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jtbell
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NanakiXIII said:Where did this 8.2 come from?
A typographical error. Thanks for catching it! I've just now corrected it to 2.4.
NanakiXIII said:Where did this 8.2 come from?
Apparently your position has shifted by 5.8 light-years
Because you are looking at changes in temporal and spatial coordinates, not absolute coordinates. In the general case, we are looking at the difference between an initial position and time and a final position and time. However, in the case of the other ('non general') LT's, it is a condition that the origins of the two frames coincide at t=t''=0. This does not have to be the case in the general LT's since we are only considering the difference between two defined sets of coordinates. For example, take jtbell's general LT;NanakiXIII said:No, I do have another question about those generalized transformations. If we can't use the Lorentz transformations between co-ordinates of S and S'', then why can we use them between intervals on S and S''? What's the difference?
There is no error. I never said there was.NanakiXIII said:Yes, but to transform between S and S'', you're still just using the Lorentz transformation. You're saying:
[tex]\Delta x^{\prime \prime} = \gamma [\Delta x - v \Delta t][/tex]
And thus:
[tex]x''=\gamma (x-vt)[/tex] and [tex] x''_0=\gamma (x_0-vt_0)[/tex]
Where is my error in this?
Socratic or not, start withNanakiXIII said:So, what I gather is that one way of looking at inverse Lorentz transformation is that there's just a plus sign because the velocity is negative. Am I in any way correct here? (I'm aware that the inverse transformations can be derived from the normal transformations, I'm just looking to know whether the thought described above is correct.)
Is that a Socratic question? I haven't a clue.
Be aware that the x and y coordinates in the presented Euclidean-Cartesian frames are not distances and time in the way the world works.NanakiXIII said:The Lorentz transformation apply per definition to intervals rather than to co-ordinates.
MeJennifer said:In reality, the physical distance between two objects is the amount of proper travel time taken for an object to go from one to the other.
The second doesn't follow from the first--if S and S'' do not share a common origin, the first is true while the second is false. As a simple analogy, consider two cartesian coordinate systems in 2D space, with the x' axis parallel to the x-axis and the y' axis parallel to the y axis, but with the origin of S' (x' = 0, y'=0) located at coordinates x=5, y=8 in the S system. In this case, the coordinate transform is just:NanakiXIII said:Yes, but to transform between S and S'', you're still just using the Lorentz transformation. You're saying:
[tex]\Delta x^{\prime \prime} = \gamma [\Delta x - v \Delta t][/tex]
And thus:
[tex]x''=\gamma (x-vt)[/tex] and [tex] x''_0=\gamma (x_0-vt_0)[/tex]
Where is my error in this?
No, quite the opposite in fact.NanakiXIII said:The Lorentz transformation apply per definition to intervals rather than to co-ordinates.