Problems with “The” Speed Limit
According to Einstein’s theory of relativity, the speed of light is a “universal speed limit.” But this raises a deeper question: the universal speed limit in relation to what?
Whenever someone tells us the speed of something, for example 50 miles per hour, we should immediately ask, “in reference to what?” Here’s why.
Imagine that someone throws a baseball in a stopped train. The throw happens in a train car with transparent sides and we can see the thrower, the ball, and the person ready to catch the ball from both inside and from outside of the train car. The thrower throws the ball at 50 MPH. Smith, who is in the train car, sees the ball travel at 50 MPH. Jones, who is outside the train car, sees the ball travel at 50 MPH.
This example is straightforward when the train is stopped. However, when the train is moving, the situation changes. Again, Smith is in the train car, and he still sees the ball traveling at 50 MPH. Jones, who is outside watching the train move past her, sees the ball traveling at 80 MPH because the train is moving at 30 MPH and the ball is moving at 50 MPH in the same direction. For Smith, because he is moving with the train, the relevant speed of the ball is simply the speed of the ball relative to him and the train. For Jones, who is at rest relative to the Earth, both the train and the ball are moving—here the same direction—and the relevant speed of the ball for her is the sum of the speeds of the ball and the train. Stated differently, the ball is moving 50 MPH relative to Smith and 80 MPH relative to Jones. If the train were moving in the opposite direction, Smith would still see the ball move at 50 MPH but Jones would now see the ball move at 20 MPH.
When the ball is moving in the same direction as the train, Jones sees the sum of the two speeds: 80 = 50 + 30. When the train is moving in the opposite direction, Jones sees the difference of the two speeds: 20 = 50 - 30.
There is no special reference spot in the universe from which we can measure speeds. It is always “speed relative to X.” This is one of the two key principles Einstein employed to undergird his special theory of relatively.
Key Principle #1 of Special Relativity
There is no reference spot in the universe that we can say is at rest and is therefore not moving. The Earth spins daily on its axis as it orbits annually around the sun, which itself orbits around the center of the Milky Way galaxy.
There is no known experiment to prove that someone who is not accelerating is either in motion or at rest. That person could be at rest in some universal sense or that person could be whizzing along at 1,000 miles an hour in uniform motion. We can’t tell.
Therefore, everything that is not accelerating is “at rest” or moving in uniform motion relative to something else that may be “at rest” or moving in uniform motion.
If two observers are in uniform motion (i.e., there’s no acceleration), even if they are moving at different speeds and different directions, then they will each experience a reality that is correct. In other words, physics will behave normally for them. Both of them could run experiments to test Newtonian physics and they will both get the same answers. We can’t say that one observer’s frame of reference is correct and the other’s is incorrect; they both have correct frames of reference. Both frames of reference are equally valid.[1], [2], [3], [4]
Moving Objects
We’ve discussed the Earth and the sun. Other objects move more quickly.
Some things rotate very quickly. “The pulsar PSR J1748-2446ad rotates 716 times a second (what is known as a millisecond pulsar) in the globular cluster Terzan 5. With an estimated radius of 16 kilometers (10 miles) that means its equator is travelling about 70,000 kilometers per second (43,500 miles per second), or 24 percent of the speed of light.”
Some things move quickly across distances. Comets come and go over the years. Cosmic rays, which are really subatomic particles, travel in all directions at speeds very close to the speed of light.
Universal Speed Limit Relative to What?
If the speed of light is the universal speed limit, what is it measured in relation to? Relative to Earth? Relative to the sun? Relative to the center of the Milky Way? Relative to Haley’s Comet? Relative to cosmic rays going from left to right? Relative to cosmic rays going from right to left?
Do you see where this is going?
If I can theoretically move from left to right at the speed of light, or close to it, relative to a cosmic ray moving from left to right, then I have exceeded the speed of light relative to a cosmic ray moving from right to left.
Similarly, if I can move from right to left at the speed of light, or close to it, relative to a cosmic ray moving from right to left, then I have exceeded the speed of light relative to a cosmic ray moving from left to right.
If a “universal speed limit” can’t be exceeded, then the mechanism that enforces that speed limit must be determined in relation to something else. If the universe has forces that won’t let me exceed the speed of light, what reference point are those forces using to measure my speed? Earth? The sun? A cosmic ray? Given a certain direction and speed (really velocity), my movement may be well within the speed of light measured versus the Earth and sun but not a particular cosmic ray.
If objects need to stay at or below the speed of light relative to all other things in the universe, then two cosmic rays moving in opposite directions violate the rule every second of every day. That cosmic ray moving at close to the speed of light from my left to my right is traveling faster than the speed of light in relation to a cosmic ray moving at close to the speed of light from my right to my left.
That seems like a crazy way to run a universe.
[1] Mook and Vargish, Inside Relativity, Princeton University Press, 1987, pg 65.
[2] Moore, Six Ideas That Shaped Physics, Unit R, McGraw Hill, 2003, pg 25.
[3] Wolfson, Einstein’s Relativity and the Quantum Revolution, The Teaching Company, 2000, Lecture 7, Einstein to the Rescue.
[4] Hey and Walters, Einstein’s Mirror, Cambridge University Press, 1997, pg 51.