# Negative quantum states

1. Jun 19, 2011

### NEILS BOHR

can somebody simply explain what is meant by NEGATIVE QUANTUM STATES , as given by dirac in his theory???i know its not as SIMPLE as i want it to be , but still I would like to know its significance in the most basic way!!

2. Jun 20, 2011

### Bill_K

You're probably talking about states with negative energy, which were once thought to exist.

3. Jun 20, 2011

### Goldstone1

The equations of Cosmology dictate there is a negative energy reseviour in our universe - it is the thing which has plauged the minds of theoreticians since the observation of universal acceleration.

Even in Dirac's equation, negative quantum states are virtual particles which have negative energies. A hole in the Dirac Sea means the presence of an antiparticle, which has ''exotic'' as it's previous existence sounded, does not contain a negative energy, just a change in the sign of their charges. The Dirac sea is then a negatively-filled sea of virtual and potential energy. Some do not like the idea, and say it's not very elegant... because there is so much of this superfluous energy.

So when we talk about the negative partner of the real particle in the vacuum, we are talking about a normal right moving wave and a left moving wave

$$i\frac{\psi_R}{\partial t} = -i\partial_x \psi_R+M \psi_L$$

$$i\frac{\psi_L}{\partial t} = +i\partial_x \psi_L+M \psi_R$$

So even though we are having to deal with negative fluctuations in the vacuum, the antiparticles we are told and believe in actually arise from this energy density in the vacuum. In fact, you can find these sorts of sums in many parts of physics. Consider the negative energy photons which make contribution to the zero-point energy field.

4. Jun 20, 2011

### Bill_K

It was once thought that the negative frequency components in the Klein-Gordon and Dirac equations represented negative energy solutions. Dirac proposed a "hole theory" in which the negative energy states were completely filled. Although the theory was soon recognized as incorrect, it's surprising how often you still hear it mentioned.

What we now realize is that the specification of a field theory must include the specification of a Hilbert space, and they were trying to use the wrong one. In place of negative energy states the correct Hilbert space contains positive energy antiparticles.

5. Jun 20, 2011

### Goldstone1

Yes, I will admit that most scientists will come to agree that the Dirac Sea is implausible, but a true scientist cannot say it is ruled out. As far as we can tell, so called ''empty space'' is thriving with virtual negative energy.

6. Jun 28, 2011

### NEILS BOHR

thank you very much for the replies..i actually encountered this while readig a book , quite old , and thats why i probably heard abt this,,,,,,,,