swansont

Atomic clocks do not require movement of the atoms. In fact, since this introduces error, the efforts over the years has been to reduce the movement to get better precision and accuracy. Ideally you'd eliminate the center-of-mass motion altogether, if that were possible. It wasn't a definition, per se. It was a classification of discussions about time. How do you get rid of time? Or introduce time to something? Speed is dx/dt By definition you must have displacement and a time interval for there to be motion. You can't separate the two. However, you can have something sit there, approximately at rest, and still have the passage of time. Which is why I think this is metaphysics and semantics.

Traveling faster than c violates causality — it's possible to get information about the outcome of an event before the event occurs, e.g. the push of a button, which means you could decide not to push the button. The scenario with the astronauts is known as the Twins Paradox. It's not traveling back in time, but deals with relativity and the notion that time depends on your frame of reference (i.e. it goes at different rates in different reference frames) rather than being universal

Need more context than that.

The oscillations are because the atom is in a coherent superposition of states — the oscillation is between the states, and you could describe that as a single state if you chose to. You can't tie any of that back to anything like a classical trajectory of an electron. (In microwave clocks these states are spin orientations of an electron) "Motion" really isn't well-defined here; it's a classical notion, and this is QM. My view on this is that "time is motion" is metaphysical, as is any "nature of time" argument. You can't get rid of motion, or stop time, to actually test anything. Doesn't the realization that time slows down for a fast-moving object actually argue against time being based on motion?

Can we invent games? How is math fundamentally different? It's a self-consistent set of rules governing what we do with numbers. There's no restriction that math actually have an application to the real world. (The best-known math does, because it's useful)

You forgot the "I live next-door to you" part.

There is a difference in the potential — a rotating system is at a fixed potential, while a linear (i.e. a and v in the same direction) system's potential is changing.

Scientists have made antihydrogen, so it's certainly possible. But since you make as much antimatter as matter (ignoring CP violation for the moment), all that antimatter is going to annihilate, and you end up with nothing extra. There's no point to it. As far as making food and water, etc, you still have the same problem of assembling the elements from the protons and neutrons, so why not just start there?

It's not impressive — 1 GW gives you 3.33 N of thrust (F = P/c, where P is power) So for a 1000 kg spaceship, that's a whopping 3.33 mm/sec^2 of acceleration. Which points to this being not feasible, except for the problem of other forms of propulsion if you want to do interstellar travel. Solar sail effectiveness drops off with the square of the distance from the sun, and chemical or ion engines need propellant. You can make as many photons as you want, and since the thrust is not wavelength dependent, you are free to choose the most efficient EM radiation generation devices for your third of a milli-g acceleration per GigaWatt.

I've seen it too. It comes and goes, though, so I just assumed it was the Gin.

You can't apply the equations or the concept of constant c if you mix the frames. In each frame the view is consistent: the fixed observers sees them travel 100,00 LY but observes that their clock ran slow. The spaceship observer sees the travel as being shortened. Neither observer sees that they have exceeded c. As I had said, it's an acceleration at g, or 1g of acceleration — the acceleration of gravity at the earth's surface. The distance you accelerate at g tells you the change in your (pseudo)potential. There is no preferred frame of reference. If you couldn't observe the Milky Way there is no way to tell if you were moving or at rest with respect to it. You can tell if you are accelerating, but not if that's because of e.g. thrust of your rocket or being at rest in a gravitational field. Location, location, location. The potential is the depth of the well. The acceleration is the slope of the sides. e.g. if g is large, it says that a small change in position gives a large change in potential, but it doesn't tell you what the potential is. The one who doesn't accelerate. Being at rest in a gravity field is an accelerated frame, which is one of the quirky concepts of GR. No. You can treat these as a kinetic dilation or a pseudo-gravitational dilation, but you don't do both. The observer in a gravitational field is at rest. If undergoing an indistinguishable acceleration, he can assume he is at rest. There would be no kinetic term for that observer. However, an external observer can just say that the person is moving, and solve for the kinetic dilation.

I disagree. The medium here is writing, and you're trying to apply the rules for a spoken debate. I think the bulk of the areas in the forum do not normally contain debate-style discussions. That's not how most scientific discussion proceed — there isn't really a case for something and a case against it; if a theory fails, it fails. It's in discussions like this, where you have stated a position and tried to make a case to support it, where this might apply. If the poster is wrong — has cited something factually incorrect or has used a logical fallacy — why is it necessary to form a cohesive counter-argument? The quote tags, properly used, reduce confusion because everyone knows to whom you are responding.

The Bohr radius is the most probable distance of the electron when you solve the Schroedinger equation. AFAICT you get the same answer because you've taken an energy and converted it to a mass and then back to an energy, i.e. you've multiplied it by 1. S orbitals have zero orbital angular momentum. The Bohr model predicts angular momentum of [math]n\hbar[/math]. The electron has spin, but that's not part of the Bohr model.

And they will observe the maps to be wrong when they are moving. You're taking measurements from two different frames, and that's not how you measure the speed of light. The acceleration is not the right thing to look at, it's the potential. Like I said, if you do it right, you'll get the same answer. The low-speed approximation for the frequency shift in a pseudo-gravitational potential from accelerating at g is g*d/c^2. If you recast that in terms of speed, it's v^2/2c^2, which is what you get if you assume it's all from the speed. The full equations are more complicated, and you can't use the approximations when the speed starts to get as big as 0.1c

It gets the energy correct. That's about it. So you can use it for energy calculations. It has orbits, not orbitals, and that's wrong. It gets the angular momentum wrong. At that point, you have to abandon it.

1. False. The ship will observe length contraction of the path of the trip. 2. False. Two sides of the same coin. You can approach the problem using either solution, and if you do it right you'll get the same answer.

The Bohr model is WRONG. It's tough to gain any insight at all from an incorrect model.

Not sure. QCD isn't my field. I think at this point you're grasping at straws. Either the atom follows the physics that has been discovered, or you disregard basically all of physics. Proposing that we essentially understand nothing about atomic physics in order to accommodate your hypothesis is a nonstarter.

First of all, you are arguing a different point — I said "The tropics aren't as well-suited to growing the wide variety of crops as in temperate zones." I never said crops were, in general, hard to grow in the tropics. It's that, as D H has pointed out, you can't grow the right crops, the ones you can store for long periods, and there tends to be a lack of variety of the staple crops. You can't have those crops migrate North and South too far, because what grows well in tropics don't grow so well outside, and vice-versa. Second, here you are discussing transplanting a crop from one place to another using ocean-going vessels, which is a bit off the mark for this thread — we're discussing development of science, or lack thereof, over the course of many thousands of years, so what's the relevance of attempts to spread a crop 220 years ago? The advantage the Eurasians had was that there was an east-west land route, all with a similar climate, so that crops were easily adopted as they migrated, and all of this happened thousands of years ago. Cassava, from what I can find, is native to South America, and brought to Africa and the South Pacific region by the Europeans — i.e. the ones who were more scientifically advanced and were regularly traveling those long distances across the oceans. The crops have to be there before science advances, not after.

I think you should just use "interaction" here. All collisions are interactions. Not all interactions are collisions.

The magnetic moment of the proton is well-known. If you want to try and take the tactic of inferring the magnetic field from the "shell curvature" (by which I assume you mean the Bohr orbit) then you need to reconcile this with the Hyperfine splitting of Hydrogen — the energy difference between the two orientations of the electron magnetic moment in that field — being h * 1420 MHz. (or ~10^-24 J) Since the Bohr magneton is ~ 10^-23 J/T, that implies about 0.1 T

You need to write down an equation for r for an arbitrary point inside the circle, and then integrate it for all points around the circle. Pick your point a distance a from the center, and draw a line to an arbitrary point on the circumference, and also draw a line from the center to that same point on the circumference. That will be your triangle. Apply the law of cosines.

You didn't use the proton's magnetic moment, and you didn't find the magnetic field properly. Where did you find an equation that said the magnetic field was the magnetic moment multiplied by the kinetic energy? (This is all ignoring your use of the Bohr model, of course)

1. Why are you using the electron magnetic moment? You are proposing the interaction of a moving electron in the proton's magnetic field. 2. Where did you get your equation for B? 3. What will the field from the proton be, at the position of the electron? 4. What will be the direction of such a force?

I'm guessing it's the unit mistake, and should be km/hr. You could contact the publisher and point that out. They might have an errata page online. Is there a URL given in the book?