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!
so... if we aimed all the Hashing power of the Bitcoin network on one address it would take 500 million years? Hey man It's only a matter of time before insane quantum computers just start cracking the codes by the second. I can imagine this will happen one day, when the Bitcoin network migrates to a new protocol based on quantum security. Those computers will tear Bitcoin apart when they finally are able to produce them in mass, and start migrating all the accounts to a new system like a block reward, Or just like the free market migrate by choice to something safer.