# Fractal Universe - 5D Space-Time: Frequency Of Cycles In Dimensional Scale

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#### topsquark

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"The special-relativistic thermodynamics is an interesting area which has not been settled to full satisfaction AFAIK but nonetheless, it should be pointed out that when you heat up a body, the individual particles of the body only gain kinetic energy--so the rest mass of the individual particles does not change. But when you see the body as a whole with its center of mass at rest (and whose constituent particles are only engaging in thermal motion), the rest mass of the full body as a whole gets increased, in particular, the heat you provide goes into the rest mass of the body as a whole"

This is exactly, what I predicted
Then you'd better check again. As benit13 said nothing changes the rest mass of a particle. It is the mass of a particle with no regard to motion. Now, when you heat something up then the particle's kinetic energy increases and the particles gain momentum. The total energy of the particle then obeys $$\displaystyle E^2 = (pc)^2 + (mc^2)^2$$, where we are using whatever average p is appropriate. But m is the rest mass and does not change under any circumstances, even when changing reference frames. Now, if we are talking about a macroscopic object its rest mass due to the individual particles stays the same, so we still get the same rest mass. What happens is the mass of the whole object reflects the extra kinetic energy contained in it. This does change the mass of the object, but not it's rest mass. The thermal energy simply gets absorbed into its total energy.

-Dan

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#### GatheringKnowledge

Then you'd better check again. As benit13 said nothing changes the rest mass of a particle. It is the mass of a particle with no regard to motion. Now, when you heat something up then the particle's kinetic energy increases and the particles gain momentum. The total energy of the particle then obeys $$\displaystyle E^2 = (pc)^2 + (mc^2)^2$$, where we are using whatever average p is appropriate. But m is the rest mass and does not change under any circumstances, even when changing reference frames. Now, if we are talking about a macroscopic object its rest mass due to the individual particles stays the same, so we still get the same rest mass. What happens is the mass of the whole object reflects the extra kinetic energy contained in it. This does change the mass of the object, but not it's rest mass. The thermal energy simply gets absorbed into its total energy.

-Dan
It's not that I want to undermine your authority or something, but I've made some google search and those are some of the results:
Does mass change with temperature? - Quora

Generally, opinions are pretty divided among physicists, however it seems, that according to the majority, heat transfer DOES indeed increase the rest mass of a macroscopic body - although this increase is very tiny. Here's also a site, which proves that the increase of electric charge is resulting in small addition of rest mass to the system:

"Both the actual increase in mass and the percent increase are very small, since energy is divided by c2size 12{c rSup { size 8{2} } } {}, a very large number. We would have to be able to measure the mass of the battery to a precision of a billionth of a percent, or 1 part in 1011, to notice this increase. It is no wonder that the mass variation is not readily observed. In fact, this change in mass is so small that we may question how you could verify it is real. The answer is found in nuclear processes in which the percentage of mass destroyed is large enough to be measured. The mass of the fuel of a nuclear reactor, for example, is measurably smaller when its energy has been used. In that case, stored energy has been released (converted mostly to heat and electricity) and the rest mass has decreased. This is also the case when you use the energy stored in a battery, except that the stored energy is much greater in nuclear processes, making the change in mass measurable in practice as well as in theory."

I would agree with your statements, if instead of "What happens is the mass of the whole object reflects the extra kinetic energy contained in it.", you would say: "...whole object radiates out the extra kinetic energy contained in it.". I might be an amateur, but I know enough about mass/energy equivalence, to say that if: "The thermal energy simply gets absorbed into its total energy.", it will actually result with a tiny increase of rest mass - but we won't measure it, since the additional mass/energy is immidiately released into the environment, due to the constant thermal radiation...

If we'll move on higher level in scale dimension, we will be able to use the same mechanism, to explain a scenario, where we hit a solid block of granite with a steel pipe, causing the increase of internal vibrations in both systems, which result in emission of a sound wave (among other waves) to the environment - so that in the end, the balance of energy emission/absorption is being maintained...

However, what matters at most for the discussion about fractal gravity and gravitational expulsion, is the ratio of energy emission/absorption. If an external source causes a constant increase of energy level in a body (or system of bodies), it's excess will be emitted into the environment, disrupting the initial balance of mass/energy equivalence. It's quite logical to me, that the additional mass/energy will in such case turn into radiation, that will influence the potential energy of another body by inducing a kinetic force on it or increasing it's level of thermal energy.

Here are examples of forces (thermal radiation, kinetic pressure of light), which are induced on matter due to emission of additional energy from a system:

And here's just another example of the same process - only here, it's the source of radiation, which is experiencing kinetic force of lift due to the potential energy of a body with greater mass (Earth):

All examples are based on the same laws of mass/energy equivalence. However, mechanical compression of a mass/energy distribution requires a different explanation - I will try to explain it better in another post...

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#### topsquark

Forum Staff
You missed the reason I made that post. The rest mass of an object never changes. What you might call the "relativitic mass" can and does.

-Dan

#### benit13

Just to clarify, the thread where GatheringKnowledge's quote was derived was talking about the rest mass of macroscopic objects. Since rest mass is a property of fundamental particles, it's a bit of an odd discussion.

I'm not really well read on the nuances of SR. However, if one was to extend the definition of rest mass to include macroscopic bodies, then I would suggest a definition where the rest mass of the macroscopic object is just the sum of the rest masses of the constituent particles:

$$\displaystyle m_0 = \sum_i m_{0,i}$$

This seems to be the definition TopSquark is using as well. This value would never change, just like the usual definition of rest mass, assuming that the number of particles is fixed (no particles leaving or entering the control volume of the macroscopic object). Technically, since every object in the universe has a temperature above 0K, this is a minimum limit to the measured mass and would never actually be measured in experiments. The higher the temperature, the higher the actual mass deviates from this one, but the error will be incredibly small even for objects with high temperatures since the speeds of particles within objects is almost always non-relativistic. Then, one can just assume that the error is negligible and use this mass in SR calculations without any difficulty or systematic errors.

In the thread, they discuss a different definition, which is one where the centre of mass of the macroscopic object is at rest but the individual masses within the object can move. If you take this definition, then this macroscopic rest mass would become a very weak function of the average speed of the particles in the object or, alternatively, a very weak function of temperature. This is not how I would definite it because it muddies the waters, but hey ho.

topsquark

#### benit13

Generally, opinions are pretty divided among physicists, however it seems, that according to the majority, heat transfer DOES indeed increase the rest mass of a macroscopic body - although this increase is very tiny. Here's also a site, which proves that the increase of electric charge is resulting in small addition of rest mass to the system:
Fair enough. In that case, rest mass would be affected by anything that affects the masses or motion of those masses (e.g. binding energy, chemical potential energy, thermodynamics).

Now that you mention it, it's probably the case that most macroscopic objects of interest (such as atomic nuclei) don't have measured masses equal to their constituents anyway because of the nuclear binding energy, so my previous suggestion in post #24 is probably not useful to anybody.

#### GatheringKnowledge

You missed the reason I made that post. The rest mass of an object never changes. What you might call the "relativitic mass" can and does.

-Dan
I think, that the problem comes from all those different terms, used to describe mass of objects. There's invariant rest mass and there's relativistic inertial mass - am I right? What I have on my mind, when I speak about "rest mass", is the mass of an object, measured in it's own "stationary" frame. What I've tried to say, is that by increasing the energy by heating/cooling and compressing a macroscale object, we will change it's mass, as it is measured in it's own frame. This is supported by all those links

EXAMPLE 28.7 CALCULATING REST MASS: A SMALL MASS INCREASE DUE TO ENERGY INPUT
A car battery is rated to be able to move 600 ampere-hours (A⋅h) of charge at 12.0 V. (a) Calculate the increase in rest mass of such a battery when it is taken from being fully depleted to being fully charged. (b) What percent increase is this, given the battery’s mass is 20.0 kg?

#### GatheringKnowledge

Just to clarify, the thread where GatheringKnowledge's quote was derived was talking about the rest mass of macroscopic objects. Since rest mass is a property of fundamental particles, it's a bit of an odd discussion.

I'm not really well read on the nuances of SR. However, if one was to extend the definition of rest mass to include macroscopic bodies, then I would suggest a definition where the rest mass of the macroscopic object is just the sum of the rest masses of the constituent particles:

$$\displaystyle m_0 = \sum_i m_{0,i}$$

This seems to be the definition TopSquark is using as well. This value would never change, just like the usual definition of rest mass, assuming that the number of particles is fixed (no particles leaving or entering the control volume of the macroscopic object). Technically, since every object in the universe has a temperature above 0K, this is a minimum limit to the measured mass and would never actually be measured in experiments. The higher the temperature, the higher the actual mass deviates from this one, but the error will be incredibly small even for objects with high temperatures since the speeds of particles within objects is almost always non-relativistic. Then, one can just assume that the error is negligible and use this mass in SR calculations without any difficulty or systematic errors.

In the thread, they discuss a different definition, which is one where the centre of mass of the macroscopic object is at rest but the individual masses within the object can move. If you take this definition, then this macroscopic rest mass would become a very weak function of the average speed of the particles in the object or, alternatively, a very weak function of temperature. This is not how I would definite it because it muddies the waters, but hey ho.
This is because in order, to create a multiscale model of a physical mechanism, you need to treat macroscale objects, as a total sum of energy, which is
"stored" in a system of "particles". By changing the state of an object, we make a definitive change in the equivalence of energies - and since nature always tries to reach balance, additional energy is released in some form into environment.

If we change the temperature of a macrosale object, rest mass of atoms/molecules will remain the same - as atomic mass is an intrinsic property of subatomic particles. By heating a macroscale object we are increasing the vibrational frequency in a system of particles and this change is definitive in macroscale frame - this is why, it has to be measurable as an inbalance in the mass/energy equivalence... I don't consider this as confusing at all...

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#### topsquark

Forum Staff
...this is why, it has to be measurable as an inbalance in the mass/energy equivalence...
I'm with you up to here, but what do you mean by "inbalance in the mass/energy equivalence." There is no imbalance... energy is conserved so long as we keep track of "source" terms, such as temperature or potential fields. Are these extra terms what you are calling an "imbalance?"

(Since we're talking about Thermodynamics of a macroscopic system I should say that I'm assuming the object is at equilibrium in contact with a heat reservoir. I hate Thermo!)

-Dan

#### GatheringKnowledge

I'm with you up to here, but what do you mean by "inbalance in the mass/energy equivalence." There is no imbalance... energy is conserved so long as we keep track of "source" terms, such as temperature or potential fields. Are these extra terms what you are calling an "imbalance?"

(Since we're talking about Thermodynamics of a macroscopic system I should say that I'm assuming the object is at equilibrium in contact with a heat reservoir. I hate Thermo!)

-Dan
Good question - I say, that' it's the imbalance between temperature of a macroscale object and it's environment. This is why the temperature is radiated out and heats up colder matter. Thing is, that such imbalance is not measurable on subatomic scale (energy of electrons remains the same) - but it becomes visible on molecular scale (molecules move faster, than before).

#### GatheringKnowledge

This is why I love discussing physics with intelligent people - sometimes a question can push my thoughts on the right track. I think, that I figured out the main difference between heat transfer and mechanical compression. While change of temperature causes external imbalance between macroscopic object and it's environment, compression causes internal imbalance between vibrational frequency of particles (molecules) and temperature of macroscopic object. External imbalance of temperature is nullified by thermal radiation, but energy used in the work needed to compress a macroscopic object becomes it's potential energy and uses kinetic energy of the external environment, to nullify the pressure differential during decompression - this is why air gets cold locally, when we use a deodorant.

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