The Relativity of Motion: Is it Relative to the Object or the Rest Frame?

[analyst5]

As it's known, one of the most fundamental aspects of relativity is that all motion is relative.
But when we apply length contraction, in our reference frame the object that we move relative to changes, so the distance may become shorter.
So my question is, when said that motion is relative, is it meant relative to the rest frame of the object or relative to the object that we measure, with the length that it's assigned to it in our reference frame.

 

[DiracPool]

It would have helped had you framed your question on rest frames in a relatively clear manner. However, we'll try anyway.

So my question is, when said that motion is relative, is it meant relative to the rest frame of the object or relative to the object that we measure.

What is the difference? They are the same thing unless you stipulate that there is some difference, which you didn't. "You" are in your inertial or "rest" frame, and the object moving relative to you is in its (object) own inertial rest frame. You apply the Lorentz transformation for length contraction by plugging in the value of the velocity the object is moving relative to your rest frame and then you get the amount by which the object has contracted relative to your perspective.

 

[analyst5]

It would have helped had you framed your question on rest frames in a relatively clear manner. However, we'll try anyway.




What is the difference? They are the same thing unless you stipulate that there is some difference, which you didn't. "You" are in your inertial or "rest" frame, and the object moving relative to you is in its (object) own inertial rest frame. You apply the Lorentz transformation for length contraction by plugging in the value of the velocity the object is moving relative to your rest frame and then you get the amount by which the object has contracted relative to your perspective.

I'll sum up this.

a) The object in its rest frame has its proper length.
b) The object viewed from my frame is length contracted.

If I'm moving relative to it, am I moving relative to the length contracted object or the object that has its proper length? Or both? The question really cannot be formulated simplier.

 

[Dale]

The phrase "X is relative" simply means that the value of X depends on the reference frame that we choose.

If I'm moving relative to it, am I moving relative to the length contracted object or the object that has its proper length? Or both? The question really cannot be formulated simplier.

You ask the question as though you think that the length-contracted object and the proper-length object are different objects. They are not different objects, they are different ways of describing the same object.

You are moving relative to the object in any reference frame. The object's length is relative, meaning that its value depends on the reference frame.

 

[ghwellsjr]

I'll sum up this.

a) The object in its rest frame has its proper length.
b) The object viewed from my frame is length contracted.

If I'm moving relative to it, am I moving relative to the length contracted object or the object that has its proper length? Or both? The question really cannot be formulated simplier.

I guess I'm having a problem understanding why you think this question is worth asking. Help me understand. The only way I could understand why you would ask this question is if you thought the two ends of the object were traveling at different speeds which would require that the object would be stretching or contracting. Is that what you're thinking?

 

[nitsuj]

I'll sum up this.

a) The object in its rest frame has its proper length.
b) The object viewed from my frame is length contracted.

If I'm moving relative to it, am I moving relative to the length contracted object or the object that has its proper length? Or both? The question really cannot be formulated [STRIKE]simplier.[/STRIKE] more simply.

lol, there is such a thing as too simple aka vague.

anyways I think I see what you are asking. From a physical perspective you are moving relative to a (the) length contracted object. Not both because..you are moving and that contraction is the physical reality from a causation perspective. It is not "proper length" because it is in motion compared to you. ( i think motion is the only cause of length contraction in SR)

You do have to note the difference between the concepts of proper length like a meter stick held in your hands & calculated length...or length measured in an "instant". Like a meter stick flying by you at some "relativistic speed". Also note how RoS applies to the "ends" of the object (as determined by direction of motion)

 

[analyst5]

The phrase "X is relative" simply means that the value of X depends on the reference frame that we choose.You ask the question as though you think that the length-contracted object and the proper-length object are different objects. They are not different objects, they are different ways of describing the same object.

You are moving relative to the object in any reference frame. The object's length is relative, meaning that its value depends on the reference frame.

Great answer, thanks.

So is it possible that the direction of motion varies between an observer and the contracted objected or the object with its proper length?

Let me explain before the question becomes misunderstood. For instance, I am moving towards a length contracted object, as viewed from my frame. Is it possible that I am moving in some other direction relative to the object in its rest frame? Or does the relative motion of the length-contracted 'version' of the object correspond to the motion of the rest frame 'version' of the object?

Sorry for my fuzziness of words, I hope you understand my question.

 

[analyst5]

I guess I'm having a problem understanding why you think this question is worth asking. Help me understand. The only way I could understand why you would ask this question is if you thought the two ends of the object were traveling at different speeds which would require that the object would be stretching or contracting. Is that what you're thinking?

I already wrote why I asked it, the only thing on my mind was basically the question 'does length contraction affect the properties of the motion of an object, direction or something else'.
For instance the object may be closer to us in our frame than in some other, and I'm wondering can this affect the motion in some way.

 

[Nugatory]

I am moving towards a length contracted object, as viewed from my frame. Is it possible that I am moving in some other direction relative to the object in its rest frame? Or does the relative motion of the length-contracted 'version' of the object correspond to the motion of the rest frame 'version' of the object?

If you are moving at velocity v, as measured in an inertial frame in which I am at rest, then I am necessarily moving at a velocity -v as measured in an inertial frame in which you are at rest. Same speed, opposite direction.

Example: I'm standing by the side of the road watching you in a car drive by, traveling due east at 100 km/hr. If you choose to consider yourself and the cart be at rest, you'll say that I and the scenery are moving due west at 100 km/hr.

 

[ghwellsjr]

Great answer, thanks.

So is it possible that the direction of motion varies between an observer and the contracted objected or the object with its proper length?

Let me explain before the question becomes misunderstood. For instance, I am moving towards a length contracted object, as viewed from my frame. Is it possible that I am moving in some other direction relative to the object in its rest frame? Or does the relative motion of the length-contracted 'version' of the object correspond to the motion of the rest frame 'version' of the object?

Sorry for my fuzziness of words, I hope you understand my question.

I still cannot understand your concerns because you are not following the advice I gave you in your other thread. Pick one frame. Describe the motions of all object/observers. Then if you want to switch to a different frame, use the Lorentz Transformation. There will be no confusion if you do it that way.

In this post, you said that you are moving in your own frame. What does that mean?

It's real simple. Objects that are moving in a frame are length contracted. Pick another frame that is moving with respect to the original one and the motions of all object can change. They can change to a new direction. They can change to a new speed. Some may be at rest. The ones that are at rest are not length contracted. The ones that are moving are length contracted along their direction of motion. The faster their speed, the more the contraction.

I showed you some of these concepts in your first thread and in the thread that was linked to in that thread. You haven't put closure on our first thread. Are you going to keep starting new threads ignoring the answers that you have been given just like Durant did in that linked thread and got himself banned?

 

[Nugatory]

Let me explain before the question becomes misunderstood. For instance, I am moving towards a length contracted object, as viewed from my frame.

You'll hear people saying "my frame", "his frame", "the frame of <something>" all the time. You have to be a bit careful with that terminology - we use it because it's convenient, but it's not very precise. Usually when someone says "my frame" they mean "a frame in which I am at rest" and it's no more specially theirs than any other frame.

 

[analyst5]

I still cannot understand your concerns because you are not following the advice I gave you in your other thread. Pick one frame. Describe the motions of all object/observers. Then if you want to switch to a different frame, use the Lorentz Transformation. There will be no confusion if you do it that way.

In this post, you said that you are moving in your own frame. What does that mean?

It's real simple. Objects that are moving in a frame are length contracted. Pick another frame that is moving with respect to the original one and the motions of all object can change. They can change to a new direction. They can change to a new speed. Some may be at rest. The ones that are at rest are not length contracted. The ones that are moving are length contracted along their direction of motion. The faster their speed, the more the contraction.

I showed you some of these concepts in your first thread and in the thread that was linked to in that thread. You haven't put closure on our first thread. Are you going to keep starting new threads ignoring the answers that you have been given just like Durant did in that linked thread and got himself banned?

I don't understand why you criticize somebody who's just joined this forum and who has little knowledge to this? Have you every wondered that your method of showing things is wrong? Dale Spam gave me a perfectly clear and straight-forward answer in his post while you keep telling me to do stuff that you know, but I'm not good at them and I need more time to understand. You talk about constructing space time diagrams, while I talk about a completely different approach on this which for some reason isn't a good one and you keep 'being angry' at me for reason. I mean, you keep talking about these mind-boggling concepts like everybody's familiar with them and then criticize me for not following your advices for which I have no knowledge to begin with. It seems to me that you don't know how to show something with an example, or by a definition, which is what I asked for.

 

[analyst5]

If you are moving at velocity v, as measured in an inertial frame in which I am at rest, then I am necessarily moving at a velocity -v as measured in an inertial frame in which you are at rest. Same speed, opposite direction.

Example: I'm standing by the side of the road watching you in a car drive by, traveling due east at 100 km/hr. If you choose to consider yourself and the cart be at rest, you'll say that I and the scenery are moving due west at 100 km/hr.

So, basically if I'm moving away from you as viewed from a frame in which I'm at rest, you're moving away from me in a frame at which you're at rest. This has nothing to do with length contraction, right? And all observers will agree upon relative motions of two bodies relative to one another?

 

[ghwellsjr]

I already wrote why I asked it, the only thing on my mind was basically the question 'does length contraction affect the properties of the motion of an object, direction or something else'.
For instance the object may be closer to us in our frame than in some other, and I'm wondering can this affect the motion in some way.

Does length contraction affect motion? No. Motion of an object in a frame results in length contraction of that object. Transform to a different frame and you can get a different motion and a different length contraction. Is that such a hard concept?

Are you thinking that transforming to different frames causes measurable, observable or otherwise noticeable differences in objects? I showed you in the link in your other thread that that is not the case. Did you read it? Are you just going to ignore my help? Are you not going to respond in your other thread?

Again, for the umpteenth time, let the Lorentz Transformation answer these question for you. Define a scenario according to an Inertial Reference Frame (IRF) and draw a diagram, like I did in your other thread. Then transform to another IRF and draw another diagram, like I did in your other thread. Look at the diagrams. See the Length Contraction. It's so easy. Why do you refuse to accept the answer provided by Special Relativity?

 

[ghwellsjr]

So, basically if I'm moving away from you as viewed from a frame in which I'm at rest, you're moving away from me in a frame at which you're at rest. This has nothing to do with length contraction, right? And all observers will agree upon relative motions of two bodies relative to one another?

How can you move in a frame in which you are at rest?

 

[analyst5]

How can you move in a frame in which you are at rest?

Lapsus. I meant if an object is moving away from me viewed from my frame.

 

[analyst5]

Again, for the umpteenth time, let the Lorentz Transformation answer these question for you. Define a scenario according to an Inertial Reference Frame (IRF) and draw a diagram, like I did in your other thread. Then transform to another IRF and draw another diagram, like I did in your other thread. Look at the diagrams. See the Length Contraction. It's so easy. Why do you refuse to accept the answer provided by Special Relativity?

I don't refuse them, in fact I want them. But I believe that I'll be able to learn much easier through examples like the Einstein's train, and then relate it to Lorentz Transformations to completely grasp the concept. Imagine if you were me and somebody offers you to do maths that's mind boggling for you. It's not so easy for me as it is for you. :/

 

[analyst5]

Ghwellsjr, may I ask you another question that seeks a straight-forward answer?
The object that we have in our frame gets length contracted if it's moving, but can we consider that the object in our frame is not the same object as the one in its rest frame?

By this I mean, do we always have a 'cross-sectional object' in a moving frame, that is composed of future and past points of the object as viewed from its rest frame? I hope you understand my question.

 

[ghwellsjr]

Ghwellsjr, may I ask you another question that seeks a straight-forward answer?
The object that we have in our frame gets length contracted if it's moving, but can we consider that the object in our frame is not the same object as the one in its rest frame?

By this I mean, do we always have a 'cross-sectional object' in a moving frame, that is composed of future and past points of the object as viewed from its rest frame? I hope you understand my question.

No, I don't understand your question.

 

[ghwellsjr]

I don't refuse them, in fact I want them. But I believe that I'll be able to learn much easier through examples like the Einstein's train, and then relate it to Lorentz Transformations to completely grasp the concept. Imagine if you were me and somebody offers you to do maths that's mind boggling for you. It's not so easy for me as it is for you. :/

I think I used to be just like you trying to understand Length Contraction and Time Dilation in isolation until Dalespam finally convinced me to always use the Lorentz Transformation and then it took me a long time before I started drawing diagrams and now I have written a computer program to make it trivial. So if you specify an in-line scenario according to an IRF, I will draw it along with any additional transformed IRF's, within reason, you desire. Deal?

But you should at least do the math for a couple events, just to convince yourself that the process is legitimate.

 

[Dale]

So is it possible that the direction of motion varies between an observer and the contracted objected or the object with its proper length?

Direction of motion is indeed frame variant (or relative). It definitely varies from frame to frame.

, I am moving towards a length contracted object, as viewed from my frame

This is not possible. By definition you are not moving in your frame. However, again, direction of motion is frame variant, so in other frames related statements can be made.

 

[analyst5]

Direction of motion is indeed frame variant (or relative). It definitely varies from frame to frame.


This is not possible. By definition you are not moving in your frame. However, again, direction of motion is frame variant, so in other frames related statements can be made.

Yes, yes, I understand the second sentence, I wrote the stuff I didn't mean.

So when we have a physical object that is moving in our plane of simultaneity, is it true that this object is always composed of past and future parts of the object viewed from its rest frame?
That's what I mean by the previous question ghwellsjr. For instance, when I'm at rest with respect to my desk I will have all of its points simultaneously in my plane of simultaneity. But if I'm moving with respect to it, I will have the cross-sectional desk, which is composed of past and future small parts of the desk in its rest frame. Is this true, or at least close to being true?

 

[analyst5]

I think I used to be just like you trying to understand Length Contraction and Time Dilation in isolation until Dalespam finally convinced me to always use the Lorentz Transformation and then it took me a long time before I started drawing diagrams and now I have written a computer program to make it trivial. So if you specify an in-line scenario according to an IRF, I will draw it along with any additional transformed IRF's, within reason, you desire. Deal?

But you should at least do the math for a couple events, just to convince yourself that the process is legitimate.

That's fair enough, I will contact you if another specific scenario comes to my mind, thanks for the offer. But first I think it's smarter that I get used to the fundamental concepts of SR and relate them to concrete examples and then analyze the diagrams to make things completely clear...

 

[Nugatory]

So, basically if [STRIKE]I'm moving away from you[/STRIKE] you're moving away from me as viewed from a frame in which I'm at rest, [STRIKE]you're moving away from me[/STRIKE] I'm moving away from you in a frame at which you're at rest. This has nothing to do with length contraction, right?

right (aside from the corrections above which I made based on your later "lapsus" post)

And all observers will agree upon relative motions of two bodies relative to one another?

All observers will agree that my velocity relative to you is the negative (same speed, opposite direction) of your velocity relative to me.

All observers, if asked to calculate what you measure to be my velocity relative to you or vice versa, will agree about the results and will agree that they're the same speed in the exact opposite directions.

However a third observer moving relative to both of us may not measure the same speed between us as you or I measure. For example: there is an observer (who is, of course, at rest relative to himself). I'm moving towards him from one side at .6c, you're moving towards him from the other side at .6c, he sees the distance between us shrinking at 1.2c. However, you and I do not see us approaching each other at 1.2c, we measure a relative speed of $\frac{15}{16}c$ - google for "relativistic velocity addition" to see why.

 

[bahamagreen]

Ghwellsjr, may I ask you another question that seeks a straight-forward answer?
The object that we have in our frame gets length contracted if it's moving, but can we consider that the object in our frame is not the same object as the one in its rest frame?

By this I mean, do we always have a 'cross-sectional object' in a moving frame, that is composed of future and past points of the object as viewed from its rest frame? I hope you understand my question.

Even if you and the distant object are at rest, your image of that object is composed of time differing parts - the most distant parts of the object are older than the closer parts. So your image of the object has an apparent mapping of simultaneity that is different than the object's own self mapping. But from your perspective, these inferred variations of the object's simultaneity (object's local time of emissions) are variations in the object's past; some ahead or behind each other, but none in the object's future, all in the object's past.

I'm not sure what that is called.

Relative motion will cause a geometric distortion of apparent length because of the same variation in time of emission travel with distance to source, but now combined with moving sources, so the more distant end of the moving object is showing you an earlier and older (not as far time advanced) position as compared to the closer end of the object which is showing a later newer more recent position.

I think this is called relativistic Doppler; it is taken into account and not part of the Lorentz contraction.

 

[analyst5]

Even if you and the distant object are at rest, your image of that object is composed of time differing parts - the most distant parts of the object are older than the closer parts. So your image of the object has an apparent mapping of simultaneity that is different than the object's own self mapping. But from your perspective, these inferred variations of the object's simultaneity (object's local time of emissions) are variations in the object's past; some ahead or behind each other, but none in the object's future, all in the object's past.

I'm not sure what that is called.

Relative motion will cause a geometric distortion of apparent length because of the same variation in time of emission travel with distance to source, but now combined with moving sources, so the more distant end of the moving object is showing you an earlier and older (not as far time advanced) position as compared to the closer end of the object which is showing a later newer more recent position.

I think this is called relativistic Doppler; it is taken into account and not part of the Lorentz contraction.

Hey bahamagreen, thanks for the reply.

I understand that while perceiving something the distant parts are actually always earlier than the closer ones due to the time light needs to travel to our senses. What I actually mean is does the same effect occur in motion, but regarding that what cannot be seen in the present moment, the events that occur in our plane of simultaneity. So while at rest with the object we consider the object to be all of its points existing simultaneously. But when moving, does this affect the plane of simultaneity in a way that our original object is now composed of future and past points of its worldtube?

 

[Dale]

So when we have a physical object that is moving in our plane of simultaneity, is it true that this object is always composed of past and future parts of the object viewed from its rest frame?

Yes, simultaneity is relative. Different frames disagree about which events are simultaneous.

Note that causality is not relative, it is absolute. So, while different frames may disagree about whether or not two things happen at the same time, all frames will agree if one thing caused another. The universe cares about causality, not simultaneity.

 

[analyst5]

Yes, simultaneity is relative. Different frames disagree about which events are simultaneous.

Note that causality is not relative, it is absolute. So, while different frames may disagree about whether or not two things happen at the same time, all frames will agree if one thing caused another. The universe cares about causality, not simultaneity.

When stated like that it seems real simple, but actually this disagreement about simultaneity does the same thing as the change of length from a reference frame, it makes observers disagree about the versions of the object.

In different reference systems the object will be composed of different particles on the worldtube of the object, right? So again, what is valid to say:

I'm moving relative to A (the object viewed from its rest frame)
I'm moving relative to A' (the object viewed from our frame, composed of future and past particles relative to the particular segment of its worldtube).

 

[Dale]

When stated like that it seems real simple

It is that simple. I don't understand the desire to add unnecessary confusion to something that is, at its core, fundamentally simple, as you stated.

it makes observers disagree about the versions of the object.

No. Observers give different descriptions of the same object.

Have you ever read the poem about the blind men describing the elephant? None of the descriptions were wrong, but none were complete either. There are not different versions of elephants in the poem any more than there are different versions of the object in relativity.

 

[analyst5]

It is that simple. I don't understand the desire to add unnecessary confusion to something that is, at its core, fundamentally simple, as you stated.

No. Observers give different descriptions of the same object.

Have you ever read the poem about the blind men describing the elephant? None of the descriptions were wrong, but none were complete either. There are not different versions of elephants in the poem any more than there are different versions of the object in relativity.

I did :)
You're right about adding confusion, it seems that it isn't so hard to understand. The biggest conceptual obstacle for me here is to understand whether the different description of the object relative to frames (composition, length) changes anything in sense of its motion, its status as an intertial frame and that kind of stuff.
Thanks for the good answer DaleSpam.

 

[nitsuj]

Hey bahamagreen, thanks for the reply.

So while at rest with the object we consider the object to be all of its points existing simultaneously. But when moving, does this affect the plane of simultaneity in a way that our original object is now composed of future and past points of its worldtube?

Wow what a clear perspective! Actually never pictured the "Length is a plane of simultaneity" AND length contraction. For me it makes length contraction very clear. The (weak?) analogy being this 2D image. Thinking of the pencil as a continuous plane of simultaneity in comparison to the plane of simultaneity of the image itself; and its length contracting dimensional rotation; as opposed to measuring its proper length in the two dimensional image. In other words the third dimension we can envision here as depth is replaced with the temporal dimension, and only with respect to the pencil and x / y orientation of the image of course

 

[ghwellsjr]

So when we have a physical object that is moving in our plane of simultaneity, is it true that this object is always composed of past and future parts of the object viewed from its rest frame?
That's what I mean by the previous question ghwellsjr. For instance, when I'm at rest with respect to my desk I will have all of its points simultaneously in my plane of simultaneity. But if I'm moving with respect to it, I will have the cross-sectional desk, which is composed of past and future small parts of the desk in its rest frame. Is this true, or at least close to being true?

I'm wondering about the motivation of your question. Here is a spacetime diagram of an object (like a desk) that is 10 feet long and stationary in an Inertial Reference Frame. One end is represented in blue and the other end in red:

Now we will transform to an IRF moving at -0.6c with respect to the original IRF:

I'm wondering if you are seeing events that used to be simultaneous in the first IRF are now at different times in the second IRF and giving you the impression that they are a combination of past and future events?

 

[analyst5]

I'm wondering about the motivation of your question. Here is a spacetime diagram of an object (like a desk) that is 10 feet long and stationary in an Inertial Reference Frame. One end is represented in blue and the other end in red:

Now we will transform to an IRF moving at -0.6c with respect to the original IRF:

I'm wondering if you are seeing events that used to be simultaneous in the first IRF are now at different times in the second IRF and giving you the impression that they are a combination of past and future events?

That's what I was going for, thanks. So when moving in our plane of simultaneity we have an object composed of past and future particles relative to the 'descripiton' of the object in its rest frame, that also gets length contracted?

 

[analyst5]

And btw, it can be concluded that distance plays a big role in the judgement of simultaneity. For moving observers, the greater distance in space is from an event, the distant the event is in time, right?

 

[Dale]

The biggest conceptual obstacle for me here is to understand whether the different description of the object relative to frames (composition, length) changes anything in sense of its motion, its status as an intertial frame and that kind of stuff

Do you feel you have overcome those conceptual obstacles, or do you still have questions?

Thanks for the good answer DaleSpam.

You are very welcome.