From Special Relativity to Feynman Diagrams.pdf

# On the other hand x c has the meaning of the time τ

This preview shows pages 35–37. Sign up to view the full content.

On the other hand x / c has the meaning of the time τ AB that a light ray takes to cover the distance x = x B x A ; therefore the condition will be satisfied if: t < τ AB . (1.65) When ( 1.65 ) holds one immediately finds that the velocity V of S with respect to S must satisfy the inequality: V > c t τ AB , (1.66) what is certainly possible with V < c . Having established under what condition it is possible to invert the chronological order of two events by a change of reference frame, let us now assume that the event A sends a physical signal at a velocity c > c and that this signal determines the occurrence of the event B . (For example, with reference to Fig. 1.9, the event A can be the pressing of a switch by the observer S at t A with the emission of a hypothetical signal of velocity c > c whose effect in B is the lighting of a lamp at a later time t B .) In this case the inequality ( 1.65 ) is certainly satisfied since t = x / c and c > c . We then reach the conclusion that, if a signal propagating at velocity c > c existed, that is if it were possible to transmit information at a velocity greater than c , then two causally related events in one reference frame would appear in a different frame in the inverse temporal sequence, thus violating the principle of causality , since the effect would precede its cause. Since we cannot give up the principle of causality, we conclude that: No physical signal can propagate at a velocity greater than the speed of light. Time dilation : Equation 1.60 provides the explicit transformation law for the time intervals. Consider a reference frame S in motion at a constant speed V relative to another frame S (the standard configuration of the two frames is understood) (Fig. 1.9 ). Suppose an observer in S is measuring the time lapse t = t B t A between two events A and B which occur in S at the same place but at different times, so that

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
24 1 Special Relativity Fig. 1.9 Event A causing event B t B > t A (for instance two successive positions of the second hand of a clock at rest in S ). If the events occur in S along the x -axis, we then suppose x = x B x A = 0. From ( 1.57 ) it then follows that x = V t . Substituting this relation in ( 1.60 ) we find t = γ ( V ) t V c 2 x = t γ ( V ) 1 V 2 c 2 = t γ ( V ) . (1.67) We conclude that the time lapse measured in S is t = γ ( V ) t > t . (1.68) This means that if an observer at rest in the frame S measures a time interval t , an observer in S will measure a lapse t greater than t by a factor γ ( V ) . As an example, let S be a spacecraft traveling at a high velocity V relative a laboratory frame S on earth, and let time in S and S be measured by two identical clocks. Suppose the observer in S measures the rate at which the clock inside the spacecraft ticks. He notices that the clock in S runs more slowly than his, that is time on the spacecraft flows more slowly than on earth.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern