Strange and Unexpected Consequences of Special Relativity


By Robert M. Hazen, Ph.D., George Mason University

Einstein got special relativity theory in its great central paradox—that time and space are relative to an observer’s reference frame. How did the consequences of special relativity change the perception of scientists with regard to the universe, space, and time?

Vector Illustration of E = mc2 on a blackboard
One of the consequences of the Theory of Special Relativity was E = mc2 or Mass-energy equivalence equation. (Image: BrainCityArts/Shutterstock)

Special relativity had strange and unexpected consequences such as length of objects vary when measured in moving reference frames, mass cannot be accelerated to the speed of light and that time and space are not independent.

Relativistic Contraction

The fractional shortening is exactly equal to the Lorentz factor. So, if you saw a yardstick moving out in space, as it got near the speed of light, the yardstick, as you measured it, would get shorter and shorter.

The real paradox would be reached when you got to the speed of light, the yardstick would appear to shrink to zero, at least if it was moving laterally to you.

Learn more about Newton’s laws of motion.

Relationship between Mass and Relative Velocity

Mass also depends on velocity. The greater the relative velocity, the greater the mass of the object. And here again, the increase in mass is inversely proportional to the Lorentz factor.

Suppose a mass out in space gets closer to the speed of light, it appears to become more massive. It also appears to have more gravitational attraction. And, if you ever could get the situation where mass was accelerated to the speed of light, it would have infinite mass.

This is the reason that one of the definitions of an object’s mass is the resistance to being accelerated by a force. And since an infinite force is necessary to accelerate an infinitely massive object, you can never accelerate a mass to the speed of light. And this is why this theory of special relativity forbids any mass from being accelerated to the speed of light.

There’s a remarkable consequence here. At least mathematically, this means that any object traveling faster than light speed can never decelerate to below light speed. You can actually have objects traveling faster than the speed of light, or they can travel slower. They just can’t travel at the speed of light according to these equations. Now, the equations may not model all situations in the universe and an interesting consequence of Einstein’s law.

Implication of Special Theory of Relativity

Infographic representing Special Theory of Relativity showing relationship between time and space for physics science education
Theory of Special Relativity is a generally accepted theory regarding the relationship between time and space. (Image: udaix/Shutterstock)

Einstein formulated the remarkable idea that if light speed is a constant in all reference frames, the consequence is that time and length and mass have to be relative. He then realized another profound implication of his special relativity theory that he hadn’t thought about at first.

The first law of thermodynamics has to apply to every reference frame. The total amount of energy has to be constant, but since mass increases with velocity, the total amount of kinetic energy (mass times velocity squared) can’t follow the energy conservation law in this case.

This led Einstein to realize there has to be an equivalence, then of mass and energy. He wrote this short revolutionary paper explaining the paradox, and he prepared the equation, E=mc2. Energy equals mass times the speed of light squared, and that’s the rest energy that corresponds to your mass.

This is a transcript from the video series The Joy of Science. Watch it now, on Wondrium.

General Relativity

Einstein’s theory of special relativity, dealing with reference frames in uniform motion is a fairly straightforward process in algebra. However, general relativity, which deals with accelerating reference frames is a different matter. It provides all sorts of new perspectives on forces in nature, and yet to actually go through the whole process of understanding is extremely difficult.

Let us consider just a simple thought experiment where if you are in a sealed, windowless room on a spaceship that was accelerating at exactly one G—that’s the acceleration of gravity at the Earth’s surface. Is there any way that you could tell that you were in a spaceship as opposed to being just on the surface of the Earth being pulled down by the Earth’s gravitational force?

The answer Einstein concluded is absolutely not, that the acceleration due to gravity at the Earth’s surface feels exactly as it would in deep space if you were in a rocket ship that was accelerating at one G. There was no way to tell those two apart.

Learn more about the quantum world.

Difference in Predictions of Newton and Einstein 

Gravitational forces and acceleration then are somehow equivalent and this is a very deep distinction. There’s arbitrariness to whether you call gravity an acceleration or force. Newton saw the connection in his laws of motion.

According to Newton, force equals mass times acceleration, so mass becomes the scaling factor between the force and the acceleration. But Einstein explored the universal equivalent from a relativistic point of view.

View of the Universe

Newton thought of the universe as a flat surface; balls roll in a straight line and at a constant velocity unless acted upon by a force. Newton would say that the moon follows a curved path around the Earth because of that gravitational force.

Einstein, however, had a new way of thinking about the universe. He saw the universe as being a series of warped surfaces, and mass warps that surface. So balls follow contours along this warped surface. An object in orbit, therefore, is following the contour around one of the deep gravitational wells.

Applications of Newtonian and Einsteinian formulations

When people did experiments, when they saw light coming from a distant object passing a galaxy or passing a star, they actually were able to measure that bending of light. The exact shape of orbits differs slightly in the Newtonian and in the Einsteinian formulations. Meticulous observations show that Einstein’s model works better than Newton’s when you make very precise and accurate measurements.

Also, Einstein predicts that the frequency—that is the color of light shining upward in a gravitational field—should decrease slightly, while light shining down on the gravitational field should increase in frequency slightly because gravity affects light, and it affects its wavelength. These predictions have also been demonstrated quite clearly using lasers.

These observations don’t mean that Newton was wrong. It only means that Newton’s laws work extremely well for low velocities, for everyday sorts of situations that we experience.

Common Questions about Special Relativity

Q: What was the difference in the way Newton and Einstein thought about the way light travelled?

Newton thought light travelled in a straight line while Einstein perceived light should follow the warping of space and thus bend.

Q: What was the consequence according to Einstein if speed of light was a constant in all reference frames?

Einstein formulated the remarkable idea that if light speed is a constant in all reference frames, the consequence is that time and length and mass have to be relative.

Q: You can never accelerate a mass to the speed of light. Why?

Since an infinite force is necessary to accelerate an infinitely massive object, you can never accelerate a mass to the speed of light.

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