Galilean Relativity

by Luke Muehlhauser on October 8, 2010 in Science

I keep saying that one of my biggest objections to the Kalam Cosmological Argument is that the argument depends on the A Theory of time, but the A Theory of time is probably false. This won’t raise eyebrows among physicists, but many of my readers have asked, “Uh… what are you talking about?”

So I’m writing a series on the nature of time. Hang in there, this is exciting stuff.

First, we have to understand Einstein’s theory of special relativity. And before that, we should understand Galileo’s concept of relativity.

But first, let me say that to some extent, everybody already understands relativity.

Imagine yourself on a cruise ship in the Pacific, traveling at a steady speed in a straight line in perfectly calm waters.1 The ship isn’t slowing or accelerating or rocking at all.

And you want to play tennis with a friend. So you go below deck to the gym and start playing. Now, I have some questions for you: Do you care whether you’re the player facing the forward-facing direction of the ship, or the backward-facing direction of the ship? Do you have to take into account the speed and direction of the ship when you hit the ball?

Of course not. You play tennis on the cruise ship exactly like you would back on solid ground.

Or imagine you’re eating lunch on an airplane. When guiding the food to your mouth, do you have to account for the fact that it is moving at 600mph? Of course not.

Or imagine you’re playing tennis in an underground base on Venus, which has a gravitational pull about equal to that of Earth. On Venus, you could be moving (relative to Earth) at 20 miles per second – very, very fast! Do you have to take that into account when you hit the tennis ball in the base on Venus? Of course not.

One more example. Imagine you’re on a planet in one of the distant galaxies that is moving away from our galaxy at astonishing speed; at 80% the speed of light! Playing tennis on that distant planet, do you have to worry about the fact that you’re moving at such mind-bending speeds relative to Earth? Nope. You just play tennis like usual. What the Earth is doing doesn’t matter to you one bit.

No place special

Why don’t you worry about the fact that the ship and the plane and Venus and the distant galaxy are moving relative to Earth? Because there’s nothing special about Earth when it comes to the laws of physics. The laws of physics work the same whether you’re on Earth or Venus, and whether you’re traveling at 20mph relative to Earth or at 80% the speed of light relative to Earth.

Earth is not special, and in fact no place in the universe is special. And if you answered the above questions about tennis correctly, then you get that. And that’s all relativity says. Relativity says there is no special place. The laws of physics work the same for everybody.


What we’ve just described is the principle of Galilean relativity: the laws of motion are the same for anyone, provided they are in uniform motion (that is, not changing in speed or direction).

(But obviously, if gravity is different, your tennis game will be different. Technically, Venus’ gravity is a bit smaller than Earth’s gravity, so the tennis ball won’t hit the ground as quickly as it would when you’re playing on Earth. And if you play tennis in uniform motion in deep space where there is not much pull from the gravity of a nearby massive object, your tennis game will be very different. But the laws of physics will be the same no matter where you are, as long as you’re in uniform motion, and even if you’re moving at 80% the speed of light relative to Earth.)

Another way to say this is that all motion is relative. Imagine you’re sitting in your chair and I sprint past you, you might say, “Woah, there, slow down!” From a physics perspective, I have every right to say, “What do you mean? You just whizzed past me in that chair of yours!” We are both moving, relative to each other. The reason we don’t talk this way is that by default we all describe motion relative to the nearby surface of the Earth. And relative to that, you are sitting still, and I was moving across the surface of the Earth.

In physics, it makes no sense to just say that something is moving. Moving relative to what? And it’s important to note that this is not just a clearer way of talking, but a fundamental truth about the nature of the universe. If you were in deep space in uniform motion, with all the windows shut and no access to the outside universe, there would be no experiment you could perform that would tell you whether you were moving relative to the Earth or the center of the Milky Way or some other object. Because the laws of motion are the same for anyone in uniform motion.

Next time, we’ll examine Einstein’s changes and elaborations to Galilean relativity theory.

  1. I took these lovely examples from Richard Wolfson. []

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{ 25 comments… read them below or add one }

Keith October 8, 2010 at 4:11 am

As a Physics teacher this warms the cockles of me ‘eart.


Luke Barnes October 8, 2010 at 6:21 am

Minor quibble, but if you are in uniform motion in deep space, then you won’t be playing tennis normally!

Unless you’re undergoing uniform acceleration, but I assume we’re a few posts away from general relativity’s equivalence principle…


The Atheist Missionary October 8, 2010 at 7:36 am

Luke, could you please add one of those automatic share post icons at the end of your posts so that readers can easily share them on twitter, facebook, etc.


Mike N October 8, 2010 at 7:59 am

Hang on, if you’re playing tennis on Venus then the gravitational pull of the earth (and indeed every other planet) will affect the motion of the tennis ball.

It simply won’t affect it enough that you would need to be in any way concerned about it or adjust your game for …

After all it’s not just the moon that affects our tides …


lukeprog October 8, 2010 at 8:07 am


Thanks for your comment! I didn’t mention tennis in deep space, so… I must have been unclear somewhere. What needs fixing?


Hermes October 8, 2010 at 8:18 am

Mike, yep. On Venus the pull of gravity from the ceiling of the room will have more of an influence on the ball.

Physicists: Is the effect of gravity a ratio of the square of the distance from the materials?


Patrick October 8, 2010 at 9:18 am

Hermes: F = G*m1*m2/r^2

m1 and m2 are the masses of the objects in question

r is the distance between them

g is just a constant

I’m not a physicist, but that should answer your question.


Reginald Selkirk October 8, 2010 at 9:50 am

Cosmologist Sean Carroll discusses time with appropriately named philosopher Craig Callendar:
The Arrow of Time and the Multiverse on Philosophy TV
(Video 01:00:45)


Hermes October 8, 2010 at 9:55 am

Patrick, yes it does. Thanks.

I have only one question/observation;

I guess that g (gravitational constant?) is experimentally derived(?), and that if we learn what g really is it will probably be representable as a formula itself even if the result just allows for a more accurately derived constant; like having extra digits of pi even if g itself has a finite number of decimal places.


Muto October 8, 2010 at 10:27 am

Yes g is experimentally derived and due to its small size very hard to measure. However we cannot say that it is in principle representable as a finite formula since many real numbers are not. Maybe the day we discover more generalized patterns in physics we will know more.


Hermes October 8, 2010 at 10:43 am

Muto, thanks.


Keith October 8, 2010 at 1:04 pm

There is a difference between “G” and “g”. “g” is different depending on which planet (or sufficiently massive enough object relative to us that we experience gravity) you happen to be on. For Earth it is 9.81 m/s^2. “G” is the constant used in the equation previously mentioned. You can get “g” for Earth by substituting the mass of the Earth (in kg) for one of the masses and the radius of the Earth (in m). “g” is thus G*Mass of Earth/Radius of Earth^2. “g” does change based on your distance from the center of the Earth (for most instances it is fine to use the radius because we don’t move vertically enough to make a noticeable difference). Technically speaking everything in the universe will gravitationally effect everything else. “G” is an experimentally determined constant. “g” is not and changes all the time.

The ceiling in the above example won’t have as much effect on the ball as will the planet because it is so less massive than the planet, even though it is much closer.


lukeprog October 8, 2010 at 1:10 pm


I added a paragraph next to Galileo’s head. I suspect that’s what you thought needed clarifying…


Muto October 8, 2010 at 1:13 pm

We were obviously talking about G.


Reginald Selkirk October 8, 2010 at 1:58 pm

Neither big G nor little g has much of anything to do with the g-spot.


Silas October 8, 2010 at 2:31 pm

Yes Luke, speed is relative, if you’re not in the presence of Chuck Norris. Then speed becomes a very universal roundhouse kick to the face.


Silas October 8, 2010 at 2:34 pm

I meant to say motion, not speed, but it still applies.


lukeprog October 8, 2010 at 3:06 pm


Objects kicked by Chuck Norris travel at speed c!


Silas October 8, 2010 at 4:04 pm

LOL! Chuck Norris jokes never get old.


lukeprog October 8, 2010 at 4:48 pm

One revolution in physics came when Einstein discovered there was an upper limit to the speed of light. Another came when Planck discovered there was a lower limit on bundles of energy. But we will certainly never discover a limit to the utility of Chuck Norris jokes.


Josh October 8, 2010 at 4:56 pm

My understanding of G (not g) is that it is more or less a conversion factor because of the units that we use. You can work in a system where many of the constants are normalized to one:


phasespace October 8, 2010 at 5:38 pm

Josh, that’s right. In astronomy, G has a value of 1 when you measure masses relative to the mass of the sun, distances in astronomical units and time in years. (eg, the sun is precisely 1 solar mass, the distance between the Earth and the sun is precisely one astronomical unit, and the time the Earth takes to go around the sun is one year). All those unitary values force G to have a value of 1 by virtue of the way that the units being measured are defined.


Keith October 9, 2010 at 5:49 am

@phasespace: nice

@Muto: then use G not g.

@Reginald: haha!


dunefish October 9, 2010 at 7:10 am

OMG! It all just became clear to me. I mean I was struggling to understand all that relativity thing for years, feeling like an idiot because I couldn’t. And now one simple post clears it all up. Amazing.
Sooo waiting for the next part! *drools*


lukeprog October 9, 2010 at 9:37 am

Great, dunefish! I’m really trying to be clear.


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