# The slowest speed?

Tags: slowest, speed
 P: 24 Just a little interesting question: Is it possible to slow something down to where its impossible to go any slower and that object has to seize to be in motion? Since there are quantums of energy, and motion is kinetic energy, there has to be a slowest speed right?
 Mentor P: 7,320 Recall that all motion is relative. So if you are the point of reference then you are moving at the slowest possible speed. What is your frame of reference?
 Sci Advisor HW Helper PF Gold P: 4,771 It's a funny question that kind of leads nowhere imo. Because if you consider the macroscopic size, then sure, a pen on a table is at rest on the table. Its speed is zero. Or so it seems! If we zoom on the edges of the pen we start seeing extreme comotion. Molecules are flying in an out of the pen like mad. This is not rest at all! Now suppose we suceed in stoping ont of those molecule. Now look closer. Again, electrons making the atoms do not seem to be at rest at all. But now that we've entered the quantum level, speed is not a concept that makes sense. There is only probability of observing the electron at such and such places.
 P: 606 The slowest speed? Slowest speed? Speed is relative. A pen on a desk is not moving in relation to the desk. Someone walking by might say that the pen is not moving because it did not experience any acceleration. But certainly the pen does move. It rotates along with the Earth and revolves around the sun with everything else on the planet. So the pen moves in relation to the center of the Earth and the Sun and the rest of the universe. I don't know if no motion on this scale is possible because I am not sure if there is a center to the universe. Motion on an atomic level is based on temperature. The molecules of the pen will always be moving. As temperature is decreased the electrons become less active. The slowest speed that electrons can move is at absolute zero. As far as I know nobody has recorded this temperature in an actual experiment. If you can state your question more clearly then you will get a clearer answer.
 P: 24 Well if you had a car going 1 mph then you slowed it down to .5 mph then .25 mph then .00005 mph... how much farther can u go? Is it possible to continuously divide up speed so that it could be say, .00000000000000000001 even?
 P: 2,218 Yeah, theres no reason not to. If its travelling at 1, 0.5, 0.25.. etc with respect to a certain obsrever, hten the smallest speed possible would be 0, as in stationary with respect to the observer.
P: 606
Yes, or even less than that all the way to 0.

 The Planck length is the scale at which classical ideas about gravity and space-time cease to be valid, and quantum effects dominate. This is the ‘quantum of length’, the smallest measurement of length with any meaning. And roughly equal to 1.6 x 10-35 m or about 10-20 times the size of a proton. The Planck time is the time it would take a photon travelling at the speed of light to across a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. No smaller division of time has any meaning. With in the framework of the laws of physics as we understand them today, we can say only that the universe came into existence when it already had an age of 10-43 seconds.
Beyond that you would not be considered to be moving in a classical sense. Distance and time lose their meaning beyond this point. The molecules that make your body are still moving.
Emeritus
P: 7,634
 Quote by Myriad209 Just a little interesting question: Is it possible to slow something down to where its impossible to go any slower and that object has to seize to be in motion? Since there are quantums of energy, and motion is kinetic energy, there has to be a slowest speed right?
There is at least one interesting special case where the idea of a slowest speed makes some sense. This is the case where you have a particle in a box. In this special case, the particles energy is quantized, and so is its momentum.

Quantuized momentum is as close as quantum mechanics comes to having a quantized speed. (Speed really isn't part of the formalism of quantum mechanics per se, but you can more-or-less think of momentum / unit mass as being speed, depending on the exact application.)

Note that if you have a particle sitting out n free space (not in a box), neither its energy nor its momentum is quantized. It's the boundary conditions of being in a box that creates the quantum energy levels.

I
 P: 1,017 ... when you cross thermodynamics, special relativity and cutting-edge quantum theory? As a couple of people have said, even when a macroscopic (or even a microscopic) body is at rest (let's just say relative to the observer), its components are bustling - internal energy. So sticking to fundemental particles, say an electron, would TD not say that, as it has energy it cannot have a temperature as low as absolute zero and so, as measuring temperature requires movement, must be moving? But if it is at rest relative to the observer, would that not be a flaw in SR - that something we know must be moving appears not to be? And then there was an article in New Scientist I read about a theory that there is a minimum distance a particle of certain energy may move related to the Plank length and the time taken to move that distance can be considered a 'quantum tick'. Have read no follow-up on that, and trying to find it again in my massive pile of NS mags would be like trying to find a needle in a stack of identical needles, but does this mean anything to anyone else? If there's any truth in it, it would indeed yield a minimum non-zero speed.
 P: 1,017 Loop quantum theory! That's the fella! There's loads of stuff about it on the strings page. How out of touch am I?!?
 P: 42 isnt the smallest length Planks length and the smallest interval of time Planks Time ? so wouldnt the lowest speed somethingthat can move (in an inertial frame) be Speed = Planks Length/Planks Time I know this probably wouldnt work at all due to uncertanty etc and is probably totally wrong with regards to quantum mechanics, but its a thought...
P: 352
 Quote by gregmead isnt the smallest length Planks length and the smallest interval of time Planks Time ? so wouldnt the lowest speed somethingthat can move (in an inertial frame) be Speed = Planks Length/Planks Time I know this probably wouldnt work at all due to uncertanty etc and is probably totally wrong with regards to quantum mechanics, but its a thought...
I have had the exact same though. I was woundering, what is the smallest thing that can exists? What is the smallest movment that can exists? So I eventually concluded that this numbers are on the Plank scale. Liek I said, I posted a thread on this a long time ago and it seems that people said the smallest movments are not nessisarely at the Plank level. So I guess this is not true.
 P: 42 ok, well I havent realy studied QM for long enough yet, but I think that there is a smallest distance an object can move - maybe it isnt planks length...I cant remember, but it would need space to be quantised which I dunno if it is... I guess we need one of those crazy theoretical physicist types to enlighten us ;-)
 P: 352 well my theory is that KE is what allows these quantom jumps through spacetime.
 P: 42 so is there any basis to this theory ? because not everything that propegates through space actually has kinetic energy
P: 1,017
 Quote by gregmead so wouldnt the lowest speed somethingthat can move (in an inertial frame) be Speed = Planks Length/Planks Time I know this probably wouldnt work at all due to uncertanty etc and is probably totally wrong with regards to quantum mechanics, but its a thought...
Well, Planck's Length/2*Planck's Time is slower. The slowest non-zero speed would, if this is true, be Planck's length divided by the maximum number of Planck's time units possible in the universe. If there are infinite units of Planck's Time in the universe, this is the same as saying that time is continuous and ignoring Planck's time altogether. If there are not then the slowest speed will be that of a particle that only moved one Planck's length in the entire life of the universe. This would mean that this particle was never subject to any unbalanced force in its lifetime, which would be amazing. Even if a particle did have this speed, matter was created after the big bang, so the slowest possible speed would be that of the earliest possible created particle, which doesn't mean that historically a particle was created at this point. This particle must have momentum to conserve the relativistic momentum of the energy that created it. So, in short, the slowest possible speed a) is not attainable in the universe, and b) depends on the fate of the universe as a whole.
P: 1,017
 Quote by gregmead because not everything that propegates through space actually has kinetic energy
What examples do you have in mind?
 P: 42 oh yea how could I have been so stupid your right of course... oops

 Related Discussions General Physics 25 Introductory Physics Homework 0 General Physics 8 Introductory Physics Homework 3 Introductory Physics Homework 5