To expand a little on what littleadv said, you can only deduct what something cost you. Even if you had done volunteer work for a charity as a sole prop you could only deduct your actual costs. If you paid an employee to do charity work or to learn something related to the business that would be deductible as a normal business expense.
Some common sense would show that if you could deduct something that didn't cost you anything (your time) you could deduct away all of your income and avoid paying taxes altogether.
Back to your more nuanced question could 2 businesses you own bill each other for services? Yes, but you will still have to pay taxes for money earned under each of them. You will also need to be careful that the IRS does not construe the transactions as being done solely to lower your tax bill.