Washington (CNN) Chief Justice John Roberts has compared the nine-justice Supreme Court to a family and said it can be "unsettling" when a new member comes along.

Gorsuch, who was confirmed last spring and this week began his first full term, has shaken relations at the high court with actions that show -- depending on one's view -- a degree of arrogance or independence.

Whether personal tensions will ease is an open question. But the larger, more consequential, query is whether the new justice, who has staked out the far right of the bench, will push other conservatives to the left.

The hardline, sometimes disdainful, approach of the late conservative Justice Antonin Scalia toward Justice Sandra Day O'Connor plainly turned off his fellow Republican appointee. Scalia's tactics appeared to help move O'Connor, who retired in early 2006, toward the court's center, including on abortion rights and campus affirmative action.

Today, the dynamic between Gorsuch and Roberts is especially intriguing. They are similar in many respects, with sterling resumes, parallel professional experience and strong conservative views.

Yet Gorsuch is not a ready ally of the chief. They have seemed in different orbits so far, on substance and style.

After his Senate confirmation last April, Gorsuch skipped the first scheduled justices-only meeting even though Roberts encouraged him to attend. He fired off a raft of dissenting opinions, some that seemed to scold his colleagues. He has dominated oral arguments, cutting off and correcting other justices, expounding on the scope of the Constitution.

With an approach that evinces the opposite of Roberts' concern for appearances, Gorsuch spoke to a gathering of the conservative Fund for American Studies at the Trump International Hotel in Washington, embroiled in litigation about unconstitutional financial benefit for the President who appointed him.

Previously, Gorsuch joined Senate Republican Leader Mitch McConnell in Kentucky for an event at the University of Louisville -- that after McConnell kept the Supreme Court seat vacant following Scalia's death for a year, refusing to hold a hearing on Judge Merrick Garland.

It can be difficult for people outside the marble walls to know truly the relationships among the nine in their private chambers. But word seeps out, through clerks and other staff, through the justices' friends, and through the justices themselves. Such communications make clear that Gorsuch has generated some ill will among justices. Signs have emerged from the bench, too, as Gorsuch has been on the receiving end of a few retorts.

Gorsuch did not respond to a request from CNN for an interview

Vanderbilt University law professor Timothy Meyer, a former clerk who testified on Gorsuch's behalf last spring, defended Gorsuch's robust approach and cautioned that it is difficult to know how relationships will evolve once the newness of the ninth justice wears off.

"He should be asking questions," Meyer said. "There are no rules about not asking questions. I was really surprised to see the negative reaction that drew."

With any small group of people, on a court or law school faculty, Meyer added, there can be a delicate adjustment. "Anytime you have people who have to work together in close ways, and someone new comes in, those kinds of things are likely to happen. ... People rub each other the wrong way, and that's going to happen with any new person whose demeanor you're not used to."

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'Always a good place to start'

Gorsuch, 50, who like all justices has life tenure and will likely serve for many decades, has revealed himself at oral arguments and in a few opinions with an admonishing tone toward colleagues. He sometimes speaks or writes as if the majority does not share his regard for the Constitution.

During arguments last Monday he said at one point, "I start with the text of the Constitution, always a good place to start." On Tuesday, during a dispute over partisan gerrymanders, he said, "Maybe we can just for a second talk about the arcane matter, the Constitution. Where exactly do we get authority to revise state legislative lines?"

As the lawyer at the lectern referred to past cases finding that the Constitution allows courts to intervene, Justice Ruth Bader Ginsburg made her case with one sentence: "Where did one-person, one-vote come from?"

The reference was to Supreme Court rulings dating to the 1960s finding state reapportionment and redistricting covered by the Fourteenth Amendment's equality guarantee.

In one dissenting opinion at the end of last term, Gorsuch declared that the majority had gone too far in interpreting a statute, writing, "If a statute needs repair, there's a constitutionally prescribed way to do it. It's called legislation." He was joined only by Justice Clarence Thomas.

He has aligned most consistently with Thomas, and a slightly lesser extent with Justice Samuel Alito, on the most controversial disputes so far.

The three of them dissented, in an opinion by Gorsuch, in a case last June brought by a married lesbian couple. The court majority rejected an Arkansas law that blocked the spouse of the birth mother from being listed on the birth certificate.

The majority opinion, unsigned, held that a birth certificate would be covered by the "constellation of benefits" flowing from the constitutional right to same-sex marriage that the justices declared in a landmark 2015 case.

Roberts did not join Gorsuch's dissent in the June dispute, although he (along with Thomas and Alito) had dissented from the Obergefell v. Hodges decision making same-sex marriage legal nationwide.

Justice Anthony Kennedy, the fifth conservative on this 5-to-4 ideologically divided bench, has slowly tacked to the left over his 30-year tenure. He wrote the decision declaring a right to gay marriage and has endorsed abortion rights and campus affirmative action.

Roberts' record suggests he would never embrace such views, and to be sure, he has been more consistently conservative than Kennedy -- or O'Connor -- since his 2005 appointment.

But Roberts, who also separated himself from Gorsuch on a religious rights case and a death penalty appeal, may be more open to negotiating with liberals if Gorsuch continues to bolster the hard right.

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Interstate rivalry

An exchange during April arguments may have signaled the emerging jockeying -- rivalry even -- between Roberts and Gorsuch.

As Roberts was referring to possible interstate routes across Montana, he said, "They're going to take -- what is it -- 95 across? Not 95. 90?"

Gorsuch interjected to set him straight: "I-80 across Montana."

Roberts responded with a jocular reference to Gorsuch's roots in Colorado. "There you go," he said. "It's that geographical diversity."

As the argument continued and other justices asked questions, Gorsuch began to have second thoughts. He checked an atlas requested from the court library, and then interrupted the session: "It's 90 across Montana. 80 across Wyoming. I'm very sorry, Mr. Chief Justice."

To laughter from spectators, Roberts rejoined, "Didn't I say 90?"