md65536

So basically, if you can start cooling the edges of the cloud, more laser light penetrates further into the cloud, but the further in, the less chance the re-emitted light has of escaping the cloud? The cooling effect occurs because of absorption, but it still requires the energy being put into the cloud to escape? The initial absorption reduces heat energy, but since you can't just increase the non-thermal energy of the atoms indefinitely, it's going to have to escape the cloud or end up increasing the heat. Does this mean that the laser cooling process is effectively using light to "poke" the atoms just right so that they emit more light energy than they absorb, so that more light energy goes out of the cloud than what goes in? PS. as a spectator up till now, I appreciate the patient informative responses. Replies that focus on discouraging amateurs don't help others who are reading.

It's a bit confusing because it's not a valid sentence with all of those question marks, but if they're changed to commas, one solution is Is this the easier solution? Oh I see, just by trying some things out:

I was curious about how many answers there might be, so I wrote code. I gave up before trying to deal with parentheses, but got the following: (11 - 17) * 13 + 2 + 19 + 101 = 44 (11 - 13) * 19 - 17 - 2 + 101 = 44 (13 + 101) / 2 - 11 - 19 + 17 = 44 (11 - 13 - 17) * 2 - 19 + 101 = 44 (13 - 17 - 19) * 2 - 11 + 101 = 44 (17 - 19 - 2) * 11 - 13 + 101 = 44 (17 - 19) * 11 * 2 - 13 + 101 = 44 (13 - 11 + 19 + 101) / 2 - 17 = 44 (11 - 17 + 19 + 101) / 2 - 13 = 44 (my answer) ((17 - 19 + 101) / 11 + 13) * 2 = 44 ((13 * 17 - 19) / 101 + 2) * 11 = 44 ((19 - 11) * 17 - 13 - 101) * 2 = 44 (13 * 17 - 19) / 101 * 2 * 11 = 44 (Commander's answer, ignoring order) Sensei's answer isn't here because it's not left-to-right order of operations. I wouldn't doubt this is a small fraction of the possible answers, but neither would I bet that it is. (I also manually culled duplicates so I may have removed too many.)

I got (101+11+19-17)/2-13=44.

Okay, but I'm trying to understand a statement that you made, because it makes no sense to me and I'm trying to figure out where the misunderstanding is. You wrote, "He’s essentially using an inertial coordinate system to show that there is no acceleration - which is trivially true." That makes NO sense to me, because you can describe a particle that's accelerating, using an inertial coordinate system. The coordinate system has nothing to do with whether the particle is properly accelerating or not. Eg. Consider an inertial observer on a train bank. A train accelerates from rest at a rate of 1 m/s^2, relative to the observer. The observer's coordinate system doesn't trivially show that there is no acceleration. Am I using the term "coordinate system" incorrectly? What I don't understand is if one can refer to a particle, and its own coordinate system, as the same thing, or if you and Anamitra are talking about different things. If I have an inertial observer and a train accelerates, I don't think I can sensibly describe it as "an accelerating coordinate system". I'm trying to find out what you're saying is trivially true.

No acceleration of what? It originally mentions and later clarifies that the acceleration of "particles" is being discussed, and that's not trivially true. If you're assuming it's reference frames being accelerated, where is that stated? This topic is confusing from the start, with seemingly some explanation or details missing?? It's difficult for me to follow if I first have to guess at the same assumptions being made, even if they're reasonable. Yes, that seems to explain what is going on, thanks. I did not get that from the discussion so far. Basically is it: specify a particle that has no acceleration, conclude that it cannot be changing speed? (I'm guessing then the main flaw in reasoning is that OP starts with equations of inertial motion, but is treating them as "the equations of general motion in SR"?)

Then I still don't understand. Particles *can* accelerate, and their motion can be described in the coordinates of an inertial observer. Why do you need an accelerating observer to describe accelerating particles? It can be described in Minkowski coordinates, why suggest Rindler? Not all particles are observers; to me it looks like where OP is talking about particles, you're describing observers. "in this article we see that the particle cannot accelerate." (emphasis mine) I understand to mean that we're talking about the case of constant gamma, ie. we're limiting ourselves to particles that don't accelerate. If you two are really on the same page and understanding each other, then I apologize. (Besides all that, a particle can accelerate and maintain constant speed relative to an inertial observer, thus constant gamma in that observer's inertial frame but only changing direction, while the particle undergoes proper acceleration, so I think I disagree with both of you however your statements are understood!)

That's not what OP literally said, and you've interpreted what OP wrote as nonsense, but still I don't know what OP really meant because it could be interpreted different ways. I don't think you two are talking about the same thing, at least in some cases like this, and I don't see how the problems can possibly be resolved if you're not even talking about the same things. I think OP needs to clarify first. Eg. in this case, Anamitra were you talking about general particles, as they are measured in various inertial frames of reference? Or particles in their own rest frames, being inertial in some inertial frames of reference and accelerating in other inertial frames of reference? Or something else? I think some consider a particle being "in" a given frame to mean that the frame is its rest frame, but I take it to mean the particle "as measured in" a given frame. Eg. a train can have a positive speed in the bank's frame. The train is in all the different frames, not just its rest frame. Is that at odds with your interpretation of OP's statement?

I'm not following this. An accelerometer that is measuring proper acceleration can be described in the coordinates of an inertial observer. My reading of what you replied to, is "An inertial observer remains inertial as measured in any other inertial reference frame, but a particle can (properly) accelerate as measured in an inertial reference frame." It only mentions particles being able to accelerate. What are you referring to when you say "there is no proper acceleration"?

Actually humans create water. How much more you'd weigh depends on what part of it you keep. Plants consume water but they don't generally hold on to the oxygen.

You're describing a (frame-dependent) moment, or an instant in time, rather than an interval of time. To describe things like "bolt here, one there" etc., you're describing events, ie. anything with a location and a time. The coordinates you use to describe the events come from a system of coordinates, in this case you're using the coordinate system of the observer, ie. the inertial frame in which your chosen observer is at rest. In those coordinates, the 2 lightning events have the same time value. The relationship you're talking about describes any pair of events separated by a space-like interval in flat spacetime, because you can always find an inertial frame in which 2 space-like separated events happen at the same time. Or, find other observers where the lightning bolts aren't simultaneous. So, there's nothing special about the 2 events being simultaneous, unless there's something special about the observer you chose. "The interval between the events is space-like" is something all observers agree on, to describe the relationship.

Yes, it's definitely an ad hominem attack. I still see the same pattern of posts on this site over many years, where newer users must deal with people who like "crackpot bashing for sport". If one of the regulars posted a question about a suspicious video about science, would you treat their post the same way? Would you focus on their name while completely ignoring the content of the post? Did you even read the post, or did you conclude all you needed to know by the title, nickname, and some assumptions? What exactly is "not even wrong" about OP's post? "you seem very tacky"??? Why do this?

I think the helicopter is below the "true horizon" in those videos (represented by the lake surface), and hills behind it make the visible horizon higher. The simplest explanation is the video producers fabricated the shot because they didn't have the footage that they wanted to illustrate the narrative. That's pervasive in modern media, and only increasing. They add, remove, combine, edit, recolor, enhance, and create the shots they want if they don't have them. They basically assemble the story they want to tell, from pieces of the story they shot. Scenes are not always in the right order or even in context, and here you have proof that they're edited. Discovery Channel shows like this aren't video evidence of scientific experiments conducted by scientists, they're science-themed entertainment. Another common thing you'll see is footage of insects, or stop-motion of plants growing, and you'll hear loud, clear chewing noises, or the "sound of plants growing", but most of the time it's just a separate sound track added in post exactly like they would do for movie sound effects. Everything is edited and processed and repackaged these days. The raw footage would be boring and dry and not fit the exciting action film percussion soundtrack. I imagine that editing is such a common practice that the producers might not have even considered that people would treat it as scientific evidence. I think the "target circle" was added in post as well. I don't think you looked very closely, they're not just the same birds, they're the same pixels frame after frame. You can see it in OP's images. They're the same shot, and one is edited. That's not something I'd expect to see on Discovery. But maybe they could blow something up when they're talking about the laser, and say "Now that's what I call doing science!"

Ah, okay, that experiment can be set up in a lot of different ways and the details will be different. If you mean it's common that each is positioned at their respective midpoints between the events when they pass, it's only because you've chosen those observers. You could choose other observers who don't have that in common. If you mean that both frames agree on where the midpoint of the train and platform are located relative to their ends, yes that's true because the length contraction factor in the direction of motion is the same everywhere (the front half and back half of the train are length-contracted by the same factor). But it is true, if you had a bunch of trains running parallel at different speeds, the 'midpoints' on each train between the two events, would all momentarily coincide. Basically, all observers would agree that the "forward" char marks on all trains line up together at some time (at the moment the lightning strikes them, of course!), and the middles line up at some time, and the "rear" char marks line up at some time. Also, a 1/4 mark of the length between the marks lines up at some time, etc.

Yessssss... but What you described can be true, but there are complications you should understand. Lets say the lightning bolts hit the 2 ends of the train simultaneously in the train frame, and M1 is in the middle of the train, and sees the lightning bolts simultaneously at the same moment M passes on the embankment (at a negligible distance from M1). Then M also sees them simultaneously. And yes, each says "The ends of the train where the char marks are, are both the same distance from me at the moment that I see the lightning." First, because of length contraction, there isn't a fixed distance they agree on. M1 might say "Both ends of the train are 100m away from me and are at rest." M might say "Both ends of the train are 80m (say) away from me and are moving." Second, because the train is moving for M, the locations of the char marks are not the locations of the lightning strikes! M can say "The lightning struck at locations x1 and x2, but by the time I'd seen them, the char marks (which were equidistant from me when I saw the lightning) had moved to locations x1+delta and x2+delta." Observer M is not at the midpoint of x1 and x2 in her frame, but at that point plus delta. M and M1, while momentarily at the same location, do not agree that that location is the midpoint of the lightning strikes, in their respective frames.

A lot of the cautious best practices depend on whether you're talking about a battery pack or a single cell. I'm not sure if charging a single cell to 4.2 v will have a noticeable effect, but if you charge a 2-cell series pack to 8.4 v, and they're not perfectly balanced, you might eg. charge one to 4.15 v and the other to 4.25 v, more likely shortening its life. Avoiding charging to full might make a pack last longer, but do nothing for charging a single cell? Letting a cell drop below 3 v once might shorten its life a little, but driving it negative in a very unbalanced battery pack will quickly cause damage. Charging with lower current is better. "Rapid charging" devices likely have shortened life span. It's also something to be aware of with replacement batteries, because a charger made for a 2400 mAh cell might stress a 2000 mAh cell. Charging at an excessively low current would be the easiest on a cell.

I just quoted the wiki page. I can't explain other than with another quote from the page: "But because the principle is so vague, many distinct statements can be (and have been) made that would qualify as a Mach principle, and some of these are false." Definitely Mach's principle doesn't answer the questions here. I see it more as philosophical in that it provides questions that can't be answered, or at least aren't settled by science. I disagree that there's evidence of what would be observed if all matter was taken away, as far as I know no one has performed such an experiment! The evidence is based on extrapolation from what we currently observe. Does the Higgs mechanism depend on other fundamental constants or measurements? I think to settle this, and to answer OP's questions about a massless universe etc, you'd first have to know if and how the fundamental constants etc. would change in such a case. You'd have to settle Mach's principle in general. I think Mach7 is not true based on current evidence, best current theoretical models, and the assumption that some specific aspects of Mach's principle are not true.

This is a variation of a variation of Mach's Principle https://en.wikipedia.org/wiki/Mach's_principle "Mach7: If you take away all matter, there is no more space." I think that if time and distance are emergent properties of the universe then nothing requires spacetime, because everything could be described in terms of whatever they're emergent from. Eg. maybe causal connections could be described using topology without geometry. In that case, c is a property of the relationship between distance and time, something describing how things are connected in the underlying universe and emerging as a speed in our possibly emergent observations and measurements of that universe. As an example or analogy, consider the emergent 3d space depicted by a 2d hologram. The observable depths and distances of that 3d space are not needed to describe the hologram completely.

But the frequency of the light changes depending on the motion of the emitter. Why is the frequency different if it's not actually in motion?

Based on others' answers, I think I'm misunderstanding what you mean by this. What you described here is fine, if you set up the experiment to get those results. Having the lightbulbs next to the observer is a good idea, because if they light up at the same time and at the same place, that can be considered a single event, and then everyone in every reference frame will agree on whether the bulbs lit at the same time or not. Similarly you can set it up so that M and M1 are at the same place at the moments the light bulbs light (ie. their world lines intersect at that event) and then everyone can agree on the simultaneity of those events. Is that what you are describing? On the other hand, adding transformers and bulbs can unnecessarily complicate things, and obfuscate what you're trying to get a grip on. Simplification is usually better. What you might be missing, is that just because the two light bulbs light at the same time, the events that caused them (in this case the lightning bolts) might not have occurred at the same time, because the information from the 2 events might not have taken the same time to get to the 2 bulbs. The simpler case is that M and M1 can both see the lightning bolts appearing simultaneous, but still disagree on whether they're "really" simultaneous, because they can disagree on their distances to the two lightning bolts. It applies the same to wires and bulbs, because you can measure the timing of the signals through the wires using light signals, and you'll get consistent results. So that suggests some "definite facts" that you're looking for: The events you're describing, and the causal relationships between them, and the light cones describing those relations, are all definite and not dependent on frame of reference.

"The interval between the two events is space-like" describes everything you're talking about here, and it has a precise definition. "Event" has a precise definition as well. There no problem here. A lightning bolt could also be described not as a single event, but as something with spatial and temporal extent. Then it could be described with some other precise definitions that effectively describe sets of events, such as "world line". If "coexist" is given a precise definition, it would be fine, but there are already words that suffice, and it's a problem if you want it to mean something more or other than the definition you give it.

If your brain was in a simulation, where every stimulus you received was somehow artificial, that could mean that everything you know (which you acquired through stimuli) might be made up. You probably wouldn't need to distinguish external stimuli (eg. the sense of touching things) vs. internal (eg. having a memory of having lived your life up to this point). That would mean the senses of remembering things could be made up... so maybe it is simulating a few minutes or just one moment in time, including any made-up memories of time before that. It could also mean that things like atoms could be made up too. Maybe the knowledge of atoms or even of there being 3 spatial dimensions is an artificial reality that is simulated in some other reality with no atoms and a different number of dimensions. As for whether it could be one "identity" being simulated, or everyone---or to put it another way, "what if I'm just a figment of someone else's mind?" etc.---I guess that's an open philosophical question related to whether there is some physical form to the feeling of having an identity, or if it's just emergent from the configuration of other physical things like brain cells. If you simulated an object's sense of being, like if you simulated the thought "I think, therefore I am" in something that otherwise wouldn't think that on its own, does that thought have any physical presence? I can think about these ideas and write them down, and I get the sense that I'm thinking them, but if other senses (eg. of touching something) could be simulated, why not the sense of having thought things? I feel like I'm here, but if that could be simulated, I don't think I'd need to exist at all. I don't see how I could prove to myself that I exist, IF the only way to test it is by sensing whether I exist, AND if what is sensed can be simulated. By a really coarse analogy, if I write a story about a character that realizes it exists, I can write convincing thoughts for it with dialog like, "I know I'm only a character in a story, but I exist!" By creating those "thoughts" on paper, I'm not making them real. You wouldn't read that dialog and claim that as evidence that the character has become real. If I myself could think up some thought test that proves to me that I exist, I could write a fictional character having those same thoughts, and yet that wouldn't really prove to anyone that the character really exists and can think. How can I as a person prove that I'm not just someone else's thought, if any action I could take to prove it could also be their thought? How could you know that the feeling of being real, is itself real?

That's not a square, only a rhombus.

Interesting shape! Am I understanding correctly that 2 opposite corners of the cut face are on the middles of edges (diagonal length 10√2) and the other two are on opposite corners of the cube (diagonal length 10√3)?

1. 2.