Quiz True or False 1 Length and time

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Quiz: True or False 1. Length and time are absolute. F 2. If we

Quiz: True or False 1. Length and time are absolute. F 2. If we only had the technology, spaceships could theoretically travel at twice speed of light. F 3. You can turn energy into matter. T 4. Light is really a collection of particles. T 5. Light is really a wave of electromagnetic energy. T

Quiz: True or False 6. Electrons in an atom can orbit the nucleus at

Quiz: True or False 6. Electrons in an atom can orbit the nucleus at any speed or radius. F 7. All laws of physics are deterministic rather than probabilistic. F 8. Relativity and quantum mechanics are esoteric concepts which have no application in everyday life. F 9. Physics is fun and I am excited about Professor Sau’s class. True, of course.

What do we mean when we talk about ? "Common sense is the collection

What do we mean when we talk about ? "Common sense is the collection of prejudices acquired by age eighteen. " Albert Einstein (1952)

Galilean transformations From http: //hyperphysics. phy-astr. gsu. edu

Galilean transformations From http: //hyperphysics. phy-astr. gsu. edu

Experiment at rest Experiment in moving frame Same result. Ball rises and ends up

Experiment at rest Experiment in moving frame Same result. Ball rises and ends up in the thrower’s hand. Ball in the air the same length of time. Experiment looks different from ground observer (parabolic trajectory, speed as a function of time) and observer on the truck. However, they both agree on the validity of Newton’s laws. Fig. 1 -1, p. 4

We have agreed that light is a wave—right? ? ? We all have enough

We have agreed that light is a wave—right? ? ? We all have enough common sense to know that waves need a medium, such as water, in which to propagate. That medium is a reference frame which may be: At rest with respect to an observer Moving with respect to an observer -or- Photo by Andrew Davidhazy Assume Galilean velocity transformation holds:

Light must travel through a medium: hypothesize that a “luminiferous ether” exists from wikipedia

Light must travel through a medium: hypothesize that a “luminiferous ether” exists from wikipedia Earth is moving with respect to the ether (or the ether is moving with respect to the earth), so there should be some directional/season dependent change in the speed of light as observed from the reference frame of the earth.

The Michelson-Morley experiment -or. How to win a Nobel prize for an experiment that

The Michelson-Morley experiment -or. How to win a Nobel prize for an experiment that “failed” The basic idea: if we were truly stationary with respect to the ether: but the earth is moving… remember?

Motion along Arm 1: Motion along Arm 2:

Motion along Arm 1: Motion along Arm 2:

The real gizmo Light travels very fast so you are looking at very subtle

The real gizmo Light travels very fast so you are looking at very subtle difference-use several passes to multiply the effect. Need to select light of a particular frequency to detect any shift. Q: Can anyone guess why the invention of lasers made the Michelson-Morley experiment more convincing? A: Because lasers emit light with a precise wavelength. This is a consequence of the #6 quiz question being false. We will talk about that later in the course.

The Solution? ? ? The speed of light in vacuum has the same value,

The Solution? ? ? The speed of light in vacuum has the same value, c=30000 m/s, in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light. Oh my goodness…how can that be right? ? ? All the laws of physics have the same form in all inertial reference frames. Alright…we know that Newtonian mechanics worked in all inertial reference frames under Galilean transformations, but does the same hold true for Maxwell’s equations of electromagnetism?

The radical consequences Speed = distance traveled (in units of length) time elapsed If

The radical consequences Speed = distance traveled (in units of length) time elapsed If the speed of light is a constant…then…length and time must be variables? ? These effects are known as length contraction and time dilation. How come you never noticed this before, and how come most of the time I can get away with Galilean transformations in your calculations? speed of light = 670 616 629 miles per hour Most of the time the speed of the object whose motion you are calculating is do slow relative to the speed of light that the discrepancy due to relativity is negligible. (Most, but not all of the time)

Time dilation Consider two clocks: At rest with respect to each other: One moving

Time dilation Consider two clocks: At rest with respect to each other: One moving with speed v: d Moving clocks run slow c. T/2 d v. T/2 c. T’/2=d (v. T/2)^2+d^2=(c. T/2)^2

T=2 d/(c*sqrt(1 -v^2/c^2)) Using: c. T’/2=d T=T’/sqrt(1 -v^2/c^2) This is because the blue clock

T=2 d/(c*sqrt(1 -v^2/c^2)) Using: c. T’/2=d T=T’/sqrt(1 -v^2/c^2) This is because the blue clock travels a greater difference in the red clock’s frame of reference, and in both frames of reference the speed of light is the same. Food for thought: which clock appears to be traveling the greater distance in the blue clock’s frame of reference? Q: From the blue clock’s perspective, which clock runs slower? A: The red clock. Q: From the red clock’s perspective, which clock runs slower? A: The blue clock. Do we have a paradox?

Simultaneity The Facts as we know them now: • The clock “ticks” were defined

Simultaneity The Facts as we know them now: • The clock “ticks” were defined by a pair of events – light pulse emitted and light pulse detected • In the red clocks perspective – the separation in time for the blue clocks ticks are further apart in time • But the light pulses can be synchronized to be emitted together when the clocks were at the same place. Conclusion: to a stationary observer in one frame, the light pulse returned to the detector at a later time in the other frame. The paradox can be avoided by noting that: Simultaneity is not an absolute concept! It depends on the point of view of the observer (for spatially separated events).

Another Consequence: Length Contraction We can measure length by measuring the amount of time

Another Consequence: Length Contraction We can measure length by measuring the amount of time it takes to travel from one end of the object to another at a particular velocity… as a matter of fact, the meter was officially redefined in 1983 as the distance traveled by light in a vacuum in 1/299, 792, 458 of a second. …but the time it takes for this travel is different depending on your frame of reference. ---length is contracted!! Time always runs slower when measured by an observer moving with respect to the clock. The length of an object is always shorter when viewed by an observer who is moving with respect to the object. The proper length of an object is defined as the length of an object measured by someone who is at rest with respect to the object.

Is this science fiction? Muons, heavy cousins of the electron, have a mean lifetime

Is this science fiction? Muons, heavy cousins of the electron, have a mean lifetime of 2. 2 microseconds. They are created when cosmic rays interact in the atmosphere. If it were not for length contraction/time dilation, they would not survive long enough to reach earth—but they do. Global positioning systems use signals from clocks on board satellites to pinpoint your position. Are GPS satellites moving fast enough that you need to account for special relativity in order to make an accurate measurement? The answer is yes.

Ice. Cube http: //www. icecube. wisc. edu/

Ice. Cube http: //www. icecube. wisc. edu/

Tune in next time when we discuss Life in the fast lane: the kinematics

Tune in next time when we discuss Life in the fast lane: the kinematics of Star Trek