# Vacuum energy density

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If mass of a particle is less than the vacuum energy density.. what would happen.. is this possible (also for some dark matter species)?

How about photons.. are they more or less than the vacuum energy density?

And what exactly is the value of vacuum energy density?

If mass of a particle is less than the vacuum energy density
It doesn't make sense to compare a mass (mass or energy) to an energy density (energy per volume).

That's like asking what happens if the speed of a horse is less than the price of an apple.

star apple
It doesn't make sense to compare a mass (mass or energy) to an energy density (energy per volume).

That's like asking what happens if the speed of a horse is less than the price of an apple.

What? For example.. there is a dark matter species the size of table but only the mass of an quark. Won't this make its density less than that of the vacuum?
Or what is the right way to ask it.. or what other words to add to relate the mass of a particle and energy density?

What? For example.. there is a dark matter species the size of table but only the mass of an quark. Won't this make its density less than that of the vacuum?
Or what is the right way to ask it.. or what other words to add to relate the mass of a particle and energy density?

or maybe the right way to ask is.. can any object have density that is less than the vacuum density? what would happen if there is.. what would it do to the object?

That's like asking what happens if the speed of a horse is less than the price of an apple.
Easy one! Then you won't be able to get to a place where they sell apples ...

Here are the direct questions (after getting my mind organized a bit):

The down quark has mass or approx. 4.79 MeV and using wiki value let’s say vacuum density is about 10^-19 joules per cubic meter (or 6.2 x 10^-6 MeV). Does it mean no particle should be less than 6.2x10^-6 MeV (normal matter or dark matter)? Or is vacuum density like the ocean where even spider lighter than its equivalent density can walk on top of it? How about the photon.. it is massless so how can it exist amidst the huge energy density of the vacuum? Please correct any misconception as I’m bit confused. Thank you.

Elementary particles don’t have a size, at least nothing ever showed one.

6.2*10^(-6) MeV (=6.2eV) per cubic meter. Or 6.2 GeV per cubic kilometer, or something like 20 GeV per cubic mile, or whatever. Why do you expect a cubic meter to be special (by picking this as volume)?

To compare energy densities you need extended, composite objects. The average density of matter in galaxies is larger than the density of dark energy. The average energy density of matter in the universe is smaller than the density of dark energy.

star apple
Elementary particles don’t have a size, at least nothing ever showed one.

6.2*10^(-6) MeV (=6.2eV) per cubic meter. Or 6.2 GeV per cubic kilometer, or something like 20 GeV per cubic mile, or whatever. Why do you expect a cubic meter to be special (by picking this as volume)?

To compare energy densities you need extended, composite objects. The average density of matter in galaxies is larger than the density of dark energy. The average energy density of matter in the universe is smaller than the density of dark energy.

Let’s use an example. If a dark matter cat has total mass of 4.79 MeV. Would the total energy density of the cat be less than the energy density of the vacuum? Or should it always be more than the energy density of the vacuum? Should a dark matter cat with diffuse body (gas-like body) need to have total energy density larger than that of the vacuum? Or is it not related?

Let’s use an example. If a dark matter cat has total mass of 4.79 MeV. Would the total energy density of the cat be less than the energy density of the vacuum? Or should it always be more than the energy density of the vacuum? Should a dark matter cat with diffuse body (gas-like body) need to have total energy density larger than that of the vacuum? Or is it not related?

Or a better question.

Can any extended object exist that has energy density less than that of the vacuum? Or is it possible to have near massless dark matter (with a size of say 1 foot by 1 foot) that has less than energy density of the vacuum?

In our ocean.. when there is heavy object with more density than water.. it sinks to the bottom. If less density it floats.. what is the analogy in the vacuum when something has less energy density that it.. what happens to the object.. what "bottom' in the vacuum will it sink? Or does it simply implode?

If you subscribe to the notion that the vacuum energy density is the ground state of the universe, it should be fairly obvious that no particle can have an energy below that of the vacuum energy density and still be recognizable as a particle. The thing about energy is there is no sensible way to assign an absolute value to the energy of any interaction. We can only measure [detect] the difference between energy levels of particles whenever they interact..Furthermore, there are different kinds of energy [charge, mass, etc.] and no convenient way to reconcile the units used to express them - e.g., how many volts are in a kilogram, or, what color is b flat? Until we devise a more utilitarian way to define energy and its units of measure the question basically becomes that of what is the sound of one hand clapping.

star apple
Can any extended object exist that has energy density less than that of the vacuum?

Do you mean "can the energy of the object plus any energy in the space it occupies be less than the energy of the space alone", the answer is "no".

Do you mean "can the energy of the object plus any energy in the space it occupies be less than the energy of the space alone", the answer is "no".

How come photons have zero mass? Imagine an large wavefront of light and photons coming from a supernova explosion that fills huge portion of space. The energy density of this light avalanche even if zero should at least be equal to the energy density of vacuum. Hence the entire light avalanche should have mass. And won't this means the photon should have mass directly coming from the vacuum energy density in addition to any relativistic mass it acquires?

How come photons have zero mass?

How come electrons have mass? Or down quarks? I could say that they have mass because of the Higgs mechanism, but then we could just move the question to this more fundamental level and ask why down quarks and electrons interact with the Higgs mechanism. The best answer to your question is that we've observed that photons behave as if they have no mass. If they do have mass, this mass must be extremely small. So small that we cannot measure it. We may find out later that they do indeed have mass, but for right now our theories have to follow our observations and say that they do not.

Imagine an large wavefront of light and photons coming from a supernova explosion that fills huge portion of space. The energy density of this light avalanche even if zero should at least be equal to the energy density of vacuum.

The energy density is non-zero, as photons have energy but no mass. This follows directly from the full Einstein equation: ##e^2=m^2c^4+p^2c^2##
The mass of a photon is zero, so the equation reduces to ##e^2=p^2c^2→e=pc##.
The energy of a photon is proportional to its momentum ##p##.

And won't this means the photon should have mass directly coming from the vacuum energy density in addition to any relativistic mass it acquires?

Why would a photon acquire mass from the energy density of free space?

star apple
How come electrons have mass? Or down quarks? I could say that they have mass because of the Higgs mechanism, but then we could just move the question to this more fundamental level and ask why down quarks and electrons interact with the Higgs mechanism. The best answer to your question is that we've observed that photons behave as if they have no mass. If they do have mass, this mass must be extremely small. So small that we cannot measure it. We may find out later that they do indeed have mass, but for right now our theories have to follow our observations and say that they do not.

The energy density is non-zero, as photons have energy but no mass. This follows directly from the full Einstein equation: ##e^2=m^2c^4+p^2c^2##
The mass of a photon is zero, so the equation reduces to ##e^2=p^2c^2→e=pc##.
The energy of a photon is proportional to its momentum ##p##.

Why would a photon acquire mass from the energy density of free space?

Ok.. now according to wiki entry on vacuum energy "However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant requires it to have a much larger value of 10^113 joules per cubic meter".. and since 1 joule is equal to 6241506479963.2 MeV then 10^113 joules is like 6241506479963.2 x 10^113 MeV.

This means our body should have energy density much less than the full vacuum energy.. Now I'd like to know what would be the effect. If an object in the ocean has density less than that of water. It floats. So what is equivalent of "float" in the huge vacuum energy in which our body energy density is much lighter and should float.. but where would the "floating" be?

As far as I know, the energy density of our body is simply added to the energy density of the space we occupy. It doesn't somehow "float" or anything.

As far as I know, the energy density of our body is simply added to the energy density of the space we occupy. It doesn't somehow "float" or anything.

How does the adding work? For example. If our physical body has certain mass and weight. How would a 6241506479963.2 x 10^113 MeV vacuum energy be added to our energy density? how does the coupling work?

I assume you just add the numbers together to get the final value for the energy density of that region of space, but I don't know much about any of the details of this topic.

Dark matter cannot form cats, or any other structures this size. As it doesn't interact via the electromagnetic interaction it only clumps on the scale of galaxies.
Ok.. now according to wiki entry on vacuum energy "However, in both quantum electrodynamics (QED) and stochastic electrodynamics (SED), consistency with the principle of Lorentz covariance and with the magnitude of the Planck constant requires it to have a much larger value of 10^113 joules per cubic meter".. and since 1 joule is equal to 6241506479963.2 MeV then 10^113 joules is like 6241506479963.2 x 10^113 MeV.
They don't require that. They suggest this would be a natural value for the constant. But we know the constant doesn't have that value, so using that is pointless.

Dark energy is everywhere, it is not replaced by objects (unlike water is by suspended objects, for example) - if you add an object you always increase the energy density.

You don't understand what vacuum energy is.

For one, it's not just "energy" (a scalar value). It's stress-energy tensor (a 4x4 matrix). If you want to work in a simple flat Minkowski space, you can do away by looking at four-momentum, but it's still a 4-dimensional vector, not a scalar.

More importantly, vacuum energy, in order to be *vacuum* energy, has to have some rather unusual properties:

(1) It's a local minimum of energy. Any fluctuations on top of it (such as adding any particles to vacuum) _increase_ energy. [this answers your question]

(2) It should be Lorentz-invariant: boosts should not change it ("moving relative to vacuum is undetectable"). This means that (in flat Minkowski space), it should have form (p, -p, -p, -p) - note the negative pressure. This is rather unusual compared to most other forms of energy you know. For example, "dust" has four-momentum (ro, 0, 0, 0), "fluid" (for example, radiation-dominated early Universe) has four-momentum (ro, p, p, p).