It's impossible to send them to an invalid address, BUT it's entirely possible to send them to an address for which no one has the key.
Take for example: 1BitcoinEaterAddressDontSendf59kuE
Check it out on blockchain. If you can brute force the private key, the coins are yours. Is it impossible? Theoretically, no, but practically...
Let's say you had a super computer that was guessing 999 trillion keys per second. It would take you 3.5 billion years to exhaust just 10% of the keyspace, which means in 3.5 billion years you would have a 10% chance of having guessed the key. Good luck with those odds!
Actually - given enough time - is it theoretically possible to crack the private key to that address?
I mean in the future computers will be 1000x more powerful than they are today.
Will our brains be blown out of our bodies?