# Motion relative to what?

1. Jul 4, 2013

### analyst5

As it's known, one of the most fundamental aspects of relativity is that all motion is relative.
But when we apply lenght 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.

2. Jul 4, 2013

### DiracPool

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.

3. Jul 4, 2013

### analyst5

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.

4. Jul 4, 2013

### Staff: Mentor

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.

5. Jul 4, 2013

### ghwellsjr

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?

6. Jul 4, 2013

### nitsuj

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)

Last edited: Jul 4, 2013
7. Jul 4, 2013

### analyst5

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.

8. Jul 4, 2013

### analyst5

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.

9. Jul 4, 2013

### Staff: Mentor

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.

10. Jul 4, 2013

### ghwellsjr

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?

11. Jul 4, 2013

### Staff: Mentor

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.

12. Jul 4, 2013

### analyst5

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.

13. Jul 4, 2013

### analyst5

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?

14. Jul 4, 2013

### ghwellsjr

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?

15. Jul 4, 2013

### ghwellsjr

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

16. Jul 4, 2013

### analyst5

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

17. Jul 4, 2013

### analyst5

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. :/

18. Jul 4, 2013

### 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.

19. Jul 4, 2013

### ghwellsjr

No, I don't understand your question.

20. Jul 4, 2013

### ghwellsjr

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.

21. Jul 4, 2013

### Staff: Mentor

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.

22. Jul 4, 2013

### analyst5

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?

23. Jul 4, 2013

### analyst5

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...

24. Jul 4, 2013

### Staff: Mentor

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

25. Jul 5, 2013

### bahamagreen

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.