What happens if you ride a light beam?
Albert Einstein proposed his celebrated special theory of relativity (STR) in 1905. At the heart of his theory was a picture that even children can understand. His theory was the culmination of a dream he had since the age of sixteen, when he asked the fateful question: what happens if you outrace a light beam? As a youth, he knew that Newtonian mechanics described the motion of objects on the Earth and in the heavens, and that Maxwell's theory described light. These were the two pillars of physics. The essence of Einstein's genius was that he recognized that these two pillars were in contradiction. One of them must fall. According to Newton, you could always outrace a light beam, since there was nothing special about the speed of light. This meant that the light beam must remain stationary as you raced alongside. But as a youth Einstein realized that no one had ever seen a light wave that was totally stationary, that is, like a frozen wave. Hence Newton's theory did not make sense. Finally, as a college student in Zurich studying Maxwell's theory, Einstein found the answer. He discovered something that even Maxwell did not know: that the speed of light is…
Frame of reference (point of view)
Inertial Frames- frame which are not accelerating, a=0. [Sports car moving at 200 km/h (constant v), a descending elevator, a man seated at the football stadium (at rest)]
Non-inertial Frames- a≠0 [Freely falling pebble towards the ground or astronaut around the Earth, the Earth revolving around the sun, spinning stars and galaxies]
Gedanken Experiment 1
*Observing the Moon: Is our moon rotating while revolving around the earth? Or Earth the one that revolves around our stationary moon? How about the stars?
Are the frames of reference different? Is there something wrong with the things we observe?
How do you tackle such questions?
Einstein said:
1.] “The laws of Physics are the same in all inertial frames of reference.” (first postulate)
What does it mean?
- All reference frames are just the same and equivalent.
- There is nothing wrong with the different frames of reference from where you do physics (observation).
For example: Suppose you are aboard seated inside a moving bus. Your seatmate would agree that you are at rest. But the policeman, standing by the sidewalk, looking at you, argues and says: NO, you are moving at the same speed as that of the bus. Then you watch the two children playing catch the ball along the aisle of the bus. Your observations of the motion of the ball, no matter how carefully done, can't tell you how fast (or whether) the bus is moving. The behavior of the ball is just the same when you do the same experiment on the ground. This is because Newton's laws of motion are the same in every inertial frame.
* An electromotive force (emf) is induced in a coil of wire by a nearby moving permanent magnet. In the frame of reference in which the coil is stationary, the moving magnet causes a change of magnetic flux through the coil, and this induces an emf. In a different frame of reference in which the magnet is stationary, the motion of the coil through a magnetic field induces the emf. According to the principle of relativity, both of these frames of reference are equally valid. Hence the same emf must be induced in both situations.
Take note that relativity emphasizes the catch-all term “laws of physics” which encompasses a whole lot of phenomena (all natural processes) that we could ever think of. This theory is really radical.
You can now answer our moon experiment and conveyor in outer space questions.
Now think about this:
We deduce that the laws of physics are Universal; it works everywhere.
-You can play badminton in Mars! =) (Classical Mechanics)
-You can heat water using a microwave oven and make some coffee even inside a fast-moving airplane. (Electromagnetism and Thermodynamics)
By experience and common sense, we already know all of this.
What does it imply?
>>>There is no universal frame of reference that can be used everywhere.
>>> It follows that there is no such thing as absolute motion!
Question: Am I at rest?
-this is a meaningless question unless you restate it. "Am I at rest with respect to the lecture hall and the Earth?"
Because all of us are moving since the Earth, our solar system, the Milky Way galaxy, and so on- are also moving
Gedanken Experiment 2:
[baseball]
While standing still, I throw a ball at a definite speed, v. (parabolic trajectory)
While riding on a bicycle at a constant velocity, I throw the same ball with the same speed, v. (longer trajectory)
[flash light]
Let’s try that again but now, using a light beam from a flashlight. Suppose we can slow down the speed of light to a speed comparable to that of the ball’s speed (which in fact we can do!) so that we could redo the experiment.
VCR: Constancy of the Speed of Light (The Universe: History Channel)
Question: If Maxwell's equations are valid in all inertial frames, then should the speed of light in vacuum also be the same in all frames and in all directions?
Einstein’s conceptual leap:
>>>the speed of light in vacuum should also be the same in all frames and in all directions.
Then, Einstein said:
[2] “The speed of light in free space (or vacuum) is the same in all inertial frame of reference and is independent of the source.” (second postulate)
Q: How fast did the light signal travelled from point A-B and back to A?
A: According to Special theory of relativity, the both light beams must travel at the same speed c.
Space and time must compensate for this constancy for it to hold true.
Time, therefore, is shorter in (2) [moving frame of reference] than in (1) [stationary reference.]
What does this tell us?
Time is not constant. One second in Mars is not one second in Venus. Time beats at different rates depending upon the relative motion of reference frames. Time is like the current in a river that meanders along the boulders and riverbanks speeding up or slowing down depending on the flow of water.
>Relativistic Time Dilation
>Mass Increase
>Length Contraction
>Mass-Energy Equivalence
Question: Since the laws of physics (or laws of nature) work everywhere, will it be the same (and still work) in the future? Were the laws of nature different a billion years ago?
Answer: Studying the spectral lines emitted from particular stars millions of lightyears from Earth, we find that the relic light has the same characteristics compared to the constituent elements found here on Earth. This means that the laws of nature hasn’t changed for billions of years and will continue to be constant still for a long time to come.
Definition: the first of two theories describing the relationship of matter, time, and space, showing that mass and energy are equivalent, and that mass, length, and time change with velocity.
The theory is based on two assumptions: that the speed of light in a vacuum is constant, and that physical laws have the same mathematical form throughout the universe. ![endif]--![endif]--![endif]--![endif]--