I am heavy or having more mass ? E=mc^2

[Kabu]

I am "heavy" or having "more mass"? E=mc^2

Well,
I was discussing a problem with my physics teacher, it is seems very simple. However, it seems also that it require a bit of philosophy :)

Here it is:
Imagine that there is an object which moves with a constant velocity in a certain direction, according to E=mc^2, the object's mass should increases.
The question now is:
Does this (increasing in mass) as an (increasing in the usm of mass/energy in the body? or it is as an (increasing in the "actual mass" of the object)?

Thx in advance

 

[STAii]

Hello Kabu, i am glad to see you here.
You know i am no expert in physics, but i will give you what i have understood so far from browsing the forums.
Mass is two kinds :
1-Rest Mass (Mass when the object's velocity is zero)
2-Relativistic Mass (Mass due to the relativistic effect).

Now since people normally understand the concept of 'mass' as the rest mass, then ,when being not technical, your mass will not increase as your speed increase (only your energy will).
But from a more physicist point of view, your 'mass' will increase, since your energy will increase, and turn out into 'relativistic mass'.

I hope i was helpfull.

 

[CJames]

I think STAii's got it right. For example, accelerating to near lightspeed will not cause you to generate a larger gravitational field, and will not ever cause you to collapse into a black hole etc.

 

[Kabu]

Uhmmm, it seems fine :)
But now: imagine now if I am making a Bar-b-q,now the "meat" did not have any velocity,it is stable in its position. However,it is gaining energy by heating it,so according to this (since we consider no mass loss because of heating eg water etc) the mass of the meat will increase...

It is fine? I think so
Thx in advance for helping

 

[Integral]

Keep in mind that any mass increase due increasing speed is NOT observable in the moving frame. So the people onboard a spsceship traveling at .9c will have the same mass as they measured before the trip started. (Unless the ships chow is very good!)

I do not believe that any energy added during cooking translates to increased mass of the food. That energy can be accounted for in the chemical changes that occur during the processes. Chemical bonds are being made and broken, all of this requires energy, that energy is provided by the cooking process. Since heating something translates to increased molecular motion, there may be a miniscule amount of relativistic mass increase, but such a small amount that it would not be measurerable.

 

[Loren Booda]

The question is: does heat have mass? Heat is a form of energy, and energy and mass are interchangable.

I believe radiant heat is composed of linear photons, energy unbound and thus not immediately massive. Resonances of matter, captured photons (heat), do register as weight. The crucial difference between these "furled" and "unfurled" photons is the curvature of the former, endowing the characteristic of mass.

Random, thermal internal energy I predict would involve both these states, in part bound and in part free.

 

[schwarzchildradius]

Of course heat and all electromag energy has mass = hf/c²

 

[chosenone]

Well maybe when you apply energy to a mass and force it into motion,since energy gives matter the ability to have gravity,and gravity is used to determine mass by weight.the faster it goes the more it weighs by the more energy you give it,because mass in motion stays in motion,as to say it keeps its energy that sent it into motion.as the mass gets bigger the gravtiy increases,the mass at near light speed shrinks in size by the massive increase on it's gravity by the energy that keeps it in motion,thus bounding it to light speed as the gravity attracts spacetime from behind it keeping it from going any faster than light.

 

[Stranger]

also...the mass increases because the kinetic energy possessed by the moving ship acts like mass...e = mc^2...again...

 

[STAii]

What chosenone is saying is against what CJames is saying.
This may lead to a confusion, so can anyon please make this point clear before the confusion starts ?
Thanks.

 

[Hurkyl]

Something that doesn't seem to get mentioned often is that Einstein's field equations for gravity are 10 separate equations divisible into 4 physically distinct categories, each having their own effect on the curvature of space-time.

Hurkyl

 

[FZ+]

STAii: Cjames is right, at least as far as current theories are concerned.(notice chosenone's use of word maybe) Unless someone corrects me, I don't think relativistic mass has an gravitational effect. Rather this mass is expressed in the idea of momentum, or rather the change of it. Chosenone missed out on the concept of time dilation.

 

[Loren Booda]

Hurkyl-

Doesn't that mean something like 256 possible coefficients for those equations?

 

[Hurkyl]

Actually, all the equations are trivial. In the appropriate units, each component of the Einstein tensor (G) is simply equal to the appropriate component of the stress-energy tensor (T). I.E.

G₀₀ = T₀₀

G₀₁ = T₀₁
G₀₂ = T₀₂
G₀₃ = T₀₃

G₁₁ = T₁₁
G₂₂ = T₂₂
G₃₃ = T₃₃

G₁₂ = T₁₂
G₂₃ = T₂₃
G₃₁ = T₃₁

Hurkyl

 

[Loren Booda]

Hurkyl-

Then where do the complicated mathematics enter?

 

[pmb]

Well there's a lot of interesting stuff here. Point by point -

re - "Imagine that there is an object which moves with a constant velocity in a certain direction, according to E=mc^2, the object's mass should increases."


Keep in mind that there are two definitions of the term "mass" in relativity in common use

(1) The "m" in E^2 - (pc)^2 = m^2 c^4 -- This is what people call "m = rest mass" or "proper mass"

(2) The "M" in p = Mv - This is what people call "relativistic mass"

Note: M = m/sqrt[1 - (v/c)^2]

I prefer the later (M) since the former is not always well defined for a system of partilces (gets a bit complicated to explain but will be more than happy to upon request). M is also the quantity which retains all the properties that one normally associates with mass.


re - "The question now is: Does this (increasing in mass) as an (increasing in the usm of mass/energy in the body? or it is as an (increasing in the "actual mass" of the object)?"

"M" increases because the moving body has more energy then the same body at rest. It is a result of both time dilation and Lorentz contraction.

"m" is an inherent property of the body.

You also asked in the subject line - " I am "heavy" or having "more mass"?"

Regardless of how you define the term "mass" - A moving bodyu wieghs more than the same body at rest. The weight is NOT given by W = mg but by W = Mg.

I have two proofs that I did on this. One of which is a full blown calculation in general relativity. See --

http://www.geocities.com/physics_world/grav_light.htm


There was a comment - "For example, accelerating to near lightspeed will not cause you to generate a larger gravitational field, and will not ever cause you to collapse into a black hole etc."

This is incorrect. First off whether a body is a black hole is not determined by the amount of mass a body has. It's determined by the amount of mass that is contained within the Schwarzschild radius in the rest frame of the body.

The strength of a gravitational field depends on the velocity of the source. In fact you can have a gravitational field even when the total rest mass (i.e. "m") is zero. For example a beam of light can generate a gravitational field. See --
http://www.geocities.com/physics_world/grav_light.htm


re - "However,it is gaining energy by heating it,so according to this (since we consider no mass loss because of heating eg water etc) the mass of the meat will increase..."

The particles of which the meat is made of increase in their velocity ( see box of particles in the first link I gave - i called it a 2-dimensional gas as I recall). However its not just kinetic energy but all forms of energy which have mass. Suppose I have a spring and I put it on a wieght scale and I read the weight then I compress the spring and place the compressed spring on the scale. Since the compressed spring has more energy it will wiegh more and thus have a greater (passive gravitational) mass.


Simply put - If you heat up a gold ball then the rest mass of the golf ball wil increase.

Even light has mass since light has energy. (has relativistic mass but not rest mass).

re - " Unless someone corrects me, I don't think relativistic mass has an gravitational effect." - That is incorrect. In fact GR people often refer to the source of gravity as Mass-Energy since the source of gravity is relativistic mass - Buy "source of gravity" I mean that relativistic mass plays the role of a gravitational charge. So if you replace the idea of charge (Note: charge does not change with speed) with relativistic mass then the analogy holds true. In fact in linearized GR the equations are nearly identical with the equations of EM (Maxwell's equations) but with charge replaced by relativistic mass.

Pete

 

[CJames]

There was a comment - "For example, accelerating to near lightspeed will not cause you to generate a larger gravitational field, and will not ever cause you to collapse into a black hole etc."

This is incorrect. First off whether a body is a black hole is not determined by the amount of mass a body has. It's determined by the amount of mass that is contained within the Schwarzschild radius in the rest frame of the body.

The strength of a gravitational field depends on the velocity of the source.

So you are saying that if an object is traveling at near lightspeed from my reference frame, it will produce a gravitational field? I'd never heard that before.

If that is true, what about from the reference frame of that object? When objects seem to gravitate toward it, how is this force explained?

the source of gravity is relativistic mass

This is lost on me. An object need not be in motion relative to me for it to have a gravitational pull, correct?

 

[Hurkyl]

I prefer the later (M) since the former is not always well defined for a system of partilces (gets a bit complicated to explain but will be more than happy to upon request).

Ooh ooh, I request, I request! I've been wondering about that bit for quite some time!

the source of gravity is relativistic mass



This is lost on me.

Recall that the total energy of a particle is the kinetic energy plus the rest energy... so a stationary particle still has energy, and thus gravitates.

Then where do the complicated mathematics enter?

(a) G = T is really a partial differential equation in disguise. T is, I believe, essentially the jacobian of momentum with respect to position... and momentum itself is computed via the derivative of position with respect to proper time.

(b) There's another side to the evolution of GR, the time evolution of mass-energy. The equations that say "matter follows geodesics" is not very pretty, and a solution of GR must simultaneously solve the the aforementioned equations along with the time evolution equations.

Hurkyl

 

[pmb]

CJames asked
"So you are saying that if an object is traveling at near lightspeed from my reference frame, it will produce a gravitational field? I'd never heard that before."

I'm sure you have. Although you may not have recognized it as such. First - all objects have a gravitational field. When you are in motion relative to the source then the magnitude of the field changes. This happens in special relativistic EM (SEM) as you probably know. Same thing in GR. Just as the field in SEM is a tensor soo too is the field in GR. When you change frames in SEM then what you're doing is changing the components of the tensor which represents the field. Same thing in GR. As you know Einstein finished his theory of general relativity in 1915 (in several papers as I recal) and in the following year published a review article on the entire thing. In that article Einstein saiod that you can "produce" a gravitational field by changing the frame of referance (something you can't do in electrodynamnics). Well not only can you created a g-field by changing the frame of referance but you can change the magnitude of the field. You can see this by reviewing the web page I posted a link top above regarding weighing a moving body.

re - "If that is true, what about from the reference frame of that object? When objects seem to gravitate toward it, how is this force explained?" - See above - all objects have a gravitational field.


re - "This is lost on me. An object need not be in motion relative to me for it to have a gravitational pull, correct?" - Correct. An object at rest has a gravitational field. When the same object is viewed from a frame of referance moving with respect to that frame the gravitational field is larger.



re - "Ooh ooh, I request, I request! I've been wondering about that bit for quite some time!" - Smart man! Always question!~ I love it! :-)


See the diagram here --

http://www.geocities.com/physics_world/4-momentum.htm


Consider two particles as an example. Refer to this diagram to get an idea of what I'm speaking about

http://www.geocities.com/physics_world/4-momentum.jpg



If they move at constant velocity or if they interact only through contact forces, then the total 4-momentum of the two particles is a well defined quantity. You simply measure the energy and momentum of each particle -- at the same time -- and then add them. But "at the same time" is not a Lorentz invariant concept. So if you're in another frame of referance and add them "at the same time" then what you're doing is really adding together two different 4-momenta - not same tow you added before. Notice that this is not a problem if the particles move at constant velocity. It's sort of like the situation in EM I can't add the Electric fields from different places and expect the resultant sum to be physically meaningful right. Same here. The 4-,momentum is mnore like a field than it is anything else. You can no longer treat time as a parameter.

Ohaninan mentions this in his text "Gravitation and Spacetime" - I put this quote on the web since people really need to see that from an authority on the subject and this is rarely if ever mentioned

http://www.geocities.com/physics_world/ohanian.htm





re - "(a) G = T is really a partial differential equation in disguise."

Actually it's G = (8*pi/c^4)T




re - "T is, I believe, essentially the jacobian of momentum with respect to position... and momentum itself is computed via the derivative of position with respect to proper time.

No. T is called the stress-energy-momentum tensor. Atually the quantities are really densities - i.e.

T^00 = energy density
T^i0 = momentum density in i-direction
T(jk) = stress tensor

The momentum density is not defeined in terms of proper time. In fact it's wise not to confuse 3-vectors with 4-vectors. People do that al to often. They get the idea the the "real" quantities in relativity are 4-vectors. While they sure are a convinience it's wise not to mix them up with 3-vectors.

For example: The 3-vector velocity of light is a well defined quantity. However its meaningless to speak of the 4-velocity of light.

Pete