I don't see how that would apply here.
Strictly speaking, only Sotomayor concurred in the original decision, Alito, Ginsburg, Breyer, and Kagan concurred in the judgement (that is, the result).
The difference is significant in general, because the decision includes the rationale, and the Alito opinion (joined by Ginsburg, Breyer, and Kagan) disagrees with the rationale of the majority opinion. (That is, the majority held trespass to be decisive, Sotomayor agreed that it was in this case, but explicitly wrote a concurrence to argue that trespass wasn't necessary for a violation, and the other four agreed that GPS was a violation, but disagreed that trespass was an appropriate consideration.)
That is, there were four justices who believed that the GPS tracker was a violation because of the trespass to the target's property, four justices who though it was a violation for other reasons, but not because it was trespass to property, and one who thought it was violation because of trespass to property as well as other reasons.
Which results in the interesting situation, in that there were different (but overlapping with Sotomayor in both) 5-vote majorities both for the violation due to trespass view and the violation due to reasons-other-than-trespass view.
One of these things is not like the others. Did Alito take the same position as the others listed here?
They may not however tamper with your personal property.
If you do not own the car and say it's a company car the police might also not need a warrant to put a GPS tracker on it if they get consent from your employer, this might also cover rental cars (not sure about leases).
That to me would be a pretty clear line between a passerby and law enforcement in this case.
"I'm curious: would they need a warrant to sit in a car outside someone's house to watch them? " -Zak
The police doesn't need a warrant for most things they due in their line of duty, most warrants are requested to compel instead of risking seeking consent not because the law mandates judicial approval.
This is true but not for the reason you cite. It would be stalking if they make a statement that will place the person in reasonable fear of harm. If they did that, in most states, it won't matter whether they are doing it as cops or not. Some states have "no lawful justification" in the text (which would protect police), but most don't.
Various states do have laws that would cover this that are not stalking (violations of various invasion of privacy, wiretapping, etc).
Most are written in the way that it will be unlawful even if they are police.
The Constitution however says nothing about "in their movements" or "in the light they reflect."
They unanimously found that the government needs a warrant to put a GPS tracker on your car.
Similar to this case, the state argued that a cop didn't need a warrant to follow a car, so why was a GPS tracker any different? It just made the police work more efficient. The court disagreed.
http://www.supremecourt.gov/opinions/11pdf/10-1259.pdf