Instantaneous coordinates of an event in space (special relativity)

[Ahmed1029]

In relativity, no signal travels faster than light, and hence if something happened away from me, I will only know about it after some time. This means I cannot measure instantly the position and time of something as it happens; this would violate special relativity. I however imagine that I might attach a tape to a particle and from the reading of the tape from my "static" position I can instantaneously know the position of the particle as it moves without any delay. How is this possible.

 

[PeroK]

How is this possible?

It isn't possible. What sort of "tape measure" did you have in mind?

 

[FactChecker]

from the reading of the tape from my "static" position I can instantaneously know the position of the particle as it moves without any delay. How is this possible.

Any change in its velocity can not be detected by you faster than the speed of light. You might assume that the velocity is constant but that would be an assumption, not a physically detected fact.

 

[Ahmed1029]

Any change in its velocity can not be detected by you faster than the speed of light. You might assume that the velocity is constant but that would be an assumption, not a physically detected fact.

I imagine if I attach a tape to a car with marks on it indicating distance, I can just look at the mark and know that how far the car is from me, unless something weird is actually happening.

 

[Ahmed1029]

It isn't possible. What sort of "tape measure" did you have in mind?

Like a rope with marks on it indicating distance

 

[PeroK]

Like a rope with marks on it indicating distance

What happens if the particle changes direction? How would you know?

 

[Ahmed1029]

What happens if the particle changes direction? How would you know?

I don't care about its velocity but rather its instantaneous position. In my imagined scenario, I would say the direction of its position vector is just the orientation of the tape wrt the point I consider to be the origin, but it's unambiguous. I imagine that I'm holding the other end in my hand or fixed to the floor, with many meters spared waiting to unroll

 

[PeroK]

I don't care about its velocity but rather its instantaneous position. In my imagined scenario, I would say the direction of its position vector is just the orientation of the tape wrt the point I consider to be the origin, but it's unambiguous. I imagine that I'm holding the other end in my hand or fixed to the floor, with many meters spared waiting to unroll

But a tape is a flexible thing. How do you know it stays in a straight line?

It might even be folded over on top of itself. The particle might be right next to you even if 100m of tape is run out.

Or, is this not a tape but an infinitely rigid rod?

 

[FactChecker]

If you are imagining an infinitely rigid tape or rod, then you are not talking about real physics. All molecular interactions within the tape is done by electromagnetic effects. The effect of any change of velocity can not travel back through the tape to you faster than light could travel. So your reading on the tape would be wrong for a while.

 

[Nugatory]

How is this possible.

As well as the answers above, you may find this FAQ helpful: https://www.physicsforums.com/insights/can-i-send-a-signal-faster-than-light-by-pushing-a-rigid-rod/

 

[Dale]

I imagine if I attach a tape to a car with marks on it indicating distance, I can just look at the mark and know that how far the car is from me, unless something weird is actually happening.

Any information about the car’s position will travel through the tape at the speed of sound in the tape. That will be much slower than $c$. There is nothing instantaneous about this information.

 

[PeterDonis]

imagine that I might attach a tape to a particle and from the reading of the tape from my "static" position I can instantaneously know the position of the particle as it moves without any delay

No, you can't. All you can know "instantaneously" is what marked location on the tape is currently passing you. Converting that into a position of the particle requires you to make a number of assumptions that cannot be checked "instantaneously"; if they turn out to be wrong, you have to wait at least one light-travel time to find that out.

 

[Dragon27]

And if your car is traveling at a constant speed in a fixed direction then you obviously don't need any tape to know its exact coordinates.

 

[pervect]

I imagine if I attach a tape to a car with marks on it indicating distance, I can just look at the mark and know that how far the car is from me, unless something weird is actually happening.

You appear to be not taking into account the light speed delay for the light to reach your eye - or some other measurement instrument, such as a camera

It also sounds like you may not be familiar with the concept of the relativity of simultaneity.

We can suggest that you need to reform your thinking, but you're the one who'll actually have to do it.

 

[Ahmed1029]

You appear to be not taking into account the light speed delay for the light to reach your eye - or some other measurement instrument, such as a camera

It also sounds like you may not be familiar with the concept of the relativity of simultaneity.

We can suggest that you need to reform your thinking, but you're the one who'll actually have to do it.

That's not the correct way to think about it. I can make the measuring instrument "my eye" as close to the tape as possible. So if the effect is delivered instantaneouly to my end of the rod, I will know it happened before the light from the particle's end reaches my eye; I will only require lifht to travel a distance dx, rather than the whole distance between the particle and me. But I now know that rigid bodies doesn't exist in that deal fashon in general relativity

 

[Rene Dekker]

We assume that the object, including the tape, has been moving at constant speed for a long time, and therefore that any effect due to acceleration have been evened out.
In that case, the tape is subject to length contraction. It is a tape that is traveling in the moving reference frame, and therefore the distance between the marks on the tape appear closer together than on a tape at rest. So at best, it will tell you how far away the object is in the moving frame, not in your own rest frame.

 

[Ibix]

But I now know that rigid bodies doesn't exist in that deal fashon in general relativity

Or, indeed, special relativity.

 

[Rene Dekker]

In relativity, no signal travels faster than light, and hence if something happened away from me, I will only know about it after some time. This means I cannot measure instantly the position and time of something as it happens; this would violate special relativity.

That is not how measurements are defined in special relativity. They are defined by local clocks.
Imagine a long line of clocks that are all synchronised with each other in the rest frame. An event is defined as the combination of the location where that event happens, and the time on the local clock located at that location. That way, you can always know the position of an object at any time, without having to worry about the time light travels to some remote observer.

 

[FactChecker]

Or, indeed, special relativity.

Or even in basic physics of the speed of sound.

 

[Dale]

That is not how measurements are defined in special relativity. They are defined by local clocks.

But he is right that even if we define the measurements locally, it still requires time to communicate the results of the measurement to a distant receiver

 

[pervect]

That's not the correct way to think about it. I can make the measuring instrument "my eye" as close to the tape as possible. So if the effect is delivered instantaneouly to my end of the rod, I will know it happened before the light from the particle's end reaches my eye; I will only require lifht to travel a distance dx, rather than the whole distance between the particle and me. But I now know that rigid bodies doesn't exist in that deal fashon in general relativity

The problem here is that in order to measure the length of the object, you have to know the location of both ends of the object at the same instant of time. One picks some instant of time, which I'll call "now", and asks "what is the position of the left end and the right end of the ruler now?"

However, the concept of "now" turns out to be observer dependent in special relativity, something that's unexpected and causes a great deal of confusion. I'll give a reference and more details later.

If instantaneous signal transmission speed were possible via a physical mechanism, there would be a physical definition of now, and special relativity could not work properly. However, there is no such physical mechanism. It takes time to communicate information from one place to another.

Your current approach appears to be based on a desire to ignore the fact that it takes time to communicate information from one location to another. And it's going to lead to problems for your understanding of special relativity, because of the issue I mentioned previously, the relativity of simultaneity.

A reference on this issue, from one of Einstein's books, is online at https://www.bartleby.com/173/9.html. The issue is called "The Relativity of Simultaneity", and the particular thought experiment is called "Einstein's train". There is a great deal of information written about it, but it is hard to get people to listen to it. Also of some interest is the paper "The challenge of changing deeply held student beliefs about the relativity of simultaneity". Google finds this currently at https://core.ac.uk/download/pdf/25353534.pdf.

I'll give an informal summary of the issue, which may or may not be clearer than Einstein's treatment. Every inertial frame of reference in special relativity has a notion of simultaneity, a notion of "now". But when when switches frames, the notions change - events that are simultaneous in frame S are not simultaneous in some different frame S' that is moving with respect to S.

To go back to the "eye" analogy, if you have only one eye, you need to specify where it's at. Is it at the left end of the ruler, or is it at the right end?

If you have two eyes, then the pair of "eyes" need to have some concept of simultaneity. This is generally taken to be associated with the inertial frame that the pair of eyes is is in. But depending on the state of motion of the observer, there are different notions of simultaneity.