Leaderboard

If you want to learn, you need to forget AI and work the problem out yourself. It sounds to me as if you have not done that. If you had, you would not be asking this question. Look up Raoult’s Law - then calculate for yourself the first part of the problem and show me how you did that. Then we can talk about the second part.

The intrinsic properties of a manifold depend entirely on the manifold itself without any reference to a higher-dimensional embedding manifold (a coordinate transformation is an embedding of a manifold into a manifold of the same dimension). The distance between two points of a manifold depends on the path between the two points. That is, for the expression: (ds)2 = guv dxu dxv ds is not an exact differential (there does not exist a function s(..., xu, ...) for which ds is the differential). This btw is why there is no absolute time in relativity. If ds were an exact differential, then: [math]ds = \dfrac{\partial s}{\partial x^u} dx^u[/math] and therefore: [math](ds)^2 = \dfrac{\partial s}{\partial x^u} \dfrac{\partial s}{\partial x^v} dx^u dx^v[/math] [math]g_{uv} = \dfrac{\partial s}{\partial x^u} \dfrac{\partial s}{\partial x^v}[/math] But the RHS of this expression, as a matrix, has zero determinant, contrary to the requirement that the metric tensor is invertible. [If the above LaTeX doesn't render, please refresh browser.]

No, AJB was a former, higly respected member of this forum. I havent found that to be the case. While D Lincoln explains when and how the Higgs was found, for example, 'Physics Explained' delves into how the Higgs field/mechanism works, how it gives rise to mass and the detected particle, all with a 'simplified' mathematical model. Check it out ... Just what I needed, another cat video. Like I already don't spend half of my internet time watching cat videos. As a former owner of two cats that I adored, I'm resisting the idea of getting another, as putting the previous ones 'to sleep' after 15 and17 years were two of the most difficult decisions I've had to make.

It's unfortunate that he seems like one of those children like Damian in "The Omen." He's liable to push you off a balcony while you're changing a lightbulb. I've noticed the Dutch are fairly immigrant friendly. If I could handle hot weather and bring my extended family, you would be calling me "neighbor."

Dear Mister President, pleased to see that you have recovered from the run of disabilities that I read in the press prevented you from serving in the military during the Vietnam war. As for Afghanistan, like many in the UK I have known someone who gave his life. He was a 19 year old friend of my grandson. It so happens his last moments were filmed and can be seen in the following video which was made by a BBC crew who were making a documentary in Afghanistan at the time. "

I was under the impression that a recent experiment has cast serious doubts on the viability of Bohmian mechanics: https://www.nature.com/articles/s41586-025-09099-4 This is essentially a direct conflict between what BM predicts in that situation, and the observed outcome. What it means is that, if I understand the implications correctly (and I’m not sure that I do), the concept of “particle” that BM is constructed on does not correspond to particles in the real universe.

“Bees use polarized sunlight scattered by the atmosphere in order to navigate; they always know where the sun is, even if it’s cloudy or behind a mountain. Then they waggle dance to inform their hive-mates about food source locations.” https://kottke.org/26/01/an-optical-compass-inspired-by-bee-vision 10.5 min video in link discusses polarization and why the sky gives us polarized light, and then gets into making an optical compass using this. It finishes up with how bees use this and the waggle dance they use to tell the hive where food is.

Hmm, Project Anchor. Missing W perhaps?😁

You need to remember though that just because you don’t understand it, doesn’t mean it’s not useful or doesn’t work. It evidently does, because we are using those findings in practical applications. I myself do not understand in detail how a mobile phone is constructed, since electrical engineering is not my area of expertise. But it still works. The average person in any math or physics department at a university isn’t a genius, with very few exceptions - they’ve just decided to put in the work necessary to learn the concepts. In-depth mastery of any subject requires time and effort, that’s just how it is.

Ahh, fond memories of Hollerith pinch card machines from the mid 70s. And a stack of cards about 6 inches high, each with one line of FORTRAN IV code, solving for the energy levels of the Helium atom by numerical methods. Tedious and frustrating, but I would gladly do it every day again, if I could be 21 years old again.

This is not about virtual particles though. It is standard undergraduate level chemical QM, involving bog-standard quantum systems, like vibrating chemical bonds or electronic states in atoms and molecules. As I said previously, although the idea of zero point energy often gets popularly associated with the energy of the vacuum, virtual particles popping in and out of existence and that weird QFT stuff, it is actually quite general to all kinds of mundane quantum system. Here's a simplified diagram of the energy well of a chemical bond between 2 atoms. The vibrational energy this system can have is restricted to certain quantised values, E₀ , E₁, E₂ etc. Notice that E₀ is not at the bottom of the well. That means there is still some kinetic energy left in the ground state - it is still vibrating a bit, in effect. You can't get that bit of energy out because it is already in the lowest allowed state. That is zero point energy, which the molecule will still have even at absolute zero. (The animation about the photon is just to point out if it doesn't have the correct energy it can't excite the vibration to the next level up. This is not important for the present discussion, it was just on the first decent diagram I found to copy.)

I had a cat scan of my abdomen this week because recent blood test showed higher than normal liver enzymes. Today I got a call from the doctor telling me everything is normal, except that my colon seemed 'full.' What he didn't know is that I really like bulky foods like vegetables, bread, beans, etc, etc. So-- he asked me if I wanted him to prescribe something for constipation. After a good laugh I explained my eating habits and that. with all the fiber I eat, I had no problem whatsoever with constipation. I felt really good about the good news in the phone call-- then realized that this was the first time in my life that a doctor called me to tell me I was full of ____.

The prequel

So basically it might help but at least it doesn't harm? If there are no downsides, I don't think it is a bad thing as such. The main worry I have with these things is that especially in recent times, they tend to get a life on their own and suddenly there will be trends on folks binging on casein (or whatever the hype of the week is). In a way I think it has become more important to work out the nuances as the internet has become a horrible amplifier of really bad ideas. Not that I am accusing this thread of anything like that, it is just a matter of professional struggle I am having.

No, I didn't, using pasteurised, it was fine. I think the culture soon overwhelms any other strains in there. I wouldn't bother heating with uht.

My app would activate every few days. I'm at work 12 hours, for 7 days every 2 weeks. Actually closer to 13 hours counting travel time. Most phones have 'health' apps or motion detectors; if no activity is detected by the phone in 12 hours, it should message your contact. Then again, I've been known to sleep for 12 hours as well ...

... and Nigeria too: Tinubu stops otter, rages Uganda dad nag. Use garret to spot subunit.

My question is does the electric company turn a profit? In my state utilities companies govern themselves. We have no idea what their expenditures are and how they figure what to charge. It would be hard to compare to other countries. Maybe compare the environmental resources used to the total utilities used a year. I heard about the resources a person uses versus the number of acres of resources per person on the show Explorations. For example someone in the US could pay less for the same amount of resources used by someone in Africa. And at the same time pay less while consuming more energy.

Regarding this bit, extremely low cost keys (that work) are likely OEM or surplus volume licensing keys that are resold (perhaps there are other sources, too). Technically, they violate the terms of service, as those keys are not supposed to be sold directly to user and could get deactivated. But I don't think it happens very often, unless the reseller is selling the same key multiple times, or perhaps a whole bundle gets somehow flagged.

Lmao @StringJunky beat me to the punchline

Pretty useless dam if it only lasts 50 years with at 30% chance of flooding. Must have been designed by a university maths dept. 😀

Where I live, it's common for people to rent an apartment and be astonished by their electric bill in the winter, because they didn't notice the apartment has electric resistance heat. (Not a heat pump, just a giant toaster.) They tend to make confused posts online, somewhat like the BBC article, quoting the total cost but no other information about usage and pricing. As electricity prices rise, electric resistance heat will get disproportionately more expensive.

The point is that the energy of the ground state (the zero point energy) cannot contribute to temperature, as there is no lower state and therefore this energy can never be extracted. It is the energy that still remains AT absolute zero. Absolute zero, remember, is just the lowest temperature you can get, i.e. there is no lower temperature. Lowering the temperature of a system in which every degree of freedom was in the ground state would require extracting heat from it - which would mean getting it to a state lower in energy than the ground state - a contradiction in terms. So the residual energy of the ground state has nothing to do with why you can't get to absolute zero. That's simply a matter of not being able, in practice, to extract 100% of the extractable energy (which is the energy of states above the ground state).

I rather suspect that the opposite might happen - he’ll become a bit of a legend in…well…let’s call it “certain circles”. Somewhat similar to what happened to Tesla.

From a QM standpoint, if all motion ceases at absolute zero, quantum particles have no momentum and their position is fixed. An impossibility according to Heisenberg. In Quantum Field Theory, this video does a better job than I could of both, QFT fundamentals, and minimum allowed energy. ( and I like his videos )

Saaw CotG in the late 70s ( my teens ). Sure, I was a skeptic also. But it did make me think. Thank you E VD.

... for your calculator?

This movie caused some heated debates in my youth. Воспоминания о будущем (1970) I was firmly in the sceptics' camp.

I think there is some market pressure (let's hope it keeps up) on tech companies to build their own power systems for server farms, e.g. wind turbines or solar or geo, with storage batteries. (Grids aren't trustworthy, so they want onsite power) I live in a public power state with 85% of its power from wind and hydro, so our rates are below the national average. (10¢/kwh, iirc) Means EVs driven here are lower carbon than in some places.

I read Chariots of the Gods when I was around 13, and then had the pleasure of hearing Isaac Asimov (who lived not far from us, and occasionally spoke or did readings at local venues) poke some fun at VonD. I guess those Egyptians did build their own pyramids after all. And the Nazca Lines weren't really an extraterrestrial airstrip. And the sarcophagus of Palenque isn't really depicting an alien sitting atop a rocket. In recent years I had read that VonD had gotten the basic idea for CotG from HP Lovecraft's Cthulhu mythos. Enough said.

Data centres are raising demand in the energy sector and doing backdoor deals to lower the cost to them at the expense of domestic consumers. Also, the domestic consumers are being put on the hook, via their bills, for the new infrastructure needed for the data centres. It is a rapidly emerging political issue there.

Newton also dabbled in alchemy. How did that work out ? I guess we're all human, and even geniuses have their faults.

One thing I learnt fairly recently is that Δ9-THC found in cannabis is a partial agonist and therefore is self-limiting in its effects, whereas synthetic cannabinoids such as JWH-018 are full agonists and therefore are potentially more dangerous.

Here is an example: aspirin: https://en.wikipedia.org/wiki/Mechanism_of_action_of_aspirin If you read that, you will see that it inhibits the production of things called prostaglandins, which have more than one role in the body, two of them being a role in the body’s inflammatory response and a role in blood clotting. So if you take aspirin for inflammation, you will also bleed more if a blood vessel is broken. That’s a side effect, especially gastro-intestinal bleeding , which can be an issue if you take a lot of aspirin. However that also means aspirin can be used to prevent unwanted blood clotting, e.g. in heart attacks. This is typical of the way many drugs work. They alter something in the biochemistry of the body, which gives one desired effect, but often they have other consequences as well, which may or may not be a problem depending on what is and also on the condition of the patient.

Answers on the Internet: Explainer: how do drugs work?

Is that the correct term, Eric? What is modern grammar cumin to? Sometimes it is just beyond bay leaf.

The rate at which it passes does, but not the existence of time itself. Religious belief is not empirical fact. You might take it as a given, but it is not. Yes, in college physics we had a lab where we did it. The rotating mirror experiment Markus described. If there was something missing there would be experimental anomalies. Which is not remotely the same thing. Works of fiction aren’t much of a rebuttal, because they’re literally made up.

Now you've got me in a logic loop, if I can't +1 this and I can't +1 myself (assuming 1 of my reply, had some sort of influence, in the past), who can I +1, Zeno?

That's very kind of you. I think, though, you will find that a large part of the reason many of us post on these forums is for the pleasure of spreading knowledge of science - and learning from one another, in the areas where are not expert, or have simply forgotten. So people like you are pushing at an open door. (It's the people who come with a fixed agenda and don't listen that are the annoying ones.😄)

No. There are time-dependent processes that do not involve motion, such as the decay of elementary particles for instance. Locally at any given location, all clocks always tick at exactly “one second per second” - so there is no meaningful way to say that it is different in different locations. The only thing that changes is the relationship of clocks in spacetime, but that’s not the same thing. Again, clocks don’t have different “speeds” - it’s only that clocks at different events are related in non-trivial ways. This may at first glance appear to say the same thing, but it doesn’t. I have personally done it twice - once in high school physics class with an apparatus basically consisting of an assembly of rotating mirrors, and once for fun using the classic setup involving marshmallows in a microwave. And there are many other ways to do it at home, it’s not really that difficult. Note though that the level of precision within such DIY tabletop experiments is naturally limited, so don’t expect too much in terms of accuracy of the final numerical value.

“around 1.4 billion years ago, during the Mesoproterozoic era (1.6 to 1.0 billion years ago), Earth’s atmosphere contained ten times more carbon dioxide than today. This high CO2 level helped maintain a climate similar to the present, even though the Sun was significantly weaker at the time. These high levels, along with temperature estimates based on the salt, indicate that the Mesoproterozoic climate was more mild than researchers theorized. The atmosphere also had 3.7% of today’s oxygen levels. While this might not seem like a lot, it’s still an unexpectedly high quantity“ https://gizmodo.com/researchers-just-sampled-1-4-billion-year-old-air-and-its-not-what-they-expected-2000706812

We just want to know stuff and we want to believe the stuff we know is correct; no time equals no history to learn from, just empty space...

You can’t BS your way past the math. It either works or it doesn’t. You can’t say you support Lorentz transforms but think that length and time are invariant because those statements contradict each other. If it’s not imaginary you have to be show it objectively exists. Being able to imagine something means absolutely nothing, because you can imagine physically impossible things. Nothing controversial about that The photons in space are not connected, nor are they matter, so this kind of connection doesn’t exist. And as has already been explained, if there was some material filling the space between us, it could not be perfectly rigid and signals within it can’t propagate any faster than c. Einstein was shown to be wrong.

It’s required by the speed of light being invariant. Having it not be invariant has implications that can be tested, and the proposal fails those tests. It’s already been investigated, which is why there’s no need to consider it. You don’t have a model. If you did we’d be able to make quantitative predictions and show how they fail to agree with experiment. The equations would allow anyone to investigate the implications rather than having to rely on whatever scenario you fabricate. One problem with redshift/blueshift is that it’s not just signals that get modified. You can move clocks and only compare them when they are at rest, next to each other. They still show relativistic effects. Charge distribution in high-speed nuclei shows length contraction — how does red- or blueshift come into that? Or in muon decay? There’s no EM radiation involved in the latter two.

Who told you that nature has any respect for or acknowledgment of your common sense? The conclusions we draw are in the framework of the best models we have. If you want to interpret them in terms of another model, feel free to present it. But all of the evidence that’s covered by the model has to fit, and contradictions must be addressed. “Common sense” is not a model and given its spectacular failures, it does not get a seat at the table. “Common sense” tells us that the earth is flat, the sun (and almost everything in space) orbits the earth, heavy things fall faster. Some people think the position of astronomical objects influence our fate. Some think black holes exert more gravity than other objects of equal mass. That the seasons are caused by the distance to the sun varying. Common sense suggests there is no gravity in space. What examples can you give, and what experience do you have that you can say what happens “often” in science? We (well, most of us doing advanced physics) know when this matters and when it doesn’t. Partly because we quantify things, because we have equations, and know the importance if significant digits in calculations. It takes more than the assumption. You need to actually show the premise is false and/or what the missing variable is, or at least provide a compelling argument that there’s something missing (as we did with the neutrino and do with dark matter)

Which is abject nonsense. Even traveling close to c, the ship will arrive after a light signal that leaves at the same time. The only data it will arrive before is data that was transmitted some time after the craft left. If the craft is transmitting, that data will beat data from earth because it doesn’t have to travel as far, but there’s nothing that should be surprising about that. If the craft is relaying data from earth, no advantage is gained because it takes time for the signal to get to the ship. Nothing beats the light signal emitted at the beginning of the trip. (You can’t assign a single time to a “constant data flow” since it is not transmitted nor received at one time.) You can’t assume your understanding is correct and deform relativity to fit everything together.