Lecture08

Lecture08 - Physics 344 Foundations of 21st Century...

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Physics 344 Foundations of 21 st Century Physics: Relativistic and Quantum Systems Instructor: Dr. Mark Haugan Office: PHYS 282 haugan@purdue.edu TA: Dan Hartzler Office: PHYS 7 dhartzle@purdue.edu Grader: Fan Chen Office: PHYS 222 chen926@purdue.edu Office Hours: If you have questions, just email us to make an appointment. We enjoy talking about physics! Help Session: Thursdays 2:00 – 4:00 in PHYS 154 Reading: Chapters 4 and 7 in Six Ideas that Shaped Physics, Unit R.
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Q1. In an inertial frame S two events are observed to occur 4 nanoseconds apart in time and separated by 3 nanoseconds of distance. An observer in another inertial frame claims to observe that these events happen simultaneously. Can they possibly be correct? Be prepared to explain your answer. A) Yes, it is possible. The events will happen simultaneously in some frame. B) No, it is not possible. The events cannot happen simultaneously in any frame. * There is a timelike separation between the pair of events. The S-frame measurements lead to a positive value of the squared interval between the events, ( 29 ( 29 2 2 2 2 2 2 2 2 2 2 1 4 3 nanoseconds 5nanoseconds s t x y z c = ∆ - + ∆ + ∆ = - = The other observer’s claim would imply a spacelike separation and, thus, a negative value of the squared interval between the events. The invariance of the squared interval means that its value for a pair of events is the same in all frames, so, it is impossible for the claim to be correct.
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Causality As we’ve seen, the relativity of simultaneity implies that inertial observers in relative motion can sometimes disagree about the time order in which pairs of events occur. For example, this spacetime diagram shows a pair of events with event 1 happening before event 2 as measured in S , but event 2 happening before event 1 as measured in S’ . 1 2 t t x x This creates a potential problem with the concept of causality. If something that happened at the location and time of event 1 could cause something to happen at the location and time of event 2, then as observed in S’ the cause would happen after the effect! Needless to say, this cannot occur. As we will see, it does not occur because of the fundamental speed limit c .
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This spacetime diagram shows the worldline of an accelerated observer. Event 1 is on that worldline, so, the observer could act at that location and time to cause things to happen at other events. What could they do to accomplish this? 1 2 t t x x 3 1. They could emit pulses of light (photons) whose dotted worldlines are shown traveling away from event 1. In principle, such pulses can cause things to happen at any event along their worldlines. For example, such a pulse could be absorbed by some object at event 3. We say that event 3 lies on the future
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Lecture08 - Physics 344 Foundations of 21st Century...

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