# I relationship between negative mass, energy and antimatter

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1. Jun 30, 2017

### martin25p2

What is the relationship between negative energy, negative mass and antiparticles? I have read some articles but I am still confused. Does negative mass exist? Does negative energy exist with the exception of the Kasimir effect which I understand. Are antiparticles really only the negatice energy solution of the quantum field equations of particles or is the CPT-symetry the major reason for their existence? As far as I understood, antimatter has positive energy and thus created only with normal matter, so why e.g. does the positron has a negative energy in the Dirac-equation? Does the Heisenberg uncertainty principle tell us that there can be negative energy exist for short time? What physical implication has that? Since energy is linked by the Einstein equation with mass, does a negative energy density not imply negative mass density? In the frame CPT, antiparticles can be seen as normal particles moving backwards in time in a mirrored space and charge reversed. What does this have for implications for entropy

Last edited: Jun 30, 2017
2. Jun 30, 2017

### Staff: Mentor

Which ones? The question as you ask it is too vague; "negative energy" and "negative mass" are not precise terms. We need to know where you are getting this from in order to be able to respond.

3. Jun 30, 2017

### martin25p2

4. Jun 30, 2017

### Staff: Mentor

Stuff like this is the reason why Wikipedia is not, in general, an acceptable source at Physics Forums. Some Wikipedia articles are excellent and some are not, and these three are solidly on the non-excellent side. Check their "Talk" pages and you will see that the best of the three is only C-class, meaning "Useful to a casual reader, but would not provide a complete picture for even a moderately detailed study."

5. Jun 30, 2017

### Staff: Mentor

Which, as @Nugatory has pointed out, is not a good source. So the general answer to all of your questions is, find a good source on quantum field theory and work through it. Then you will understand better the kinds of things you are asking about.

To briefly answer your questions as you ask them, no, "negative energy" and "negative mass" are not useful concepts in QFT, and antiparticles are not "negative energy versions" of particles, nor are they "particles moving backwards in time". (The latter misconception arises from a clever trick that Feynman came up with to make it easier to calculate amplitudes in the path integral version of QFT, but he meant it only as a convenience for experts, not as a claim about any real property of antiparticles.) Antiparticles are the CPT conjugates of their corresponding particles.

6. Jul 10, 2017

### martin25p2

[Moderator's Note: This post and the following four have been merged into this thread.]

Why does the antiparticle go forward in time? According to the Feyman-Stückelberg equation, one can either speak of a positive energy particle going backwards in time or a negative energy particle (its' antiparticle) going forward in time.
But taking a look on the negative energy solution of the Dirac-equation, especially the wave-function part, I have a hard time seeing this. It is (E*t), which according to my thinking is either a positive energy particle going backwards in time or a negative particle going forwards in time. Can somebody help me out?

Another question is energy conservation: I realize that the wave-functions look the same, but do we not need to impose energy conservation. I am used to have a specific amount of energy of the system at each point of time, I have a hard time to see that I can just "flip" the sign of the energy when I want to go to a different time direction.
Can someone explain?

Last edited by a moderator: Jul 11, 2017
7. Jul 10, 2017

Staff Emeritus
I don't even know what this means. How would you measure such a thing? And if you can't measure it, how is it science?

8. Jul 10, 2017

### Staff: Mentor

This is a computational trick to make calculations easier, not a claim about the actual physics. The physics is that an antiparticle is the CPT conjugate of a particle. Nothing goes backwards in time.

9. Jul 11, 2017

### bahamagreen

The world lines of particles and antiparticles are distinguishable in what way?

10. Jul 11, 2017

### vanhees71

The only thing there is to the Feynman-Stückelberg trick is that in the free-field decomposition you write a creation instead of an annihilation operator in front of the negative-frequency modes, e.g., for a charged Klein-Gordon field
$$\hat{\phi}(x)=\int_{\mathbb{R}^3} \mathrm{d}^3 \vec{p} \frac{1}{\sqrt{(2 \pi)^3 2 E}} \left [\hat{a}(\vec{p}) \exp(-\mathrm{i} x \cdot p )+ \hat{b}^{\dagger}(\vec{p}) \exp(+\mathrm{i} x \cdot p) \right ]_{p^0=+E},$$
where $E=\sqrt{m^2+\vec{p}^2}>0$.

Everything by definition moves "forward in time".

Last edited: Jul 11, 2017
11. Jul 11, 2017

### vanhees71

To make it very clear again. Relativistic QFT is constructed such that it is (a) causal and (b) has a stable ground state, i.e., the Hamiltonian is bounded from below. The ground-state energy is chosen to be 0 for convenience. Particles and antiparticles both have only positive mass and positive energy eigenvalues. For free scalar particles, I've given the formalism in the previous posting.

What you read about "negative mass" in the news these days refers to quasiparticles and should not be taken too seriously. To understand quasiparticles even the NY times (which has one of the best science columns) is indadequate. A good source is vol. 9 of Landau&Lifshitz's theory book series (Landau is the inventor of the quasi-particle treatment of many-body systems by the way).