# Galilean Relativity & Inertial Frames

1. Sep 5, 2010

### am2010

I just want to make sure I understand this correctly. Please critique:

Under Galilean relativity, Newton's Law of Inertia retains the same form under any inertial frame of reference. There are relative velocities between inertial frames but its possible to determine absolute velocities under Newtonian mechanics because of Newton's contention of absolute space. Thus through an absolute frame (which he labeled to be the 'fixed stars') one can determine whether a body is moving or at rest relative to another body.

Law of Inertia in its most simplest form does not explain fictious forces/inertial forces/non-inertial frames.

Thanks

2. Sep 5, 2010

### am2010

I hear the shrills of crickets in the night. Am I to assume that this explanation is correct then?

3. Sep 6, 2010

### K^2

No, there is no absolute velocity under Galilean Relativity. There is no experiment that will tell you how fast you are moving.

4. Sep 6, 2010

### am2010

Then how could Newtonian mechanics claim the existence of an absolute frame of reference when the Galilean tranformation gave a beautiful expression for relative velocities? Plus, what would be the reason for upholding a view of absolute space-time?

Last edited: Sep 6, 2010
5. Sep 6, 2010

### K^2

There is no absolute frame of reference in Newtonian Mechanics.

6. Sep 9, 2010

### Cleonis

Let me elaborate on that.

In preparation the following example:
Let's say we have a measuring device that operates on electric induction. This device detects the magnetic fields associated with change of electric current. When that device detects something, we can backtrack several steps:
- There is change of current strength
- Given there's change of current strength we know current is flowing
- Given there's current flowing we know there are charge carrier's that can move freely

We don't know how much current is flowing, but we do know that current is flowing!

Current is change of charge position over time.
Change of current strength is change of current over time
Explicitly: change of current strength is the time derivative of current.

Now, what if we work along the following reasoning:
- An accelerometer measurses change of velocity
- Given there's change of velocity we know there is velocity
- Given there is velocity there must be position.

This is the same backtracking as in the induction example.
Velocity is the time derivative of position
Acceleration is the time derivative of velocity.

It is conceivable that Isaac Newton reasoned as follows: acceleration derives from velocity. Since acceleration is detectable velocity must exist in the same sense as acceleration. Since velocity must exist in as real a sense as acceleration position must exist in just as real a sense.
Conversely, if position and velocity would not exist at all then acceleration could not exist at all.

I don't know whether Isaac Newton actually reasoned that way, but it is consistent with his usage of the concept of absolute space. If you assume that acceleration is a derivative entity, dependent for its very existence on velocity existing in the same sense, then you have to assume the existence of absolute velocity.

Conversely, if you assume that acceleration and velocity are independent entities, then there are no logical implications.

Last edited: Sep 9, 2010