t discuss personnel matters, but any insinuation I make staffing or editorial decisions based solely on political viewpoints is false.”

It’s really offensive to ask a heterodox columnist to suck up to her colleagues so they wouldn’t criticize her pieces. But that’s how the NYT rolls, and it’s the reason why Bari Weiss, among others, also left the paper. And note the weasel word “solely” in Kingsbury’s quote above.

For nine years (2013-2022), Paul was editor of the paper’s Book Review section, and then three years ago she moved to op-ed. I saw immediately that her columns were bucking the paper’s own ideology, and I believe I predicted (or at least worried) that she’d be fired for heterodoxy.  Nevertheless, I discussed her pieces often (she was liberal and thoughtful but not “progressive”), and, when I heard her head was on the chopping block, I compiled a list of the columns that were likely to have irritated the top op-ed editors. Here’s a bunch of screenshots:

Despite the announcements by other venues, up to now Paul hasn’t said a word about her leaving, and her columns still appeared in the paper—though less often. Today, though, she verified the rumors by writing her farewell column, which you can read by clicking the headline below or seeing it archived here.  And it’s clear from what she writes that she parted ways with the paper over her ideology and determination to tell the truth as she saw it. The NYT doesn’t like the truth if it doesn’t comport with “progressivism”.

A few quotes from Paul’s piece (indented). They lead me to believe that yes, she’s leaving because of what she wrote about and said.

This is my final column for The Times.

In the memo I wrote three years ago when applying for this job after 11 years at The Times Book Review, I vowed “to write to Times readers rather than to Twitter or to Slack.” I knew my positions, fundamentally liberal but often at odds with what had become illiberal progressive dogma, would ruffle feathers. But as I explained, “I want to write about that vast center/liberal space and to address what people really think and believe but are often too afraid to say.”

. . . I wasn’t looking to be loved or even liked. I had friends and family for that. I wanted to write what I believed to be the truth, based on facts and guided by fairness, but never driven by fear.

She lists some topics that, I’m guessing, the NYT probably wasn’t keen on:

But the reporting I’m most proud of is when I used my voice to stand up for people whose lives or work had come under attack, whether they were public figures or were dragged into the public eye because they’d dared to speak or act in ways that unjustly elicited professional or social condemnation: A popular novelist ostracized for alleged “cultural appropriation.” A physician assistant who was excoriated on social media for standing up to bullies. A Palestinian writer whose appearance at a prominent book fair was canceled. An early beneficiary of affirmative action who dared to explore its unintended consequences. Vulnerable gay teenagers who described being misled by a politicized medical establishment into dubious gender transition treatments. A public university president who was driven away by a campus besieged with political division. Social work students and faculty undermined by a school that had betrayed its own principles. A public health expert who risked opprobrium from his peers by calling out his profession on groupthink.

And it seems to me that much of her piece is simply a disguised lecture to the paper, letting them know that, as Jack Nicholson said, “You can’t handle the truth!”

Several years ago, The Times ran a campaign with the tagline “The truth is hard.” The way I’ve interpreted this is that the truth may be hard for some people to hear, but the truth should never be hard for journalists to tell. In our efforts to shed light on difficult subjects or to question conventional wisdom, we should never refrain from speaking what we believe to be the truth. Not because we think others can’t handle it and certainly not because we cannot handle it ourselves.

Readers are smarter and more thoughtful than the news media sometimes gives them credit for. They don’t need our protection. When journalists hold back, readers can sense they aren’t getting the full story. This sows doubt and skepticism at a time when readers desperately need news they can trust.

At the end, she thanks the readers for their feedback, both good and bad, and expresses hope that her pieces led people to examine their own views.  Here’s the sad last paragraph:

Though I am leaving The Times, I will not be leaving behind these principles in my work as a journalist. Readers depend on our telling the truth more than ever.

This is a brave woman, for she surely realized that her columns and their topics wouldn’t go down well with her editors. Nevertheless, she persisted. I wish her Ceiling-Cat-speed and hope she continues to publish her views at some other widely-read venue. Thanks, Ms. Paul, for your contributions.

Tara Tanaka has returned (this video was not shown for two years) with a lovely video of Roseate Spoonbills (Platalea ajaja) feeding, preening and dunking on her property. They remind me of my ducks!

Tara’s notes are indented below; her Vimeo page is here and her flickr page here.

A Vision in Pink

In the spring of 2023 we had at least 16 Roseate Spoonbills visit our swamp, some of them here for almost two months.  Two of the birds were adults in full breeding plumage, and the rest were juveniles likely fledged the summer before.  All of the birds in this video are juveniles.  In the traveling I’ve done I’ve never seen 16 Roseate Spoonbills at one time, and to have that many here in our cypress swamp for such a long time was quite a gift.

This video includes some of the highlights of their time here, with the opening and closing scenes shot from the living room (!)  They bathed, preened, dried, fed and spent a lot of time roosting.  I’m not sure I’ve ever seen a bird species that had so much time to just roost without having to hunt for food — they must be very efficient feeders.  One day there were very high winds and three of the spoonbills tried to hunker down in a large cypress where a wise old Wood Stork was easily riding out the winds.  The old stork chose a very large branch and faced into the wind, while the young spoonies struggled to keep their balance in the middle of much smaller branches. 

Last spring I kept hoping that some or all of these birds would return and nest, but I never saw even one spoonbill last year.  I keep looking out the window hoping that this will be their year to nest here.

As these are all juveniles, I put a photo of adults from Wikipedia below. It’s labeled: “Foraging roseate spoonbills at Merritt Island, Florida, United States.”  An excerpt from the article:

Little is known about the roseate spoonbill’s behavior outside of their foraging habits. This species feeds in shallow fresh or coastal waters by swinging its bill from side to side as it steadily walks through the water, often in groups. Moreover, the spoon-shaped bill allows it to sift easily through mud.

The bird feeds on crustaceans, bits of plant material, aquatic insects, mollusks, frogs, newts and very small fish (such as minnows) ignored by larger waders.[24][25][26] In Brazil, researchers found roseate spoonbill diets to consist of fish, insects, crustaceans, mollusks, and seeds, all foraged from limnetic/freshwater habitats.

Ke Wu, CC BY-SA 4.0, via Wikimedia Commons

Here’s their range: year-round is purple, and breeding range is blue. You can see that in the U.S. they are year-round only at the tip of Florida and along the Gulf Coast:

Cephas, CC BY-SA 4.0, via Wikimedia Commons

 

The quantum double-slit experiment, in which objects are sent toward a wall with two slits and then recorded on a screen behind the wall, creates an interference pattern that builds up gradually, object by object. And yet, it’s crucial that the path of each object on its way to the screen remain unknown. If one measures which of the slits each object passes through, the interference pattern never appears.

Strange things are said about this. There are vague, weird slogans: “measurement causes the wave function to collapse“; “the particle interferes with itself“; “electrons are both particles and waves“; etc. One reads that the objects are particles when they reach the screen, but they are waves when they go through the slits, causing the interference — unless their passage through the slits is measured, in which case they remain particles.

But in fact the equations of 1920s quantum physics say something different and not vague in the slightest — though perhaps equally weird. As we’ll see today, the elimination of interference by measurement is no mystery at all, once you understand both measurement and interference. Those of you who’ve followed my recent posts on these two topics will find this surprisingly straightforward; I guarantee you’ll say, “Oh, is that all?” Other readers will probably want to read

• this post on measurement
  • (and perhaps this one too about how to make a measurement permanent)
• these posts on interference for one particle and for two particles
  • (and perhaps this one and this one for more examples)

The Interference Criterion

When do we expect quantum interference? As I’ll review in a moment, there’s a simple criterion:

• a system of objects (not the objects themselves!) will exhibit quantum interference if the system, initially in a superposition of possibilities, reaches a single possibility via two or more pathways.

To remind you what that means, let’s compare two contrasting cases (covered carefully in this post.) Figs. 1a and 1b show pre-quantum animations of different quantum systems, in which two balls (drawn blue and orange) are in a superposition of moving left OR moving right. I’ve chosen to stop each animation right at the moment when the blue ball in the top half of the superposition is at the same location as the blue ball in the bottom half, because if the orange ball weren’t there, this is when we’d expect it to see quantum interference.

But for interference to occur, the orange ball, too, must at that same moment be in the same place in both parts of the superposition. That does happen for the system in Fig. 1a — the top and bottom parts of the figure line up exactly, and so interference will occur. But the system in Fig. 1b, whose top and bottom parts never look the same, will not show quantum interference.

Fig. 1a: A system of two balls in a superposition, from a pre-quantum viewpoint. As the system evolves, a moment is reached when the two parts of the superposition are identical. As the system has then reached a single possibility via two routes, quantum interference may result. Figure 1b: Similar to Fig. 1a, except that when the blue ball is at the same location in both parts of the superposition, the orange ball is at two different locations. At no moment are the two possibilities in the superposition the same, so quantum interference cannot occur.

In other words, quantum interference requires that the two possibilities in the superposition become identical at some moment in time. Partial resemblance is not enough.

The Measurement

A measurement always involves an interaction of some sort between the object we want to measure and the device doing the measurement. We will typically

• use a small object to carry out the basic initial measurement, and then
• amplify the result so that it can be made permanent.

For today’s purposes, the details of the second step won’t matter, so I’ll focus on the first step.

Setting Up

We’ll call the object going through the slits a “particle”, and we’ll call the measurement device a “measuring ball” (or just “ball” for short.) The setup is depicted in Fig. 2, where the particle is approaching the slits and the measuring ball lies in wait.

Figure 2: A particle (blue) approaches a wall with two slits, behind which sits a screen where the particle’s arrival will be detected. Also present is a lightweight measuring ball (black), ready to fly in and measure the particle’s position by colliding with it as it passes through the wall. If No Measurement is Made at the Slits

Suppose we allow the particle to proceed and we make no measurement of its location as it passes through the slits. Then we can leave the ball where it is, at the position I’ve marked M in Fig. 3. If the particle makes it through the wall, it must pass through one slit or the other, leaving the system in a superposition of the form

• the particle is near the left slit [and the ball is at position M]
  OR
• the particle is near the right slit [and the ball is at position M]

as shown at the top of Fig. 3. (Note: because the ball and particle are independent [unentangled] in this superposition, it can be written in factored form as in Fig. 12 of this post.)

From here, the particle (whose motion is now quite uncertain as a result of passing through a narrow slit) can proceed unencumbered to the screen. Let’s say it arrives at the point marked P, as at the bottom of Fig. 3.

Figure 3: (Top) As the particle passes through the slits, the system is set into a superposition of two possibilities in which the particle passes through the left slit OR the right slit. (The particle’s future motion is quite uncertain, as indicated by the green arrows.) In both possibilities, the measuring ball is at point M. (Bottom) If the particle arrives at point P on the screen, then the two possibilties in the superposition become identical, as in Fig. 1a, so quantum interference can result. This will be true no matter what point P we choose, and so an interference pattern will be seen across the whole screen.

Crucially, both halves of the superposition now describe the same situation: particle at P, ball at M. The system has arrived here via two paths:

• The particle went through the left slit and arrived at the point P (with the ball always at M),
  OR
• The particle went through the right slit and arrived at the point P (with the ball always at M).

Therefore, since the system has reached a single possibility via two different routes, quantum interference may be observed.

Specifically, the system’s wave function, which gives the probability for the particle to arrive at any point on the screen, will display an interference pattern. We saw numerous similar examples in this post, this post and this post.

If the Measurement is Made at the Slits

But now let’s make the measurement. We’ll do it by throwing the ball rapidly toward the particle, timed carefully so that, as shown in Fig. 4, either

• the particle is at the left slit, in which case the ball passes behind it and travels onward,
  OR
• the particle is at the right slit, in which case the ball hits it and bounces back.

(Recall that I assumed the measuring ball is lightweight, so the collision doesn’t much affect the particle; for instance, the particle might be an heavy atom, while the measuring ball is a light atom.)

Figure 4: As the particle moves through the wall, the ball is sent rapidly in motion. If the particle passes through the right slit, the ball will hit it and bounce back; if the particle passes through the left slit, the ball will miss it and will continue to the left.

The ball’s late-time behavior reveals — and thus measures — the particle’s behavior as it passed through the wall:

• the ball moving to the left means the particle went through the left slit;
• the ball moving to the right means the particle went through the right slit.

[Said another way, the ball and particle, which were originally independent before the measurement, have been entangled by the measurement process. Because of the entanglement, knowledge concerning the ball tells us something about the particle too.]

To make this measurement complete and permanent requires a longer story with more details; for instance, we might choose to amplify the result with a Geiger counter. But the details don’t matter, and besides, that takes place later. Let’s keep our focus on what happens next.

The Effect of the Measurement

What happens next is that the particle reaches the point P on the screen. It can do this whether it traveled via the left slit or via the right slit, just as before, and so you might think there should still be an interference pattern. However, remembering Figs. 1a and 1b and the criterion for interference, take a look at Fig. 5.

Figure 5: Following the measurement made in Fig. 4, the arrival of the particle at the point P on the screen finds the ball in two possible locations, depending on which slit the particle went through. In contrast to Fig. 3, the two parts of the superposition are not identical, and so (as in Fig. 1b) no quantum interference pattern will be observed.

Even though the particle by itself could have taken two paths to the point P, the system as a whole is still in a superposition of two different possibilities, not one — more like Fig. 1b than like Fig. 1a. Specifically,

• the particle is at position P and the ball is at location ML (which happens if, in Fig. 4, the particle was near the left slit and the ball continued to the left);
  OR
• the particle is at position P and the ball is at location MR (which happens if, in Fig. 4, the particle was near the right slit and the ball bounced back to the right).

The measurement process — by the very definition of “measurement” as a procedure that segregates left-slit cases from right-slit cases — has resulted in the two parts of the superposition being different even when they both have the particle reaching the same point P. Therefore, in contrast to Fig. 3, quantum interference between the two parts of the superposition cannot occur.

And that’s it. That’s all there is to it.

Looking Ahead.

The double-slit experiment is hard to understand if one relies on vague slogans. But if one relies on the math, one sees that many of the seemingly mysterious features of the experiment are in fact straightforward.

I’ll say more about this in future posts. In particular, to convince you today’s argument is really correct, I’ll look more closely at the quantum wave function corresponding to Figs. 3-5, and will reproduce the same phenomenon in simpler examples. Then we’ll apply the resulting insights to other cases, including

• measurements that do not destroy interference,
• measurements that only partly destroy interference,
• destruction of interference without measurement, and
• double-slit experiments whose interference can’t be located in physical space,
• etc.