In the Old Testament, there were certain crimes that were punishable by death. God explicitly commanded that if anyone committed such crimes, he was to be put to death by his fellow citizens. Here is an example of how God commanded a man to be stoned to death for "picking up sticks on the sabbath day":
“And it came to pass, when the children of Israel were in the wilderness, and had found a man gathering sticks on the sabbath day, That they brought him to Moses and Aaron and the whole multitude. And they put him into prison, not knowing what they should do with him. And the Lord said to Moses: Let that man die, let all the multitude stone him without the camp. And when they had brought him out, they stoned him, and he died as the Lord had commanded.” (Numbers 15:32–36, D-R)
Incidentally, those who teach that capital punishment is contrary to the will of God, always and everywhere, have not appreciated the fact that God commanded capital punishment.
Is this still strictly binding on Catholics? If my Catholic neighbor is picking up sticks on Sunday, should I gather the neighbors and stone him?
In the New Covenant, two elements of the Sabbath were transformed. First, the Sabbath was moved from Saturday (the seventh day of creation) to the Sunday (which is mystically the "eighth" day of creation since it stands outside of time). The reason for this is that Christ perfectly fulfilled the Sabbath precept by allowing his incorrupt body to remain perfectly at rest in the tomb on Holy Saturday. Moreover, His glorious resurrection on Easter Sunday reconstituted a new creation of which He was the firstfruits or first portion.
“But now Christ is risen from the dead, the firstfruits of them that sleep.” (1 Corinthians 15:20, D-R)
For this reason, the New Covenant observes the day of His resurrection - the first day or Sunday. We do this not because of Constantine (what a silly and tired explanation), but because the Apostles observed Sunday:
“And on the first day of the week, when we were assembled to break bread, Paul discoursed with them, being to depart on the morrow. And he continued his speech until midnight.” (Acts 20:7, D-R)
“On the first day of the week, let every one of you put apart with himself, laying up what it shall well please him: that when I come, the collections be not then to be made.” (1 Corinthians 16:2, D-R)
So the day has changed from the Old to the New, but also the requirements. Saint Thomas Aquinas teaches that the standards of rest are mitigated in the New Law
In the New Law the observance of the Lord's day took the place of the observance of the Sabbath, not by virtue of the precept but by the institution of the Church and the custom of Christian people. For this observance is not figurative, as was the observance of the Sabbath in the Old Law. Hence the prohibition to work on the Lord' day is not so strict as on the Sabbath: and certain works are permitted on the Lord's day which were forbidden on the Sabbath, such as the cooking of food and so forth. And again in the New Law, dispensation is more easily granted than in the Old, in the matter of certain forbidden works, on account of their necessity, because the figure pertains to the protestation of truth, which it is unlawful to omit even in small things; while works, considered in themselves, are changeable in point of place and time. Summa theologiae II-II, q. 124, a. 4, ad 4.
Thomas describes the New Law Lord's Day (Sunday) as "not so strict" as the Old Law Sabbath (Saturday). Cooking food is an example. This was forbidden in the Old but it is allowed in the New.
So what is forbidden? Thomas states that "servile work" is still forbidden on the Lord's Day (Sunday). What qualifies as servile work?
Thomas distinguishes three kinds of servile work: Servitude to sin (eg, gossip). Servitude to another man (eg, working for an employer). Servitude to God (eg, attending Mass). Thomas indicates that the first two are forbidden on the Lord's Day, but the third is allowed. In fact, we avoid servitude to sin and man so that we can have perfect servitude to God. They day belongs to God.
Of course, there are times when necessity leads one do something that one would not likely do on the Lord's Day. Thomas gives examples:
[One] is bound to provide necessaries both for himself and for his neighbor, chiefly in respect of things pertaining to the well-being of the body, according to Proverbs 24:11, "Deliver them that are led to death": secondarily as regards avoiding damage to one's property, according to Deuteronomy 22:1, "Thou shalt not pass by if thou seest thy brother's ox or his sheep go astray, but thou shalt bring them back to thy brother." Hence a corporal work pertaining to the preservation of one's own bodily well-being does not profane the Sabbath: for it is not against the observance of the Sabbath to eat and do such things as preserve the health of the body. For this reason the Machabees did not profane the Sabbath when they fought in self-defense on the Sabbath day (1 Maccabees 2), nor Elias when he fled from the face of Jezabel on the Sabbath. For this same reason our Lord (Matthew 12:3) excused His disciples for plucking the ears of corn on account of the need which they suffered. On like manner a bodily work that is directed to the bodily well-being of another is not contrary to the observance of the Sabbath: wherefore it is written (John 7:23): "Are you angry at Me because I have healed the whole man on the Sabbath day?" And again, a bodily work that is done to avoid an imminent damage to some external thing does not profane the Sabbath, wherefore our Lord says (Matthew 12:11): "What man shall there be among you, that hath one sheep, and if the same fall into a pit on the Sabbath day, will he not take hold on it and lift it up?" Summa theologiae II-II, q. 124, a. 4, ad 3.
So enjoy a blessed Lord's Day. Our Blessed Lady has often complained that Catholics no longer observe the Lord's Day and she has asked for great sanctity in this way. In closing, here is a promise from Isaiah for all those that seek to keep the Sabbath:
“Blessed is the man that doth this, and the son of man that shall lay hold on this: that keepeth the sabbath from profaning it, that keepeth his hands from doing any evil. And let not the son of the stranger, that adhereth to the Lord, speak, saying: The Lord will divide and separate me from his people. And let not the eunuch say: Behold I am a dry tree. For thus saith the Lord to the eunuchs, They that shall keep my sabbaths, and shall choose the things that please me, and shall hold fast my covenant: I will give to them in my house, and within my walls, a place, and a name better than sons and daughters: I will give them an everlasting name which shall never perish. And the children of the stranger that adhere to the Lord, to worship him, and to love his name, to be his servants: every one that keepeth the sabbath from profaning it, and that holdeth fast my covenant: I will bring them into my holy mount, and will make them joyful in my house of prayer: their holocausts, and their victims shall please me upon my altar: for my house shall be called the house of prayer, for all nations.” (Isaiah 56:2–7, D-R)