To be totally honest, these laws will only seem 'strange' if you remain ignorant to the fact that although a modernsied country, much of Jordanian law is rooted in its Arab heritage.
A little bit of respect and understanding will prevent you falling foul of these laws:
Around 92% of the population are Muslim (93% of them are Sunni). While Jordan is home to one of the oldest Christian communities in the world (and about 4% of Jordanians are Christian), it's illegal to encourage conversion to the Christian faith, and certain sects of Christianity – such as Jehovah's Witnesses – are not officially recognized as religions.
Attempting to convert Muslims is illegal. Judaism is legal, but only just. This has been going on for centuries, so as a visitor, it's a good idea to stay out of it!
If the muslim faith doesn't like it, Jordan doesn't like it either. This includes homosexuality, consumption of alcohol outside of approved venues, and possession of pornographic material – whether in public or private.
It should be noted that homosexuality is not strictly illegal in the country. But, public displays of affection (including those between men and women) are frowned upon.
Adultery is defined as sexual relations with anyone you aren't married to, and the only legally-recognized marriage in Jordan is between a man and a woman. Due to negative public opinion, visiting homosexuals may be judged and punished for violating the adultery law far more severely than visiting heterosexuals.
Alcohol is a controlled substance in Jordan, but fines for public intoxication or drinking outside a bar are far less serious than those for possession, use, or trafficking in harder drugs.
If you bring marijuana, cocaine, heroin, or any other drug into the country and you're found out, the authorities will be very heavy-handed. Leave the recreational substances at home.
If you rent a car, be very careful. The driver is always guilty in an accident, and may be imprisoned or have to cough up heavy compensation payments to everyone else.
It's important to note that extremely serious offenses may result in the death sentence. It would have to be extremely serious, such as inciting treason, and you won't be stupid enough to do something that bad.
But with the recent civil unrest in the Middle East, the Jordanian government is more anxious about foreign nationals speaking out against the status quo. If you attempt to make a political point during your stay in Jordan, you may find the law comes down hard on you.
On your departure from Jordan, your luggage may be searched for security reasons to check for illegal drugs, and to prevent the removal of antiquities.
Taking pictures of government and military buildings in Jordan (as in many places around the world) is forbidden. Depending on the mood of the guards, it could get you a stern warning, a fine, or short imprisonment.
Though this is not illegal, it's considered extremely rude (almost to the point of public indecency), to take a picture of someone without his or her consent.
The two main things that you should remember about proper behavior in Jordan:
People will understand if you don't know all the finer points of custom and manners, though you will do yourself a favor by attempting to learn. However, a basic level of respect for how other people conduct their lives is essential. Cultural pride is a huge part of what it means to be Arabian and Jordanian.
If you visit during the holy month of Ramadan, or when visiting places of religious significance, always display the utmost level of respect for their practices – regardless of your feelings about politics or philosophy. You are in someone else's home, this is what you are supposed to do, no matter where you are. Dress modestly, behave courteously, and follow everyone's lead.
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