Effect of Length Contraction

Question

As we know moving objects have a shorter length as seen from a rest frame.

$$L=L_0 \sqrt{1- \frac{v^2}{c^2} }$$

The first question that arises, is length contraction real or just imaginary for an observer in the rest frame? Secondly what about atomic distances, do they also get shorter as the object moves faster and faster? Atomic distances also effect the intermolecular forces, how do they get balanced? Many quantum problems have length as a parameter, how do you justify that the results will be the same? And finally, does length contraction mean space contraction? As in muon half life problems, one explains in the muon frame the distance travelled by the muon will be shorter.

What is a real length ? Is it when there are simultaneously noticed positions of endpoints and the length is calculated as their distance? Or, can endpoints be measured not simultaneously ? If you vote for the former as obvious common sense choice, it leads to multiple simultaneous real lengths. — Poutnik, Feb 08 '20 at 13:55
Does this answer your question? "Reality" of length contraction in SR — John Rennie, Feb 08 '20 at 15:34

score 2 · Answer 1 · answered Feb 08 '20 at 13:25

The length contraction is very much real. The formula you have written down however is definitely incorrect. It should be $$L=L_o\sqrt{1-\frac{v^2}{c^2}}$$ The thing is that space isn't absolute, it isn't so that the separation between two points is independent of the observer. The separation seen by observer depends on their motion. I am not sure about what happens at subatomic scales, my best guess is that in the quantum world the distances are quite fuzzy, as there isn't an exact position determined for quantum particles. Yes teh effect is similar to time dilation.

The effects of special relativity can be understood at the atomic scale in models like quantum field theory. For instance the measurement of electric and magnetic fields depends on frame of reference. — Charlie, Feb 08 '20 at 13:55

score 2 · Answer 2 · answered Feb 08 '20 at 13:56

Length contraction and space contraction are the same thing, just different words for the same physical effects.
Yes, in length/space contraction the physical dimensions of atoms and molecules are affected along with everything else. The interatomic forces are also modified, in such a way that equilibrium is maintained (for a body in internal equilibrium).
In quantum physics all such effects are incorporated into the full quantum theory, called quantum field theory, but not into the simpler version of quantum theory which you typically meet first.

Effect of Length Contraction

2 Answers2