Reference Frames in Physics

Modern Physics

by Ronnie Lorilla

​Special Relativity

​The mechanics of objects moving at high velocities, near the speed of light, in contrast to Newtonian mechanics, which deals with velocities found in daily life. Einstein is quoted as saying, “Common sense is that layer of prejudice laid down prior to the age of sixteen.”

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This remark was prompted by the realization that the laws of special relativity are contrary to our common sense because we do not travel at speeds near the speed of light.

​General relativity

​Treats gravitational fields as equivalent to acceleration. The theory relates to the physics of the stars and even to the evolution of the universe—cosmology

​Frames of reference

​Newton’s laws apply in any nonaccelerating frame of reference, called an inertial frame, that is, one with constant velocity. According to Newtonian physics, if the laws of mechanics are valid in one inertial frame of reference, they must be valid in any inertial frame of reference.

​The person at the station may say that he is at rest while the train moves past in one direction; the person on the train may say that she is at rest and that the station is moving past in the opposite direction. As long as the frame of reference is nonaccelerating, there is no way to prove that any given frame of reference is absolutely at rest, nor is there a preferred frame of reference.

​The special theory of relativity

​Einstein suggested that absolute motion has no meaning, that all motion is relative. He formulated two basic postulates for the special theory of relativity.

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

• The speed of light is the same regardless of the frame of reference of the observer.

These simple postulates led to profoundly different ways of viewing the universe.

Multiple Choice

Mass energy relation is

• E=mc2

• E=T+V

• E=T-V

• M=Ec2

Multiple Choice

On a train travelling at 0.6c, an observer sitting in the middle of a train carriage sees 2 lights at each end of the carriage turn on simultaneously. What would an observer on the platform see?

• Both lights turn on simultaneously

• The front light turn on first

• The rear light turn on first

• The lights flash

Multiple Choice

What is the formula for special relativity?

• $$E=MC^2$$

• $$E=MS^2$$

• $$C=ME^2$$

• $$M=EC^2$$

Multiple Choice

1.If you were in spaceship traveling at the speed close to the speed of light (with respect to the earth) you would notice that___________

• your pulse rate is different than normal

• your mass is different than normal

• some of your physical dimensions were smaller than the normal

• none of these effects occur

Multiple Choice

The speed of light (c) =

• 3 x 10⁸ miles/hour
• 3 x 10⁸ meters/second
• 3 x 10⁸ kilometers/hour
• none of these

Multiple Choice

The special theory of relativity was derived by:

• Galileo
• Newton
• Einstein
• Sitter

Multiple Choice

A postulate is something that is accepted as true at the beginning of a logical article.

• True
• False

Multiple Choice

How many postulates are there in the special theory of relativity?

• 1
• 2
• 3
• 4

Multiple Choice

The speed of light is constant in all frames of reference.

• True
• False

Multiple Choice

Which of the following is not a consequence of special relativity?

• Moving objects appear shorter in length (thinner) than stationary objects.
• Time appears to move at a different rate for objects moving relative to each other.
• Mass and energy are the same thing: if you increase an object’s energy, you also increase its mass.
• Nothing is certain; everything is relative.

Multiple Choice

When you approach a light source, the light from that source has a speed 

• greater than c. 
• less than c. 
• equal to c.
  

Multiple Choice

If Penny, carrying a 40 m pole, is running at 0.87c can observer Bill standing at the center of a 20m barn simultaneously close both the doors with the pole inside as Penny runs through?

• No, because in Bill's reference frame the barn is 9.9 m and the pole is 40 m

• No, because in Bills's reference frame the barn is 20 m and the pole is 40 m

• Yes, because in Bill's reference frame the pole is 19.7 m and the barn is 20 m

• Yes, because in Bill's reference frame the barn is 40.6 m and the pole is 40 m

​Addition of velocities

​This equation yields the following equation for the speed of a light beam from a rider coming toward you with a speed of v:

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​This equation for adding velocities gives the correct results as predicted by the second postulate of special relativity.

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​Time dilation

​All clocks in the universe do not keep time together. Time dilation is the effect that a moving clock runs slower than an identical stationary clock. The expression is

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​Furthermore, not only does the clock run slower but so also does any physical process affected by the passing of time such as chemical and biological processes. Therefore, to the person in the moving frame, no change in time interval can be detected because all methods of measuring time are slowed by the same factor. All is relative.

Multiple Choice

Einstein's time dilation equation was derived by very, very advanced mathematics.

• True
• False

Multiple Choice

Based on the concepts of Special Relativity time travel is...

• not possible

• possible only in the ability to travel into the past.

• possible only in the ability to travel to the future.

• possible to travel either forward or backward in time.

Multiple Choice

A rocket leaves Earth and travels to a star that is 20 light years as seen by the Earth. The speed of the rocket is 0.8c relative to the Earth. The time for the trip as measured on by the astronauts in the spaceship is

• 25 years

• 20 years

• 16 years

• 12 years

Multiple Choice

Since all references frames are equal, what is the apparent paradox about the twin's ages.

• In Jo's reference frame Betty travelling on the spaceship at 0.8c should age faster than Jo.

• In Betty's reference frame, she is standing still and Earth is moving away at 0.8c, therefore Betty will be older than Jo when she returns.

• In Jo's reference frame Betty is moving at 0.8c, therefore the distance she needs to travel is longer than 6 light years.

• Since Betty is travelling at 0.8c her relativistic momentum is less than her Newtonian momentum.

​Lorentz Contraction

​The Lorentz contraction is the effect that an observer moving with an object of a given length will find the object to be shortened compared to an observer at rest relative to this motion. (Note that this shortening occurs only in the direction of motion.) Again, all is relative. Because all distances in the direction of motion are shortened for the moving observer, there is no comparison length for the traveling observer to use to detect the change. The equation is

Multiple Choice

This expression $$\frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$   represents

• time dilation

• the relativistic (Lorentz) factor

• length contraction

​The twin paradox

Imagine one twin in a rocket ship traveling toward a star and returning at nearly the speed of light. The other twin stays home. The stay-at-home twin insists that she stayed at rest and the other twin moved. The twin in the rocket ship insists that she was at rest while the earth zoomed away from her and then returned.

The contradiction is that each can claim that the other moved and, therefore, was the one who aged less. Who did age the most? (It is not possible to have relative gray hair.)

To resolve the paradox, realize that the problem is not symmetric. When the rocket ship twin was leaving the earth, slowing to a stop in outer space, turning around to come home, and slowing to a stop at the earth’s surface, she accelerated and decelerated; therefore, her frame of reference was not an inertial frame of reference. The traveling twin aged less.

​Relativistic momentum

​The definition of momentum and energy must be generalized to fit within special relativity. The correct expression for relativistic momentum is

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​Note that when v is low, the denominator is nearly 1, so momentum approaches the familiar equation: p = mv. This equation can be interpreted to mean that the mass is velocity-dependent:

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When v is zero, the mass equals mo. The term mo is called the rest mass.​

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Multiple Choice

There are two twins on Earth. One flies off on a spacecraft traveling 90% of 'c' while the other twin stays on Earth. Which of the following is TRUE?

• The twin on the spacecraft will age more slowly than the Earth-bound sibling

• Time in each frame of reference proceeds differently at different speeds

• This is an example of the 'Twin Paradox'

• All answers are true

Multiple Choice

At what speed will an electron’s relativistic momentum be exactly 1.5 times its Newtonian momentum?

• 0.5c

• 0.87c

• 0.75c

• 0.6c

Multiple Choice

At what speed will an electron’s relativistic momentum be exactly 1.5 times its Newtonian momentum?

• 0.5c

• 0.87c

• 0.75c

• 0.6c

Multiple Choice

Which one of the following is a true statement about momentum?

• Newtonian momentum remains constant as speed is increased.

• Relativistic momentum doubles when speed is doubled.

• At low speeds Newtonian momentum is just slightly greater than relativistic momentum

• An object travelling at 1.00c would have an infinite amount of momentum.

Multiple Choice

On the spaceship travelling at 0.8c, what is the distance Betty measures to star A (6 ly away in Earth's reference frame), and much time passes for her to reach the star system?

• The distance is 3.6 lightyears, so it takes her 4.5 years.

• The distance is 6 lightyears which takes her 4.5 years.

• The distance is 5 lightyears, so it takes her 6.25 years.

• The distance is 6 light years which takes her 7.5 years

​Relativistic energy

​Einstein proposed the famous mass-energy equivalence equation: E=mc² This energy is the sum of the kinetic and rest energies. The relationship shows that mass is a form of energy; therefore, a statement of conservation of energy must include the concept of mass. Because c is such a large value, a small mass is equivalent to an enormous energy

​The kinetic energy of a mass is

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​Quantum Mechanics

​Not only was classical mechanics unsuccessful in explaining motions near the speed of light, it also could not explain the behavior of matter on the atomic level. Quantum mechanics is required to analyze the behavior of molecules, atoms, and nuclei.

​Blackbody radiation

​A blackbody is an ideal thermal object that absorbs all radiation falling on it at low temperatures and is also a perfect radiator. The curves of radiation intensity versus wavelength could not be explained by classical physics. Max Planck (1858–1947) developed an equation for blackbody radiation that agreed with the data. This derivation required two assumptions:

​Blackbody radiation

​Blackbody radiation

​The radical nature of Planck’s vision is the assumption of quantized energy states. The terms discrete and quantum referred to considering the energy as coming in packets instead of as a continuous flow; thus, the molecule will change energy states only if the amount of energy absorbed or radiated is a discrete amount of energy.