Length is the measure of intervals in space?

[sahilmm15]

What does 'intervals' mean here?

 

[Dale]

In an inertial frame the interval, $s$, is given by $ds^2=-c^2 dt^2+dx^2+dy^2+dz^2$

 

[Ibix]

What's the context for this? @Dale is assuming (reasonably) that you are asking about special relativity. Is that correct? If not, can you provide a longer quote from where you found your title question?

 

[sahilmm15]

What's the context for this? @Dale is assuming (reasonably) that you are asking about special relativity. Is that correct? If not, can you provide a longer quote from where you found your title question?

I was studying units and dimensions and it defined length as I stated.

 

[Dale]

Hmm, I think that we need an exact quote or specific reference. You can ignore what I said since it doesn’t seem to be relevant to your actual question. But you need to clarify considerably.

 

[Ibix]

I was studying units and dimensions and it defined length as I stated.

I suspect all it's saying is that "length is what we call the difference in position of two points". Contrast, for example, duration which is what we call the difference in time (or "interval") between two events.

I have to say I find this kind of definition to be fairly useless - it's just swapping one set of words for another. One great quote from Einstein is that "time is what clocks measure". He's saying that he neither knows nor cares what time is - just that his experience is that devices we call clocks measure it, and that's enough for science to work with. Similarly, length is what a ruler measures.

If that doesn't make sense, you'll have to follow Dale's advice and give us a longer quote and/or a reference we can look at.

 

[sahilmm15]

Hmm, I think that we need an exact quote or specific reference. You can ignore what I said since it doesn’t seem to be relevant to your actual question. But you need to clarify considerably.

 

[Dale]

Yes, having read the reference I agree with @Ibix. They could have said “length is a measure of distance” or something similar. They are not trying to make a deep statement, they are just saying “length is length” in other words.

 

[sahilmm15]

time is - just that his experience is that devices we call clocks measure it, and that's enough for science to work with. Similarly, length is what a ruler measures.

If that doesn't make sense, you'll have to follow Dale's advice and give us a longer quote and/or a reference we can look at.

Dear mentors, I need help in this particular matter. My brain is so dumb it thinks it needs to understand everything. Why can't you understand it simply, why do you want to get into complexities. It thinks that it needs to perfectly understand what's written before going somewhere advanced. It strives for 'Perfection'. It is ruining me. It tells "Hey go and understand that first". But the reality is, What you wrote 'length is what ruler measures'. It says no these definitions don't work, think like "scientists". I try to convince my brain that as you gain more problem solving ability, more experience than these words would make appropriate sense. But it doesn't understand. It doesn't allow me to proceed further by taking something simply. Please help me!

 

[sahilmm15]

Yes, having read the reference I agree with @Ibix. They could have said “length is a measure of distance” or something similar. They are not trying to make a deep statement, they are just saying “length is length” in other words.

Check this. It is much simpler.

 

[Dale]

What you wrote 'length is what ruler measures'. It says no these definitions don't work, think like "scientists".

Sorry @sahilmm15’s brain, it works perfectly. In fact, this sort of definition is scientifically the best approach and should be used whenever possible. Operational definitions ground the rest of your definitions in experiments and make sure that you are doing experimental science and not just math.

 

[Ibix]

My brain is so dumb it thinks it needs to understand everything. Why can't you understand it simply, why do you want to get into complexities. It thinks that it needs to perfectly understand what's written before going somewhere advanced

It's worth remembering that science attempts to describe the real world (in enough detail that we can then make predictions about it). This means that, at a fundamental level, the objects we manipulate in our theories don't really have definitions in terms of words. We just have to appeal to our common experience of the real world.

We have the idea that some things are close together and some things are far apart. How do you teach a child what "far apart" means? You show them pictures of things far apart and say "these things are far apart". There's no form of words you can use to describe it. We just all have the experience of it being a long way to the shops, but the park is close by (or whatever), and thus we have an experience of distance.

Length is simply a quantitative version of that. Instead of "far" we say that we can lay 1,000 standard-length objects (and we'll call our standard length object a 1m rule) between here and there. But I can no more explain to you what length is than I can explain what blue looks like to a blind man.