# Two Lorentz Boosts Causing Rotation - Measurable w/ Gyroscope?

• Ookke
In summary, Lorentz boosts can cause rotation when combined, as seen through the concept of Thomas precession. This rotation can be measured by using a gyroscope and observing the precession relative to distant stars. Two observers with different accelerations may have different final orientations, and this can be determined by measuring the precession of their gyroscopes. However, a single boost does not cause rotation, so the reason for this effect when combining boosts is still not fully understood. It is possible that this rotation may not be physically observable, but with sensitive enough equipment, it may be detectable when using multiple engines in a rocket.
Ookke
It seems that combining two Lorentz boosts cause rotation:

https://en.wikipedia.org/wiki/Lorentz_transformation#Composition_of_two_boosts

Do you think this rotation is something that could be measured by gyroscope? Or is it like space rotates around the accelerating observer, and the observer has no means to measure this rotation locally?

If I get this right, we could accelerate two observers differently so that they finally have the same velocity vector (and common rest frame), and their final orientation is not the same, although the initial orientation is. So the accelerations have somehow created a difference in orientation, but can we determine, which one of the observers has performed this rotation, or how this should be interpreted? Thanks.

Ookke said:
Do you think this rotation is something that could be measured by gyroscope?

Yes: https://en.wikipedia.org/wiki/Thomas_precession

Ookke said:
So the accelerations have somehow created a difference in orientation, but can we determine, which one of the observers has performed this rotation, or how this should be interpreted?

Yes: just have each carry a gyroscope and see which one precesses relative to the distant stars, as well as by what angle, when they reconvene.

Nugatory
Ok, nice. But if no single boost causes any rotation, why would two boosts in a row do that? It's like space remembers that we already had boost in one direction, and when we have another, this mysterious Thomas rotation takes place.

Maybe I'm thinking this rotation too literally. Assuming that we have sensitive enought test equipment, should we detect us turning in a rocket that first uses its rear engine, then its side engine? At which point we should expect to detect this turning, if at all?

## 1. What is a Lorentz boost?

A Lorentz boost is a transformation that describes the effect of relative motion on the measurements of space and time between two observers. It is an essential concept in the theory of special relativity.

## 2. How does a Lorentz boost cause rotation?

A Lorentz boost involves a change in the direction of motion of the observer, which can result in a rotation in the measurements of space and time. This is due to the fact that space and time are relative and depend on the observer's frame of reference.

## 3. What is a gyroscope and how is it used to measure rotation caused by Lorentz boosts?

A gyroscope is a device that measures angular velocity and orientation. It consists of a spinning mass or rotor that maintains its orientation in space, even when the frame of reference is rotating. By measuring the changes in the orientation of the gyroscope, we can determine the rotation caused by Lorentz boosts.

## 4. Can the rotation caused by two Lorentz boosts be measured in a laboratory setting?

Yes, the rotation caused by two Lorentz boosts can be measured in a laboratory setting using a gyroscope. This effect has been experimentally verified and is an important concept in the theory of special relativity.

## 5. Are there any practical applications of understanding the rotation caused by two Lorentz boosts?

Yes, understanding the rotation caused by two Lorentz boosts is crucial in many modern technologies, such as navigation systems and GPS. It also has implications in the study of particle physics and can help us better understand the behavior of subatomic particles.

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