The Minimum Speed in the Universe: An Exploration of the Cosmic Limit

[wabbit]

Yes, you can use just your own clock and radar to establish the time and distance to remote events but during that process, you must apply Einstein's second postulate that each radar signal takes the same amount of time to reach its target as it takes for the return echo to get back to you. This is where you define what simultaneity means between a local clock and a remote event.

Look at the first article of Einstein's 1905 paper entitled "Definition of Simultaneity" where he uses the word "defined" or "definition" 13 times.

Sure, You define coordinates, so you define simultaneity which means equal time coordinate.

 

[ghwellsjr]

Sure, You define coordinates, so you define simultaneity which means equal time coordinate.

Does this mean you are ready to retract your statements from post #15?

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.

 

[wabbit]

As I made clear in this statement, I was referring to synchronisation as a process involving two clocks. Since you mean something else by this (namely defining simultaneity from an observer's viewpoint), my statement stands but it doesn't contradict yours.

 

[nitsuj]

See the link in my previous post and you will see where it is "defined".

pulled from the paper "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A."


Is that what you were referring to as being "invariance of c defined"? I really thought it is postulated to be invariant, by the SR postulate.

... the speed of light is defined to be the same value in any inertial reference frame ...

to me the above is about invariance something I assume is true for every observer, below is about defining the value, something I can measure and calculate..

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.

 

[nitsuj]

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.

To what level of precision? the concept of "speed" is somewhat* different in the case of an invariant one. who cares the "speed" (value)

*understatement

 

[ghwellsjr]

As I made clear in this statement, I was referring to synchronisation as a process involving two clocks. Since you mean something else by this (namely defining simultaneity from an observer's viewpoint), my statement stands but it doesn't contradict yours.

Please don't get my comments mixed up with others. I never discussed synchronization and I didn't even bring up simultaneity. I just agreed with your comment regarding a single observer's clock and radar. My point is that it is not possible to measure the propagation of light, instead it is defined to be c in every Inertial Reference Frame.

I object to your statement that light "is already known experimentally to travel at the invariant speed". You are claiming that it is possible to measure the propagation of light rather than recognizing that it is defined or postulated or stipulated or assumed. We measure the invariant speed, c, with a two way or roundtrip setup. Do you see the difference?

 

[bahamagreen]

Speed c is a maximum and an "absolute" speed in the sense that it will be found to be the same in every IRF... the word "absolute" being operative to the OP's question about a minimum speed... I'm supposing that the OP is looking at SR and I think the full version of the OP's question might be:

If all IRFs have a maximum speed of c,
and all IRFs agree on the value of c,
how is it that individual IRFs each have a minimum speed,
but those minimum speeds do not agree when compared (mutually observed)?

The implication of the question seems to be that if absolute maximum speeds agree, so should the absolute minimums, yet they don't; how can there be an absolute (universal) maximum speed but not a corresponding universal absolute minimum speed?

This is the kind of question where the logical baggage of the word "absolute" may be getting lost during the flight. We have two words that seem to mean the same thing: speed and motion.
Per Wiki:
Motion: "In physics, motion is a change in position of an object with respect to time."
Speed: "...the speed of an object is the magnitude of its velocity (the rate of change of its position);..."

I can't explain it, but what is very weird is if the word "speed" is replaced with "motion", then the role of the word "absolute" seems to take on a different sense. If one is saying "speed" but thinking of "motion" in a natural verbal-logical fashion, there is a seemingly logical argument that has confused many...

Two non-accelerating objects in relative motion...
Verbal-logically;
- both are in absolute (certain) relative motion with respect to the other
- therefore, at least one of the two objects must be in absolute (certain) motion without having to specify that the motion is relative; relative motion is motion, thus it implies the existence of absolute motion without further stipulation of reference
- therefore, there is an absolute rest with respect to absolute motion
- one of the objects might be at absolute rest, but not both; both may be in absolute motion

This kind of logic finds absolute rest by finding absolute motion from relative motion. Using "motion", it seems by verbal-logic that any relative motion demonstrates absolute motion without having to identify an at-rest motion of no magnitude - it is implied from absolute motion in spite of not being able to assign a magnitude to either the absolute motion or absolute rest.

From a Classical / Euclidean standpoint, the certainty of relative motion, hence the certainty of motion itself, hence the certainty of absolute motion and therefore absolute rest seems pretty strong. The weakest link may be in the step where the certainty of relative motion leads to the certainty of motion itself, leading from the certainty of motion itself, to that there be certainty of absolute motion prior to knowing (and not having to know) what reference that absolute motion uses as its absolute rest... but this still seems pretty strong.

Yet, when the argument is shifted to "speed" rather than motion, even before evoking SR, the sense of the implications don't hold the same. The subsequent steps of the argument are now flimsy and confused because relative speed seems to take the argument differently than relative motion... the natural language sense of motion must be a little different from that of speed?

 

[ghwellsjr]

Speed c is a maximum and an "absolute" speed in the sense that it will be found to be the same in every IRF...

Speed c is "found to be the same in every IRF"? No, it is defined to be c in every IRF.

The remainder of your post appears to me to be at odds with the stated purpose of this forum--to teach relativity--it's not to try to understand the confusion that the OP is suffering from or to try to second-guess what his real concern is. If he doesn't want to come back and clarify, there's no point in trying to go beyond the obvious and simple answer that has been provided multiple times: zero.

 

[Khashishi]

In quantum mechanics, Heisenberg uncertainty principle puts a minimum on $\Delta p \Delta x$ which sort of puts a limit on speed. It's not a barrier like c, but anything below that limit is smeared out.

 

[Nick666]

If he doesn't want to come back and clarify, there's no point in trying to go beyond the obvious and simple answer that has been provided multiple times: zero.

I read all the replies, and I'm hoping I'm the one that will get clarification

The idea of minimum speed just accidentaly popped in my mind the other days when reading threads here about the (maximum) speed of light etc.

And I googled to see what I get and I got this result.

http://arxiv.org/pdf/1211.3612v1.pdf

"This research aims to consider a new principle of symmetry in
the space-time by means of the
elimination of the classical idea of rest including a
universal minimum limit of speed in the subatomic
world. Such a limit, unattainable by the particles, represents
a preferred inertial reference frame
associated with a cosmological background field that breaks
Lorentz symmetry. So there emerges
a modified relativistic dynamics with a minimum speed related
to the Planck length of the early
universe, which leads us to search for a quantum gravity at low energies"

 

[nitsuj]

Please don't get my comments mixed up with others. I never discussed synchronization and I didn't even bring up simultaneity. I just agreed with your comment regarding a single observer's clock and radar. My point is that it is not possible to measure the propagation of light, instead it is defined to be c in every Inertial Reference Frame.

I object to your statement that light "is already known experimentally to travel at the invariant speed". You are claiming that it is possible to measure the propagation of light rather than recognizing that it is defined or postulated or stipulated or assumed. We measure the invariant speed, c, with a two way or roundtrip setup. Do you see the difference?

You referenced a section of the paper titled Definition of Simultaneity that defines c to be 1/2 a round trip, circumnavigating the simultaneity issue of measuring c one way. That says nothing (directly) about invariance, which is postulated; not defined, implicit is it's assumed always true...not sure how stipulated can fit in there.

It is already postulated to travel at an invariant speed, which is known experimentally to still be true.

I don't object to their statement; it says nothing about measuring "the propagation of light", which of course isn't possible...but measuring-calculating the one way speed is, as you pointed out that process is defined.

Invariance does not mean maximum.

 

[ghwellsjr]

You referenced a section of the paper titled Definition of Simultaneity that defines c to be 1/2 a round trip, circumnavigating the simultaneity issue of measuring c one way.

No it doesn't, the definition of c is given for the full round trip, not 1/2:

That says nothing (directly) about invariance,

That says nothing about invariance, either directly or indirectly. It's simply a statement about the experimentally derived fact of the universally measured round trip speed of light.

which is postulated; not defined, implicit is it's assumed always true...not sure how stipulated can fit in there.

In the introduction, Einstein states his second postulate concerning the one-way speed of light "that light is always propagated in empty space with a definite velocity c". In the first article, he goes into detail and uses the terms "defined" and "definition". These are not in conflict with his first term. I use the additional terms "assumed" and "stipulated" in contrast to "measured" or "experimentally determined".

It is already postulated to travel at an invariant speed, which is known experimentally to still be true.

There is no experiment to show that light propagates at c, only that it is compatible with the second postulate.

I don't object to their statement; it says nothing about measuring "the propagation of light", which of course isn't possible...but measuring-calculating the one way speed is, as you pointed out that process is defined.

Agreed.

Invariance does not mean maximum.

I didn't say it did.

 

[Nugatory]

The idea of minimum speed just accidentaly popped in my mind the other days when reading threads here about the (maximum) speed of light etc.

And I googled to see what I get and I got this result.

http://arxiv.org/pdf/1211.3612v1.pdf

Stuff like this is the reason that not all arxiv papers are acceptable references here. It's an interesting speculation, but it's still far from part of accepted scientific thinking. Unless and until these ideas can be leveraged to solve some currently unsolved problem, explain some otherwise unexplainable experimental observation, or improve our current solutions they will remain that way.

 

[nitsuj]

No it doesn't, the definition of c is given for the full round trip, not 1/2:

That says nothing about invariance, either directly or indirectly. It's simply a statement about the experimentally derived fact of the universally measured round trip speed of light.

The idea it has to be measured by a defined method, is because it is invariant. otherwise there would be no simultaneity issues with moving clocks

In the introduction, Einstein states his second postulate concerning the one-way speed of light "that light is always propagated in empty space with a definite velocity c". In the first article, he goes into detail and uses the terms "defined" and "definition". These are not in conflict with his first term. I use the additional terms "assumed" and "stipulated" in contrast to "measured" or "experimentally determined".

definite is not the same word as defined. "always" & "definite velocity" is about invariance...not what ever the value maybe or how to measure it.

There is no experiment to show that light propagates at c, only that it is compatible with the second postulate.

I don't know what you mean with " no experiment to show that light propagates at c". A method to measure the DEFINITE speed is defined. The fact that it's invariant, is still observed to be true.

Here is a link with a table of the history of calculations of the speed of light, first of which was in 1676 using predicted & observed orbits.

Here is another wording, speaking to the definition of a second and the implication..."This defines the speed of light in vacuum to be exactly 299,792,458 m/s." taken from here, which is different from the defined method to measure light traveling that speed.

 

[LTadam]

Hi all. I think this is an interesting question. I think that minimum speed is so hard to define because there are no true inertial reference frames without first defining an inertial reference frame.

 

[PWiz]

there are no true inertial reference

Theoretically, they exist. Practically, they don't.

without first defining an inertial reference frame.

An inertial frame of reference is a well defined concept. The minimum speed which can exist will always be 0.

 

[William Turley]

What is the minimum speed in the universe ?

why not consider negative speed, i.e. where were you prior to now?

 

[Nugatory]

why not consider negative speed, i.e. where were you prior to now?

People often say "speed" when they mean "velocity" or vice versa, but when we're being careful with words "speed" refers to the magnitude of a velocity vector and therefore is never negative. That's why the speedometer of a car starts at zero and doesn't have any room for negative speeds - if I'm driving north at 30 km/hr my velocity is 30 km/hr north, and if I'm driving south my velocity is -30 km/hr, but either way the speedometer reads 30 km/hr and that's my speed relative to the surface of the earth.

 

[nitsuj]

People often say "speed" when they mean "velocity" or vice versa, but when we're being careful with words "speed" refers to the magnitude of a velocity vector and therefore is never negative. That's why the speedometer of a car starts at zero and doesn't have any room for negative speeds - if I'm driving north at 30 km/hr my velocity is 30 km/hr north, and if I'm driving south my velocity is -30 km/hr, but either way the speedometer reads 30 km/hr and that's my speed relative to the surface of the earth.

Or maybe more interestingly...how does one "envision" a "negative" speed, to your point of it being directionless. And I'm not getting much from

i.e. where were you prior to now?

to know which way is which (assuming velocity was intended meaning, as you inferred).

 

[theodoros.mihos]

I think there is no confuse if we make a 2D Minkowski's diagram. For all frames, even for angles up to 45 degrees (any that can mean) we can define speed and velocity both well. And for all, the minimum speed is zero.

 

[ghwellsjr]

The idea it has to be measured by a defined method, is because it is invariant. otherwise there would be no simultaneity issues with moving clocks

definite is not the same word as defined. "always" & "definite velocity" is about invariance...not what ever the value maybe or how to measure it.

I don't know what you mean with " no experiment to show that light propagates at c". A method to measure the DEFINITE speed is defined. The fact that it's invariant, is still observed to be true.

Here is a link with a table of the history of calculations of the speed of light, first of which was in 1676 using predicted & observed orbits.

Here is another wording, speaking to the definition of a second and the implication..."This defines the speed of light in vacuum to be exactly 299,792,458 m/s." taken from here, which is different from the defined method to measure light traveling that speed.

OK, please tell me what is the defined method to measure the DEFINITE speed of light that you have mentioned so many times in this post.

 

[nitsuj]

OK, please tell me what is the defined method to measure the DEFINITE speed of light that you have mentioned so many times in this post.

Any measurement that ultimately "employs" the equation that "works around" the issue of RoS. It will definitely equal c

I can't do equations, but the one used to determine the "common time", that is defining simultaneity of the clocks assuming one way speed of light is 1/2 round trip.

tb-ta = t'a - tb ...best i can do...but it's in the paper you linked to. Just below the paragraph "defining" the "common time" required to ...

 

[Rob Benham]

I was just going to suggest introducing the CMB into the discussion. The use of the CMB to stabilize a NASA U2 aircraft to better measure the . . . CMB has fascinated me for years. It almost seemed to suggest some sort of spacetime datum, but of course, that's not possible. :-(

(George Smoot. Work done after the gondola series)

 

[ghwellsjr]

OK, please tell me what is the defined method to measure the DEFINITE speed of light that you have mentioned so many times in this post.

Any measurement that ultimately "employs" the equation that "works around" the issue of RoS. It will definitely equal c

I can't do equations,

Are you saying you don't understand what the above equation means?

but the one used to determine the "common time", that is defining simultaneity of the clocks assuming one way speed of light is 1/2 round trip.

What do you mean by "one way speed of light is 1/2 round trip"? It sounds like you are saying the one way speed of light is 1/2 of whatever you measure for the round trip. Is that what you mean?

tb-ta = t'a - tb ...best i can do...but it's in the paper you linked to. Just below the paragraph "defining" the "common time" required to ...

 

[nitsuj]

Are you saying you don't understand what the above equation means?

What do you mean by "one way speed of light is 1/2 round trip"? It sounds like you are saying the one way speed of light is 1/2 of whatever you measure for the round trip. Is that what you mean?

Yes I don't know what the above equation is. What is two times a times b? Or is it two times ab because its same as ba...by definition?

Yes that is what I mean...by Einstein's definition.

 

[ghwellsjr]

Yes I don't know what the above equation is. What is two times a times b? Or is it two times ab because its same as ba...by definition?

Einstein didn't give a good explanation of that equation so I will. AB is the distance between A and B measured with a rigid ruler, t_A is the time on the clock at A when a light pulse is emitted from A, which then propagates to a mirror at B which reflects it back to A and t'_A is the time on the same clock at A when the reflected light pulse gets back to A. To calculate the "average" round trip speed of the light pulse we take double the distance between A and B and divide it by the total time that the light was in transit which is the difference between the two clock readings. Apparently, Einstein's audience was familiar enough with the requirement to use a round trip when measuring the speed of light that he didn't go into any detail about it.

What do you mean by "one way speed of light is 1/2 round trip"? It sounds like you are saying the one way speed of light is 1/2 of whatever you measure for the round trip. Is that what you mean?

Yes that is what I mean...by Einstein's definition.

No, Einstein is saying that the time on the clock at B is set so that the light pulse takes 1/2 of the round trip time interval to make each leg of the trip. In other words it spends half the time getting to the mirror and half the time getting back and clock B is set accordingly. That makes the unmeasurable one-way speed of light equat to the measured round trip speed.

Can you see now why it is impossible to measure the one-way speed of light? (Look it up in wikipedia if you need more help.)

 

[ash64449]

Measuring the speed of light in a round trip is possible since the emission and receiving events can be measured readily by a single clock.

By understanding the total distance traveled, and dividing this number by duration of time gives you the measured speed of light.

But measuring the speed of light in a single half-way of round trip is impossible since you need for that two clocks.

Well,it would have been possible if we synchronize the clocks beforehand.But to synchronize the clocks by Einstein's definition in his published paper requires you to assume that light travels at the speed c and then by setting that clock B, clocks get synchronized.

It means clocks are synchronized in such a manner that light speed has a value of c when measured in a half-way trip.

Is this what you meant ghwellsjr? is that the reason why measuring halfway round trip speed of light impossible?

 

[Rob Benham]

Given that measuring the speed of light over short distances requires a very precise clock, is there any significant time taken for the photons to be 'processed'* by the mirror to send them on their return journey?

*I've just read a little on what takes place but it seemed even more complex than I remember. Nowhere did I find a typical time taken.

 

[nitsuj]

Einstein didn't give a good explanation of that equation so I will. AB is the distance between A and B measured with a rigid ruler, t_A is the time on the clock at A when a light pulse is emitted from A, which then propagates to a mirror at B which reflects it back to A and t'_A is the time on the same clock at A when the reflected light pulse gets back to A. To calculate the "average" round trip speed of the light pulse we take double the distance between A and B and divide it by the total time that the light was in transit which is the difference between the two clock readings.

I found Einstein explained it well and far more structured.

No, Einstein is saying that the time on the clock at B is set so that the light pulse takes 1/2 of the round trip time interval to make each leg of the trip. In other words it spends half the time getting to the mirror and half the time getting back and clock B is set accordingly.

That makes the unmeasurable one-way speed of light equate to the measured round trip speed.

There is no "this makes". That IS the defined part. That the round trip of light is equal to the one way trip.Yes I do know why we cannot measure one-way, a main reason is because the speed c is invariant, clocks that move relative to each other are not synchronized. One cannot carry a clock from the start point to the finish and have the clocks (start clock / finish clock) share a "common time" (be synchronized).

While A-B and B-A are lengths, Einstein effectively used light to equate that as "time", the exact time required to get from a-b-a. Same idea as the light second unit.

Again from the paper you are referring to "We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A."

If AB BA were truly lengths, he would have explicitly stated AB + BA since both would be known exactly. This was about the time for LIGHT to travel those distances. In turn only AB is used and it's defined as 2 times AB for the total time.

So since someone can determine the time for an a-b-a trip by definition one can deduce (rather simply, though not provable) that is the same value as the 2AB.

It took 4 seconds for a full trip of 2 light seconds each way. 2*2ls / 4 = 1 Ha and all I needed were definitions.

 

[ghwellsjr]

Measuring the speed of light in a round trip is possible since the emission and receiving events can be measured readily by a single clock.

By understanding the total distance traveled, and dividing this number by duration of time gives you the measured speed of light.

But measuring the speed of light in a single half-way of round trip is impossible since you need for that two clocks.

Well,it would have been possible if we synchronize the clocks beforehand.But to synchronize the clocks by Einstein's definition in his published paper requires you to assume that light travels at the speed c and then by setting that clock B, clocks get synchronized.

It means clocks are synchronized in such a manner that light speed has a value of c when measured in a half-way trip.

Is this what you meant ghwellsjr? is that the reason why measuring halfway round trip speed of light impossible?

Yes.