Physics 2 - Lecture 13: Special Relativity - Huynh Quang Linh
The Ultimate Speed Limit
Einstein’s second postulate immediately implies the
following result: It is impossible for an inertial observer to
travel at c, the speed of light in vacuum.
We can prove this by showing that travel at c implies a logical contradiction.
Suppose that the spacecraft is moving at the speed of light c relative to an
observer on the earth, so that If the spacecraft turns on a headlight, the
second postulate now asserts that the earth observer measures the
headlight beam to be also moving at c Thus this observer measures that the
headlight beam and the spacecraft move together and are always at the
same point in space. But Einstein’s second postulate also asserts that the
headlight beam moves at a speed relative to the spacecraft, so they cannot
be at the same point in space. This contradictory result can be avoided only
if it is impossible for an inertial observer, such as a passenger on the
spacecraft, to move at c. As we go through our discussion of relativity, you
may find yourself asking the question Einstein asked himself as a 16-yearold student, “What would I see if I were traveling at the speed of light?”
Einstein’s second postulate immediately implies the
following result: It is impossible for an inertial observer to
travel at c, the speed of light in vacuum.
We can prove this by showing that travel at c implies a logical contradiction.
Suppose that the spacecraft is moving at the speed of light c relative to an
observer on the earth, so that If the spacecraft turns on a headlight, the
second postulate now asserts that the earth observer measures the
headlight beam to be also moving at c Thus this observer measures that the
headlight beam and the spacecraft move together and are always at the
same point in space. But Einstein’s second postulate also asserts that the
headlight beam moves at a speed relative to the spacecraft, so they cannot
be at the same point in space. This contradictory result can be avoided only
if it is impossible for an inertial observer, such as a passenger on the
spacecraft, to move at c. As we go through our discussion of relativity, you
may find yourself asking the question Einstein asked himself as a 16-yearold student, “What would I see if I were traveling at the speed of light?”
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02/01/2023
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- SPECIAL RELATIVITY Albert Einstein (1879-1955) Tran Thi Ngoc Dung – Huynh Quang Linh – Physics A2 HCMUT 2016
- Einstein’s Postulates Einstein’s first postulate, called the principle of relativity,states:The laws of physics are the same in all inertial frames of reference. dW Einstein’s second postulatedt states: The speed of light in vacuum is the same in all inertial frames of reference and is independent of the motion of the source
- All observers see light flashes go by them with the same speed v No matter how fast the guy on the rocket is moving!! c Both guys see the light flash travel with velocity = c
- The Lorentz Coordinate Transformation Event A observed in reference frame O at y’ y t’ (x,y,z,t) , is observed at in ereference frame O’(x’,y’,z’,t’) t V=const The relationships between (x,y,z,t) and x’ (x’,y’,z’,t’) are given by the Lorentz O’ Coordinate Transformation O x t=t’=0 , OO’ z z’ v t x x vt 2 x' ; y' y; z' z; t' c v2 v2 1 1 c2 c2 v t' x' x' vt' 2 x ; y y'; z z'; t c v2 v2 1 1 c2 c2
- The Lorentz Velocity Transformation The relationships between The velocity of a point mass in the RF O and RF O’ u(ux ,uy ,uz ),u'(u'x ,u'y ,u'z ) v2 v2 u 1 u 1 u v y 2 z 2 u' x ; u' c ; u' c x v y v z v 1 u x 1 u x 1 u x c2 c2 c2 v2 v2 u' 1 u' 1 u' v y 2 z 2 u x ; u c ; u c x v y v z v 1 u'x 1 u'x 1 u'x c2 c2 c2
- Relativity of Simultaneity In RF O, two events A and B happen simultaneously :tA=tB In RF O’, two events A and B happen at time, t’A,t’B given by: B occurs v v t A 2 x A t B 2 x B y before A ' c ' c y’ t A t B v v 2 v 2 1 1 c2 c2 v O’ (t B t A ) 2 (x B x A ) O ' ' c x’ t B t A x v 2 xA xB 1 z’ c2 z tA tB ' ' t B t A , x B x A t B t A A occurs v (x x ) before B 2 B A A and B ' ' c ' ' t B t A x B x A t B t A occur v 2 v 1 simultaneou c2 sly O’ ’
- Relativity of Time Intervals –Time Dilation In a particular frame of reference, suppose that two events occur at the same point in space. The time interval between these events, as measured by an observer at rest in this same frame (which we call the rest frame y y’ of this observer), is t Then an observer in a t’=t’ -t’ o v 2 1 second frame moving with constant speed v x’A, relative to the rest frame will measure the time O O’ t x’ v x t' x' z z’ 2 t c ; x' 0 v2 t' 1 t t' c2 v2 1 to c2 t to v2 1 c2
- Proper Time (Thời gian riêng) There is only one frame of reference in which a clock is at rest, and there are infinitely many in which it is moving. Therefore the time interval measured between two events (such as two ticks of the clock) that occur at the same point in a particular frame is a more fundamental quantity than the interval between events at different points. We use the term proper time to describe the time interval between two events that occur at the same point.
- RELATIVISTIC DYNAMICS dp Classical dynamics v<<c, m const,F ma dt Relativistic dynamics: v c, mo m v m dp p mv o v2 F v2 1 1 c2 dt c2
- Relativistic Kinetic Energy 2 moc 2 2 1 EK E Eo moc moc 1 v2 v2 1 1 c2 c2 v2 1 v c : E m c2 (1 ) 1/ 2 1 m v2 K o 2 o c 2 1 E m v2 K 2 o
