I'm talking about a continuous analog channel.
- Why can't it support infinite bandwidth?
- Is there a physics reasons for it say for electrical signals?
Information bandwidth is dependent on signal to noise ratios. At absolute zero, quantum level signal quantization and quantum noise will limit the lower bound on the noise floor. At higher temperatures, thermal noise creates a higher noise floor in any information receiving equipment. There may also be an upper limit on power density in a signal before its mass equivalent creates a black hole, which may be problematical in terms of information conservation. In terms of transmitters, at some point you will melt the wires.
But in terms of pure math, there is no (aleph zero) finite limit on the amount of information that a single real number (one sample) can contain.
In addition to hotpaw2's answer, attempting to increase the bandwidth by increasing the frequency range will also fail at some point. The impedance of a capacitor is given by
Z = 1 / (2 π f C)
where f is the frequency and C the capacitance. Any two bits of metal separated by an insulator form a capacitor. As the frequency increases towards infinity, the impedance tends towards zero. In other words, every bit of metal in your circuit ends up shorted to every other bit of metal. At that point, it becomes impossible to generate the signal in the first place.