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Special Relativity

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Special Relativity

The theory of special relativity is a scientific theory that focuses on the interaction between time and space and how the laws of physics are the same in all inertial frames. In this article, we will explore Einstein's theory of special relativity, the Michelson-Morley experiment, simultaneity and time dilation, length contraction, and some examples of special relativity.

Einstein's Theory of Special Relativity

Albert Einstein's theory of special relativity is one of the most important developments in physics. It explains how speed affects mass, time, and space and says that:

  • The mass of an object approaching the speed of light is limitless, as is the energy necessary to move it.
  • No object with mass can move at the speed of light.

When we consider movement across enormous distances, this cosmic speed limit stimulates new areas of physics and science fiction. Einstein created the theory of special relativity with two simple postulates and careful measurements.

Special Relativity, Similarity to trigonometry, StudySmarterAlthough special relativity includes observations and experiments, it is founded on logically connected postulates, much like trigonometry. flickr.com

First Postulate of Special Relativity

Einstein's first postulate concerns reference frames. All velocities are measured in relation to a reference frame. Here are some basic examples:

  • If a man is running, his motion is measured relative to his starting point or the ground he is running on.
  • If you throw a ball in the air, the ball's motion is measured relative to your standing position.

According to the first postulate of special relativity, the laws of physics are the same and can be stated much more simply in all inertial frames of reference than in non-inertial ones.

In an inertial frame of reference, a body at rest remains at rest, or a body in motion continues at a constant speed in a straight line unless impacted by an outside force. Also, the laws of physics seem to be much simpler in inertial frames. See the following example:

When you are on a plane flying at a constant speed and altitude, physics seems to work the same way as when you are standing on the surface of the earth. But if the plane is taking off, things are a little trickier.

In such a case, ie, when a plane is taking off, F, which is the net force of an object, does not equal the multiplication of mass and acceleration ( ma ). Instead, it is equal to ma plus a postulated force. Here is an example:

Let's say the speed of the plane is V0. When you throw a ball inside the plane at a velocity of v, you will see the ball moving at a velocity of v, but to a person who is standing on the earth, it will appear to be moving at a velocity of v + V0.

Not only are the laws of physics much simpler in inertial frames; they also are the same for all inertial frames since there is no preferred frame or absolute motion.

One of the most important outcomes of this first postulate is the famous mass-energy equivalence equation E = mc ^ 2 that applies to a force in a near light moving frame.

Second Postulate of Special Relativity

The second postulate deals with the speed of light. The laws of electricity and magnetism say that in a vacuum, light travels at approximately 3.00 * 10 ^ 8 m / s. However, they make no mention of the frame of reference in which light travels at this speed. The question is whether c (the speed of light) is constant or whether it is relative, in which case, for instance, an observer traveling at the speed of light might see the light waves as stationary.

Einstein concluded that an object with mass could not travel at the speed c. He also stated that light in a vacuum must travel at the speed c, which is 3.00 * 10 ^ 8 m / s, relative to any observer. It follows that:

  • The speed of light ( c ) is a constant and is independent of the relative motion of the source.
  • While the speed of light in a vacuum is 3.00 * 10 ^ 8 m / s, it is lower when traveling in matter.

Special Relativity: Michelson-Morley Experiment

The Michelson - Morley experiment, conducted in 1887, was designed to determine the presence of the luminiferous aether, a postulated medium pervading space that is assumed to carry light waves. If the aether were to carry the light waves, the flow of the aether would change the light velocity by carrying the photons and adding more speed.

The experiment measured the speed of light from different directions to detect the relative motion of the light and whether the aether would modify its velocity. The result was negative in that Albert A. Michelson and Edward W. Morley found no significant difference between the speed of light in different directions. These results opened a way for a line of research that led to special relativity, which is why the experiment came to be known as the 'most famous' failed 'experiment'.

Special Relativity: Simultaneity and Time Dilation

Can time intervals be different from one observer to another? Intuitively, we think of time as a process that is the same for everyone. However, in some cases, time seems to be going faster or slower. These different perceptions are related to the accuracy of the measuring of time. If you consider how time is measured, you will see that this is determined by an observer's relative motion with regard to the process being measured.

Special Relativity, Example of time dilation, StudySmarterA foot race's elapsed time is the same for all observers, except that it is affected by the observer's relative velocity. flickr.com

Simultaneity

Simultaneity describes the relationship between two occurrences supposedly happening at the same moment in a frame of reference. See the following example:

A fireworks show in Paris and another one in New York appear to be happening at the same moment. However, these two events will appear to be observed at different times by an observer on earth and another one moving from New York to Paris at near the speed of light. The second observer will see the fireworks in Paris earlier than the ones in New York, while the observer on earth will see the two events happening simultaneously.

This is called relativity of simultaneity, which means that when someone observes two events as occurring at the same time (for example, by getting light from these events), they are said to be simultaneous. However, to all observers, two occurrences are not always happening at the same time.

Time Dilation

Time dilation is the concept that time is measured differently for moving objects than for stationary objects as they travel through space.

Time dilation occurs when one observer moves relative to another observer, causing time to flow more slowly. For example, time moves slowly in the International Space Station, with 0.01 seconds elapsed for every 12 earth months.

Let's say an observer is moving at a velocity of v and the proper time is Δt0, which is the time measured by the observer at rest relative to the event being observed. This proper time is related to the time Δt, which is measured by an observer on earth. We have already seen that c is the speed of light. is a constant that can be determined as explained in the equation below:

where

Special Relativity: Length Contraction

Imagine you are traveling with a friend and discussing how many kilometers you have left to go. You and your friend may give different answers, but if you measured the road, you would come to an agreement because, traveling at everyday speeds, you would arrive at the same measurement.

However, this is not the case in relativistic speeds close to the speed of light. The phenomenon of length contraction occurs when the length of a moving item is measured to be shorter than its proper length. Proper length (L0) is the length you get when an observer at rest relative to both points measures the distance between the two. See the example below:

Let's say that, to an observer on earth, a muon is traveling at a velocity of 0.950c for 7.05 * 10 ^ -6 s from the time it has been seen until it disappears. It travels a distance of:

This is relative to earth. In muon's frame of reference, its lifetime is Δt0:

Our example envisages an observer on earth, so 7.05 * 10 ^ -6 s is Δt, and you need Δt0 to find the length from muon's reference. As we saw before:

So if you put in the known parameters, you get:

Now you can determine the length relative to the observer ( L ):

In conclusion, the distance between the muon appearing and it disappearing depends on who measures it and how the observer is moving relative to it.

Special Relativity, Example of length contraction, StudySmarter People may describe distances differently; in relativistic speeds, they really are different. flickr.com

Special Theory of Relativity Examples

Examples of us being able to observe special relativity in our daily lives include:

  • Gold's yellow color. White light is a combination of all the colors of the rainbow. For gold, wavelengths tend to be longer when light is absorbed and re-emitted. As a result, the spectrum we perceive has a lower concentration of blue and violet waves. Because yellow, orange, and red light have a longer wavelength than blue light, they make gold look yellowish.

  • Mercury in liquid form. Similar to gold, electrons are kept close to the nucleus because of their speed and increased mass in mercury. Because mercury's atoms are only bound together weakly, it melts at lower temperatures and appears as a liquid.

Special Relativity, Example of Special Relativity, StudySmarterMercury in liquid form is a perfect everyday example of special relativity. flickr.com

Special Relativity - Key takeaways

  • Special relativity is an explanation of how speed affects mass, time, and space. It is one of the most important developments in the history of physics, as it changed the way we perceive time and space.
  • Einstein's theory of special relativity is based upon two postulates. The first says that all velocities are measured in relation to a reference frame. The second states that the speed of light (c) is a constant and is independent of the relative motion of the source.
  • Time dilation means that time is measured differently for moving objects than for stationary ones as they travel through space at relativistic speeds.
  • The phenomenon of length contraction occurs when the length of a moving object is measured to be less than its proper length measured in its rest frame.

Frequently Asked Questions about Special Relativity

The theory of special relativity says that (1) all velocities are measured in relation to a reference frame, and (2) the speed of light (c) is a constant and is independent of the relative motion of the source.

General relativity is concerned with gravity and acceleration, whereas special relativity is concerned with speed and time.

The theory of special relativity explains how speed affects mass, time, and space. As an item approaches the speed of light, its mass and the energy required to move it become limitless. It is thus impossible for any substance to go faster than the speed of light.

Final Special Relativity Quiz

Question

 Who proposed the theory of special relativity?

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Answer

 Albert Einstein.

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When was the theory of special relativity conceived?


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Answer

 In 1905.

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Question

What is Einstein's first postulate regarding the theory of special relativity about?


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Answer

Reference frames.

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What is Einstein's second postulate regarding the theory of special relativity about?


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Answer

The speed of light.

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Question

In which context are all laws of physics the same to any observer?


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Answer

In an inertial frame of reference.

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Question

The speed of light in a vacuum is constant. Is the speed of light in matter lower or higher?

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Answer

It is lower than c.

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Question

What is the speed of light (c) in a vacuum?


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Answer

It is 3.00 * 10 ^ 8 m / s.

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Question

What was the aim of the Michelson-Morley experiment?


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Answer

Comparing the speed of light in different directions to detect the relative motion.

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Question

 Which famous equation was provided by the theory of special relativity?


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Answer

E = mc ^ 2.

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Question

 Which year was the Michelson-Morley experiment conducted?


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Answer

1887.

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Question

In which circumstances is length contraction possible?


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Answer

In relativistic speeds.

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Question

What is the name of the concept that states that the distance between two points depends on who measures it?


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Answer

Length contraction.

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Question

What is the length you get when an observer at rest relative to both points measures the distance between them?

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Answer

Proper length.

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Question

Which phenomenon occurs when one observer moves relative to another observer, causing time to flow more slowly?


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Answer

Time dilation.

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Question

Which concept states that when two occurrences are said to be simultaneous, they are not always occurring at the same time to all observers?

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Answer

Relativity of simultaneity.

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Question

 Can you give two examples of special relativity in real life?

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Answer

Gold's yellow colour and mercury in liquid form.

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Question

What are relativistic speeds?


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Answer

Speeds that are close to the speed of light.

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Question

Which experiment is also known as the most famous 'failed' experiment?


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Answer

Michelson-Morley experiment.

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Did the Michelson-Morley experiment pave the way for Einstein's theory of special relativity?

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Answer

 Yes, it did.

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Question

What was the other important point of Einstein's second postulate of special relativity?


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Answer

An object with mass cannot travel at the speed of light (c).

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Question

When they examined the speed of light in perpendicular directions, what kind of differences do Michelson and Morley observe?

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Answer

No substantial difference.

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Question

Which of the following was the first substantial evidence against the aether hypothesis?

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Answer

Michelson-Morley experiment.

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Question

Which of the following eliminated the possibility of a stationary aether?

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Answer

Michelson-Morley experiment.

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Question

Which device was the main component of the Michelson-Morley experiment?

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Answer

Michelson interferometer.

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Question

Which of the following did the Michelson-Morley experiment prove?

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Answer

There is no aether.

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Question

 Did Einstein know about the Michelson-Morley experiment?

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Answer

Yes he did.

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Question

Does light need a medium to transmit it?


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Answer

No it doesn't.

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Question

What was the given name for light's required medium at the time it was accepted? 


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Answer

Luminiferous aether

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Question

The purpose of the Michelson-Morley experiment was to prove the existence of luminiferous aether. True or false?


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Answer

True.

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Question

When did the Michelson-Morley experiment take place?


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Answer

1887.

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Question

An interferometer is a sensitive optical device that compares the light's two mutually vertical directions' optical path lengths. True or false? 


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Answer

True.

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What did the Michelson-Morley experiment disprove?


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Answer

Aether hypothesis.

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What is a hypothetical medium for transmitting light and heat (radiation)?


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Answer

 The Aether.

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Before their experiment, Michelson and Morley were successful in confirming Fresnel's drag coefficient, which was also seen as proof of what?


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Answer

The theory of existence of aether.

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When did Michelson and Morley confirm Fresnel's drag coefficient?


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Answer

 In 1886, 1 year before their experiment.

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What does Einstein’s first postulate about the theory of special relativity propose?

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Answer

The laws of physics are the same in all inertial frames of reference.

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What does Einstein's second postulate about the theory of special relativity propose?

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Answer

The speed of light is constant at c = 3.00 * 10 ^ 8 m / s in a vacuum.

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Question

A muon is observed by an observer on Earth and travels at a velocity of 0.620c for 10.0s from the moment it is spotted until it vanishes. Find the length relative to the observer.


Hint: Use the length contraction equation.

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Answer

1,460[km]

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Question

Calculate the rest energy of a 1.85 grams mass.

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Answer

1.665 * 10 ^ 14 [J]

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Which of the following is true?

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Answer

Speed of light is constant in a vacuum regardless of the observer's speed.

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Question

Choose the correct answer.

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Answer

The laws of physics are the same in all inertial frames

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Question

Which of the following is false?


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Answer

Newton's addition of velocities is correct in the case of light.

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Question

What is the symbol for the speed of light?

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Answer

 c

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Question

What is the value of the constant speed of light in a vacuum?


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Answer

3.00 * 10 ^ 8 m / s

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Question

What are the two types of relativistic energy?


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Answer

Total energy and rest energy.

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What is the equation for calculating rest energy?


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Answer

E0=mc^2

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Is energy conserved when converting from mass to energy?


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Answer

Yes

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Question

When an observer moves through space relative to another observer what happens for the observer on the move?


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Answer

Time flows more slowly

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Question

The proper length is the length obtained when the distance between two points is measured by an observer who is at rest relative to both points. True or false?


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Answer

True

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Question

The proper time is the time the observer measures at rest relative to the event being observed. True or false?


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Answer

 True

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