Science

A team has used a process known as DNA origami to make electrochemical sensors that can quickly detect and measure biomarkers.

A computer science team has developed a sensor-based technology that could revolutionize commercial beekeeping by reducing colony losses and lowering labor costs. The technology uses low-cost heat sensors and forecasting models to predict when hive temperatures may reach dangerous levels. The system provides remote beekeepers with early warnings, allowing them to take preventive action before their colonies collapse during extreme hot or cold weather or when the bees cannot regulate their hive temperature because of disease, pesticide exposure, food shortages, or other stressors.

Researchers demonstrated that brewing tea naturally adsorbs heavy metals like lead and cadmium, effectively filtering dangerous contaminants out of drinks. Researchers tested different types of tea, tea bags and brewing methods. Finely ground black tea leaves performed best at removing toxic heavy metals. Longer steeping times helped tea remove larger amounts of contaminants.

Mars may have once been home to sun-soaked, sandy beaches with gentle, lapping waves according to a new study.

A new artificial intelligence model measures how fast a patient's brain is aging and could be a powerful new tool for understanding, preventing and treating cognitive decline and dementia.

A comparison of 263 species supports the idea that large animals have higher rates of cancer than smaller ones. But the increase is less than expected, suggesting they have evolved ways to lower their risk

In 2007, astronomers discovered the Cosmic Horseshoe, a gravitationally lensed system of galaxies about five-and-a-half billion light-years away. The foreground galaxy’s mass magnifies and distorts the image of a distant background galaxy whose light has travelled for billions of years before reaching us. The foreground and background galaxies are in such perfect alignment that they create an Einstein Ring.

New research into the Cosmic Horseshoe reveals the presence of an Ultra-Massive Black Hole (UMBH) in the foreground galaxy with a staggering 36 billion solar masses.

There’s no strict definition of a UMBH, but the term is often used to describe a supermassive black hole (SMBH) with more than 5 billion solar masses. SMBHs weren’t “discovered” in the traditional sense of the word. Rather, over time, their existence became clear. Also, over time, more and more massive ones were measured. There’s a growing need for a name for the most massive ones, and that’s how the term “Ultra-Massive Black Hole” originated.

The discovery of the enormously massive black hole in the Cosmic Horseshoe is presented in new research. It’s titled “Unveiling a 36 Billion Solar Mass Black Hole at the Centre of the Cosmic
Horseshoe Gravitational Lens,” and the lead author is Carlos Melo-Carneiro from the Instituto de Física, Universidade Federal do Rio Grande do Sul in Brazil. The paper is available at arxiv.org.

There was a revolution in physics in the late 19th/early 20th century as relativity superseded Newtonian physics and propelled our understanding of the Universe to the next level. It became clear that space and time were intertwined rather than separate and that massive objects could warp spacetime. Even light wasn’t immune, and Einstein gave the idea of black holes—which dated back to John Michell’s ‘dark stars’—a coherent mathematical foundation. In 1936, Einstein predicted gravitational lensing, though he didn’t live long enough to enjoy the visual proof we enjoy today.

Now, we know of thousands of gravitational lenses, and they’ve become one of astronomers’ naturally occurring tools. They exist because of their enormous black holes.

The lensing foreground galaxy in the Cosmic Horseshoe is named LRG 3-757. It’s a particular type of rare galaxy called a Luminous Red Galaxy (LRG), which are extremely bright in infrared. LRG 3-757 is also extremely massive, about 100 times more massive than the Milky Way and is one of the most massive galaxies ever observed. Now we know that one of the most massive black holes ever detected occupies the center of this enormous galaxy.

“Supermassive black holes (SMBHs) are found at the centre of every massive galaxy, with their masses tightly connected to their host galaxies through a co-evolution over cosmic time,” the authors write in their paper.

Astronomers don’t find stellar-mass black holes at the heart of massive galaxies and they don’t find SMBHs at the heart of dwarf galaxies. There’s an established link between SMBHs and their host galaxies, especially massive ellipticals like LRG 3-757. This study strengthens that link.

The research focuses on what’s called the MBH-sigmae Relation. It’s the relationship between an SMBH’s mass and the velocity dispersion of the stars in the galactic bulge. Velocity dispersion (sigmae) is a measurement of the speed of the stars and how much they vary around the average speed. The higher the velocity dispersion, the faster and more randomly the stars move.

When astronomers examine galaxies, they find that the more massive the SMBH, the greater the velocity dispersion. The relationship suggests a deep link between the evolution of galaxies and the growth of SMBHs. The correlation between an SMBH’s mass and its galaxy’s velocity dispersion is so tight that astronomers can get a good estimate of the SMBH’s mass by measuring the velocity dispersion.

However, the UMBH in the Cosmic Horseshoe is more massive than the MBH-sigma e Relation suggests.

“It is expected that the most massive galaxies in the Universe, such as brightest cluster galaxies (BCGs), host the most massive SMBHs,” the authors write. Astronomers have found many UMBHs in these galaxies, including LRG 3-757. “Nonetheless, the significance of these UMBHs lies in the fact that
many of them deviate from the standard linear MBH?sigmae relation” the researchers explain.

LRG 3-757 deviates significantly from the correlation. “Our findings place the Cosmic Horseshoe ~1.5 sigma above the MBH?sigmae relation, supporting an emerging trend observed in BGCs and other massive galaxies,” the authors write. “This suggests a steeper MBH?sigmae relationship at the highest masses, potentially driven by a different co-evolution of SMBHs and their host galaxies.”

This figure from the research shows the relationship between the SMBH mass and the host effective
velocity dispersion. The black solid line represents the relation from previous research in 2016, with dashed and dotted lines showing the 1 sigma and 3 sigma scatter, respectively. Horseshoe is labelled and clearly deviates from established relationship. The other galaxies labelled nearby also contain UMBHs that deviate significantly. Image Credit: Melo-Carneiro et al. 2025.

What’s behind this decoupling of the MBH?sigmae relation in massive galaxies? Some stars might have been removed from the galaxy in past mergers, affecting the velocity dispersion.

LRG 3-757 could be part of a fossil group, according to the authors. “The lens of the Horseshoe is unique in that is at ? = 0.44 and that has no comparably massive companion galaxies — it is likely a fossil group,” they write.

Fossil groups are large galaxy groups that feature extremely large galaxies in their centers, often LRGs. Fossil groups and LRGs represent a late stage of evolution in galaxies where activity has slowed. Few stars form in LRGs so they’re “red and dead.” There’s also little to no interaction between galaxies.

“Fossil groups, as remnants of early galaxy mergers, may follow distinct evolutionary pathways compared to local galaxies, potentially explaining the high BH mass,” the authors write.

LRG 3-757 could’ve experienced what’s called “scouring.” Scouring can occur when two extremely massive galaxies merge and affects the velocity dispersion of stars in the galaxy’s center. “In this process, the
binary SMBHs dynamically expel stars from the central regions of the merged galaxy, effectively reducing the stellar velocity dispersion while leaving the SMBH mass largely unchanged,” the authors explain.

Another possibility is black hole/AGN feedback. When black holes are actively feeding they’re called Active Galactic Nuclei. Powerful jets and outflows from AGN can quench star formation and possibly alter the central structure of the galaxy. That could decouple the growth of the SMBH from the velocity dispersion.

Artist view of an active supermassive black hole and its powerful jets. Image Credit: ESO/L. Calçada

“A third scenario posits that such UMBH could be remnants of extremely luminous quasars, which experienced rapid SMBH accretion episodes in the early Universe,” the authors write.

The researchers say that more observations and better models are needed “to explain the scatter in the ?BH ? sigma e relation at its upper end.”

More observations are on the way thanks to the Euclid mission. “The Euclid mission is expected to discover hundreds of thousands of lenses over the next five years,” the authors write in their conclusion. The Extremely Large Telescope (ELT) will also contribute by allowing more detailed dynamical studies of the velocity dispersion.

“This new era of discovery promises to deepen our understanding of galaxy evolution and the interplay between baryonic and DM components,” the authors conclude.

The post One of the Most Massive Black Holes in the Universe Lurks at the Center of the Cosmic Horsehoe appeared first on Universe Today.

In the summer of 2022, the journal Nature Human Behavior put out a notice that it could reject articles that were “stigmatizing” or “harmful” to different groups, regardless of the scientific content. The problems with this stand, which were immediately called out by Steve Pinker, Michael Shermer, and others, is that what is seen as stigmatizing or harmful is pretty much a subjective matter, and, as Pinker tweeted:

I think the journal and its editor were taken aback by this and similar reactions to their statements, and on Day 2 of our USC conference on Science and Ideology in January, the Chief Editor of the journal, Stavroula Kousta, walked back their statement a bit in here 24-minute talk (go here to here her talk; it’s the first one on the video).

But the walking-back didn’t mean that Nature Human Behavior was becoming less woke. Indeed, it just published a ridiculously repetitive and trite paper about how science needs “allyship” to produce a “diverse, equitable, and inclusive academia.” It’s not that STEM isn’t seeking a diversity of groups and viewpoints—though, inevitably, “diversity” in their sense means “diversity of race or sex”—but that this article says absolutely nothing new about the issue. What the journal published now is a prime example of virtue-flaunting that, in the end accomplish nothing.  You can read it by clicking on the screenshot below (it should be free with the legal Unpaywall app), and you can get the pdf here.

The piece begins with the usual claim of “harm”: the same issue that the same journal discussed before:

In academia, despite recent progress towards diversity, biases and microaggressions can still exclude and harm members of disadvantaged social groups.

The person who sent me this article wrote “No citations are given for this claim about bigotry and discrimination at the most liberal, open, welcoming institutions that have ever existed in human history. Amazing.”

The article then gives these figures, which are baffling because one would expect younger women to drop out more rather than less frequently. But they may be correct; I am just not sure that they reflect misogyny:

Such patterns of marginalization are not specific to students. Among US faculty members, for example, women are 6%, 10% and 19% more likely to leave each year than their men counterparts as assistant, associate and full professors, respectively.

I suspect that these departures have little to do with ongoing “structural bias” against women academics, not only because no instances of inbuilt structural bias are actually given, but also, at least for women, a big and recent review by Ceci et al. found either no bias against women’s achievements in academic science or a female advantage—save for teaching evaluations and a slight difference in salary, about 3.6% lower salary for women.   However, the authors do not dismiss the possibility and importance of bias against women.

At any rate, if you haven’t heard come across this advice about “allyship” before, and are an academic, you must be blind and deaf. I’m not going to reprise the paper for you, as you’ve heard it all before.

I’m assuming that well-meaning people agree with me that marginalized scientists should be treated just like everyone else.  But how many times do we need to hear that? At any rate, this paper rings the chimes again, singling out six areas where we’re told how to behave. These are direct quotes.

1.) Listen to and centre marginalized voices.

2.) Reflect on and challenge your own biases (I guess you determine them by taking an “implicit bias” test, a procedure that’s been severely criticized

3.)  Speak up to include and support disadvantaged groups

4.)  Speak out against bias when it happens

5.)  Advocate for institutional initiatives to promote equity and inclusion

6.)  Dismantle institutional policies and procedures of exclusion

#4 and #6 are no-brainers, though, speaking personally, I don’t know of any institutional policies and procedures of exclusion in biology.  The rest are ideological statements assuming that everyone except for the marginalized is biased, and that the way to achieve inclusion is to promote “equity” (do they even know what “equity” means?) And, of course, the entire program reflects the tenets of DEI, which are on the chopping block in the U.S.

Now this article isn’t as bad as ones on feminist glaciology or ones maintaining that Einstein’s principle of covariance supports the view that minorities have an equal claim to objectivity..  No, it’s just superfluous, a farrago of what decent human beings already do, misleading assertions about bias, mixed with patronizing advice that we already follow. It accomplishes nothing save further erode the credibility of editor Kousta.

Here’s the conclusion:

For allyship to be effective in academia, it must be grounded in a deep commitment to DEI. This means recognizing that allyship is not a one-time event, but an ongoing process of learning, reflection and action. Moreover, it needs to go above and beyond symbolic or superficial acts (performative allyship) to demonstrate substantial and meaningful support that is recognized as beneficial by those it is meant to serve (substantive allyship). It is noteworthy to understand and accept that we will make mistakes along the way. No one is perfect, and as explained above, allyship requires a willingness to engage in humility and self-reflection. When mistakes are made, it is important to listen to feedback from disadvantaged groups, take responsibility for any harm caused, and commit to doing better in the future.

In conclusion, everyone can engage in allyship and work to challenge and dismantle systemic bias, creating a more just, equitable and inclusive academic community for all.

At least they used “equitable” properly, meaning “treating people fairly.”  But couldn’t the whole article have consisted of just that sentence?

Preserved wooden spears from hundreds of thousands of years ago seem to have been suitable for throwing, not just close-range attacks

The site of a deep-sea mining test in 1979 had lower levels of biodiversity when researchers revisited it in 2023 compared with undisturbed areas nearby

From the perspective of complex systems, the study reveals the universality, specificity, and explanatory power of underlying rules governing urban system evolution.

Scientists have developed an AI-powered tool that detects 64% of brain abnormalities linked to epilepsy that human radiologists miss.

Trigger(nometry) warning: semi-conservative video.

I can’t remember who recommended I watch this video, which features satirist, author, and Triggernometry co-host Konstantin Kisin speaking for 15 minutes at a meeting of the Alliance for Responsible Citizenship (ARC). The group is described by Wikipedia as “an international organisation whose aim is to unite conservative voices and propose policy based on traditional Western values.”

The talk is laced with humor, but the message is serious:  Kisin argues that societies based on “Western values” are the most attractive, as shown by the number of potential immigrants; but they are endangered by the negativity and “lies” of those who tell us that “our history is all bad and our country is plagued by prejudice and intolerance.” To that he replies that people espousing such sentiments still prefer to live in the West. (But of course that doesn’t mean that these factors still aren’t at play in the West!)  Kisin then touts both Elon Musk (for “building big things”) and (oy) Jordan Peterson for “reminding us that our lives will improve if we accept that “honesty is better than lies, that responsibility is better than blame, and strength is better than weakness.”

He continues characterizing the West as special: “the most free and prosperous societies in the history of humanity, and we are going to keep them that way.” To accomplish that, he promotes free speech as the highest of Western values, and rejects identity politics, arguing that “multiethnic societies can work; multicultural societies cannot.” Finally, he claims that human beings are good, denying (as he avers) the woke view that “human beings are a pestilence on the planet.”  Kisin calls for more reproduction and making energy “as cheap and abundant as possible.”

The talk finishes with the most inspiring thing Kising says he’s ever heard: that we’re going to die; ergo, we have nothing to lose. “We might as well speak the truth, we might as well reach for the stars, we might as well fight like our lives depended on it—because they do.”  I’m not exactly sure what he means, nor do I feel uplifted or inspired by these words, which don’t really tell us why he thinks the tide is turning. And, at the end, I could see where this optimistic word salad came from: it’s in Wikipedia, too:

[The ARC] is associated with psychologist and political commentator Jordan Peterson. One Australian journalist identified the purpose of ARC as follows: “to replace a sense of division and drift within conservatism, and Western society at large, with a renewed cohesion and purpose”.

Do any readers get inspired by this kind of chest-pounding?  I have to add that I do like Triggernometry, one of the few podcasts I can listen to, but I’m not especially energized by the co-host’s speech.

Type-1 diabetes, IBD, multiple sclerosis, rheumatoid arthritis, coeliac disease and lupus are all caused by the body attacking itself. But new therapies that reset the immune system could offer lasting help

A SpaceX Falcon 9 rocket is about to launch a number of missions, including a private lunar lander, a lunar satellite for NASA and a prospecting probe for an asteroid-mining company

If you’re following this site, you’ll know that 22 biologists (including me) sent a letter to three ecology and evolution societies who had issued a statement directed at the President and Congress that biological sex was a spectrum and a continuum in all species. The statement claimed without support that it expressed a consensus view of biologists, although the members of the societies were not polled.

Of course this behavior could not stand, and so Luana Maroja cobbled together a letter to those societies noting that the biological definition of sex was based on the development of the apparatus evolved to produce gametes, and that this showed that all animals and plants had only two sexes: male and female. As Richard Dawkins pointed out, even the three Society Presidents used the sex binary in their own biological work.

The letter has now accumulated more than a hundred signatures.  If you are an anisogamite and want to sign the letter, this is a reminder that the deadline for signatures is in about a week: 5 p.m. Monday, March 3. You can sign it this way (from Luana’s post on Heterodox STEM);

The societies for the Study of Evolution (SSE), the American Society of Naturalists (ASN) and the Society for Systematic Biologists (SSB) issued a declaration addressed to President Trump and all the members of Congress (declaration also archived here), proffering a confusing definition of sex, implying that sex is not binary.

We wrote a short letter explaining that sex is indeed defined by gamete type.

We are now collecting more signatures from biologists who agree to have their name publicly posted. If you are a biologist (or in a field related to biology) want to add your name, just fill in the bottom of this form (it contains the full text of our letter and a link to the tri-societies’ letter).

Please fill in all the blanks, including your name, position, and email, and we ask that you have something to do with biology. Also, we will most likely post the letter with names, so if you want to remain publicly anonymous but agree with our sentiments, just write your own personal email to the Society presidents (two of them have emails in the original letter). Nobody’s email will become public if I decide to post the final letter and signers on this site.

It takes about one minute to fill in the form, so if you want to send a message to these three societies, you know what to do.

We have contributions from two people, but I am holding onto those, as it appears that this feature will become sporadic in the future. That’s sad, no?

Venus differs from Earth in many ways including a lack of internal dynamo driving global magnetosphere to shield potential life from solar and cosmic radiation. However, Venus possesses a dense atmosphere and, in a recent study, planetary scientists conducted simulations of the Venusian atmosphere to determine radiation penetration to the lower cloud layers. Their calculations revealed that the atmospheric thickness provides adequate protection for life at what’s considered Venus’s “habitable zone,” located 40–60 km above the surface.

Venus, the second planet from the Sun, is often called Earth’s “sister planet” because of its comparable size and composition. Yet its environment couldn’t be more different or extreme. It has a thick carbon dioxide atmosphere with sulfuric acid clouds that have created a runaway greenhouse effect, making Venus the solar system’s hottest planet—surface temperatures in excess of 475°C. The Venusian landscape features volcanic plains, mountains, and canyons under atmospheric pressure exceeding 90 times Earth’s. Despite these inhospitable conditions, Venus remains an object of scientific interest, with researchers studying its geology and atmosphere.

Venus

In 2020, scientists found phosphine in Venus’s atmosphere which, on Earth, is mostly made by biological processes or in other words – living things. This discovery was somewhat unexpected and facilitated a fresh look at Venus as a possible home for life. Surprisingly perhaps, Venus does have a “habitable zone” in its clouds about 40-60 km up, where the temperature and pressure aren’t too different from Earth’s. While the planet’s surface is totally uninhabitable, high up in the atmosphere might actually support some kind of microbial life that’s adapted to acidic conditions. A new piece of research has been exploring if the thick Venusian atmosphere would protect any such life that may have evolved or whether intense radiation bathes its habitable zone. 

The spectral data from SOFIA overlain atop this image of Venus from NASA’s Mariner 10 spacecraft is what the researchers observed in their study, showing the intensity of light from Venus at different wavelengths. If a significant amount of phosphine were present in Venus’s atmosphere, there would be dips in the graph at the four locations labeled “PH3,” similar to but less pronounced than those seen on the two ends. Credit: Venus: NASA/JPL-Caltech; Spectra: Cordiner et al.

The research, that was led by Luis A. Anchordoqui from the University of New York has revealed surprising results. The team discovered that despite Venus lacking a magnetic field and orbiting closer to the Sun, the radiation levels in its potentially habitable cloud layer are remarkably similar to those at Earth’s surface. Using the AIRES simulation package (AIRshower Extended Simulations – simulates cascades of secondary particles from incoming high energy radiation) the team generated over a billion simulated cosmic ray showers to analyse particle interactions within Venus’s atmosphere. 

Their findings show that at equivalent atmospheric depths, particle fluxes on Venus and Earth are nearly identical, with only about 40% higher radiation detected at the uppermost boundary of Venus’s habitable zone. This suggests Venus’s thick atmosphere provides substantial radiation shielding that might be sufficient for potential microbial life.

The research suggests that cosmic radiation wouldn’t significantly hinder life in Venus’s cloud layer. Any potential microorganisms that were there would face radiation levels similar to those on Earth’s surface. On Earth, life has found a way across a wide range of environments that span many kilometres, this is known as its life reservoir. Venus doesn’t have such a great reservoir so if radiation were to sterilise the habitable clouds, there’s no equivalent to Earth’s subsurface biosphere that could eventually recolonise the region. This means life needs to persist continuously in its atmospheric habitat without being able to move to other parts of the planet.

Source : The Venusian Chronicles

The post Although it Lacks a Magnetic Field, Venus Can Still Protect With in its Atmosphere appeared first on Universe Today.

Why do I find the word particle so problematic that I keep harping on it, to the point that some may reasonably view me as obsessed with the issue? It has to do with the profound difference between the way an electron is viewed in 1920s quantum physics (“Quantum Mechanics”, or QM for short) as opposed to 1950s relativistic Quantum Field Theory (abbreviated as QFT). [The word “relativistic” means “incorporating Einstein’s special theory of relativity of 1905”.] My goal this week is to explain carefully this difference.

The overarching point:

• in QM, an electron really is a particle, at least to the limited extent that QM can handle that notion;
• in QFT, an electron is at best a “particle”, with the word in quotation marks
  • (and I personally prefer the term wavicle.)

I’ve discussed this to some degree already in my article about how the view of an electron has changed over time, but here I’m going to give you a fuller picture. To complete the story will take two or three posts, but today’s post will already convey one of the most important points.

There are two short readings that you may want to dofirst.

• The first is an article about the distinction between physical space (within which all objects actually are located) and the abstract space of possibilities (which consists of all ways that the objects in a physical system could be arranged in physical space.) This issue, essential in quantum physics of any type, will be crucial below.
• The second is a short section of a blog post that explains how QM views an isolated object in a state of definite momentum — i.e. something whose motion (both speed and direction) is precisely known, and whose position is therefore completely unknown, thanks to Heisenberg’s uncertainty principle.

I’ll will review the main point of the second item, and then I’ll start explaining what an isolated object of definite momentum looks like in QFT.

Removing Everything Extraneous

First, though, let’s make things as simple as possible. Though electrons are familiar, they are more complicated than some of their cousins, thanks to their electric charge and “spin”, and the fact that they are fermions. By contrast, bosons with neither charge nor spin are much simpler. In nature, these include Higgs bosons and electrically-neutral pions, but each of these has some unnecessary baggage. For this reason I’ll frame my discussion in terms of imaginary objects even simpler than a Higgs boson. I’ll call these spinless, chargeless objects “Bohrons” in honor of Niels Bohr (and I’ll leave the many puns to my readers.)

For today we’ll just need one, lonely Bohron, not interacting with anything else, and moving along a line. Using 1920s QM in the style of Schrödinger, we’ll take the following viewpoints.

• A Bohron is a particle and exists in physical space, which we’ll take to be just a line — the set of points arranged along what we’ll call the x-axis.
• The Bohron has a property we call position in physical space. We’ll refer to its position as x1.
• For just one Bohron, the space of possibilities is simply all of its possible positions — all possible values of x1. [See Fig. 1]
• The system of one isolated Bohron has a wave function Ψ(x1), a complex number at each point in the space of possibilities. [Note it is not a function of x, the points in physical space; it is a function of x1, the possible positions of the Bohron.]
• The wave function predicts the probability of finding the Bohron at any selected position x1: it is proportional to |Ψ(x1)|2, the square of the absolute value of the complex number Ψ(x1).

Figure 1: For a Bohron moving along a line, physical space is the x-axis where the Bohron (blue dot) is located. The space of possibilities, the set of all possible arrangements of our one-Bohron system (red star) is the the x1-axis. This subtle but important distinction becomes clearer when we have two or more Bohrons; the physical space is unchanged, but possibility space is totally different. A QM State of Definite Momentum

In a previous post, I described states of definite momentum. But I also described states whose momentum is slightly less definite — a broad Gaussian wave packet state, which is a bit more intutive. The wave function for a Bohron in this state is shown in Fig. 2, using three different representations. You can see intuitively that the Bohron’s motion is quite steady, reflecting near definite momentum, while the wave function’s peak is very broad, reflecting great uncertainty in the Bohron’s position.

• Fig. 2a shows the real and imaginary parts of Ψ(x1) in red and blue, along with its absolute-value squared |Ψ(x1)|2 in black.
• Fig. 2b shows the absolute value |Ψ(x1)| in a color that reflects the argument [i.e. the phase] of Ψ(x1).
• Fig. 2c indicates |Ψ(x1)|2, using grayscale, at a grid of x1 values; the Bohron is more likely to be found at or near dark points than at or near lighter ones.

For more details and examples using these representations, see this post.

Figure 2a: The wave function for a wave packet state with near-definite momentum, showing its real (red) and imaginary (blue) parts and its absolute value squared (black.) Figure 2b: The same wave function, with the curve showing its absolute value and colored by its argument. Figure 2c: The same wave function, showing its absolute value squared using gray-scale values on a grid of x1 points. The Bohron is more likely to be found near dark-shaded points.

To get a Bohron of definite momentum P1, we simply take what is plotted in Fig. 2 and make the broad peak wider and wider, so that the uncertainty in the Bohron’s position becomes infinite. Then (as discussed in this post) the wave function for that state, referred to as |P1>, can be drawn as in Fig. 3:

Figure 3a: As in Fig. 2a, but now for a state |P1> of precisely known momentum to the left. Figure 3b: As in Fig. 2b, but now for a state |P1> of precisely known momentum to the left. Figure 3c: As in Fig. 2c, but now for a state |P1> of precisely known momentum; note the probability of finding the Bohron is equal at every point at all times.

In math, the wave function for the state at some fixed moment in time takes a simple form, such as

where i is the square root of -1. This is a special state, because the absolute-value-squared of this function is just 1 for every value of x1, and so the probability of measuring the Bohron to be at any particular x1 is the same everywhere and at all times. This is seen in Fig. 3c, and reflects the fact that in a state with exactly known momentum, the uncertainty on the Bohron’s position is infinite.

Let’s compare the Bohron (the particle itself) in the state |P1> to the wave function that describes it.

• In the state |P1>, the Bohron’s location is completely unknown. Still, its position is a meaningful concept, in the sense that we could measure it. We can’t predict the outcome of that measurement, but the measurement will give us a definite answer, not a vague indefinite one. That’s because the Bohron is a particle; it is not spread out across physical space, even though we don’t know where it is.
• By contrast, the wave function Ψ(x1) is spread out, as is clear in Fig. 3. But caution: it is not spread out across physical space, the points of the x axis. It is spread out across the space of possibilities — across the range of possible positions x1. See Fig. 1 [and read my article on the space of possibilities if this makes no sense to you.]
• Thus neither the Bohron nor its wave function is spread out in physical space!

We do have waves here, and they have a wavelength; that’s the distance between one crest and the next in Fig. 3a, and the distance beween one red band and the next in Fig. 3b. That wavelength is a property of the wave function, not a property of the Bohron. To have a wavelength, an object has to be wave-like, which our QM Bohron is not.

Conversely, the Bohron has a momentum (which is definite in this state, and is something we can measure). This has real effects; if the Bohron hits another particle, some or all of its momentum will be transferred, and the second particle will recoil from the blow. By contrast, the wave function does not have momentum. It cannot hit anything and make it recoil, because, like any wave function, it sits outside the physical system. It merely describes an object with momentum, and tells us the probable outcomes of measurements of that object.

Keep these details of wavelength (the wave function’s purview) and the momentum (the Bohron’s purview) in mind. This is how 1920’s QM organizes things. But in QFT, things are different.

First Step Toward a QFT State of Definite Momentum

Now let’s move to quantum field theory, and start the process of making a Bohron of definite momentum. We’ll take some initial steps today, and finish up in the next post.

Our Bohron is now a “particle”, in quotation marks. Why? Because our Bohron is no longer a dot, with a measurable (even if unknown) position. It is now a ripple in a field, which we’ll call the Bohron field. That said, there’s still something particle-like about the Bohron, because you can only have an integer number (1, 2, 3, 4, 5, …) of Bohrons, and you can never have a fractional number (1/2, 7/10, 2.46, etc.) of Bohrons. This feature is something we’ll discuss in later posts, but we’ll just accept it for now.

As fields go, the Bohron field is a very simple example. At any given moment, the field takes on a value — a real number — at each point in space. Said another way, it is a function of physical space, of the form B(x).

Very, very important: Do not confuse the Bohron field B(x) with a wave function!!

• This field is a function in physical space (not the space of possibilities). B(x) is a function of physical space points x that make up the x-axis, and is not a function of a particle’s position x1, nor is it a function of any other coordinate that might arise in the space of possibilities.
• I’ve chosen the simplest type of QFT field: B(x) is a real number at each location in physical space. This is in contrast to a QM wave function, which is a complex number for each possibility in the space of possibilities.
• The field itself can carry energy and momentum and transport it from place to place. This is unlike a wave function, which can only describe the energy and momentum that may be carried by physical objects.

Now here’s the key distinction. Whereas the Bohron of QM has a position, the Bohron of QFT does not generally have a position. Instead, it has a shape.

If our Bohron is to have a definite momentum P1, the field must ripple in a simple way, taking on a shape proportional to a sine or cosine function from pre-university math. An example would be:

where A is a real number, called the “amplitude” of the wave, and x is a location in physical space.

At some point soon we’ll consider all possible values of A — a part of the space of possibilities for the field B(x) — so remember that A can vary. To remind you, I’ve plotted this shape for A=1 in Fig. 4a and again for A=-3/2 in Fig 4b.

Figure 4a: The function A cos[P1 x], for the momentum P1 set equal to 1 and the amplitude A set equal to 1. Figure 4b: Same as Fig. 4a, but with A = -3/2 . Initial Comparison of QM and QFT

At first, the plots in Fig. 4 of the QFT Bohron’s shape look very similar to the QM wave function of the Bohron particles, especially as drawn in Fig. 3a. The math formulas for the two look similar, too; compare the formula after Fig. 3 to the one above Fig. 4.

However, appearances are deceiving. In fact, when we look carefully, EVERYTHING IS COMPLETELY DIFFERENT.

• Our QM Bohron with definite momentum has a wave function Ψ(x1), while in QFT it has a shape B(x); they are functions of variables which, though related, are different.
  
  
• On top of that, there’s a wave function in QFT too, which we haven’t drawn yet. When we do, we’ll see that the QFT Bohron’s wave function looks nothing like the QM Bohron’s wave function. That’s because
  • the space of possibilities for the QM wave function is the space of possible positions that the Bohron particle can have, but
  • the space of possibilities for the QFT wave function is the space of all possible shapes that the Bohron field can have.
• The plot in Fig. 4 shows a curve that is both positive and negative but is drawn colorless, in contrast to Fig. 3b, where the curve is positive but colored. That’s because
  • the Bohron field B(x) is a real number with no argument [phase], whereas
  • the QM wave function Ψ(x1) for the state of definite momentum has an always-positive absolute value and a rapidly varying argument [phase].
• The axes in Fig. 4 are labeled differently from the axis in Fig. 3. That’s because (see Fig. 1)
  • the QFT Bohron field B(x) is found in physical space, while
  • the QM wave function Ψ(x1) for the Bohron particle is found in the particle’s space of possibilities.
• The absolute-value-squared of a wave function |Ψ(x1)|2 is interpreted as a probability (specifically, the probability for the particular possibility that the particle is at position x1. There is no such interpretation for the square of the Bohron field |B(x)|2. We will later find a probability interpretation for the QFT wave function, but we are not there yet.
  
  
• Both Fig. 4 and Figs. 3a, 3b show curves with a wavelength, albeit along different axes. But they are very different in every sense
  • In QM, the Bohron has no wavelength; only its wave function has a wavelength — and that involves lengths not in physical space but in the space of possibilities.
  • In QFT,
    • the field ripple corresponding to the QFT Bohron with definite momentum has a physical wavelength;
    • meanwhile the QFT Bohron’s wave function does not have anything resembling a wavelength! The field’s space of possibilities, where the wave function lives, doesn’t even have a recognizable notion of lengths in general, much less wavelengths in particular.

I’ll explain that last statement next time, when we look at the nature of the QFT wave function that corresponds to having a single QFT Bohron.

A Profound Change of Perspective

But before we conclude for the day, let’s take a moment to contemplate the remarkable change of perspective that is coming into our view, as we migrate our thinking from QM of the 1920s to modern QFT. In both cases, our Bohron of definite momentum is certainly associated with a definite wavelength; we can see that both in Fig. 3 and in Fig. 4. The formula for the relation is well-known to scientists; the wavelength λ for a Bohron of momentum P1 is simply

where h is Planck’s famous constant, the mascot of quantum physics. Larger momentum means smaller wavelength, and vice versa. On this, QM and QFT agree.

But compare:

• in QM, this wavelength sits in the wave function, and has nothing to do with waves in physical space;
• in QFT, the wavelength is not found in the field’s wave function; instead it is found in the field itself, and specifically in its ripples, which are waves in physical space.

I’ve summarized this in Table 1.

Table 1: The Bohron with definite momentum has an associated wavelength. In QM, this wavelength appears in the wave function. In QFT it does not; both the wavelength and the momentum are found in the field itself. This has caused no end of confusion.

Let me say that another way. In QM, our Bohron is a particle; it has a position, cannot spread out in physical space, and has no wavelength. In QFT, our Bohron is a “particle”, a wavy object that can spread out in physical space, and can indeed have a wavelength. (This is why I’d rather call it a wavicle.)

[Aside for experts: if anyone thinks I’m spouting nonsense, I encourage the skeptic to simply work out the wave function for phonons (or their counterparts with rest mass) in a QM system of coupled balls and springs, and watch as free QFT and its wave function emerge. Every statement made here is backed up with a long but standard calculation, which I’m happy to show you and discuss.]

I think this little table is deeply revealing both about quantum physics and about its history. It goes a long way toward explaining one of the many reasons why the brilliant founding parents of quantum physics were so utterly confused for a couple of decades. [I’m going to go out on a limb here, because I’m certainly not a historian of physics; if I have parts of the history wrong, please set me straight.]

Based on experiments on photons and electrons and on the theoretical insight of Louis de Broglie, it was intuitively clear to the great physicists of the 1920s that electrons and photons, which they were calling particles, do have a wavelength related to their momentum. And yet, in the late 1920s, when they were just inventing the math of QM and didn’t understand QFT yet, the wavelength was always sitting in the wave function. So that made it seem as though maybe the wave function was the particle, or somehow was an aspect of the particle, or that in any case the wave function must carry momentum and be a real physical thing, or… well, clearly it was very confusing. It still confuses many students and science writers today, and perhaps even some professional scientists and philosophers.

In this context, is it surprising that Bohr was led in the late 1920s to suggest that electrons are both particles and waves, depending on experimental context? And is it any wonder that many physicists today, with the benefit of both hindsight and a deep understanding of QFT, don’t share this perspective?

In addition, physicists already knew, from 19th century research, that electromagnetic waves — ripples in the electromagnetic field, which include radio waves and visible light — have both wavelength and momentum. Learning that wave functions for QM have wavelength and describe particles with momentum, as in Fig. 3, some physicists naturally assumed that fields and wave functions are closely related. This led to the suggestion that to build the math of QFT, you must go through the following steps:

• first you take particles and describe them with a wave function, and then
• second, you make this wave function into a field, and describe it using an even bigger wave function.

(This is where the archaic terms “first quantization” and “second quantization” come from.) But this idea was misguided, arising from early conceptual confusions about wave functions. The error becomes more understandable when you imagine what it must have been like to try to make sense of Table 1 for the very first time.

In the next post, we’ll move on to something novel: images depicting the QFT wave function for a single Bohron. I haven’t seen these images anywhere else, so I suspect they’ll be new to most readers.

Tracks and footprints found in New Mexico are by far the earliest evidence of people using primitive vehicles to transport things