According to the philosophy of physicalism, any purely scientific view of reality has no place for notions of good or evil, right or wrong, justice or injustice.  It is entirely neutral, neither preferring nor disdaining either side. It asserts that there is no objective standard of morality. 

The opposite view is that morality is not unscientific; it is merely non-physicalist.

Is there some way to prove the matter, one way or the other? 

Yes, there is, but society is so complex, the human mind so inscrutable, that it takes years, even centuries, for a social experiment to produce verifiable results.  Oftentimes, the outcomes of social policies are completely opposite to those that were predicted by the experts. 

The following bit of recent history provides an example. 

Up until the 1960s, the out-of-wedlock birthrate in most segments of society was small, despite there being no reliable contraceptives widely available.  One overwhelming reason for the low incidence of premarital pregnancy was social opprobrium.  For a young, unmarried woman to be known not to be a virgin was considered shameful.  For her to become pregnant was scandalous.  The prospect of being humiliated was a powerful inducement, for women, to delay sexual intercourse until marriage. 

The advent of the birth control pill changed all that, and as history shows, the incidence of out-of-wedlock motherhood, which was supposed to have been dramatically reduced, instead dramatically increased.  Why? 

The birth control pill helped to reduce the stigma of losing one's virginity before marriage.  This, in turn, indirectly reduced the stigma of premarital pregnancy.  This, in turn, reduced the perceived need for the birth control pill.  Once the initial phase of these events had occurred, the floodgates were opened, and what quickly followed was what is called the Sexual Revolution. 

This revolution was supposed to have freed women from the injustice of sexual repression.  Instead, it led to millions of women becoming pregnant and abandoned, left on their own, to raise their fatherless children.  Many of them were, as a result, raised in poverty and amid crime.  The welfare state sought to correct this mistake by subsidizing single motherhood.  This, in turn, predictably increased what it subsidized. 

Today, the harm wrought by the abandonment of sexual morality has left us with a society that cannot even recognize the good and natural differences between the sexes, even to the point of denying that there are two complementary sexes, and certainly denying that they are a naturally ordained partnership, one without which, society suffers consequences so pervasive that many people call them good. 

The illusion is now deeply ingrained that sexual morality is an antiquated notion, and that its violations have no harmful consequence.

Worse yet, casual acceptance of homosexuality and transsexuality has morphed from mere tolerance to the present state of enforcement.  Small, confused children can be subjected to the radical procedure of so-called transitioning from their birth sex to a chosen sex.  This can be done in opposition to the parents' wishes, as indeed, pregnant teenage girls can have their pregnancies aborted with neither the knowledge nor consent of their parents. 

To interfere is to be accused of child abuse.  Even to openly advocate Judeo-Christian standards of morality can bring about ridicule, and even significant penalties.  The social opprobrium that once reduced the social ills of out-of-wedlock childbirth now falls upon those who would reduce those ills by upholding moral standards, the violation of which has terrible consequences, as Bishop Fulton J. Sheen warned us, when he said, "Moral truth is vindicated by the ruin that follows when it has been repudiated."

We are now at the point where pedophilia is gaining traction as a so-called sexual orientation. 

Where will all this end?  The experts say, a Utopian society.  When have they been right?