# Can energy exist without mass?

#### diffusion

Hey guys, my first post here. I need a little help answering this seemingly simple question: can energy exist without mass?

At first I thought this an easy answer. Simply, no. Einsteins famous equation E=mc^2 shows us that energy and mass are directly proportional, so without mass, the value of E= 0. But after thinking some more it doesn't seem like such an easy answer. For example, light carries both energy and momentum in the form of photons, yet photons are said to be massless. How can they be massless when they carry energy and momentum? I'm still a little confused about the whole invariant/relativistic mass concept.

Also, vacuum energy is said to be an energy that exists in space even in the complete absence of matter. Again, how can this energy exist without matter?

So, to make things easy, I'd just like to know: Can energy exist without mass? And, if possible, could someone please explain the points stated above about the energy of massless photons and vacuum energy. Thanks.

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#### mgb_phys

Science Advisor
Homework Helper
e=mc^2 doesn't say that mass and energy are proportional, it says that mass and energy can be converted into each other, or alternatively that mass is a form of stored energy.

One of the big leaps of quantum mechanics is that momentum can exist without mass, photons can have momentum without having mass.
The other is that everything with momentum has a wavelength even 'solid' objects.

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#### ZapperZ

Staff Emeritus
Science Advisor
Education Advisor
2018 Award
Hey guys, my first post here. I need a little help answering this seemingly simple question: can energy exist without mass?

At first I thought this an easy answer. Simply, no. Einsteins famous equation E=mc^2 shows us that energy and mass are directly proportional, so without mass, the value of E= 0. But after thinking some more it doesn't seem like such an easy answer. For example, light carries both energy and momentum in the form of photons, yet photons are said to be massless. How can they be massless when they carry energy and momentum? I'm still a little confused about the whole invariant/relativistic mass concept.

Also, vacuum energy is said to be an energy that exists in space even in the complete absence of matter. Again, how can this energy exist without matter?

So, to make things easy, I'd just like to know: Can energy exist without mass? And, if possible, could someone please explain the points stated above about the energy of massless photons and vacuum energy. Thanks.
You need to read an entry in our FAQ in this section of PF because you have the common misconception about that infamous Einstein equation. Furthermore, photons have no mass in the conventional sense, but yet, it carries energy (and momentum, and spin).

Zz.

#### olgranpappy

Homework Helper
Hey guys, my first post here. I need a little help answering this seemingly simple question: can energy exist without mass?

At first I thought this an easy answer. Simply, no. Einsteins famous equation E=mc^2 shows us that energy and mass are directly proportional...
Except that equation is wrong. If by "mass" you mean "rest mass" which you always should mean when you say mass (an invarient quantity), then Einstein's equation should read
$$E=\sqrt{m^2c^4+p^2c^2}$$
where p is momentum.

If the mass is zero, as it is for a photon,
$$E=pc$$
which is *not* necessarily zero.

#### rcgldr

Homework Helper
Do photons really have momentum, or does the momentun only exist when the photons are converted into mass + energy via capture by electrons?

#### diffusion

Thanks for the responses. But as for the intitial question I'm still not sure. Can energy exist without any matter anywhere in the universe? Not sure if you would classify photons as matter, and what about vacuum energy?

#### olgranpappy

Homework Helper
Do photons really have momentum, or does the momentun only exist when the photons are converted into mass + energy via capture by electrons?
well, then, by conservation of momentum, the photon did "really" have momentum.

#### jtbell

Mentor
In order to detect a photon, you have to "capture" it and thereby destroy it. So you might as well ask, do photons really exist at all, or are they simply a convenient mathematical shorthand for a certain kind of transfer of energy and momentum in which the E and p disappear at one point and reappear at another point after a time interval given by $\Delta t = \Delta x / c$?

#### LURCH

Science Advisor
First of all, I think the uncertainties about Rest Mass vs Relativistic Mass are at the center of your confusion. By most models, photons do have energy, which they carry in the form of Relatvivstic Mass only. So yes all enegry has mass but, as has been mentioned earlier, the word "mass" by itself almost allways means Rest Mass, so that's a bit of a red herring

As for this:
Thanks for the responses. But as for the intitial question I'm still not sure. Can energy exist without any matter anywhere in the universe? Not sure if you would classify photons as matter, and what about vacuum energy?
It's a more complicated question than you might imagine. For the simple answer, and the one I think you're looking for, yes. If half the matter in the universe were converted to antimatter, and came instantly into contact with all the remaining "normal" matter, or by some other means all of the matter in the universe could be reacted with (a course of action I do not in any way endorse), the result would be the conversion of all matter into energy.
The question then gets complicated when we ask if such energy can be said to "exsit" without any matter around to observe it. But I don't think thats the sort of thing you were asking.

#### ryan_276

hi diffusion,
It's look like great question...........

#### Maxwell's Demon

So, to make things easy, I'd just like to know: Can energy exist without mass? And, if possible, could someone please explain the points stated above about the energy of massless photons and vacuum energy. Thanks.
The special case of photons is confusing just because of the way it’s phrased. Photons don’t have any ‘rest mass,’ all of their energy is associated with their frequency in motion, like a wave on the sea: the wave doesn’t exist if it isn’t moving - so it can possess energy (and an equivalent mass) as it moves, but it has no ‘rest mass.’ And as far as energy and mass goes, I find it easier to think of them as mass/energy, because they’re the same thing being called by different names, like a millimeter is just a smaller unit of a meter: both are units of length.

Vacuum fluctuations are an entirely different issue; they’re composed of ‘virtual particles’ which exist simultaneously in positive and negative energy states which perfectly cancel out (as far as we can tell). The baseline energy state is zero, but there are tiny regions above and below that baseline state in constant rapid fluctuation…so it’s a ‘fuzzy’ baseline, much like electrons occupy ‘fuzzy’ valence shells (in fact, electron shells appear to be ‘fuzzy’ because of the vacuum fluctuations that constantly bump them around).

What I find really interesting about vacuum fluctuations, is that we can confine a region of the fluctuations to forbid all non-integer wavelengths from existing in the space between two closely-placed metal surfaces. This exclusionary zone possesses a vacuum fluctuation energy level –below- the ‘zero’ baseline. The energy difference between the inside of the plates and the outside of the plates causes the plates to move together, and that effect is called the Casimir force. Recent theory suggests that it may also be possible induce a –positive- Casimir energy difference between two surfaces to make them push apart a little: Inverting the Casimir force

That’s my understanding of it anyway. Maybe the local experts can offer greater clarification.

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#### Loren Booda

One of the simplest cosmological models using the equations of general relativity is for a massless but energized universe. De Sitter space could meet this condition.