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Alcaraz won his last match against a qualifier in the opening round of the Barcelona Open, but was in visible discomfort and withdrew before his next match.
Photographs and videos on his social media channels show him in a training session in Murcia on Tuesday, sporting the longer hair he has grown out during his absence.
A competitive return is still a few weeks off at least, however, meaning he will at best be carrying almost five months' worth of rust into the US Open if he plays.
But with wrist injuries in tennis, waiting longer can help prevent the problem recurring.
"The biggest risk of injury is a previous injury - if you have had it once, you are more likely to have it in the future," Ross adds.
"If a player can get back over a period of a few months and they don't have a reoccurrence, generally they will be OK.
"But some things can become chronic and the pressure of the sport to come back, earn money by playing, and keep your ranking points, is a risk."
One of the key challenges of a wrist injury is psychological - once a player has suffered a painful injury in the joint that controls so much of their technique, it can be difficult to fully trust it again.
"Wrists aren't easy", said Sir Andy Murray, having suffered injuries in both wrists in his early 20s.
"When the ball is low you know you really have to use your wrist to get the ball up and down, or when the ball is coming fast and quite high you need to use your wrist a lot to bring the ball down.
"It's difficult when you try to come back [from a wrist injury], because the pain that you feel when you initially hurt it, mentally it's very difficult to let go of."
