Exploring Relativistic Mass with pmb_phy: A Conversation on Its Relevance

[Aer]

If you prefer, we can ignore the concept of "relativistic mass" altogether and just talk about the total energy of a composite object in its center-of-mass frame.

This is stupid, then we would just be talking about adding up the masses and kinetic energy to get the total energy.

 

[JesseM]

What makes you so sure? Do you have any sources that tell us how "rest mass" should be defined for a composite object made up of many individual particles which are in motion relative to each other?

I already did! It is the sum of all the constituents own rest masses.

I didn't ask you to just repeat the assertion, I asked if you had any sources that back up your assertion. Show me a source that specifically addresses the issue of composite objects made up of sub-objects in motion relative to one another. If you don't have a source, you're just guessing, you don't really know if the physics community would agree with your definition.

 

[JesseM]

This is stupid, then we would just be talking about adding up the masses and kinetic energy to get the total energy.

Sure, and this would be equal to the sum of the relativistic masses. What's the problem here? Why do you doubt that the total energy is the thing that determines the resistance to acceleration of the composite object?

 

[Aer]

Again, forget relativistic mass and just talk about energy. The reason I think it's the total energy rather than the sum of all the rest masses that determines weight is because I have several sources written by experts which say that it's the total energy that determines resistance to acceleration (inertia).

How about you link to these sources instead of just saying they exist. If this were true, then the theory as it is now defined is wrong. I'd don't claim that the theory is neccessarily right - but let's be clear, are we talking about the theory or experiments?

One experimental proof should suffice. Someone's personal opinion is not experimental proof.

 

[JesseM]

If I have objects in my car moving at .9999999999999999999999999999999999999999999999c bouncing all over the place, what is the mass of my car?

That depends on how the physics community chooses to define the mass of a composite object. I have no reason to doubt that Tom Roberts and learningphysics are giving the standard definition, and you haven't provided any sources that indicate otherwise. But ignoring the issue of definitions, I'm confident that the same force will not accelerate your car as quickly as if the objects in your car were moving slower (in the center-of-mass frame of the car), ie the inertia of the car will be different, since two expert sources have said this is true.

 

[Aer]

I'm confident that the same force will not accelerate your car as quickly as if the objects in your car were moving slower (in the center-of-mass frame of the car), ie the inertia of the car will be different, since two expert sources have said this is true.

I'd be more than happy to see these sources. This would do nothing but undermine the foundations of SR and probably neccessitate modifications to GR.

 

[JesseM]

How about you link to these sources instead of just saying they exist.

The sources I'm talking about are the ones I already linked too--the FAQ written by a physicist at Virginia Tech, and the mathpages.com page. I can look for more if you like.

If this were true, then the theory as it is now defined is wrong.

Why? Perhaps it is just your understanding of the theory that is wrong.

 

[Aer]

The sources I'm talking about are the ones I already linked too--the FAQ written by a physicist at Virginia Tech, and the mathpages.com page.

Well your sources are crap and I've already shown you why.

I can look for more if you like. Why? Perhaps it is just your understanding of the theory that is wrong.

No, my understanding is just fine.

 

[Aer]

You might want to look to experimental proof before you go believing anything. I am not saying I believe any of this - only that it is what the theory says. To my knowledge, there has been no experiment to confirm that rest masses are the true "rest mass" of any object (composite or otherwise).

 

[Aer]

Before you go on posting any more drivel, please read my post explaining energy, mass, et al completely: read here

And just an FYI, I compiled this from an expert source, it is not just my own personal understanding.

 

[JesseM]

Well your sources are crap and I've already shown you why.

No you haven't. Your only comment about the FAQ was the incorrect statement that the author didn't contradict the questioner, and you didn't say anything about the mathpages.com page at all.

No, my understanding is just fine.

Well, would you care to explain the basis for your statement "then the theory as it is now defined is wrong"? What obvious flaw do you see in the idea that resistance to acceleration is proportional to total energy in the center-of-mass frame?

 

[Aer]

No you haven't. Your only comment about the FAQ was the incorrect statement that the author didn't contradict the questioner, and you didn't say anything about the mathpages.com page at all.

And then he proceeds to answer the question as if Einstein actually said that.

Well, would you care to explain the basis for your statement "then the theory as it is now defined is wrong"? What obvious flaw do you see in the idea that resistance to acceleration is proportional to total energy in the center-of-mass frame?

Did you read my post completely?

Anyway, I said it would undermine the foundations. Acceleration is measured in the objects rest frame. You want to say that relative velocity in a gravitational potential increases the objects inertia - which means the acceleration would have to be measured in the rest frame of the gravitational potential. But this is kind of meaningless as it assumes the gravitational potential has a rest frame, perhaps it is the rest frame of the massive body creating the potential - OK, sounds acceptable. All of this seems to be pointing to a local ether around massive bodies. SR prohibits local ethers - in fact, it assumes they don't exist.

 

[JesseM]

And then he proceeds to answer the question as if Einstein actually said that.

No he doesn't, the first sentence he writes is "Actually, here's the way it should be said: energy and mass are related." Saying "actually, here's the way it should be said" indicates that the way the questioner said it was incorrect.

You still haven't addressed the mathpages.com page, either.

Did you read my post completely?

Yes, I'm already familiar with that stuff.

Anyway, I said it would undermine the foundations. Acceleration is measured in the objects rest frame.

But for a composite object, there is no frame in which every part of it is at rest. The best you can do is the center-of-mass frame.

You want to say that relative velocity in a gravitational potential increases the objects inertia - which means the acceleration would have to be measured in the rest frame of the gravitational potential.

What are you talking about? I never said anything about looking at the frame of the "gravitational potential" (presumably you mean the frame of the source of this potential?), I said that according to the sources I mentioned, inertia is a function of the total energy in the object's own center-of-mass frame. This would be just as true for an object in empty space being accelerated by some non-gravitational force (or even accelerated by a collision rather than a constant force) as it would be for an object in a gravitational field.

 

[EnumaElish]

The concept of relativistic mass [...] only exists in frames other than the frame of the actual object. You have an infinite number of "relativistic masses" according to your definition.

As a general statement I am with you here. One cannot open up this box (relativistic mass) and then deny this consequence, as far as I am able to follow the subject.

 

[Aer]

You still haven't addressed the mathpages.com page, either.

Yes I did

Yes, I'm already familiar with that stuff.

Apparently you don't understand it.

But for a composite object, there is no frame in which every part of it is at rest. The best you can do is the center-of-mass frame.

You are assuming an objects inertia will increase with an increase in energy content. What is your basis for this? Inertia only increases with mass, and mass is only defined as "rest mass" in physics. "Relativistic mass" is on the fringe edge of physics, in fact, it is not even mentioned in any of my physics textbooks.

*and was never brought up in any physics lecture.

 

[JesseM]

Here is another source saying that the mass of a compound object (the inertial mass, presumably) is proportional to the total energy rather than just the sum of the rest masses--this one is part of the virtual visitor center of Stanford's Linear Accelerator:

In fact Einstein's relationship tells us more, it says Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy.

And http://www.phy.duke.edu/courses/100/lectures/Rel_2/Rel2.html is a page from a Duke University physics course which gives an example involving an inelastic collision:

Example: An Inelastic Collision

* Consider a situation where two identical particles move toward each other along a straight line, with equal speeds. They collide and stick together.

* Conservation of momentum gives

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq22a

from which we conclude that V = 0, so the final object is at rest.
*
* Conservation of total relativistic energy gives

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq23

since V = 0. We thus find

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq24

* Since $$\gamma$$ > 1, this shows that the mass of the final object is larger than the sum of the original masses. The lost kinetic energy has been converted to rest energy (mass).

* The classical explanation for the loss of kinetic energy attributes it to conversion into thermal energy (heat): the final object will have a higher temperature, or more specifically a larger internal energy.

* This suggests that the mass of a compound object is a measure of its total energy content, including thermal energy and the binding energies that hold its atoms or molecules in place.

If the two colliding masses were inside a box, would you say that the inertia of the box would be different before the collision than after, since the rest mass of the combined object is higher than that of the sum of the rest masses of the objects before they collided?

 

[Aer]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

In fact, if you have just 2 objects, 1 inside the other moving at .9c. Do we know for a fact that this kinetic energy will add to the inertia? Would this be a simple test to confirm? Show me the evidence!

 

[JesseM]

Yes I did Your reply ignores the fact that the energy of a composite object is not equal to the sum of the rest energies of all the particles making it up.

You are assuming an objects inertia will increase with an increase in energy content.

I'm not assuming it, I have posted a bunch of sources that say this.

Inertia only increases with mass, and mass is only defined as "rest mass" in physics.

...and you have no source for this, it's just your faulty understanding of what relativity says. It is simply not true that inertia only increases with increases in rest mass in relativity (if it were, then it would be just as easy to accelerate something moving at 0.999999c as it is to accelerate the same object at rest).

"Relativistic mass" is on the fringe edge of physics, in fact, it is not even mentioned in any of my physics textbooks.

That's why I keep saying that we can talk in terms of total energy rather than "relativistic mass" (although given the definitions it's trivial to go back and forth between these). The rest mass of a composite object is equal to the total energy in its center-of-mass frame divided by c^2, and the inertia of a compound object is proportional to its total energy or "rest mass". See? No need to refer to relativistic mass at all. You keep disagreeing with this, although I've now presented four reputable sources to support it and you've presented a big fat zero sources to support your claims.

 

[JesseM]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

I doubt that it's true that there have been no experimental tests of this. But leaving that aside for now, do you agree that the theory of special relativity says that the inertia is proportional to the total energy?

 

[Aer]

Mass has the property that the mass of a compound object is the sum of the mass of the constituents, corrected for binding energy

Is this the same as your "compound object". That was from the first link I clicked on upon doing a search on google.

 

[Aer]

Your inelastic collision example assumes the kinetic energy to be converted to rest energy - it doesn't explicitly say that this is true. If the collision were to really happen, are you saying no energy would be given off upon binding together? I don't think this assumption is correct. You must prove this assumption if you want to use that example.

 

[JesseM]

Mass has the property that the mass of a compound object is the sum of the mass of the constituents, corrected for binding energy

Is this the same as your "compound object". That was from the first link I clicked on upon doing a search on google.

It's unclear whether he's talking about a compound object where the parts are in motion relative to each other, though. I'm also not sure what type of "mass" he's talking about. But I'll send him an email to ask about this.

 

[Aer]

Well he also says "m is frame-independent". I take this to mean that no matter how fast an object is moving, its mass is m - and this is true whether it is contained within another object at rest or not.

 

[Aer]

And doesn't a hot air balloon rise? OK - bad reference.

 

[JesseM]

Your inelastic collision example assumes the kinetic energy to be converted to rest energy - it doesn't explicitly say that this is true. If the collision were to really happen, are you saying no energy would be given off upon binding together?

Sure, it's probably a simplified example, but if the collision happened in a vacuum then energy couldn't escape through soundwaves, so the only other way for it to escape would be through electromagnetic radiation...I suppose the example assumes this loss is negligible. In any case, you could assume the collision happens in a sealed box with mirrored insides, so no energy would escape the box. If the rest mass of the combined object is different than the sum of the rest masses of each object before the collision (photons have zero rest mass, of course), would you say that the inertia of the box will change? Do you think that this is what the theory of relativity would predict?

 

[JesseM]

And doesn't a hot air balloon rise?

What does that have to do with it? A balloon rises because of the buoyancy force--any object in a fluid will experience an upwards force equal to the weight of the volume of fluid it displaces, so the object will rise if this is greater than its own weight.

 

[Aer]

If the rest mass of the combined object is different than the sum of the rest masses of each object before the collision (photons have zero rest mass, of course), would you say that the inertia of the box will change?

You are assuming the assertion that the rest mass of an object is a measure of the total energy of its constituents in posing that question! I'll put it this way, if an experiment was conducted as stated above and the conclusion was that the mass increased, then there would be a basis for the assertion.

Otherwise, it is just that - an assertion. There is no proof one way or the other. However, I choose to go with m being frame independent - which to me, implies the mass of a compound object will be the sum of its constituent's rest masses.

I think we should agree to leave it at that. This discussion is going to go nowhere for either of us I am afraid.

 

[Aer]

What does that have to do with it? A balloon rises because of the buoyancy force--any object in a fluid will experience an upwards force equal to the weight of the volume of fluid it displaces, so the object will rise if this is greater than its own weight.

You must have missed where I said -Bad reference-

 

[εllipse]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

I'm surprised this topic is a source of debate. I would have thought whether or not particles weigh more as they approach the speed of light would have been addressed quite plainly by general relativity. I, however, don't know much about GR so I hope someone who knows how to work the GR equations will jump in and solve this (pervect?). If GR doesn't address this, then somebody needs to fix that. Anyway, here's a little excerpt from The Elegant Universe (page 52):

The faster something moves the more energy it has and from Einstein's formula we see that the more energy something has the more massive it becomes. Muons traveling at 99.9 percent of light speed, for example, weigh a lot more than their stationary cousins. In fact, they are about 22 times as heavy--literally.

Of course, being a layman text, Greene may be using the terms "weigh" and "heavy" very generally (as we can see he uses the term "mass" generally; he's obviously talking about relativistic mass in this text, but he doesn't specifically state so). He might not be talking about how much such things weigh in the Earth's gravitational field (although the fact that he clarifies with the word "literally" seems to indicate that he's not using the term "heavy" in a general context), but just how hard it is to push them faster. Which brings me to another point:

In fact, if you have just 2 objects, 1 inside the other moving at .9c. Do we know for a fact that this kinetic energy will add to the inertia? Would this be a simple test to confirm? Show me the evidence!

What is your explanation for why we can't accelerate particles faster than the speed of light in particle accelerators? The explanation I've heard is this: If we create a large electromagnetic field and accelerate a charged particle, its resistance to further acceleration increases. This means that we'd have to use an even stronger electromagnetic field to accelerate it by the same amount. As the speed of the particle approaches the speed of light (in our reference frame), we require more and more energy to accelerate it, and to push it to the speed of light we would require infinite energy. Why would we require more and more energy? Well, to reiterate, the particle's resistance to acceleration increases, so it takes more energy to accomplish the same amount of acceleration. What's another word for resistance to acceleration? Inertia. And, of course, gravitational mass is another word for inertial mass, and gravitational mass is what decide's a body's weight.

However, I do not know whether "inertia" and "inertial mass" are related. That seems to be the point of possible confusion to me. I hope somebody will clear this up.

And please, don't rail on me, Aer. You asked for a debate; I'm just providing the information I have available to me and hoping for some clarification.

 

[JesseM]

You are assuming the assertion that the rest mass of an object is a measure of the total energy of its constituents in posing that question! I'll put it this way, if an experiment was conducted as stated above and the conclusion was that the mass increased, then there would be a basis for the assertion.

You seem to be shifting the goalposts--originally I took you to be arguing that my and learningphysics' assertions about what the theory of relativity predicts were wrong, not that they were right but that you thought the theory itself was wrong. So once again, are you or are you not disagreeing with the assertion that the theory predicts inertia is proportional to total energy?

Incidentally, here's one piece of evidence--if you have a chemical reaction where heat is given off, the inertial mass of the products will be measured to be slightly less than the inertial mass of the reactants, and the difference in inertial mass turns out to be exactly proportional to the heat energy given off divided by c^2.

 

[JesseM]

You must have missed where I said -Bad reference-

So you were talking about your own example, rather than the webpage you linked to? I thought a "reference" meant an outside source of confirmation.

 

[Aer]

You seem to be shifting the goalposts--originally I took you to be arguing that my and learningphysic's assertions about what the theory of relativity predicts were wrong,

We clearly do not define mass to be the same thing, you say mass is M = γ * m.

I claim mass is m, not M. M is relativistic mass and is mentioned nowhere in any of my physics textbooks, why is that?

Incidentally, here's one piece of evidence--if you have a chemical reaction where heat is given off, the inertial mass of the products will be measured to be slightly less than the inertial mass of the reactants, and the difference in inertial mass turns out to be exactly proportional to the heat energy given off divided by c^2.

They lost energy in binding together - i.e. binding energy, that is no surprise.

 

[Aer]

So you were talking about your own example, rather than the webpage you linked to? I thought a "reference" meant an outside source of confirmation.

It was a joke - nevermind!

 

[Aer]

I'm surprised this topic is a source of debate.

Yes, everyone who assumes relativistic mass to be real is always surprised that relativistic mass is a source of debate.

 

[Aer]

What is your explanation for why we can't accelerate particles faster than the speed of light in particle accelerators?

Read this thread completely! I am not going to repeat myself ad infinitum