October 9th, 2012, 10:58 PM
Einstein maintained that gravity was a matter of geometry. Yet physicists today still search for a gavity force, such as gravity waves. Can anybody explain to me what's going on?
I put this question to Wattenburg but didn't get a satisfactory answer.
Here's a simplified answer (whether it's satisfactory or not, you'll have to judge for yourself): Indeed Einstein's GR says that gravity is a consequence of spacetime geometry which, in turn, is a function of mass. Gravitational waves may be thought of as ripples or propagating geometric distortions in spacetime, caused by, e.g., an accelerated mass. These waves are analogous to EM waves that propagate through space (as a consequence of accelerated charge in this case).Originally Posted by slush33
Einstein himself predicted the existence of gravitational waves (I believe around 1916-1917). Efforts to detect them on earth have failed so far, but their existence has been inferred from observations "out there" (look up "Hulse-Taylor pulsar" or something like that; its orbital decay matches the predictions of energy loss by radiation of gravitational waves).
Last edited by tk421; October 10th, 2012 at 12:40 AM.
I am moving all the off topic, nonsense posts and their responses out to a thread in the trash. All posts about non-standard physics and random nonsense will be removed.
The other three fundemental forces of interaction in Quantum Physics are: the strong nuclear force, weak nuclear force and electromagnetism. All of these forces interact with particles with their own particles specifically called 'guage bosons' which mediate those forces. Namely; Gluons, W&Z Bosons and the Photon. These particles have all been observed and interact with all kinds of other classification of particles (Hadrons, Leptons etc). However, gravity as we know it thanks to Einstein is expressed as geometry, the curving of spacetime due to mass (as in dimensions, as in shapes (geometry)).Yet physicists today still search for a gravity force, such as gravity waves.
This does not fit with the other three fundemental forces of interaction in Quantum Physics because it doesn't require a mediating particle however, it does have a mediating wave. This is because a wave in order to be a wave has to have time in which it is observed, in which case pertains to geometry, however a particle; doesn't.
In quantum physics there is a well known behaviour called 'Wave/Particle duality'. Which means that particles can exihibit both wave and particle like properties. Photons for example can be expressed as a wave (a wave of light) and a packet of energy called a photon (particle). However, you can only observe one type of behaviour at the same time. This is known as the uncertainty principle, and there are many examples of this effect as wave/particle duality that tried to solve it, however they often end up facing difficulties when applying to the macro, or 'real world' scale if you will. One particular example is Schrodinger's Cat.
The main point of all of this is that the three fundemental forces of interaction that can be quantized, gravity isn't one. And that is because wave/particle like behaviour is on the atomic scale (Micro Scale). Gravity as we know it has to be impossibly more larger to be observed because the force of gravity compared to the other 3 is impossibly weak, so much that to observe the gravity within an atom becomes an impossible task. The only thing close to observing and quantizing gravity, its the discovery of the Higgs Boson, which gives particles mass. The discovery of this particle will help teach us the circumstances in which gravity can exist and how it will have an effect on all particles, which in turn might help us quantize it and help find the graviton, gravity's gauge boson.
In a nutshell, gravity cannot be quantized because its effects are too large to be observed as a particle, and can only be observed at best, as a wave. For the time being at least.
A small paradox of gravity.
It says that the universe is expanding.
We can assume that gravity would slow down this expanding.
But it is actually speeding up.
It means that gravity goes to zero point.
If this is correct then we need to take zero gravity as a point of thinking.
Maybe the zero gravity can help us to understand everything about gravity.
=
Interesting point of view, never quite thought about it this way, but it's quite true.
There is another, more fundamental difference between gravity and the other forces - the strong and electroweak interactions are described via quantum fields in space-time, whereas gravity is space-time itself ! You can thus write down consistent QFTs of the other three forces, but once you attempt to establish a field of massless spin-2 vector bosons in space-time and quantize it, you arrive at unphysical infinities. Why ? Because the approach is fundamentally wrong - rather than quantizing a field in space-time, one should attempt to quantize space-time itself; this is pretty much the approach that loop quantum gravity (LQG) and causal dynamical triangulation (CDT), among others, have taken. It remains to be seen wether any of these models will yield physically meaningful results, though; in any case, rewriting the metric of GR in terms of Ashtekar variables was quite a brilliant idea, IMHO.
No, it only means that the vacuum has a non-vanishing energy density, which links up nicely with certain ideas of QFT.
Yes. What's going on is that many physicists today have a shaky knowledge of classical electromagnetism, and they elevate abstraction above reality. Quantime's post was well received, it's fairly typical of "what physicists think", but let me demonstrate the problems with it. Sorry Quantime, nothing personal. OK, here we go step by step:
The other three fundamental forces of interaction in Quantum Physics are: the strong nuclear force, weak nuclear force and electromagnetism.
There's nothing I care to say about this, see wikipedia.
All of these forces interact with particles with their own particles specifically called 'guage bosons' which mediate those forces. Namely; Gluons, W&Z Bosons and the Photon. These particles have all been observed and interact with all kinds of other classification of particles (Hadrons, Leptons etc).
Hold it right there. Ask youself this: Does a magnet shine? No it doesn't. Are there any little twinkling flashes of light coming from the comb that you use to pick up a piece of paper? No. Are there any actual photons moving back and forth between the proton and the electron in the hydrogen atom? No. Because the QED mediator of elecromagnetism is the virtual photon not the photon. And QED is a field theory. The virtual photon isn't a real photon, it's more like you divide a field up into little squares and say each square is a virtual photon. It's the same kind of thing for gluons. They are virtual particles, and they have not been observed. The W and Z bosons are said to mediate the weak interaction, which typically involves neutrinos. Ask yourself how with their huge mass, that this can possibly be true in any "flying messenger particle" sense.
we know it thanks to Einstein is expressed as geometry, the curving of spacetime due to mass (as in dimensions, as in shapes (geometry)).
Einstein didn't say exactly this, as you may pick up from discussions Markus and I have been having, but it's close enough for our purpose.
This does not fit with the other three fundamental forces of interaction in Quantum Physics because it doesn't require a mediating particle,
This is back to front. The other forces don't fit in with gravity because Quantum Physics "denies the geometry of classical electromagnetism". See this book for something about that: Geometry of Electromagnetic Systems.
however it does have a mediating wave.
No it doesn't. There are no gravitational waves flitting back and forth between you and the ground.
This is because a wave in order to be a wave has to have time in which it is observed, in which case pertains to geometry, however a particle; doesn't.
An electromagnetic wave is a transient passing field variation, whilst the electron exibits a standing electromagnetic field. There's obviously something wrong in saying the electromagnetic wave pertains to geometry whilst the electron's electromagnetic field doesn't, because we can make an electron (and a positron) from an electromagnetic wave in pair production.
In quantum physics there is a well known behaviour called 'Wave/Particle duality'. Which means that particles can exihibit both wave and particle like properties. Photons for example can be expressed as a wave (a wave of light) and a packet of energy called a photon (particle). However, you can only observe one type of behaviour at the same time. This is known as the uncertainty principle, and there are many examples of this effect as wave/particle duality that tried to solve it, however they often end up facing difficulties when applying to the macro, or 'real world' scale if you will.
The wording here causes some confusion. A long-frequency radio wave is not made up of a storm of tiny point-particles called photons. I think it's better to say that a photon is a wave that can appear pointlike when it interacts with more of the same.
One particular example is Schrodinger's Cat.
Schrodinger proposed his cat to demonstrate the absurdity of the Copenhagen Interpretation of quantum mechanics. Sadly it nowadays used to promote quantum weirdness.
The main point of all of this is that the three fundemental forces of interaction that can be quantized, gravity isn't one. And that is because wave/particle like behaviour is on the atomic scale (Micro Scale). Gravity as we know it has to be impossibly more larger to be observed because the force of gravity compared to the other 3 is impossibly weak, so much that to observe the gravity within an atom becomes an impossible task.
The real problem is the separation of fields. Imagine one photon propagating through space. Think of it as a single electromagnetic wave, one electromagnetic field variation. It's better to think of it as a pulse of electromagnetic four-potential, but nevermind that. The main thing is that it's just one photon. It isn't surrounded by a cloud of other photons. Describing the electromagnetic field variation that it is as being caused by other photons is disastrously self-referential. You can detect this field variation with a radio, you cannot detect some blizzard of point-particles. Our knowledge of Einstein's general relativity tells us that this photon has a gravitational effect. This electromagnetic field variation has a gravitational field. We can't actually detect that for a single photon, but we are confident that it's there. We can put this photon through pair production, and consider the electron. It isn't an electromagnetic field variation, it exhibits a standing electromagnetic field. It exhibits a gravitational field too. Ditto for the positron. Now place the positron next to the electron, and hold it there. From some distance we observe no net electromagnetic field, but the gravitational field is still there. Why? Because it's a trace of the electromagnetic field variation or field. It isn't something separate and distinct. But people think it is, invent gravitons as something distinct from their virtual photons, and then go round in circles because whilst they know QED like the back of their hand, they do not understand classical electromagnetism.
The only thing close to observing and quantizing gravity, its the discovery of the Higgs Boson, which gives particles mass. The discovery of this particle will help teach us the circumstances in which gravity can exist and how it will have an effect on all particles, which in turn might help us quantize it and help find the graviton, gravity's gauge boson.
This is a myth I'm afraid. The Higgs mechanism is thought to be responsible for only 1% of the mass of matter. You can read more about this Gian Giudice's Zeptospace Odyssey, a book about the LHC. He's a CERN physicist who describes the Higgs mechanism as "frightfully ad hoc" and "the toilet of the standard model". If pressed on E=mc² and why a radiating body loses mass, IMHO you might be able to twist his arm and get him to admit that he thinks that that percentage is wrong.
In a nutshell, gravity cannot be quantized because its effects are too large to be observed as a particle, and can only be observed at best, as a wave. For the time being at least.
As you can imagine, I don't agree with this. I'd say the real problem is that people get it wrong from the off, and go up blind alleys.
You seem to be forgetting that gravitational waves only mediate changes in the gravitational field. A static gravitational field between yourself and the ground ( both masses being constant ) does not require any waves.however it does have a mediating wave.
No it doesn't. There are no gravitational waves flitting back forth between you and the ground.
EDIT : Gravitational waves then do not correspond to individual gravitons, but to a coherent superposition state of many such particles.
A gravitational wave isn't made out of particles, Markus. Nor is an electromagnetic wave. Ditto for field. In a gravitational field I fall down. And if was an electron, I'd "fall" towards a proton. In both cases it's a field interaction rather than literal particles flying back and forth. In QED the "accounting units" of this are virtual photons, but people can't make it work with accounting units for gravity. Let me give you an idea of how I think one starts with this:
Take a sheet of graph paper, and across the bottom of it draw a gentle horizontal hump to represent the four-potential of a photon. It's the integral of the typical electromagnetic sine wave. Now draw a gentler horizontal hump above that, and repeat with even spacing up the page until at the top your horizontal line is flat. Now draw multiple vertical lines on the page to form a grid. Each cell of the grid that is not absolutely square represents a virtual photon. Those on the left are skewed to the right and vice versa.
Take a second sheet of graph paper, and do a similar drawing not for a single photon, but for multiple photons overlapping one another horizonally. You don't start off with a hump, you start with a horizontal line level with the top of your first hump on the first drawing. Your next horizontal line is level with the top of your second hump, and so on. You can do a bit of tracing to speed it up a little. When you've finished, each cell of the grid that is not absolutely square is a virtual graviton. Those nearer the bottom are more rectangular.
While I admit that I am not an expert on gravitons, it would appear that at least the corresponding Wikipedia article agrees with my understanding which I derive from my general though limited knowledge of QFT. I quote :
"However, experiments to detect gravitational waves, which may be viewed as coherent states of many gravitons, are underway (e.g., LIGO and VIRGO)."
The wikipedia guys are pretty good, but they don't always get it right. It would be better to say: a single electromagnetic wave is a photon, a single gravitational wave is a graviton. You can view an electromagnetic wave or field as many virtual photons, and you can view a gravitational wave or field as many virtual gravitons. Try that drawing, and hopefully you'll appreciate that virtual photons and virtual gravitons aren't all that different to one another.
I understand that - the only real difference between the two ( in the wave picture ) is their polarization states.
My point was simply this - a single particle corresponds to a single wavefront. This is the exact same for both EM and gravitational waves. While it is easy to get a single photon ( e.g. via emission by an electron falling into a lower state ), I do not see how that is possible for gravitons, since they mediate changes in the gravitational field, and these changes happen at a finite speed and aren't quantized. You would thus always observe more than one wavefront, and hence a coherent superposition of many gravitons.
The question as to whether it is even physically possible ( and meaningful ) for a single gravitational wavefront to exist is an interesting one, which I don't think can be answered until we have a consistent theory of quantum gravity. Fact is however that there is no conceivable and practical technology that could possibly detect a single graviton; G-wave detectors as they are will always find coherent many-particle states.
You're still seeing the various fields as totally different things Markus. You and thousands others, which is why we do not have a consistent theory of quantum gravity. Think of the current-in-the-wire. The electrons have their electromagnetic field, and the protons have theirs. But because the electrons are moving, the fields don't quite cancel, and what's left over is what we call a "magnetic field". It isn't actually a field in its own right, because the field concerned is the electromagnetic field, and that "magnetic field" is merely a remnant trace of two sets of electromagnetic fields. OK, now stop those electrons. Guess what? The fields still don't quite cancel, only now we call the remanant trace a gravitational field. When it comes to a single photon, don't forget that a photon has a gravitational effect. And it has a quantum nature. It's mediating a change in electromagnetic field and gravitational field. Do the drawings and remember what we were talking about re potential being more fundamental than field. On your second drawing, what's below the bottom flat horizontal line, and what's above it?
We don't have such a theory because no one has as per yet been able to self-consistently quantize space-time. The problem is largely mathematical - but it's only a matter of time.
It is irrelevant whether the electrons are moving or not. In either case they have both an EM field and a gravitational field.The fields still don't quite cancel, only now we call the remanant trace a gravitational field.
Photons do not mediate changes in the gravitational field, only in the EM field.When it comes to a single photon, don't forget that a photon has a gravitational effect. And it has a quantum nature. It's mediating a change in electromagnetic field and gravitational field.
No Markus, that's not the reason.
Aaaagh! You haven't done that drawing!
Oh yeah? You have a mirror-box containing a photon. You open the box. A radiating body loses mass. The photon travels across space. You trap it in a second box. As a result the mass of the box1 system is reduced whilst the mass of the box2 system is increased. The gravitational field of box1 is reduced whilst that of box2 is increased. Their electromagnetic fields however, remain unchanged.
I'm afraid Markus, that some of the things that you take for granted on the authority of some textbook or respected figure, are wrong. The problem is conviction, not mathematics.
Not wanting to start a flame war, I say only this to you - if you seriously believe that photons mediate changes in the gravitational field, then you should really go back to studying the basics. But then again - since you appear to reject textbooks as valid sources of data, it appears you're stuck with what you believe...
I've studied the basics Markus. That's why I know so much. Now forget the siren calls of textbook groupthink and conviction, set belief aside, and think it through for yourself. You said photons do not mediate changes in the gravitational field, only in the EM field. But look at that scenario I described. Don't let your Morton's Demon dismiss it. Steel yourself, and look at it. You've read Einstein's E=mc² paper. You know a radiating body loses mass whilst an absorbing body gains it. You know I'm not describing something nonsensical. You can find no flaw in it. And yet you insist that photons do not mediate changes in the gravitational field, only in the EM field. Even though the photon did the opposite. So something doesn't add up, now does it? Oh, and do those drawings like I asked you to, and tell me what's under the line and what's above it. Here's a clue that will hopefully lead you to that ohmygawd moment.
Maybe. You can lead a horse to water, but you can't make him drink.
Nice talking to you Markus!
The only thing that does not add up here is your apparant failure to understand that the photon mediates a change in the source of the gravitational field ( i.e. the energy content of the box ), not a change in the gravitational field itself.
Come on now, seriously ?! Thus far I thought of you as a mature discussion partner, but statements like the above almost make me doubt that impression.
I'm mature, Markus, and I genuinely meant what I said. Please note that you've shifted from:
if you seriously believe that photons mediate changes in the gravitational field
to:
the photon mediates a change in the source of the gravitational field.
Now try the scenario wherein we have no box1, but instead we trap some random photon from space in box2. The gravitational field of the box2 system has changed, end of story. We have no evidence that any other particle is involved. We have no evidence of any particles called gravitons being involved. And yet the gravitational field has changed whilst the electromagnetic field hasn't.
With respect, you're mixing up virtual and real particles here. The virtual photon is said to mediate electromagnetic field interaction. It isn't a real photon. Like I said, magnets don't shine and hydrogen atoms don't twinkle. Nowadays people seem to think the virtual photon is short-lived real photon, but it isn't. That's a myth that's grown up over the years. The Casimir effect hasn't helped. It demonstrated the reality of vacuum fluctuations, but they aren't the same thing as virtual particles. The force involved is very very weak whilst electromagnetic interaction is extremely strong. The reality underlying virtual photons is any electromagnetic potential/wave/field phenomena. The evanescent wave is a good example. It's a standing wave, also known as the near field. Check it out on google.
Thank you for a perfect demonstration of your complete failure at physics: you are now claiming that there is no electromagnetic difference between a system with one free photon and a system with one photon trapped in a box.
Farsight, I suggest you take a very careful look yourself at what you have written here. I really can't say any more.
I've checked it through Markus. I missed out an "a" but other than that there's nothing wrong with it that I can see. If you think I'm mistaken please advise, and I'll be only too happy to eat some humble pie and give my apologies.
Edit:
See this or this and this re the evanescent wave. For the first paper see section 3, where you can read:
"It is important to distinguish between real and virtual photons. Classically these may be associated with the far field and near field respectively arising from single charges and ensembles of charges. Alternateively they correspond to free and forced oscillaltions of the vacuum."
Last edited by Farsight; October 16th, 2012 at 03:31 AM.
There is no need for an apology, I would just like you to understand that the photon only mediates a change in the source of the gravitational field, not in the field itself. Remember that photons are spin-1 particles because they couple to 1-forms as their source, whereas gravitions are spin-2 because they couple to 2-forms, mathematically. They are not the same thing, even though some of their properties are similar.
The fact remains that the gravitational field changed and the electromagnetic field did not. And I have to say you still seem to be conflating photons with virtual photons and thinking of gravitons as something akin to real photons. That isn't how it is. The graviton is a hypothetical "particle" which is said to mediate gravitational field interaction. But it's a virtual particle, like a virtual photon is a virtual particle. And like the virtual photon it isn't something that flies back and forth at the speed of light. Instead it's a field quantum. A "chunk" of field. It ought to be called a virtual graviton, and with that in mind once you did the drawings you'd hopefully realise that it ought to be conflated with the virtual photon. Remember we don't really seek a quantum theory of gravity, we seek an improved quantum field theory that incorporates gravity. See the bottom half of the attachment below for something like drawing 1. The whole thing is a photon, each square is a virtual photon. The sine wave at the top is the derivative of the potential.
Sorry to interrupt this "friendly" conversation, but can someone - without analogy or hand waving - explain to a non-physicist what is meant by the phrase "mediates the XXX force"
See fundamental interaction on wikipedia. It's fairly reasonable. Check out the paragraph at the bottom of the overview:
"The modern (perturbative) quantum mechanical view of the fundamental forces other than gravity is that particles of matter (fermions) do not directly interact with each other, but rather carry a charge, and exchange virtual particles (gauge bosons), which are the interaction carriers or force mediators."
Note though that the very next sentence illustrates the issue I've been trying to clarify:
"For example, photons mediate the interaction of electric charges, and gluons mediate the interaction of color charges".
It isn't photons, it's virtual photons. This article by Matt Strassler gets it across:
"...The best way to approach this concept, I believe, is to forget you ever saw the word “particle” in the term. A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle. A particle is a nice, regular ripple in a field, one that can travel smoothly and effortlessly through space, like a clear tone of a bell moving through the air. A “virtual particle”, generally, is a disturbance in a field that will never be found on its own, but instead is something that is caused by the presence of other particles, often of other fields...
...This disturbance is important, because the force that the two electrons exert on each other — the repulsive electric force between the two particles of the same electric charge — is generated by this disturbance. (The same is true if an electron and a positron pass near each other, as in Figure 2; the disturbance in this case is similar in type but different in its details, with the result that the oppositely charged electron and positron are attracted to each other.) Physicists often say, and laypersons’ books repeat, that the two electrons exchange virtual photons. But those are just words, and they lead to many confusions if you start imagining this word “exchange” as meaning that the electrons are tossing photons back and forth as two children might toss a ball..."
It means that some particle or another is a carrier of a certain fundamental force. For example, the massless spin-1 photon is the carrier of the electromagnetic force, hence it "mediates" changes in the electromagnetic field. The massless ( as per yet hypothetical ) spin-2 graviton would "mediate" changes in the gravitational field.
You are deviating from the subject. The photon is not the particle mediating changes in the gravitational field, but merely the source of these changes.
Thanks, but I do not understand the phrase "carrier of a fundamental force". Specifically, I don't understand what it means to"carry force". Sorry to be dim
And can you explain why this mysterious "carrier of forces" is somehow promoted to the rank of "mediator" between changes in fields. Recall you used the word "hence"
Oh, and Farsight - if someone asks a genuine question and asks for detail, a response containing only links - especially Wikipedais links - is less than helpful, and strongly suggests the respondent doesn't really have a helpful response of their own.
One can only speculate why.......
Last edited by Guitarist; October 16th, 2012 at 12:52 PM.
Read what I linked to, Guitarist. If I hadn't provided any links you would have thought I was just making it up. Let's check that out shall we?
It's merely a figure of speech. Force is exerted, not carried. And it's exerted by "virtual particles" which is another figure of speech. Those virtual particles are field quanta, "chunks of field". It's as if you draw a grid over a field and say each cell is a virtual particle. Force is exerted between two particles when their fields interact, and as a result those particles move. In electromagnetism this force can be linear and/or rotational. The linear force is associated with what's called the "electric field" whilst the rotational force is associated with what's called the "magnetic field". Note though that no such fields exist, the field concerned is the electromagnetic field. In the current-in-the wire situation the electromagnetic fields of the electrons and protons alost cancel, but not quite. The electrons are moving, and the residual effect is what we call a magnetic field.
I can't. I share the view that potential is more fundamental than field, which means the "mediator" is more fundamental than the field it mediates.
Ok, you would probably be one of the very last persons on this forum who I'd call dim
At the same time though I don't quite get your question - in the standard model of particle physics, the fundamental forces ( strong, weak, electromagnetism and gravity - these are just interactions between particles ) are thought of as the excitations of quantum fields. These field excitations correspond to "virtual bosons", which "carry" a fundamental force. For example, an electron might interact with another electron through the exchange of one or more virtual photons. Some of these bosons are massless and move at the speed of light ( e.g. the photon and the graviton, which is why these two fields are thought to extend into infinity as the particles don't decay ), others are massive and thus limited in range. All of these bosons carry energy and momentum, both of which are conserved, so the exchange of a boson between two particles has a measurable physical effect. In that sense one says that virtual bosons "carry" a force, i.e. they have a measurable effect when they are exchanged between particles.
As for the term "mediator" : consider gravitation for example. Static gravitational fields act instantaneously as we all know, precisely because it is static and no exchange of particles is necessary. However, changes in the gravitational field propagate at the speed of light, because these changes are "mediated" by the carrier boson, the ( hypothetical ) graviton, which moves only at the speed of light. Hence the term "mediation", which is just convention.
This is the short, simplified version - entire volumes have been written on this subject !
Doublepost deleted.
I just referred to virtual photons in the context of electromagnetism in response to Guitarist's general question.
Anyway, if you're interested, here's that second picture, where the single photon is replaced by a series of horozonatally overlapping photons. Think of each cell of the grid that is not absolutely square as a (virtual) graviton.
grid.jpg
A spin-2 particle looks the same after a 180-degree rotation. Here's a cell from the previous picture before and after after a 180-degree rotation.
Spin-1.jpg
OK then, what exactly is a quantum field? Is it a "field of quanta" or is it a quantized field? Is there a difference?
Second, how do you "excite" a field?
And the "interactions" you mention - are these interactions between elements of the same field at different spacetime points, or are they interactions between different fields at the same spacetime point, where I am assuming - probably incorrectly - that the field elements are the particles you mention
A field is a physical quantity which maps either values or quantum operators to each point in space-time. A quantum field is quantised in the sense that the operators used have discreet eigenvalues. Is there a difference ? Good question, not sure about that.
At this point you have me cornered, because I have not yet gotten to the stage where I can make any sense of the maths underlying this process. I picture it much like a pebble thrown into a still pond - the surface of the pond gets perturbed from its equilibrium, thus creating ripples. Something similar happens in the quantum field, but I am unclear about the exact details, except that they also involve perturbations from the ground state ( mathematically this happens via creation and annihilation operators acting on state vectors in Hilbert space ). I still have much to learn in this area, so I am not qualified to answer your question in more detail.Second, how do you "excite" a field?
Neither. The field is present throughout all of space-time, so for example when two spatially separated electrons interact they do it via the photon field of quantum electrodynamics, i.e. by exchanging photons, even though the electrons themselves aren't manifestations of that field, only their interaction is.are these interactions between elements of the same field at different spacetime points, or are they interactions between different fields at the same spacetime point, where I am assuming - probably incorrectly - that the field elements are the particles you mention
It seems you are taking an interest in quantum field theory, Guitarist ?
There are four funemental forces of interaction in Quantum Physics, these forces are mediated by what is called a 'Guage Boson', it carries the properties neccesary for the retrospective force to exist in the known universe of 3 space dimensions plus one of time. For example, a photon is the guage boson (mediator of force) for electromagnetism. This photon helps electrons flowing in electric current thus producing magnetic induction by giving the electrons energy (electrons are called leptons), by giving them energy they allow the electron to either 'jump up' to a higher energy level (orbital ring around the nucleus of the atom) or escape the atom completley, thus create an ion. This effect creates ions to exist therefore creating dipole moments which are gaps of charge allowing 'charge' electrons to fit in again, or 'flow' through dipole moments to allow current.
The other fundemental force of interaction have similar effects respecively to their forces. The guage bosons exist however in explanation as particles, not waves. Again resulting to the wave/particle duality problem and the uncertainty principle, which cannot model or map the gravitational 'particle' because even as a wave (much more observable), it is hardly visible. This is because gravity against the other fundemental forces is so very very weak it cannot be measured. It would be like huge crane moving a girder and then measuring how much one particle of 'wind' helps out. Now imagine the cranes power being a mere photon (which is the base level detection of an electron microscope) and then finding the bit of wind, nearly impossible given current technology.
This is how I understand it, I may have gaps in my understanding here but that's the gist of it. Without a guage boson none of the forces can exist.
Sorry to interrupt, but I said earlier that I'd studied the basics. I'd like to try to get this across:
The latter. Quanta is derived from quantus which means how much. A field is a spatial "condition". It is not something separate from space and overlaid upon it, it describes the state of space, usually in a region where effects are non-negligible. A quantum field is one where certain mathematical techniques such as canonical quantization can be employed to construct a model that accurately predicts measurable field interactions.
You change the state of space in some given manner.
An interaction is usually between two fields over all spatial points for some duration. However a single field can interact with itself.
This might sound unfamiliar, but see Einstein talking about the history of field theory in 1929. Here's a few excerpts:
"Faraday was this favored spirit. His instinct revolted at the idea of forces acting directly at a distance which seemed contrary to every elementary observation. If one electrified body attracts or repels a second body, this was for him brought about not by a direct action from the first body on the second, but through an intermediary action. The first body brings the space immediately around it into a certain condition which spreads itself into more distant parts of space, according to a certain spatio-temporal law of propagation. This condition of space was called 'the electric field'...
People slowly accustomed themselves to the idea that the physical states of space itself were the final physical reality, especially after Lorentz had shown in his penetrating theoretical researches that even inside ponderable bodies the electro-magnetic fields are not to be regarded as states of the matter, but essentially as states of the empty space in which the material atoms are to be considered as loosely distributed...
It is only natural that attempts were made to represent the material particles as structures in the field, that is, as places where the fields were exceptionally concentrated...
The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric...
It is easy to show, for instance, in the case of three-dimensional space, how such a continuum differs from a Euclidean.
To this extent the geometry now used is not only a specialization of the Riemannian but also a generalization of the Euclidean geometry. My opinion is that our space-time continuum has a structure of the kind here outlined..."
Well, that confusing set of passages was helpful only to cherry-pick to introduce new confusions later!
A field is a region in space that, for every point in that field, indicates a direction and a magnitude. The gravitational field around the Earth, for example, indicates a direction (roughly towards the Earth) and a magnitude (an amount that decreases as the square of the distance from the center of the Earth). This magnitude is an acceleration on an object in the field. Most of the field interactions that we think about are ones that introduce acceleration.
(Note that acceleration is something that is geometry dependent. If we change the geometry properly then the acceleration disappears. Then whatever we said was the source of the field is now the source of a certain kind of geometry. This is what GR does to gravity. )
Roughly, quantum field theory attempts to explain the presence of fields through the interaction of quanta of a specific energy levels. In a quantum field theory, the amount of energy introduced to an object through the field must be introduced in some integer multiple of a quantity; standard field theory uses continuous quantities of energy exchange. QFT also builds off of quantum mechanics, so there is more going on there.
It is possible to use QFT for various fields within the context of GR, but it is not yet possible to make GR itself into a QFT in a way that makes anybody happy.
That’s wrong I’m afraid PhysBang. A field can be a scalar field. A vector field is associated with direction and magnitude. See for example these teaching notes for more.
You've made another error re energy quanta. It’s a common mistake, so no sweat. See the black body radiation section of the wikipedia article on Max Planck. See this bit:
"The central assumption behind his new derivation, presented to the DPG on 14 December 1900, was the supposition, now known as the Planck postulate, that electromagnetic energy could be emitted only in quantized form."
This is perfectly correct. However the next bit isn't:
"in other words, the energy could only be a multiple of an elementary unit E=hv where h is Planck's constant, also known as Planck's action quantum (introduced already in 1899), and ν (the Greek letter nu, not the Roman letter v) is the frequency of the radiation. Note that the elementary units of energy discussed here are represented by hv and not simply by h. Physicists now call these quanta photons, and a photon of frequency v will have its own specific and unique energy. The amplitude of energy at that frequency is then a function of the number of photons of that frequency being produced per unit of time."
We can contrive the emission of single photons or single electromagnetic waves at any frequency we choose, and we can vary that frequency smoothly. That means we can vary the energy smoothly. It can be any indiscriminate value we like. There are no actual elementary units of energy. Now see the Planck's constant article and note this: "Planck discovered that physical action could not take on any indiscriminate value." The action h in E=hf (aka E=hv) associated with the photon cannot take any indiscriminate value. Instead, it's the same for all photons. This is what QFT builds off.
E=hv is, as you have correctly stated, the energy of one photon. Of course you can vary this smoothly, but it always remains the energy of one photon, and as such it is the elementary unit of energy at a given frequency level. You cannot have half photons or quarter photons, you can only have multiples of one photon as the total energy : E(n) = n*hv for any given v.
Nevertheless there is no elementary unit of energy Markus. Saying "at a given frequency level" doesn't make it so, because that frequency can change smoothly, and the energy can change smoothly too. The quantum nature of the photon lies with the action, not the energy. Imagine I call out "Lights camera action!" and you start winding the handle of on old-style movie camera. There's a pen sticking out of the end of the handle, drawing a line on a moving scroll of paper. That line traces out a sine wave. Regardless of how fast you wind the handle, your action is the same, and the sine wave is always the same height. Look at some pictures of the electromagnetic spectrum.. The depicted amplitude is the same regardless of frequency. That's the quantum of quantum mechanics, not the myth wherein energy can only be the multiple of some elementary unit. Can you see the circular action in the depiction on the wikipedia wind wave article? Electromagnetic waves, wherein one wave is one photon, are something like wind waves where regardless of frequency, all the waves are the same height.
I don't think you understand what I was trying to say. At a given frequency v, we find that electromagnetic radiation has a total energy which is strictly a multiple of (hv). In other words, an electromagnetic field always comes in complete wave-fronts, you will never observer a wave-front and a half; for example you only observe either one complete wave-front, or two complete wave-fronts, corresponding to either one or two photons. You never observe one-half photons. Therefore electromagnetic radiation is quantized, with the basic unit being one complete wave-front, regardless of the frequency. That is the basic unit - one wave-front.
The frequency itself is of course allowed to vary smoothly, but the result at any given frequency is always complete wave-fronts ( photons ).
I don't disagree with that Markus. Even in Compton scattering where the electron acquires some of the incident photon energy-momentum, we're still left with one complete photon. It has a longer wavelength, it isn't half a wave.
But I'd say that doesn't address the common feature of photons/electromagnetic waves which is the same regardless of wavelength/frequency. Ocean waves are complete waves too, but they do not share a common feature.
That is because they are oscillations of composite systems of many particles, not elementary waves.
Fine. The point is that electromagnetic radiation is not quantized because the basic unit is one complete wave, but because all such waves share a common feature regardless of wavelength. Remember we were talking about gravitational waves, wherein LIGO has attempted to detect a length-change in the arms of the interferometer? If gravitational waves were like electromagnetic waves, then regardless of wavelength, the length change would always be 3.86 x 10ˉ¹³ m. However we do not expect that because gravitational waves are the result of composite systems of many particles. They aren't elementary waves with a quantum nature.
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