That depends... where in New Jersey? The short answer is probably yes.
The city of Philadelphia shares a border with New Jersey
Philadelphia is right on the New Jersey border. The Delaware River forms the eastern perimeter of Philadelphia and New Jersey is right across the river. So technically less than a mile.
Philadelphia to Florence, New Jersey is 46 min (27.9 mi) via I-95 N
New Jersey to Connecticut takes 7 hours.
No. Newark is in New Jersey. All of the trains that go from New York to New Jersey terminate in Manhattan. You can use the subway to get from Brooklyn to New York and then take a train to Newark, NJ.
You need to be more specific. Where in New Jersey do you want to go? If you want to go to Jersey City, for example, you can take the Path Train at the 34th Street/Herald Square MTA Train Station.
That would depend heavily on what part of New Jersey you are driving from. Philadelphia and New Jersey share a border so it is possible to cross from one to the other in a matter of seconds.
New Jersey Transit (the New Jersey branch of the New York City commuter trains) go as far as Trenton and Bay Head. If you transfer to local trains from Trenton (or continue onto Philadelphia and again transfer to local trains), you can reach even the southernmost parts of New Jersey.
by train or by crossing a bridge
The distance from Philadelphia, Pennsylvania, to Princeton, New Jersey, is 38 miles. That equals 62 kilometers or 33 nautical miles.
The constitution as proposed in philadelphia
New Jersey.