• Question: what is machs principle?

    Asked by shobhit to David on 22 Jun 2013.
    • Photo: David Freeborn

      David Freeborn answered on 22 Jun 2013:

      Take a walk out into a field on a clear, cloudless night. Stand still, and gaze at the stars. They should appear stationary. They are not moving with respect to your motion.

      Now suppose you are walking forwards at a perfectly steady, perfectly regular speed, so regular that you don’t feel you are moving. It will look as if the objects around you like the trees are moving backwards, past you, whilst you remain stationary. We can say that from your “reference frame”, you are stationary, but the trees are moving backwards. From the trees’ “reference frame”, they are stationary, and you are moving forwards. This is called “Galileo’s Principle of Relativity”.

      What if you started spinning around though? Would you still be stationary, from your reference frame? You would be able to see the Universe spinning around you, the stars would seem to be rotating if you looked up at them. It would be as if you are stationary, but the whole Universe is spinning.
      Well- not quite.
      When you rotate, you are able to feel a centrifugal force due to your mass. If you span around fast enough, your arms would be flung out to your sides, due to the centrifugal force. So you *would* be able to tell that you are rotating.

      The physicist and philosopher Ernst Mach wanted to understand why we are able to tell that we are rotating. He said, it didn’t make sense to talk about absolute space, but we can tell we are rotating to the rest of the Universe, and rotation needs to be understood “relative” to all the other objects in the Universe.

      The principle wasn’t well known until Einstein used it in his theory of General Relativity. Einstein realised that the mass of all the objects in the Universe affects the “metric” of the Universe- that is they affect the space-and-time geometry of the Universe. When we accelerate or rotate, we are doing so against a space-and-time whose geometry is affected by all the other objects in the Universe.