0
$\begingroup$

I watched a presentation where special relativity was mentioned as being essential to understand electromagnetism, as in the case of current flowing in a cable, a charge moving next to the cable, due to length contraction of SR feels one charge more than the other.

I also read electromagnetism was later quantized through Quantum Electrodynamics. But as far as I know QM is background dependent, that is, the theory needs an unchanging coordinate system to work. How can such a system be combined with length contraction? Or is the problem with general relativity with changes the coordinate system all together, but here with EM / SR simple contraction in existing coordinate system works fine?

$\endgroup$
0

2 Answers 2

2
$\begingroup$

SR is introduced by the use of 4-vectors an contractions of those such that they are Lorentz invariant. Since the 4-position $x^\mu = (t, \vec{x})$ transform under Lorentz transformations, length contraction and time dilation are already taken into account.

Respect to "QM is background dependent, that is, the theory needs an unchanging coordinate system to work. How can such a system be combined with length contraction?"; if that background is the ground state and therefore the zero-point energy you don't have to worry about it in QM since it does not affect dynamics. It is only relevant for cosmology (i.e., dark energy) and other similar issues.

$\endgroup$
2
$\begingroup$

Quantum mechanics is often taught to students as though it were a background dependent theory of waves, but this is not its formal mathematical structure as shown by the Dirac-Von Neumann axioms. Strictly quantum mechanics is an observer dependent theory of probabilities for measurement results. Waves appear in the calculation, not in the physics. It is thus formulated on a synchronous slice for an inertial observer with position coordinates derived from measurement procedures, exactly as Einstein did in his original paper on special relativity. Even in relativistic quantum mechanics, time is a parameter, not an observable like position.

For this to work, two (inertial) observers with the same information must calculate the same probabilities for results of measurements which they can both observe, regardless of how they are moving. This does impose relativistic covariance on wave functions. However the wave function becomes less important. The wave function for a particle initially confined at a point would immediately spread outside the light cone (faster than light). This is resolved because wave functions are neither physical nor observable. They are replaced with field operators, which obey the locality (or microcausality) condition, that the (anti-)commutator is zero outside the light cone. This condition ensures that no effects propagate faster than light, and also ensures the consistency of the theories for observers moving differently, and using different definitions of synchroneity.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.