Gallilean v/s Lorentz transformation

[PhysicsEnjoyer31415]

TL;DR Summary

Why do we still use gallilean transformation if Lorentz transformation works for all velocities equal to and approaching 'c' . Also by using Gallilean transformations it is possible to get values of relative velocity more than 'c' which is not possible ....So is this because it is practically the same for v<c or just because it is a prerequisite to lorentz transformation?

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[Orodruin]

You can ask the same question about why we still use Newtonian gravitation when we have general relativity. The answer is that it is much simpler to apply and for most applications the predictions are indistinguishable. Obviously, when we enter realms where there is a relevant difference, such as objects moving at high relative velocities, then Lorentz transformations must be applied to get a result compatible with experiments.

Newtonian physics is also much easier to understand as so much more of it appears "intuitive" to more people. Most engineers will never need relativity and so they can make do with the conceptually easier Newtonian physics. (Of course, if you work enough with relativity, it also becomes "intuitive", which in essence is just our brains telling us that we are familiar enough with something that we can discern the main results without going into much detail.) Who do you prefer building your bridge: An engineer using Newtonian physics or an engineer using relativistic physics, but taking three times as long and possibly getting it wrong because it became conceptually difficult?

 

[Ibix]

Newtonian physics is conceptually and mathematically much easier than relativity, and for most applications in every day life the answers will be the same to the precision you can measure.

If I drive at 60mph for an hour and return home, this is a twin paradox scenario and I will have aged less than my twin who stayed at home. 60mph is about 30m/s, which equates to a $\gamma$ of about $1+5\times 10^{-15}$, which means I'm about 20 picoseconds younger after my hour journey. That's indistinguishable from "I'm the same age as my twin", so why pay the price of the additional maths?

 

[PhysicsEnjoyer31415]

Oh .....now that makes so much more sense.

 

[haushofer]

We call this idea the correspondence principle: different theories are used in different regions. No theory is "the ultimate theory"; some theories just happen to be broader applicable. The correspondence principe guarantees you that for v<<c Einstein's theory of special relativity effectively becomes Newton's theory of motion (both on the level of equations of motion and underlying symmetries).

Try to use Einstein's theory of General Relativity to describe the free fall motion of a rock here on Earth and you'll understand why we turn to Newton.

 

[Orodruin]

Try to use Einstein's theory of General Relativity to describe the free fall motion of a rock here on Earth and you'll understand why we turn to Newton.

I mean ... That particular piece of phenomenology is not that hard in GR ...

 

[PhysicsEnjoyer31415]

We call this idea the correspondence principle: different theories are used in different regions. No theory is "the ultimate theory"; some theories just happen to be broader applicable. The correspondence principe guarantees you that for v<<c Einstein's theory of special relativity effectively becomes Newton's theory of motion (both on the level of equations of motion and underlying symmetries).

Try to use Einstein's theory of General Relativity to describe the free fall motion of a rock here on Earth and you'll understand why we turn to Newton.

Oh ok just another question that do we have anything better than einstein's SR and GR as of now ?

 

[haushofer]

I mean ... That particular piece of phenomenology is not that hard in GR ...

Relatively speaking.

 

[haushofer]

Oh ok just another question that do we have anything better than einstein's SR and GR as of now ?

No. Not for gravitational phenomena or non-quantum dynamics like classical electromagnetism, that is.

 

[cianfa72]

If I drive at 60mph for an hour and return home, this is a twin paradox scenario and I will have aged less than my twin who stayed at home. 60mph is about 30m/s, which equates to a $\gamma$ of about $1+5\times 10^{-15}$, which means I'm about 20 picoseconds younger after my hour journey. That's indistinguishable from "I'm the same age as my twin", so why pay the price of the additional maths?

Just to be sure: the fact that you aged less than your twin who stayed at home, is invariant since both you and your twin's timelike worldlines share the same start and return events respectively.

However the above is not symmetric (from your point of you is your twin moving), since you and not your "at home twin" undergo proper acceleration at some point/event along your timelike worldline.