Is Energy Defined by Shape or Matter in General Relativity?

[LightningInAJar]

TL;DR

Energy vs matter shape.

Physical objects have well defined shapes, but does energy ever create well defined shapes or can it only take shape within matter?

 

[Baluncore]

Energy always takes the shape of a $ symbol.

 

[phinds]

Does energy have shape?​

Here's an exactly equivalent question: Does color have shape?

 

[DaveE]

No.

Although you might want to read about entropy. It's not the answer to your question, but it's sort of related, in a crude way.

 

[jbriggs444]

Energy is not some kind of magical fluid that exists in its own right. It is an attribute that [collections of] objects have. Like "position", "weight" or "color". Feynman has an entertaining description for you here.

That said, you could get a block of tungsten and a blow torch and sign your name in glowing letters. The resulting pattern of thermal energy would have a discernable shape for a while.

 

[gmax137]

That said, you could get a block of tungsten and a blow torch and sign your name in glowing letters.

The voice of experience?

 

[LightningInAJar]

Matter certainly has shape though? At least in solid state?

 

[phinds]

Matter certainly has shape though? At least in solid state?

What do you think?

 

[LightningInAJar]

What do you think?

Just want to make sure the word shape is used the same way. So energy doesn't exist without matter and doesn't really take a shape beyond that of a material thing it acts upon?

 

[jbriggs444]

Just want to make sure the word shape is used the same way. So energy doesn't exist without matter and doesn't really take a shape beyond that of a material thing it acts upon?

Energy can exist as a property of fields. It does not require matter.

Some of the fields that we consider for this are pretty weird with the result that the associated energy is not always localizable.

 

[phinds]

Just want to make sure the word shape is used the same way. So energy doesn't exist without matter and doesn't really take a shape beyond that of a material thing it acts upon?

A beach ball has a shape. A beach ball has a color. A color does NOT have a shape.

 

[berkeman]

Summary:: Energy vs matter shape.

does energy ever create well defined shapes

https://www.sciencenewsforstudents.org/wp-content/uploads/2021/06/1030_LL_lightning_feat.jpg

 

[Shane Kennedy]

Summary:: Energy vs matter shape.

Physical objects have well defined shapes, but does energy ever create well defined shapes or can it only take shape within matter?

Is there any such thing as pure energy, or could Matter BE energy of a particular form ?

 

[Ibix]

Is there any such thing as pure energy,

No. You can have matter (with some amount of energy) or radiation (with some amount of energy) and you can convert between the two. Converting matter to radiation and/or other matter can change between mass and energy, but mass and matter are not synonyms.

"Converting something to pure energy" is a science fiction trope.

 

[berkeman]

Thread closed temporarily for cleanup of some off-topic posts and replies.

 

[berkeman]

An off-topic thread hijack and the responses have been deleted. Thread is back open. Let's try to stay with mainstream science in the thread, even though the thread start was a bit on the borderline...

 

[Melbourne Guy]

Summary:: Energy vs matter shape.

Physical objects have well defined shapes, but does energy ever create well defined shapes or can it only take shape within matter?

The EIA has a straightforward explanation, @LightningInAJar, that may help inform your thinking on the nature of energy:

https://www.eia.gov/energyexplained/what-is-energy/

 

[collinsmark]

One can determine the "shape" of energy, in any given localized region of space, by measuring the gravitational potential within that localized region of space. It's complicated though for a number of reasons, one of which being that energy is relative: it's dependent upon one's choice of reference frame. But ultimately, for a given frame of reference, measuring the gravitational potential or gravitational acceleration can be used as a way to obtain localized energy density.

As an example of another reason why this can be complicated, let's start with something simple, like electrostatic energy. The electrostatic energy W of a given volume can be calculated using

W=\frac{1}{2} \int \rho V d \tau
where,
W is the energy,
ρ is the charge density at any particular location,
V is the electrostatic potential (not to be confused with volume) at any given location,
and dτ is the differential volume (e.g., dτ could be dxdydz for Cartesian coordinates).

This might lead one to believe that the energy is contained exclusively within the charge, since the integrand is zero everywhere where there is no charge (since ρ is only nonzero when the charge density is nonzero).

But wait! there's another way!

W=\frac{\varepsilon_0}{2} \int_{all \ space} E^2 d \tau
where,
W is the energy,
ε0 is the electrical constant (a.k.a., permittivity of free space),
E is the magnitude of the electric field (not to be confused with energy),
and dτ is the differential volume.

Note that this integral must be done for all space, even in places where the charge density is zero!

So which is it? Is the energy in the charge or is it in the field? Well, both approaches will give you the correct answer for the energy. But only the latter (the energy is contained within the field) is compatible with general relativity.

So as a way to measure the "shape" of electrostatic energy, we can say
\frac{\varepsilon_0}{2} E^2 = \mathrm{electrostatic \ energy \ per \ unit \ volume}
which gives you a "shape" of sorts. (Again, E here is the magnitude of the electric field, not to be confused with energy.)

Okay, but what about other sorts of energy like matter? It's complicated for some of the same reasons. You could integrate over the mass density to get the total mass, then plug that into W=mc^2, which would give you the correct answer. Or you could integrate the square of the magnitude of the gravitational acceleration over all space, and get the answer that way.

The method of integrating the gravitational field over all space is more general however, since it's independent of what type of energy is involved. It works for electrical energy, kinetic energy (details may depend on choice of reference frame), matter energy, thermal energy, all forms of energy. So in that respect, gravitational potential, and the magnitude of gravitational acceleration is a measure of energy density: it has a "shape," so to speak, and it can be measured and quantified.

[Edit: All I'm trying to say here is that gravitational fields are linked to variations in energy density. You can measure the gravitational field, and that tells you something about the energy density.]

 

[meekerdb]

No. But in a sense energy-density has a shape in general relativity. The stress-energy density at a point is a 2nd rank tensor, which can be thought of as an ellipsoid in stress-energy space.