That is a pretty ambiguous term.
Dependence is when you need the drug to feel baseline and lack of it will cause withdrawal.
Tolerance is when you need more of the drug to achieve the same effects.
Addiction is when you continue to consume the drug even after it starts negatively effecting your life and you can't stop.
A person physically dependent on pain killers for legitimate pain may not be considered an addict, while someone who hasn't used heroin in 20 years might still say they have an addiction to it.
physically addicted to me means the chemical processes in the brain which effect addiction, however it is often used to mean dependence.
With respect to your questions dependence will set in after a few days of use but symptoms of withdrawal won't be "notable" for a couple weeks. As for addiction, it can happen after your first dose, your second, never happen at all, or for those with an addictive personality who just need to try it once - you can almost be addicted before your first taste. The chances are the longer you use the more likely you are to become addicted though.
edit:
Say that I've got two or three weeks of consecutive use. According to you, this will lead to minor withdrawal symtoms. What can you tell me about them? Would I, for example, still be able to go to work and interact with people (I have a social job) without too much trouble? Or would I already need some benzo's to get me through the day?
We can't possibly answer this OP. The severity is variable, the symptoms are variable, and the nature of your work and social life and ability to handle all this is complete unknown.
Also, if I were physically addicted, how long after my last dose (snorted) would the withdrawal symptoms start i.e. if I've gone 24 hours without WD's, would it be safe to say that I'm not physically addicted?
For internasal heroin 12-24 hours is a good amount of time to expect the onset of acute withdrawal symptoms.
I'm going to close this thread now as the answer to the question "How many days can I take heroin straight without becoming dependent" has no exact answer and is just the opinions of how much withdrawal counts as withdrawal and all this is different for everybody anyways. The less you take the better off you'll be.
Check out the following threads for more information and you can ask any more questions about withdrawal in the relevant megathread.
The Opioid Withdrawal Megathread and FAQ
The Basic Biology of Drug Addiction
If you have any questions or concerns feel free to PM me.