Question

In the twin paradox situation, a fellow student objects to the argument that Anna's acceleration is the root of the asymmetry. "All motion is relative! Anna is accelerating relative to Bob. but Bob is accelerating relative to Anna." Answer this objection.

Short answer

The objection is based on a misinterpretation. While it's true that uniform motion is relative, acceleration isn't. Anna’s acceleration, inevitable during her turn-around in the voyage, breaks the symmetry between her and Bob’s experiences. So, despite Bob appearing to accelerate from Anna's perspective, the physical reality of her own accelerated motion is undeniable and causes her to age less upon her return to Earth.

Step-by-step solution

Understand the Twin Paradox

The twin paradox is a thought experiment rooted in Einstein's special theory of relativity. Let's say Anna and Bob are twins, and Anna embarks onto a space voyage near light speed while Bob stays on Earth. According to special relativity, both Anna and Bob would deem the other's clock to be ticking slower (time dilation). However, when Anna returns to Earth, it will be seen that she aged less than Bob, contrary to the symmetry one can expect from the principle of relativity. This is the paradox.

Understand the Role of Acceleration in Special Relativity

In Einstein's special relativity, the laws of physics are identical in all inertial frames of reference - those moving at constant velocity. However, acceleration breaks this symmetry as it isn't relative, unlike constant velocity motion. In the twin paradox scenario, Anna's journey involves heavy acceleration periods when she turns around to return to Earth. This is where she breaks the symmetry, and her clock runs slower than Bob's as viewed from an inertial frame of reference (i.e., Bob's frame).

Answering the Objection

The false assumption in the student's objection is that all forms of motion, including acceleration, are relative. In special relativity, only uniform motion is relative. An observer can be said to be at rest or moving at a constant velocity simply depending on one's frame of reference. But an accelerating observer is accelerating in all frames. So in the twin paradox, while Anna does see Bob to be accelerating and herself at rest during her turn-around, due to their different circumstances - one actually undergoing the physical stresses of acceleration, the other not - we should not equate their experiences. Therefore, it's only Anna's acceleration that leads to the asymmetry and causes her to age less than Bob.

Key concepts

Special Relativity

Special relativity, introduced by Albert Einstein in 1905, revolutionized our understanding of space and time. One of its central ideas is that the laws of physics are the same for all observers moving at constant speed—these are called "inertial frames." So, if you're in a train moving smoothly at a constant speed, the laws of physics you experience are the same as someone standing still on the ground.

A key principle of special relativity is that there is no absolute state of rest. Everything is relative—which means motion is always described with respect to something else. This is why Anna sees Bob's clock moving slower and vice versa when they are moving relative to each other. However, special relativity doesn't apply directly when acceleration comes into play, because Einstein's theory originally dealt only with inertial frames, where objects move at a constant velocity.

• Laws of physics are uniform in all inertial frames.
• No absolute rest state—motion is relative.
• Acceleration introduces complexity into the theory.

Time Dilation

Time dilation is a fascinating phenomenon predicted by special relativity. It suggests that time as observed by different observers depends on their relative motion. In the twin paradox, both Anna and Bob observe each other's time ticking slower when moving at nearly the speed of light. This feature arises because the speed of light is always the same for all observers, no matter how fast they are moving relative to each other.

Time dilation is more pronounced as speeds approach that of light. This means that, theoretically, if Anna were to travel through space close to light-speed, she could age only a few hours, while years might pass for Bob on Earth.

• Time appears to slow down for objects moving close to light speed.
• Simultaneous experiences can vary greatly for different observers.
• Crucial for understanding scenarios like the twin paradox.

Acceleration in Physics

Acceleration plays a significant role in distinguishing between different types of motion. Unlike constant velocity and uniform motion, which special relativity explains, acceleration requires a deeper look. When an object accelerates, its position changes non-uniformly in comparison to other objects.

In the context of the twin paradox, Anna's acceleration is not relative. Unlike time dilation which is purely relative, acceleration affects the very framework of space and time around the accelerating object. Consequently, Anna's experience is physically different—she undergoes changes in velocity that Bob does not. This breaks the symmetry that special relativity assumes for relative motion.

• Acceleration is a non-relative form of motion.
• It affects spacetime directly, unlike constant velocity.
• Accelerated frames can detect acceleration through techniques like feeling a force.