When it comes to particles, only photons are more abundant than neutrinos, yet detecting neutrinos is extremely difficult. Scientists have gone to extreme lengths to detect them, including building neutrino observatories in deep, underground mines and in the deep, clear ice of Antarctica.
One of their latest efforts to detect neutrinos is KM3NeT, which is still under construction at the bottom of the Mediterranean Sea. Though the neutrino telescope isn’t yet complete, it has already detected the most energetic neutrino ever detected.
The Universe is flooded with them, yet they’re extremely difficult to detect. They’re like tiny, abundant ghosts and are sometimes called “ghost particles.” They have no electric charge, which limits the ways they interact with matter. The fact that they only interact through gravity and the weak nuclear force explains their elusiveness.
Neutrinos can’t be seen and are only detected indirectly on the rare occasions when they interact with matter through the weak force. These interactions release Cherenkov Radiation that detectors can sense. Detectors have to be very large to catch these rare interactions. Km3NeT (Cubic Kilometre Neutrino Telescope) features thousands of individual detectors in each of two sections. At the end of 2024, Km3NeT was only 10% complete, yet on February 13th, it detected an extraordinarily energetic neutrino.
The detection is presented in new research in Nature titled “Observation of an ultra-high-energy cosmic neutrino with KM3NeT.” The KM3NeT Collaboration is credited with authorship.
“The detection of cosmic neutrinos with energies above a teraelectronvolt (TeV) offers a unique exploration into astrophysical phenomena,” the paper states. “Here we report an exceptionally high-energy event observed by KM3NeT, the deep-sea neutrino telescope in the Mediterranean Sea, which we associate with a cosmic neutrino detection.”
This is an artist’s impression of a KM3NeT installation in the Mediterranean. Underwater neutrino detectors take advantage of location to track these fast particles. Image Courtesy Edward Berbee/Nikhef.Though neutrinos themselves are undetectable, the muons created by their rare interactions with matter are detectable. In this detection, the muon’s energy level was 120 (+110/-60) petaelectronvolts (PeV). High-energy neutrinos like these are produced when “ultra-relativistic cosmic-ray protons or nuclei interact with other matter or photons,” according to the paper.
Because neutrinos seldom interact with matter and aren’t affected by magnetic fields, they could originate from extremely distant places in the Universe. These are called cosmogenic neutrinos rather than solar neutrinos, the more plentiful type that comes from the Sun. Cosmogenic neutrinos are more energetic than solar neutrinos because they’re created by cosmic rays from high-energy astrophysical phenomena like active galactic nuclei and gamma-ray bursts. Since they travel virtually unimpeded from distant sources, they can provide insights into their sources.
In terms of energy level, there are two types of neutrinos: atmospheric and cosmogenic. Cosmogenic neutrinos are more energetic and less plentiful than atmospheric neutrinos. “The neutrino energy is thus a crucial parameter for establishing a cosmic origin,” the paper states.
“The energy of this event is much larger than that of any neutrino detected so far,” the paper states. This could be the first detection of a cosmogenic neutrino and it could be the result of ultra-high energy cosmic rays that interact with background photons.
“Of interest in this article are neutrino interactions that produce high-energy muons, which can travel several kilometres in seawater before being absorbed,” the paper states. As these muons travel through the water, they lose energy. The amount of energy lost in each unit of travel is proportional to the muon’s energy level. By recording the signals and their time of arrival at different individual detectors in the KM3NeT array, scientists can then reconstruct the muon’s initial energy level and its direction.
This figure shows side and top views of the event in (a), with the Eiffel Tower shown for scale. The red line shows the reconstructed trajectory of the muon created by the neutrino interaction. The hits of individual photomultiplier tubes (PMTs) are represented by spheres stacked along the direction of the PMT orientations. Only the first five hits on each PMT are shown. The spheres are colour-coded relative to the first initial detection, and the larger they are, the more photons were detected, equating to energy level. Image Credit: The KM3NeT Collaboration, 2025.“The muon trajectory is reconstructed from the measured times and positions of the first hits recorded on the PMTs, using a maximum-likelihood algorithm,” the paper states. The new detection is referred to as KM3-230213A. The 21 detection lines registered 28,086 hits, and by counting the number of PMTs that are triggered, the researchers can estimate the muon energy at the detector.
This figure shows the number of detections in a simulation of the KM3-230213A event. The simulation helps researchers determine the true muon energy. “The normalized distributions of the number of PMTs participating in the triggering of the event for simulated muon energies of 10, 100 and 1,000?PeV,” the authors write. The vertical dashed line indicates the observed value in KM3-230213A with 3,672 PMT detections. Image Credit: The KM3NeT Collaboration, 2025.The KM3NeT Collaboration detected the most energetic neutron ever while still incomplete, and that bodes well for the future. However, the incomplete facility did limit one aspect of the detection. There’s uncertainty about the direction it came from. “A dedicated sea campaign is planned in the future to improve the knowledge of the positions of the detector elements on the seafloor,” the authors write. Once that campaign is complete, the data from KM3-230213A will be recalibrated.
Still, the researchers learned something about the direction of its source, albeit with an uncertainty estimated to be 1.5°. At the vast distances involved, that’s a significant uncertainty. “The probability that KM3-230213A is of cosmic origin is much greater than any hypothesis involving an atmospheric origin,” the paper states.
The researchers identified some candidate sources.
“Extragalactic neutrino sources should be dominated by active galactic nuclei, and blazars are of particular interest considering the very-high energy of KM3-230213A,” the paper states. “To compile a census of potential blazar counterparts within the 99% confidence region of KM3-230213A, archival multiwavelength data were also explored.”
The researchers identified 12 potential source blazars in different survey catalogues.
The red star in this figure shows KM3-230213A. The three concentric red circles show the error regions within R(68%), R(90%) and R(99%). Selected source candidates and their directions are shown as coloured markers. The colours and marker type indicate the criterion according to which the source was selected, e.g. VLBI is Very Large Baseline Interferometry. The sources are numbered according to their proximity to KM3-230213A. Image Credit: The KM3NeT Collaboration, 2025.Neutrinos are abundant yet elusive. They pass right through the Earth unimpeded, and about 100 trillion of them pass through our bodies every second. Detecting them is important because of what they can tell us about the Universe.
The extraordinary energy level of this neutrino is significant in neutrino astrophysics. It shows that nature can generate ultra-high-energy neutrinos, possibly from blazars, which are active galactic nuclei with jets pointed right at us.
“This suggests that the neutrino may have originated in a different cosmic accelerator than the lower-energy neutrinos, or this may be the first detection of a cosmogenic neutrino, resulting from the interactions of ultra-high-energy cosmic rays with background photons in the Universe.”
The post An Unfinished Detector has Already Spotted the Highest-Energy Neutrino Ever Seen appeared first on Universe Today.
In 1974, science fiction author Larry Niven wrote a murder mystery with an interesting premise: could you kill a man with a tiny black hole? I won’t spoil the story, though I’m willing to bet most people would argue the answer is clearly yes. Intense gravity, tidal forces, and the event horizon would surely lead to a messy end. But it turns out the scientific answer is a bit more interesting.
On the one hand, it’s clear that a large enough black hole could kill you. On the other hand, a black hole with the mass of a single hydrogen atom is clearly too small to be noticed. The real question is the critical mass. At what minimum size would a black hole become deadly? That’s the focus of a new paper on the arXiv.
The study begins with primordial black holes. These are theoretical bodies that may have formed in the earliest moments of the Universe and would be much smaller than stellar-mass black holes. Anywhere from atom-massed to a mass several times that of Earth. Although astronomers have never found any primordial black holes, observations do rule out several mass ranges. For example, any primordial black hole smaller than 1012 kg would have already evaporated thanks to Hawking radiation. Anything larger than 1020 kg would gravitationally lens stars in the Milky Way. Since we haven’t detected these lensing effects, they must at the very least be exceedingly rare. If they exist at all.
Some theoretical models argue that primordial black holes could be the source of dark matter. If that’s the case, observational limits constrain their masses to the 1013 – 1019 kg range, which is similar to the mass range for asteroids. Therefore, the study focuses on this range and looks at two effects: tidal forces and shock waves.
Tidal forces occur because the closer you get to a mass, the stronger its gravity. This means a black hole exerts a force differential on you as it gets near. So the question is whether this force differential is strong enough to tear flesh. Asteroid-mass black holes are less than a micrometer across, so even the tidal forces would cover a tiny area. If one passed through your midsection or one of your limbs, there might be some local damage, but nothing fatal. It would be similar to a needle passing through you.
But if the black hole passed through your head, that would be a different story. Tidal forces could tear apart brain cells, which would be much more serious. Since brain cells are delicate, even a force differential of 10 – 100 nanonewtons might kill you. But that would take a black hole at the highest end of our mass range.
Shockwaves would be much more dangerous. In this case, as a black hole entered your body, it would create a density wave that would ripple through you. These shockwaves would physically damage cells and transfer heat energy that would do further damage. To create a shockwave of energy similar to that of a 22-caliber bullet, the black hole would only need a mass of 1.4 x 1014 kg, which is well within the range of possible primordial black holes.
So yes, a primordial black hole could kill you.
While that makes for a great story, it would never happen in real life. Even if asteroid-mass primordial black holes exist, the number of them out there compared to the vastness of space means that the odds of it happening to anyone in their lifetime are less than one in 10 trillion.
Reference: Niven, Larry. “The Hole Man.” Analog Science Fiction/Science Fact (1974): 93-104.
Reference: Robert J. Scherrer. “Gravitational Effects of a Small Primordial Black Hole Passing Through the Human Body.” arXiv preprint arXiv:2502.09734
(2025)
The post What Would Happen if a Tiny Black Hole Passed Through Your Body? appeared first on Universe Today.
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.
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.
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!
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.
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 NumbersBefore 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
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 DimensionWe’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:
[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 TimeThis 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 ExamplesBelow 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?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.Here’s Bill Maher’s latest 9-minute comedy/news schtick from Real Time, called “New Rule: In Love with A.I.” It’s based on the rising number of American women who are engaged in relationships or romantic role-playing with AI. After all real men come with a number of disadvantages, like cheating and dressing like John Fetterman, while AI can be programmed to be caring, empathic, and even match the kind of temperament that a woman wants.
As for men, well, Maher likes the old-fashioned real kind, as do I.
Notice that Pamela Paul is on the show, and was introduced as a NYT op-ed columnist, so perhaps she wasn’t fired.
As you probably know, Hagan Scotten, an assistant U.S. attorney, was asked to dismiss the corruption indictment against NYC mayor Eric Adams after U.S. Attorney Danielle Sassoon (a Republican) resigned from the Department of Justice rather than be involved in dismissing a criminal indictment on political tit-for-tat grounds. Here’s Scotten’s own letter of resignation to Trump’s goon Emil Bove, who ordered Sassoon to get Scotten to do the dirty work.
You can download the letter here from the NYT.
The last sentence of the second paragraph will live on as a defense of our Republic, which I fully believe will stand over the next four years.
h/t: David
Four days ago I presented NYT columnist Ross Douthat’s favorite argument for God’s existence. (Douthat is a pious Catholic.) That argument turned out to be pretty lame: it was the claim that “the universe was intelligible and we can use reason to understand it.” On top of that sundae, he placed the cherry of “also, humans can go far beyond this: they can do stuff like playing chess or the piano—things we couldn’t possibly have evolved to do.” (I am giving my characterizations here, not his quotes.)
If you have two neurons to rub together, and know something about evolution, you can easily see why this argument is not convincing evidence for a deity, much less the Catholic deity. Nor is it evidence for the existence of an afterlife, a crucial claim that bears on Douthat’s latest column, one that lays out what he sees as the best argument against the existence of God. That argument is what I’ve called the “Achilles heel of theism”: the existence of physical evil that inflicts suffering and/or death on undeserving (“innocent”) people.
The previous column was an excerpt from his new book, Believe, Why Everyone Should Be Religious, and I’m sure the “evil” issue is also an important one in his book. But this column doesn’t say it’s an excerpt, so it’s not self-plagiarism. Nevertheless, I find Douthat’s reasoning still pretty weak, for he gives five lame arguments why we should dismiss the existence of evil as a telling argument against God.
Douthat is turning into the C. S. Lewis for Generation X, someone who proffers superficially appealing but intellectually weak arguments simply to buttress the longings of those who want there to be a God. I think the NYT itself is catering to this slice of society, for it’s increasingly touting religion to its readers. Do you agree? And if you do, why would the NYT be doing this?
You can read Douthat’s arguments by clicking on the screenshot below, or you can find the full article archived here:
Douthat begins by again dismissing naturalism as strong evidence against a god:
The most prominent argument that tries to actually establish God’s nonexistence is the case for naturalism, the argument that our world is fundamentally reducible to its material components and untouched in its origins by any kind of conscious intention or design. But unfortunately, no version of the case for naturalism or reductionism is especially strong.
Well, I’d say that two things do strengthen “the case for naturalism.” The first is that the laws of physics appear to apply everywhere in the universe, and quantum mechanics predicts what we see to an extraordinary degree of accuracy. There is no “god parameter” in these laws; they are perfectly naturalistic. (I suppose Douthat would respond that our ability to discern the laws of physics is itself evidence for God.)
Second, even in our own everyday life, the known laws of physics seem to account for everything without anything major missing. I won’t go into this; just read Sean Carroll’s two pieces, “The Laws Underlying The Physics of Everyday Life Are Completely Understood” and “Seriously, The Laws Underlying The Physics of Everyday Life Really Are Completely Understood.” Carroll is not maintaining that we understand everything about physics (e.g., black energy); his thesis is this:
Obviously there are plenty of things we don’t understand. We don’t know how to quantize gravity, or what the dark matter is, or what breaks electroweak symmetry. But we don’t need to know any of those things to account for the world that is immediately apparent to us. We certainly don’t have anything close to a complete understanding of how the basic laws actually play out in the real world — we don’t understand high-temperature superconductivity, or for that matter human consciousness, or a cure for cancer, or predicting the weather, or how best to regulate our financial system. But these are manifestations of the underlying laws, not signs that our understanding of the laws are incomplete. Nobody thinks we’re going to have to invent new elementary particles or forces in order to understand high-Tc superconductivity, much less predicting the weather.
But I digress, but so did Douthat, who says that “the anti-reductionist argument” (against god) “clearly wins out.” Perhaps in his mind it does, but he’s hardly unbiased!
Douthat then specifies the argument from evil that he finds the most telling argument against God, but for the rest of the article he manages to argue that it’s not very telling:
So instead of talking about an argument for disbelief that I struggle to take seriously, I’m going to talk about an argument that clearly persuades a lot of people not to have religious faith and does have a form of empirical evidence on its side. That’s the argument from evil, the case that there simply can’t be a creator — or at least not a beneficent one — because the world is too laden with suffering and woe.
He then, like C. S. Lewis, hastens to reprise what he just said: that this is an argument against a particular kind of god, one that is beneficent or omnbeneficent. And that god, of course, is the Abrahamic God, including Douthat’s. So if God is kindly and all-good, why does he let little children die of leukemia, or get other diseases that cause immense suffering, not to mention the same suffering in innocent adults (or are they all sinners?). And why do tsunamis, volcanoes, and earthquakes kill millions of people, many of whom don’t deserve to die regardless of your criteria for whether someone is a “good person”.
Douthat responds with some answers that I’ve put under headings I invented. His responses rest largely on his claim that we don’t know that there is too much suffering.
We don’t know that there’s too much suffering!
The other interesting point about this argument is that while its core evidence is empirical, in the sense that terrible forms of suffering obviously exist and can be extensively enumerated, its power fundamentally rests on an intuition about just how much suffering is too much. By this I mean that many people who emphasize the problem of evil would concede that a good God might allow some form of pain and suffering within a material creation for various good reasons. Their claim, typically, is that our world experiences not just suffering but a surfeit of suffering, in forms that are so cruel and unusual (whether the example is on the scale of the Holocaust or just the torture of a single child) as to exceed anything that an omnipotent benevolence could allow.’
Indeed, various apologists have countered the Argument from Suffering by saying that suffering is an inevitable concomitant of the kind of world that God would want to create, presumably the best of all possible worlds. (Unless, that is, he’s created the world as a theater for his own amusement.) Suffering, they say, is an inevitable byproduct of free will, which we must have because to get to Heaven we must freely choose Jesus as our savior. Putting determinism aside (while accepting its truth), this is not a satisfactory answer. God knows already (as do the laws of physics) whether we’ll choose Jesus, and he could make us all choose Jesus while still thinking that it really was a free choice. (It’s not free if God knows it in advance!) Besides, how does a kid with a terrible, fatal disease result from free will? Free will for cancer cells? And what about other non-moral “physical evils” like earthquakes?
Well, theologians have worked that one out, too. To have a viable planet, they say, we have to have tectonic plates, whose shifting results in earthquakes and other sources of mortality. But if God was omnipotent, he could have created such a world! Here we see another dumb argument, but theologians are paid to make such arguments, not to find the truth.
Finally, I see “too much suffering” as is “any more suffering than is required by God’s plan”. But how do we judge that? Even if everything is made right on Judgment Day, with the kids who die young automatically going to Heaven (this is another inane theological response), there was more suffering than necessarily to achieve that end. Kids could die painlessly! I say that any suffering at all that cannot be explained by human reason is too much suffering, and if Douthat responds, “well, we don’t know God’s plan,” I would say, “Well, you don’t seem to know much about God. How do you know that he’s benevolent and that there’s a Heaven?” And here I must stop to recount a passage from Hitchens’s book attacking Mother Theresa: The Missionary Position:
Mother Teresa (who herself, it should be noted, has checked into some of the finest and costliest clinics and hospitals in the West during her bouts with heart trouble and old age) once gave this game away in a filmed interview. She described a person who was in the last agonies of cancer and suffering unbearable pain. With a smile, Mother Teresa told the camera what she told this terminal patient: “You are suffering like Christ on the cross. So Jesus must be kissing you.” Unconscious of the account to which this irony might be charged, she then told of the sufferer’s reply: “Then please tell him to stop kissing me.”
At any rate, it’s in this section of this article that Douthat reveals his confirmation bias. He’s making counterargument only to knock them down, because, of course, he has to believe. (I’d love to ask him, “Ross, since you can rationalize evil this way, is there anything that would make you reject belief in God?” Look at this:
Of course, as a Christian, I don’t think [the Argument from Evil is] a good reason to choose against my own tradition, which brings me to the second challenge. . .
Of course! He will never find a good reason to choose against his own “tradition.” (Note: In Faith Versus Fact I at least lay out a scenario that would make me tentatively accept the existence of Jesus and the Christian God.) This brings us to Douthat’s second reason to downplay the force of the Argument from Evil:
The Bible shows a lot of evidence for undeserved evil. This is a “this-I-know-because-the-Bible-tells-me-so” argument, and it’s dumb, because it doesn’t touch the problem. It only says that God was not omnibenevolent in the Bible.
To the extent that you find the problem of evil persuasive as a critique of a God who might, nevertheless, still exist, you would do well to notice that important parts of that critique are already contained within the Abrahamic tradition. Some of the strongest complaints against the apparent injustices of the world are found not in any atheistic tract, but in the Hebrew Bible. From Abraham to Job to the Book of Ecclesiastes — and thence, in the New Testament, to Jesus (God himself, to Christians) dying on the cross — the question of why God permits so much suffering is integral to Jewish and Christian Scripture, to the point where it appears that if the Judeo-Christian God exists, he expects his followers to wrestle with the question. Which means that you don’t need to leave all your intuitive reactions to the harrowing aspects of existence at the doorway of religious faith; there is plenty of room for complaint and doubt and argument inside.
This is the kind of palaver that C. S. Lewis shoveled down the gaping maws of British Christians, as if they were baby birds begging for a meal. Because there is contradictory evidence for an omnibenevolent God in the Bible (cf., the story of Job), God wants us to ponder the question and raise doubts. The problem with this is that the Bible doesn’t give us any answers to the question of evil.
We shouldn’t rely on our intuitions about whether there’s “too much evil” to count against God’s existence. This is simply the first argument above, repeated:
Then the third challenge: Having entered into that argument, to what extent should you treat your personal intuitions about the scale of suffering as dispositive? I don’t just mean the intuition that something in the world is out of joint and in need of healing. I mean the certainty that those wounds simply cannot be healed in any way that would ever justify the whole experience, or the Ivan Karamazov perspective that one should refuse any eternal reconciliation that allows for so much pain. Those are powerful stances, but should a mortal, timebound, finite creature really be so certain that we can know right now what earthly suffering looks like in the light of eternity? And if not, shouldn’t that dose of humility put some limit on how completely we rule out God’s perfect goodness?
This is the “suffering will be compensated in ways we can’t understand” argument. But if Douthat believes in God because experience tells him it’s right to believe, how can his experience allow him to dismiss arguments against his benevolent God? This is just a “God works in mysterious ways” argument, but I could note that it’s more reasonable to assume that God is playing with people for his own amusement, and doesn’t really care whether good always prevails. But wait! There’s more!
Suffering is overrated. Things aren’t as bad as they seem because privileged atheists exaggerate how bad suffering is.
This again is a repeat of previous arguments with a twist thrown in. I can’t believe Douthat really makes this argument, but he does:
From what perspective are you offering this critique of God? If you are in the depths of pain and suffering, staring some great evil in the face, adopting atheism as a protest against an ongoing misery, then the appropriate response from the religious person is to help you bear the burden and not to offer a lecture on the ultimate goodness of God. (Indeed, in the Book of Job, the characters who offer such a lecture stand explicitly condemned.)
But given that atheism has increased with human wealth and power and prosperity, we can say that some people who adopt this stance are doing so from a perspective of historically unusual comfort, in a society that fears pain and death as special evils in part because it has contrived to hide them carefully away. And such a society, precisely because of its comforts and its death-denial, might be uniquely prone to overrating the unbearability of certain forms of suffering, and thereby underrating the possibility that a good God could permit them.
I’m dumbfounded. Is this even an argument? I’ll leave smarter readers to deal with it, and pass on to Douthat’s fifth way of dismissing the Argument from Evil:
There’s a lot of good in the world as well, perhaps too much good! So we need God to explain why things are so good.
This is a defense I haven’t heard before, probably because it’s so weird and lame. Let’s look at it first:
Then the last challenge: If the intuition against a benevolent God rests on the sense that we are surfeited with suffering, the skeptic has to concede that we are surfeited in other ways as well. Is it possible to imagine a world with less pain than ours? Yes, but it’s also very easy to imagine a world that lacks anything like what we know as pleasure — a world where human beings have the same basic impulses but experience them merely as compulsions, a world in which we are driven to eat or drink or have sexual intercourse, to hunt and forage and build shelter, without ever experiencing the kind of basic (but really extraordinary) delights that attend a good meal or a good movie, let alone the higher forms of eros, rapture, ecstasy.
Indeed, it is precisely these heights of human experience that can make the depths feel so exceptionally desolating. This does not prove that you can’t have one without the other, that there is a necessary relationship between the extremes of conscious experience.
But it makes the problem of good — real good, deep good, the Good, not just fleeting spasms and sensations — at least as notable a difficulty for the believer in a totally indifferent universe as the problem of evil is supposed to be for the religious believer.
Well, we’re evolved to seek out those things that increase our survival and reproduction, and that seeking is facilitated by neurologically connecting these fitness-conferring features with pleasurable or appealing feelings. We love sweets and fats because for most of our evolutionary history they were good for us, so natural selection worked on our taste buds and brain to make their consumption pleasurable. Orgasms almost certainly evolved as a form of extreme pleasure that drives us to reproduce: those who get the most pleasure leave the most genes. Further, for most of our evolutionary history we lived in small, close-knit groups in which members knew each other. That would lead to the evolution of reciprocity: doing good and helping others because it keeps the group together (with you retaining your fitness) and leading to various forms of “moral” thinking and behavior. As for “eros, rapture, and ecstasy,” why can’t they be byproducts of seeking the kind of enjoyment associated with higher fitness? I will grant here that I don’t understand how the widespread making of and appeal of music occurred, but does that give evidence for God? Do music and art simply constitute too much good stuff to appear in a secular world?
In the end, I see naturalism (including evolution) as able to explain good and especially physical evil, while Douthat’s idea of God can explain good by assumption, but has to be stretched further than Gumby to explain physical evil.
But again I would level this challenge at Douthat, whom I see as deluded: What observations or occurrences would convince you that your belief in the Christian God, and in your Catholicism, is wrong? If kids dying in intractable pain won’t do it, I don’t think anything will.
Further, Mr. Douthat, what evidence would convince you that there is an afterlife: a Heaven, a Hell, or both? Even if you accept Douthat’s specious evidence for the existence of a divine being, I have no idea why, aside from the Bible and propagandizing by believers, he accepts the existence of an afterlife. Yet its existence would seem to be crucial for justifying how evil can exist in God’s world.
Here’s a guy far smarter and more eloquent than I making the argument from evil on Irish television. Stephen Fry got into trouble for saying this, and almost was charged with blasphemy or hate speech.
It’s Sunday, and that means photos (of butterflies now) by John Avise. John’s captions and IDs are indented, and you can enlarge the photos by clicking on them.
Butterflies in North America, Part 10
This week continues my many-part series on butterflies that I’ve photographed in North America. I’m continuing to go down my list of species in alphabetical order by common name. Now we’re up to some of the M’s. Most of this week’s photos happen to have been taken in Florida.
Malachite (Siproeta stelenes), upperwing:
Malachite, underwing:
Mallow Scrub-Hairstreak (Strymon istapa):
Mangrove Buckeye (Junonia genoveva), upperwing:
Mangrove Buckeye, underwing:
Mangrove Skipper (Phocides pigmalion), upperwing:
Mangrove Skipper, underwing:
Marine Blue (Leptotes marina):
Marine Blue, female above:
Marine Blue female below:
Martial Scrub-Hairstreak (Strymon martialis) upperwing:
Martial Scrub-Hairstreak, underwing: