where is the distance?

[michel123456]

here is a simple diagram, one could use to explain the difference between distance and displacement.

Four points ABCD forming a square. And something moving along the path AB, BC, CD, DA. After the round, distance of travel is the sum of distances, displacement is null.

 

 

Elementary. But because we are talking about motion, or displacement, and because we know that we need time to travel, let's introduce Time. We are obtaining something like this:

 

 

That may look a little bit more complicated, but it is only a developpement of the previous diagram. Now we see clearly the difference between distance & displacement.

Is that clear to you?

Really, where is the distance? is that the sum of AB, BC, CD, DA, or the sum of AB', B'C'', C''D''',D'''A'''' (the red path)?

[insane_alien]

the distance doesn't involve time. so it is AB,BC,CD,DA

[DJBruce]

The distance would just be the sum of AB, BC, CD, DA. Your second diagram really does not seem to provide any more insight into the difference between distance and displacement. At least not to me.

[michel123456]

the distance doesn't involve time. so it is AB,BC,CD,DA

Right.

The distance would just be the sum of AB, BC, CD, DA. Your second diagram really does not seem to provide any more insight into the difference between distance and displacement. At least not to me.

Right.

The only insight it provides concerns the fact that when you teach pupils that displacement is null, the intuitive reaction is to say "how is that possible, you just told me the object moved, so something must have happened". That "something" that happened is the translation through time. Even standing at rest, point A went to point A''''. And the object that travelled through points ABCD in reality has been translated automatically in time too.

Here, again, there is lack of vocabulary. Translation in time is not motion, although my diagram may be confusing. Because I could not find any word for expressing "motion in time", I used to speak about "totion". Maybe it should be better to use "chronotion", but both look quite peculiar. So i'll stay at "translation in time".(I do not use "flowing" because it has inherent signification related to motion).

 

 

Let's say now that B' is a star. The ray of light emitted from this star to point A (the observator) is represented by the red path, because light travels (the word "travel" includes both space & time, because nothing can travel a distance with zero time).

[Mr Skeptic]

If you introduce time, you have a net displacement on the time axis only (in your reference frame).

[michel123456]

If you introduce time, you have a net displacement on the time axis only (in your reference frame).

 

Right. But you are a victim of vocabulary too. "displacement on the time axis"????

Displacement is null. Meaning "displacement in space", which the regular meaning of the word "displacement"

How to call "displacement in time"? 500 years of physics since Galileo, and no word for it?

[jajrussel]

I think that insane_alien is correct in the assertion that distance doesn't involve time, but that is because I see distance being an effect of energy, and time only as a good measure of the effect. Unless you force me to move at a certain speed it would likely take me longer to complete the circuit than say someone half my age, so time has no effect on the distance. The second diagram does not allow me to complete the circuit, but I can follow the path, again with the same result. However, not only will the person half my age complete the journey sooner, I would also be forced to travel further than that person in order to complete the journey, except for the fact that the path I am following is moving in sync with my destination. The diagram does allow for this following the red line. In reality AB, BC, CD, DA never change in definition, so there is no need to change the labels with each plain of the diagram. The time line is a sufficient marker. The answer should be AB, BC, CD, DA, but in keeping with your diagram it is AB', B'C'', C''D''', D'''A''''.

Edited January 1, 2010 by jajrussel
I meant D'''A'''', not D'''A

[Mr Skeptic]

Right. But you are a victim of vocabulary too. "displacement on the time axis"????

Displacement is null. Meaning "displacement in space", which the regular meaning of the word "displacement"

 

You can measure displacement on any axis. Why limit yourself to only spatial displacement and only in your own frame of reference?

 

How to call "displacement in time"? 500 years of physics since Galileo, and no word for it?

 

"Later" or "earlier" depending on the orientation.

[jajrussel]

In regard to displacement. Unless there is a significant change in the distance traveled while it is being traveled I would think that displacement would cancel out of the equation or at least fall within the probability allowed for an incorrect answer + or -.

[michel123456]

You can measure displacement on any axis. Why limit yourself to only spatial displacement and only in your own frame of reference?

 

Are you saying that displacement is not null? If I had presented only the second diagram (the plane one), you surely had assured that displacement is null, as it is assumed in any physics book.

 

 

"Later" or "earlier" depending on the orientation.

Hm, yes. But is the word "earlier" defined in a physical way? For me the words "earlier" & "later" are words of the common language. Those words that do not help in understanding what is physically happening. When I say "earlier", it is like time (what is that?) were "flowing" upon my existence. When I say "traveling in time", it is like I (I suppose I know what it is) was traveling not is space anymore, but in time; a situation more familiar that makes you confident in expressing the assumation that displacement is not null anymore.

[Mr Skeptic]

Are you saying that displacement is not null? If I had presented only the second diagram (the plane one), you surely had assured that displacement is null, as it is assumed in any physics book.

 

Correct. But as soon as you involved velocities, you involved displacement along the time axis as well, which did not cancel out. The difference? Ask someone in a different reference frame than yours, if the two points are spatially the same. You'll realize that space and time are connected.

 

Hm, yes. But is the word "earlier" defined in a physical way? For me the words "earlier" & "later" are words of the common language. Those words that do not help in understanding what is physically happening. When I say "earlier", it is like time (what is that?) were "flowing" upon my existence. When I say "traveling in time", it is like I (I suppose I know what it is) was traveling not is space anymore, but in time; a situation more familiar that makes you confident in expressing the assumation that displacement is not null anymore.

 

"Earlier" would be before the event in question, or if you prefer, along the time axis in the direction of decreasing entropy. Later would be after the event in question, or along the time axis in the direction of increasing entropy.

 

The units on the time axis are seconds (or another measure of time), but there is also no reason that you cannot use spatial units such as the meter to measure it instead. Just as people use light-years or light-seconds to measure distance using a time unit, you could use light-meters (time it takes light to travel a meter) to measure time using a spatial unit.

[michel123456]

I can't argue with anything you said. We have reached a 100% agreement.

Now, if B' were a star, and if we were standing at point A....

The ray of light coming from B' travels at SOL, both in time & space, along the red line. I suppose you agree.

Where is the distance? Or in other words, measuring the redshift of B', are we measuring a distance upon the red trajectory, or its projection upon the ABCD plane?

[jajrussel]

I get the feeling that you are implying that the red line AB' when compared with line AB indicates displacement. If that is the case and AB' is the time line, and AB is your distance the only way to accurately compare them is to draw a line from B' to B and from A'''' to A which you sort of have. Now draw a line from B' intersecting line A'''' A forming an intersect point so that you have a square. Which should not bother you because it sort of brings us back to your first diagram and you seem to like the idea of using a square to show displacement. Now if you want you can add another red line from intersect point A''''A to B. Now compare the distance between intersect point A''''A and B' with the distance between A and B any distance displacement should show up there. Now Compare the length of one red line to the other red line. Any time displacement should show up there.

Better yet, avoid the confusion go back to you first diagram and draw a red x connecting your corners, then take your measurements. It took me a while to figure out that the only accurate way to read your time line was in how it intersected with AB. The turns just added to the confusion. Unfold the second diagram then look at it.

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Just in case what I said was a little confusing. Your second diagram is a map that when unfolded comes complete with map coordinates and a diagonal time line.

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I think in my own fumbling way I have figured out what you are saying.

 

At one point I thought that there might be displacement due to the fact that I am turning. It takes time to turn, and the time it takes to turn would not be accounted for in the sum total distance, but when I unfolded your diagram I found that I was moving in a straight line and only had an apparent choice to do otherwise.

 

So, now I refold the diagram, with the awareness that except for AB the rest of the positions are apparent, and that should I see a star at B' that its position is only apparent, so measuring the redshift can only result in a measurement that is apparent, and that unless I know the displacement I can not actually figure out where the star actually is?

Am I getting close to figuring out what you are saying?

[michel123456]

There are 2 meanings.

1.First go back to the first diagram, This kind of diagram you will find in any school book about the difference between distance & displacement. This is such a basic I don't want to go futher in. See for example here:http://physics.info/displacement/

 

You will observe that the concept of Time is absent. For an object travelling upon the path ABCD, distance is a certain amount of space (measured in meters or feet) and displacement is null. But once you introduce the time axis, you realize that some "displacement" has been taken place. This is not a regular displacement, because the word "displacement" we learn at school means displacement "in space". The new "displacement" takes place in time, and should be called otherwise, to eliminate any ambiguity. So in other words, all the above has been set up only to show what happens when the concept of time is introduced.

 

2.About my last question concerning the distance from a star. Take the second diagram & eliminate everything.Except point A, point B, and point B'.

If B is a star, the only way you have to measure its distance from you is through its EM radiation that is subjected to the restrictions of Speed Of Light. The star in point B, is not observed at point B, but at point B'. And the distance measured is of course the AB' distance. There is no doubt about it, and anyone having some basic information in astronomy will explain that better than I do. The question was meant only to introduce a doubt and make people think. Point B' may not be a star, the diagram has no scale. It may be the cup of tea upon your desk. And in this case too, the distance measured is also the diagonal AB'. It is always the diagonal AB' ,if you accept the cornerstone of Relativity i.e. that C is absolute & nothing can travel faster than C. In this case, if I am right, the measured distance is never the AB distance. But I may be wrong.

[jajrussel]

If B' is the cup of tea sitting on my desk the length of time it takes the light bouncing off of it to reach my eye is going to be very short so the diagonal position will nearly be the straight line position, so the cup may as well be sitting where it appears to be. If it is a star, well given what you have stated so far, knowing B' is only an apparent position I can only accept that the diagonal is an inaccurate measure of position. The star is not where it appears to be, so when I try to determine where it actually is, I can start by saying it is not there. Then try to figure out where B is based on where A and B' is. If I figure out where B is, then point out where it is to a friend, there had better be something shiny there, or they are going to assume that my cup of tea does not actually contain tea. They may be right.

Edited January 3, 2010 by jajrussel
Sometimes my spell checker makes a fool of me.

[michel123456]

If B' is the cup of tea sitting on my desk the length of time it takes the light bouncing off of it to reach my eye is going to be very short so the diagonal position will nearly be the straight line position, so the cup may as well be sitting where it appears to be.

Exactly.

If it is a star, well given what you have stated so far, knowing B' is only an apparent position I can only accept that the diagonal is an inaccurate measure of position.

Yes & no. Yes it is inaccurate in the sense that the star is not where it appears to be, as you said, see my comment below. And No, because we can make quite accurate mesurement of distance to the star as we observe it at point B'.

The star is not where it appears to be, so when I try to determine where it actually is, I can start by saying it is not there.

Yes. But in the verb "is" you mean "is at present time".It looks self evident, but it is not. In fact, what happens is that the star was at point B' (belonging to the past), and at present time, the star is somewhere else.

Then try to figure out where B is based on where A and B' is.

A is yourself, the observator, it is the point of your own FOR. The measurement AB' is valuable only for you.

If I figure out where B is,

In order to figure out where B is, you have to apply a projection of your measurement upon the ABCD plane. Projection means geometry, and for each geometry, for each Theory, you will obtain a different position of B, and a different AB distance. According to the Standard Model , the projection is not orthogonal, due to the expansion of the Universe. The AB distance is estimated as a multiple of the AB' measurement.(about 6 times larger, if I recall well)

then point out where it is to a friend, there had better be something shiny there, or they are going to assume that my cup of tea does not actually contain tea. They may be right.

Sort of. All the above concerning the star position is exactly the same as concerning your cup of tea. There is no scaling in Relativity that changes the Theory in regard with dimension. The Theory is the same for big & for small: a reason why there is no common understanding with Quantum Mechanics.

The fact that there is no scaling in Relativity makes me think that what is true for a star must be true for a cup of tea as well. In other words, as I mentionned before, when you measure the distance from yourself to your cup of tea, even with a solid iron stick, the measured distance is always the AB' diagonal. But I may be wrong on this. Some interaction with other forum members should be good here.

Edited January 3, 2010 by michel123456

[jajrussel]

The diagram declared where B is. I was just wondering where the star is. (Not a question.)

 

I have accepted that what I see at B' is in fact at B, but only because you say so. To this point we have been talking about a star that is not where it appears to be. Basically, what I am doing is measuring to where the star was in the past, at B' the observation is the stars past..

So, applying the same thought to my cup of tea what I am doing is measuring from my position to where my cup was in the past. I get that. I never really thought about it this way until now, but I get it.

When you consider the beginning and the end, we are drowning in the past. I can only see so far, and everything I see is the past in regard to Alpha – Omega.

The question is; How far into the past can you reach? When I reach for my tea cup its location in the past is within my grasp, my sense of where it is, is reasonably accurate. The star on the other hand could lead me on a merry chase, if I don't start off with the assumption that where I have measured to, is only a single footprint that leads to where I want to go, and is not actually where I want to go. If I assume that B' is where I want to go, then that assumption is inaccurate.

Now, time in regard to me. Everything I see is in the future. Disregard my shortcomings, and I could possibly go there. In regard to me the only direction I can go is into the future. In regard to me I can not see the past, I can only remember it. If I can't see it I can not go there. In regard to me the present is very small, the future is very large, and all I can do is assume the past because I remember it. Yes I could overlay Alpha – Omega and myself, make all kinds of bold statements then dare anyone to question them, but it is apples and oranges. As you have pointed out before our vocabulary has its shortcomings and those shortcomings allow bold statements.

Now, to your statement that the distance is always the diagonal. Yep! It is one of those bold statements. Any straight line that intersects another can be a diagonal. The statement is true.

 

As to your diagram though. In the real word a star can move in any conceivable direction. Your diagram has plenty of dimension, but it also points out which direction we are to view time as going, So in keeping with the diagram I can only only follow the red line, even if it is my desire to simply go from A to B. All of which seems to me to be the basses of your statement.

The diagram declares how I am to see the world. So, in keeping with your diagram it is my opinion that a star observed at B' can not actually be at B, it has to be at C''. The distance assumed, by the statement that what is observed at B' is actually at B. The stars direction of movement is declared by the diagram, so the statement must agree with the diagram, or the statement is wrong...

So, is the measured distance still the diagonal? I am not saying that it isn't, I am just asking if it is, and can I now say the measured distance, point B' is now a portion of the actual distance point C''? I could not say this when the stars reported position was at point B.

If I am allowed to say that B' is a portion of C'', I can now make a logical statement that opposes the view that the measured distance is always the diagonal distance.

Edited January 4, 2010 by jajrussel

[michel123456]

Hum, pause.

You said

Everything I see is in the future.

 

No. Sorry for being abrupt. Everything I see is in the past. It may look weird but think about it twice.

Choose a target. You want to go to the Moon. Or to the kitchen. Look at the kitchen door, which is about 5 meters from you. The door you are looking at is some micro-seconds in the past because the image of the door needed some time to reach your eyes. For simplicity, let's say the door is 5 microseconds from you (in reality it is much less). You make one step in direction of the kitchen, and the door is now at 4 microseconds from you. Another step, the door is three microseconds from you, and so on, till you reach the door, at zero microseconds from you. O.K.?

The door that you saw, the target, is not in the future. You just made a construction in your mind putting this door as your target, a meeting point in the future. But the observed object was in the past.

Everything we observe belongs to the past. Nothing observable in the future. And, what is most astonishing, nothing observable in the present.

[pywakit]

Hum, pause.

You said

 

No. Sorry for being abrupt. Everything I see is in the past. It may look weird but think about it twice.

Choose a target. You want to go to the Moon. Or to the kitchen. Look at the kitchen door, which is about 5 meters from you. The door you are looking at is some micro-seconds in the past because the image of the door needed some time to reach your eyes. For simplicity, let's say the door is 5 microseconds from you (in reality it is much less). You make one step in direction of the kitchen, and the door is now at 4 microseconds from you. Another step, the door is three microseconds from you, and so on, till you reach the door, at zero microseconds from you. O.K.?

The door that you saw, the target, is not in the future. You just made a construction in your mind putting this door as your target, a meeting point in the future. But the observed object was in the past.

Everything we observe belongs to the past. Nothing observable in the future. And, what is most astonishing, nothing observable in the present.

 

I have always been fascinated with the speed of a photon. And you are so right. We see nothing in the present tense. All is in the past. Kind of cool how our brains have little problem with the short distances. Wish they worked as easily in the long ones ...

[jajrussel]

I don't believe that I have disagreed with the view of time that you present. I simply have more than one view of time. I see the door as existing in the past, and I see the door as existing in the future, and I can assume the door in the present somewhere in the middle. When I used the term in regard to me in my last post I was simply changing my point of reference.

At the moment my knowledge of relativity is somewhat limited, but I have to admit that even though I know my knowledge of relativity is limited, I have allowed myself to believe that it is okay to view the universe from different reference points. To tell the truth, I pretty much thought that relativity demanded it. Maybe I am wrong.

I don't want to shock you, but I even have a third view of time that I haven't completely thought out.

Lastly, if you were abrupt, I did not notice. If it was meant that I notice, I apologize. I can be dense sometimes.

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Actually, I worded how I see the door wrongly. How I should have worded it is.

I see the door in the past, approach it in the future, and pass through it in the present. Having done so if I want to approach the door again, I see it in the past, approach it in the future, and pass through it in the present.

[michel123456]

I hope we made an agreement, supposing that you have understood what I meant, and reversely, having understood what you meant.

 

So, the question remains: when you measure a distance, is the measurement you take upon the ABCD plane, or on the diagonal ?

It has been answered that "the distance doesn't involve time." And yes, of course, by definition, it is right. But what about the measurement of the distance?

I really don't know if the difference is clear. One thing is the distance as defined mathematically, the other is the measurement. Be careful that in science, measurement equals observational evidence.

[jajrussel]

It has become clear to me at this point that the only way the answer can be clear, is if you can find two lines on the square plane that are of different distance/length, so that you can compare them. Assuming that a diagonal is a straight line and every straight line is equal to the diagonal as you propose. All of your straight lines are equal in distance/length. The equation is above my limited talent. I made the assumption that any diagonal would equal the straight line distance/length, or be (+or-) in distance/length. I can only conclude that my assumption is wrong. I will retire to my corner and allow someone else the opportunity to solve the puzzle.

[michel123456]

It is not clear to me if we understand each other.

My intention was to make clear that in each measurement of distance, there is a part of space, and there is a part of time.

In other words, in each measurement of distance, time is included.

Here below a simple diagram to explain what I mean. Taking only points A, B, and B'. A is the observation point, B is an object, and B' is the point where the object was 2 seconds ago.(the numbers are taken only for clear understanding).

Here we are:

 

 

The measured distance is AB'. The astronomer is aware of the phenomena, and makes a correction in order to estimate the AB distance, the correct one, where B is supposed to be at present time. No problem, no mistakes.

As far as I can understand, that means that, in the AB' measurement, there is a part of the "real distance", wich is the AS segment, and a "correction part" due to the time elapsed, that is the SB' segment. So we have a "space part" and a correction "time part". We can see on the diagram that the "space part" (distance AS) is much bigger than the "time part" (the SB' distance). And really, if you had to measure a closer object , like your cup of tea, you would see that the "space part" of the measured distance is huge, about 99,999999999%, and the "time part" would be negligible, about 0.000000001%, maybe less.

Please it is time to correct me if any mistakes, because there is a development.

Edited January 6, 2010 by michel123456

[Sisyphus]

I don't understand why you're calling it a "space part" and a "time part." That is just needlessly confusing. It's a calculation of spatial distance, full stop. Yes, there is a difference between the observed location and the present location. So what?

[jajrussel]

The last diagram presented is flawed. Any statement that you make must fit within the logical statement of the diagram. The diagram shows that time is moving one direction. You then state that B' is the past position of B. The statement does not fit the logic expressed by the diagram. I know that you understand what I am saying. You can change the diagram so that it fits the statement, change the statement, or leave it like it is so everyone can see that what you are saying doesn't make sense.

When you have B going in the right direction. You will then notice that the measured distance is a portion of the actual distance, and is not the actual distance.