Question

A friend says, "It makes no sense that Anna could turn on lights in her hands simultaneously in her frame but that they don't turn on simultaneously in another - she decides to do it, and it's done" By considering the tractable, if somewhat unrealistic, situation of Anna's thought being communicated to her hands by light signals, answer this objection.

Short answer

Due to the finite speed of information transmission, in this case, the light, and the principles of special relativity, particularly the principle of simultaneity, it is possible that two events (here, lights turning on simultaneously in Anna's frame) may not appear simultaneously in another frame of reference in relative motion to Anna's frame.

Step-by-step solution

Understanding the scenario

Before we delve into solving the problem, let's first try to understand the scenario. We have Anna, who is able to turn on lights in her hands at the same time according to her perspective, or her frame of reference.

Understanding the light signals

Our job here is to explain why these lights don't turn on at the same time in another frame of reference. This is due to the fact that Anna's thought being communicated to her hands by the speed of light. Even in an ideal, unrealistic scenario where her thoughts would instantaneously reach her hands (travel at infinite speed), because of the finite speed of light, the light from one hand has to travel further than the other to reach an observer, leading to a perceived delay.

Relativity Principle Concept

Understanding the principle of special relativity will help us understand why this is the case. According to this principle, physical laws should appear the same to all observers, regardless of their relative motion. Therefore, while the lights in Anna's hands appear to turn on simultaneously from her viewpoint, they won't appear to do so from another viewpoint, that is in relative motion to her.

Principle of Simultaneity

The principle of simultaneity is an aspect of relativity. It states that the sequence of events that one observes can depend on the observer's reference frame. Because of the finite speed of information transmission, in this case, the speed of light, events that appear simultaneous in one frame might not in another. So with this principle applied, the friend's statement can be explained.

Key concepts

Frame of Reference

Understanding physics often begins with the concept of a frame of reference. It is essentially a viewpoint or perspective from which measurements are made and events are observed. Imagine you are sitting on a train watching the world pass by outside your window. Everything you see and measure, be it speed or distance, is relative to your position on the train. Conversely, a person standing on the platform will have a different perspective and set of measurements for the same events.

For example, in the case of Anna turning on the lights simultaneously, she is in her own frame of reference. An important takeaway here is that what seems simultaneous to her may not seem so to an observer in a different frame. Why is this important? Because it addresses the confusion regarding the disagreement of events between different observers. In special relativity, such disparities are not errors, but manifestations of how our universe works, governed by the laws of physics that are consistent but also relative to the observer’s frame.

Speed of Light

The speed of light is a fundamental constant in the universe, measured at approximately 299,792 kilometers per second (or about 186,282 miles per second). Within the theories of special and general relativity, the speed of light is not just a high velocity; it's a critical limit that represents the fastest speed at which information or matter can travel through spacetime. It's also the same in all directions and frames of reference that are at rest or in uniform motion.

Now, let's bring Anna into this again. Even if Anna's thoughts could instruct her hands to turn on the lights instantaneously, the light from her hands takes time to travel to an observer, especially if that observer is not equidistant from both of Anna’s hands. For observers in different frames of reference, this means they would perceive the lights as turning on at different times due to the finite speed of light – highlighting a key feature of relativity where simultaneity is not universal.

Principle of Simultaneity

The principle of simultaneity is an intriguing aspect of special relativity, asserting that two events occurring at the same time in one frame of reference may not be simultaneous in another. This principle masks the universe we live in as relative, rather than absolute, in terms of temporal measurements.

Returning to our example with Anna, if two observers are standing at different distances from her, the light from her hands, switched on at the same moment in her frame, reaches these observers at different times. Their frames of reference, regarding Anna, are different and thus, the events are not simultaneous for them. The person closer to Anna's left hand will see the left light first, while the person closer to the right hand will see the right light first. This counterintuitive realization combines with the finite speed of light to endorse the concept that simultaneity is not an absolute condition but is relative to each observer's unique frame of reference.