View Full Version : Volume of energy in space to volume of mass

Bogie

2006-Sep-27, 02:24 AM

If all space (S) contains energy; the energy density of space (“SED”) is determined by its energy (E) divided by its volume (Ve). “SED” = E/Ve

If mass is composed of energy, mass (M) ; the energy density of matter (“MED”) is determined by its mass divided by its volume (Vm). “MED” = M/Vm.

Energy (E) is related to mass (M) in proportion to the speed of light squared (C^2). E = MC^2.

Is it correct to say Ve = Vm*C^2?

Is it correct to say C^2 = 34,596,000,000 f/second^2?

is it correct to say Ve = Vm*34,596,000,000 f/second^2?

01101001

2006-Sep-27, 02:39 AM

Is it correct to say Ve = Vm*C^2

I don't see where that comes from. And does it make sense? The volume-of-some-energy is equal to the product of the volume-of-some-matter and light-velocity-squared? The units don't work.

Is it correct to say C^2 = 34,596,000,000 f/second^2

What's "f"? Feet? Square-feet? Has to be some square-distance measure or the units don't work here either. I don't recognize your constant 34,596,000,000.

I'm lost.

Edit: 186000^2 = 34596000000 ? So you're after speed of light in miles^2/s^2? 186000 miles/sec is not a great estimate (better 186282.397 mi / second), but OK. So "f" is square miles?

GOURDHEAD

2006-Sep-27, 02:41 AM

is it correct to say Ve = Vm*34,596,000,000 f/second^2? Not in the context inferred. E =mc^2 is a conversion formula related to specific mass. A specified volume can, and often does, contain both mass and electromagnetic energy.

Bogie

2006-Sep-27, 12:25 PM

I don't see where that comes from. And does it make sense? The volume-of-some-energy is equal to the product of the volume-of-some-matter and light-velocity-squared? The units don't work.Is there any logic in the thought that if the energy in space can be equivalent to the energy in matter, then the volume of space that holds that equivalent energy would be huge relative to the volume of the matter? My question pertains to the volume relationship between energy in space and energy in matter.

If I assume the average energy density of space and the average energy density of an atom of hydrogen, then would the relationship be that the volume of space would be (186282.397 mi / second)^2 times the volume of hydrogen? How can the units of measure be worked out?

Then if that relationship can be made between the energy density of space and the energy density of a given mass, then if the mass could be converted to energy at the average energy density of space it would occupy such and such a volume of space at average energy density.

From another thread we used the average energy density of space and the mass of a very tiny particle:

The mass equivalent of "7x10^-17 eV" is ~1.2 x 10-52 kg, or ~1.2 x 10-49 g. At "10^-29g/cm^3", you would need ~1 x 10-26 cc of space for this mass.

While trivially tiny for astronomers, such a volume is waaaaaaay beyond what our particle physics colleagues deal with, in terms of 'tiny particles'.This gave us a conversion from the energy in space at average energy density to the energy in a tiny mass.

Now I am wondering if there is a way to express a general volume relationship between energy in space and energy in mass?

Nereid

2006-Sep-27, 01:13 PM

If all space (S) contains energy; the energy density of space (“SED”) is determined by its energy (E) divided by its volume (Ve). “SED” = E/Ve

If mass is composed of energy, mass (M) ; the energy density of matter (“MED”) is determined by its mass divided by its volume (Vm). “MED” = M/Vm.

Energy (E) is related to mass (M) in proportion to the speed of light squared (C^2). E = MC^2.

Is it correct to say Ve = Vm*C^2?

Is it correct to say C^2 = 34,596,000,000 f/second^2?

is it correct to say Ve = Vm*34,596,000,000 f/second^2?As has already been pointed out, it seems that several different things are being muddled together here, to create confusion.

Perhaps you might consider something more concrete? Any given volume of space, anywhere in the universe, will contain some atoms/nuclei/electrons/neutrinos/photons/... - you could imagine doing a census of all those, and calculating the 'mass-energy' contained in that volume, by converting the masses of the particles to energy (using E = mc2); and dividing by the volume gives you a number for the 'energy density of (my sample volume of) space'.

However, you may be interested in the behaviour of the denizens of your sample volume, wrt gravity. If so, then you need to dust off your textbook on General Relativity. And when you do that, you will find that the above is OK .... provided that the volumes aren't too big, or the mass-energy isn't too big, or ... In a universe where GR is a very good description of the behaviour of mass-energy and space (as our universe appears to be), you have to be quite careful to be very clear what you're trying to do, and use terms which make sense (= "are consistent") within the context of your goal.

01101001

2006-Sep-27, 01:25 PM

Is there any logic in the thought that if the energy in space can be equivalent to the energy in matter, then the volume of space that holds that equivalent energy would be huge relative to the volume of the matter?

I'm not sure why it would be huge. You're happening to be using a large number for a constant of proportionality because you're measuring c arbitrarily in miles/second. (Aside, for curiosity, what was that "f" unit you had in there?) If you measure c in equally arbitrary units of lightyears/year, the constant would be 1 lightyear/year and the constant squared, 1 (lightyear/year)^2. Huge?

As for the logic...

A given quantity of space would correspond to a certain quantity of energy. OK. A given quantity of matter would correspond to a certain quantity of energy. OK. And, one could derive that a given quantity of space would correspond, via energy, to a certain quantity of matter. I can handle that.

But, one measures quantity of space in cubic-distance units, and one measures quantity of mass in mass units. And, so, I am utterly lost.

How do you make the leap to presuming a relationship between a given volume of space and certain volume of matter? Matter isn't measured by volume. What does "volume of matter" mean to you?

What is the volume, in cubic meters, of a kilogram of matter?

Nereid

2006-Sep-27, 01:32 PM

Is there any logic in the thought that if the energy in space can be equivalent to the energy in matter, then the volume of space that holds that equivalent energy would be huge relative to the volume of the matter? My question pertains to the volume relationship between energy in space and energy in matter.

If I assume the average energy density of space and the average energy density of an atom of hydrogen, then would the relationship be that the volume of space would be (186282.397 mi / second)^2 times the volume of hydrogen? How can the units of measure be worked out?

Then if that relationship can be made between the energy density of space and the energy density of a given mass, then if the mass could be converted to energy at the average energy density of space it would occupy such and such a volume of space at average energy density.

From another thread we used the average energy density of space and the mass of a very tiny particle:This gave us a conversion from the energy in space at average energy density to the energy in a tiny mass.

Now I am wondering if there is a way to express a general volume relationship between energy in space and energy in mass?To answer the last question (I bolded it), no.

The killer is the word "general" - as the universe seems to have great respect for General Relativity*, your general question is tied up with energy (and its conservation) in GR. As this Weiss and Baez webpage (http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html) makes clear, this is a tricky topic ... leading to my general answer to your general quesion (no, there is no simple, easy way to relate volume, energy, and mass, as you have asked, in general).

Of course, the answer to a slightly different, general question is "sure, it's the GR field equations!"

*this is, of course, a somewhat silly way to write the following: GR has been tested, directly and indirectly, in many different regimes, and has (so far) passed all tests. Or, if you prefer: GR seems to accurately describe the behaviour of the universe, and its consistuents, everywhere we've been able to observe, so far.

Bogie

2006-Sep-27, 02:00 PM

Would it help if I refer to mass instead of matter? A given mass can be thought of as its equivalent energy regardless of the volume of the mass (density*volume = mass).

Space is said to have energy density, and in fact the average energy density of space is lambda. Space, at average energy density, has volume.

What is the volume of space equivalent to a given mass i.e. is there a relationship?

Do we have to recreate Einstein’s field equations to simply state the relationship?

Nereid

2006-Sep-27, 02:08 PM

Would it help if I refer to mass instead of matter? A given mass can be thought of as its equivalent energy regardless of the volume of the mass (density*volume = mass).No.

Space is said to have energy density, and in fact the average energy density of space is lambda. Space, at average energy density, has volume.This is straight out of the pages of a cosmology textbook ... and so comes from GR.

What is the volume of space equivalent to a given mass i.e. is there a relationship?In general, no.

Do we have to recreate Einstein’s field equations to simply state the relationship?From the way you've worded this post, yes - AFAIK, lambda is meaningful only wrt a GR-based cosmological model ... and lambda is at the heart of what you seem to be asking about here.

Bogie

2006-Sep-27, 02:19 PM

This is straight out of the pages of a cosmology textbook ... and so comes from GR.Yes, right from GR.

In From the way you've worded this post, yes - AFAIK, lambda is meaningful only wrt a GR-based cosmological model ... and lambda is at the heart of what you seem to be asking about here.Yes. Lambda is the average energy density of space.

Now tell me again, why can't mass be stated in terms of the energy density of space?

Is it because it can't be? Or is it because I'm not allowed to use GR, only certain people are licensed to use it?

Tensor

2006-Sep-27, 03:09 PM

Yes, right from GR.Yes. Lambda is the average energy density of space.

Now tell me again, why can't mass be stated in terms of the energy density of space?

What you are looking for is called the Stress-Energy Tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor).

Is it because it can't be? Or is it because I'm not allowed to use GR,

Heheheheh, go ahead and use it.

only certain people are licensed to use it?

Nahhhhh, but only certain people bother to learn it right (including the math) due to the huge investment of time.

Bogie

2006-Sep-27, 03:32 PM

What you are looking for is called the Stress-Energy Tensor (http://en.wikipedia.org/wiki/Stress-energy_tensor).

Heheheheh, go ahead and use it.Try to use it you mean? :) Thank you.

Nahhhhh, but only certain people bother to learn it right (including the math) due to the huge investment of time.Before I make an investment I like to know if there is a possible profit. If the only profit requires more of an investment than I can afford, ... yikes. Let me test my understanding of the tensor you linked.

The amount of energy in space is determined by several variables. Pressure, momentum, density ... ?

The tensor equation uses a matrix to assign values for the variables at any given point in space? or at any given combination of those variables?

Can't we just say space at average energy density and get a ball park estimate of volume of space that is equivalent to a given mass? A rule of thumb so to speak?

Tensor

2006-Sep-28, 02:37 AM

Try to use it you mean? :) Thank you.

I didn't want to say that, as it might have sounded condensending. You are quite welcome.

Before I make an investment I like to know if there is a possible profit. If the only profit requires more of an investment than I can afford, ... yikes.

If you want to understand, you have to make the investment. The question then becomes, do you want to understand bad enough.

Let me test my understanding of the tensor you linked.

The amount of energy in space is determined by several variables. Pressure, momentum, density ... ?

The tensor equation uses a matrix to assign values for the variables at any given point in space? or at any given combination of those variables?

Close enough for government work and those not investing in learning Differential Geormetry. As long as you realize that there are quite a few terms in that tensor that the link doesn't show you.

Can't we just say space at average energy density and get a ball park estimate of volume of space that is equivalent to a given mass? A rule of thumb so to speak?

One problem is the average varies so much from volume to volume that the answer you get is really no answer at all. The other problem you are free to use the four-vectors to bring all the disparte parts together, but you might as well use Stress-Energy tensor. Believe it or not, the tensor is a shortcut.

Bogie

2006-Sep-28, 03:31 AM

Close enough for government work and those not investing in learning Differential Geormetry. As long as you realize that there are quite a few terms in that tensor that the link doesn't show you. I am a retired accountant, so close enough for government is ingrained in me. I never want to have to invest in tensors unless I know why I'm doing it. Just what can I expect to find out about the energy denstiy of a volume of space relative to mass?

One problem is the average varies so much from volume to volume that the answer you get is really no answer at all. The other problem you are free to use the four-vectors to bring all the disparte parts together, but you might as well use Stress-Energy tensor. Believe it or not, the tensor is a shortcut.I have one example of the relationship I am looking for. The mass equivalent of "7x10^-17 eV" (a tiny mass, maybe a photon) is ~1.2 x 10-52 kg, or ~1.2 x 10-49 g. At "10^-29g/cm^3" (lambda), you would need ~1 x 10-26 cc of space for this mass.

I just want to simplify this to easy terms that I can use when I talk about energy conversions to matter. For example, would I be close if I used the following relationship between the volume of space at average energy density to an equivalent mass: The volume of space of one cubic meter at lambda contains the energy equivaltent to the mass of one proton, or would this work: The volume of space in a sphere that could contain the Milky Way galaxy is equivalent to the mass of the black hole in its center? Just some rules of thumb as a thinking and talking aid.

Any suggestions for an example that makes sense? I assume that the expansion of the universe does not change the relationship between the energy density of space and the equivalent mass (matter energy) represented by that energy.

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