Relationship between location and energy?

[md65536]

Here are some aspects of relationships between location and energy:

 

1. To change an object's location requires energy. If an object has velocity relative to something else (such that relative location changes), it has potential energy. To change velocity requires a transfer of energy.

 

2. In a Bose-Einstein condensate, which has very little thermal energy, the location of particles becomes undefined. Particles act as if they are simultaneously everywhere in the matter.

 

3. If an object falls into a black hole, light from it is redshifted indefinitely. Is it reasonable to say that one wavelength of the light is simultaneously traveling to our eyes at c, and stuck at the event horizon, so the infinite redshifting is equivalent to stretching that one wavelength of light across an ever-expanding distance? As the light energy is lost to the black hole, its location becomes undefined... instead of being in a specific point, it gets stretched indefinitely.

 

4. According to the conjectured holographic principle, a location in our 3d universe maps to all locations on a 2d topological manifold and vice versa. In some vague sense, any quantum of energy can exist everywhere, but some property gives it locational definition in our 3d universe.

 

 

Can these ideas be combined into one relationship between location and energy?

The energy of something would be related to the degree to which that something is "focused" or well-defined locationally. Greater energy means sharper focus into a specific location. If you want to determine the precise location of something either you would need to use a lot of energy to do so, or that something would need to have a lot of energy. The more precision you need, the more energy is needed.

 

Mass, which is a form of energy, would be related to the specificness of location. More energy means more specific location. Inertia could be expressed in terms of specific location (including moving locations); the difficulty in overcoming inertia is related to the difficulty of modifying locational specification. This would probably imply that the location of a moving object is better defined (ie can more precisely be determined) than a similar stationary object??? -- is there any accepted theory that speaks to this?

 

 

 

One last conjecture in case there's nothing zany enough in the above: If location is emergent (which I believe it is, along with all of geometry), would this imply that energy is also emergent? I'd previously thought that energy was invariant and a fundamental aspect of the universe... I still think it must be, but I'm not sure.

 

(Energy is conserved -- except for vacuum energy??? -- which means it is invariant, but it can be converted to different forms which are different for different observers, so the form that energy takes is not invariant. In conclusion I don't quite know what this means.)

 

Or does this conjecture make sense?: The form of a quantity of energy is equivalent to its location. (I don't think I said that right... anyone have ideas?)

Edited May 16, 2011 by md65536

[ajb]

Energy is a frame dependant quantity, which is worse than just depending on the location (points on space-time). Importantly, energy cannot be locally described by a tensor.

[lemur]

How is 'location' in any sense absolute, or maybe I should say less than relative? To me, objects always move relative to the objects they exchange energy with.

[md65536]

Energy is a frame dependant quantity, which is worse than just depending on the location (points on space-time). Importantly, energy cannot be locally described by a tensor.

Meaning that energy takes different forms in different frames?

Is the total energy of a system (including for example the entire universe) invariant, and just changes form depending on frame of reference?

 

 

Perhaps I'm using the wrong word "location", if it means a precise point in space. Instead I want to describe position with a variable degree of uncertainty or precision. So size too, I guess... a quantum of energy has a range of uncertain possible locations.

 

How is 'location' in any sense absolute, or maybe I should say less than relative? To me, objects always move relative to the objects they exchange energy with.

I agree it's completely relative. So it's not location that's important, such as specified by some spatial coordinates relative to any origin. The values of those coordinates (or its distance from origin) don't affect something's energy or mass.

 

It would be precision of location that would be related to energy.

 

The conjecture might be restated: The energy of something is proportional* to the precision of its location.

 

(Now the specific location or whether it's relative to something else, doesn't matter.)

 

 

* I want to say "equivalent" but I don't know how to account for different forms of energy, or "somethings" that are made up of multiple quantities of energy and can thus have greater overall energy but may not have a proportional degree of locational uncertainty.

Edited May 16, 2011 by md65536

[lemur]

I agree it's completely relative. So it's not location that's important, such as specified by some spatial coordinates relative to any origin. The values of those coordinates (or its distance from origin) don't affect something's energy or mass.

 

It would be precision of location that would be related to energy.

 

The conjecture might be restated: The energy of something is proportional* to the precision of its location.

 

(Now the specific location or whether it's relative to something else, doesn't matter.)

 

 

* I want to say "equivalent" but I don't know how to account for different forms of energy, or "somethings" that are made up of multiple quantities of energy and can thus have greater overall energy but may not have a proportional degree of locational uncertainty.

This is the way I begin thinking about location and energy without imagining a fixed coordinate system that defines things relative to something external to them: imagine you have two points that can't rotate. These two points can move in any way relative to each other but the one can only interpret its location relative to the other in terms of distance increasing or decreasing. It can experience changes in force and momentum as it changes directions of motion relative to other imaginary points, but its location can only be measured in relation to the only other existing point in its universe, which it only becomes more or less distant from. Does that make any sense?

 

edit: a more concrete example might be if you were orbiting the sun along in a spacesuit, and you would have no idea what your position was relative to anything except the sun, then you would not know if your location was changing within your orbital path except in theory. You would only observe yourself to be stationary relative to the sun. If you accelerated or changed direction, you could experience force but without any other points of reference, you would have no basis for perceiving that your location changed except insofar as your distance to the sun changed.

Edited May 16, 2011 by lemur

[swansont]

1. To change an object's location requires energy. If an object has velocity relative to something else (such that relative location changes), it has potential energy. To change velocity requires a transfer of energy.

 

No, these are not consistent with the definitions of the terms in standard physics. Potential energy depends on position, not velocity, and a force perpendicular to the motion will change velocity but does no work, so there is no transfer of energy.

[md65536]

No, these are not consistent with the definitions of the terms in standard physics. Potential energy depends on position, not velocity, and a force perpendicular to the motion will change velocity but does no work, so there is no transfer of energy.

Potential energy depending on location fits the conjecture better than velocity does.

Is it a general case? Does any change in relative position involve some change in potential energy?

 

I can't actually imagine how kinetic and/or potential energy relates to the idea. I shouldn't have mentioned it.

 

 

[granpa]

I am not sure what the op is saying but if you look at the Bohr model

then when you add energy to an orbiting electron it goes to a higher level and slows down

Its potential energy increases but its kinetic energy decreases.

as a result the particles wavelength is bigger and the particle is 'spread out' over a larger area.

i.e. less localized.

Edited May 17, 2011 by granpa

[md65536]

This is the way I begin thinking about location and energy without imagining a fixed coordinate system that defines things relative to something external to them: imagine you have two points that can't rotate. These two points can move in any way relative to each other but the one can only interpret its location relative to the other in terms of distance increasing or decreasing. It can experience changes in force and momentum as it changes directions of motion relative to other imaginary points, but its location can only be measured in relation to the only other existing point in its universe, which it only becomes more or less distant from. Does that make any sense?

You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively.

The other spatial dimensions (representing orientation) are irrelevant -- do you mean in general, or as it pertains to this thread?

 

I don't think I agree. I don't think the most elementary particles are one-dimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities.

 

 

As it pertains to the conjecture, I'd say that the size and the shape of a particle's "spatial range" is what matters (the range perhaps defined by a probability wave that specifies the possible locations of the particle and the probability of it being in any particular location. A "larger wave" would mean less locational precision, which I'm suggesting corresponds to lower energy). Unless the possible range is isotropic (ie. it's shape would need to have spherical symmetry?), then the orientation would be important.

 

I am not sure what the op is saying but if you look at the Bohr model

then when you add energy to an orbiting electron it goes to a higher level and slows down

Its potential energy increases but its kinetic energy decreases.

as a result the particles wavelength is bigger and the particle is 'spread out' over a larger area.

i.e. less localized.

Yes... this seems to be in direct contradiction to my conjecture.

It would seem that the location of the particle (the electron?) is less precisely defined in a higher energy state.

Unless there's some other property that shrinks and allows greater precision, the conjecture does not account for electrons and must be wrong.

Electrons ruin all my ideas! Are you sure we have to consider their existence at all???

 

[lemur]

You're describing relative location in terms of only distance, implying that one dimension is enough to define the relative location between 2 points exclusively.

It was just an example of how the concept of location is relative to the points in question. The point is that no fixed coordinate systems exist; only actual points moving relative to each other.

 

The other spatial dimensions (representing orientation) are irrelevant -- do you mean in general, or as it pertains to this thread?

what are 'spatial dimension' relative to? It is like the concept of aether.

 

I don't think I agree. I don't think the most elementary particles are one-dimensional, and the relative orientation of 2 particles might be important especially when it comes to light, or velocities.

It sounds like you're trying to imply some form of absolute perception. My point is that particles are only ultimately relative to each other insofar as they interact directly. Beyond direct interactions, you're only dealing with abstract spatial relations, which can't be more than a composite of overlaid orientations derived from various observations.

Edited May 17, 2011 by lemur

[md65536]

It sounds like you're trying to imply some form of absolute perception. My point is that particles are only ultimately relative to each other insofar as they interact directly. Beyond direct interactions, you're only dealing with abstract spatial relations, which can't be more than a composite of overlaid orientations derived from various observations.

No, I agree everything's relative. I just think the additional dimensions are important. Since you reduced location to distance, I assumed you were talking about spherical coordinates while considering only the distance dimension.

 

 

Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters.

 

But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 non-coplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work.

 

 

Certainly, the distinction between whether locations are considered relative or absolute is relevant to the thread, and I hadn't considered it in the original post. But I think that any theory that attempts to describe reality would have to consider locations to be relative.

Edited May 17, 2011 by md65536

[lemur]

Your example of orbiting the sun is not the best example, because the sun is essentially the same in any orientation. But if instead you were orbiting Earth, and say you wanted to land, then yes your relative distance is important, but if it mattered where on Earth you landed, and whether you landed on your head or on your butt, then relative orientation also matters.

 

But this is all beside the point because as soon as you add a third point that's not collinear, an angle dimension becomes relevant, and if you add a fourth point that's not coplanar to the other 3, a 3rd dimension becomes relevant. With 4 non-coplanar points, I don't think your example of choosing an arbitrary axis and origin where you can ignore a dimension, will work.

The only reason I disagree with your approach is because I think you are looking for reasons to justify dimensions and location on the basis of the physical nature of the systems. What I am doing is looking for examples that make it possible to think about how location is relative. Obviously once you start thinking in terms of a planet like Earth with distinguishable surface-points, it becomes possible to plot any location at any altitude on a line extended from some axis of the planet. This works especially well using a planet like Earth that is viewed as dominantly solid/fixed, but what if you wanted to define locations relative to systems that aren't solid/fixed? You would have to either identify stable aspects of the system and define location relative to those, but what if those weren't available or they were moving?