# The Peripatetic Albert, Round 3

1. Sep 16, 2004

### OneEye

...And so, I was driving north from McPherson toward Salina, explaining Special Relativity to my wife and oldest daughter (and however many of the other children were actually listening). As I did so, I used our Suburban as an example, explaining how that, in the absence of any absolute coordinate system, there was no real way to tell whether the Suburban was moving over the road, or the road was moving under the Suburban.

About that time, we turned onto the highway - and I realized that, I had either used the steering wheel to turn the car in relation to the earth, or I had used the steering wheel to turn the earth in relation to the car - and that, motion being purely relative, either could be as true as the other.

Now, here was a remarkable fact: Assuming the car to be at rest (which Special Relativity requires me to be able to do), it seems that I was actually able to change the orientation of the entire earth simply by turning the steering wheel!

Now, that's power steering!

How does Special Relativity explain this curiousity?

Last edited by a moderator: Sep 16, 2004
2. Sep 16, 2004

### humanino

That does not seem to be a paradox to me : when you turn, you are not an inertial observer anymore ! You have been accelerated.

3. Sep 16, 2004

### humanino

Sometimes when I walk, I like to think I am having to Earth roll under my feet :shy:

4. Sep 16, 2004

### geometer

Actually, you left out a critical detail. If you were undergoing completely unaccelerated motion, there is no experiment that will tell you whether you are moving or the earth is moving in your example. However, in a car, it's just about impossible to be completely unacclerated; bumps are acclerations, the swaying of the car is an acceleration, obviously, even minute changes in your speed are accelerations.

5. Sep 16, 2004

### OneEye

Okay, then...

How does GR explain this?

(I can't help but think that we've missed the point, though. Essentially, we see what appears to be a blatant abrogation of fundamental laws - the energy required to change the earth's direction is many orders of magnitude greater than the energy required to change the car's direction - so how can we say that the principle of relativity is upheld in this scenario? I don't think that promoting the problem to a GR question helps this observation. Further, I have heard several board members, much more knowledgeable than me, make SR analyses of non-linear circumstances not unlike this. But if we are going to say that "SR only applies to straight-line motion," then fine. In that case, I welcome a GR explanation.)

6. Sep 16, 2004

### humanino

What is wrong with this ?
I don't think
has any relevance for the problem. However, the whole thing looks solved to me by the previous one.

7. Sep 16, 2004

### humanino

Contrary to you, the Earth has not been accelerated ! Besides, you would have to change the direction of the entire Universe :surprised

8. Sep 16, 2004

### OneEye

But this is exactly my point: What reason have I to believe that it is I, not the earth, which has been accelerated - other than resorting to classical mechanics? Observationally, by the principle of relativity, neither idea should have any advantage over the other. Is it me moving, or the earth, or the entire universe? Why would one observational perspective have any advantage over another?

9. Sep 16, 2004

### humanino

No, you can measure a force. There was no force on the earth.

Well, strictly speaking, there was the exact same and opposite force, and it did move. But its inertia or mass is so huge, that it did not really affect it much.

10. Sep 16, 2004

### a1_phy

well i suggest u perform this thought experiment..keep a glass of water i n ur car and on earth beside and turn ur car...u will easily see which body is being accelerated by observing the movement in the water in the glass...
so it is u who is accelerating since a device to measure force records one in ur frame(accelerated that is) and not in the frame of reference of the earth

11. Sep 16, 2004

### humanino

Welcome a1_phy ! Very good argument.

12. Sep 17, 2004

### gonzo

One-eye, relativity applies to velocity not acceleration. Acceleration is not relative.

13. Sep 17, 2004

### OneEye

Very good. So, then, we have a principle, related to mass and force, which mitigates the principle of relativity: Where force can be calculated, the principle of relativity no longer applies: One can tell with certainty which object is moving when one is able to calculate the force.

Right?

14. Sep 17, 2004

### OneEye

I don't believe that this is quite right. I believe that the correct statement is, "Special Relativity applies only to velocity; you must use General Relativity to evaluate questions of acceleration."

15. Sep 17, 2004

Staff Emeritus
No, this is an urban legend. You can treat accleration in SR, and people have done it in other threads on this board; look up "relativistic rocket". What is more true is that GR is a complete theory of forces and accelerations whereas SR is a special case. It is correct that accelerations are not Lorentz-invariant or covariant. They follow a different change-of-frame law.

16. Sep 17, 2004

### humanino

Wrong. Let us sum up what has been collected here : there is an inertial reference frame for the system Car/Earth. In this frame, the acceleration is undergone by the car. The acceleration of the Earth is negligible. If you had a very precise mean of measurement, you could in theory notice the force on Earth, but such an accuracy would probably require to take into account the whole solar system.

You can locally make acceleration disappear by changing the referential. Only locally. The free-fall observer not noticing the Earth gravitational field has a limited spave around him, otherwise he would notice the spherical shape.

You raised the question of energy. Let us assume now that you want to turn very fast. Very very fast. Let us say there is no limit on the energy you can spend for this turn. If you turn too fast, you will really be able to produce a serious force on Earth !

17. Sep 17, 2004

### OneEye

selfAdjoint: Thank you for weighing in on this. But let me be sure that I understand what you are saying:

You are saying that SR does apply in the case I originally posited; that the fact that I "accelerated" (not necessarily true, but we will say that it is) or moved in a non-linear fashion does not disallow an analysis of the situation using SR. Is that correct?

I would really like to nail this down, since I have had several questions answered in like manner: "Your scenario does not apply, since you are accelerating, and SR is not useful to consider acceleration." But I have seen other posters who seem to indicate that SR is as useful for non-linear motion (e.g., rotary/orbital motion) as it is for linear motion - and my original case seems to be reducible using the theorem of the addition of velocities from SR. So, I have always doubted the "SR is only for linear velocity" disqualifications which I have heard.

Am I right to doubt?

18. Sep 17, 2004

### humanino

Always right to doubt.

At least I did not tell you SR does apply when acceleration is here. I only wanted to point that there are two inertial frames, before and after the turn, but the interesting moment is in the middle.

19. Sep 17, 2004

### geometer

Nothing wrong with your answer, I was agreeing with you and showing that even if you are moving in a straight line in a car, you are probably not even then an inertial observer.

20. Sep 17, 2004

### geometer

I have to disagree humanino, an observer in an isolated laboratory can detect an acceleration. You can't transform accelerations away.