# Why can some forms of energy be relative?

1. Aug 22, 2011

### skeleton

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SUBJECT
There are various forms of energy; some are potential while others are kinetic. An object or particle can have its energy change when work is performed upon it. Likewise, it may loss some of its energy when it does work on another object.

EXAMPLE
Through the course of work, the object many even change its energy composition from one arrangement to another.

1) For example, a stationary object atop a table may have high potential energy and no kinetic energy; later the object may fall to the floor and its two forms of energy will reverse.

2) A chemical explosive would have high chemical energy. After detonation, its chemical energy is lower but the thermal energy of its transformed molecules would be high, and the kinetic motion energy of object put in motion would also increase.

3) An atomic nucleus could have high nuclear energy until nuclear decay arises. Thereafter, the ejected neutrons would have high motion energy (which later transforms the entire system to increase its thermal energy).

QUANDARY
It seems that some energy types are absolute while others are relative. It is well known that the kinetic energy of motion is relative to the reference frame. Meanwhile chemical energy of a molecule's orbital electron is quantized and invariant. Meanwhile, an object is able to change its energy composition from one arrangement to another. This seems to violate the "Conservation of Energy" seems absolute energy types are inherently invariant while relative energy types are variable relative to arbitrary reference frames.

QUESTION
- Are my assumptions and understanding correct above and below?
- How can the Law of "Conservation of Energy" allow some energy forms to be relative while others are absolute?

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ENERGY

Potential energy
- Gravitational energy (ie: U = -G*m1*m2/r)
- Chemical energy (ie: molecular orbital bonds)
- Nuclear energy (ie: atomic nuclear bonds)
- Dark energy {I will not include this hereafter.

Kinetic energy
- Motion energy (ie: KE = 1/2*m*v^2) .. for one particle system.
- Thermal energy (ie: E = f*1/2*k*T) .. for many particle system.
- Radiant energy (ie: EMF = h*v)
- Electrical energy (ie: E = F/q)

The following are not additional unique forms of energy; instead they are specific examples of the above general forms. Mechanical energy (this is merely colloquial naming of potential and kinetic energy):
- Mechanical energy_PG (ie: Ug = m*g*h) { Gravitational
- Mechanical energy_PS (ie: Us = 1/2*k*x^2) { Chemical
- Mechanical energy_KE (ie: Us = 1/2*m*v^2) { Motion

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ FORCES

Gravitational
- Gravitational energy (ie: U = -G*m1*m2/r)

Electro-magnetic
- Chemical energy (ie: molecular orbital bonds)
- Radiant energy (ie: EMF = h*v)
- Electrical energy (ie: E = F/q)

Nuclear weak & Nuclear strong
- Nuclear energy (ie: atomic nuclear bonds)

Momentum
- Motion energy (ie: KE = 1/2*m*v^2) .. for one particle system.
- Thermal energy (ie: E = f*1/2*k*T) .. for many particle system.

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ABSOLUTE ENERGIES

All three Potential energies seem to be absolute parameters of a system. This is because their energies are a manifestation of the interaction of properties of matter. Gravitational energy results from the force field of the mass of a particle. Chemical energy is from the electrical force field of the electron, when the electron is confined to an orbital. Nuclear energy is from the force field of the nucleons.
- Gravitational energy { Partially relative.
- Chemical energy { Non-relative (absolute).
- Nuclear energy { Non-relative (absolute).

Two of the four kinetic energies seem also to be absolute parameters. This includes the radiant energy, which is a manifestation of the photon's frequency of vibration. Also included is the electrical energy, which is the manifestation of the electrical field of an electron when put into motion amongst a string of conductive atoms (wire).
- Radiant energy { Partially relative.
- Electrical energy { Non-relative (absolute).

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~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ RELATIVE ENERGIES

This leaves the other two kinetic energies, which seem to be non-absolute (relative) parameters. Note: a system in a thermal state is little more than motion energy but where interest is given to the collective group of individual particles, with their kinetic energies averaged for simplification.
- Motion energy { Entirely relative.
- Thermal energy { Entirely relative.

So motion energy and thermal energy are of the same mechanism - a quantization of momentum (p). Note: 1/2*m*v^2 = 1/2*p^2/m. While momentum is relative to the reference datum via the velocity term, its mass is absolute. It is the velocity term (v) that causes motion energy to be relative.

Relative velocity
v = v(object) - v(reference observer)

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Note, special relativity states that mass of a particle is relative to the frame of reference.

Special Theory of Relativity
E = gamma*m*c^2
gamma = 1/[1-(v/c)^2]^0.5
m = invariant (rest) mass
v = relative velocity
gamma*m = relativistic mass for given frame of reference

The above reveals that Gravitational energy is not absolute, rather it is relative. So, even mass (m) is relative.

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z = f.emit/f.obsv - 1 { Photon has frequency of vibration.
z = [(1+v/c)/(1-v/c]^0.5 - 1 { Motion is in radial direction.
z = [1/(1-v^2/c^2)^0.5] - 1 { Motion is in transverse direction.

Radiant energy (E=h*f) is dependent upon a photon's frequency. However, that frequency is relative to the motion of the observer. As such, the observer's measurement of the photon's inferred energy is relative. So, even EMF radiation is relative.

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2. Aug 22, 2011

### xts

I haven't checked all calculations "below", but generally those "above" are correct.

Conservation principle works in any reference frame you chose. Some forms of energy may, however, differ between frames. That is not only the case of kinetic energy (changing with velocity, which may be different in moving frames), but also gravitational potential energy (where is our floor?), electrostatic energy (where is a reference level? on left or right electrode?), etc. But for every fixed frame, the Energy Conservation Principle works. Even your example nuclear energy may be considered in at least two useful frames: one is based on zero = separate nucleons, other on zero = stable nucleus.

3. Aug 23, 2011

### A.T.

Conservation of Energy doesn't mean that total energy is the same in every frame. It means that in every inertial frame total energy is conserved over time, for closed systems.

4. Aug 23, 2011

### vanhees71

Energy is the time component of a four vector and thus changes under Lorentz boosts accordingly. Why should energy be a scalar? It's not a scalar in Galilean physics either!

5. Aug 23, 2011

### Hootenanny

Staff Emeritus
Unless I'm very much mistaken, energy is a scalar. As you say, it is a component of the four-momentum.

6. Aug 23, 2011

### Staff: Mentor

In general relativity a component is not a scalar. Scalars and components and tensors are defined by the way that they transform under arbitrary coordinate transformations. A scalar doesn't change, but components of a tensor do change so they are different.

In earlier physics the term "scalar" is rather loosely used to describe any quantity that is not associated with a direction, i.e. a number. In that loose sense energy is a scalar, but vanhees71 was using the more rigorous distinction related to how it transforms.

It is always irritating when the same term can have such different meanings.

7. Aug 23, 2011

### Hootenanny

Staff Emeritus
Apologies, I have never come across this terminology before. Perhaps it was for this very reason that my Gen. Rel. course referred only to invariants (rather than scalars). Then again, my Prof. used to use scalars to refer to the components of the stress-energy tensor.

Oh well, I shall butt out of the conversation now!

8. Aug 23, 2011

### ZealScience

Because energy is a conservative quantity but not an invariant. Many quantities are not invariant but conservative, such as momentum. There is no necessary link between conservation and invariance.

9. Aug 23, 2011

### Staff: Mentor

It sounds like your GR prof was using non-standard terminology, but I like his terminology and think that it is better than the standard terminology.