OT: LOTD and a Q for the brainiacs

Also see Mach's principle. Something I grappled with as a high school student when thinking about rotating systems. The way I happened on it was to ask myself, "What does rotation mean for a rigid object otherwise entirely alone in a universe?" The answer I gave myself was that the question would no longer make any sense to ask. It would instead be meaningless. I was later told I wasn't the first to ask, nor answer, similarly.

Jon

Serious question: does the universe have a fixed object called the center? Then it would not be alone - its motion could be described in terms of the center.

-- Les Cargill

One of the things that had helped me think about what I was earning as a teenager in high school, was to reduce situations to absurdly simple ones.

For example, in thinking about individual human rights I would reduce the situation to one human being only on an entire planet and then ask myself the question, again. Then I would make that two people. And ask again. Etc.

I learned a lot by carefully thinking through these ideas to see how my perspectives changed and evolved as the situations I presented to myself also did. What sometimes starts out as one idea may bifurcate into two distinct ones, soon after. In some ways, this isn't unlike how physical forces such as the strong and weak nuclear may become the same under the right circumstances (near the big bang moment) and may yet separate into what seems distinct and new ideas when the situations are changed.

As I mentioned above, I did this also for the idea of rotating systems. Asking what it means to have a rotating rigid object in a universe with nothing else in it seemed like an important question to ask. And deciding then that the question no longer had any meaning "felt correct." As I said, it was another decade before I found out that Einstein had used the very same thought process and called it Mach's Principle in some of his writings. A happy circumstance.

(At the time, I hadn't read nor had any idea about others perhaps wondering about this, though I felt some may have. But none of my textbooks talked about things in this way and I began to wonder if perhaps it hadn't been considered, since it wasn't being talked about within my limited exposures.)

The idea of Einstein's interpretation of Mach's Principle (which he fashioned in a particular way that makes it uncertain whether Mach intended the same thing, or not) was used by Einstein in discussing his approach towards the general theory of relativity and it is is an interesting one to consider and discuss. It's also simple to get across to others and requires no math, to at least talk about, anyway.

There are situations, closed time-like curves, where this question becomes yet more interesting. I haven't spent much time on it; though I've read a small amount. But in general, I don't think any of this is really settled quite yet.

For me? Hmm. Here's a question for you. Imagine you are a photon emitted by a star a million light years away and a million years ago and absorbed by someone's eye on Earth, tonight. How much time passed from the point of view of the photon? How much distance was travelled?

Jon

Um... learning....

Jon

Zero

Intriguing answer. First one I came up with, too.

Now, think about what the entire universe then looks like, from that perspective? (Clue: examine the two seed equations involved in Einstein's development of his special theory of relativity and ask yourself what _meaning_ may be suggested at.)

Jon

yep..

from the photons perspective, no time at all.... it was absorbed immediately after it was emitted.

light has no time

Mark

Rich Grise wrote: > Today's xkcd made me LOL: >

Yes.

The hard thing about coordinate transformations is keeping everything straight.

First of all, if you have a vector V in one coordinate system, you can express it as V' in another coordinate system, but it's still the same vector. (Relativity makes this a bit harder, but it's really the bookkeeping that'll cross you up if you aren't careful.)

Say you have a vector V, expressed in a frame rotating with an angular velocity _Omega_. The vector might be the velocity of a marble sliding frictionlessly on a turntable, measured in rotating Cartesian coordinates. Since the motion is frictionless, in the lab frame it moves in a straight line at a constant speed, but in the rotating frame it accelerates.

The rate of change of a vector _V_ in a frame rotating at Omega is

d_V_/dt = d_V_lab/dt + _Omega_ cross _V_

(the vector cross product). The cross product of two vectors is another vector, perpendicular to both of the operands and having length equal to the product of their lengths times the sine of the angle between them. (Wikipedia will have the exact expression for it.)

When you take that apart into its radial and tangential components, you get centrifugal and Coriolis acceleration, respectively. If you don't try to stop the marble from sliding, no force is required, and it just does what it does. If you want to keep it in one place, however, you have to exert real force to counteract the centrifugal and Coriolis forces.

(This is from memory so I may have a sign backwards someplace.)

Cheers

Phil Hobbs

Well, from that perspective there is no time or space. And as an exercise for our readers, integrate that with the holographic model of the universe (which is 2D) and report back

And the speed of dark is infinite

Not quite what I was leading towards. More like time and space are inextricable, one must arise with the other.

In case it helps:

x = c t x' = c t'

From those, special theory falls out with what amounts to simple algebra. If valid, and experimental evidence supports it well so far, then there is another interesting question that arises without going any further. Imagine what those two _may_ imply. Think simply.

Jon

Well...our _galaxy_ has a center, so Relatively Speaking (aunts, uncles, cousins, etc). one could say that is a "fixed object"...

As far as the photonwas concerned, it was EYE-mediate.