Jones conducted research at the Idaho National Laboratory, in Arco, Idaho where, from 1979 to 1985, he was a senior engineering specialist. He wasprincipal investigator for experimental muon-catalyzed fusion from 1982 to 1991 for the U.S. Department of Energy, Division of Advanced Energy Projects. From 1990 to 1993, Jones studied fusion in condensed matter physics and deuterium under U.S. Department of Energy and Electric Power Research Institute sponsorship. Jones also collaborated in experiments at other physics labs, including TRIUMF (Vancouver, British Columbia), KEK (Tsukuba, Japan), and the Rutherford Appleton Laboratory at Oxford University.

Jones' interests also extend to archaeometry, solar energy and, like many professors at BYU, archaeology and the Book of Mormon.  For example, he has sought radiocarbon dating evidence of the existence of pre-Columbian horses in the Americas, and has interpreted archaeological evidence from the ancient Mayans as supporting his faith's belief that Jesus Christ visited America.

On September 22, 2005 Jones presented his views on the collapse of the World Trade Center towers and World Trade Center 7 at a BYU seminar attended by about 60 people. Pointing to the speed and symmetry of the collapses, the characteristics of dust jets, and reports of molten metal in the debris, Jones suggested that the evidence defies the mainstream collapse theory and favors explosive or Thermite-based demolition. He called for further scientific investigation to test the controlled demolition hypothesis and the release of all relevant data by the government.  Shortly after the seminar, Jones placed a paper "Why Indeed Did the WTC Buildings Collapse?" on the Physics department web site.

He subsequently defended the research twice more at BYU,^{[citation needed]} also at Idaho State University, Utah Valley State College, University of Colorado at Boulder and University of Denver, the Utah Academy of Science, Sonoma State University, University of California at Berkeley, and the University of Texas at Austin. 

Jones' paper has been the center of controversy both for its content and its claims to scientific rigor.  Jones' early critics included members of BYU's engineering faculty;  shortly after he made his views public, the BYU College of Physical and Mathematical Sciences and the faculty of structural engineering issued statements in which they distanced themselves from Jones' work. They noted that Jones' "hypotheses and interpretations of evidence were being questioned by scholars and practitioners," and expressed doubts about whether they had been "submitted to relevant scientific venues that would ensure rigorous technical peer review."

Some of Jones' colleagues have defended his work on 9/11 to varying degrees,  and Project Censored lists his 9/11 research among the top mainstream media censored stories of 2007.

Jones maintains that the paper was peer-reviewed prior to publication within a book "9/11 and American Empire: Intellectuals Speak Out" by D.R. Griffin, however it has never been published in an independent peer-reviewed journal. The paper was also posted on the Internet site of the "Journal of 9/11 Studies", which was co-founded by Jones for the purpose of "covering the whole of research related to 9/11/2001", was co-edited by him, and which has recently slowed publication, having posted a notice that potential contributors were encouraged to submit their prospective work to other, more mainstream, publications.  The paper also appears in Global Outlook,  a magazine "seeking to reveal the truth About 9/11" and in a volume of essays edited by David Ray Griffin and Peter Dale Scott.

On September 7, 2006, Jones removed his paper from BYU's website at the request of administrators and was placed on paid leave.