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Eugene Shubert
the new William Miller
Joined: 06 Apr 2002
Posts: 1006
Location: Richardson Texas
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 Posted: Sat Sep 13, 2003 8:51 am Post subject: Special Relativity Tutorial |
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| Quote: | | What is a precise definition of an inertial reference frame? |
Think of an incredibly long ruler that's flying through space under it's own inertia with a clock attached at each point. Also assume that the ruler isn't rotating. That's an inertial frame of reference.
If you want an accelerating frame of reference, think of that very long ruler as accelerating in such a manner that no part of the ruler experiences any stretching or compression.
If you want a rotating frame of reference, imagine a big spinning disk.
| Quote: | | How do two inertial frames of reference relate to one another? |
Consider the simplest case, i.e., in one spatial dimension. Here's the picture:
Imagine two rulers E and E' that slide on each other with a relative velocity v. Suppose an event happens at the point x on ruler E. Then the clock at point x, motionless on that ruler, reads some time t when the event at x occurred. If the other ruler E' is moving with respect to ruler E, sliding along the same line, then the event recorded as (x,t) in E is recorded as (x', t') in E'. x' is the location on the ruler E' marking the location of the event and t' is the time according to the clock at x'.
| Quote: | | If I am in one frame how can I recognize or observe another frame? |
All this becomes clear when you go through a mathematically precise derivation of special relativity. Learn the basics first.
For a derivation of the Lorentz transformation that continues the explanation that I've already given, which doesn't rely on any notion of simultaneity (immature or otherwise) and that doesn't presuppose Einstein's constancy of light postulate, see
www.everythingimportant.org/relativity |
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Eugene Shubert
the new William Miller
Joined: 06 Apr 2002
Posts: 1006
Location: Richardson Texas
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| Posted: Thu Oct 02, 2003 11:55 am Post subject: The newsgroup sci.physics.relativity |
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| Bilge wrote: | | Congratulations. You managed to define inertial in terms of, well, inertia. Now, do you have a definition that doesn't use the term you are defining to define itself? |
Understand the word inertia
| Bilge wrote: | | Don't use any terms you can't define non-circularly. For example, "moving at a constant velocity" is not a definition, unless you can define "constant velocity" in some way other than "inertial". Ditto for "straight line" and "non-rotating". Try again. |
"We cannot define anything precisely! If we attempt to, we get into that paralysis of thought that comes to philosophers, who sit opposite each other, one saying to the other, 'You don't know what you are talking about!' The second one says 'What do you mean by know? What do you mean by talking? What do you mean by you?', and so on." —Richard P. Feynman, The Character of Physical Law. |
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Eugene Shubert
the new William Miller
Joined: 06 Apr 2002
Posts: 1006
Location: Richardson Texas
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| Posted: Thu Nov 11, 2004 11:12 pm Post subject: The Shubertian Clock |
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| David Thomson wrote: |
Hi Eugene,
I read your paper, but didn't take the time to step through the math.
| Quote: | Conclusion
What we have actually constructed is a colossal, universal, everywhere present clock: The clock is wondrously intricate. It has an infinite number of moving parts, but don't ask me what they're made of. Each part moves at a unique speed and every possible speed has been represented.
The most distinguishing feature of this clock is that time is well-defined for every "inertial frame of reference" and that, irrespective of how time is computed, the Lorentz transformation ensures the same consistent, unambiguous mathematical answer, no matter the state of motion you are in or the comparing frame you use." |
Can you expand on this a little more? |
Dave,
The clock is a metaphor. The whole paper describes the clock. Conceptualizing it with moving lines is very easy. You remember what a ruler looks like. You know that rulers have equally spaced markings. Recall the picture on page 2. http://www.everythingimportant.org/relativity/special.pdf
The simplest Shubertian clock consists of 2 rulers (or invisible lines if you're daring enough to believe in them) that slide by each other in steady motion. Observers on the rulers can use the passing of the markings of the other ruler as indicating equal time intervals. If you can imagine the markings as having numbers attached, then you can create formulas. If, for instance, you're on ruler L at position x and the point x' of ruler L' flies by and is directly overhead, then, at that instant, the time T, according to your wristwatch, is T = -x'/u + xi(x). The time when x and x' meet according to the observer on L' is T' = x/u + zeta(x'). That's the most general mathematical solution. The advanced math comes in when you have three or more sliding rulers, all moving at different speeds, and you want your time formulas to work and give you consistent answers irrespective of whatever other comparing ruler you use. I'm really just repeating myself. You need to study the careful reasoning of the paper step by step. |
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