Do Objects Near Light Speed Shrink?

Do objects travelling near the speed of light shorten? This question relates to the concept of Lorentz contraction in special relativity. The speed of light is constant from the observer's perspective, regardless of the speed of the source. As an object approaches the speed of light, an observer will see its length along the direction of motion shorten. This is because the speed of light remains constant, and so the time it takes for light to reach the front and back ends of the object differs, causing the object to appear shortened.

The speed of light is constant from an observer's POV

The speed of light is constant from an observer's point of view, regardless of the motion of the observer or the light source. This has been proven through various experiments and is a fundamental constant of the universe.

To understand this concept, we must first recognise that the speed of light is an enigmatic phenomenon that has intrigued scientists and laypeople for centuries. No matter where or when it is observed, light consistently travels at the same speed in a vacuum. This speed remains constant for all observers, whether they are measuring it from a stationary or moving position.

Let's consider an example to illustrate this principle. Imagine we have two points, A and B, with a laser beam being shot from A to B. Initially, both points are stationary, and the speed of light is measured as expected. Now, let's introduce movement to point B, so it is now dynamic and moving away from point A. Intuitively, one might assume that it would take longer for the laser beam to reach point B due to the increased distance. However, surprisingly, the speed of light remains constant even in this scenario. This constancy of light speed holds true regardless of the relative motion of the observer or the light source.

This phenomenon can be explained by the theory of special relativity, which was developed by Einstein. According to special relativity, there is no such thing as an objective velocity, and time and distance are not absolute concepts. Instead, they are relative to the observer's frame of reference. In the case of our example, the motion of point B introduces a change in the frame of reference, but the speed of light remains constant despite this change.

The constancy of the speed of light has profound implications and has led to the development of new concepts such as time dilation, length contraction, and the relativity of simultaneity. These concepts help explain how the speed of light can remain constant even when an observer or the light source is in motion.

In conclusion, the speed of light is an intriguing aspect of our universe that has captured the curiosity of many. Its constancy, regardless of the observer's motion, is a fundamental principle supported by experimental evidence and theoretical explanations. This phenomenon challenges our intuition and has led to a deeper understanding of the nature of space, time, and motion.

The Lorentz contraction: an object's left end appears shorter, and its right end appears longer

The Lorentz contraction, also known as the Lorentz-FitzGerald contraction, is a phenomenon where an object travelling at a substantial fraction of the speed of light appears shorter in length to a stationary observer. This phenomenon is only noticeable at extremely high speeds and is only in the direction in which the body is travelling. For example, if a train is moving from left to right, the left end of the train will appear shorter, and the right end will appear longer. This effect is a result of the properties of space and time and is not due to any physical changes in the object, such as compression or cooling.

The concept of Lorentz contraction was first proposed by Irish physicist George FitzGerald in 1889 and later independently developed by Dutch scientist Hendrik Lorentz. The idea was introduced to reconcile the classical understanding of physics with the results of the Michelson-Morley experiment, which showed that the speed of light is constant for all observers, regardless of their relative motion.

The Lorentz contraction can be understood through the relativity of simultaneity, which states that events that are simultaneous in one frame of reference may not be simultaneous in another. In the context of the train example, an observer standing on the platform will see the light reach the left side of the train first and then the right side. However, an observer on the train will see the light reach both sides simultaneously. This difference in the perception of simultaneity leads to the appearance of length contraction for the stationary observer.

It is important to note that the Lorentz contraction is not simply a visual effect. While objects in motion may not appear shortened in photographs, the contraction can be directly measured at the exact location of the object's endpoints. Additionally, the contraction only occurs in the direction of motion, and dimensions in other directions remain unaffected.

Length dilation: an observer sees distances between non-simultaneous events as dilated by a factor of gamma

Length contraction is a phenomenon where a moving object's length is measured to be shorter than its proper length, which is the length measured when the object is at rest. This effect is usually only noticeable when the object is travelling at a substantial fraction of the speed of light.

Length contraction is only observed in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds and can be ignored for all regular purposes. It only becomes significant as the object approaches the speed of light relative to the observer.

Length contraction can be derived from time dilation, according to which the rate of a "moving" clock is lower compared to two "resting" clocks. Time dilation has been experimentally confirmed multiple times and is represented by the relation:

> T = T0 * gamma

Suppose a rod of proper length L0 at rest in S and a clock at rest in S' are moving alongside each other with speed v. Since, according to the principle of relativity, the magnitude of relative velocity is the same in either reference frame, the respective travel times of the clock between the rod's endpoints are given by:

> T = L0/v in S and T'0 = L'/v in S'

Thus, L0 = Tv and L' = T'0v. By inserting the time dilation formula, the ratio between those lengths is:

> L'/L0 = T'0v/Tv = 1/gamma

Therefore, the length measured in S' is given by:

> L' = L0/gamma

So, since the clock's travel time across the rod is longer in S than in S' (time dilation in S), the rod's length is also longer in S than in S' (length contraction in S').

Length contraction can also be derived from the following:

In an inertial reference frame S, let x1 and x2 denote the endpoints of an object in motion. In this frame, the object's length L is measured by determining the simultaneous positions of its endpoints at t1=t2. Meanwhile, the proper length of this object, as measured in its rest frame S, can be calculated by using the Lorentz transformation. Transforming the time coordinates from S into S' results in different times, but this is not problematic since the object is at rest in S' where it does not matter when the endpoints are measured. Therefore, the transformation of the spatial coordinates suffices, which gives:

> x'1 = gamma * (x1 - vt1) and x'2 = gamma * (x2 - vt2)

Setting L = x2 - x1 and L'0 = x'2 - x'1, the proper length in S' is given by:

> L'0 = L * gamma

Therefore, the object's length, measured in the frame S, is contracted by a factor gamma:

> L = L'0/gamma

Likewise, according to the principle of relativity, an object that is at rest in S will also be contracted in S'. By exchanging the above signs and primes symmetrically, it follows that:

> L0 = L'/gamma

Thus, an object at rest in S, when measured in S', will have the contracted length:

> L' = L0/gamma

Length contraction: an observer sees a shortening of an object by a factor of 1/gamma

Length contraction is a phenomenon where a moving object's length is measured to be shorter than its proper length, which is the length measured when the object is at rest. This effect is usually only noticeable when an object is travelling at a substantial fraction of the speed of light.

Length contraction is also known as Lorentz contraction, named after Hendrik Lorentz, who, alongside George Francis FitzGerald, first postulated the idea in 1892. Albert Einstein later derived the contraction from his postulates in 1905.

The Lorentz factor, defined as:

> {\displaystyle \gamma (v)\equiv {\frac {1}{\sqrt {1-v^{2}/c^{2}}}}}

Where:

> {\displaystyle v} is the relative velocity between the observer and the moving object

> {\displaystyle c} is the speed of light

The length of an object, as observed by a stationary observer, can be calculated using the formula:

> {\displaystyle L={\frac {1}{\gamma (v)}}L_{0}}

Where:

> {\displaystyle L} is the length observed by an observer in motion relative to the object

> {\displaystyle L_{0}} is the proper length (the length of the object in its rest frame)

Substituting the Lorentz factor into the above formula gives:

> {\displaystyle L=L_{0}{\sqrt {1-v^{2}/c^{2}}}}

In this equation, both {\displaystyle L} and {\displaystyle L_{0}} are measured parallel to the object's line of movement.

Length contraction is only in the direction in which the body is travelling. For standard objects, this effect is negligible at everyday speeds and can be ignored for all regular purposes.

The ladder paradox: a ladder travelling at light speed fits inside a garage shorter than its rest length due to Lorentz length contraction

The ladder paradox is a thought experiment in special relativity that demonstrates the counterintuitive effects of length contraction when an object moves at relativistic speeds. In this scenario, a ladder travelling at a significant fraction of the speed of light can fit inside a garage that is shorter than its rest length. This is due to the Lorentz length contraction, which causes objects travelling at near-light speeds to contract along the direction of motion.

The thought experiment involves a ladder, parallel to the ground, travelling horizontally at relativistic speed and therefore undergoing a Lorentz length contraction. The ladder passes through the open front and rear doors of a garage which is shorter than the ladder's rest length. To a stationary observer, the moving ladder appears contracted and can fit entirely inside the building as it passes through. On the other hand, from the perspective of an observer moving with the ladder, it is the building that undergoes a Lorentz contraction, and the ladder remains too long to fit. This poses an apparent discrepancy between the realities of both observers.

The paradox arises due to the mistaken assumption of absolute simultaneity. The ladder is said to fit into the garage if both ends can be inside the garage simultaneously. However, in relativity, simultaneity is relative to each observer, making the answer to whether the ladder fits inside the garage dependent on their frame of reference. From the garage's frame of reference, the ladder is shortened by its high velocity and fits inside. In contrast, from the ladder's frame of reference, the garage is contracted even further, making the ladder too long to fit.

The resolution to the paradox lies in understanding the relativity of simultaneity. What one observer considers to be two simultaneous events may not be simultaneous to another observer. When the ladder is said to "fit" inside the garage, it means that the back and front of the ladder were inside the garage at the same time, which is relative to the observer's frame of reference. Thus, two observers will disagree on whether the ladder fits based on their relative motion, highlighting how perspective affects measurements in relativity.

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