# Do vibrations increase an object's mass or weight?

does a vibrating object recieve an increase of mass or weight? and if it does, at what frequency or intensity does it need to vibrate at, and what is the rate of increase? is there a formula for it? and also, is it possible to change an onject's state with vibrations alone? like from gas to solid, or liquid to gas. i know something similar can be done with both heat and vibrations which create plasma. but can it be done with vibrations alone?

• Did you hear about Einstein's theory of special relativity? – my2cts Dec 12 '18 at 21:52
• yeah, but i don't really understand it. i'm like, 16 and from a backwater country so i can't say i'm very knowledgable about physic theories. care to explain? – Mortimer The Third Dec 12 '18 at 22:11
• Yes, I would recommend you watch pbs space time on their videos about mass. Short answer is E=mc^2. For your other question I don't know what your definition of vibration is because heat is vibrations... – Matthew Liu Dec 12 '18 at 22:13
• really? i thought heat was a byproduct of vibrations, or vibrations being a byproduct of heat. never thought of them as the same entity – Mortimer The Third Dec 12 '18 at 22:23

## 2 Answers

@Mortimer The Third Great to have you on the site! Weight and mass are separate but related quantities. Weight is the force exerted by gravity on mass. At least, that's what physicists believed until 1905, when Albert Einstein published his ideas on relativity. It became clear that mass of an object is just the total energy of the object at rest, up to a factor of $$1/c^2$$. So if you raise the temperature of an object by causing internal vibrations to increase, then its mass and thus its weight will increase. Here is a link to a discussion onbooks on relativity for beginners. https://www.quora.com/What-is-the-best-book-for-self-learning-Special-and-General-Theory-of-Relativity-What-are-some-beginner-and-advanced-level-books-on-these-topics

does a vibrating object receive an increase of mass or weight?

It all depends on the framework and the frameworks depend on the magnitudes of the variables.

In the everyday dimensions of classical mechanics, classical electromagnetism, and thermodynamics the answer is "no". *Mass is a conserved quantity *, defined as

$$F=ma$$

usually this m is called the inertial mass, the resistance to a change in velocity ( acceleration)

and heating will not do anything to the mass on a scale or in interactions. All commerce of products on earth depends on having the mass a conserved quantity.

When the velocities of the objects become very high, one needs a different framework for compatibility of the mechanics model with the data. In that model the inertial mass changes, the higher the acceleration the larger the resistance, and that is the famous $$m$$ appearing in $$E=mc^2$$ . This is [called relativistic mass,]1

$$m_{rel}=E/c^2$$

where $$E$$ is the energy of the object and $$c$$ the velocity of light, and this is with the algebra of special relativity.

This will be useful for calculating how much fuel is needed to reach velocities close to the velocity of light in star travels.

Special relativity has to do with four vectors, and relativistic mass has fallen by the wayside, as a quantity that is a function of velocities and not invariant.

What is used and characterizes particles and ensembles of particles in the small dimensions is the invariant mass, the "length" of the four vector of a particle , or the length of the sum of the four vectors for an ensemble of particles. Energy and momentum are conserved quantities in inertial systems in special relativity and one can easily keep track of the energy budget in this formalism.

Note that the invariant mass is only conserved for the individual particle. The addition of four vectors does not lead to the sum of the masses as the invariant mass of the sum. One has to calculate it. Only when all the particles are at rest, no velocities, the masses can be summed, and they represent, according to the special relativity algebra, the minimum energy of the system.

Thus, when having particles in motion, the addition of the fourvectors will give a fourvector with a mass larger than the rest mass. If, as it happens in nuclear physics, where nuclei are bound, the addition of the four vectors of a bound system will give a mass smaller than the sum of the constituents. Example is the deuterion, the nucleus of deuterium, composed of a neutron and a proton:

The sum of the proton and neutron masses is 2.015941 u

while the mass of the deuterion is 2.013553 u , smaller, because it is a bound state.

one $$u = 3.9654 x 10^{-30}$$ kg

This is true for all bound states, and the everyday objects are all bound states by the electromagnetic interaction, so it should hold that the sum of the fourvectors will add up to an invariant mass smaller then the sum of the masses of the constituent.

Within this caveat, if energy is transferred to a crystal and it starts vibrating , without breaking up, it means that there is less binding energy in total and this will be evident in the sum of the four vectors of the constituents, which will be larger, and thus the invariant mass of the crystal will be larger. The effect though will be very very small, note the values above, and not detectable with the scales we use to measure and weigh masses. Only with very accurate experiments specially designed one would be able to see the difference

is it possible to change an object's state with vibrations alone? like from gas to solid, or liquid to gas

If you consider boiling water as vibrations transferred from the heat input to the body, yes. Change of phase happens by breaking energy bounds.