Minimum speed of interaction of matter

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boit
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hi physicists, i have a gnawing question that could be put to rest with experiment but i lack the tools and challenged in ideas. we all know that the speed of light in vacuum is the maximum that can be attained in the universe. also light does not accelerate to that speed, it just begin to exist at that speed in vacuum. now my to question: is there a minimum speed in the universe? i just begun to think that at very short distances, say nano metres range acceleration is never constant. like matter takes in energy without moving for a nano second or so then instantly move at a speed like say ten nano metres per second. what do you guy think? i could give a longer statement but am using a phone.
 
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There is always a reference frame where whatever you are looking at is at rest, so there is no minimum speed.
 
I've just finished reading the guidelines and i can't tell if I've been politely warned. I guess it is cranky to imagine anything starting at zero relative speed suddenly attaining a subluminal speed in no time.