Sunday, 05 December, 2004

The 20th of November issue of New Scientist ran a story about the search for negative mass. Having thought about negative mass it would have to have some strange properties to exist in the universe.

Firstly, as mentioned in the article, it would be repulsed by gravity instead of being attracted. A blob of matter made out of negative mass dropped from your hand would rise like a helium balloon and eventually leave the atmosphere and drift out into space.

I thought about this carefully and wondered where does the energy come from for this effect to happen? I quickly concluded that the energy must come from convertion of the negative mass to energy! How did I reach this conclusion?

I borrowed Einstien's thought experiment with regard to photons climbing out of a gravitation field. Imagine a tower with a magical machine at both the bottom and the top. The machine at the bottom of the tower converts a given mass into one photon with exactly the energy contained in the mass and fires up towards the top of the tower. The machine at the top does the reverse, it turns the single photon back to a piece of matter equal in energy to the photon.

From this simple set-up we can quickly determine that a photon must lose energy climbing out of a gravitational field. Why? Well, let's first assume the opposite; that a photon doesn't lose energy climbing out of a gravitational field. We start the process by dropping a weight over the side of the tower. It accelerates as it falls due to the influence of gravity and therefore gains kinetic energy. When it reaches the bottom of the tower the energy stored in the mass of the weight and the total kinetic energy are converted into a single photon. The photon climbs up the tower to the top where it is converted back into a mass. But this time the weight has more mass and therefore more energy than it did the first time it started the process. We've created energy out of nothing which is a clear violation of the first law of thermodynamics. The conclusion? The photon must lose energy as it climbs its way out of a gravitational field. If you don't like the idea of "magic" devices then consider the same experiment where the conversion process has an efficiently less than one hundred percent. I'll leave the analysis of that problem as an exercise to the reader.

When light leaves the surface of the earth and goes off into space it loses exactly the amount of energy that a mass of equal energy would need to remove itself from earth and go off into space. This energy is not lost in the speed of the light since light always moves at the same speed, which is around three hundred million metres per second, but it is lost via a reduction in the light's frequency. This has a number of important consequences such as that objects with a large gravitational field appear colder and time runs more slowly the "deeper" into the field you go.

I'll digress from the discussion of negative mass to justify these points because I feel they're quite cool. The reduction in temperature of an object in a large gravitational field is a fairly straightforward to prove. When the blackbody radiation of the object attempts to leave the gravitational field the light is all red shifted by an equal amount since the amount of energy lost is proportional to the amount of energy the photon had in the first place. This has the effect of shifting the blackbody-radiation profile downwards. Therefore, if we measure the tempreture of the object outside the gravitational field we'll conclude it's colder than it really is.

The time dilation effect is really suprising but is also pretty straightforward providing you know the background physics. Light is a physical clock of sorts. The frequency of light amounts to a certain number of wave crests per second so in principle we could build a clock to count these waves crests and therefore accurately measure time. Suppose we were viewing at a large distance a clock field that was placed on the surface of a Neutron star. When we looked at the clock we would count less wave crests per second than someone looking at the clock from the surface of the star.

Okay, so that's one example of a clock running slow in a gravitational field. How do we know we get an identical effect for other types of clocks such as swinging pendulums or the decay of uranium atoms? The answer lies in the principle of relativity; that is, that there are no preferred frames of references in the universe, everything depends on your relative situation with regard to what your observing. If some processes slowed more than others then this would hint at a prefered and universal concept of time. The universe would have a master clock as such and our experience of time would be linked to that clock. Clearly this flies in the face of the principle of relativity so we must conclude that the world doesn't work this way. If one physical process slows down all of them do and they all slow by exactly the same amount.

So back to our discussion on negative mass. All we need to do to start exploring the physics of negative mass is to modify Einstien's thought experiment slightly. Replace a magical mass to light convertor with a magical mass to anti-mass convertor. If we drop our weight over the side it will fall down the tower towards the mass to anti-mass convertor. When the weight hits the bottom it is convertor to anti-mass and the mass starts to float back up the tower. At the top it bumps into the anti-mass to mass convertor and starts to fall down and we repeat the process ad infinitum.

If the anti-mass didn't lose energy when it climbed through the gravitational field we'd have a serious problem because the machine would be creating energy out of nothing. So it must lose energy from somewhere to be consistent with the first law of thermodynamics and the only store of energy the anti-mass has its mass. Therefore, when an object composed of anti-mass rises in a gravitational field it converts it's mass into kinetic energy.

It's interesting that anti-mass is permitted by the physics of today but it hasn't been observed. More over, there is no process known that can produce anti-mass. To me it implies theres a "squaring" going on somewhere that we don't know about. If I had to hedge my bet I'd say that theres some unknown quantity that's involved in the quantum description of gravity that you square to obtain the mass of a particle. That way a particle's mass would always have to be positive provided that it didn't make sense to represent the quantity as a complex number.


14:21:51 GMT | #Randomness | Permalink
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