On the interpretation of a spacetime diagram

GregAshmore

Quote by JesseM

What does "actually shorter" mean?

...

"In error" with regards to what? You seem to have this quasi-metaphysical notion of the "true value" of various quantities, but in physics all quantities can only be measured relative to a particular choice of measurement procedure...

You assume that all measurements provide an accurate picture of reality. How does this square with the fact (as reported by Taylor and Wheeler--I didn't work out the math myself) that no matter how fast an object is moving away from us, we will never measure its speed as greater than 0.5c?

The only place light might enter into it would be in the definition of simultaneity, but there are other ways to define simultaneity in a given frame that don't make use of light, like the slow transport method.

The equations of special relativity have the form they do because they start with the observed nature of light--its speed is the same for all observers. The nature of light is thus tightly bound to the characteristics of time and space which flow from the equations.

I must sign off for a few days and see how my ideas work out on the spacetime diagram.

GregAshmore

Quote by bobc2

I think you have that exactly right, GregAshomre.

This is certainly correct.

I think most any special relativity physicist would agree with Born's characterization.

You've done a nice job of summarizing the situation, but Greg, I think I would not agree with this characterization. However, you probably have some good company among physicists on this point. The thing that is usually cited to bolster your view is that it is common practice to relate the 4th dimension as X4 = ict, where the imaginary number is associated with the 4th dimension. However, I think this is artificially contrived as I'll try to show in the sketches below where I've derived the Lorentz transformation (rotation only) modeling space as strictly 4-dimensional.

I'll have a look at your sketches after I see how my concept works out. See you in a few days.

GrayGhost

You are correct that Lorentz considered the Fitzgerald contraction a physical deformation of the electron field about the atom. They assumed the body contacted in an aether that does not.

Einstein's length contraction is completely different, yes. If an aether exists, it doesn't matter at all per SR. Consider 2 bodies of the same frame, one in front of the other separated by some proper distance s. Now, assume yourself in motion wrt said bodies, with velocity vector parallel wrt the center-line connecting the 2 bodies. While viewed in motion, not only do the moving bodies length-contract, but all the space between them (and within them) does as well. IOWs, it's not that the moving body contracts in a space that does not ... but rather that the way in which space and time are measured changes with a change in one's own state of motion. This is why you remain unaffected when (say) 10 moving observers measure your length differently. Yet, their measurements are correct, and quite real. Theoretically, with sophisticated enough measuring systems using lasers, light signals must reveal what the math of SR predicts for any of said 10 moving measurers.

GrayGhost

bobc2

Quote by GrayGhost

You are correct that Lorentz considered the Fitzgerald contraction a physical deformation of the electron field about the atom. They assumed the body contacted in an aether that does not.

Einstein's length contraction is completely different, yes. If an aether exists, it doesn't matter at all per SR. Consider 2 bodies of the same frame, one in front of the other separated by some proper distance s. Now, assume yourself in motion wrt said bodies, with velocity vector parallel wrt the center-line connecting the 2 bodies. While viewed in motion, not only do the moving bodies length-contract, but all the space between them (and within them) does as well. IOWs, it's not that the moving body contracts in a space that does not ... but rather that the way in which space and time are measured changes with a change in one's own state of motion. This is why you remain unaffected when (say) 10 moving observers measure your length differently. Yet, their measurements are correct, and quite real. Theoretically, with sophisticated enough measuring systems using lasers, light signals must reveal what the math of SR predicts for any of said 10 moving measurers.

GrayGhost

Nice summary of the situation, GrayGhost.

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