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Did you Know? Energy is Relative Too

There are many levels to relativity theory. While scientists like Galileo and Newton believed in relative motion, they did not conceive of Einstein’s Special or General Theory of Relativity. Let’s do some thought experiments together that may help you understand some things about relative motion and energy.

Thought question: Can an apple travel at 1,000 mph in empty space?

In your mind, take an apple (I’m using a honeycrisp) and place it in empty space, with no other matter in sight. Now, ask yourself, where is it? Quickly you will realize that position is relative. You need something else there in order to answer this question. Go ahead and place the Earth 5,000 miles from it. Now you know where the apple is; it’s 5,000 miles from the Earth.

Now let’s go back to just the apple; no Earth. How fast is it moving? Just as quickly, you realize the question is meaningless. We require another object. Put the Earth back where it was. Ok, now you can measure the apple’s speed and velocity. It’s not moving toward or away from the Earth, so 0 m/s, which means no speed, and no velocity (remember here that velocity is just speed in a certain direction). Is this “no speed” the same as its speed when there was no Earth? Think about it a bit.

The answer is, “No, absolutely not.” The first question was meaningless since there was nothing to compare the motion to, but the second is something you can measure and has meaning. The apple’s motion, we say, is only real relative to another object. So now you know the answer to the thought question: Can an apple travel at 1,000 mph in empty space? No, there is no motion in empty space. Motion requires more than one object. It is relative.

Now, go ahead and place the apple in an

apple cannon and shoot it at 1,000mph toward the Earth. Assuming we didn’t make applesauce and the apple is still whole, we can now measure its speed and velocity. It’s traveling toward the Earth at 1,000mph. Well good, let’s hope it doesn’t hit anyone when it gets there. That’s a fast apple!

New Thought Question: How fast is an apple on a table moving?

Speaking of fast apples, let’s now catch the apple in our fancy non-bruising fast-apple catching machine and place it on our table. Now, add our solar system and the rest of the known universe to our model. Now I ask you, how fast is it moving?

“It’s not,” you say. “You just placed it on the table.”

True enough. If the table is not moving, then the apple is not moving. Now, catch the quick lift to the Moon, get off, and look at the apple again (with your handy-dandy super pocket telescope). Is it moving now?

“Yes, it’s rotating with the Earth.”

Yeah, and at your latitude, it’s going about 700mph, just with the rotation!

Let’s move on, figuratively, and think about how fast the apple would be traveling if you jumped aboard a starship and headed out above the solar system. Now how fast do you see the apple going? Now it doesn’t just have the speed from rotation, but add to that (or subtract, depending on the time of day, and your angle) the motion of Earth traveling around the Sun at 66,500mph. That’s a fast apple!

Image Credit: NASA

But wait, there’s more. It turns out our Sun is traveling around the Milky Way Galaxy at an average of 514,000mph, meaning our apple is moving more than half a million miles an hour, being part of the Milky Way. But that’s not all, act now and you can learn that the Milky Way is part of a galaxy cluster called the Local Group and this Group is moving (compared to other groups of galaxies) at a whopping 1.4 million miles an hour! Now you can rename your apple: The Flash!

“Ok”, you say, “So what, I’ve got an Apple Superhero. What good is that?”

Well, now that you know your apple has many different motions, let’s see what its kinetic energy is (reminder: Kinetic Energy is energy of motion, and is directly related to one half an object’s mass times its velocity squared, or KE = ½mv^2).

The faster an object moves, the more kinetic energy it has. Not to bore you with the math, but if you think about the equation a bit, when you double the speed of your apple, its energy quadruples. This is due to the squaring of the velocity (i.e. two squared is four). Ok, enough math. We’ll keep it mainly conceptual now, with only references to the math.

Imagine now with me, if you will, how your apple’s energy must change when we move from resting table apple to Moon apple, to Sun apple, to Galaxy apple, to Galaxy Cluster apple. Ok, I lied, a bit more math here, bear with me: If you go from 700mph (Earth’s rotation) to 1.4 million mph (Local Group movement), that’s a 2,000 times increase in speed (a simple division problem). Two thousand squared is 4 million, so that’s 4 million times the energy that your apple now has because it is traveling with the Local Group, compared to the energy given to the apple as a result of the Earth's rotation.

Is your brain hurting yet? Hope this is not too painful, but now, you are probably wondering: How can my apple have all of those energies at once? The answer: energy too, is relative, especially when we’re talking about kinetic energy. If someone asked you about your apple’s kinetic energy when it was out in empty space, the question would be just as meaningless as its position or motion. Once you place it in a room, on a table, now you can measure its kinetic energy; it has zero kinetic energy here. Then later, it has different kinetic energies for each different viewpoint. This shows you that kinetic energy means nothing by itself and is just as relative as position and speed or velocity.

Now, fortunately, if you understand that, you understand the type of relativity that Galileo and Newton believed in. Unfortunately, only part of it is true. The good thing is, it's the large part that is true. Even considering Einstein’s Relativity theories, the ideas we just discussed are still correct.

The specifics of how much an object increases in energy when it moves faster now goes by a different equation; one developed by Einstein in his Special Theory of Relativity (video link here). Fortunately, your apple would have to be traveling roughly 80 million mph in order for its kinetic energy to change a noticeable amount from the original equation. Therefore, the good old high school equation: KE = ½ mv^2 is going to be good enough to explain the change in energy for our Apple Superhero!

So, the next time you are stopped by a police officer for speeding, well, you have many new ways you can answer the officer. You can just tell her that she’s speeding too; that we can’t not speed. Just look at our motion around the Sun and we’re already clocking 66,500mph before we hit the accelerator! Or, you could explain to her that you were not moving at all, compared to your vehicle. Or, you could tell her about the Local Group and how we’re all traveling over a million miles per hour! Either way, in all likelihood, you’ll still end up with a ticket, but depending on the officer, maybe she’ll give you a warning 😉.


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