Special Relativity: Intuitive Explanation

During the early years of the twentieth century, Albert Einstein revolutionized our understanding of the physical world. In 1905 he proposed his special theory of relativity, which fatally undermined common assumptions about the nature of the space and time. One of the major predictions of the special relativity is the differences in measurement of time and length between observers moving at different relative speeds. Time seems to move slower for objects that are moving faster than us. This is called time dilation. Also, measurement of the same length in direction of movement is different for observers moving at different speeds. This is called length contraction. The goal of this post is to explain why length contraction and time dilation happens without resorting to complex mathematical derivations, the use of non-intuitive spacetime diagrams, and comparisons with Newtonian physics.

There is only one speed: speed of light

The primary observation that leads to predictions of time dilation and length contraction by Special Relativity is the constancy of light’s speed. This is true, no matter how fast the observer (the agent who is emitting light) moves. Many experiments including famous Michelson-Morely experiment have shown this to be true.

If you break the matter to small enough pieces everything moves at only one speed, the speed of light. So in a sense, there is only one speed and everything moves at that speed. This is different than velocities we observe at the macro scale. You can imagine a particle moving at speed of light in a back and forth manner which makes its total displacement in time much smaller than its speed. This is in fact at the heart of understanding Special Relativity.

Slower displacement than the speed

The matter at small scale is composed of electrons, protons, and neutrons. Protons and neutrons themselves are made of quarks. Both quark and electron can be moving at speed of light if they were not confined by Higgs field, electromagnetic field, and gluon field. If we break matter into small enough pieces, it consists of particles that move at speed of light but are confined by forces from different fields which reduces their combined speed to slower than light speed.

You can think of the matter as a box of light speed particles that is confined with forces of different fields. Every small particle moves at the speed of light but their velocities don’t always align in the same direction to move the whole box.

Matter composed of confined light speed particles

For a stationary matter, its particles move at speed of light in all directions but particles are equally likely to move in any direction so that they cancel each other’s movements and the matter as whole stays in the same place.

In a stationary matter, a particle is equally likely to move in any direction. Each arrow shows a potential velocity a particle can have. Since light speed is the only speed, it is easier to choose the units such that light speed is 1 in all our diagrams.

If the matter starts to move at a velocity (V=v/c), while the speed of individual particles stays constant at light speed, from the view of the person moving with the matter, the speed of each particle should appear different such that they contribute to the total velocity V.

In a moving matter, all particle’s speeds should get modified from the point of the view of the observer moving with it.

Particles moving in direction of V should seem to move slower as they take longer to reach particles in front of them. Particles in front are on average moving away at speed equal to V. On the other hand, particles moving in the opposite direction of the matter’s movement should appear to move much faster. Particles in the back are displacing toward particles in front on average at speed V.

So if the matter starts displacing, the person moving with the matter should measure the speed of light in each direction as shown in the following diagram.

If the measurement of time and distance don’t change with changes in speed, we should measure different light speeds in different directions.

But according to experiments such as Michelson-Morely, the speed of light should stay constant in all directions no matter how fast we move. This means that either measurement of time or space or both changes for moving observer in a way that they still measure light speed constant in all directions. In order to better understand changes in time and space, we need to talk about the nature of the time and its relation to space.

True nature of time and its relation to space

Time is an indicator of change in the universe. If the universe never changes, time never passes. We get old because our body goes through changes and these changes are driven mostly by molecules going through different chemical reactions. Chemical reactions themselves are driven by the interaction of particles of matter with each other. At small enough scale passage of time is the number of interactions particles of matter have with each other. The faster they interact the faster time goes by.

Going back to the box of light-speed particles representing matter, the passage of time is dependent on the average measured distance between the particles and their speed. If the speed of light-like particles in a moving matter comes out to be lower in our derivations than the speed of light, it is the case that either time is slowing down or length is contracting in such a way that light-like particles will end up moving at the same speed as light for an observer moving with the matter.

Time dilation

As mentioned before, if the measurement of time and length don’t change, a moving matter seems to experience different light speeds in different directions.

What measurement of light speed for a moving observer should be if time dilation or length contraction don’t occur

Since passage of time is the interaction of particles with each other, and the number of interactions is calculated from back and force speed of particles in each direction and its reverse, the average speed in each direction and its reverse should be an indication of how fast the time is progressing. The figure below shows these average speeds for a moving matter. It is built from the diagram above but average speed is calculated from a pair of forward and backward speed in each direction.

Average speed in each direction without time dilation or length contraction. These average speeds give us a skinny ellipse. The blue circle is what the experiment tells us these speeds should be. A constant speed of light in all direction.

Now we know time is orthogonal to all spatial directions, so if we dilate time (clocks running slower for the observer) all measured speeds will increase in all directions. The amount of dilation is driven by the smallest average speed which is in the orthogonal direction to the movement.

Time dilation calculation is simple Pythagoras theorem

After time dilation the speeds will increase in every direction:

After time dilation, the speeds in an orthogonal direction to movement matches experiment

Even though speeds orthogonal to the direction of movement now match experimental observations, speeds parallel to the direction of movement still need modification to match experiment.

Length contraction

After applying time dilation, speeds parallel to the movement still come out to be less than the speed of light. Length contraction in direction of movement is needed to match the speed of light. Average speed in a parallel direction to movement without time dilation and length contraction is average of 1+(V/C) and 1-(V/C), which is 1- (V/C)².

Applying time dilation and then length contraction brings this speed to 1.

After both time dilation and length contraction along the direction of movement, the speed of light is constant in every direction and matches experimental results

Conclusion

Understanding special relativity doesn’t require mastery of complicated math or a full understanding of classical Newtonian physics. If we start from postulates we should be able to drive Lorentz transformation with limited mathematical or physical knowledge.