Oh dear - a very common problem in apartment living. These are my suggestions (the first two require you to be incredibly nice and exercise all your diplomatic skills):
- the key first step is to get your upstairs neighbours to acknowledge that there is a problem. So the next time their TV volume is at an unacceptable level, you need to go up there and invite them to come down to your apartment while leaving the volume as is, and listen to it from your floor below. I would recommend couching your request in language such as, 'I'm terribly sorry about this and I am sure you think I am being ridiculously over-sensitive/exaggerating the problem, so please could I ask you to come down to my apartment, listen for yourselves, and tell me if you think I'm being unreasonable.' When nicely put, this is a very difficult invitation to refuse, and if the volume is as bad as you say it is, it will not be possible for them to come down, listen, and tell you that you're crazy and they can't hear a thing. (I would recommend issuing this invitation when they haven't just settled in to watch their favourite show - or at any rate suggest they come down at the next commercial break...)
- the second step, if the above goes as hoped, would be to agree with them the specific volume setting on their TV that will satisfy you both. Again, this depends on whether you can manage this dialogue amicably and maintain good relations, but depending on the type and age of their TV equipment, it is possible to pre-set the volume level at which the TV comes on, in which case you should request that you all agree the appropriate setting and that is set accordingly. Again, you can suggest to them that they decide this (eg have one of them remain downstairs in your apartment with you to listen while the other goes back upstairs and turns the volume down to what ultimately you all agree is a livable-with level - the key here being that you ask the neighbour who has stayed downstairs with you to suggest themselves what you should be prepared to live with).
If the above does not work, and negotiation is impossible, then your other alternatives are:
- speak to your landlord or apartment building management and have them intervene.
- I do not know if this is feasible where you live, but in a number of countries it is in fact illegal to cause noise disturbances. Legislative measures tend to apply more to noise that affects large numbers of people in the immediate vicinity, but it may be worth your investigating this. When I lived in the UK and was kept awake night after night by an illegal club that began operating behind my building, I was able to call in an environmental noise civic group that worked with the police and had the club shut down.
Both the above measures, obviously, worsen relations between you and your neighbours. The preferable solution might be not to do so, and to undertake soundproofing.
- It is possible to soundproof via a variety of means: you can lay soundproofing tiling on your ceiling, or you can have soundproofing material injected into the gap between your neighbour's floorboards and your ceiling. You can ask the landlord to pay for this, or you might consider it worth it to pay for it yourself. I had this done, ironically in a situation that was the other way around (very loud television volume coming up to my apartment from the one below) and it was very effective.
I hope these thoughts help!