Messenger particles and black holes

[Warp]

In General Relativity gravity is described as being a consequence of spacetime geometry. In Quantum Mechanics the different forces are described as being mediated by quanta. One of the predictions of QM is the existence of a particle that mediates gravity, namely the graviton.

What I do not understand is how this would reconcile in any way with the predictions of GR. Most prominently, GR predicts that nothing can escape the event horizon of a black hole (because inside the event horizon all geodesics point toward the center, which means that there just is no way out and, in fact, there's no way for anything to avoid falling into the center; just advancing in time makes everything go towards the center). Hence no particle could possibly mediate the gravity between a black hole and everything else (because no such mediator particle is able to leave the black hole).

The same goes for electric field. GR predicts that a black hole can have an electric charge (which can be measured from the outside). QM predicts that electromagnetic force is mediated by particles (photons, I think). But such particles (such as photons) could never leave a black hole in order to mediate with anything.

How is this reconciled?

 

[Naty1]

Such things can't be fully reconciled yet; we don't have the mathematics, we don't have an all inclusive theory and model.

What I do not understand is how this would reconcile in any way with the predictions of GR.

It does does not 'reconcile' very much. But the views are more complemenary than in confict except maybe at the central singularity. Suggest you read about QUANTUM GRAVITY to see such 'reconciliation' possibilities...as yet unrealized...more below.

But such particles (such as photons) could never leave a black hole in order to mediate with anything.

correct; so the electromagnetic field, any rotation charge and gravity are currenly described as phenomena that reside on the outside of a BH...'remnants' from before the black hole forms. Leonard Susskind, among others, views this as information 'smeared' across the horizon before the BH is formed and as subsequent matter is consumed by the BH. In other words, the horizon can be described as a hologram...a two dimensional surface containing all the informationm of the 'three dimensional' interior.

Roger Penrose describes it this way:

There is no mass as we know it (inside); inside all particles have been destroyed and gravitational effects remain outside the event horizon along with a few characteristics (electric charge, spin, etc).

Mitchelle Porter of these forums posted previously this as a description :

, when you arrive at the horizon, your degrees of freedom get holographically smeared across it, once again mingling with all the black hole's prior degrees of freedom (also located on the horizon), which all eventually leak away as Hawking radiation...

Another view [as the central singularity is approached, way sinide the horizon]:

Marcus: When very compressed, the distinction between matter and space disappears and one gets down to a stew of microscopic degrees of freedom, which we don't yet know how to model mathematically...And the reason people call it FOAM is because by Heisenberg the geometry would have been very chaotic and unsmooth and hard to pin down.

[Being near a BH singularity is where 'quantum foam' [Heisenberg uncertainty] merges space, time, etc. ]

Much of all this 'ambiguity' arises because of coordinate dependencies...here is Kip Thorne's description of one 'reconciliation' from BLACK HOLES AND TIME WARPS.

QUOTE]Finkelstein's reference frame was large enough to describe the star's implosion ...simultaneously from the viewpoint of far away static observers and from the viewpoint of observers who ride inward with the imploding star. The resulting description reconciled...the freezing of the implosion as observed from far away with the continued implosion as observed from the stars surface...an imploding star really does shrink through the critical circumference without hesitation...That it appears to freeze as seen from far away is an illusion...General relativity insists that the star's matter will be crunched out of existence in the singularity at the center of the black...[/QUOTE]

So at present we have limited different 'observational' vantage points, [different perspectives] including string theory, quantum gravity, general relativity, and others.
Final 'reconcilation awaits a unified theory, maybe 'quantum gravity'.

Perhaps it's a bit like some blindfolded people in this situation: you feeling an elephant's ear, me the tail, somebody else a leg...just what is "this thing" we have 'discovered',,,oh yeah, and it is a 'black' so it is 'invisible' and we wouldn't know a lot more if sighted!.

 

[Bill_K]

Rewind.

Warp, In the first place photons are not messenger particles, they are force carriers. Messenger particles are something else. Secondly, they do not emerge from charged objects at the speed of light.

There are two kinds of photons: transverse and longitudinal. Transverse photons are real particles responsible for light waves. Indeed, they travel at the speed of light and carry energy and information. Longitudinal photons on the other hand are virtual particles responsible for Coulomb fields. In the usual description of QED their influence is transmitted instantaneously. Since they carry no information and no energy, this is perfectly consistent with relativity.

Many posts here on PF are attempts to understand Coulomb fields by thinking of photons as projectiles. But one should not picture a Coulomb field as a collection of photons emerging from the origin at the speed of light (or trying to) - that is not even close to a correct description.

 

[Ger]

Two 'kind' of photons? if one makes a conversion between two different sets of co-ordinates, you will have 'longitudinal' and 'transversal'. Photons are part of the electromagnetic field, depending on interpretation, including light. One can assign a photon a mass but that doesn't make it a mass like projectile.

As long as an particle is not at the sigularity, it can escape and will have quite some high energy value. Once in energy can disappear, just like it once came to existence a long time ago in the 'empty' space.

 

[Q-reeus]

OP has raised afresh interesting issues. Never did get anything like a sensible answer myself to for example this:

Notwithstanding points on nature of vp's (virtual photons) made in #3, we have in QED the concept of vp exchange between charged particles. Stochastic though in nature, a finite mean exchange *rate* must apply, otherwise there is just a classical static field and vp is meaningless as concept. Now for a Schwarzschild BH any external hovering 'observer' charge sees all temporal processes as frozen solid at the BH event horizon or further 'in'. Exchange rate logically ceases to apply then between hovering charge and an at-or-below event horizon free-falling charge. Yet GR community blithely talks of charged BH's as though there is no issue here. And logically one may extend this to ask about graviton exchange in the same light. So someone with answers please shoot me down kindly.

 

[Bill_K]

a finite mean exchange *rate* must apply, otherwise there is just a classical static field and vp is meaningless as concept.

One of the first steps taken in QED is to show that the longitudinal photons can be summed, yielding a classical Coulomb field. As you say, it is static, and there is no exchange rate. Sorry if you do not consider this sensible, Q-reeus.

 

[Q-reeus]

One of the first steps taken in QED is to show that the longitudinal photons can be summed, yielding a classical Coulomb field. As you say, it is static, and there is no exchange rate. Sorry if you do not consider this sensible, Q-reeus.

I defer to your expert knowledge Bill K. Interesting that a truly static field is not foreign to quantum world - maybe concept of ZPF fluctuations has confused me on that. Mind explaining in layman's terms then what place and meaning for the term 'virtual photon exchange'? Exchange in what sense exactly?

 

[Bill_K]

Q-reeus, The problem arises, I think, in taking the interaction too literally, as if the exchange of photons was a classical process. Popular accounts often picture it as a game of badminton in which the two charges bat photons back and forth to each other. I remember seeing an animation with two armies of photons with clenched fists marching in line, one to the left and one to the right.

Remember, too, that the Coulomb field is a rather specialized case. QED applies to many other situations in which a description in terms of virtual photons is easier to understand. It was a puzzle to the early workers in QED how could a static, instantaneous Coulomb interaction be consistent with relativity. Dirac originally proposed that the longitudinal photons be left unquantized and treated as a separate classical field. We now realize they very nicely combine.

In QED a charged particle can emit a photon which is then absorbed by another, and we draw a Feynman diagram to illustrate it. But this is Quantum Mechanics, and in the framework of Quantum Mechanics we must add together all possible ways a process can occur. This means integrating - the photon can be emitted at any time t₁, and then absorbed at any time t₂. We integrate over both times. The photon does not have to travel at c because it is virtual. In fact t₂ can be equal to t₁, or even precede it.

The result of the integration gives a contribution to the total energy: e₁e₂/r, exactly reproducing the Coulomb potential. Notice it is not done with armies of photons! Just one photon, emitted and absorbed in all possible ways.

 

[Q-reeus]

Q-reeus, The problem arises, I think, in taking the interaction too literally, as if the exchange of photons was a classical process. Popular accounts often picture it as a game of badminton in which the two charges bat photons back and forth to each other. I remember seeing an animation with two armies of photons with clenched fists marching in line, one to the left and one to the right.

In QED a charged particle can emit a photon which is then absorbed by another, and we draw a Feynman diagram to illustrate it. But this is Quantum Mechanics, and in the framework of Quantum Mechanics we must add together all possible ways a process can occur. This means integrating - the photon can be emitted at any time t1, and then absorbed at any time t2. We integrate over both times. The photon does not have to travel at c because it is virtual. In fact t2 can be equal to t1, or even precede it.

The result of the integration gives a contribution to the total energy: e1e2/r, exactly reproducing the Coulomb potential. Notice it is not done with armies of photons! Just one photon, emitted and absorbed in all possible ways.

Thanks Bill K for clearing that one up - I admit to being duped by that above described popularization. Let's see if I now have this basically right. If say two charges q₁, q₂, have a static relationship - no relative motion, then vp exchange is a one-off process - no continuous back-and-forth. Hence each charge resides in the other's static Coulomb field. On the other hand if even slight relative motion occurs (classical radiation - real photon emission, can be assumed negligible), there is a continual vp exchange process in order to 'update' the changed mutual field configuration and energy. Or at least that's the picture I get from mulling over here:
http://en.wikipedia.org/wiki/Static...gral_formulation_of_virtual-particle_exchange
where probability amplitude Z = exp(-iET), T is elapsed time, E is the energy change due to the disturbance (I take 'disturbance' there as implying non-static field distribution).

Is that about right? If so, it still leaves a problem imo if say q₂ resides free-falling at BH event horizon, and q₁ is whizzing by the BH in a hyperbolic trajectory. From q₁ perspective, the clock has stopped for q₂, so it's difficult to see that from q₁'s position any finite rate vp emission process is possible at q₂, because the very idea of process implies finite temporal change of some sort. So ok allowing that vp propagation can be superluminal, there must still be an action at q₂ 'over time' for emission to make sense as a process. It's here that at least from my layman's pov, rate comes back into the equation - assuming it takes two to tango re vp exchange (non-static relationship).

Without turning this into a SR/GR topic, should point out a classical outlook that imo reinforces above thoughts. An infalling spherical shell of charged dust particles of net mass m simply adds to the total BH mass M to give M+m. Notice though that this implies a conservative exchange between potential and KE - an external observer concludes that as the horizon is approached, mass m is becoming entirely kinetic in nature. A hovering observer close to the event horizon concurs - and notices that the charge-to-'relativistic-mass' γm ratio q/γm of dust infalling by at highly relativistic speed is becoming arbitrarily small (γ the usual SR factor 1/√(1-(v/c)²) locally measured). Ergo; if externally determined m is invariant during infall, and q/γm tends to zero, where is there any charge left re outside view, once the horizon is reached (or assymptotically close to being reached from external pov)?

This imo is entirely analogous to say spin up of a charged flywheel - mass but not charge grows. If one gently lowers the flywheel towards the BH, it's externally observed mass would normally decrease toward zero, since work is being extracted in the lowering process. But one might continually feed the flywheel via electrical cable to increase spin rate such that externally observed mass remains constant - but clearly this will not translate to a locally maintained mass/charge ratio - a fact reflected surely as externally observed. My conclusion is that charge invariance fails when gravity is present - and 'vp exchange-rate freeze' seems to nicely dovetail.

Realizing this flies in the face of consensus opinion, how is it all wrong?

 

[Warp]

I suppose the answer to my original question can be summed up as "like everything else in quantum mechanics, it doesn't work in the intuitive way; instead, it works in weird ways"?

 

[Q-reeus]

I suppose the answer to my original question can be summed up as "like everything else in quantum mechanics, it doesn't work in the intuitive way; instead, it works in weird ways"?

Warp - let's try and bump things back into action. I share your continued perplexity, but from a somewhat different perspective, as is evident from the emphasis on temporal rate in my previous posts. It would be nice if someone tackled that raised in #9 with convincing explanations. Re the interesting observation made earlier that as I take it virtual photon mediation is considered in QED as overall instantaneous (net result summed over all possible spacetime paths), it may be asked in what sense 'instantaneous' has any operational meaning. That's because it is both theoretically in classical EM and experimentally confirmed by antenna engineers that the axial 'near field' (read: purely longitudinal Coulomb field) of an electric dipole oscillator obeys the usual phase delay relation exp i(ωt-kr), no differently to the transverse (1/r radiative & transverse components of the 1/r² 'induction' & 1/r³ 'static Coulomb' fields) - as per any respectable textbook on EM, or for instance here: http://en.wikipedia.org/wiki/Dipole_antenna#Near_Field

[Above is deficient in part as I failed to mention the 1/r² induction field also has an axial component, in phase quadrature to that of the 1/r³ 'static' field component. Both together may be considered the retarded Coulomb field, and it's true that very close in the sum of those two yield essentially 'instantaneous' longitudinal field propagation as determined by phase delay wrt dipole current - for steady-state oscillation that is. At any rate in progressing further out there is a rapid approach to normal phase delay.]

The folks who came up with QM and QED were no dills and fully understood the above classical EM situation. Which is all the more puzzle for me that instantaneous coulomb field transmission is evidently a tenet of QED. If it were so then by my reckoning a strange immunity to gravitational redshift aught to be evident for the case of a radially oriented dipole oscillator deep inside a gravitational potential. But my betting is normal redshift will be observed. Sure this purely longitudinal radially oriented oscillating field drops off as 1/r³ [plus the 1/r² 'induction' component as per above edit] and is not radiative, but it exists and is in principle detectable at any remote distance. Except that is if it happens to hit the event horizon of a notional BH, in which case externally determined frequency goes to zero, and one expects the field strength also. Of course the situation must be one of free-fall at or near an event horizon - which only makes it worse in terms of externally detected field strength and frequency, as SR and otherwise hovering GR redshifts multiply by each other.

Above all suggests to me longitudinal vp propagation is effected very similarly to transverse real photon propagation. The latter uncontroversially asymptotically snuffs out for an external observer when an arbitrarily oriented dipole oscillator approaches a notional BH event horizon, and given that a static field is in QED explained by longitudional virtual photons, there is a seemingly obvious conclusion to draw. As said in #9 - that conclusion is against established opinion, but cannot see anything obviously wrong with the above either. So, who would care to answer this bit, and also deal with the unanswered stuff in #9? And maybe make Warp and me a little less head scratchy. Bump...bump.