I Question about length contraction

[SiennaTheGr8]

Just to explicitly state a fundamental point (not sure if this is the source of confusion here):

Two observers with different rest frames can assign the same spacetime coordinates to ONE event. By convention we choose this event so that it has coordinates (x,t) = (0,0) for both frames (i.e., both frames label it the origin event), because that makes the math easier. Then the observers will disagree on the spacetime coordinates of every other event. For a given frame, the x-coordinate of an event represents the spatial location of that event relative to the origin event (negative value would just mean it's in the direction we define as negative), while the t-coordinate of the event represents the time at which that event occurred relative to the origin event (negative value would just mean that it happened before the origin event).

Maybe that helps? (I'm in a hurry and don't have time to proofread really, so sorry if this was word salad.)

 

[SiennaTheGr8]

(And I was specifically talking about the case of 1 spatial dimension. In the general 3+1D case, the observers agree not only on the spacetime coordinates of the origin event, but also on the coordinates of all events that occur simultaneously with the origin event in the plane that's perpendicular to the frames' axis of relative motion.)

 

[SiennaTheGr8]

(I think.)

 

[A.T.]

Time dilation works differently. It only applies to my comparison of your reference to mine...

I don't see the difference.
Time dilation relates durations measured in different frames.
Length contraction relates lengths measured in different frames.

 

[Nathan123]

Just to explicitly state a fundamental point (not sure if this is the source of confusion here):

Two observers with different rest frames can assign the same spacetime coordinates to ONE event. By convention we choose this event so that it has coordinates (x,t) = (0,0) for both frames (i.e., both frames label it the origin event), because that makes the math easier. Then the observers will disagree on the spacetime coordinates of every other event. For a given frame, the x-coordinate of an event represents the spatial location of that event relative to the origin event (negative value would just mean it's in the direction we define as negative), while the t-coordinate of the event represents the time at which that event occurred relative to the origin event (negative value would just mean that it happened before the origin event).

Maybe that helps? (I'm in a hurry and don't have time to proofread really, so sorry if this was word salad.)

Thanks for explaining the coordinates.

 

[PeterDonis]

I still don't understand what exactly is the meaning of the coordinate -.75.

Then my advice is to ignore most of what I posted about it, and just keep this in mind:

If what you really mean is to ask, what is the meaning of the spatial coordinate $x' = - 0.75$ for event E, in the ship frame? then here is the answer: it has no special meaning in the ship frame, given that we've picked event A as the "starting event" for the ship.

In other words, in the scenario as you posed it and as you are thinking about it, the spatial coordinate $x' = - 0.75$ of event E in the ship frame is just a distraction; it doesn't mean anything useful, and you should just ignore it.

 

[Nathan123]

I don't see the difference.
Time dilation relates durations measured in different frames.
Length contraction relates lengths measured in different frames.

Going back first to math of PeterDonis, I still think that it explains 1 and 2 and not 3 and 4.

I will try to explain here how I see length contraction working very differently than time dillation, which is the basis of this whole thread.

The only reason there is time dilation is because we are comparing one frame of reference to another. If A sees B moving and B sees B not moving, A will say that Bs time slows down.
So
1. Only A = no time dilation
2. A comparing B sees time dilation for B
3. Only B = no time dilation
4. B comparing A sees time dilation for ALength contraction from everything I have read and seen works differently.

Here anything you see moving, you will see it contracted.

So if you see a ship moving, only the ship gets contracted. If you are in a car and everything is moving towards you then everything gets contracted.

So
1. A (on earth) has no distance contraction between ship and earth.
2. A comparing B will say that B has distance contraction between ship and Earth because B sees everything moving.
3. B (on ship) will have distance contraction between ship and Earth because it sees everything moving.
4. B comparing A will not have distance contraction for A because A doesn't see eveything moving.
So time dilation is 2 and 4 and length contraction is 2 and 3.
And this is causing me issues that the ship reaching Earth coinside for 1 and 2 but diverge for 3 and 4.

 

[SiennaTheGr8]

I know you're trying to be clear, @Nathan123, but it's difficult to follow what you're writing.

In any case, the distinction between "distance" and "length" is an important one in this context. I suggest carefully reading and re-reading PeroK's post above.

Here's a relevant video (note what he says about length contraction and time dilation not really being two sides of the same coin):

 

[A.T.]

The only reason there is time dilation is because we are comparing one frame of reference to another.

Correct.

Length contraction from everything I have read and seen works differently.

It works exactly analogous. You are comparing lengths measured in two different frames.

Here anything you see moving, you will see it contracted. So if you see a ship moving, only the ship gets contracted.

Contracted compared to its proper length measured in its rest frame. So you are again relating measurements in two different frames (its rest frame, and the frame where it moves).

 

[PeterDonis]

I will try to explain here how I see length contraction working very differently than time dillation

You are failing to take heed of what I said before:

your understanding has to start with the understanding that you are the one who is making a mistake here.

You should not be trying to explain how you see it. You should be discarding how you see it, and trying to learn how everyone else sees it, since your way of seeing it is wrong and ours is right.

Length contraction from everything I have read and seen works differently.

No, it doesn't. Take this:

So
1. Only A = no time dilation
2. A comparing B sees time dilation for B
3. Only B = no time dilation
4. B comparing A sees time dilation for A

And substitute "length contraction" for "time dilation" and you will have four statements about length contraction that are just as valid as the four statements you make here about time dilation. They work the same.

Here anything you see moving, you will see it contracted.

Substitute "time dilated" for "length contracted" here and you will have a true statement about time dilation. They work the same.

if you see a ship moving, only the ship gets contracted

Because only the ship is moving; you have specified, implicitly, that everything else is at rest relative to you. So, again, substitute "time dilated" for "length contracted", and you will have a true statement about time dilation: if the ship is the only thing moving, it is the only thing that gets time dilated, relative to you.

If you are in a car and everything is moving towards you then everything gets contracted.

Why switch from ship to car here? If you are in the ship--that, above, you said was the only thing moving relative to you before--then you have switched yourself to the ship frame, in which, now, the ship is the only thing that is not moving. So of course everything else will get length contracted relative to you. But, again, substitute "time dilated" for "length contracted" here and you will have a true statement about time dilation: everything else will get time dilated relative to you. The two work the same.

1. A (on earth) has no distance contraction between ship and earth.

You are confusing yourself here because you are thinking of "distance" as a single object, and asking yourself whether that object is "length contracted" or not. That's not the right way to look at it. The "distance between the ship and earth" depends on which event you pick as the "starting point" for the ship, and which frame you use. In other words, the "distance" in different frames is a distance between different pairs of events.

In terms of my post #37, in the Earth frame, the distance between the ship and Earth (when the ship starts) is the distance between events A and E. But in the ship frame, the distance between the ship and Earth (when the Earth starts, since in this frame the Earth is what moves) is the distance between events A and C. So there is no one "object" that corresponds to "the distance between the ship and Earth". That ordinary language term refers to different objects--different curves in spacetime--in different frames. This is a key reason why trying to reason about all this in ordinary language is not a good idea.

2. A comparing B will say that B has distance contraction between ship and Earth because B sees everything moving

3. B (on ship) will have distance contraction between ship and Earth because it sees everything moving.

4. B comparing A will not have distance contraction for A because A doesn't see eveything moving.

Your language is very muddled here, and you are confusing yourself with this muddled language. Read my paragraph just above for a better way to look at it.

So time dilation is 2 and 4 and length contraction is 2 and 3.

I have no idea what you mean by this. None of your 1., 2., 3., 4. mention time dilation at all. You are confusing yourself with muddled language.

this is causing me issues that the ship reaching Earth coinside for 1 and 2 but diverge for 3 and 4.

Your analysis is so confused at this point that I can't figure out how you are drawing this conclusion. But however you are doing it, it's wrong.

 

[Nathan123]

You are failing to take heed of what I said before:
You should not be trying to explain how you see it. You should be discarding how you see it, and trying to learn how everyone else sees it, since your way of seeing it is wrong and ours is right.
No, it doesn't. Take this:
And substitute "length contraction" for "time dilation" and you will have four statements about length contraction that are just as valid as the four statements you make here about time dilation. They work the same.
Substitute "time dilated" for "length contracted" here and you will have a true statement about time dilation. They work the same.
Because only the ship is moving; you have specified, implicitly, that everything else is at rest relative to you. So, again, substitute "time dilated" for "length contracted", and you will have a true statement about time dilation: if the ship is the only thing moving, it is the only thing that gets time dilated, relative to you.
Why switch from ship to car here? If you are in the ship--that, above, you said was the only thing moving relative to you before--then you have switched yourself to the ship frame, in which, now, the ship is the only thing that is not moving. So of course everything else will get length contracted relative to you. But, again, substitute "time dilated" for "length contracted" here and you will have a true statement about time dilation: everything else will get time dilated relative to you. The two work the same.
You are confusing yourself here because you are thinking of "distance" as a single object, and asking yourself whether that object is "length contracted" or not. That's not the right way to look at it. The "distance between the ship and earth" depends on which event you pick as the "starting point" for the ship, and which frame you use. In other words, the "distance" in different frames is a distance between different pairs of events.

In terms of my post #37, in the Earth frame, the distance between the ship and Earth (when the ship starts) is the distance between events A and E. But in the ship frame, the distance between the ship and Earth (when the Earth starts, since in this frame the Earth is what moves) is the distance between events A and C. So there is no one "object" that corresponds to "the distance between the ship and Earth". That ordinary language term refers to different objects--different curves in spacetime--in different frames. This is a key reason why trying to reason about all this in ordinary language is not a good idea.
Your language is very muddled here, and you are confusing yourself with this muddled language. Read my paragraph just above for a better way to look at it.
I have no idea what you mean by this. None of your 1., 2., 3., 4. mention time dilation at all. You are confusing yourself with muddled language.
Your analysis is so confused at this point that I can't figure out how you are drawing this conclusion. But however you are doing it, it's wrong.

Thanks for your help. But we will have to close this. Some of the points being made are currently beyond what I have learned about SR, and some of the points I am making are not comming across. So it makes no sense to take this further.

One parting point to think about. If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena. This is not analogous to time dilation where I need to include a second frame of reference. This is the basis for the difference I was trying to offer. I may be wrong about what I said, but I am not sure.

 

[PeterDonis]

we will have to close this.

Fair enough. A note for the future, though: there is no need to quote an entire post; that just clutters up the thread. Just quote the particular things you are responding to (highlight it and click either the "quote" or "reply" button that pops up--the latter is what I usually use, as it pastes the quote directly into the edit box for adding a new post). If your response is just a general one, as your last post was, you don't really need to quote anything.

 

[jbriggs444]

One parting point to think about. If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena. This is not analogous to time dilation where I need to include a second frame of reference.

One needs two frames either way. An object's rest frame where the proper length or proper time is measured and an observer's frame where a different coordinate length or coordinate time is measured.

[If one takes a parting shot in a "let's close this" message, fair play allows for responses]

 

[Mentz114]

Thanks for your help. But we will have to close this. Some of the points being made are currently beyond what I have learned about SR, and some of the points I am making are not comming across. So it makes no sense to take this further.

One parting point to think about. If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomenon. This is not analogous to time dilation where I need to include a second frame of reference. This is the basis for the difference I was trying to offer. I may be wrong about what I said, but I am not sure.

That is a strange thing to say. What can you mean ? The thing you are observing also has a rest frame whether you 'need' it or not.

 

[A.T.]

If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena.

Length contraction is not about what you "see". It's about relating length measurements in two frames, the second frame being the rest frame of the object.

 

[Janus]

Thanks for your help. But we will have to close this. Some of the points being made are currently beyond what I have learned about SR, and some of the points I am making are not comming across. So it makes no sense to take this further.

One parting point to think about. If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena. This is not analogous to time dilation where I need to include a second frame of reference. This is the basis for the difference I was trying to offer. I may be wrong about what I said, but I am not sure.

I know that you have decided to drop things here, but I'm going to add one more post anyway. (mainly because I went to the trouble of creating the following animations, and I don't want to feel like I wasted my time entirely.)

We have the Earth (blue sphere) and the ship (green cone). The white lines are 6/10 of a light year apart as measured by the Earth. Both Earth and ship have a clock, and I've added a third clock at the right white line.
In the first animation, we show events according to the Earth rest frame. As the nose of the ship touches the right line, its clock reads zero, as does both the Earth clock and the right line clock. (I paused the animation here so make this clear)
The ship moves from right to left at 0.6c.
This takes 1 yr in this frame as shown by the times ticking off on the Earth and right line clocks. The ship clock is time dilated, ticks 0.8 as fast, and thus reads 0.8 years upon reaching Earth. The animation is paused again before repeating so the final clock values can be easily noted.

The same events according to the ship:
Now it is the Earth, and right line moving to the left. The ship still starts at the right line, reading zero, while the clock at the right line also reads zero.
The right line and Earth are however now 0.8 x .6 = 0.48 ly apart. At 0.6 c, it will take 0.8 yrs for the Earth to reach the ship, and thus the ship clock reads 0.8 yrs when they meet.
During that time, the ship will measure both the Earth and right line clocks as ticking at a rate of 0.8 as fast as his own, and accumulating 0.8 x 0.8 = 0.64 yr. (if the right line didn't leave the animation, you would see it reading 0.64 yr when the Earth reaches the ship.) Even though the Earth clock only accumulates 0.64 yr between the time the right line leaves the ship's vicinity and the Earth arrives, its clock still reads 1 yr upon arrival. This because, due to the relativity of simultaneity, It does not read 0 when the ship and right line are adjacent to each other, but already reads 0.36 yrs.
In the Earth rest frame, the events of the Earth clock reading zero and the right line clock reading zero are simultaneous, while in the rest frame of the ship, they are not. The Earth clock reads 0.36 yr ahead of the right line clock.*

* we will assume that the ship and Earth had a constant 0.6c relative velocity even before the events shown here. In other words, in the Earth frame, the ship comes in from the right edge of the animation at 0.6 c, and then starts its clock from zero when it passes the right line. The Earth clock also starts running from zero at this moment according to this frame. In the ship frame, the ship still starts its clock from zero when passing the right line, but the Earth clock will have already been running, having started at zero some time before that moment.

 

[Ibix]

One parting point to think about. If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena.

Contracted compared to what? Its length in its rest frame, of course. Even your question assumes the existence of a second frame of reference.

 

[PeterDonis]

If i see something moving, I will see it contracted. I do not need a second frame of reference for this phenomena. This is not analogous to time dilation where I need to include a second frame of reference.

Bzzt! Wrong again. You do not need a second frame of reference to see an object moving relative to you as time dilated. Again, take the first three sentences of this quote, replace "length contracted" with "time dilated", and you have a true statement about time dilation. They both work the same.

How many times am I going to have to make this point before you grasp it?

 

[Nathan123]

Contracted compared to what? Its length in its rest frame, of course. Even your question assumes the existence of a second frame of reference.

Yes compared to its rest frame, but I don't need to consider that it is now resting (for itself) in order for me to have its length contracted from its rest frame. Time dilation needs me to consider that the second frame is now at rest for itself.

 

[PeterDonis]

I don't need to consider that it is now resting (for itself) in order for me to have its length contracted from its rest frame. Time dilation needs me to consider that the second frame is now at rest for itself.

Wrong again. If you insist that you need to consider a "rest frame" for the object for time dilation, then you also do for length contraction; if a rest frame is needed to define the "rest" rate of the object's clock ticking, then it is also needed to define the "rest" length of the object. The two work the same.

At this point further discussion is futile because you are continuing to repeat your incorrect understanding without even attempting to address the repeated corrections you have been given. And this even after you have admitted that a lot of what is being discussed is beyond your current level of understanding of SR.

Thread closed.

 

[PeterDonis]

some of the points I am making are not comming across

One final note: you are misstating this. We all understand the points you are making; but we also know they are wrong. That's why we are disagreeing with you.

Once more: you need to understand that you are the one making a mistake here. You don't need to explain to us how you look at these things. You need to unlearn your way of looking at them and learn the correct way. If you can't or won't take the time to do that, future threads of yours on this topic are likely to be short-lived. We have given you every chance in this thread to improve your understanding; trying to rehash these points in future threads will not be viewed favorably.

I may be wrong about what I said, but I am not sure.

We are sure. You are wrong.

 

[Nugatory]

@Nathan123
Best thing you can do: get hold of a copy of Taylor and Wheeler's book "Spacetime Physics" and work carefully through it.