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**Frames of Reference and Relativity**

SPH4U – Grade 12 Physics Unit 5

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**Frames of Reference & Relativity**

Einstein’s theory of relativity began with the study of light and questions about it’s motion. Since Einstein could not actually observe light (since it moves too fast) he had to think on a purely theoretical basis or use “thought experiments”.

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A Thought Experiment Thought experiments are hypothetical situations used to understand difficult to analyze situations. The power of the thought experiment is the questions that arise, not necessarily the answers to the questions.

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A Thought Experiment At the age of 16, Einstein showed the power of the thought experiment technique by imagining he could chase a beam of light until he was alongside it. Use the following questions to discuss Einstein’s thought experiment: (a) Could you catch up to the beam of light? (b) If you could, would the beam remain stationary, relative to you? (c) What would the beam consist of? (d) According to Maxwell, why couldn’t the beam remain stationary? (e) Could you see the beam of light in a mirror?

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**A Thought Experiment (a) Could you catch up to the beam of light?**

Intuitive reasoning based on Newton’s laws of motion tells us that we should catch up with the light waves.

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A Thought Experiment (b) If you could, would the beam remain stationary, relative to you? The light waves should appear stationary, that is, light will stand still relative to the observer.

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**A Thought Experiment (c) What would the beam consist of ?**

Classically, the beam should be some form of a wave front of energy.

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A Thought Experiment (d) According to Maxwell, why couldn’t the beam remain stationary? According to Maxwell’s theory, and all reliable observations, there is no such thing as stationary light; no one has ever held a stationary clump of light in the palm of his or her hand. Light always travels at 3.00 x 108 m/s in a vacuum— no slower, no faster. (And as we will see in this chapter, in all frames of reference.)

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**A Thought Experiment (e) Could you see the beam of light in a mirror?**

If the light is stationary relative to the observer, it would not flow to the observer nor be reflected from a mirror.

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**Frames of Reference and Relativity**

Classical laws of motion developed by Newton work at low speeds (low being small compared to the speed of light). Einstein’s theories are necessary when considering motion at high speeds (high= speeds that approach the speed of light).

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**Frames of Reference and Relativity**

We have discussed frames of reference earlier in the semester. Recall: a frame of reference is an arbitrary origin and set of axes from which to measure the changing position of a moving object. Most often we choose Earth as our frame of reference, assuming it to be stationary, and measure all positions of a moving object relative to some origin and set of axes fixed on Earth.

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**Frames of Reference and Relativity**

Recall: Any frame of reference in which the law of inertia holds is called an inertial frame of reference; that is, if no net force acts on an object at rest, it remains at rest, or, if in motion, it continues to move in a straight line at a constant speed.

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**Frames of Reference and Relativity**

A non-inertial frame of reference often occurs when a reference frame is accelerating. When a vehicle changes speed, or turns sharply while maintaining a constant speed, odd things appear to happen – a ball on the floor for example might suddenly start to move to the back of the vehicle, even though there is no ‘observed force’ acting on the ball if you’re in that reference frame. Recall that we said that a “fictitious force” acts on the ball if you’re in that frame of reference.

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**Frames of Reference and Relativity**

It is clear that the analysis of motion in non-inertial frames is complicated. Looking at the same motion from any inertial frame provides a much simpler analysis, consistent with Newton’s laws. This leads us to three important statements about relative motion and frames of reference:

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**Frames of Reference & Relativity**

1) In an inertial frame of reference, an object with no net force acting on it remains at rest or moving in a straight line with a constant speed. 2) The laws of Newtonian mechanics are only valid in an inertial frame of reference. 3) The laws of Newtonian mechanics apply equally in all inertial frames of reference; in other words, all inertial frames of reference are equivalent as far as adherence to the laws of mechanics is concerned.

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**Frames of Reference & Relativity**

Note: In general, for any two inertial frames moving with respect to each other, there is no physical meaning in the question, “Which of these two frames is really moving?”

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**Frames of Reference & Relativity**

For example, if you drop a ball while in car moving at a constant speed (an inertial frame of reference) the ball will fall straight down. If you drop a ball while in a car that is not moving (another inertial frame of reference) the ball will AGAIN fall straight down. The same thing happens whether or not you are moving. Therefore you cannot tell by looking at the motion of the ball which reference frame was moving.

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Shortcut Symbols

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Recall Question 1 Imagine a bus that is moving forward at 30 m/s. Inside the bus, there is a ball moving forward (the same direction the bus is moving) across the floor at 10 m/s. Let’s consider reference frame 1 (S1) to be inside the bus. Let’s consider reference frame 2 (S2) to be outside the bus standing on the road Let’s consider reference frame 3 (S3) to be in another car that is moving forward beside the bus at 20 m/s. What is the ball’s speed in S1? What is the ball’s speed in S2? What is the ball’s speed in S3?

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Recall Question 1 Imagine a bus that is moving forward at 30 m/s. Inside the bus, there is a ball moving forward (the same direction the bus is moving) across the floor at 10 m/s. Let’s consider reference frame 1 (S1) to be inside the bus. Let’s consider reference frame 2 (S2) to be outside the bus standing on the road Let’s consider reference frame 3 (S3) to be in another car that is moving forward beside the bus at 20 m/s. What is the ball’s speed in S1? 10 m/s What is the ball’s speed in S2? 40 m/s What is the ball’s speed in S3? 20 m/s

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**Question Does this work the same for light?**

For example, if light emitted from Ms. Moncrief’s red flashlight has a speed of c as measured on the Earth, then would light emitted from the same flashlight on a spaceship moving past the Earth at a speed of 1/10 the speed of light, appear to be moving at 11/10 the speed of light to someone standing on the Earth?

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**Question Does this work the same for light?**

Does the speed of light depend on the reference frame from which it is observed? Einstein used work done by Michelson and Morley (see pages 577 in your text) to answer this question. It is in fact part of the special theory of relativity:

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**Einstein’s Special Theory of Relativity**

The “special theory of relativity” is a subset of Einstein’s General Theory of Relativity, which is more complex and deals with gravitation and non-inertial frames. The relativity principle: all the laws of physics (motion, energy, optics, electricity, etc.) are valid in all inertial frames of reference. The constancy of the speed of light: light travels through empty space with a speed of c = 3.00 x 108 m/s relative to all inertial frames of reference.

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**Einstein’s Special Theory of Relativity**

NOTE: These are stated a little differently in your text. Check out pages 577 & You might want to write out the alternative way of stating these in your notes. The relativity principle: all the laws of physics (motion, energy, optics, electricity, etc.) are valid in all inertial frames of reference. The constancy of the speed of light: light travels through empty space with a speed of c = 3.00 x 108 m/s relative to all inertial frames of reference.

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**Einstein's Special Theory of Relativity**

The first one is pretty straight forward and we have already discussed it. The implications of the second….

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**Einstein's Special Theory of Relativity**

Imagine the Lady of Physics and Dr. Quantum are doing an experiment to measure the speed of light coming from a lighthouse. The Lady of Physics is moving toward the lighthouse at a high speed and Dr. Quantum is moving away from the lighthouse at a high speed. They would still measure the same value for the speed of light. The speed of the light coming from the lighthouse is unaffected by their motion, which is very different from if they were both trying to measure the speed of a ball rolling underneath the lighthouse.

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**Imagine the Lady of Physics and Dr**

Imagine the Lady of Physics and Dr. Quantum are doing an experiment to measure the speed of light coming from a lighthouse. The Lady of Physics is moving toward the lighthouse at a high speed and Dr. Quantum is moving away from the lighthouse at a high speed. They would still measure the same value for the speed of light. The speed of the light coming from the lighthouse is unaffected by their motion, which is very different from if they were both trying to measure the speed of a ball rolling underneath the lighthouse.

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**Some Wacky Consequences of Relativity**

Time intervals are different depending on the reference frame you are in. The passage of time would be different for you standing on the earth than it would be for someone moving on a spaceship that is travelling close to the speed of light. (We will discuss this more tomorrow).

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**Some Wacky Consequences of Relativity**

Simultaneity the occurrence of two or more events at the same time.

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**The Simultaneity Thought Experiment**

Say the Lady of Physics is standing stationary on a railway platform halfway between two lampposts L1 and L2. The lampposts are connected in the same circuit. The Lady of Physics sees the lights come on and go off at exactly the same time because the lights are connected and because they are equidistant from her. Dr. Quantum is seated on the train, directly across from where the Lady of Physics is standing. If the train is at rest, Dr. Quantum sees the lights flash on and off simultaneously. If the train is moving with a speed v toward L2 will Dr. Quantum still say the lights go on and off simultaneously?

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Say the Lady of Physics is standing stationary on a railway platform halfway between two lampposts L1 and L2. The lampposts are connected in the same circuit. The Lady of Physics sees the lights come on and go off at exactly the same time because the lights are connected and because they are equidistant from her. Dr. Quantum is seated on the train, directly across from where the Lady of Physics is standing. If the train is at rest, Dr. Quantum sees the lights flash on and off simultaneously. If the train is moving with a speed v toward L2 will Dr. Quantum still say the lights go on and off simultaneously?

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**The Simultaneity Thought Experiment**

No. Because Dr. Quantum is moving in the direction of L2, it will take light from L2 less time to reach him because that light has less distance to travel than light coming from L1. So Dr. Quantum sees the light from L2 before he sees the light from L1.

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**The Simultaneity Thought Experiment**

The Lady of Physics says the two events are simultaneous. Dr. Quantum says the two events are not simultaneous, but rather happened one after the other.

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**The Simultaneity Thought Experiment**

Conclusion: two events that are simultaneous in one frame of reference are in general not simultaneous in a second frame of reference that is moving with respect to the first. Simultaneity is not an absolute concept.

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Homework Read section 11.1 in your text. Add information from your reading into your notes. Questions on page 579: Pg. 579 # 1-4, 6, 8, 10

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Special Relativity (Math) Reference from Tipler chapter 39-1 to 39-3 Newtonian relativity Einstein’s postulates Lorentz transformation Time dilation.

Special Relativity (Math) Reference from Tipler chapter 39-1 to 39-3 Newtonian relativity Einstein’s postulates Lorentz transformation Time dilation.

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