Hold a ruler. For Newton it is the same length however you move, standing still or rushing past. Einstein said no: motion changes length, time and mass. This whole section is one question: are these quantities absolute or relative?
1. In Newton's eyes, all three are absolute
Classical mechanics is also called Newtonian mechanics. It assumes three fundamental quantities: space, time and mass.
By Newton, space is absolute and exists in itself. It is not tied to anything outside, and the surroundings do not affect it. So the length of a body does not depend on the motion of the body or of the observer.
Time is the same story. By Newton it is an absolute quantity that flows uniformly, depending on nothing outside, and it is universal. Two things follow: the time between two events is the same for every observer, and events that are simultaneous for one observer are simultaneous for all, whatever their state of motion.
Mass is absolute too. In Newtonian mechanics it does not depend on motion, and by the law of conservation of mass it neither falls nor rises through action and reaction.
2. What Einstein changed
Einstein proved that space, time and mass change with motion, so the three are not absolute. The change has three names, one for each quantity.
Length contraction: the length of a moving body being smaller than its length at rest. Length contracts with motion.
Time dilation: the time interval of an event in one frame appears longer when watched from another frame moving relative to it.
Relativity of mass: when a body moves, its mass increases. This is also called increase of mass with motion.
By Einstein, space, time and length are none of them absolute; all are variable.
See it happen. Push the ship towards the speed of light.
relativitydrag the handle
Length, time and mass as speed rises
Now match each claim to its owner.
gridHint: absolute or relative?
Whose claim?
quantity
Newton
Einstein
space
Length does not depend on motion
A moving body's length contracts
time
Time flows equally for all observers
The interval grows in a moving frame
mass
Mass does not change with motion
Mass increases with motion
Newton's view. Space is absolute, so however the body or observer moves, the length is the same.
Einstein's view. Length shrinks with motion. This is length contraction.
Newton's view. Time is absolute and universal and flows uniformly; no observer's motion changes it.
Einstein's view. Seen from a moving frame the interval grows. This is time dilation.
Newton's view. Mass is independent of motion, and by conservation of mass action and reaction leave it unchanged.
Einstein's view. A moving body gains mass. This is relativity of mass.
sort themThe name gives it away.
Which effect changes which quantity?
Pick up a name, then drop it in the box of the quantity it changes.
Right. Next one.
Not yet. Look at the word in the name: length, time or mass?
All in place. Length shrinks, the time interval grows, mass rises.
3. Mass, energy and a speed limit
In classical mechanics mass and energy stand apart, independent of each other. In the special theory of relativity Einstein showed they are equivalent. The mass-energy relation: E = mc².
Motion also has a limit. No body with mass can travel at the speed of light or faster.
cut from the noteRecall first.
State the definitions
QuestionWhat is length contraction?
AnswerThe length of a moving body being smaller than its length at rest is called length contraction.
QuestionWhat is time dilation?
AnswerThe time interval of an event in a frame at rest appears longer from another frame moving relative to it. This is time dilation.
QuestionWhat is relativity of mass?
AnswerWhen a body moves its mass increases. This is relativity of mass, or increase of mass with motion.
4. Check yourself
Three questions, starting with the first.
check yourselfpick one answer
Question 1
Which equation expresses the equivalence of mass and energy in the special theory of relativity?
E = mv² mixes up momentum and kinetic energy; it is not the mass-energy relation.
½mv² is kinetic energy, not the equivalence of mass and energy.
Right. The equivalence of mass and energy is expressed by E = mc².
mgh is potential energy, not the relativistic mass-energy relation.
The second: choose by asking absolute or relative.
check yourselfpick one answer
Question 2
According to Einstein's theory, in a very fast moving frame: i. length decreases ii. mass increases iii. time interval increases
i. Length decreases ii. Mass increases iii. The time interval increases
i and ii are true, but iii is true too: the time interval grows in a moving frame, so this is incomplete.
i and iii hold, but ii holds as well: mass grows with motion, so all three are true.
ii and iii hold, but i holds as well: a moving body's length contracts, so all three are true.
Right. Length contraction, mass increase and time dilation are all results of Einstein's theory.
The last one, with a moment's thought.
check yourselfpick one answer
Question 3
Under which mechanics do Newton's laws of motion fall?
Quantum mechanics concerns the discrete energy of atoms; Newton's laws came long before it.
Relativistic mechanics is Einstein's; it changes the Newtonian ideas.
Wave mechanics is not the class to which Newton's laws of motion belong.
Right. Classical mechanics is the one known as Newtonian mechanics.
The whole section on eight cards.
cut from the notetap to turn over
Eight cards
QuestionBy Newton, what is space like?
AnswerAbsolute: it exists in itself, is unrelated to anything outside and is unaffected by the surroundings.
QuestionBy Newton, what kind of quantity is time?
AnswerAn absolute quantity that flows uniformly without depending on anything outside.
QuestionWhat did Einstein change in Newton's view of space, time and mass?
AnswerHe proved they change with motion, so they are not absolute.
QuestionWhat is length contraction?
AnswerThe length of a moving body being smaller than its length at rest.
QuestionWhat is time dilation?
AnswerThe increase in the time interval of an event in a frame when seen from a frame moving relative to it.
QuestionWhat is relativity of mass, or increase of mass with motion?
AnswerThe increase of a body's mass when it moves.
QuestionWhat is Einstein's mass-energy relation?
AnswerE = mc².
QuestionWhat speed can a body with mass never reach or exceed?
AnswerIt cannot travel at the speed of light or faster.
Source: Physics 1st Paper, Classes 11-12 (NCTB), Chapter 1 “Physical World and Measurement”, section 1.5.