Lawla jaoo AAalayhi bi-arbaAAati shuhadaa fa-ith lam ya'too bishshuhada-i faola-ika AAinda Allahi (surah An Nur: 13)

Tafseer Tafheem-ul-Quran by Syed Abu-al-A'la Maududi

(24:13) Why did the slanderers not bring four witnesses (to prove their charge)? Now that they have not brought witnesses, they themselves are liars in the sight of Allah. *14

Law laa jaaa`oo `alaihi bi-arba`ati shuhadaaa`; fa iz lam yaatoo bishshuhadaaa`i fa ulaaa `ika `indal laahi humul kaaziboon

*14) ` .... in the sight of Allah": in the Law of Allah, or according to the Law of AIlah. Obviously, in Allah's knowledge, the accusation was by itself false and its falsehood was in no way dependent on the production of witnesses by the accusers.
Here nobody should have the misunderstanding that failure to bring witnesses is being regarded as the basis and argument to prove that the accusation was false, and that the Muslims are also being told to regard it as a manifest calumny only because the accusers did not bring four witnesses. This misunderstanding can arise if one dces not keep in view the background of the actual incident. As a matter of fact, none of the accusers had actually witnessed the thing which they were uttering with their tongues. The only basis of their accusation was that Hadrat `A'ishah had been left behind from the caravan and afterwards Safwan had brought her to the camp on his camel. From this nobody with a little common sense could conclude that Hadrat `A'ishah's being left behind was intentional. These are not the ways of those who do these things. It cannot happen that the wife of the army commander quietly stays back with a man, and then the same man makes her ride on his camel and makes haste to catch up with the army at the next halting place in the open daylight at noon. The situation itself warranted that they were innocent. There could, however, be some justification in the charge if the accusers had seen something with their own eyes, otherwise the circumstances on which the accusers had based their accusation did not contain any ground for doubt and suspicion.