Is it possible to make a trillion dollar invention or exploration? I mean an invention or exploration that will be valued at trillion dollars.
A trillion dollars is nominal, there's no indication of when this invention is going to be worth a trillion dollars. Maybe in 100 years, this question would be worth a trillion dollars, but a Coke would cost a trillion trillion dollars.
But, to understand your point - you're asking if there's an invention that could make a trillion dollars in a short-term basis - and the answer is unlikely. The wheel is probably a trillion trillion dollar invention. The car, the telephone, synthetic fertilisers, so many things could be worth trillions, counting from the time they were invented - 50-100 years ago. But did one person make a trillion dollars from it? No. The richest inventor (re: http://www.forbes.com/2008/03/05/amazon-dyson-billionaire-ent-billionaires08-cx_pm_0306billionaireinventors.html) invented Nutella, and is worth USD 11 bil now. Nutella itself is probably worth 10s of billions of dollars as a product/investment. So... no its improbable that in the short term any invention would be worth or make you a trillion dollars.
Sure, because dollars are nominal goods. Perhaps a ticket to Star Wars Episode CXVIII will cost one trillion dollars. If you meant today, without huge changes in the price level:
Yes, there is way more than one trillion dollars of wealth in the world. Depending on the laws of physics and psychology there is probably something you would be able to market for this amount. (Private luxury homes in other dimensions.) Coming up with it is another question, but there is no law of economics that makes this impossible.
There is no such things.
All human invention are incremental.
Otherwise, there will be endless backtrack argument of invention, i.e. AI , computing, C programming, First computing program, first computer, printing press, paper. All this invention/progress added up will cost more than trillions.