Relativistic Energy of Antimatter

[benk99nenm312]

Hi. I was wondering, as I never really knew for certain, does antimatter have positive or negative relativistic energy?

 

[Dale]

Positive. A positron has the same rest mass as an electron, just opposite charge and spin.

 

[benk99nenm312]

Positive. A positron has the same rest mass as an electron, just opposite charge and spin.

This can't be true. From what I have been told, a positron has negative rest mass. It is essentially going backwards in time. If it didn't, how would a black hole evaporate?

Anyway, I was asking whether the relativistic mass is positive.

 

[ZapperZ]

This can't be true. From what I have been told, a positron has negative rest mass. It is essentially going backwards in time. If it didn't, how would a black hole evaporate?

Anyway, I was asking whether the relativistic mass is positive.

Who told you that? Would you argue also with the http://pdg.lbl.gov/" ? In this forum, we require not only exact citation, but also valid and reputable sources, not simply hearsay.

If the mass of an antimatter isn't negative, then asking for "relativistic mass" is positive is moot, isn't it?

BTW, you may want to look around the forum, especially the FAQ thread in the General Physics forum, on why we try not to use the term "relativistic mass".

Zz.

 

[benk99nenm312]

Who told you that? Would you argue also with the http://pdg.lbl.gov/" ? In this forum, we require not only exact citation, but also valid and reputable sources, not simply hearsay.

If the mass of an antimatter isn't negative, then asking for "relativistic mass" is positive is moot, isn't it?

BTW, you may want to look around the forum, especially the FAQ thread in the General Physics forum, on why we try not to use the term "relativistic mass".

Zz.

I was just coming into change that post. I got my facts mixed up. I was being silly. :tongue2:

Although, if antimatter has positive mass, what has negative mass?

My point earlier was that black hole evaporation is supposedly due to the production of matter and antimatter close to the black hole. When the particles become real is when the mass of the black hole shrinks, ergo, the particle that fell in has negative energy from the observer's frame of reference, and the black hole has emitted a positive energy particle.

BTW: This is true, and you can find this example in many books and online sources, such as Kip Thorne's "Black Holes and Time Warps" and Wikipedia. I have even seen this example on TV.

So, how does antimatter always have positive energy? What's the truth? There are contradictions in my head, and possibly phisics.

 

[fasterthanjoao]

BTW: This is true, and you can find this example in many books and online sources, such as Kip Thorne's "Black Holes and Time Warps" and Wikipedia. I have even seen this example on TV.

ZapperZ's point about citing good, reliable sources is an excellent point, and one that is constantly made here. Unfortunately, "somewhere in a kip thorne book" and on tv don't cut it :) Fortunately, however!, wikipedia is good enough for a student at your own level.

http://en.wikipedia.org/wiki/Hawking_radiation

I shall say again benk99nenm312, that it's great that you're interested in physics and are obviously pursuing knowledge through popular science books etc. but you should try to avoid coming off with such an air of understanding: having heard of physics terminology, even if you know what it refers to, is no way close to understanding. It's misleading for people that don't know anything about your background and may be confusing.

For an interesting introduction to the origins of anti-matter, have a look at the cern website:

http://livefromcern.web.cern.ch/livefromcern/antimatter/history/AM-history01.html

Although, if antimatter has positive mass, what has negative mass?

Also, hopefully that cern article will clear up some of your understanding but I'm unsure why you're determined for something to have negative mass? As far as I understand it, particles with negative mass have been postulated in some theories, and even had their properties described - but currently there is no known particle that exists with a negative mass.

 

[benk99nenm312]

"That it's great that you're interested in physics and are obviously pursuing knowledge through popular science books etc. but you should try to avoid coming off with such an air of understanding."

- You're right. I don't know why or how I come off that way, but I seem not to notice it when I do.

I read that cern article you showed me, and found something confusing about it. On the first page, it states "just as the equation x2=4 can have two possible solutions (x=2 OR x=-2), so Dirac's equation could have two solutions, one for an electron with positive energy, and one for an electron with negative energy." This seems to say negative energy, but which energy, rest or relitivistic? Also, any form of energy, rest or relitivistic, would indicate a negative mass. E=mc^2. It goes on to say that Dirac proposes that the antiparticle has only opposite charge. this confuses me. Does antimatter have negative energy or not?

Also, you were wondering why I was determined that there existed a particle with negative mass. I wrote something about black hole evaporation. Do you see what I'm getting at, or is there something I missed?

 

[Ich]

This seems to say negative energy, but which energy, rest or relitivistic?

Both. Energy would be negative, but mass positive. Kind of E=-mc².
You have a point here, but look at http://en.wikipedia.org/wiki/Dirac_equation#Hole_theory": Antiparticles still have positive energy.

Also, you were wondering why I was determined that there existed a particle with negative mass. I wrote something about black hole evaporation. Do you see what I'm getting at, or is there something I missed?

It's not about matter/antimatter here, it's about virtual particles. They owe the universe energy, and if the BH inhibits their vanishing, it has to pay the bill. It doesn't matter whether a particle or an antiparticle escapes.

 

[malawi_glenn]

Although, if antimatter has positive mass, what has negative mass?

Nothing, as we know of, has "negative mass".

 

[fasterthanjoao]

Also, you were wondering why I was determined that there existed a particle with negative mass. I wrote something about black hole evaporation. Do you see what I'm getting at, or is there something I missed?

There isn't much to add to what Ich says, other than that for your instruction - there are complicated forces at work here. There are many things to consider here, an understanding of particle physics would be useful so that you may understand what Ich is really talking about when he says 'virtual particles'.

Have a look at:
http://www.symmetrymagazine.org/cms/?pid=1000345

 

[Dale]

this confuses me. Does antimatter have negative energy or not?

Your question has been answered and re-answered several times. Antimatter has positive energy.

Consider an electron-positron anhilation at rest. If the positron had negative energy then the electron-positron pair would have 0 net energy and their anhilation would produce no photons.

This is not what happens. What happens is that photons whose total energy is twice the mass-energy of the electron are produced. This clearly demonstrates that the mass of the positron is positive. Since the mass is positive the energy is positive (gamma is strictly positive).

Relativistic speeds, black holes, and particles moving backwards in time are all totally irrelevant to the question of a positron's energy.

 

[benk99nenm312]

Both. Energy would be negative, but mass positive. Kind of E=-mc².
You have a point here, but look at http://en.wikipedia.org/wiki/Dirac_equation#Hole_theory": Antiparticles still have positive energy.

It's not about matter/antimatter here, it's about virtual particles. They owe the universe energy, and if the BH inhibits their vanishing, it has to pay the bill. It doesn't matter whether a particle or an antiparticle escapes.

Thanks guys. Now I know that antimatter has positive energy, but now I want to know why.
I read the wikipedia article, and I have a quote here, "Dirac further reasoned that if the negative-energy eigenstates are incompletely filled, each unoccupied eigenstate – called a hole – would behave like a positively charged particle. The hole possesses a positive energy, since energy is required to create a particle–hole pair from the vacuum."
I'm starting to get it, but is there any other way to explain this... in simpler, more conceptual terms? Pictures, anything?

 

[fasterthanjoao]

Thanks guys. Now I know that antimatter has positive energy, but now I want to know why.

I think that since you're still at high school level, the terminology and concepts that would be used to explain this work would be meaningless. If your interest in physics carries on to university then the answer - also the reason that it was originally disregarded - will become clear. In physics, 'why?' can be one of the most difficult questions to answer :)

 

[Dale]

Now I know that antimatter has positive energy, but now I want to know why.

Why should antimatter have negative mass (energy)? Please avoid any irrelevant tangents like relativistic speeds, black holes, and particles moving backwards in time.

 

[George Jones]

My point earlier was that black hole evaporation is supposedly due to the production of matter and antimatter close to the black hole. When the particles become real is when the mass of the black hole shrinks, ergo, the particle that fell in has negative energy from the observer's frame of reference, and the black hole has emitted a positive energy particle.

And this positive energy "particle" could be either a particle or an anitparticle. See

https://www.physicsforums.com/showthread.php?p=620350#post620350.

 

[Al68]

Now I know that antimatter has positive energy, but now I want to know why.

The same reason matter has positive energy. The prefix "anti-" refers to charge and spin, not mass. All known particles either have (positive) mass or not.

 

[Ich]

Why should antimatter have negative mass (energy)? Please avoid any irrelevant tangents like relativistic speeds, black holes, and particles moving backwards in time.

Because they have been predicted from the second solution of E²=m²+p². From my understanding, it's not a trivial thing to explain why these states are not realized in nature (other than saying that they are runaway solutions). "Moving backwards in time" is just the natural result if you divide four momentum by mass.
Really, I'd say that benk99nenm312 has a valid and interesting question here, and he deserves an answer. But I don't have one, I've been always content with knowing that antimatter has positive energy.

 

[malawi_glenn]

Because they have been predicted from the second solution of E²=m²+p². From my understanding, it's not a trivial thing to explain why these states are not realized in nature (other than saying that they are runaway solutions). "Moving backwards in time" is just the natural result if you divide four momentum by mass.
Really, I'd say that benk99nenm312 has a valid and interesting question here, and he deserves an answer. But I don't have one, I've been always content with knowing that antimatter has positive energy.

No they was predicited from the solutions to the Dirac Equation, where we have one solution u(p,s) and one solution v(p,-s). And one can show that these solutions also have the opposite charges, e.g under charge-conjugation: C v = u etc.

This "backward in time motion" results from the propagator of these states; a physical particle propagating forward in time is represented by a positive frequency STATE which is propagated forward in time. A physical antiparticle propagating forward in time is represented by a negative frequency STATE propagated backward in time.

Source: any book on relativistic quantum mechanics, e.g Gross (Wiley)

 

[Al68]

Because they have been predicted from the second solution of E²=m²+p². From my understanding, it's not a trivial thing to explain why these states are not realized in nature

Antimatter does exist in nature. Are you referring to some hypothetical exotic matter with negative mass instead of antimatter?

 

[benk99nenm312]

And this positive energy "particle" could be either a particle or an anitparticle. See

https://www.physicsforums.com/showthread.php?p=620350#post620350.

Thanks. You're sites helped a lot.

 

[benk99nenm312]

No they was predicited from the solutions to the Dirac Equation, where we have one solution u(p,s) and one solution v(p,-s). And one can show that these solutions also have the opposite charges, e.g under charge-conjugation: C v = u etc.

This "backward in time motion" results from the propagator of these states; a physical particle propagating forward in time is represented by a positive frequency STATE which is propagated forward in time. A physical antiparticle propagating forward in time is represented by a negative frequency STATE propagated backward in time.

Source: any book on relativistic quantum mechanics, e.g Gross (Wiley)

Even though you are correct, I think he was more referring to the solution of Einstein's Equation E=+/-mc^2. This solution produces the positive and negative results for energy, and was also predicted by Dirac. E^2=p^2c^2 gives you a square root as well, so I guess the concept still stands no matter which equation you use.

 

[Dale]

Because they have been predicted from the second solution of E²=m²+p². From my understanding, it's not a trivial thing to explain why these states are not realized in nature (other than saying that they are runaway solutions).

I agree that is an interesting question, but I just don't think it has anything to do with antimatter. In other words, the anti-particle of a particle is defined as a particle with the same mass and opposite charge. So any discussion about antimatter and negative mass is purely semantic.

AFAIK there is no name for a particle with the negative mass and same charge of a particle, nor is there a name for a particle with the negative mass and the opposite charge of a particle. Maybe a nega-particle (short for negative)?

 

[Al68]

AFAIK there is no name for a particle with the negative mass and same charge of a particle, nor is there a name for a particle with the negative mass and the opposite charge of a particle. Maybe a nega-particle (short for negative)?

Exotic matter.
http://en.wikipedia.org/wiki/Exotic_matter. The article has some obvious typos and simple mistakes.

Exotic matter (negative mass) would exhibit gravitational "repulsion" with itself, and would accelerate in the opposite direction of any force applied. So it would still be attracted to positive mass, assuming the equivalence principle holds, since it would also have negative inertial mass. The negative inertial mass would cause the "force" in the direction away from the positive matter to result in acceleration toward the positive matter.

But the positive matter (positive inertial mass) would accelerate away from the negative matter, so they would basically accelerate together indefinitely. Pretty strange.

Of course there is no evidence that exotic matter exists.

 

[malawi_glenn]

Even though you are correct, I think he was more referring to the solution of Einstein's Equation E=+/-mc^2. This solution produces the positive and negative results for energy, and was also predicted by Dirac. E^2=p^2c^2 gives you a square root as well, so I guess the concept still stands no matter which equation you use.

Have you actually derived and solved the Dirac eq. ?

The E^2 = p^2c^2 + m^2c^4 has two solutions and is "why" the Klein Gordon equation get's positive and negative "energies/frequencies". But Klein-Gordon eq. are for bosons, i.e not elementary matter particles. The Dirac equation is linear in p and m, but still get's this particle-antiparticle parts if you solve it.

 

[Dale]

Exotic matter.
http://en.wikipedia.org/wiki/Exotic_matter. The article has some obvious typos and simple mistakes.

Ahh, thanks. So I wonder if you would call a particle with positive elementary charge and negative .51 MeV mass an exotic-positron, an exotic-anti-electron, or an anti-exotic-electron. It gets to be cumbersome, but any of those would be clear.

 

[benk99nenm312]

Have you actually derived and solved the Dirac eq. ?

The E^2 = p^2c^2 + m^2c^4 has two solutions and is "why" the Klein Gordon equation get's positive and negative "energies/frequencies". But Klein-Gordon eq. are for bosons, i.e not elementary matter particles. The Dirac equation is linear in p and m, but still get's this particle-antiparticle parts if you solve it.

Right. Any solution to the Dirac equation is automatically a solution to the Klein–Gordon equation, but the converse is not true. The Klein Gordon solution can be negative (square root), but you can't say that for the Dirac Equation. I believe we are in agreement.