Emmy Noether showed that for every symmetry in a theory there is a corresponding conserved current. The ideas of energy and momentum I am familiar with are cases of such Noether currents that exist as vector for particles in relativistic theories and a combination of vector and scalar in non-relativistic theories. This holds true for both classical and quantum mechanics.
Please note I said for particles. GR is a field theory and its Noehter currents are conserved fields. The Einstein stress energy tensor can be taken as a Noether current of GR. Similar statements for all advanced theories of physics I am familiar with.
In both the case of particles and fields energy and momentum or stress energy field can be said to describe part of the symmetry of the theory.
So Chipper Q can you help me to understand what you mean by the quote about energy and space time not mixing?
So Chipper Q can you help me to understand what you mean by the quote about energy and space time not mixing?
I meant something along the lines that a stable energy pattern (described by some wave equation, like for a photon, or an electron) doesn't “fill a volume” of space (given by some instantaneous position), rather it “displaces the region” of space (i.e., in a hydrogen atom, space is displaced only where the quarks and electrons are, but not between them).
When one refers to curved space (say, near a black hole), does this mean that a nearby particle's world line is what is curved (and not actually space itself)?
Chipper Q:
Thank you for taking the time to respond.
You seem to be imply that you can fix the position at any instant of time. It seems to me that violates the Hiesenburg uncertainty principle.
If the path is curved what is causing the the deviation from a straight line?
All solutions to GR I know of include holes in space. If we are talking about a isolated spining object the hole is space is a disk. If it is an isolated non-spining object the hole is a point.
You seem to be imply that you can fix the position at any instant of time. It seems to me that violates the Hiesenburg uncertainty principle.
I wasn't trying to imply that, but I certainly understand the objection. It's tough for us to know where something like that is from moment to moment, but how can nature not know, since the particle has to be somewhere, even if the “somewhere” is a superposition of locations. Wherever that may be, I was suggesting that space is “displaced”, rather than “filled”.
Chipper Q:
Your statement “the particle has to be somewhere” holds for quantum mechanics. Quantum field theory says among other things that each finite region of space-time is filled with an infinite number of particles of all possible types. It is only when you sum over all the particles that you can assign a probability to the existence of each type of real particle in the region. It can still be said that each particle has an unknowable but definite position for the duration of its existences. It seems to me if you put a hole in space-time along each particles world line it would fragment space time into isolated patches or delete space-time altogether.
Chipper Q:
I am posting this as a separately because I didn’t want to present two such different lines of thoughts in the same post.
Your statement “the particle has to be somewhere” holds for only for Fermions. For Bosons the opposite is true a Boson can not be reduced to one dimensional world line. In GR light is frequently treated as geometric rays but this no more captures the true nature electromagnetism then it do similar treatments in high school physics text. Quantum Electrodynamics is one of the two best tested theories devised by human ingenuity (the other being GR). But based on what I have learned about QE it would not work if photons obeyed the principle you suggest.
Your statement “the particle has to be somewhere” holds for quantum mechanics. Quantum field theory says among other things that each finite region of space-time is filled with an infinite number of particles of all possible types. It is only when you sum over all the particles that you can assign a probability to the existence of each type of real particle in the region. It can still be said that each particle has an unknowable but definite position for the duration of its existences.
Yes, and so the point (with regard to the line of reasoning) is that an interaction will occur between the 'finite region of space time' and anything propagating through it.
Quote:
Your statement “the particle has to be somewhere” holds for only for Fermions. For Bosons the opposite is true a Boson can not be reduced to one dimensional world line.
I understand there are fundamental differences between fermions and bosons, but as profound (and symmetric?) as the differences are, nothing seems to propagate faster than “c”. Hence, all fundamental particles in the Standard Model have some components in common, where their interaction with regard to traversing a 'finite region of space time' results in the observed limits on propagation (as the line of reasoning goes).
So for some component, this “interaction” implies transfer of energy, and it implies a finite limit for maximum velocity (and hence a maximum transfer rate). For me, it helped to imagine an “ideal turnstile” of sorts, but whatever the mechanism, the laws of motion are preserved (e.g., an object in motion stays in motion), from “at rest” to “c”.
Then, to account for observed gravitational effects, the line of reasoning holds that these 'finite regions of space time' are quantized in a preferentially orthogonal network of “turnstiles” [on the order of the Plank Scale?], whose region of space time can be displaced by an interaction, when the (collapsed?) sum over all particles is perturbed by the proximity of something with fundamental components indicative of energy having “mass”. The end result for some concentration of masses, is the perceived gravitational field. [The density of turnstiles is slightly less where the concentration of mass is commensurately higher?]
Perhaps a better way of saying it is that there is a coupling between energy and finite regions of space time? And that space time comes in packets?
Quote:
It seems to me if you put a hole in space-time along each particles world line it would fragment space time into isolated patches or delete space-time altogether.
Uh, as far out on a limb as this line of reasoning already is, does is make sense to say that separating packets of adjacent space time is analogous to trying to pull quarks apart? Which is to say that a void between adjacent packets must be filled (to some extent, considering the energy transfer of the aforementioned interaction) by energy (mass), and beyond that (or in the absence of mass) a new space time packet would be formed.
At any rate, it's I who am grateful for your time, Mark, especially if this line of reasoning is way off base, or not what you otherwise expected.
Emmy Noether showed that for
)
Emmy Noether showed that for every symmetry in a theory there is a corresponding conserved current. The ideas of energy and momentum I am familiar with are cases of such Noether currents that exist as vector for particles in relativistic theories and a combination of vector and scalar in non-relativistic theories. This holds true for both classical and quantum mechanics.
Please note I said for particles. GR is a field theory and its Noehter currents are conserved fields. The Einstein stress energy tensor can be taken as a Noether current of GR. Similar statements for all advanced theories of physics I am familiar with.
In both the case of particles and fields energy and momentum or stress energy field can be said to describe part of the symmetry of the theory.
So Chipper Q can you help me to understand what you mean by the quote about energy and space time not mixing?
RE: So Chipper Q can you
)
I meant something along the lines that a stable energy pattern (described by some wave equation, like for a photon, or an electron) doesn't “fill a volume” of space (given by some instantaneous position), rather it “displaces the region” of space (i.e., in a hydrogen atom, space is displaced only where the quarks and electrons are, but not between them).
When one refers to curved space (say, near a black hole), does this mean that a nearby particle's world line is what is curved (and not actually space itself)?
Chipper Q: Thank you for
)
Chipper Q:
Thank you for taking the time to respond.
You seem to be imply that you can fix the position at any instant of time. It seems to me that violates the Hiesenburg uncertainty principle.
If the path is curved what is causing the the deviation from a straight line?
All solutions to GR I know of include holes in space. If we are talking about a isolated spining object the hole is space is a disk. If it is an isolated non-spining object the hole is a point.
RE: You seem to be imply
)
I wasn't trying to imply that, but I certainly understand the objection. It's tough for us to know where something like that is from moment to moment, but how can nature not know, since the particle has to be somewhere, even if the “somewhere” is a superposition of locations. Wherever that may be, I was suggesting that space is “displaced”, rather than “filled”.
Chipper Q: Your statement
)
Chipper Q:
Your statement “the particle has to be somewhere” holds for quantum mechanics. Quantum field theory says among other things that each finite region of space-time is filled with an infinite number of particles of all possible types. It is only when you sum over all the particles that you can assign a probability to the existence of each type of real particle in the region. It can still be said that each particle has an unknowable but definite position for the duration of its existences. It seems to me if you put a hole in space-time along each particles world line it would fragment space time into isolated patches or delete space-time altogether.
Chipper Q: I am posting this
)
Chipper Q:
I am posting this as a separately because I didn’t want to present two such different lines of thoughts in the same post.
Your statement “the particle has to be somewhere” holds for only for Fermions. For Bosons the opposite is true a Boson can not be reduced to one dimensional world line. In GR light is frequently treated as geometric rays but this no more captures the true nature electromagnetism then it do similar treatments in high school physics text. Quantum Electrodynamics is one of the two best tested theories devised by human ingenuity (the other being GR). But based on what I have learned about QE it would not work if photons obeyed the principle you suggest.
RE: Your statement “the
)
Yes, and so the point (with regard to the line of reasoning) is that an interaction will occur between the 'finite region of space time' and anything propagating through it.
I understand there are fundamental differences between fermions and bosons, but as profound (and symmetric?) as the differences are, nothing seems to propagate faster than “c”. Hence, all fundamental particles in the Standard Model have some components in common, where their interaction with regard to traversing a 'finite region of space time' results in the observed limits on propagation (as the line of reasoning goes).
So for some component, this “interaction” implies transfer of energy, and it implies a finite limit for maximum velocity (and hence a maximum transfer rate). For me, it helped to imagine an “ideal turnstile” of sorts, but whatever the mechanism, the laws of motion are preserved (e.g., an object in motion stays in motion), from “at rest” to “c”.
Then, to account for observed gravitational effects, the line of reasoning holds that these 'finite regions of space time' are quantized in a preferentially orthogonal network of “turnstiles” [on the order of the Plank Scale?], whose region of space time can be displaced by an interaction, when the (collapsed?) sum over all particles is perturbed by the proximity of something with fundamental components indicative of energy having “mass”. The end result for some concentration of masses, is the perceived gravitational field. [The density of turnstiles is slightly less where the concentration of mass is commensurately higher?]
Perhaps a better way of saying it is that there is a coupling between energy and finite regions of space time? And that space time comes in packets?
Uh, as far out on a limb as this line of reasoning already is, does is make sense to say that separating packets of adjacent space time is analogous to trying to pull quarks apart? Which is to say that a void between adjacent packets must be filled (to some extent, considering the energy transfer of the aforementioned interaction) by energy (mass), and beyond that (or in the absence of mass) a new space time packet would be formed.
At any rate, it's I who am grateful for your time, Mark, especially if this line of reasoning is way off base, or not what you otherwise expected.