LHC and partical decay - time question -

*arindamsinha*

Quote by PAllen

...It is you that does not understand SR well enough to see the whole picture.

That I can agree with completely.

nitsuj

Quote by PAllen

If I say you are aging slow, and you say I am aging slow, who is right? We both are, and this is pure relative motion time dilation, and is observer dependent. However, in the case particles in an accelerator ring, not only do we lab observers see them lasting long, but a hypothetical observer going around with them would conclude we are aging very fast (no Doppler involved - they compare their clock with one 'on the wall of the accelerator' on each circuit). This invariant aspect makes it 'differential aging' rather than pure time dilation. It is different from atmospheric muon to ground tests - there a hypothetical observer moving with the muon would consider that we are aging slow by the same factor we think the muon is aging slow.

So the term Time Dilation is specific to symmetrical cases? Everything else you said seems plain as day to me, that said I cannot understand how there is no length contraction / RoS ect because of the constant acceleration.

DaleSpam

Quote by arindamsinha

In the end, it is purely about the velocity and the Lorentz factor 1/√(1-v²/c²) in both cases.

The Lorentz factor only applies to inertial frames. That is why you can use it for the reference frame of cosmic muons but not for the reference frame of accelerator muons.

PAllen

Quote by nitsuj

So the term Time Dilation is specific to symmetrical cases? Everything else you said seems plain as day to me, that said I cannot understand how there is no length contraction / RoS ect because of the constant acceleration.

You could conceivably talk about time dilation for coordinates built from an accelerator muon frame. For non-inertial motion you can only talk about local frames in a unique way; then there are many approaches for extending a local frame to coordinate patch. However, typically, it cannot cover much spacetime. So you have a non-unique, quasilocal, coordinate patch in which time dilation takes a complex form [edit: really, the metric takes a complex form; the metric then determines time dilation for a specific path in the coordinates]. Further, in such a coordinate patch, you would typically have features like light and clock paths with coordinate speed greater than c; and your time coordinate would not be everywhere timelike (unless you restrict coverage of your patch even more). Note, this is all SR here - I am not referring to GR at all, just the issues involved in setting up coordinates such that an arbitrary non-inertial world line is the time axis, and coordinate time represents clock time along this world line, and distance coordinates represent proper distance from it according to some reasonable simultaneity convention. Given, especially, the non-uniqueness of all of this, it is rarely useful to talk about an accelerator muon's coordinates (and therefore, about time dilation from the accelerator muon's point of view - that requires such coordinates).

For these reasons, in the accelerator case, we choose to focus on the coordinate independent differential aging rather than the coordinate dependent, complex, time dilation.

nitsuj

Thanks for the explanation PAllen, it's more clear for me now.

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nitsuj Recognitions: Gold Member	Thanks for the explanation PAllen, it's more clear for me now.