I’m trying to find a science fiction short story I read in the late 70s/early 80s, possibly in an older anthology: it was likely written in the 50s or 60s.

It’s about time travel and its limits: basically, humanity has found a way to travel backwards in time but not physically, just as onlookers.

So it’s used in forensics to travel back to when a crime has been committed and see who the felon is: I remember one of the characters saying that if you’ve been murdered they cannot prevent that nor bring you back to life but at least they have the means to capture your murderer.

I think they’re using kind of floating balls with built-in cameras for the task but I’m not sure about this, it could be from another story.

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    The Dead Past? It doesn't have anything about catching your murderer though. – John Rennie Mar 26 '20 at 11:13
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    The alien visitors in Clarke's Childhood's End also have similar technology to look back at high-profile crimes, but that is a novel, not a short story. – b_jonas Mar 26 '20 at 11:20
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    @b_jonas: The Overlords don't have any kind of time traveling crime solving abilities. The only crime described in any detail is a kidnapping, and it was solved by reasoning and detective work. – JRE Mar 26 '20 at 16:20
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    There was a story in the late '40s called "Private Eye" by Lewis Padgett (Henry Kuttner and C.L. Moore pen name). The premise was that there was a machine that could basically look back in time, so crime investigators used it extensively. The protagonist decided to murder someone, so he devised a plan to manipulate his victim into getting into a fight with him. He ended up so distorting his life that after he succeeded in his plan, he was basically lost. – user888379 Mar 26 '20 at 21:31
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    Sounds sorta like The Light of Other Days, but that was written much later. – jmoreno Mar 27 '20 at 0:09

I suggested in a comment that the story might be The Dead Past by Isaac Asimov, and although it is only a vague match to the description a reply suggests it might be the story so I'll post more details.

The story hinges around a technology called the chronoscope that allows users to see images from the past, but no time travel is involved. The chronoscope works because the particles called neutrinos travel from the past to the present¹ and can be detected as images from the past.

The mismatch with the question is because the chronoscope was suppressed as soon as it was realised that "the past" is any time more than a moment ago and the chronoscope's ability to image from a moment ago makes it able to spy on anyone anywhere in the world. So it is not used for catching murderers or indeed solving any crimes.

¹ neutrinos do indeed travel from the past to the present, but sadly only at one second per second

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    The chronoscope was no good for observing the past more than some few decades back. That's why all the supposed papers written using the chronoscope for archeology were written from regular research. The limitation of "recent past" makes it useful for solving crimes and viewing current event at a distance with a very short delay. – JRE Mar 26 '20 at 16:24
  • It is actually destroyed to prevent a possible "crime" from being solved. – LSerni Mar 26 '20 at 16:58
  • Everything travels, the idea is that neutrino patten is altered less by the passage of time – Mad Physicist Mar 26 '20 at 20:58
  • So, I've found and read the story: it rang a bell as memories surfaced from having read it in my younger days but sadly now I can say this wasn't the story I was looking for. Thank you for your help anyway! – Zab Zonk Mar 27 '20 at 9:48
  • There is nothing in the story about the device being used to solve crimes. – SJuan76 Mar 27 '20 at 19:24

I seem to remember one such story by Orson Scott Card, part of his "Pastwatch" series (it has novels such as this; the GoodReads entry is about the largest novel, The Redemption of Christopher Columbus).

"Pastwatch I" machines supplied exactly what you said, and were used for both historical research and murder solving. I remember some observation such as, "there was no longer such a thing as an unsolved murder".

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    One confounding factor is the only short story version I've found, "Atlantis" (hatrack.com/osc/stories/atlantis.shtml) wasn't published until 1992. – FuzzyBoots Mar 26 '20 at 13:43
  • Thank you but none of these can be the story, they were published too late. – Zab Zonk Mar 26 '20 at 13:56
  • Also, spoilers for the Christopher Columbus book (only one I've read so far), but rot13(Gurl jrer hygvzngryl noyr gb fraq crbcyr onpx culfvpnyyl). – Darrel Hoffman Mar 26 '20 at 18:36

Very low likelihood of what you are looking for but in the "Fuller's Apprentice" by Angela Holder, mages dispensed justice by using spells to go back in time to witness prior events. Include for completeness of time-travel-without-physically-going-back-in-time.

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