## Gravity: one more thing

I am a great admirer of James Clerk Maxwell.

And amongst his greatest achievements was the prediction that waves in electric and magnetic fields should travel at the speed of light.

He arrived at his prediction by considering the observed strength of static electric magnetic fields.

• For example, studies had established the strength of the force from a given amount of electric charge at a given distance.
• This electrical force was characterised by a constant called (for historical reasons) the permittivity of free space. It was given the symbol ε0 – the greek letter ‘epsilon’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric charge.
• Similarly, studies had established the strength of the magnetic force from a given electric current at a given distance.
• This magnetic force was characterised by a constant called (for historical reasons) the permeability of free space. It was given the symbol μ0 – the greek letter ‘mu’ with a subscript of zero. It was considered to represent in some way how ‘disturbed’ the space was around an electric current.

Maxwell analysed these static experiments and predicted that there should be coupled waves in the electric and magnetic fields and that they would travel with a speed of:

And when Maxwell calculated this number he arrived at a number very close to the previously measured speed of light.

He observed that this was unlikely to be a coincidence and concluded that light was a wave in the electromagnetic field.

I can still remember how I felt when – aged 19 – I followed Maxwell’s footsteps and ‘discovered’ this connection: I was gob-struck!

Other waves

This type of formula is typical of expressions for the speed of waves. For example, the speed of a wave on a stretched wire or string is given by:

where T is the tension in the string and m is the mass per unit length of the string.  So a wave will travel quickly when the string is taut and low mass.

And in general we expect the speed of waves to reflect how the medium in which the waves travel responds to a disturbance.

Gravity waves

And that is why last years’ announcement (LIGO, Popular Report) that gravity waves travel at the speed of light is so profoundly important.

This discovery implies that there is a connection between:

• electricity and magnetism – responsible for just about all the phenomena we experience around us – and…
• gravity – which is associated with space and time and mass.

Alternatively, it could indicate a connection between them both and something else we don’t know about.

But the experimental fact of this connection astounds me as much if not more than the connection that Maxwell made.

And it makes me wonder just what he would have to say about the discovery.

Now I know this connection is not ‘new’: I can remember being told that gravity waves would travel at the speed of light many years ago.

But the discovery of the experimental fact of the speeds of light and gravity being equal seems to me to be more profound than the mere expectation that it should be so.

You can see more about the discovery in the LIGO video below

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