Weird physics question - relativistic immobility

[KrazyHorse]

Why the **** are you going to play his little game? What a joke. He could at least have asked for the laplacian in spherical coords or something.

[Kuciwalker]

That would only be true for the Yl0 (that's an L, not a 1) modes....but you're almost there....

Having all the pixels be divisible into isolatitudinal sets means each set will either be constant-amplitude or have a sinusoidally varying amplitude? (It's not obvious to me whether the points are spaced equally along the latitude line.)

edit: ok, I just saw the other post. got it.

[Ben Kenobi]

Try this Kuci.

x = r * cos(phi) * sin(theta)
y = r * sin(phi) * sin(theta)
z = r * cos(theta)

It's the right answer.

Simplest transform in the world. I see.

[Blaupanzer]

KH, I call upon your wisdom in context of the original thread title. Is not C a constant? If it is, could a ship speed up relative to that scale to approach C. Could it slow down on that same scale to 0? Just curious as this thinking comes to mind when reading some science fiction.

[Kuciwalker]

Blau, you're not making any sense. There's no difference between "speeding up" and "slowing down"; deceleration is just acceleration in the opposite direction.

[KrazyHorse]

Is not C a constant? If it is, could a ship speed up relative to that scale to approach C. Could it slow down on that same scale to 0?

I have NO idea what this is supposed to mean. I'm not being facetious or mocking you. I just don't understand.

We have 2 observers, A and B, traveling apart from each other at 0.9c (this is the relative velocity of A wrt B, or alternatively of B wrt A). A launches a rocket ship R toward B which undergoes constant acceleration (note: constant acceleration does not necessarily mean what you think it does in this context).

A sees R starting at 0 velocity. What is the velocity of R that B sees? The same as A's, of course; 0.9c (away from B)

After some time A sees R having 0.9c velocity (toward B). What velocity does B see R as having? 0!

Some later time A sees R having 0.99c velocity (toward B). What velocity does B see R as having? To answer this question you actually need to know relativity. The answer is 0.826c (toward B).

So B saw R initially flying away from him, slowing to a halt and then flying toward him faster and faster. A saw R initially at rest, then flying toward B faster and faster

So according to A R's speed was increasing from the first moment. But no matter how fast R goes there's always some observer who will tell you that R is at rest (or even going the opposite direction to the one A thinks it's going).

That's as simple as I can make it.

[Blaupanzer]

Thanks. I hesitate to beat a dead horse (truly a waste in every sense). But in E=MC squared, the constant c is given as a number ~ 186,000 miles per second or thereabouts. We innocent and unindoctrinated souls therefore see that light goes that fast whatever else is going on. Is that speed also relative to the observer or have I found a pear in the apple orchard and become confused?

[Alinestra Covelia]

I've heard it said that the idea of having a "zero" speed as a minimum which you measure other speeds from is really a fallacy. The actual constant should be the speed of light, which does not change, and all else is relative to that.

Maybe KH can clarify though. It would make sense that the concept of a zero speed is hard to pin down absolutely, since in his first few posts KH showed how difficult it is to even define a "fixed" point in the universe to take as the zero point.

[KrazyHorse]

Thanks. I hesitate to beat a dead horse (truly a waste in every sense). But in E=MC squared, the constant c is given as a number ~ 186,000 miles per second or thereabouts. We innocent and unindoctrinated souls therefore see that light goes that fast whatever else is going on. Is that speed also relative to the observer or have I found a pear in the apple orchard and become confused?

I have no idea what the hell you're asking me here. What does c being a constant have to do with anything?

[KrazyHorse]

If observer A and observer B are traveling at less than the speed of light relative to each other (this is the case for all massive objects in the context of special relativity) and if one observes something going at the speed of light then the other will also necessarily observe it going at the speed of light (though they may disagree on direction)

However, observer A and observer B will DISAGREE about the speed of anything NOT going at EXACTLY the speed of light.

[KrazyHorse]

I've heard it said that the idea of having a "zero" speed as a minimum which you measure other speeds from is really a fallacy. The actual constant should be the speed of light, which does not change, and all else is relative to that.

This doesn't make any sense. There's no such thing as measuring speeds "relative to" another speed.

Velocities are measured relative to a FRAME OF REFERENCE. You pick a frame, you measure the velocity of an object RELATIVE TO THAT FRAME. "The speed of light" is not a reference frame. It is a number.

The theory of relativity tells you how to go from one frame to another frame. In other words, it tells you that if, in observer A's f.o.r. you see object R at position X with velocity V then in observer B's f.o.r. (where you know B's velocity relative to A, call it vAB) object R is at position X' with velocity V'. The special thing about the speed of light is that if |V| = c then as long as |vAB| < c we get that |V'| = c as well. So all reasonable (not translight relative to each other) observers agree on the speed of a light beam.

[KrazyHorse]

The point is that there is no "special" or "preferred" frame of reference where the laws of physics are different. If something has zero speed in my frame of reference then it has nonzero speed in somebody else's frame of reference. The nearest thing we have to a preferred frame of reference in my mind is the frame of reference of the CMB. We're traveling at about 600 km/s relative to that frame, which is why we see the CMB as being significantly hotter in one direction than the other (the dipole moment of the CMB). Even in the CMB's own frame of reference there is still some anisotropy, but that is a fundamental anisotropy which comes from actual density perturbations in the surface of last scattering, which is different than the anisotropy induced by our motion relative to the CMB's frame.

[Kuciwalker]

The point is that there is no "special" or "preferred" frame of reference where the laws of physics are different.

I think the thing that confuses people is that why "the speed of light" is a law of physics and "the speed of me" is not.

[directed at Ali and Blau]
The reason the speed of light is a physical constant is because it emerges from Maxwell's equations of electromagnetism. These four equations govern classical electromagnetic interactions. One of these equations predicts that a changing electric field results in a changing magnetic field, and another predicts that a changing magnetic field results in a changing electric field. One of Maxwell's key observations was that these equations give rise to self-propagating "changing electric and magnetic fields" - i.e. light waves. The speed at which these waves propagate is based on two constants that occur in those two equations: the "permissivity of free space", which essentially defines how strong the electric force is, and the "permeability of free space", which is the same for the magnetic force.

At this point, people suddenly said "wait, there doesn't seem to be any medium for these waves to travel through", which really didn't make any sense because prior to that point a wave was pretty much defined in terms of a medium. So people invented the idea of "the ether" and everyone was happy. The ether was, in effect, a preferred reference frame, which previously had not existed in Newtonian mechanics. If you were moving relative to the ether, then the speed of light relative to you would appear to change, and therefore necessarily the values of those constants.

This was all well and good until people actually tried to measure our velocity relative to the ether (essentially the question Ali is asking), and found out that... they couldn't do it. The measured velocity was always zero, even for two observers that were clearly moving relative to each other. This discovery, that the speed of light was constant and that the ether as understood couldn't exist, wasn't resolved until Einstein came up with special relativity.

With the discovery of special relativity there was, once again, no preferred reference frame (i.e. no ether).

[Blaupanzer]

So, if we were or became a spacefaring people, we would have no fixed reference for speed regarding ships travelling from solar system to solar system? This would make interception of ships or objects not in the f.o.v. a real *****. To say nothing of occupant aging anomalies when comparing those on high speed ships vice those on the departure or arrival planets. Most science fiction appears to gloss this over despite the relativity theories being older than the sci-fi genre.

[Japher]

This is why we need warp technology!