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-Eric

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- Thread starter Chemical_Penguin
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-Eric

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Maybe time-reversed momentum transfers?

Suppose fermions A and B are positioned left and right respectively.

Repulsive interaction: A photon raised by A carries momentum rightward toward B. The A fermion repels leftward. Later, B fermion eats photon and repels rightward. Momentum has been exchanged. Result: A and B move away from each other.

Attractive interaction: Run the film backwards. B fermion moves toward A in order to send momentum leftward via photon. Earlier, A moves toward B in order to receive momentum by eating photon. Momentum has been exchanged. Net result: A and B move toward each other.

Weird?

Try this.

MathPages: Attractive Forces From Quantum Exchanges --->

http://www.mathpages.com/home/kmath535/kmath535.htm

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Set up the situation by having two charges particles at a large enough distance so that their position space wavefunctions don't overlap. L is the particle on the left, R the one on the right. There is a probability amplitude that L will emit and photon and a probability amplitude that it will absorb a photon. Quantum mechanics tells us to add the amplitudes. The (complex) photon wavefunction will consequently encode an amplitude for "positive momentum" and "negative momentum"...this sums of the fact that we cannot distinguish between L emitting a photon, which is subsequently absorbed by R from the situation where L absorbs a photon that was emitted by R. The photon wavefunction is also proportional to the charge of L: qL.

Now to determine how R is affected by the photon. The rules tell us to multiply the photon wavefunction by the unperturbed R wavefunction. The result is a sum of two wavefunctions giving two bumps in position space: one that corresponds to the photon shifting the peak of R's wavepacket left and another for the photon shifting of the peak right. R's wavefunction is proportional to its charge qR. Therefore, the resulting total amplitude is proportional to the product qL*qR.

The rules then tell us that if we want to know what the probability for the possible final results are, we should square the total wavefunction. But so far everything has been symmetric in the following sense: even if the left wavefunction is + and the right part of the wavefunction is -, the numbers going into the two amplitudes are the same. Therefore, squaring the total amplitude will tell us that there is equal probability for R to be shifted toward or away from L.

The problem is that we have jumped the gun. In quantum mechanics we must be careful to include all the possibilities of interaction...including no interaction! That is, we have to include the amplitude for there to be no photon exchange. Thus, before squaring, we add R's original bump wavepacket (located at position 0) to the amplitude with the two bumps (one to the left and one to the right). If the product qL*qR>0 (same sign charges), then the left bump is + and the right one -, so when they combine with the central + bump, the result is a larger + bump to the left of 0, and smaller on the right side of 0. Squaring the result, there is a large probability that R is shifted away from L: repulsion.

If qL*qR<0 (opposite sign charges), the left bump is - and the right one is -, so when you add the central + bump (non-interacting wavefunction) you get a bump that is larger and to the right of 0, while smaller to the left of 0. After squaring, there is a high probability that R is shifted toward L: attraction.

We have only done the analysis at the level of one-photon interaction, but that is enough to get the essence: even and odd photon number interactions will serve to cancel out amplitudes for same charge attraction, and opposite charge repulsion.

Thus, forces in classical mechanics arise from quantum mechanics in a subtle but beautiful way...using classical analogies is dangerous.

- #5

Rut Roh

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Well, with me, it usually begins with a pair of tight fitting jeans........

(I am so sorry, Chemical Penguine. I know this is a serious question, but I just had to do this. This post has been like having an itch just out of scratchable reach.I have wanted to post that line ever since I read your post the first time. Now, maybe I can get my mind back on other things more suitable for somebody divorced but not dating.)

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Wow Javier, thank you soooo much! I didn't grasp it 100% but surprisingly I understood most of it! Thanks again!

-Eric

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These are rules but it is not proven why they work.

When I said negative energy photons I wasn't referring to time.I really mean photons which if they strike a normal mass would cause it to move towards the direction they came from.Although they are moving in one direction their momentum is in the other.

Such photons if energetic enough could yield a positron with negative mass and an electron with negative mass-both these masses would repel normal matter.I believe gravity has a negative energy force carrier and that this causes masses to come together.However I won't say more because this isn't theory development section!

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Not a "totally different analogy " .If you insists on this sort of analogies imagine "two guys* throwing and catching boomerangsChemical_Penguin said:

-Eric

in order to get attractive force".These analogies for virtual photon exchange are quite bad and missleading if you understand them literally (personally I don't like them at all).

____

*Better is to imagine a boy and girl in this case.But again it depends on a person's taste.

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kurious said:These are rules but it is not proven why they work.

When I said negative energy photons I wasn't referring to time.I really mean photons which if they strike a normal mass would cause it to move towards the direction they came from...[deleted text]...However I won't say more because this isn't theory development section!

I agree not to make this into a debate...I don't want to stray too far from the original question, but since there were disagreeing responses, I'll just state what the standard understanding is for the record, and leave it for others to decide (or ignore) for themselves. First, I'll get to the punchline: there is no observation of negative mass-energy states, and to date, no reason for them to exist (there is a technical reason why "negative mass-energy states" can be in a theory at the level of the Lagrangian, but all propagating degrees of freedom [i.e., the observed ones] have positive energy about the stable vacuum state, so these particles won't be mediating any interactions, etc.).

In quantum field theory (which quantum electrodynamics is formulated in...an extremely well-tested theory), if you want conservation of a type of quantum number (e.g. electric charge), then it is a theorem that there must exist partner particles for every type of particle. These partners are called "antiparticles" since they have opposite quantum numbers relative to their partners. The photon is an example of a particle which is its own anti-particle partner. Both particles manifestly have positive energy in this framework. So where did this "negative energy" business originate?

Before people were doing proper quantization of fields, they noticed that when attempting to describe a relativistic electron (using a relativistic "Schrodinger equation" modified for a spin 1/2 particle), there were apparently states of the electron that had negative mass-energies, and that in quantum mechanics there is consequently a non-zero probability of tunneling from a positive energy spectrum of states to a negative energy spectrum of states. Thus there would be an instability in the energy of an electron: it would keep getting more and more negative energy with no stable state. Dirac attempted to solve the problem by saying that there are electrons filling the "negative energy sea", and since they are identical particles as well as fermions, the positive energy states are bounded below (i.e., the Pauli exclusion principle is in action). In other words, the mass-energy of an observed electron is the "Fermi energy" of the system. Later, it was suggested that instead the problem would be fixed by saying that there must be a particle that has positive energy but opposite quantum numbers to the electron (and the same mass); there are no negative energy particles to propose. This particle was discovered (the positron).

Thus, the negative energy interpretation and the later anti-particle prediction were ad-hoc band-aids that signaled a new theory (like the ad-hoc assumptions of the Bohr model to fix the problems there is a hind-sighted signal that there is a new theory underlying the description of the electron bound to the nucleus: quantum mechanics). This new theory was the quantum theory of *fields*, from which anti-particles are a necessary consequence if you want to have certain conserved quantum numbers...something that observation tells us we should have. This is the framework from which I was working in my repsonse to the original question. Using this framework, we *do* see how particles can attract (and repel) each other via mediators. In fact, you can construct a measurable (macroscopic) electrostatic potential with a basis of positive energy photons as we should be able to do if we are to make contact with the macroscopic world...this potential is the one coming from the classical Maxwell equations.

With regard to the rules I mentioned in the previous post are rules from quantum mechanics. Not knowing why the rules work is equivalent to saying that we don't know why quantum mechanics works...true, but it is well tested, so this is not really an issue. There isn't an alternative theory that works in which we *do* know why nature works that way. And quantum fields are what you get when you marry special relativity with quantum mechanics. Again, we don't know *why* quantum field theory should describe nature, but its predictions are well tested, so as far as we have seen it *does* describe nature.

Cheers.

- #10

arivero

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Yep,this is the only way to go therearivero said:Instead of boomerangs, use quantum mechanics.

- #12

arivero

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On the other hand, I have never heard of attractive *radiation* (ie via real bosons, not virtual ones) but I could be deaf.

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I thought that the generally accepted theory was that while like forces repel , unlike forces attract. Thus electrons which approach each other exchange a greater number of virtual photons than would be the case if they were further apart , resulting in a greater deflection or repulsion. While virtual photons exchanged between electrons and protons results in the electrons attraction to the nucleus. According to quantum theory there is no such thing as action at a distance , all interactions , including those of attraction and repulsion takes place due to the exchange of either ‘virtual’ or ‘real’ photons. This raises an interesting question with regard to the conduction of electrical energy in an electrical conductor. We know that real photons are excluded from the electrical conduction process by the Pauli exclusion principle , therefore it must be the case that electrical energy is conducted by virtual photons. If we examine this scenario more closely we find that this conclusion does not hold up to scrutiny , precisely because of the HUP which allows the existence of ‘virtual’ photons in the first place and which would dictate that (a) that the momentum passed on from electron to electron by the exchange of ‘virtual’ photons would not be sufficient to allow for conduction and that (b) the energy thus acquired by an electron would also not be sufficient to account for observed phenomenon. This being so , a serious revision of our concept of how electrical energy is conducted through an electrical conductor is called for .

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