Q: What is the best way to understand relativity theory? Why is it so counter intuitive?

Physicist: 1) Pictures and math.  2) Work through and understand the “train struck by lightning” and “barn running pole vaulter” thought experiments, to better understand the relationship between space and time.  3) Pick up a book on modern physics and do a mess of random homework problems.  4) Build something that involves relativity.

As for the second question; This is one of my favorite examples of the Allegory of the Cave.  Intuition is based on experience and the mental wiring we have evolved and inherited.  Almost everything we interact with day to day is smaller than a mile, slower than 60mph, weighs less than a ton, and takes less than a year.  At the scales we’re used to the laws of physics are fairly intuitive.  Humankind spent tens of thousands of years thinking that light is instantaneous.  And who could blame them?  Magellan took a leisurely three years to work his way around the planet (easy to imagine), whereas light can do it in about 1/7 of a second (hard to imagine).

Gamma (\gamma) is a term that shows up a lot in special relativity, and describes how much things get messed up by moving fast (time dilation, length contraction, mass increase, …).  It’s fairly easy (pre-calculus easy) to show that \gamma = \frac{1}{ \sqrt{1-v^2/C^2} }.  Notice from the graph below that relativistic effects are barely noticeable until around V= 0.5 C (C is the speed of light).

Gamma vs. Velocity.  Gamma = 1 is the normal, every day experience.

Gamma vs. Velocity. Gamma = 1 is the normal, every day experience.

On this graph the speed of light is at V=1.  For comparison, the speed of sound is around V = 0.000001, and the fastest that any human has ever traveled is around V = 0.00003.  You can use \gamma to show that Astronauts and Cosmonauts that have spent years in orbit, traveling in excess of 7.5 km/s, still lose less than one second of time total, compared to people on the ground.

When physical laws work actively on scales we’re used to, they tend to become intuitive.  The laws of the very big, small, old, hot, cold, fast, … are the same laws, we just experience a special case.

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3 Responses to Q: What is the best way to understand relativity theory? Why is it so counter intuitive?

  1. metal-fan-666 says:

    The light clock is by far the easiest thought experiment to get a grip on relativity. the only thing it requires is a very basic understanding of right angled triangles.

    The right angle is the largest angle in a right angled triangle. this has to be so as the sum of the internal angles of a triangle is 180 degrees, thus if a right angled triangle had another angle 90 degrees or higher then it couldn’t be a triangle. As it is the ‘widest’ angle, the side opposite that has to be the longest side (the hypotenuse).

    With that much understanding you can grasp relativity. now for a little creative thinking.

    Lets say someone (Person 1) is inside some moving object, a train for example. There is another person (person 2) standing outside, watching the train pass by.

    Lets say Person 1 has his favorite contraption on board. It is a simple mechanism, consisting of a flashlight on the floor of the train and a mirror on the roof. when the flashlight is turned on, lets say for 1 single light pulse, the light pulse travels from the floor to the mirror on the ceiling and back to the flashlight again. We could throw some numbers at this but it is not really neccessary.

    Lets say Person 1 activates this ‘light pulse’ as the train passes Person B.

    Person 1 would see the light pulse travel a fixed distance to the ceiling, and that same fixed distance back to the ground. Essentially, they would see this:

    *Person 1*

    —– ceiling/mirror
    ^I
    I I
    I I
    I I
    I I
    I I
    I v
    —- floor/flashlight

    This is Person 1′s ‘>>frame of reference< direction of train.

    As the train is not stationary, and the speed of light is fast but not instantaneous, the flashlight must have moved forward (as it is connected to the train) at least a little bit. Person 2 sees the light move at an angle (2 dimensions) , while Person 1 sees it travel in a straight line then back (1 dimension).

    examining the above diagram:

    C

    / i \

    / i \

    / i \

    / i \

    / i V

    B———A———-D

    Look at the triangle CABC, it is a right angled triangle. The line CB is the hypotenuse as it is opposite the right angle (angle CAB is 90 degrees).

    That means:

    Person 1 saw the light travel from Point A (floor) to point C (ceiling) and back to point A.

    Person 2 saw the light travel from Point B (flashlight when the ‘light pulse’ is created) up to the roof (Point C) and back to the floor again at Point D (that is, the flashlight in its new position).

    Clearly, the Line BC+CD is longer than AC+CA. Again, we can use some numbers but it is of little relevance as the only important thing to understand is that 2 different observers viewed the same event occur but both have a different account of that event.

    How can anything travel two different distances in the same amount of time while supposedly traveling at the same speed?

    Either the speed of light was different for the 2 observers, or the 2 observers experienced time differently. As it is currently an established norm that light always travels at the same speed (a widely held belief) the only ‘rational’ explanation is that the two observers experiences of time were different.

    Now, imagine this train going very fast. The faster the train goes, the longer the distance Person 2 sees the light beam travel. Thus, the closer you travel to the speed of light, the larger the difference between your experience of time and the time experienced by someone else >>outside your frame of reference<<.

    There are some other issues like length contraction involved but these are of little importance at this stage as this is for a base understanding of relativity. Both of the obeservations made by Person 1 and Person 2 can be tested over and over again with the same results, leading to the idea that no frame of reference is incorrect. If all of the above is true, then we can only come to the following conclusions, of which one or more must be true.

    a) the speed of light is variable
    b) time is experienced differently by people in different frames of reference
    c) things get 'shorter' in their direction of travel.

    As everything is in motion _relative_ to everything else (are you stationary right now or are you spinning thousands of kilometers per hour through space), relativity must be taken into account. Thankfully when you do the calculations, you need to be traveling at very high speeds before any relativistic effects become meaningful.

  2. metal-fan-666 says:

    my apologies for the formatting error, it seems spaces in diagrams arent dealt with well. Point C should be directly aboive Point A, with the slashes joining BC and CD. This was supposed to be an exaggerated example of another diagram that has gone missing between the first and last diagrams.

    I would do it again but i assume the same issue would occur

  3. Pingback: Q: How do velocities add? If I’m riding a beam of light and I throw a ball, why doesn’t the ball go faster than light? | Ask a Mathematician / Ask a Physicist

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