Mordred

Your welcome that was what I meant by your OP being extremely close to accurate

To answer your question particles are field excitations. The pointlike characteristics is where the wavefunction is a quanta of energy. That is your particle. The wavelike characteristics is the probability distribution of finding the above quanta at a given location. So when you get right down to it there is no need for Wave-particle duality once you treat the particle as a field excitation. Which is what the above paper is describing

Here lets save time https://redirect.viglink.com/?format=go&jsonp=vglnk_148435658654413&key=6afc78eea2339e9c047ab6748b0d37e7&libId=ixwjkyqa010009we000MAki55j4ju&loc=https%3A%2F%2Fwww.physicsforums.com%2Fthreads%2Fthe-vacuum-fluctuation-myth-comments.892500%2Fpage-7&v=1&out=http%3A%2F%2Fwww.google.ca%2Furl%3Fsa%3Dt%26source%3Dweb%26cd%3D9%26ved%3D0ahUKEwiNgcSLubfRAhWogVQKHRtBBLEQFgg1MAg%26url%3Dhttps%253A%252F%252Farxiv.org%252Fpdf%252F1204.4616%26usg%3DAFQjCNEqAKaDGcbyMG2ax22sA9BakBSaTQ%26sig2%3DOLrYE7fyEIHsA3zMw400rQ&ref=https%3A%2F%2Fwww.physicsforums.com%2Fthreads%2Fthe-vacuum-fluctuation-myth-comments.892500%2Fpage-6&title=The%20Vacuum%20Fluctuation%20Myth%20-%20Comments%20%7C%20Page%207%20%7C%20Physics%20Forums%20-%20The%20Fusion%20of%20Science%20and%20Community&txt=http%3A%2F%2Fwww.google.ca%2Furl%3Fsa%3Dt%26amp%3Bsourc...G2ax22sA9BakBSaTQ%26amp%3Bsig2%3DOLrYE7fyEIHsA3zMw400rQ "But the puzzle of wave-particle duality in this experiment can be resolved by switching to an all-fields perspective" The author of the above goes into good detail on the above quote

Ok First define the wavefunction according to QM. Then define mathematically the particle. There is a specific reason I want you to look in detail on these two questions. Wave-particle duality is a little sneaky when described in Heuristic terms. Your above is close but not quite right. Hint "what is the definition of a particle under QM" ?

Better question what is mass. Definition "Resistance to inertia change" in other words its a kinenatic desciptive. No time doesn't cause curvature either. Spacetime curvature is a geometric system that maps freefall motion in accordance to geodesic Worldlines. Its a mathematical descriptive of relations. Not an entity unto itself. http://www.scienceforums.net/topic/89395-what-is-space-made-of/page-1 Energy is simply the "ability to perform work" Stick to the physics definitions without trying to apply an entity quality to terms such as mass, energy, spacetime etc. They are properties

Feyman has excellent lectures. I would ask any further questions not directly related to "what is space" please start another thread I'll be more than happy to reply there. I don't want this thread to describe the body of physics 😉

Spin is a property but one that is quantized. A VP being "off shell" may or may not exhibit spin. The minimum measurable quantizable value is [latex] E=\hbar w [/latex]. In QFT this defines the creation/annihilation operators (math term). The reason a VP isn't measurable is that they have insufficient energy to cause action to affect even the most ideal detection instrument.

Ok good images I can distinquish the problem using these. The external lines are your excitations (particles) these are termed your real particles. The internal ziggly lines on the right image is your fluctuations (virtual particles) it is those internal lines that is the issue. The external lines are renormalizable the internal lines are not. The external lines can induce effective action. While the internal lines has insufficient energy to do so. This is all described under S-matrix theory. Lattice QCD shows that an external line is really a boundary confined collection of fluctuations(VP) that sum up under confinement to an excitation. (particle) Spots in your eyes are more a biology discussion. I don't know the proper terminology but in essence your receptors are still sending delayed signals

Not at this point the problem with quantum gravity lies within a term called "renormalization" which is a very complex topic. Part of the problem with renormalization lies within the Heisenburg uncertainty principle itself. Just to be clearer there, when you hear the term "the problem is quantization" A quanta is the nimimum energy to cause "observable action". Action is a term to describe kinematic motion. Whats often described as a virtual particle for example cannot perform action as it is less than a quanta. The term particle itself is a classical misnomer as all particles are a field excitation. A field being a collection of excitations in this case. A field deviod of excitations being what is termed your zero point energy in QM. Under Cosmology true vacuum. However the Heisenburg uncertainty principle causes difficulty even after all excitations are removed. An excitation being a quanta, a fluctuation being VP of energies less than a quanta. I'm being a bit heuristic but this is where the problem lies between quantum gravity and relativity for a full blown TOE.

yes mass is resistance to inertia change so your common relation is momentum and factors that affect change in momentum. The stress tensor doesn't identify the cause but describes the influence to momemtum. Energy is "the ability to perform work." This all relates back to your Newton laws of inertia under a collective organization in your stress tensor. Spacetime curvature itself is a geodesic map of freefall motion. Described as the particles worldline. The stress tensor gives us the momentum based components of that map. So literrally any dynamic/interferance or interaction that can induce a resistance to inertia change is a form of mass. These are described under the stress tensor.

Not purely mathematical they are in essence fluid dynamic terms. flux is particles/unit area/unit time) across surfaces of constant x, y and z. Vorticity is a type of motion of those particles often described as the curl component. In essence describing rotational fluids. Classical examples being whirlpools etc. The curl component of the Maxwell equations being another example of vorticity. In essence vorticity is your angular momentum terms. Angular momentum being skew-symmetric

There is three main components to the stress tensor. Momentum, flux and vorticity.

I've always preferred stating the stress tensor instead of mass. Far more accurate but then many wouldn't know what the stress tensor is. @Tom one can apply a numeric description to anything in nature. That does not mean numbers are intrinsic to anything. Numbers are simply another form of language. A method of descriptive. Strange and Stingyjunky already covered the important details to Brownsfan77 post but I will add Any form of field can influence spacetime whether its electromagnetic, a matter field, the strong force etc. Using electromagnetic field to bend light is just one example but not the only one. While its great you showed that an electromagnetic field can bend light. So can other forms of either force or matter fields. With or without the presence of an electromagnetic field such as two asteroids far removed from any magnetic field. Another key distinction between gravity and any other force field is that gravity matches spin 2 statistics (which includes its thermodynamic character via Bose-Einstein statistics) No other known field does. Electromagnetic follows spin 1. So a GW wave is significantly different from an electromagnetic wave. We have now detected GW waves and confirmed the spin 2. Keep in mind a field is a mathematical abstract device to describe any collection of objects/events etc. Then again mass is also an abstract device to describe resistance to inertia change. Mathematics and physics simply describes what we understand as reality or aspects of it. Spacetime curvature is a mathematical geometric description of relations. Space is a description of volume, too often posters seek what it is fundamentally made up of due to trying to understand how it can curve. What curves includes additional relations causing resistance to inertia change.

No it works for all orbitting bodies but only predominantly two body systems for good accuracy. Accuracy gets Elusive on three or more bodies. At least his laws do.

Just to clarify vectors are orthogonal but not all degrees of freedom are. example being a spinor Just to clarify vectors are orthogonal but not all degrees of freedom are. example being a spinor. Though we model spinor rotations under orthonormal basis. ie some of the groups involved are orthogonal but other groups can be unitary ie (SU) is special unitary while SO groups are orthogonal. Not all symmetry groups fall under orthogonal groups. Thats more on how the symmetry groups are constructed than on the required dimensions. I mention that simply to be aware not all groups are orthogonal groups

Pretty good post fairly on target to the OP. Mathematically think of these extra dimensions as additional degrees of freedom. So you can add as many dimesions to describe the possible degrees of freedom. Each interaction counts as a degree of freedom ie in string theory or Kaluzu-Klien. So for example a complex object such an electron I need three dimensions to describe its volume aspects 1 for time an an additional one for its charge behavior

Sure he does, he understands physics. Mainly one of the earliest lessons in relativity massive objects cannot reach c. Has nothing to do with whether or not its being observed

Swansonts last comment reminded me of the analogy.

Lol here is color superposition http://www.google.ca/url?sa=t&source=web&cd=&ved=0ahUKEwjItIT6pNnRAhVI6GMKHZhwCXEQFghtMBU&url=http%3A%2F%2Fwww.johnboccio.com%2Fcourses%2FPhys14_2005%2FQM_P6H%2FSuperposition_A.pdf&usg=AFQjCNFFqz4v5Uxjl4vj31oosy1kaeBSSw&sig2=np0jmetChytaKIAFM3OIxQ

lol believe me you don't want to see the superposition equations in QFT treatments

I'm no expert on typing so quite frankly the wrong person to ask. I simply point out it comes down to studied efficiency and there studies of maximizing the efficiency in keyboard layouts. QWERTY isn't the only layout just one of the more commonly used

Sure there is, finger movement vs comfort studies I Don't know the study layout for the numeric but the alphabet portion follows QWERTY studies. http://www.userlab.com/Downloads/QWERTY.PDF However here is a pertinant numerical keyboard study http://www.google.ca/url?sa=t&source=web&cd=&ved=0ahUKEwiDwK7TlNbRAhVN8WMKHdoGAmE4ChAWCCcwAQ&url=http%3A%2F%2Fcommons.erau.edu%2Fcgi%2Fviewcontent.cgi%3Farticle%3D1173%26context%3Ddb-theses&usg=AFQjCNFAbzilCYGGr66RVJf1SP_3-AKSHg&sig2=XTBYvnzw9dpwarZejqB9BA

In point of detail under GR gravity doesn't escape a Bh. Spacetime curvature itself is gravity and has no need to escape

Then perhaps you should clarify what you are truly stating as the energy/mass relations also apply to any field as well Clarify this statement as reading your replies your being inconsistent All particles are essentially field excitations under boundary binding conditions. ie a quanta in a finite (point-like )region. Mass and energy is literrally different mathematical treatments to describe the properties of what is commonly referred to as particles. mass is resistance to inertia change energy is the ability to perform work. A field being an abstract device to describe any collection of objects/events They are fundamentally two properties of the same thing. Much like an object has properties of length/volume (3d object) Or density/pressure and temperature. OK I recognize this is far too advanced for most people but lets look at a Spinless particle under QFT treatment. the state of a system is governed by the Schrodinger equation [latex]i\hbar\frac{\partial}{\partial t} |\psi,t\rangle=H|\phi,t\rangle[/latex] where H is the Hamilton for the notation [latex]\langle | | \rangle[/latex] this is the Dirac bra-ket notation which is a convenient vector notation. so a simple system with no forces acting upon it of a spinless non relativistic particle is [latex] H=\frac{1}{2m}P^2[/latex] where m is the particles mass and P the momentum operator. in the position basis the first equation becomes [latex] i\hbar\frac{\partial}{\partial t}\psi (x,t)=\frac{\hbar^2}{2m}\nabla^2\psi(x,t)[/latex] where [latex]\psi(x,t)=\langle x|\psi,t\rangle[/latex] to generalize this spinless particle above in relativistic motion take [latex] H=+\sqrt{P^2c^2+m^2c^4}[/latex] [latex]H=mc^2+1/2m P^2+...... [/latex] the ..... denoting higher order corrections with the Hamilton and Schrodinger the above becomes [latex]i\hbar\frac{\partial}{\partial t}\psi(x,t)=+\sqrt{-\hbar^2c^2\nabla^2+m^2c^4\psi(x,t)}[/latex] there I just described a spinless particle in both relativistic and non relativistic treatment. However the last equation requires some limits to avoid infinities. Without going into detail as the above is tricky enough to understand we end up with the Klein_Gordon equation [latex]i\hbar^2\frac{\partial^2}{\partial t^2}\psi(x,t)=(-\hbar^2c^2\nabla^2+m^2c^4)\psi(x,t)[/latex] the point being is the above shows a particle is not some bullet but a field excitation. how we measure that field excitation requires observer treatments described by relativity. How one measures a field of the above spinless objects are also under observer corrections via the redshift equations regardless of whether you are measuring a vacuum/field/object/particles the observer influence is always a factor. One can correlate the above to any particle via its spin ie electrons spin 1/2 etc

Lol I could probably write a more accurate and better quality article in my sleep.