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The Atlantic on the government’s attacks on science

Why Evolution is True Feed - Mon, 02/17/2025 - 9:15am

A lot of what the Trump administration is doing is aimed at health and science, and not necessarily in a good way.  The most obvious blunder is the appointment of Robert F. Kennedy Jr., a palpably unqualified man with some bizarre views, as Secretary of Health and Human Services,  the person who advises the President on all health matters. Given Trump’s abysmal ignorance of science, having someone like RFK Jr. guiding government policy is scary.

There’s a lot of beefing as well about the government cutting the “overhead” (money given to universities, supposedly to support the infrastructure of grants) uniformly to 15%, down from over 60% in some cases (each university negotiates it rate with the government). This slashing will reduce university budgets substantially. But in some cases in which a university has huge endowments, like Harvard ($53 billion),  I can’t shed many tears over that. Given that in many cases we simply don’t know where overhead goes, the assumption has been that many schools simply use it as a source of money for almost anything, and that means that the taxpayers are unwittingly subsidizing not just scientific research, but universities in general.

At any rate, the potential damage that the Trump administration will do to American science is outlined in this new Atlantic article by Katherine Wu.  It doesn’t cohere like a good science piece should, but at least lays out some scary things in store for American science. To me, the scariest is the hiding of already-obtained scientific results, financed by taxpayers, that were publicly available but are no long so.

Click below to see the article, or find it archived here.

First, the payoff for funding science. I hope this is accurate as it’s characterizing science as “research and development”:

Every dollar invested in research and development has been estimated to return at least $5 on average—billions annually.

It also looks as if the National Science Foundation is on the chopping block:

The administration’s actions have also affected scientific pursuits in ways that go beyond those orders. The dismantling of USAID has halted clinical trials abroad, leaving participants with experimental drugs and devices still in their bodies. Last week, NIH announced that it would slash the amount its grants would pay for administrative costs—a move that has since been blocked by a federal judge but that would substantially hamper entire institutions from carrying out the day-to-day activities of research. The administration is reportedly planning to cut the budget for the National Science Foundation. Mass layoffs of federal workers have also begun, and two NIH scientists (who asked not to be identified for fear of professional repercussions) told me they participated in a meeting this morning in which it was announced that thousands of staff across the Department of Health and Human Services would be let go starting today. Robert F. Kennedy Jr. has now become the head of that department, after two confirmation hearings in which he showed a lack of basic understanding of the U.S. health system and a flagrant disregard for data that support the safety and effectiveness of various lifesaving vaccines. (The White House did not return repeated requests for comment.)

It’s not clear whether the DEIrestrictions described in the previous post will severely impede science. Wu says this:

Many also expect that the moratorium on DEI-focused programming will have severe impacts on who is able to do the work of science—further impeding women, people of color, and other groups underrepresented in the field from entering and staying in it.

But it’s not clear the restrictions will have that effect, nor that making science more “diverse” (not just via race, but in other traits) will improve our understanding of nature.

There are restrictions on Social-Justice-aimed projects, but again, many of these have been a waste of money and effort, performative efforts not aimed at understandind science, and will we simply have to see how this shakes. But those who do such work are beefing about what the government did. Here’s an example of a peeved but woke scientist whose work I’ve often criticized (click screenshot to go to thread). Most of the commenters don’t support Fuentes’s griping:

 

One problem is that the government is looking for suspicious grants by doing word searches, and those searches include terms like “environment,” “climate”, and “race”.  It’s a quick way to find suspicious grants, but you have to evaluate their quality, not simply defund them because they come up in a keyword search.

Here’s what I find most distressing about what the government did (besides appointing RFK Jr.):

In yesterday’s executive order, Trump highlighted the importance of “protecting expert recommendations from inappropriate influence and increasing transparency regarding existing data.” But that is exactly what the administration’s critics have said it is already failing to do. At the end of last month, the CDC purged its website of several decades’ worth of data and content, including an infectious-disease-surveillance tool as well as surveys tracking health-risk behaviors among youths. (On Tuesday, a federal judge ordered the government to restore, for now, these and other missing data and webpages to their pre-purge state.) And as soon as the Trump administration started pulling data sets from public view, scientists started worrying that those data would reappear in an altered form, or that future scientific publications would have to be modified.

I’m not as worried about the reappearance of data in altered form as I am about the simple removal of data—data funded by us, the American taxpayers—from public view. Fortunately, a judge stopped the data removal, but that may be temporary.

What will be the outcome? While Wu thinks this will reduce trust in science, I’m not so sure about that, especially given that trust in science fell strongly during the Biden administration, and trust is reduced simply because science is getting mixed up with politics in every administration. What worries me more is the vulnerability of science to the whims of the administration—an administration that seems to care more about key words than about research itself.  My view is that the government is entitled to vet science funding and cut waste if it wants, but that governments are poorly equipped to judge scientific merit. A grant that looks wasteful may come up with useful results, though of course there are some that simply look like government funded-virtue flaunting. It’s best if a generous dollop of money is allocated to science, and then scientists themselves decide how to dole it out, for they are the best equipped people to do so. In this I agree with Wu’s conclusion:

There will undoubtedly be periods, in the coming weeks and months, when the practice of science feels normal. Many scientists are operating as they usually do until they are told otherwise. But that normalcy is flimsy at best, in part because the Trump administration has shown that it may not care what data, well collected or not, have to say. During his Senate confirmation hearings, Kennedy repeatedly refused to acknowledge that vaccines don’t cause autism, insisting that he would do so only “if the data is there.” Confronted by Senator Bill Cassidy with decades of data that were, in fact, there, he continued to equivocate, at one point attempting to counter with a discredited paper funded by an anti-vaccine group.

In all likelihood, more changes are to come—including, potentially, major budgetary cuts to research, as Congress weighs this year’s funding for the nation’s major research agencies. Trump and his administration are now deciding how deep a rift to make in America’s scientific firmament. How long it takes to repair the damage, or whether that will be possible at all, depends on the extent of the damage they inflict now.

I’m just glad that I don’t have to apply for science grants any more.

Categories: Science

CAR T-cells enable record-breaking 18-year nerve cancer remission

New Scientist Feed - Mon, 02/17/2025 - 8:00am
A person with neuroblastoma, which occurs when developing nerve cells in children turn cancerous, has remained tumour-free for over 18 years thanks to CAR T-cell therapy
Categories: Science

From headaches to tics, how mass nocebo effects spread real symptoms

New Scientist Feed - Mon, 02/17/2025 - 8:00am
Social media is enabling health symptoms and mass psychogenic illnesses to spread quickly around the world. But by knowing how it happens, you can protect yourself
Categories: Science

Most DEI endeavors in higher education are declared illegal

Why Evolution is True Feed - Mon, 02/17/2025 - 7:30am

The time has come that many have feared but many will celebrate: DEI (“diversity, equity, and inclusion) is effectively gone from campuses by federal order.

Inside Higher Ed reports; click headline to read:

An excerpt:

The Education Department’s Office for Civil Rights declared all race-conscious student programming, resources and financial aid illegal over the weekend and threatened to investigate and rescind federal funding for any institution that does not comply within 14 days.

In a Dear Colleague letter [JAC: see below] published late Friday night, acting assistant secretary for civil rights Craig Trainor outlined a sweeping interpretation of the Supreme Court’s 2023 ruling in Students for Fair Admissions v. Harvard, which struck down affirmative action. While the decision applied specifically to admissions, the Trump administration believes it extends to all race-conscious spending, activities and programming at colleges.

. . . . .The letter mentions a wide range of university programs and policies that could be subject to an OCR investigation, including “hiring, promotion, compensation, financial aid, scholarships, prizes, administrative support, discipline, housing, graduation ceremonies, and all other aspects of student, academic, and campus life.”

“Put simply, educational institutions may neither separate or segregate students based on race, nor distribute benefits or burdens based on race,” Trainor writes.

Backlash to the letter came swiftly on Saturday from Democratic lawmakers, student advocates and academic freedom organizations.

“This threat to rip away the federal funding our public K-12 schools and colleges receive flies in the face of the law,” Senator Patty Murray, Democrat of Washington, wrote in a statement Saturday. “While it’s anyone’s guess what falls under the Trump administration’s definition of ‘DEI,’ there is simply no authority or basis for Trump to impose such a mandate.”

But most college leaders have, so far, remained silent.

Since virtually every institution of higher learning depends on some federal funding, this gives colleges the choices of abandoning DEI or abandoning federal money. You know which they’ll prefer. The former, of course, but they’ll try to have both, sometimes by duplicitous practices.

Since the Supreme Court has declared that universities can’t use race as a basis for admitting students, but will allow them to identify their race in essays (this is a backdoor many colleges use to promote affirmative action), the letter also deals with that:

The Dear Colleague letter also seeks to close multiple exceptions and potential gaps left open by the Supreme Court ruling on affirmative action and to lay the groundwork for investigating programs that “may appear neutral on their face” but that “a closer look reveals … are, in fact, motivated by racial considerations.”

Chief Justice John Roberts wrote that colleges could legally consider a student’s racial identity as part of their experience as described in personal essays, but the OCR letter rejects that.

“A school may not use students’ personal essays, writing samples, participation in extracurriculars, or other cues as a means of determining or predicting a student’s race and favoring or disfavoring such students,” Trainor wrote.

It would be hard to determine, though, whether colleges are actually doing this. Essays and the like aren’t banned—only their use for race-based admissions, and that would be a lot harder to prove than what Harvard did, which was give Asian applicants lower “personality scores” in a way that could be statistically affirmed. Further, the elimination of standardized tests as a requirement for application—another backdoor approach to promoting affirmative action—is also now banned:

Going even further beyond the scope of the SFFA decision, the letter forbids any race-neutral university policy that could conceivably be a proxy for racial consideration, including eliminating standardized test score requirements.

The department has never revoked a college or state higher education agency’s federal funding over Title VI violations. If the OCR follows through on its promises, it would be an unprecedented exercise of federal influence over university activities.

The letter is likely to be challenged in court, but in the meantime it could have a ripple effect on colleges’ willingness to continue funding diversity programs and resources for underrepresented students.

On top of that, there will be no more race or gender-based graduation ceremonies (Harvard had at least ten “affinity graduations”), no more ethnically-segregated dormitories, no more segregation of any type. As the letter notes (my emphasis):

Although SFFA addressed admissions decisions, the Supreme Court’s holding applies more broadly. At its core, the test is simple: If an educational institution treats a person of one race differently than it treats another person because of that person’s race, the educational institution violates the law. Federal law thus prohibits covered entities from using race in decisions pertaining to admissions, hiring, promotion, compensation, financial aid, scholarships, prizes, administrative support, discipline, housing, graduation ceremonies, and all other aspects of student, academic, and campus life. Put simply, educational institutions may neither separate or segregate students based on race, nor distribute benefits or burdens based on race

Of course this will be challenged in court, though I don’t see a clear reason why the executive branch can’t make such a policy since the Supreme Court has disallowed race-based admissions.  In the meantime, you can find the whole letter at this site (this one was sent to Harvard, but they’re all the same), or click on the screenshots below, where I’ve given just a short excerpt.  Colleges will be poring over the whole four-page letter.

My Chicago colleague Dorian Abbot, who’s opposed to DEI, wrote a short piece about this on Heterodox Substack with this information about how to report violations:

If you want to report something but are concerned about potential retaliation, Jonathan Mitchel at Faculty, Alumni, & Students Opposed to Racial Preferences (FASORP) has offered to file the complaints with OCR. You can give information anonymously at the FASORP website, including any documents, websites, or other relevant information. The website does not track IP addresses and you can use a VPN before navigating to it if you want to be extra safe.

If you have any information about ongoing illegal discrimination, it is essential to report it as soon as possible. General Council at every educational institution needs to quickly understand and advise their administration that discrimination really is illegal and must stop immediately.

As for me, I have mixed feelings, and have gone back and forth on this issue in the past few years. On the one hand, I’m strongly opposed to requiring DEI statements for hiring or promotion.  This is illegal compelled speech and, in fact, is banned by the University of Chicago’s 1970 Shils Report. Nor do I think that there should be preferential admission on the basis of race, nor the elimination of standardized tests as a sneaky way to increase “diversity”, though I have suggested that when two candidates are equally qualified, the minority candidate might be favored.

The fact is that, historically, minorities have been disadvantaged by bias in a way that has affected them over the long term. In my view, the way to remedy this is not through “equity”—a misguided claim that groups should be represented in all institutions in the same proportion as in the general population.  The proper remedy is equal opportunity, but of course that is a much harder remedy than simply forcing equity on institutions through preferential treatment. But equal opportunity from birth is the only way to guarantee that groups are truly treated equally now, and seems the fairest solution.

Besides the possibility of preferential admission when students have equal records (this is of course illegal under the present “Dear Colleague” letter), the only DEI that I think colleges and universities need is a small office—or even just a procedure—for dealing with reported instances of bias against students or university members, and those reports cannot be anonymous. In the meantime, DEI should consist of promulgating these two statements:

1.) All students should be treated equally regardless of ethnicity, religion, disability, ideology, and so on

2.) Any instances of bias or harassment of students can be reported here (give link or location).

It will be interesting to see what happens in the next three years, but we can be sure that once the Democrats re-assume power, all of the above will be deep-sixed.

Categories: Science

Readers’ wildlife photos

Why Evolution is True Feed - Mon, 02/17/2025 - 6:15am

Today we have volume IV of Robert Lang’s 13-set series of photos from his recent trip to the Pantanal, today featuring birds. Robert’s captions are indented, and you can enlarge the photos by clicking on them.

Readers’ Wildlife Photos: The Pantanal, Part IV: Birds

Continuing our mid-2025 journey to the Pantanal in Brazil, by far the largest category of observation and photography was birds: we saw over 100 different species of birds (and this was not even a birding-specific trip, though the outfitter also organizes those for the truly hard core).

Not all of what we saw was so gracious as to pose sufficiently close, still, and well-lighted to get a good photo, but the Pantanal still offered much better photo opportunities than did the Amazon a few years ago, where most of the birds presented as a tiny black silhouette high in a distant tree. Although I usually try to say a few words about each photo in my RWP contributions, there’s just to many here, so in most, I’ll just give the name and species and move on, proceeding alphabetically by common name. (Species identification are courtesy of our guide, augmented sometimes by Merlin Bird ID. Corrections gratefully accept.)

A female anhinga (Anhinga anhinga), in its characteristic holding-out-the-wings-to-dry pose:

Bare-faced curassows (Crax fasciolata), male on the left, female on the right:

And a female with its crest up:

A bare-faced ibis (Phimosus infuscatus):

Black-backed water tyrant (Fluvicola albiventer). Quite a scary name for such a small, unassuming bird

Black-bellied whistling ducks (Dendrocygna autumnalis):

Black-collared hawk (Busarellus nigricollis), this one flying:

A black-crowned night heron (Nycticorax nycticorax):

A black-fronted nunbird (Monasa nigrifrons):

And that’s all for this installment. We’re not even out of the B’s. (Heck, we’re not even out of the “black-“s!) More to come soon!

Categories: Science

Breaking the Curse of the Habitable Zone

Universe Today Feed - Mon, 02/17/2025 - 6:13am

The Habitable Zone is a central concept in our explorations for life outside the Earth. Is it time to abandon it?

The Habitable Zone is defined as the region around a star where liquid water can exist on the surface of a planet. At first glance, that seems like a good starting place to hunt for alien life in other systems. After all, there’s only one kind of life known in the universe (ours) and it exists in the Habitable Zone of the Sun.

But researchers have long noted that the Habitable Zone concept is far too restrictive. Besides the examples of the icy moons in our own solar system, life itself is able to alter the chemistry of a planet, shifting its ability to retain or remove heat, meaning that the un-habitable regions of a distant system might be more clement than we thought.

Even if we restrict ourselves to the basic biochemistry that makes Earthly life possible, we have many more options than we naively thought. Hycean worlds, planets thought to be englobed by water surrounded by thick hydrogen atmospheres, once thought to be too toxic for any kind of life, might be even more suitable than terrestrial worlds.

What about tidally-locked planets around red dwarf stars, like our nearest neighbor Proxima b and the intriguing system of TRAPPIST-1? Conditions on those planets might be hellish, with one side facing the incessant glare of its star and the other locked in permanent night. Neither of those extremes seem suitable for life as we know it. But even those worlds can support temperate atmospheres if the conditions are just right. A delicate balancing act for sure, but a balancing act that every life-bearing planet must walk.

Our galaxy contains billions of dead stars, the white dwarves and neutron stars. We know of planets in those systems. Indeed, the first exoplanets were discovered around a pulsar. Sometimes those dead stars retain planets from their former lives; other times the planets assemble anew from the stellar wreckage. In either case, the stars, though dead, are still warm, providing a source of energy for any life that might find a home there. And considering the sheer longevity of those stars the incredibly long history of our galaxy, life has had many chances to appear – and sustain itself – in systems that are now dead.

Who needs planets, anyway? Methanogens could take advantage of the exotic, cold chemistry of molecular clouds, feasting on chemicals processed by millennia of distant high-energy starlight. It might even be possible for life to sustain itself in a free-floating biological system, with the gravity of its own mass holding on to an atmosphere. It’s a wild concept, but all the foundational functions of a free-floating habitat – scaffolding, energy capture and storge, semi-permeable membranes – are found on terrestrial life.

We should absolutely continue our current searches – after all, they’re not groundless. But before we invest in the next generation of super-telescopes, we should pause and reconsider our options. We should invest in research that pushes the edges of what life means and where it can exist, and we should explore pathways to identifying and observing those potential habitats. Only after we have extended research along these lines can we decide on a best-case strategy.

In other words, we should replace a goal, that of finding life like our own, with a vision of finding life wherever we can. Nature has surprised us many times in the past, and we shouldn’t let our biases and assumptions get in the way of our path of discovery.

The post Breaking the Curse of the Habitable Zone appeared first on Universe Today.

Categories: Science

Eight habits that could keep your heart healthy

New Scientist Feed - Mon, 02/17/2025 - 6:00am
From staying active to getting plenty of sleep, there are many ways to keep your heart healthy
Categories: Science

How to Visualize a Wave Function

Science blog of a physics theorist Feed - Mon, 02/17/2025 - 5:45am

Before we knew about quantum physics, humans thought that if we had a system of two small objects, we could always know where they were located — the first at some position x1, the second at some position x2. And after Isaac Newton’s breakthroughs in the late 17th century, we believed that by combining this information with knowledge of the objects’ motions and the forces acting upon them, we could calculate where they would be in the future.

But in our quantum world, this turns out not to be the case. Instead, in Erwin Schrödinger’s 1925 view of quantum physics, our system of two objects has a wave function which, for every possible x1 and x2 that the objects could have, gives us a complex number Ψ(x1, x2). The absolute-value-squared of that number, |Ψ(x1, x2)|2, is proportional to the probability for finding the first object at position x1 and the second at position x2 — if we actually choose to measure their positions right away. If instead we wait, the wave function will change over time, following Schrödinger’s wave equation. The updated wave function’s square will again tell us the probabilities, at that later time, for finding the objects at those particular positions.

The set of all possible object locations x1 and x2 is what I am calling the “space of possibilities” (also known as the “configuration space”), and the wave function Ψ(x1, x2) is a function on that space of possibilities. In fact, the wave function for any system is a function on the space of that system’s possibilities: for any possible arrangement X of the system, the wave function will give us a complex number Ψ(X).

Drawing a wave function can be tricky. I’ve done it in different ways in different contexts. Interpreting a drawing of a wave function can also be tricky. But it’s helpful to learn how to do it. So in today’s post, I’ll give you three different approaches to depicting the wave function for one of the simplest physical systems: a single object moving along a line. In coming weeks, I’ll give you more examples that you can try to interpret. Once you can read a wave function correctly, then you know your understanding of quantum physics has a good foundation.

For now, everything I’ll do today is in the language of 1920s quantum physics, Schrödinger style. But soon we’ll put this same strategy to work on quantum field theory, the modern language of particle physics — and then many things will change. Familiarity with the more commonly discussed 1920s methods will help you appreciate the differences.

Complex Numbers

Before we start drawing pictures, let me remind you of a couple of facts from pre-university math about complex numbers. The fundamental imaginary number is the square root of minus one,

which we can multiply by any real number to get another imaginary number, such as 4i or -17i. A complex number is the sum of a real number and an imaginary number, such as 6 + 4i or 11 – 17i.

More abstractly, a complex number w always takes the form u + i v, where u and v are real numbers. We call u the “real part” of w and we call v the “imaginary part” of w. And just as we can draw a real number using the real number line, we can draw a complex number using a plane, consisting of the real number line combined with the imaginary number line; in Fig. 1 the complex number w is shown as a red dot, with the real part u and imaginary part v marked along the real and imaginary axes.

Figure 1: Two ways of representing the complex number w, either as u + i v or as |w|eiφ .

Fig. 1 shows another way of representing w. The line from the origin to w has length |w|, the absolute value of w, with |w|2 = u2 + v2 by the Pythagorean theorem. Defining φ as the angle between this line and the real axis, and using the following facts

  • u = |w| cos φ
  • v = |w| sin φ
  • eiφ = cos φ + i sin φ

we may write w = |w|eiφ , which indeed equals u + i v .

Terminology: φ is called the “argument” or “phase” of w, and in math is written φ = arg(w).

One Object in One Dimension

We’ll focus today only on a single object moving around on a one-dimensional line. Let’s put the object in a “Gaussian wave-packet state” of the sort I discussed in this post’s Figs. 3 and 4 and this one’s Figs. 6 and 7. In such a state, neither the object’s position nor its momentum [a measure of its motion] is completely definite, but the uncertainty is minimized in the following sense: the product of the uncertainty in the position and the uncertainty in the momentum is as small as Heisenberg’s uncertainty principle allows.

We’ll start with a state in which the uncertainty on the position is large while the uncertainty on the momentum is small, shown below (and shown also in Fig. 3 of this post and Fig. 6 of this post.) To depict this wave function, I am showing its real part Re[Ψ(x)] in red and its imaginary part Im[Ψ(x)] in blue. In addition, I have drawn in black the square of the wave function:

  • |Ψ(x)|2 = (Re[Ψ(x)])2 + (Im[Ψ(x)])2

[Note for advanced readers: I have not normalized the wave function.]

Figure 1: For an object in a simple Gaussian wave packet state with near-definite momentum, a depiction of the wave function for that state, showing its real and imaginary parts in red and blue, and its absolute-value squared in black.

But as wave functions become more complicated, this way of doing things isn’t so convenient. Instead, it is sometimes useful to represent the wave function in a different way, in which we plot |Ψ(x)| as a curve whose color reflects the value of φ = arg[Ψ(x)] , the argument of Ψ(x). In Fig. 2, I show the same wave function as in Fig. 1, depicted in this new way.

Figure 2: The same wave function as in Fig. 1; the curve is the absolute value of the wave function, colored according to its argument.

As φ cycles from 0 to π/4 to π/2 to 3π/4 and back to 2π (the same as φ = 0), the color cycles from red to yellow-green to cyan to blue-purple and back to red.

Compare Figs. 1 and 2; its the same information, depicted differently. That the wave function is actually waving is clear in Fig. 1, where the real and imaginary parts have the shape of waves. But it is also represented in Fig. 2, where the cycling through the colors tells us the same thing. In both cases, the waving tells us that the object’s momentum is non-zero, and the steadiness of that waving tells us that the object’s momentum is nearly definite.

Finally, if I’m willing to give up the information about the real and imaginary parts of the wave function, and just want to show the probabilities that are proportional to its squared absolute value, I can sometimes depict the state in a third way. I pick a few spots where the object might be located, and draw the object there using grayscale shading, so that it is black where the probability is large and becomes progressively lighter gray where the probability is smaller, as in Fig. 3.

Figure 3: The same wave function in Figs. 1 and 2, here showing only the probabilities for the object’s location; the darker the grey, the more likely the object is to be found at that location.

Again, compare Fig. 3 to Figs. 1 and 2; they all represent information about the same wave function, although there’s no way to read off the object’s momentum using Fig. 3, so we know where it might be but not where it is going. (One could add arrows to indicate motion, but that only works when the uncertainty in the momentum is small.)

Although this third method is quite intuitive when it works, it often can’t be used (at least, not as I’ve described it here.) It’s often useful when we have just one object to worry about, or if we have multiple objects that are independent of one another. But if they are not independent — if they are correlated, as in a “superposition” [more about that concept soon] — then this technique usually does not work, because you can’t draw where object number 1 is likely to be located without already knowing where object number 2 is located, and vice versa. We’ve already seen examples of such correlations in this post, and we’ll see more in future.

So now we have three representations of the same wave function — or really, two representations of the wave function’s real and imaginary parts, and two representations of its square — which we can potentially mix and match. Each has its merits.

How the Wave Function Changes Over Time

This particular wave function, which has almost definite momentum, does indeed evolve by moving at a nearly constant speed (as one would expect for something with near-definite momentum). It spreads out, but very slowly, because its speed is only slightly uncertain. Here is its evolution using all three representations. (The first was also shown in this post’s Fig. 6.)

I hope that gives your intuition some things to hold onto as we head into more complex situations.

Two More Examples

Below are two simple wave functions for a single object. They differ somewhat from the one we’ve been using in the rest of this post. What do they describe, and how will they evolve with time? Can you guess? I’ll give the full answer tomorrow as an addendum to this post.

Two different wave functions; in each case the curve represents the absolute value |Ψ(x)| and the color represents arg[Ψ(x)], as in Fig. 2. What does each wave function say about the object’s location and momentum, and how will each of them change with time?
Categories: Science

China launches hunt for ways to protect data from quantum computers

New Scientist Feed - Mon, 02/17/2025 - 2:00am
Efforts to develop next-generation cryptography algorithms that can't be broken by quantum computers are already underway in the US, but now China has announced it will seek its own solutions
Categories: Science

Pompeii’s streets show how the city adapted to Roman rule

New Scientist Feed - Mon, 02/17/2025 - 12:00am
Pompeii only came under Roman control around 160 years before its destruction – and its traffic-worn streets show how the locals adjusted their business operations
Categories: Science

So it begins: Robert F. Kennedy Jr. is confirmed as HHS Secretary and immediately starts dismantling US federal science infrastructure

Science-based Medicine Feed - Mon, 02/17/2025 - 12:00am

The nightmare has come true. Robert F. Kennedy Jr. has been confirmed as HHS Secretary and didn't wait long to start dismantling federal science and health programs. The White House even formed a "MAHA commission" to draw up a battle plan.

The post So it begins: Robert F. Kennedy Jr. is confirmed as HHS Secretary and immediately starts dismantling US federal science infrastructure first appeared on Science-Based Medicine.
Categories: Science

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