# Dimensional Properties of Energy

## Main Question or Discussion Point

Howdy,
I am studying the dimensional properties of energy. I know it is thought that matter is a form of bound energy- wavicles. In this form, energy definitely occupes 3 dimensional planes and moves in each similtaneously.

However, i am curious as to other types of energy- unbound, and what are thier dimensional properties. It is obvious that unbound energy moves in x/y/z planes vectorily, but does it really occupy 3 planes at a time as matter?

If unbound energy was actually 3-dimensional like matter, then wouldn't it have gravity? Hypothetically, can energy exist in only 2 dimensions? If so, in what form? What about one dimension only?

Also, what types of energy are there besides electromagnetic? Is heat possible without particles to excite?

I'm studying planck era physics and this is important for me to understand.

Cheers and thanks ahead of time,

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First of all you must define what you mean by "dimension". There are mathematical definitions of dimension but what does it mean physically? What property of the physical universe can we identify with dimension? The number of coordinates needed to locate an object in space? This leads to the question of what is "space"? Loop quantum gravity has a very nice definition of what space might be, you might want to take a look at it.

Second, the "wavicle" is both a particle and a wave. So it is not purely a wave, hence it is not pure "energy".

In classical mechanics energy is simply the ability of an object to do work, but in QM and in GR energy becomes a more subtle concept. In reality no one truly understands QM that's why things like energy and wavicles seem to have such magical properties.

FSC729 said:
First of all you must define what you mean by "dimension". There are mathematical definitions of dimension but what does it mean physically? What property of the physical universe can we identify with dimension? The number of coordinates needed to locate an object in space? This leads to the question of what is "space"? Loop quantum gravity has a very nice definition of what space might be, you might want to take a look at it.
In a mathematical sense, a dimension is a dichotomous line. Quantum physicists theorize that a planck length and a planck time is a quanta of space/time, which they call the "fuzziness" of space, but i'm skeptical. I know there are at least 3 physical dimensions because i can move in all 3 similtaneously, but i don't know whether they are smooth or fuzzy.
I'll check out loop QG- thanks for the tip!
Second, the "wavicle" is both a particle and a wave. So it is not purely a wave, hence it is not pure "energy".
Right, but sometimes electromagnetic energy seems to act entirely like one or the other. Could it be that EM energy is a transitory or hybrid stage between primitive wave energy and advanced matter energy?
In classical mechanics energy is simply the ability of an object to do work, but in QM and in GR energy becomes a more subtle concept. In reality no one truly understands QM that's why things like energy and wavicles seem to have such magical properties.
Yeah, one of my physics buddies said that the ultimate reason for force and energy was "magic". Do you know what forms of energy besides matter exert gravity? Does electricity?

cheers,

Last edited:
ZapperZ
Staff Emeritus
2018 Award
Right, but sometimes electromagnetic energy seems to act entirely like one or the other. Could it be that EM energy is a transitory or hybrid stage between primitive wave energy and advanced matter energy?
From my perspective, there appears to be the hint of a misuse of the so-called "wave particle duality" here. I strongly suggest that, if you DO hold this view, you first read the FAQ in the General Physics forum. You cannot jump straight into "Beyond the Standard Model" without understanding the fundamental of what has already been established. There is nothing "different" in QM with regards to those two seemingly-different behavior. So it isn't a "transition".

Zz.

Staff Emeritus
Gold Member
Dearly Missed
Wave-particle DUALITY is the prototype of all the other dualities that have turned up in physics. In all cases it's not "either/or"; nor is it simple "both". It's "BOTH when seen from a richer perspective". And in each case the richer perspective is precisely the heart of the theory in which the duality occurs. The duality is the signal that the richer perspective applies. In QM that perspective is the complex Hilbert space of states and the operators that act on them.

You are asking some profound questions, but it is unclear what level of detail you require in an answer. I suspect you will find little to help you in LQG, not because the answers to your question are not found there, but because you will not be familiar with the language in which the answers are presented. Well anyway I suspect that is why I cannot find the answers to your questions in LQG. I have been studying the formalism for some time now but still am not qualified to understand the proofs.

However I suspect from your phrasing that your curiosity can be satisfied, or at least mollified, without going so deep.

You seem to have some geometry, since you mention x,y,z planes. Have you considered the idea of a Cartesian plane as an intellectual construct, in which sense it has little or nothing to do with particles, charges, and other observable phenomena? Euclidian geometry deals with straight lines and flat planes, but we have no reason to believe that these things exist except in the strictly local sense. Einstein showed us that a straight line viewed from one location can be viewed as curved from another location. In fact modern mathematicians often forgoe the idea of straight lines entirely and speak only of curves and edges. Modern physics finds that the mathematics of curved surfaces is more useful than straight line trigonometry.

I should like to encourage you to examine your own phrases carefully to remove any verbal stumbling blocks. When you say things like "I know that...." or "it is obvious..." or even "definitely occupies....", you are inviting contradiction. I sense that you are trying to form a solid basis from which to progress, but it will serve you poorly if your platform turns out in the end to be rotten. Better to examine each piece carefully.

I have also heard it said that matter is a form of bound energy, which might better be thought of as 'wavicles.' You must see of course that this answer merely divides the question. What is matter? It is energy, and it is bound, and to remind us of these things, we will now call it "wavicles" instead of matter. Now we must wonder, what is energy, what does it mean to be bound? We paste the label "wavicle" over these new questions, but how are we better off asking "what is a wavicle" than we were when we asked, "What is matter?"

Perhaps energy is more fundamental than matter, and the idea of matter as bound energy really is a deeper insight. We might say "bound" means only that the energy is found within some boundaries, and leave the question of why it stays bound within boundaries for another time. Then we are left with, What is energy? Perhaps energy is indeed more fundamental than matter. Maybe there is only one kind of energy, and in its different forms it makes up all the different kinds of matter.

So we look at some of the kinds of energy with which we have some familiarity. Electromagnetism. Heat light and sound. A year or so of intense guided study at a college or university with physical laboratories and dedicated lecturers will get you there. Of course I presume you have the arithmatic, geometry, algebra, trigonometry, and calculus to follow the math. You can get a feel for physics without the math, but if you want to follow the proofs, math is not optional. You ask good questions, which is a promising talent, but I can only give you a feel for the answers without the mathematics.

"If unbound energy was actually 3-dimensional like matter, then wouldn't it have gravity? " By Occam let's just ask if energy has gravity. By the equivalence principle, yes.

"can energy exist in only 2 dimensions? "

Well you may be confusing two different uses of the idea of dimension here. Let's look at E=mc^2, which in words is the familiar Einstein mass-energy equivalence formula, read "Energy is mass multiplied by the squared velocity of light." We can use dimensional analysis to find the dimensions of energy from this formula.

Mass is a unit of measure, and we tie it to physical reality by means of an object, a certain carefully maintained standard, which can be replicated by counting out a certain number of atoms of a certain reasonably common substance. Mass then is a measure, a dimension if you will, a gauge, by which we can compare reasonably local substances to each other.

Velocity is a unit of distance, space if you will, multiplied by the inverse of time. We commonly sense velocity in terms of miles per hour or meters per second or the like. Length divided by time. Now it is a subtle point that space and time are the same thing, which is called the Einstein Space-time equivalence and is related by c, the speed of light, which is taken to be constant in all frames of measurment. In fundamental work, we often just call the speed of light a unit, so it has a numerical value of one, and of course the square of one is one, so we are left with E=m x 1, or just E=m. This is concise but not very savory. We wanted a feel for what mass is, and then we wanted a feel for what energy is, and now we have the feel that they are the same thing. What progress have we made?

Let's put c back in to try to recover our geometric sense of dimension. Since c is a velocity, it has units of distance over time, so the square has units of distance squared over time squared. We know the square of distance by feel, and only have to think of the flat surface of a piece of paper to get a sense of squared distance. But what are we to make of the idea of inverse time squared? How can time be squared? How do we get a feel for that? In c^2 we seem to have a surface divided by time and then divided by time again. What is this thing of dividing by time and then dividing by time again? Well, in a slightly reduced case, we have the example of distance divided by time and then divided by time again. That is acceleration and you can feel it everytime you ride in an automobile, or any time you initiate or cease movement at all actually.

We often speak of the curve of acceleration, and to really get a good feel for this you need that college physics lab, or a good high school equivalent, and a certain amount of math. It turns out that if you think of velocity as a straight line on a two dimensional spacetime graph, then acceleration is a curved line. You will plot these things many times in a good physics class. Now perhaps I have given you the tools to see c^2 as a curved surface. If not ask me again and I will give you more detail.

Then we can see that energy is mass multiplied by a curved surface. How do you multiply mass by a curved surface? I could divide mass by a curved surface, maybe, by distributing the mass as an infinitesimal dust evenly across the curved surface. That isn't the same as multiplication, it is the inverse. How do I distribute a curved surface evenly across a mass? Well again it may be helpful to look at a simpler case. How do I distribute a line across a mass? I can distribute a mass across a line by dividing the mass up evenly along the line, as by drawing a mass of metal into a thin wire. What is the inverse of this operation? Maybe if I move the mass along the line, adding up all the values of the distribution as I go along. Then unless I use some discrete distance, moving the mass a distance at a time, I quickly get an infinite answer. Infinities are not welcome in physics. Even if I use a carefully chosen discrete distance, the mass adds up to very large amounts quickly. To prevent this, I might consider an average, that is, divide the time and the distance each into some discrete value, and then multiply by that value, or renormalize, after I am done.

Well that has confused me so I suspect it has confused you too. Instead, let me close here, as I have used up this available time, with another way to find the inverse of an operation. Turn it upside down. We have the idea of mass multiplied by a curved surface. The inverse of this idea is to distribute a dust of the matter which has the mass evenly across the surface. Then turn that curved surface upside down, or inside out, really, and consider the implications of mass distrubuted in the shape of a hollow sphere. Where is the center of gravity of that sphere? Or, where is the center of charge, if the sphere is covered in charged particles? It turns out that the math is the same, just the geometry of a sphere, with inverse square law and all. Now consider this: the center of charge, or the center of gravity, is not in a place where there is any matter. The mass can be seperate from its charge, or from its gravity. Now if charge or gravity is energy, what do we mean when we say that mass and energy are the same thing? If they are truely one thing, how can there be physical, spatial seperation?

We are forced by these considerations to go past our ideas of matter and energy, and to begin to question our notions of space and time directly. Are space and time geometrical, as mass and energy are geometrical? Some people think so.

Thanks,

Richard

ZapperZ said:
From my perspective, there appears to be the hint of a misuse of the so-called "wave particle duality" here. I strongly suggest that, if you DO hold this view, you first read the FAQ in the General Physics forum. You cannot jump straight into "Beyond the Standard Model" without understanding the fundamental of what has already been established. There is nothing "different" in QM with regards to those two seemingly-different behavior. So it isn't a "transition".
Zz.
thanks Zapper,
i surmise that "beyond the standard model" is for the most advanced in the field- of which i am only a beginner, but my question doesn't seem to fit as well into any other genre, because it does indeed poke at the standard model.
Have you considered that the "regard" towards these seemingly inseparable qualities is more because of fear of prolonged ignorance than because of a real understanding of how 2 distinct properties are connected?

i'm attempting to educate myself, and i do appreciate your aid in the process. cheers,

ZapperZ
Staff Emeritus
2018 Award
thanks Zapper,
i surmise that "beyond the standard model" is for the most advanced in the field- of which i am only a beginner, but my question doesn't seem to fit as well into any other genre, because it does indeed poke at the standard model.
But if you are only a "beginner", do you think it is logical to be putting out such advanced ideas when you haven't fully understood the basic, fundamental knowledge?

Have you considered that the "regard" towards these seemingly inseparable qualities is more because of fear of prolonged ignorance than because of a real understanding of how 2 distinct properties are connected?
Obvously, you haven't read the FAQ. What if there are NO "2 distinct properties"? Doesn't that make your whole point moot?

I would also caution you to re-read the PF Guidelines, especially on overly speculative posts.

Zz.

Wave-particle DUALITY is the prototype of all the other dualities that have turned up in physics. In all cases it's not "either/or"; nor is it simple "both". It's "BOTH when seen from a richer perspective". And in each case the richer perspective is precisely the heart of the theory in which the duality occurs. The duality is the signal that the richer perspective applies. In QM that perspective is the complex Hilbert space of states and the operators that act on them.
wow this really does help clear up my confusion. You are saying that a wave has never been observed independent of particals, and particals have never been observed independent of waves?
Hrm, what about at nearly zero Kelvin, when nearly all of the brownian energy is removed from matter? What about a pure energy pattern- can heat migrate through a vacuum?

Meanwhile, I'll check out Hilbert space of states- thanks for the tip!
cheers,

ZapperZ
Staff Emeritus
2018 Award
Hrm, what about at nearly zero Kelvin, when nearly all of the brownian energy is removed from matter? What about a pure energy pattern- can heat migrate through a vacuum?
While you're checking up on Hilbert space, check out what is "infrared radiation" and how the sun transfers heat to the earth.

Zz.

rtharbaugh1 said:
You are asking some profound questions, but it is unclear what level of detail you require in an answer. I suspect you will find little to help you in LQG, not because the answers to your question are not found there, but because you will not be familiar with the language in which the answers are presented. Well anyway I suspect that is why I cannot find the answers to your questions in LQG. I have been studying the formalism for some time now but still am not qualified to understand the proofs.However I suspect from your phrasing that your curiosity can be satisfied, or at least mollified, without going so deep.
hello Richard,
you are a true friend towards my cause. Thanks for dealing so gently with my ignorance, while at the same time not being dismissive towards my "profundity".
I've been reading a bit of LQG, and you are right to say it is a bit laboriousness to pick through the jargon. I'd much prefer someone like you to "bubba-ize" it for me, if you'd like.
You seem to have some geometry, since you mention x,y,z planes. Have you considered the idea of a Cartesian plane as an intellectual construct, in which sense it has little or nothing to do with particles, charges, and other observable phenomena? Euclidian geometry deals with straight lines and flat planes, but we have no reason to believe that these things exist except in the strictly local sense. Einstein showed us that a straight line viewed from one location can be viewed as curved from another location. In fact modern mathematicians often forgoe the idea of straight lines entirely and speak only of curves and edges. Modern physics finds that the mathematics of curved surfaces is more useful than straight line trigonometry.
I see your point well: the more i learn about relativity and the perspective of calculus math, the wider the gap seems to be between euclidian geometry and the curved planes of space. However, i also suspect that this gap is an illusion- calculus is not a re-invention of math, it operates under the same parameters as Euclidian geometry, but it concentrates on a different perspective- leibnitz's infintesimals etc. The calculus system seems to have “life” and “motion” relative to the stagnant classical math, but even calculus uses a Cartesian system as a foundation, because it is the most practical representation of mathematical axioms.(set theory is also useful but not as visually practical)

Even though we suspect a curved nature in seemingly straight lines, the curvature is relative. If a straight line appears curved in one way from one perspective, then it probably is curved a different way from a different perspective. Assuming this curvature is due to the bending of space itself and not an illusion from the bending of light due to gravity, the average of its infinite irregularity is a straight line.

Question: is distance in curved space longer than if it were predicted with a straight line? If we measure curved space using a straight line, then everything we use to measure the distance is curved as well, canceling out the seeming discrepancy of perspective. Who's to say this doesn't carry over into our Cartesian thought construct? If space is “actually curved”, then whats to say that the cartesian coordinate system isn't “actually curved” as well. The advent of calculus and other math dealing with curves seems to suggest this underlying nature- again because calculus is not a reinvention of math, but rather a useful manipulation using the same maxims.
I should like to encourage you to examine your own phrases carefully to remove any verbal stumbling blocks. When you say things like "I know that...." or "it is obvious..." or even "definitely occupies....", you are inviting contradiction. I sense that you are trying to form a solid basis from which to progress, but it will serve you poorly if your platform turns out in the end to be rotten. Better to examine each piece carefully.
Noted. I'll be more cautious from now on.
I have also heard it said that matter is a form of bound energy, which might better be thought of as 'wavicles.' You must see of course that this answer merely divides the question. What is matter? It is energy, and it is bound, and to remind us of these things, we will now call it "wavicles" instead of matter. Now we must wonder, what is energy, what does it mean to be bound? We paste the label "wavicle" over these new questions, but how are we better off asking "what is a wavicle" than we were when we asked, "What is matter?"
Perhaps energy is more fundamental than matter, and the idea of matter as bound energy really is a deeper insight. We might say "bound" means only that the energy is found within some boundaries, and leave the question of why it stays bound within boundaries for another time.
I have a theory called “charter gravity portal” which attempts to explain it, but its still in its crude egocentric stages of development.
Then we are left with, What is energy? Perhaps energy is indeed more fundamental than matter. Maybe there is only one kind of energy, and in its different forms it makes up all the different kinds of matter.
So we look at some of the kinds of energy with which we have some familiarity. Electromagnetism. Heat light and sound. A year or so of intense guided study at a college or university with physical laboratories and dedicated lecturers will get you there. Of course I presume you have the arithmatic, geometry, algebra, trigonometry, and calculus to follow the math. You can get a feel for physics without the math, but if you want to follow the proofs, math is not optional. You ask good questions, which is a promising talent, but I can only give you a feel for the answers without the mathematics.
I took 2 semesters of trig-based physics as a requirement for a biology degree. A big reason for why i chose biology instead of physics, and also why i loathed my required coursework in chemistry, is the fact that i am not mathochistic. I learned just enough to be dangerous, but not enough to be potent.
Heat and sound appear to be energy patterns in particles, but i suspect light can travel through the vacuum of space. Doesn't this differentiate light from the other 2?
"If unbound energy was actually 3-dimensional like matter, then wouldn't it have gravity? " By Occam let's just ask if energy has gravity. By the equivalence principle, yes.
heeeeyy now wait up a sec.... where are these convenient principals coming from? I don't think the razor should mutilate my original question here, because the bound state of energy might be the only state which exerts gravity, though we know that light is effected by gravity. Lets rephrase it in a way which will not allow you to be so slippery:
Does light, heat, or sound have gravity?(and can you reference me to the hard evidence?)
"can energy exist in only 2 dimensions? "
Well you may be confusing two different uses of the idea of dimension here. Let's look at E=mc^2, which in words is the familiar Einstein mass-energy equivalence formula, read "Energy is mass multiplied by the squared velocity of light." We can use dimensional analysis to find the dimensions of energy from this formula. Mass is a unit of measure, and we tie it to physical reality by means of an object, a certain carefully maintained standard, which can be replicated by counting out a certain number of atoms of a certain reasonably common substance. Mass then is a measure, a dimension if you will, a gauge, by which we can compare reasonably local substances to each other.Velocity is a unit of distance, space if you will, multiplied by the inverse of time. We commonly sense velocity in terms of miles per hour or meters per second or the like. Length divided by time. Now it is a subtle point that space and time are the same thing, which is called the Einstein Space-time equivalence and is related by c, the speed of light, which is taken to be constant in all frames of measurment. In fundamental work, we often just call the speed of light a unit, so it has a numerical value of one, and of course the square of one is one, so we are left with E=m x 1, or just E=m. This is concise but not very savory. We wanted a feel for what mass is, and then we wanted a feel for what energy is, and now we have the feel that they are the same thing. What progress have we made? Let's put c back in to try to recover our geometric sense of dimension. Since c is a velocity, it has units of distance over time, so the square has units of distance squared over time squared. We know the square of distance by feel, and only have to think of the flat surface of a piece of paper to get a sense of squared distance. But what are we to make of the idea of inverse time squared? How can time be squared? How do we get a feel for that? In c^2 we seem to have a surface divided by time and then divided by time again. What is this thing of dividing by time and then dividing by time again? Well, in a slightly reduced case, we have the example of distance divided by time and then divided by time again. That is acceleration and you can feel it everytime you ride in an automobile, or any time you initiate or cease movement at all actually. We often speak of the curve of acceleration, and to really get a good feel for this you need that college physics lab, or a good high school equivalent, and a certain amount of math. It turns out that if you think of velocity as a straight line on a two dimensional spacetime graph, then acceleration is a curved line. You will plot these things many times in a good physics class. Now perhaps I have given you the tools to see c^2 as a curved surface. If not ask me again and I will give you more detail.
Wow, you have actually answered my question quite well so far. I have indeed plotted acceleration as a curve- i remember one experiment in particular involving a friction minimalizing device like an air hockey table. I wonder if plotting acceleration as a straight line would cause velocity to look like a curve... probably not.

I get frustrated with physics sometimes because the reasoning is so circular. Every term is defined in reference to another term! However, your digestion of E=MC2 is very telling. So far, i've gathered that Energy is described in terms of various “dimensions”, namely mass and something analogous to acceleration. Distance is a single dimension, and when divided by time by time, we have acceleration. However, Einsteins's formula uses a 2 dimensional cartesian plane divided by time divided by time, which is a more evolved phenomena than acceleration, since it involves an extra dimension. On to mass:
Then we can see that energy is mass multiplied by a curved surface. How do you multiply mass by a curved surface? I could divide mass by a curved surface, maybe, by distributing the mass as an infinitesimal dust evenly across the curved surface. That isn't the same as multiplication, it is the inverse. How do I distribute a curved surface evenly across a mass? Well again it may be helpful to look at a simpler case. How do I distribute a line across a mass? I can distribute a mass across a line by dividing the mass up evenly along the line, as by drawing a mass of metal into a thin wire. What is the inverse of this operation? Maybe if I move the mass along the line, adding up all the values of the distribution as I go along. Then unless I use some discrete distance, moving the mass a distance at a time, I quickly get an infinite answer. Infinities are not welcome in physics. Even if I use a carefully chosen discrete distance, the mass adds up to very large amounts quickly. To prevent this, I might consider an average, that is, divide the time and the distance each into some discrete value, and then multiply by that value, or renormalize, after I am done.
Well that has confused me so I suspect it has confused you too. Instead, let me close here, as I have used up this available time, with another way to find the inverse of an operation. Turn it upside down. We have the idea of mass multiplied by a curved surface. The inverse of this idea is to distribute a dust of the matter which has the mass evenly across the surface. Then turn that curved surface upside down, or inside out, really, and consider the implications of mass distrubuted in the shape of a hollow sphere. Where is the center of gravity of that sphere? Or, where is the center of charge, if the sphere is covered in charged particles? It turns out that the math is the same, just the geometry of a sphere, with inverse square law and all. Now consider this: the center of charge, or the center of gravity, is not in a place where there is any matter. The mass can be seperate from its charge, or from its gravity. Now if charge or gravity is energy, what do we mean when we say that mass and energy are the same thing? If they are truely one thing, how can there be physical, spatial seperation?
We are forced by these considerations to go past our ideas of matter and energy, and to begin to question our notions of space and time directly. Are space and time geometrical, as mass and energy are geometrical? Some people think so.
Thanks, Richard
Hrm this part is a bit more difficult to follow but it think i get the gist of what you're saying.

It's interesting to me that in both math and physics, one of the biggest challenges is try to get around extremes like infinity and absolute nothing. It appears that the only practical application we get out of these sciences comes from looking at infinity in a finite way.

If you are correct in saying that mass can be separated from its gravity and charge, then this is interesting indeed. I wouldn't think of gravity as energy really, but rather the curvature of space/time associated with matter. Maybe this constitutes potential energy- but mass itself is potential energy! However, if unbound energy such as EM is indeed a more primitive than matter, it is curious why gravity would only be associated with an advanced stage, assuming EM doesn't have gravity.

So far, questioning notions has helped me develop my own theories, and you have been a valuable agent towards that end. I hope you will not find replying to my response too laborious, but i would appreciate further clarification in the areas mentioned.

cheers,