joigus

There would be lots of diffraction. Direction would change considerably. Photon ending up just about anywhere. In vacuum photons don't change rapidity. In medium, they do, according to refraction index.

I won't, that's for my notebook for the time being. The equation doesn't make sense anyway. I'm having fun with the mathematical problem. I've re-derived the eqs. for hyperbolic motion, which I had forgotten, in case I need to explain them later. Your mathematical problem can be solved under assumptions of which you have provided no information. You haven't clarified whether \( T \) is proper time or coordinate time. Your equation makes dimensional sense if \( c=1 \) and all velocities are dimensionless. But you haven't said that, creating a lot of confusion. It's implied on your blog, though --see below--, when you say, If you choose velocities as dimensionless, you're OK, because a t-dependent parameter that appears in solving the eq. is, \[ \left[\frac{FT}{M}\right]=MLT^{-2}\times T\times M^{-1}=LT^{-1} \] Another thing you haven't clarified is whether force, velocity and acceleration are collinear. I have assumed that, because you should first tackle that one before getting into other cases. I've had to go through different hypotheses, like constant 4-force (derivative of 4-momentum with respect to proper time), constant rate of energy supply; \( T \) being proper time or \( T \) being coordinate inertial time. I've tried to study all the cases you could fork into. Something you should understand is that there is no universal character to how a particle moves under given circumstances. The law of motion is not a universal law under different assumptions for \( F \); it's just how that particle is moving under given circumstances. The key assumption seems to be \( F = \) constant. That is not universal. That just represents how you decide to push the particle. On your blog, advertising link removed by moderator where I've finally been able to take a look at your "derivation", I've been able to spot a couple more mistakes. There's no such thing as Lorentz mass dilation formula. And saying that energy is always force times distance is grossly mistaken. Also mistaken is assuming that momentum rate of change can be taken to be \( \frac{MV}{T} \). Neither can anything depend on \( \frac{V-V_0}{T-T_0} \) --finite differences-- in the equation of motion, because of well-known symmetry properties. This question of symmetry properties I leave for Markus, because he's the one dealing with that aspect on this thread.

What a goblet of nonsense! No. But people have. I remember a conversation with J.M.R. Parrondo years ago. I loved Feynman's work, but he didn't seem to find it so fascinating, for some reason. He was busy finding flaws in it. Apparently he found one in the chapter on thermodynamics and the ratchet, and that's what led him to Parrondo's paradox. My take on it is that even in error, Feynman was incredibly inspiring.

I'm no expert, but some "nice" sites, after clicking the "more options" button, allow you to disable all the cookies. Others inform you of different kinds (session variables, tracking, and so on). Although it's always up to you, of course. I'm sorry it didn't work for you. I thought a direct link to the video could work. I did disable the tracking cookies, if I remember correctly. What about just disagree? You will have to rely on the website's honesty, that that will disable all.

It doesn't really say anything. It's a video of some kind of analogical experiment. https://i.imgur.com/FfWg4GU.mp4 I hope a direct link to the video helps (it's very short.)

This is something I hadn't thought about. It makes a lot of sense.

Of course, most of us here are seasoned enough not to notice the telltale signs of the squids' strategy. Make it blurry. This particular squid has an alternative weapon: He throws Bible paragraphs at you.

Ok. If you're done discussing me, we can talk some physics. You still haven't addressed my question: Is your T proper time of coordinate time? Proper time is time in the non-inertial reference frame co-moving with the particle. Coordinate time is time as measured from an observer sitting somewhere and not subject to forces. The solving of the problem is very different. Also, the constant force is constant 4-force? (the derivative of 4-momentum with respect to proper time) If so, the solution of your "horrible" equation is trivial --as calculus is concerned--. I have solved it and I get a cubic in v, with coefficients depending on t. Assuming that's proper time. It doesn't look completely out of whack (it reminds me of solutions of hyperbolic motion), but you obviously have made some relevant conceptual mistake, that's why you're getting inconsistent units. Hyperbolic motion is the closest you can get in special relativity to uniformly accelerated motion. It's not exactly as I said, a constant 4-force. A constant 4-force seems to be what you're implying. I just want to know where the hell you have "derived" your equation from. Related to @studiot's comments: I am assuming everything is collinear and you don't mean a dot product. I also recommend you read carefully @Markus Hanke's comments. Instead of going into a tantrum, try to interact with the users. It's all I can say. But, as long as you got personal, just a couple more things: I've read Feynman's Lectures since I was 16, What do You Care what Other People Think too. Also, I can tell a jay from a tit, from a robin, from an avocet, from a gannet, etc. Not all of them, but just one blob of colour and in some cases I can distinguish two very close species one from one another, male from female, and one-year immature seagulls from adults. So yes, as an amateur ornithologist, I can tell. In other cases, apparently different species are grouped under same name because they happen to be male and female of the same. So names do help. Names are a useful mental tool. So Feynman was wrong about that one. But he was a genius. He turned other people crazy by insisting on his own names and notations, though. And a last thing: As to self-loving narcissism, how about coming up with a silly equation and naming it "the Frogton Universal Force Law"?

Mmmm. I don't know. There are several things going on, and gravity is not helping. I see it more as an illustration of osmotic pressure, or diffusion, than mechanical pressure. Also increase in entropy. Pressure would be more like the balls pushing a wall. For that I would recommend computer simulation. Some like this from Wikipedia:

That's enough of that, then. Isn't it?

Boy, that was hilarious!!! +1

In my understanding, a hypersurface is a relative concept. When you have an n-dimensional manifold (that in itself is a generalisation of a surface), any n-1 dimensional manifold embedded in it is called a hypersurface with respect to the n-dimensional manifold. I was kind of unsure if that concept was standard or it was just a local tradition, and here's what I've found --LMGIFY: https://en.wikipedia.org/wiki/Hypersurface The really powerful concept is manifold, that Studiot mentions (in general, no reference to it being a surface, embedded in anything). There are also polytopes, that Studiot mentions too, and fractals could be interesting as well, if you're interested in irregularities of geography. Studiot is building towards a classification of most all different objects of geometry. But I think the "descriptor" that you're groping towards may possibly be the manifold and its local charts. How many variables you need to map the thing give you the dimension. Riemann intended "manifold" as a generalisation of "surface." The subject of geometry is vast indeed.

Just for the record, I agree of course that @Arete's answer was far better than mine in particular. I fail to see whether quoting me by an unintelligible fragment of text like, was intended as criticism, or an accident when using the quoting function. Anyway, just in case it was addressed to me... I also think the question was a very good one, and would like to see more questions like this, so that --I at least-- can learn more from the exchange. It's a good example of something everyone interested in biology have asked themselves at some point, and where simple "common sense" can, and does, mislead you. As Phi said, you asked whether the line of reasoning was wrong. And although I'm no expert, I will insist here on what I think are the main flaws in my own words as a non-expert, and hoping either Arete or others can clarify further, or correct me where I'm wrong. Of the two main most common fallacies I see, one of them has already been pointed out. Namely: most mutations are neutral, not deleterious. The other is the common misrepresentation of evolution that the "fulcrum" of it, so to speak, is the individual: (my emphasis) when the basic unit on which the lottery is played is the gene, or to be more precise, genotypic sequences. I think that's what Arete meant when they said, Beneficial changes accrue to the genetic sequence --not to the individual--, in the sense that it becomes more frequent in the population, even across species, as Arete has made transparently clear. I would say the genes for glicolysis have been impressively successful. They "couldn't care less" whether their host is a tomato or a dolphin, let alone this or that tomato or dolphin. You can think of it in a rather cynical --but hopefully useful-- way, which is: The individual is just a carrier of the "meaningful" genetic sequence; once it's played its sexual, nurturing, etc. role, it's disposable. While the organism is alive, it benefits, of course, from using winner genes.

If something that has long been proven incorrect seems obvious to you, you should review your criterion for attributing obviousness.

Oh, sorry. I forgot: Yes.

Thanks for smudging a perfectly clear concept.

I'm not a comedian, but I play one on scienceforums.net

You completely missed Huxley's meaning. Now why doesn't that surprise me. When a new theory is born implying a shift in the way we think about certain problems, most people are still so comfortable with the previous one that they contemplate the new ideas as "heresy." When the new theory finally becomes well established, people grow used to it, to the point that it becomes a common tool. Most of the scientific community accommodates to a new comfort zone. To the point that what previously was a heresy becomes now a "superstition." The words "heresy" and "superstition" are not to be taken literally, of course. That's called a simile (if, e.g., you use the word "like" or "as") or a metaphor (if you identify the analogous terms.)

Consider a frame-shift mutation. This kind of mutation is surely always deleterious. The individual dies even before it's born. So it's not like a person winning the lottery. Come to think of it, genetic material is some kind of template that uses the individual as a clever editing technique. I'm sorry if it sounds bleak, but that's the way it seems to be. But, OTOH too, not all mutations are deleterious. There are several molecular mechanisms of hedging you bets, or trying to have your cake and eat it too. I would say that anywhere along the molecular mechanisms of replication, transcription, and translation; whenever you see redundancy, there is at least the possibility of hedging your bets. If you have a series of codons that give rise to synthesis of, eg, an essential enzyme; and you have this sequence repeated over and over, consider the possibilities: you will always have the essential enzyme synthesized, buy you will have copies of it, like when you have copies of a text from a previous template, so that you can work on them to produce several alternative versions, but never lose your backup. Another mechanism of trying combinatorics is eukaryotic splicing, in which the organism tries several alternative "cut and paste" possibilities in between transcription and translation. Paraphrasing Sir Humphrey Appleby in Yes, Minister: "Really, minister, the possibilities are endless" (when you have huge redundancy in your nucleic acids)

I didn't mean it in that sense. "Entertain" as in, "The Bradfords always entertained lavishly at Christmas." You forgot your camouflage then.

This Wiley Miller cartoon summarizes it pretty well: https://www.gocomics.com/nonsequitur @Phi for All can no longer say I owe the community in jokes. I've posted three today and debated on a physics thread that is itself a joke.

“Sixty is the worst age to be,” said the 60-year-old man. “You always feel like you have to pee and most of the time you stand there and nothing comes out.” “Ah, that’s nothing,” said the 70-year-old. “When you’re seventy, you don’t have a bowel movement any more. You take laxatives, eat bran, sit on the toilet all day and nothing’ comes out!” “Actually,” said the 80-year -old, “Eighty is the worst age of all.” “Do you have trouble peeing, too?” asked the 60-year old. “No, I pee every morning at 6:00. I pee like a racehorse on a flat rock; no problem at all.” “So, do you have a problem with your bowel movement?” “No, I have one every morning at 6:30.” Exasperated, the 60-year-old said, “You pee every morning at 6:00 and crap every morning at 6:30. So what’s so bad about being 80?” “I don’t wake up until 7:00.” ---------------------------------------------------------------------------- A store that sells husbands has just opened in New York City,… Where a woman may go to choose a husband. Among the instructions at the entrance is a description of how the store operates. You may visit the store ONLY ONCE! There are six floors and the attributes of the men increase as the shopper ascends the flights. There is, however, a catch… You may choose any man from a particular floor, or you may choose to go up a floor,.. But you cannot go back down except to exit the building! So, a woman goes to the Husband Store to find a husband… On the first floor the sign on the door reads: Floor 1 – These men all have jobs, and will love their wife. She then goes to the second floor,… The second floor sign reads: Floor 2 – These men all have jobs, will love their wife, and love kids. She thinks for a while, and then goes to the third floor,… The third floor sign reads: Floor 3 – These men all have jobs, will love their wife, love kids, and are extremely good looking. “Wow,” she thinks, but feels compelled to keep going. She goes to the fourth floor and the sign reads: Floor 4 – These men all have jobs, will love their wife, love kids, are drop-dead good-looking and help with the housework. “Oh, mercy me!” she exclaims, “I can hardly stand it!” Still, she goes to the fifth floor and the sign reads: Floor 5 – These men all have jobs, will love their wife, love kids, are drop-dead gorgeous, help with the housework, and are excellent in bed. She is so tempted to stay,… But she goes to the sixth floor and the sign reads: Floor 6 – You are visitor no. 43,630,912 to this floor. There are no men on this floor. This floor exists solely as proof that women are impossible to please. Thank you for shopping at the Husband Store. Watch your step as you exit the building, and have a nice day!

The similarities are uncanny. But I don't think he is.

Oh, boy. You are so mathematically illiterate this is gonna take some time... Edit: Ok. I'm sorry. I take it back. So what's your problem. You have a magic trick to divide 0 by 0? There is a "magic" trick, but you haven't set up the problem properly. Seems like you're clueless. Are you clueless about these things? When t goes to zero (in the denominator), the numerator goes to zero for at least three reasons: the integration range shrinks to zero, the integrand goes to v(0), which is zero, the v factor outside the integral is zero. So it's zero divided by zero. Your eq. has nothing to do with dropping a ball. It's a different eq. of motion. I can't disprove your derivation for the very simple reason that you haven't shown any. Edit: You don't know what hyperbolic motion is, do you? Otherwise you couldn't possibly be asking such dumb questions. Why don't you just ask?

We'll always be there for you. Next time I falter, I'm sure you'll be there for me too. That's a question for BJ and Yusef.