Could escaping gravitrons be an explanation of dark energy?

[david.mueller]

I am not a scientist, however I am very interested in quantum mechanics and string theory at a basic level. One thing when learning about string theory that struck me as being particularly interesting is the branes described by the "M" theory.
Let me start my query with three assumptions. 1. "M" theory is correct. 2. Gravitrons exist, and (3) are made up of (or are) closed strings rather than open or stuck strings that can "float" freely in between parallel universes. Could these escaping gravitrons, that would surely have a residual effect on other planes, be the explanation of dark energy? To the best of my knowledge nothing is really known about it other than that it surely exists. Has anyone thought of this previously?

Also on an extended view: could these gravitons act in all universes as a sort of fountain of youth for our universe? In other words, could it be possible that this gravitron/dark energy constantly expands our plane of existence until the membrane surrounding it collides with a nearby universe, and thereby creating a whole new big bang?

Any serious response is appreciated!

 

[mitchell porter]

This is a many-layered question!

First, I want to correct a wrong impression which is entirely natural for someone who doesn't know the details of physical theory, and which isn't specific to gravitation. It's the idea that all the gravitons are shooting off into hyperspace, where they might get lost, build up in numbers, and so on. This actually would apply to some gravitons, but the wrong impression is that gravitation in general involves such a process.

But it's even simpler if we just talk about the electric field associated to an electron. We all learn that electricity, magnetism, and light are all aspects of the same thing - the electromagnetic field - and that photons are the quanta of electromagnetism. So does that mean that an electron, or any particle with an electric field, is emitting an unending stream of photons? That should sound problematic because the photons should carry energy and this would violate conservation of energy.

One of the peculiar concepts of quantum mechanics as applied to fields - so, quantum field theory - is that of the "virtual particle". It's bound up with the fact that quantum mechanics deals in probabilities and uncertain outcomes. For a technical discussion previously held on this forum, see https://www.physicsforums.com/showthread.php?t=482956", especially the link to Arnold Neumaier's FAQ... but if I can just jump to the conclusion, a static electric field of a single particle does not consist of photons streaming into the vacuum never to return, it consists of virtual photons which only have a conditional existence - at least by the usual empiricist or operational standards of reality used in quantum physics. If there was another charged object there, which could "measure" or otherwise be influenced by that electric field, then these virtual photons would get to show up indirectly, because there would be observable, quantitative changes in the motion of both the electron source of the field and the second object which the field was acting upon, which could be understood (in a particle picture) as being due to the exchange of virtual photons between the two objects.

But a photon only gets to be real - again, by these same pragmatic standards of reality - if it actually goes on to lead an independent existence from objects that emit it or absorb it. For example, if an electron undergoes accelerated motion - e.g. moving in a circle - then classically it will generate electromagnetic waves, and quantum mechanically this means that it is emitting "real" photons.

This is a potentially paradoxical distinction, because it may seem that a photon is virtual only if it gets reabsorbed before a measurement is made, and surely our "real" photon, streaming away into space, will eventually get absorbed by something; yet this absorption can't retrospectively make its existence unreal. The distinction between virtual and real photon might seem like an unnecessary obfuscation - it's virtual if it was absorbed before you could measure it directly, it's real otherwise. But in fact there's an issue here which is fundamental to the way that probability works in quantum mechanics, at least in the "sum over histories" version of the theory. One of the phenomena which makes quantum probability different to ordinary probability, is that different possibilities can "cancel": for example, in the famous double-slit experiment, the dark regions are explained as being dark because there are two paths for the photon to arrive at the dark region, but their "probability amplitudes" cancel. This does not make sense in terms of ordinary probability: if there are two ways that something can happen, it never means that in total, it becomes less likely to occur! But something analogous does, nonetheless, occur in quantum theory - but it can only occur if the different "histories" don't leave undeniable traces of their existence by interacting with something external. If they do, they "decohere" and the "destructive interference" of quantum probabilities, in which multiple possibilities can mutually cancel each other, cannot occur.

You may think that doesn't make sense and I would actually agree. If, in explaining to ourselves what quantum theory means, we have to abuse the concept of probability like this, it does mean that we don't understand its ultimate truth, not that probability has "counterintuitive" properties. Nonetheless, this picture of quantum theory is probably the most intuitive one we have, because it allows us to visualize physical processes. They are "random", but it's a strange form of randomness where probabilities can cancel. And though it is ultimately a little illogical, we do have very precise methods for calculating those probabilities, and they give us the correct answers experimentally, so one has to give the picture a little respect, even if it can't be the very last word about the nature of reality.

Returning from the wilderness of quantum ontology, what I wanted to do was to correct the idea that the existence of a gravitational field, or of an electric field, consists of a stream of "real" particles (or strings) radiating into the void. A static field, if it is to be understood in terms of particles (or strings) is to be understood as a standing probability distribution of virtual photons (or gravitons). You can certainly have a real photon or graviton that is actually radiating away into space, but it will have to be generated by a motion on the part of the source of the field.

So if we finally switch to thinking about the gravitational interactions of braneworlds in hyperspace, the very first point is that the gravitons, the closed strings which mediate their gravitational interaction, will be virtual, unless they are generated by motion at the source, in which case they will be gravitational waves. Gravitational waves appear to be a real phenomenon - there is a famous binary pulsar whose two members are slowly spiralling in towards each other, and this change of motion is attributed to gravitational energy being radiated away. But to a first approximation, if the braneworlds act gravitationally upon each other, it will be because of their static gravitational fields, which (analysed in terms of individual particles or strings) are made of virtual gravitons which aren't leaking into the hyperspace between the braneworlds and building up - only the "real" gravitons can do that.

So that's the very very first thing to say in response to your question. It's all really just a prelude to tackling it seriously, using the theories we have. Any string cosmologist who was going to think about explaining dark energy in terms of braneworld gravitational radiation or gravitational interactions would already know these distinctions (real versus virtual) because they are basic to quantum field theory, which (from a string perspective) is the approximation to string theory which treats the strings as zero-length point particles. With that prelude out of the way, we can really start to address the question, and of course here it becomes extremely challenging, because we are dealing with incomplete, highly speculative theories. Nonetheless, I'm quite sure something like this idea has been articulated, and I will attempt in a subsequent reply to say something about it. But that will have to wait for tomorrow.

 

[david.mueller]

First, let me thank and applaud you for taking on that question so quickly and thoroughly.

 

[david.mueller]

My first question would have to be about the "sum of histories" model you mentioned.

"but it can only occur if the different "histories" don't leave undeniable traces of their existence by interacting with something external. If they do, they "decohere" and the "destructive interference" of quantum probabilities, in which multiple possibilities can mutually cancel each other, cannot occur. "

I understand that the model says that any possible path that light can follow is a "history", and that all exist. However some amplitudes cancel each other out, and if there is no interference then all but one amplitude is cancelled.
That is as far as i go on the subject. Clarify if possible/necessary. Now what exactly do you mean that destructive interference cannot occur if there are traces of the histories left?

 

[mitchell porter]

The sum over histories is for determining the probability that, starting from physical state "A", the object, region of space, etc ends up in state "B". You consider all possible sequences of events that start with A and end with B, add their amplitudes (mathematically, the amplitude is "e to the power of i times the action", where the action is something like "energy density x space x time"), and then square the absolute value (because the amplitudes are complex numbers, not probabilities).

So let's suppose state "A", the way you start out, is with two electrons heading towards each other, and state "B", the way you end up, is with two electrons heading away from each other. It's a collision and the electrons come close to each other, rebound, and move apart.

I assume you have seen Feynman diagrams, which are a graphical shorthand for histories, but are also an algebraic notation used to calculate amplitudes - there are rules for translating the elements of a Feynman diagram into factors in the final calculation. Here, going from A to B, we would need to be concerned with Feynman diagrams where there are two electrons going in and two electrons coming out, and then all the different possibilities in between - the electrons just shoot past each other, they shoot past but exchange a photon or two or ten, they exchange photons and rebound, all sorts of possibilities. Each diagram will make a contribution to the final probability.

But now consider a Feynman diagram where one of those intermediate photons doesn't get absorbed - it just goes flying off to infinity. We are actually now dealing with a different final state, we could call it B'. B was "two electrons flying apart", and B' is "two electrons and a photon flying apart". The key observation is that this history is no longer relevant for calculating the probability of going from A to B; it's relevant for the probability of going from A to B'. For the probabilities of quantum histories to sum, whether destructively or constructively (constructively means that they reinforce rather than cancel), the histories have to end in exactly the same way - the circumstances have to converge on the same overall final state. It makes sense: if you want to know the probability of a transition from A to B, you don't care about transitions from A to B'. And that photon which gets away in the case of B', is an example of an external trace of the history. You might only care about the electrons, but in reality whether there's a stray photon can matter as well.

This can be dramatically illustrated in the case of the double-slit experiment: if you have detectors at the slits, to determine which way the particle went (which slit it went through), the interference pattern on the screen disappears! And that is because a history where the particle went through the right-hand slit and left a trace of its passage there has a different overall outcome than a history where the particle went through the left-hand slit and left a trace of its passage there, even if, in both cases, it ended up at the same point on the screen. The screen is the same, but the states of the detectors are different - in one class of history, the state of the right-hand detector has changed, in another class of history, the state of the left-hand detector has changed. Conceptually it's exactly the same as the case of the rebounding electrons, and whether or not an extra photon came flying out of the collision as well.

You can read about this if you look up "which-way measurements": if you have a which-way measurement, the interference pattern disappears. Even more dramatically, there are "quantum eraser" experiments, where a which-way measuring interaction occurs, but the system is set up so that the trace of the interaction will be removed before the particle reaches the screen, and in this case the interference pattern is restored.

 

[mitchell porter]

There are some other details in the original version of this question that I might want to expand upon. It distinguishes between open strings, which end on branes, and closed strings, which are gravitons and can move in the space off the branes. That is how things are described in string theory. But in M-theory, the description is a little different. The 1-dimensional strings, both open and closed, are revealed to actually be 2-branes, with one of their dimensions wrapped around the new, 11th-dimension of M-theory. So an open string, which was just a line in string theory, is actually a cylinder in M-theory; and a closed string is a donut. Also, the "D-branes" of string theory, on which the open strings end, become new objects in M-theory, which aren't always branes. They can instead just be regions of 11-dimensional space with a particular geometry (I'm thinking of the "Kaluza-Klein monopole" corresponding to a D6-brane).

Also, we assuredly do not yet understand the mutual relations between all these objects. I certainly don't, but it's not just a matter of what I haven't learnt. People are still writing tentative papers about the relationship between the M2-brane and the M5-brane, for example. It looks like you should be able to make an M5-brane from M2-branes. That is not so surprising, because in string theory the D-branes are actually http://physics.stackexchange.com/questions/7933/why-arent-d-branes-and-strings-independent-degrees-of-freedom" , and since strings are actually M2-branes, it stands to reason that the other M-objects are made of condensed M2-branes. What's more interesting is the possibility that the M5-brane is equally fundamental - that an M2-brane is just a degenerate M5-brane. It all suggests, and it is widely expected, that M-theory has some other undiscovered formulation, in which all the branes and non-branes descend from some other kind of entity.

But so far, none of this matters for braneworld cosmology, which you can model using approximations where even the string level of description doesn't matter much. If we are going to talk about the gravitational interactions of braneworlds, the logical place to start would be the Randall-Sundrum model, so I'll try to write about that next.