The theory of quantum fields is very strange, indeed, I must admit. Usually in books they introduce a quantum field from the standpoint of a vibrating string in one dimension. Along the string are discrete points or masses that when one of which are disturbed a disturbance is created along the length of the string in the from of a wave. As a result, each mass or point is displaced by a certain amount at a specific time, which makes sense. Even when you pass this case into the case of the continuum in which the points are ever so close together it still makes sense.(adsbygoogle = window.adsbygoogle || []).push({});

But the problem comes when we try to insist that a point particle can be described by a field which has a value at every space-time point. To make matters worse we are now using Minkowski space which is 4-dimensional and the time and space are mixtures of one another. There is no analogy between the original displacement in the string and a displacement of the field in Minkowski space because each space-time point may not move or be displaced. So how can a particle be described by a field which has infinitely many degrees of freedom? Even if we tried to describe this in the one-dimensional case it still makes no sense.

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# Quantum Fields as having infinite degrees of freedom?

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