What is the minimum speed in the universe ?
Zero. But not everyone will agree what is zero speed.
The point about the speed of light is that it is invariant. Everyone agrees its value relative to them, so you don't need to specify relative to what. That's not true for any other speed.
But might there be a smallest measurable velocity from quantum gravity arguments ?
There is a natural time scale from the cosmological constant, so I am wondering whether perphaps one planck length per cosmological time unit might provide a lower limit. Maybe some principle about how velocity can be measured, the curvature effect of lambda... Or maybe not : )
How can everyone agree that the value of the speed of light is relative to them and not agree what is zero speed or what it is relative to? I think it would be clearer if you said the speed of light is defined to be the same value in any inertial reference frame but the speed of any massive object can be different in different inertial reference frames.
Also, to address the question, any object at rest in an inertial reference frame has a speed of zero according to that reference frame. It doesn't matter if there are also any observers at rest in that reference frame.
If you are going to use "relativity", either "special" nor "general", you should certainly know that speed is relative! Given any object in the universe, there exist a coordinate system in which it has speed 0. Since "speed" (unlike "velocity") is never negative, the "minimum speed" possible is obviously 0.
If you meant "velocity" rather than "speed", which is a vector quantity, then you can always set up a coordinate system in which something (a light beam, say) is moving down the x-axis with velocity, relative to you, of -c. In that sense, the "minimum velocity" is -c.
Relatively speaking, is it really possible for something to have zero speed? Wouldn't that imply that if an object has zero speed it can not change position, which would mean it is at absolute rest?
As I said in post #5, an object at rest in an inertial reference frame has a speed of zero in that reference frame. Having a speed of zero according to an inertial reference frame and being at rest in that reference frame mean the same thing. But just because it has zero speed in one inertial reference frame doesn't mean or imply that it is at absolute rest because we can transform to another reference frame moving at some speed with respect to the first reference frame and then the object has that same speed in the new reference frame. No reference frame is any better than any other. That's what relativity says.
Yes of course, no argument there. But I was thinking of the OP's question in 'absolute' terms, if you will. As it is not possible to say an object can be at absolute rest, then by the same logic it can not be possible to say an object has an absolute speed of zero, or any absolute speed for that matter.
So the minimum speed 'in the universe' can not be determined. Only the minimum speed in an inertial reference frame.
If it's not possible to talk about absolute rest or speeds, then why are you thinking in those terms?
All speeds require an inertial reference frame according to Special Relativity, not just a minimum speed.
Was just trying to answer the op's question of course :)
Yes hence why I said
I don't know how I feel about that word, defined. We defined the speed of light to be the same? I thought we just noticed that it was.
A light pulse will pass me and you at c by our own measurements whether we are at rest with respect to each other or not. However an object travelling at any other speed (possibly stationary by my measurements) will not in general have the same speed by yours.
There's a qualitative difference between the concept of a "maximum speed" (which everyone agrees on) and the concept of "zero speed" (which is a frame-dependent quantity), which is what I was getting at, and I think what you are saying too. I didn't think I was being too cryptic, but maybe I was.
Well, you need a synchronization convention to measure one-way speeds, and the standard synchronization method uses the one-way speed of light, this speed is necessarily a defInition.
Why ? Doesn't the standard method use light because it is already known experimentally to travel at the invariant speed?
But actually I don't see where you need synchronization to measure a velocity. One observer can do that alone, he doesn't need to talk to anyone else. And he can also compare relative (to him) velocity of waves emitting by two other sources without ever synchronizing with those sources - and see whether that velocity is independent of the motion of those sources relative to him.
The normal concept of speed doesn't apply to the universe, because we don't know anything that it would be moving with respect to, unless there are other universes we don't konw about.
.You could talk about the speed of expansion or contraction of the universe.
But the mere definition of velocity is distance traveled/time employed, how would you now the time employed without sychronizing? This time employed is a difference between the readings of two distant clocks.
I don't think so, you are measuring the wave as it passes near you, using your own clock in your own lab.
Or for a moving object you can use radar ranging, again involving only your own clock.
I can't think of a velocity measurement done using a distant clock(*). The velocity of an object relative to me does not depend on that object having a clock of its own.
(*) well yes redshift of light emitted by that object does that, but in GR this measures a combination of velocity and gravity - in SR it does measure velocity but you can also use reflection (radar) redshift, which does not depend on the object internal clock I think. The measurements you do are defined by your (local) apparatus, not by someone else's.
You need synchronization to measure a one-way velocity. You calculate the one-way speed by dividing the distance travelled by the difference between the start and end times - and you need a synchronization convention to determine at least one of those times.
However, none of this has any bearing on the original question, for which the answer is of course "zero".
Sure you can see the wave passing without the need of synchronization, but seeing the wave passing is not a measurement of velocity.
On the other hand, radar involves the two-way speed of light, so you have to define its one-way speed anyways.
I still don't like that word. You mean define c=c? Or less arbitrarily, c =2.99...x10^8m/s? I don't see how that is a definition, and not just an observation. When I think of a definition, I think of ##\Phi=B\cdot A##, the definition of magnetic flux. We made that quantity up, it did not exist before someone defined it. c, however existed always. The speed of light in a vacuum has always been the same, even before we took our first measurements of it.
We made up the quantity "speed" as well, that's not the problem.
The thing is you run into a circular argument when you try to set up things so that you can masure this quantity, especifically with synchronization.
The quantity, not the value.
Oh OK I missed the significance of that "one way" mention. For that you need a choice of coordinates (which implies a choice of simultaneity), I understand - but still your own clock is enough : you can measure the two events with your local equipment, and for instance assign them radar coordinates, and from this, differences in time and a distance.
But if the point is that some coordinates depend on remote clocks, of course I won't argue with that.
Edit - I probably misunderstood the original comment, I thought it said you always needed to synchronize two clocks before you could measure a (one way) velocilty - I am not disagreeing with with what you say, that it implies a simultaneity convention.
Yes, the two way speed of light is observed, but the one-way speed is defined necessarily, it cant be other way. With this I mean the actual value has to be defined.
I'm not sure I understand your point actually, do you mean the actual real number c has always existed?
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