But time by time lots of theory and experiments made their assumption wrong.
Is there anything in using time by time in the above sentence whereas it refers changing things with time.
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Time by time is not an English idiom.
You may use timespans like this—hour by hour, day by day, year by year—but that expression means “in each succeding timespan” and is used with a following comparative like more:
Year by year it became more obvious that their assumption was wrong.
If what you mean is “repeatedly, over many timespans” you may say “timespan after timespan”:
Year after year, experiments and developing theory repeatedly proved their assumption wrong.
You may also use time in this construction; but here time does not signify a timespan but an occasion:
Time after time, experiments and ...