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Been trying to remember this one and haven't found it despite extensive googling. This was young-adult or magazine anthology fiction about a family that ends up time traveling, but can't get back to their own time easily because of two factors: they are low on energy/fuel and the short jumps paradoxically take more energy than long jumps. They end up traveling all the way to the end of the universe (heat death?) and note that local scientists are trying to solve the problem of how they can exist in a world where the electrons are all disappearing due to decay (i.e. need to come up with a proton-only technology. Did I dream this or was this really a work of fiction I read at some point?

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    Remarkable premise -- must have been a highly charged story!
    – user48960
    Commented Aug 14, 2015 at 23:14
  • You're sure the problem was electron decay, not proton decay?
    – user14111
    Commented Sep 20, 2017 at 4:17
  • @user14111 That's a very peculiar question to ask. Do you know of a story where protons are said to decay? Definitely post it as an answer then.
    – Flater
    Commented Sep 20, 2017 at 15:29
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    @Flater As a matter of fact, proton decay is featured in Gregory Benford's novelette "Matter's End", which is not the answer to this question as it does not remotely match the rest of the description. The reason for my "very peculiar" question is that proton decay has been theorized by real world physicists; electron decay, as far as I know, has not (what would electrons decay into?).
    – user14111
    Commented Sep 20, 2017 at 22:23

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You didn't dream it, it's one of my favorite (not so) short stories: Poul Anderson "Flight to forever", published in Isaac Asimovs "The last man on earth". Despite it's not a family but two scientist who try to get back home.

From Goodreads.com:

A Science Fiction novella about a scientist who invents a time travel machine and travels about a hundred years into the future with his assistant but discovers that they can only travel forward in time. They decide to continue travelling forward in hopes that science discovered a way to travel backward in time so they could return home. They keep stopping at various times

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  • "Flight to Forever" (available for free at the Internet Archive) is a great story but IMO doesn't match the question very well at all. Nothing about short jumps taking more energy than long jumps; the problem is that only short-range travel backwards in time is possible. Nothing about particles disappearing due to decay.
    – user14111
    Commented Sep 19, 2017 at 23:25

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