An elderly person, no. An older child with ADHD? Possibly, yes.
Would you physically punish a normal 8 year old boy who deliberately pushes his 5 year old brother down the stairs and then laughs at him as the 5 year old lays crying?
"Punish" and "punishment", those words I focus on. Do you want to punish or do you really want to make sure your child learns what he did was wrong and why and what consequences might happen if he does it again.
We all agree you have to do something that will teach your 8 year old that what he did:
1-was dangerous;
2-can not happen again;
3-and that laughing at someone you hurt is wrong.
In regards to l- you can not get that lesson across simply slapping a child's bum-you must find a way to explain it as best you can depending on the level of your child's speaking-at 8 they can understand the basics of danger;
In regards to 2, same as 1 but you have to explain why it can not happen again and you do that by linking it to the injury the bevahiour caused or could cause;
In regards to 3, its twofold in components: i- is a private meeting to deal with the entire matter-your child will not learn if they feel humiliated in front of others; ii-you have to teach empathy by asking your 8 year old how he would feel if someone did the same thing to them-you have to ask them and let them answer to have that sink in-they need to connect a bad feeling to themselves as to what they did-then you need as part of the closure of that lesson to have them apologize to the brother and hug them-when you do the time out depends-if the action was done in the heat of a fight-do the cool off alone first-if it was joking around horseplay-you might want to do the time out at the very end after the apology and it may not even be necessary if it was not intentional-however since you said it was deliberate-I would do the word lessons first, followed by the cool off-the key is the tone of your voice not the loudness-the louder it is the less likely the boy will hear you-the calmer and clearer and lower your voice the better it is-be intense and focused, not shrill and angry or your child can not learn a positive lesson from it.
Now all of the above is easy for me to say. I am not the parent in the heat of the moment. I have hindsight. I am emotionally dettached. I do not have other stuff going on.
I get its not easy but my point is a slap on the bumb would not do a damn thing to turn the behaviour into a learning moment.
SO back to the word "punishment" I think you would really prefer to turn a negative act into a learning moment so that the person does not do it again and to do that you mix your responses to teach both thinking and reasoning skills, empathy (how others feel) as the most important part of the response with "punishment" or a negative consequence such as a time out as the follow up to making sure the lesson sinks in.
Keep in mind "punishment" is negative reinforcement and you know it does not work well without other kinds of enforcement techniques to deter anything and it does not teach. By itself it will cause unitended consequences such as trauma or anxiety or fear that will then get triggered in the future everytime a similiar event happens with someone else.
8 years old in my opinion means the child can learn from words and negative consequences linked to the wrong doing as soon as it happens. The longer you take to teach the lesson, the less likely it will work.
We think physical punishment works-but all it does is negatively reinfoce a reaction with pain. Pain is not something that teaches-in fact it prevents the person from learning-they don't learn they simply learn to fear pain and feel humiliated. Not an effective tool for anything but an immediate temporary cessation of a certain behaviour.
Look I get it. Your child bites another child, you yell no and maybe slap their hand.
However once a child is able to fully express themselves with words, its time to use those words as a tool reinforced by a time out or some kind of consequence limiting what they find enjoyable or fun to teach a lesson. That method teaches there is give and take. Simply hitting does not.
Hope that makes sense.