Sisyphus

Yes. So for example an object at 0.99C has about 40 times the kinetic energy as an object at 0.5C. Yes. What energy? It takes the same amount of energy to "decelerate" something from 0.98C to 0.95C as it does to accelerate it from 0.95C to 0.98C. There is no extra. I don't really know what this means, so I'll just say to keep in mind that kinetic energy is relative. The object might be going at 0.98C in our rest frame, but there is also a reference frame in which its velocity is zero. There is no event that can occur at 0.98C that wouldn't happen for an object at rest, because it is also at rest.

It's not really like a circuit, and it's not atom sized. It's electron sized. It behaves just like a large charged body would if you were to rotate it. Spin is an intrinsic property of electrons. You can think of it as an irreducible quantum of angular momentum.

All magnetic fields are ones that occur because an electrical field is moving. If you're thinking of something like a bar magnet, then the motion is the spin of the electrons contained therein, all aligned in the same direction.

It's not different from meters. In fact, that's the example I used. Graphs of y=2x, y=x^2, or y=x^37 are all showing a relationship between two variables, the horizontal and vertical dimensions. There's no reason they can't be in units of meters. "The vertical height is proportional to the 37th power of the horizontal distance." No 37-dimensional object need be involved. Now, if you were going to graph y=x+z, you would need three dimensions.

Oh, I'm sure it can be represented by objects of any number of dimensions, but the point is all you need is two. You also only need two to represent y=x^3, or y=x^1000, since they're all just representing the relationship between 2 variables. Acceleration is not adding a dimension, it is just a non-linear relationship between two dimensions.

No more than the curve graphed by y = x^2 is three dimensional. Which is to say, it isn't.

I don't know how to respond to that. It's not true. What difference does holding in the hand make? Or, ok, how about this. I'm holding two identical boxes in my hand, containing the same number of hydrogen atoms. However, the hydrogen atoms in box A are moving around faster than in box B. Box A will be heavier. Relativity, right in the palm of your hand! It actually exists. "Happen" implies that something is changing, so no. Though certainly you can have changes if you involve acceleration between frames, as with the twin paradox, etc.

Unfortunately it's difficult to consider one aspect without the other. Kinetic energy, like distance, time, and relativistic mass, depends on frame of reference. Relative to someone sitting inside it, the plane has no kinetic energy. Relative to the ground, it has a lot. Relative to Mars, it has a lot more than that. Of course nothing is changing. But no perspective is more real than another. That's the point. There is one reality, but one reference frame is only a slice of that reality. The image is cycling through a range of slices.

Yes, the object actually is 10cm in one frame and actually is 20cm in another. Perhaps you're not clear or consistent about what "a question of measurements" is supposed to mean. I'm talking about relativistic mass.

But no one is saying it is a physical deformation, just that no measurement is more "real" than the other, which is to say that they are both real. It is 20cm long, and it is 10cm long, and it does not change. That's not a contradiction. I think a good way to think of it is to keep in mind that objects simply do not have single, absolute properties like length, but rather length in a given reference frame. For some reason people find this a lot easier to grasp for some properties than others. What is your velocity? Not an answerable question unless you specify a reference frame. What is your length and mass? Also not answerable, for the same reason. I suppose it's just a matter of direct experience. People can handle measuring a car's speed relative to a road while knowing the road is on a spinning planet orbiting a star, or measuring walking speed inside an airplane they know is moving far faster than that with relative to the ground. But we have no direct experience with speeds and masses large enough for relativity to matter, and so "what is your mass relative to X" still sounds strange to most people, who insist that one answer is right in some absolute sense while others are just illusion.

They do often use NaCl on the roads, so it will certainly work. The other salt they use is CaCl2, which works faster and at lower temperatures and is less environmentally damaging, but is also somewhat more expensive and can be slippery itself. I wouldn't use salt to melt a big pile of snow, though, just because you would need a lot. Better to shovel, then use salt, so the last bits melt and traction improves. There's a reason they plow the roads and then salt them.

That is not a research paper. And almost all of the basic facts are wrong. For example, we are nowhere near the galactic equator.

The galaxy's mass is mostly in a fairly flat disk shape for the same reason the orbits of all the planets of the solar system are close to being in the same plane. It's a spinning, gravitationally bound cluster of matter, and that is the plane of its total angular momentum. The spiral arms are not fixed structures, but waves of high density, like traffic jams on a highway.

Motivation.

Close to it, yeah. But distorted because the Earth's density is greater closer to the center. .

So in other words, it is not even true, as I suspected. The 25 hour thing for humans was based on flawed and now discredited research, and humans are not at all unique in not keeping perfect 24 hour time themselves: http://en.wikipedia.org/wiki/Circadian_rhythm

Just like with a spring, there would be highest acceleration (but zero velocity) at either end, and it would be 9.8m/s^2. The lowest acceleration (but highest velocity) would be passing the center of mass, at which point the acceleration would be zero.

I use Firefox too and like it, though the only others I have experience with are IE and Safari. So what add-ons do you other Firefox users have? I'm using: Adblock Plus: No ads! Download Statusbar: puts download manager on the status bar instead of a separate window Downloadhelper: download and/or convert embedded flash or videos NoScript: Blocks all javascript/java/flash until you give permission, allows whitelist and blacklist for familiar sites Screengrab: Button to save all or part of web page as an image Smoothwheel: Smooths out scrolling for ease of reading and allows customization

It doesn't seem credible that humans would naturally have a 25 hour cycle while all other animals would naturally have a 24 hour cycle. Do other animals, when kept for extended periods of time at the bottom of mineshafts, maintain 24 hour cycles? How consistent is the 25 hour cycle for humans? Is it merely an average in a wide range? Do all other animals, in fact, keep rigid schedules by clock's time, or do they, for example, go by sunrise and sunset? Furthermore, just anecdotally, I get up at the same time every day, without an alarm clock. (I have one, but I haven't failed to wake up shortly before it goes off in probably years.)

lemur, it seems like you are insisting on a "qualitative model" to be some robust analogy to a classical physics situation. Why? I'll tell you why not: because it doesn't work. It is impossible to model an atom with classical physics. That's why there is quantum physics. So what's the appeal of it? "To understand what it actually is," sure. But what does that mean? Would picturing it as little balls orbiting around a center make it more understood? No. It would just make it more familiar, which is not the same thing. And it would make it so you could have a mental image of it, which is not the same as understanding it, either. The fact is that quantum behavior, which is outside our ordinary experience, is what is real. And ordinary experience, with things like orbits and solid objects that have particular locations at all times, are the illusion. Or rather, they are emergent phenomena, but simply not how the world works on a fundamental level. Put together enough little wavicles, and you start to get something that looks like a coffee mug (for example). Just like if you put together enough ones and zeroes, you start to get something that looks like Firefox (for example). And what you're essentially saying is that for any of those ones or zeroes, there simply must be some way to model it as a web browser, or else we don't really understand what a one or a zero is. Does my tortured analogy make sense?

Not exactly. The light wave itself is red in one frame of reference, and blue in the other. It is in fact a property of the light itself. Also, note that the distance is not the same in both reference frames. When the ship is next to the planet, observers on the planet and on the ship will disagree as to how far away the galaxy is. And they would both be correct. I don't understand any of the above. It seems like word salad.

Yes, yes, and yes.

Actually, no, it isn't. It is approximately 1 calorie. The energy needed to raise the temperature of water is not entirely constant. Joules and calories are not measures of "work energy" and "heat energy." They are measures of energy. The same thing.

It is misleading because nowhere is information traveling at greater than C, relative to any observer. Nevertheless, it is impossible to "set their watches" between reference frames, and have them agree on the time that other events occur. That doesn't really matter. The lack of simultaneity is not the result of just travel time for the information. That can be compensated for.

If they collide in one reference frame, they will collide in all reference frames. It's the "at the same instant" that is the problem, because there is no such thing.