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Special Relativity

Hey,

The thing I'm struggling with on this topic is knowing which object is for T0, T, L, L0. Sometimes it seems really arbitrary and I don't get it.

Does anyone have any tips on how to know for sure when to use T0, L0 etc?

Thanks!
@uberteknik
what are you defining to be T, T0, L and L0?
Reply 3
Avatar for tomlam
tomlam
15
t0 and l0 are time and length observed by a stationary observer respectively. Just like zero for capacitors means the initial voltage or current, you use this as a standard
Remember, they both dilate as you go faster. The question will always tell you which frame of reference they want it (or you can infer it).
ie: electron going at 0.994c for 0.5s what is the time observed by the electron?
0.5xsqrt(1-0.994^2) equals 0.054s as observed by the electron.

If you're still struggling, you can get the book "calculations for a-level physics" which is like £20 new or £5 used. If you have the time to practice, this is an excellent book.
Original post by tomlam
t0 and l0 are time and length observed by a stationary observer respectively. Just like zero for capacitors means the initial voltage or current, you use this as a standard
Remember, they both dilate as you go faster. The question will always tell you which frame of reference they want it (or you can infer it).
ie: electron going at 0.994c for 0.5s what is the time observed by the electron?
0.5xsqrt(1-0.994^2) equals 0.054s as observed by the electron.

If you're still struggling, you can get the book "calculations for a-level physics" which is like £20 new or £5 used. If you have the time to practice, this is an excellent book.


stationary with respect to what? :holmes:

remember time dilates; length contracts. if they both dilated we'd have a major inconsistency
Reply 5
Avatar for tomlam
tomlam
15
Original post by Implication
stationary with respect to what? :holmes:

remember time dilates; length contracts. if they both dilated we'd have a major inconsistency

Well, you know what I mean. the 0 essentially means in the normal or "actual" frame of reference, you know, it will tell you in the question how it wants you to answer.
Original post by tomlam
Well, you know what I mean. the 0 essentially means in the normal or "actual" frame of reference, you know, it will tell you in the question how it wants you to answer.


but the whole point of special relativity is that there is no such thing as an 'actual' or 'normal' frame of reference!

there are such quantities as 'proper time' and 'proper length' - which are occasionally denoted by t0 anf l0 - but they are defined with respect to a specific frame of reference. for example, my proper time is the time as measured by a clock in my reference frame; your proper time is the time measured by a clock in your reference frame.
Reply 7
Avatar for tomlam
tomlam
15
Original post by Implication
but the whole point of special relativity is that there is no such thing as an 'actual' or 'normal' frame of reference!

there are such quantities as 'proper time' and 'proper length' - which are occasionally denoted by t0 anf l0 - but they are defined with respect to a specific frame of reference. for example, my proper time is the time as measured by a clock in my reference frame; your proper time is the time measured by a clock in your reference frame.


Yes, that's essentially what I was saying.
Original post by Nikhilm
Hey,

The thing I'm struggling with on this topic is knowing which object is for T0, T, L, L0. Sometimes it seems really arbitrary and I don't get it.

Does anyone have any tips on how to know for sure when to use T0, L0 etc?

Thanks!


It's probably easiest to simply remember 'time dilates and length contracts'. Then if you want to know the value of a time interval as measured in a frame moving with respect to that of the original measurement, apply your Lorentz transformation in the direction that makes the time larger. With distance, apply the transformation in the direction that makes it smaller.

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