Taking empirical Spacetime measurements.

[geordief]

If we are an observer at the origin of a possible set of events ,what are the actual empirical methods of taking measurements to give a numerical value to an event that occurs subsequently?

 

I am situated at ,say Jodrell Bank at the point in spacetime [0,0,0,0,] and there is an event that we can say is located at [x,y,z,ct]. How do I empirically and repeatably* make those 4 measurements?

 

I have no problem (I hope) with the "ct" measurement but how ,in practice would I make the spacial measurements? Can I bounce a beam of light off them if the system is set up to do that?

 

Are there any other ways to do it?

 

*obviously not repeatably for the same event although perhaps the same event could be measured by countless different observers.

[swansont]

It depends on the precision you need or want. You could use a meter stick. Or a wheel of known circumference and a counter. But an EM measurement works, too.

[geordief]

Is it possible to have the 4 measurements taken at the "same time" or is that an a priori impossiblity and something that has to be adjusted* for?

 

Unless distances are very small the extremities ** of the physical metre sticks will be "wobbly" .Can't the measurements taken that way only be

approximate?

 

* do we just choose our level of precision/approximation?

 

** not just the extremities but it is the extremities that "make the measurement"

Edited April 25, 2016 by geordief

[swansont]

All measurements are approximate. The issue is the level of uncertainty.

 

It's in principle possible to measure the four coordinates at the same time, but without context, one can't tell how important that is. If the target is stationary, it shouldn't matter when you measure the spatial coordinates.

 

You bounce a laser off the target and you will know its position at the time of the reflection.

[geordief]

If the target is not stationary. is it possible to take these 4 measurements together ?

 

Does the target need to be extremely close to the origin/observer for this to be possible?

 

Does it have to be specified that the measurement at the origin [0,0,0,0] must also be done successfully?

 

Is the result of those 8 measurements still an approximation to whatever degree of precision the setup allows?

 

Hope I am not waffling........

[swansont]

If the target is not stationary. is it possible to take these 4 measurements together ?

 

Does the target need to be extremely close to the origin/observer for this to be possible?

 

Does it have to be specified that the measurement at the origin [0,0,0,0] must also be done successfully?

 

Is the result of those 8 measurements still an approximation to whatever degree of precision the setup allows?

 

Hope I am not waffling........

 

 

You will know where it was when the laser reflected off of it. How is this 8 measurements? Assuming you are at the origin, you are measuring position and time. Some kind of angular measurement in 2D, a time delay measurement for r, and a time measurement for t. The latter two being from the same clock.

 

There will always be some limit on the precision of any of those measurements.

[geordief]

 

 

You will know where it was when the laser reflected off of it. How is this 8 measurements? Assuming you are at the origin, you are measuring position and time. Some kind of angular measurement in 2D, a time delay measurement for r, and a time measurement for t. The latter two being from the same clock.

 

There will always be some limit on the precision of any of those measurements.

(been gathering my thoughts)

 

The 8 measurements were (overcautiously perhaps, but hopefully not wrongly) including 4 implied measurements[0,0,0,0,] at the start (origin) of the experiment...

 

Anyway,have I understood it correctly now that the distance r (to the target) you have mentioned is exactly numerically identical to the distance (ct) measured by a light clock apparatus provided that r is separated from the origin by a vacuum and it is targeted with a laser traveling from the origin at the speed,c?

 

So one measurement of the time can simultaneously measure both the distance to the target and the lapse of time with 100% accuracy (if we take time here as simply a measurement of the distance traveled by the light in the clock)

 

PS : If I want to make a spacetime measurement between 2 events I simply take 2 separate measurements on the same clock and apply the normal spacetime distance formula ds^2= dr^2-d[ct]^2 ? (perhaps the sign is reversed)

[swansont]

(been gathering my thoughts)

 

The 8 measurements were (overcautiously perhaps, but hopefully not wrongly) including 4 implied measurements[0,0,0,0,] at the start (origin) of the experiment...

 

Anyway,have I understood it correctly now that the distance r (to the target) you have mentioned is exactly numerically identical to the distance (ct) measured by a light clock apparatus provided that r is separated from the origin by a vacuum and it is targeted with a laser traveling from the origin at the speed,c?

 

So one measurement of the time can simultaneously measure both the distance to the target and the lapse of time with 100% accuracy (if we take time here as simply a measurement of the distance traveled by the light in the clock)

 

PS : If I want to make a spacetime measurement between 2 events I simply take 2 separate measurements on the same clock and apply the normal spacetime distance formula ds^2= dr^2-d[ct]^2 ? (perhaps the sign is reversed)

 

 

 

NOTHING can be measured with 100% accuracy.

 

You have a ranging system. You can measure what direction it's pointed (two angles). You time tag when a pulse is sent, and when it returned. The midpoint is when it was reflected. Half of the duration gives you the distance, via d = ct. (Or ct/n, correcting for the index of refraction of the air.)

 

Four measurements.

[geordief]

 

 

 

NOTHING can be measured with 100% accuracy.

 

True, I misspoke.. I was trying to get across the idea that one measurement can serve to measure 2 things . The distance traveled by the light in the light clock can be said to be identical in theory to the distance traveled by the light in the laser traveling to the target and back to the receiver next to the light clock.

 

I was trying to make that point because I think it was actually the first time I had specifically realised it was the case and I was hoping to get corroboration that it was in fact true.

 

If we measure the time elapsed I think we are in fact measuring the distance traveled by a ray of light in the light clock and if a beam of light is simultaneously sent to and reflected back from a target then the distance traveled by both rays of light will (in a vacuum) be as numerically identical as it is possible for them to be.

[swansont]

True, I misspoke.. I was trying to get across the idea that one measurement can serve to measure 2 things . The distance traveled by the light in the light clock can be said to be identical in theory to the distance traveled by the light in the laser traveling to the target and back to the receiver next to the light clock.

 

I was trying to make that point because I think it was actually the first time I had specifically realised it was the case and I was hoping to get corroboration that it was in fact true.

 

If we measure the time elapsed I think we are in fact measuring the distance traveled by a ray of light in the light clock and if a beam of light is simultaneously sent to and reflected back from a target then the distance traveled by both rays of light will (in a vacuum) be as numerically identical as it is possible for them to be.

 

 

For the distance you need to time tag the emitted pulse and the return. You get the time for free, though, if you have a clock instead of a stopwatch.

[geordief]

Thanks, I am happy now.