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Einstein's rods


geordief
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Einstein talks about creating a coordinate system  with a lattice of imaginary measuring  rods of unit length  along the spatial axes.

In the real world  would such a rod's length have to be measured as a spatio-temporal distance?

 

In practical terms ,if we put a person at the origin of the coordinate system  and put such a rod in his/her hand   and ask him to actually measure it  how could he  do this without recourse   to a time element in the procedure?

 

If he simply counted all the protons fortuitously along the rod's length the next question seems to be  "how do you measure the length of the individual proton without there being a time element to the procedure?" 

 

Would that measurement not also be a tempero-spatial measurement ?(and on and on)

 

Must any  unit of spatial distance inevitably be some kind of fraction of a  light-second ?

 

Am I getting the hang of this or over complicating things?

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27 minutes ago, geordief said:

Einstein talks about creating a coordinate system  with a lattice of imaginary measuring  rods of unit length  along the spatial axes.

In the real world  would such a rod's length have to be measured as a spatio-temporal distance?

 

In practical terms ,if we put a person at the origin of the coordinate system  and put such a rod in his/her hand   and ask him to actually measure it  how could he  do this without recourse   to a time element in the procedure?

 

If he simply counted all the protons fortuitously along the rod's length the next question seems to be  "how do you measure the length of the individual proton without there being a time element to the procedure?" 

 

Would that measurement not also be a tempero-spatial measurement ?(and on and on)

 

Must any  unit of spatial distance inevitably be some kind of fraction of a  light-second ?

 

Am I getting the hang of this or over complicating things?

You calibrate a length, of say, one meter, on some transportable item. Let’s call it a “meter stick”

I measure the rod by comparing it with the meter stick. Why do you think there is a temporal component to this? The length is independent of time.

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I think what's bothering @geordief is the fact that the photons from the tip of the measuring rod reach the observer's eyes with a delay.

If that's the case, my explanation would be that Einstein's definition is based implicitly on the assumption that you can always measure rods' lengths by comparing them to a ruler at rest with respect to different observers. IOW, you can completely fill space time with as many rulers as you need, each of them at rest with whatever observers you want to discuss, and whatever their state of (inertial) motion.

Later introductions to SR appeal to light signals.

Is that anything like what troubles you, @geordief, and have I been any helpful?

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2 hours ago, geordief said:

Einstein talks about creating a coordinate system  with a lattice of imaginary measuring  rods of unit length  along the spatial axes.

In the real world  would such a rod's length have to be measured as a spatio-temporal distance?

It would be helpful if you were to provide a precise reference to the particular case you are referring to.

In his book Relativity, which I believe you have, Einstien 'talks about' measuring rods in several different circumstances.

Are you perhaps referring to chapter XII ?

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1 hour ago, studiot said:

It would be helpful if you were to provide a precise reference to the particular case you are referring to.

In his book Relativity, which I believe you have, Einstien 'talks about' measuring rods in several different circumstances.

Are you perhaps referring to chapter XII ?

No ,I just had  chapter II in mind 

https://www.coursehero.com/file/p7hr8lu/If-for-instance-a-cloud-is-hovering-over-Trafalgar-Square-then-we-can-determine/

 

(although  I  did ,ambitiously  have the moving rods of chapter XII  as my next preoccupation)

But I think  @swansontmay have disabused me of the notion that there is some kind of a "proto unit" of spatial distance that I would need to give meaning/reference  to the 1 metre rod.

https://www.scienceforums.net/topic/125530-einsteins-rods/?do=findComment&comment=1182529

I feel that I see now that distance measurements are relative and so different lengths can be compared to each other without the need to refer to some absolute unit of spatial distance.

 

For the purposes of creating a rod of unit  spatial distance any convenient length will do .

 

@joigus  I think I was hung up over the mistaken idea  that there was some kind of fundamental unit of spatial distance to which all rods or rulers had to be compared.

There seemed to be a process  involving time  in that but I now feel it is unnecessary (and wrong)

 

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8 hours ago, geordief said:

For the purposes of creating a rod of unit  spatial distance any convenient length will do .

 

You got it exactly. +1

 

8 hours ago, geordief said:

There seemed to be a process  involving time  in that but I now feel it is unnecessary (and wrong)

There is  a 'process' involving time which is the difficulty Einstein realised in talking about the relativity of simultaneity.

That is why he talks about a physical rod or line of them and introduces the idea of all being in the same frame.

He then goes on to derive the fact that any measurement of length will depend upon the frame of measurement.

 

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