# Minimum speed in relativity

1. Jan 10, 2010

### BkBkBk

i was thinking,C is the maximum speed something can travel through space,in there a minimum,and is this absoloute zero?

2. Jan 10, 2010

### Edi

Something like Planck's length divided by Planck's time ? As going slower than that would mean standing still.
But it doesn't have to be true. And is kinda purely theoretical.
It requires quantization of space and such. In relativity... its all relative, so no..

3. Jan 10, 2010

### sylas

As pointed out recently in another thread; plank length divided by Planck time is the speed of light.

4. Jan 10, 2010

### nicksauce

The Planck length divided by the Planck time is c.

There is no minimum speed in relativity. You can always construct a Lorentz boost to take a object's speed to whatever you want.

5. Jan 10, 2010

### BkBkBk

from what i can understand,does that mean that,even if an object seems not to be movingfrom your inertial frame,you could always move to a frame of reference where it is moving (have i misunderstood the lorentz boost?)

6. Jan 10, 2010

### espen180

Yes, you can always construct a frame where an object is standing still, moving and/or accelerating.

7. Jan 10, 2010

### Edi

minimum distance divided by minimum time is max speed... (??)

8. Jan 10, 2010

### nicksauce

9. Jan 10, 2010

### sylas

Just look up the definitions. The wikipedia article on Planck units is adequate for this. The definitions and values are:
$$\begin{array}{lll} \text{P. time} & \sqrt{\frac{\hbar G}{c^5}} & 5.39 \times 10^{-44} \; s \\ \text{P. dist} & \sqrt{\frac{\hbar G}{c^3}} & 1.616 \times 10^{-35} \; m \end{array}$$​

It was discussed also in the thread [thread=368108]Traveling at c-(1 planck length/planck time), then accelerate. What happens?[/thread].

Cheers -- sylas

10. Jan 10, 2010

### atyy

Yes, there is a minimum speed and it is zero.

11. Jan 10, 2010

### BkBkBk

we can define it as 0 relative to us,but its not specifically "at rest" is it,and what i was wondering is,even though it it isnt moving relative to us,there is uncertainty in its position,so is there a minimum we can define it to be,(or am i wrong in saying that there is uncertainty,is that only a microscopic phenomenon,or does it apply to macroscopic objects aswell?)

12. Jan 10, 2010

### Staff: Mentor

Why not? In our reference frame it is certainly and specifically at rest.
That has nothing to do with relativity, that is quantum mechanics. The uncertainty principle states that $\Delta x \, \Delta p = \hbar/2$. So for a macroscopic object like a 70kg human body, if we were to measure it to be "at rest" to within 1 picometer/millenium then the most accurately we could know the position is:
$$\Delta x = \frac{\hbar}{2 \Delta p} = 0.02 \, picometer$$
Which should be close enough for any purpose.

Last edited: Jan 10, 2010
13. Jan 10, 2010

### BkBkBk

now thats the sort of answer i was looking for,thank you Dalespam :)

one thing,though, you've said "That has nothing to do with relativity" but then gone on to give me an example of a macroscopic object, im a little confused as to whether we can actually apply the uncertainty principle to macroscopic objects?or is that still a question of where the barrier lies between the micro and macroscopic world?

14. Jan 10, 2010

### atyy

In quantum mechanics, if you prepare 100 "particles" (a bit hard to define what a particle is), each in an identical way, and you measure the momentum of each of 50 particles and you always get the same answer (say 0), then if you measure the position of each of the next 50 particles, you will get all sorts of different answers. However, the different positions are of different particles, so it doesn't mean that each particle did not have 0 momentum.

15. Jan 10, 2010

### Staff: Mentor

Yes, the uncertainty principle always applies, there is no barrier between the micro and macroscopic world. The point was that even though it always applies, it is not always important.

In any case, more relevant to the OP, atyy just explained that the uncertainty principle does not prevent something from being at rest in some reference frame, even when we are talking about small particles.