# A non-inertial frame is non-inertial with respect to what?

1. May 23, 2010

### marcosschiavi

Considerer a closed box into space:

• In constant acceleration.
• Turning around its axis.

Einstein used the first case as a thought experiment (http://galileo.phys.virginia.edu/classes/252/mass_and_energy.html) that led to the general theory of relativity: the occupant of the box could be considered (locally) under the action of a gravitational field.
.
We could consider the "gravity" as seen by the accelerated reference a fictitious force, but is not also fictitious the magnetic field (http://galileo.phys.virginia.edu/classes/252/rel_el_mag.html) [Broken] that arises when a charge moves? We could postulate a field that arises when a mass is accelerated (See note below)…

My point is: why a framework that rotates can’t be considered to be a good one? If the rest of the universe didn’t exist could someone say that it does rotate? It rotates in relation to what? Does it make sense to say that the universe as a whole rotates? (how could we know if it does?)

However, leaving aside the centrifugal force (we could postulate a field that arises when a mass is rotated), for such a rotating reference frame the speed of light is not a limit. The velocity of a distant star, for instance, would seem to be near infinite.

So, would not the value of the speed of light be a result from the presence of the rest of the universe? If so, maybe the presence of a large mass could change the speed of light constant!

Note: My law of gravitation would be something like this: "all accelerated body generates a gravitational field proportional to its mass". Thus, given a rocket and an static observer, the gravity felt by the astronaut would be much greater than that perceived by the observer, because for the first the whole universe is being accelerated while for the second only the rocket :)

Last edited by a moderator: May 4, 2017
2. May 23, 2010

### Staff: Mentor

The inertial-ness or non-inertial-ness of a reference frame is not a relative attribute. It is not inertial or non-inertial with respect to something, it is just inertial or non-inertial.

I don't know if you are familiar with the details of General Relativity. In GR coordinate systems are almost completely arbitrary. You can use nearly any set of four numbers to label the events in spacetime. A rotating set of coordinates is every bit as good as any other set of coordinates, the coordinates themselves are just labels and have no physical meaning.

In order to link the coordinates to physics you have to use something called a metric. This is what allows you to convert from the arbitrary coordinates to physical things like distances measured by rods, times measured by clocks, and accelerations measured by accelerometers. Even if some coordinate is changing faster that c, using the metric you will always find that light travels on a "null geodesic" in a coordinate independent sense.

3. May 23, 2010

### Naty1

You might get some insights here:

http://en.wikipedia.org/wiki/Inertial_frame_of_reference

I don't understand your postulate....and this is espcially vague:

Something that does not exist rotates?

"Does it make sense to say that the universe as a whole rotates? (how could we know if it does?)"

Here is one rotating universe.....does not appear to be ours.
http://en.wikipedia.org/wiki/Gödel_metric

4. May 24, 2010

### bcrowell

Staff Emeritus
There are no good or bad frames of reference in GR. Rotating and nonrotating frames are equally valid. However, you can tell if you're in a rotating frame if you notice that there's a Sagnac effect.

Yes, even if the rest of the universe didn't exist, you could still tell whether your laboratory was rotating, by measuring whether there was any Sagnac effect. For a good nontechnical discussion of this, see C. Brans and R. H. Dicke, Physical Review 124 (1961) 925.

In this sense, the rotation of your laboratory is absolute, not relative, so rotation is not totally Machian in GR.

See this lecture,
http://nobelprize.org/nobel_prizes/physics/laureates/2006/smoot-lecture.html , at "Also in 1967 Dennis Sciama published a paper..." for a discussion of an actual empirical test of whether our universe does in fact rotate.

If you're more than casually interested in this topic, you should try to obtain a copy of Rizzi and Ruggiero, ed., Relativity in Rotating Frames: Relativistic Physics in Rotating Reference Frames. It's absurdly expensive to buy, but I borrowed a copy via interlibrary loan.

5. May 30, 2010

### marcosschiavi

I appreciate the answers. In “light” of them would like to reformulate my question. Suppose the universe ceases to exist (or never existed). From my laboratory I send several rays of light and from their trajectories I determine a metric for the universe. In function of this metric I determine that I am "rotating" in relation to an inertial frame. My question is: does it makes sense to rotate in relation to the void ("ether")? Would not it be more reasonable to assume that is the rest of the universe which determine a metric and that without it (the rest of the universe) the concept of rotation is meaningless?

My biggest doubt already was answered but I would like to know if my reasoning is correct ...

Last edited: May 30, 2010
6. May 30, 2010

### bcrowell

Staff Emeritus
Did you read the paper by Brans and Dicke that I referred to in #4? This is exactly what that paper is about.

Brans-Dicke gravity is essentially ruled out, since the parameter $\omega$ is constrained by observation to be unreasonably large. Therefore the universe doesn't seem to be as Machian as you, Einstein, and Brans and Dicke would have preferred. The concept of rotation in an empty universe is not meaningless; you can detect it based on the Sagnac effect.

7. May 30, 2010

### Staff: Mentor

8. May 31, 2010

### marcosschiavi

I think that now I understand.

If there is nothing outside my lab there is also no spacetime "outside" it. So all we can say is that my universe (my lab) is rotating by making measures. We can’t ask WHY it’s rotating. All we can do is use the laws of physics to determine how things will evolve.

An inertial frame is something special. We can use measures to find one. It seems absurd to me that there are arbitrary things, but there are many things “arbitrary” like the position of the bodies in the universe and the value of the physical constants. For a non-inertial frame strange things would happen like velocities near infinity but we can determine the “correct” perspective using an inertial frame.

There is no meaning in saying that something is moving if there is no referential, but it does have meaning in saying that something is rotating if there is no referential because we can measure it (though it still seems odd to me).

P.S. Perhaps in the future some new Einstein will eliminate the concept of inertial frame as the concept of ether was eliminated from the pre-relativistic physics ...

Last edited: May 31, 2010