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Infinity.

paug

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HR - did you ever get past high school or freshman physics?

Probably not. He sure does like to fling the terms around though, while COMPLETELY lacking an understanding in what he's saying. If you don't grasp the basic concepts of physics, you shouldn't be tackling a "problem" like this. Not that I know what the problem/purpose of this thread even is - HR's posts are getting more and more desultory and nonsensical.
 
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pgp_protector

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ArnautDaniel

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Where as
1) Anything without boundaries must be infinite
2) HR's lack of scientific understanding knows no bounds

Therefore HR must poses infinite ignorance of science.

QED

I think you may have found the first non-mathematical infinity in this thread.

:thumbsup:
 
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Holy Roller

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About your last paragraph - do you have any sources on this? It almost sounds like supersymmetry meets nuclear fission. And yeah, the antiparticle out of nowhere is a little bizarre. The idea of a process that's required to create a surplus of usable energy that also involves making exact duplicates of reactants beforehand? Also, how would annihilation give the same energy output (should really give a lot more) and somehow leave barium and krypton nuclei behind? Annihilation doesn't really like matter leftovers! Perhaps reading the sources will clear things up a little...

I think the basic idea that things that are illegal in classical mechanics can be legal in QM. Knowing that, the idea says that when the mass gets accelerated to near light-speed (hence acqires near-infinite mass), statistics takes over and allows this E=MC2 to happen, provided the energy presents itself from the mass before it can even be observed.
We also see violations of this type in the virtual vacuum, where particles and antiparticles materialize and annihilate so quickly that the process--illegal in CM--takes place without the possibility of observing it.

As for the rest of this quote - I'm sorry, but I still can't accept it. You're talking about the masses becoming infinite before becoming energy - the problem with this is, the only way they're going to gain mass (via relativity) is for enough energy to be supplied to them in the first place. If you claim the reactants reach an infinite mass, then conservation laws alone require that an infinite amount of mass/energy be supplied to the reactants. Again, it requires sourcing an impossible amount of energy and upon fission the release of an incredibly fatal amount of energy for all existence.


I have to make the distinction between rest mass and relativistic mass.




The increase in effective
mass with speed is given by the expression


mrele.gif


It follows from the Lorentz transformation when collisions are described from a fixed and moving reference frame, where it arises as a result of conservation of momentum.

For v = 1 c, m =infinite m0


The increase in relativistic effective mass makes the
speed of light c the speed limit of the universe. This increased effective mass is evident in cyclotrons and other accelerators where the speed approaches c. Exploring the calculation above will show that you have to reach 14% of the speed of light, or about 42 million m/s before you change the mass by 1%.




What I did is I entered the number "1" for v (the speed of the massive particle), which as you can see is the speed of light. Notice how the Lorentz Transformation generated an "Infinity" as the result. That means that if you accelerate a particle to the speed of light, its mass becomes infinite. I didn't say this; Albert Einstein said it.​


So what happens to your "incredibly fatal amount of energy for all existence?" Since mass is simply defined as, "A resistance to a change in motion," there is nothing fatal about the amount of this energy; the mass, when it = c, simply becomes resistant to any further attempts at changing its' motion, that's all. If we have an infinite gravitational mass, then things might get scary. But in the meantime, we're discussing inertial and not gravitational masses. There is a difference.​

Inertial mass = resistance to a change in motion. If it's infinite, no big deal.
Gravitational mass = how much you weigh. IF it's infinite, then the Universe has problems.​

You keep saying that the mass becoming infinite and in doing so transforms into energy.
Yes, per the equation above (Einsteins not mine so don't blame me).
Maybe I should point out that the E and p Lorentz transforms don't actually apply to photons?
Or anything else that moves at light-speed for that matter. P=0 when v=c.
I'm assuming you got them from the wikipedia article on the Lorentz factor, it's further down the page. Sorry if you knew this already, but from trying to determine your train of thought, it seems like you think that the gamma photons have to follow the E and p Lorentz transforms too, and the only way to do that is to have the initial reactant mass go to infinity to get an appropriate Lorentz factor - but that isn't necessary as the E and p transforms will never apply to photons. Is this in any way relevant to what you were thinking? Actually, I wasn't really suggesting anything gravitational. I just thought "infinite yield explosion = BAD." ;)

Again, when v = c, P will always = 0. For this reason there was a misinterpretation on your part with regards to how you thought I was interpreting the lorentz contractions.



I'm glad you mentioned black holes. It's already been pointed out that they don't contain infinite mass,

You're correct and I am guilty in being unclear. Black holes can't have infinite gravitational mass. Why? Because the idea would violate conservation laws, that's why. If a very large star collapses to make a black hole, then the gravitational mass of that new black hole can only be as much as the mass of the star that did the collapsing; increasing gravitational mass to the system violates conservation of mass.

A black hole does have infinite inertial mass, however. That's why a black hole's density may also be infinite.
In other words, it's technically impossible to move a black hole using any means. Whichever direction the star was moving at the time of its collapse, that's the direction it will move and continue to move as a black hole.​



but from the POV of someone being pulled into one at their very centre they have a gravitational singularity where density appears to go to infinity (again, black holes really aren't my strong point, so I'm loth to say that this is a good example of an infinity, maybe it's just apparently present because our understanding of the laws of physics breaks down at that point in spacetime).
So maybe we'll end up talking about black holes now - but I have to say, HR, I think we're all curious to know what the overarching point of this thread is?​






The point of this thread is? To discuss infinity, my good chap! :D:thumbsup:





More instances of infinity, BTW:​



As the object passes through the event horizonFrom the viewpoint of the falling object, nothing particularly special happens at the event horizon. In fact, there is no (local) way for him to find out whether he has passed the horizon or not. An infalling object takes a finite proper time (i.e. measured by its own clock) to fall past the event horizon. This in contrast with the infinite amount of time it takes for a distant observer to see the infalling object cross the horizon.?


 
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ArnautDaniel

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I'm confused, are you all using v for velocity or volume?

Normally if density = m/v you mean that v is the volume.

But then I keep seeing all these equations using v for velocity.

Or is v a volume going to zero as the velocity goes to that of light?
 
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Belk

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You're correct and I am guilty in being unclear. Black holes can't have infinite gravitational mass. Why? Because the idea would violate conservation laws, that's why. If a very large star collapses to make a black hole, then the gravitational mass of that new black hole can only be as much as the mass of the star that did the collapsing; increasing gravitational mass to the system violates conservation of mass.

A black hole does have infinite inertial mass, however. That's why a black hole's density may also be infinite.
In other words, it's technically impossible to move a black hole using any means. Whichever direction the star was moving at the time of its collapse, that's the direction it will move and continue to move as a black hole.​

[/left]

So all black holes are moving at the speed of light?

http://van.physics.uiuc.edu/qa/listing.php?id=1411
 
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[serious]

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I think the basic idea that things that are illegal in classical mechanics can be legal in QM. Knowing that, the idea says that when the mass gets accelerated to near light-speed (hence acqires near-infinite mass), statistics takes over and allows this E=MC2 to happen, provided the energy presents itself from the mass before it can even be observed.
We also see violations of this type in the virtual vacuum, where particles and antiparticles materialize and annihilate so quickly that the process--illegal in CM--takes place without the possibility of observing it.
There is no such thing as "near infinite mass" Any finite mass is infinitely distant from infinite mass. We do see increases in apparent mass at high velocities of course. This has NOTHING to do with statistics so I'm not sure why that's in there. E=MC^2 "happens" regardless of velocity by the way. In fact, relativistic effects (the phrase you were looking for) happen at any velocity. Since all motion is relative, there exists both a rest frame and a multitude of non rest frames for any object. As far as the energy of the vacuum (the term for the spontaneous creation and destruction of virtual particles and antiparticles) that has nothing to do with E=MC^2 so again, I'm not sure why you are bringing it up.

THe whole paragraph reads like a word salad. You bounce around between unrelated topics misusing terms and failing to tie the disjointed concepts together.
I have to make the distinction between rest mass and relativistic mass.


What I did is I entered the number "1" for v (the speed of the massive particle), which as you can see is the speed of light. Notice how the Lorentz Transformation generated an "Infinity" as the result. That means that if you accelerate a particle to the speed of light, its mass becomes infinite. I didn't say this; Albert Einstein said it.​
It is impossible to accelerate any massive particle to the speed of light. This would require an infinite amount of energy. Photons travel the speed of light only by virtue of being massless particles.
So what happens to your "incredibly fatal amount of energy for all existence?" Since mass is simply defined as, "A resistance to a change in motion," there is nothing fatal about the amount of this energy; the mass, when it = c, simply becomes resistant to any further attempts at changing its' motion, that's all. If we have an infinite gravitational mass, then things might get scary. But in the meantime, we're discussing inertial and not gravitational masses. There is a difference.​
Gravitation works on relativistic mass. We have observed proof of this via gravitational lensing. if a massive particle reaches the speed of light, it will have infinite energy, infinite mass, and infinite gravitation.
Inertial mass = resistance to a change in motion. If it's infinite, no big deal.
Gravitational mass = how much you weigh. IF it's infinite, then the Universe has problems.​
and what, pray tell, do you think the difference between the two is?

Yes, per the equation above (Einsteins not mine so don't blame me).
No. This has already been explained to you by numerous people numerous times. The energy of any particle/system is finite The mass of any particle/system is finite. In fact, the total energy (including mass) of a system is invariant in any given inertial reference frame.

And I'm sorry, some one else can sort out the rest of the mess you've posted.​
 
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Holy Roller

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So all black holes are moving at the speed of light?

http://van.physics.uiuc.edu/qa/listing.php?id=1411

The general idea is that when the infinite inertial mass of the black hole turns into energy IAW E=MC2, then that energy gets drawn back into the black hole, as it cannot escape that event horizon. For this reason an infinitely massive black hole may remain perfectly massive and non-energetic.
 
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Holy Roller

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[serious];48949445 said:
There is no such thing as "near infinite mass" Any finite mass is infinitely distant from infinite mass. We do see increases in apparent mass at high velocities of course. This has NOTHING to do with statistics so I'm not sure why that's in there. E=MC^2 "happens" regardless of velocity by the way. In fact, relativistic effects (the phrase you were looking for) happen at any velocity. Since all motion is relative, there exists both a rest frame and a multitude of non rest frames for any object. As far as the energy of the vacuum (the term for the spontaneous creation and destruction of virtual particles and antiparticles) that has nothing to do with E=MC^2 so again, I'm not sure why you are bringing it up.

THe whole paragraph reads like a word salad. You bounce around between unrelated topics misusing terms and failing to tie the disjointed concepts together. It is impossible to accelerate any massive particle to the speed of light. This would require an infinite amount of energy. Photons travel the speed of light only by virtue of being massless particles. Gravitation works on relativistic mass. We have observed proof of this via gravitational lensing. if a massive particle reaches the speed of light, it will have infinite energy, infinite mass, and infinite gravitation. and what, pray tell, do you think the difference between the two is?No. This has already been explained to you by numerous people numerous times. The energy of any particle/system is finite The mass of any particle/system is finite. In fact, the total energy (including mass) of a system is invariant in any given inertial reference frame.

And I'm sorry, some one else can sort out the rest of the mess you've posted.

Usually when someone starts saying something like, "What you're saying sounds like word salad. You aren't making any sense! Can you please clarify this?! You don't know what you're talking about!" it's always symptomatic of intellectual pride. The general idea being that the individual is just skimming over the unclear post without reading it, thinking, "this guy doesn't know what he's talking about, so I'll just skim through it to look for things to criticize..." The truth of the matter, however, is it's always the guy with the intellectual pride who has the stunted intellect. As you will learn in the proceeding posts (and further research on your part), you were premature to criticize my postings. Intellectual pride (all of it unwarranted, BTW) will further prevent you from issuing the apology.
Only critical, forced reading on your part will get you to this position (the position of learning you are wrong, followed by you learning something new, and my position). Will you let yourself think critically for once? Or, are you just going to skim through this post of mine like you did all the other ones?

Here is what I said that induced the confusion. I'll go through it step-by-step:

I think the basic idea that things that are illegal in classical mechanics can be legal in QM.
Something like spontaneous particle/antiparticle creation is illegal in classical mechanics but legal in quantum mechanics. Classical mechanics is that branch of physics up to but not including relativity, time-wise.
Knowing that, the idea says that when the mass gets accelerated to near light-speed (hence acquires near-infinite mass), statistics takes over and allows this E=MC2 to happen, provided the energy presents itself from the mass before it can even be observed.
QM (Quantum Mechanics) is a purely statistical enterprise. Determining where photons land on a screen in a diffraction experiment is determined by statistics, because we can never know where photons land on a screen. We can only use something called sum over histories to get an approximation where the photons will land. Because of this, QM becomes a science of statistics. So when I said, "Statistics takes over", I mean uncertainty with regards to the mass (infinite or finite?) of the particle takes over; we can't know with certainty (and never can) whether or not the particle acquires infinite mass before turning into energy during the E=MC2 process.
We also see violations of this type in the virtual vacuum, where particles and antiparticles materialize and annihilate so quickly that the process--illegal in CM--takes place without the possibility of observing it.
Again, I reaffirm the idea that illegal phenomena that happens according to classical mechanics is legal in quantum mechanics. Again, I use the idea of virtual particle pairs.
I have to make the distinction between rest mass and relativistic mass.
What I did is I entered the number "1" for v (the speed of the massive particle), which as you can see is the speed of light. Notice how the Lorentz Transformation generated an "Infinity" as the result. That means that if you accelerate a particle to the speed of light, its mass becomes infinite. I didn't say this; Albert Einstein said it.​
Rest mass is different than relativistic mass. The former is the mass of an inertial reference frame that's not really moving very fast compared to the reference frame that's carrying out the observation on it. The latter--relativistic mass--is a mass that is moving and accelerating very quickly relative to the person observing it.
I entered v=c in the program at hyperphysics.com and it outputted "infinity."
So what happens to your "incredibly fatal amount of energy for all existence?" Since mass is simply defined as, "A resistance to a change in motion," there is nothing fatal about the amount of this energy; the mass, when it = c, simply becomes resistant to any further attempts at changing its' motion, that's all. If we have an infinite gravitational mass, then things might get scary. But in the meantime, we're discussing inertial and not gravitational masses. There is a difference.

Inertial mass = resistance to a change in motion. If it's infinite, no big deal.
Gravitational mass = how much you weigh. IF it's infinite, then the Universe has problems.
Here I illustrate the difference between inertial and gravitational masses. One requires an acceleration, the other does not.
Yes, per the equation above (Einsteins not mine so don't blame me).
Or anything else that moves at light-speed for that matter. P=0 when v=c.
Again, when v = c, P will always = 0. For this reason there was a misinterpretation on your part with regards to how you thought I was interpreting the lorentz contractions.
Here I tell Cabal that everything I am discussing is extrapolated from Einstein's equations and not my own.
I inputted values into his equations and got infinity as a result.
I didn't say mass becomes infinite before it turns into energy, Einstein said it. He has my unbounded admiration because so.


You're correct and I am guilty in being unclear. Black holes can't have infinite gravitational mass. Why? Because the idea would violate conservation laws, that's why. If a very large star collapses to make a black hole, then the gravitational mass of that new black hole can only be as much as the mass of the star that did the collapsing; increasing gravitational mass to the system violates conservation of mass.
A black hole does have infinite inertial mass, however. That's why a black hole's density may also be infinite.
In other words, it's technically impossible to move a black hole using any means. Whichever direction the star was moving at the time of its collapse, that's the direction it will move and continue to move as a black hole.​
Here I clarify my discussion on masses, and that I should have said "gravitational mass" or "inertial mass" when discussing the mass of a black hole.

I hope this helps. If it doesn't, you are either still reading it too fast, or your understanding of these matters is below what is required for you to participate constructively in this thread.
Everything I have been discussing is on an elementary, layman level. I can't see why we are having the problems in comprehension.
 
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Radagast

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The inverse square law ...

And given the inverse square law, an infinite mass would exert an infinite force on everything in the universe, which would then collapse.
 
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Holy Roller

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And given the inverse square law, an infinite mass would exert an infinite force on everything in the universe, which would then collapse.

Lulz...
At least you're beyond saying "The inverse square law of the gravitational field is..."
 
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Holy Roller

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Poe's Law states:
“ Without a winking smiley or other blatant display of humor, it is impossible to create a parody of Fundamentalism that SOMEONE won't mistake for the real thing"[1] ” Poe's Law relates to fundamentalism, and the difficulty of identifying actual parodies of it. It suggests that, in general, it is hard to tell fake fundamentalism from the real thing, since they both sound equally ridiculous. The law also works in reverse: real fundamentalism can also be indistinguishable from parody fundamentalism. For example, some conservatives consider noted homophobe Fred Phelps to be so over-the-top that they think he's a "deep cover liberal" trying to discredit more mainstream homophobes.
 
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Cabal

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I think the basic idea that things that are illegal in classical mechanics can be legal in QM. Knowing that, the idea says that when the mass gets accelerated to near light-speed (hence acqires near-infinite mass), statistics takes over and allows this E=MC2 to happen, provided the energy presents itself from the mass before it can even be observed.
We also see violations of this type in the virtual vacuum, where particles and antiparticles materialize and annihilate so quickly that the process--illegal in CM--takes place without the possibility of observing it.

Still not really sounding too plausible to me - got any links to papers on this stuff?

I have to make the distinction between rest mass and relativistic mass. What I did is I entered the number "1" for v (the speed of the massive particle), which as you can see is the speed of light. Notice how the Lorentz Transformation generated an "Infinity" as the result. That means that if you accelerate a particle to the speed of light, its mass becomes infinite. I didn't say this; Albert Einstein said it. So what happens to your "incredibly fatal amount of energy for all existence?" Since mass is simply defined as, "A resistance to a change in motion," there is nothing fatal about the amount of this energy; the mass, when it = c, simply becomes resistant to any further attempts at changing its' motion, that's all. If we have an infinite gravitational mass, then things might get scary. But in the meantime, we're discussing inertial and not gravitational masses. There is a difference.

I see where you're getting the m -> infinity from. However, my objection isn't with the maths, it's with the conclusion. The correct conclusion is, you physically can't get anything with nonzero m to travel at c. The rest of my objection regarding energy output is related to my general bewilderment at the idea that for every single U236 fission, we need to supply an infinite amount of energy to increase the reactant velocity to c, and all that comes out is a piddly 200 MeV and a few nuclei?

You're correct and I am guilty in being unclear. Black holes can't have infinite gravitational mass. Why? Because the idea would violate conservation laws, that's why. If a very large star collapses to make a black hole, then the gravitational mass of that new black hole can only be as much as the mass of the star that did the collapsing; increasing gravitational mass to the system violates conservation of mass.

A black hole does have infinite inertial mass, however. That's why a black hole's density may also be infinite. In other words, it's technically impossible to move a black hole using any means. Whichever direction the star was moving at the time of its collapse, that's the direction it will move and continue to move as a black hole.

http://en.wikipedia.org/wiki/Inertia

Really need to interject here - there is no difference between gravitational and inertial mass. Einstein actually said as such, in fact, it's pretty much the fundamental basis of GR.
 
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necroforest

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(no, i didn't read every page so this is probably in there somewhere)

Consider the open interval (0,1) [which is the set of all real numbers x such that 0 < x < 1].
1. This interval is finite (it has an upper and lower bound)
2. This set is of infinite cardinality (it has an infinite number of members)
3. This set has no maximum value - for every number in the set, there are an infinite number of numbers that are greater than that number.
4. This set has no minimum value - same thing, except 'less than'
5. This set has more elements than the seemingly 'more infinite' set of the integers (..., -2, -1, 0, 1, 2, ...)
 
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Wiccan_Child

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(no, i didn't read every page so this is probably in there somewhere)

Consider the open interval (0,1) [which is the set of all real numbers x such that 0 < x < 1].
1. This interval is finite (it has an upper and lower bound)
2. This set is of infinite cardinality (it has an infinite number of members)
3. This set has no maximum value - for every number in the set, there are an infinite number of numbers that are greater than that number.
4. This set has no minimum value - same thing, except 'less than'
5. This set has more elements than the seemingly 'more infinite' set of the integers (..., -2, -1, 0, 1, 2, ...)
To generalise necroforest's last point: some infinities are larger than others. There are an infinite number of positive integers, and there are an infinite number of negative integers. But the number of integers (positive, negative, and other) is larger still, and is infinite. Thus, the former infinities are smaller than the latter infinity. Confusing? It should be: it drove Georg Cantor mad (allegedly...).
 
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Holy Roller

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Still not really sounding too plausible to me - got any links to papers on this stuff?
I see where you're getting the m -> infinity from. However, my objection isn't with the maths, it's with the conclusion. The correct conclusion is, you physically can't get anything with nonzero m to travel at c. The rest of my objection regarding energy output is related to my general bewilderment at the idea that for every single U236 fission, we need to supply an infinite amount of energy to increase the reactant velocity to c, and all that comes out is a piddly 200 MeV and a few nuclei?
http://en.wikipedia.org/wiki/Inertia
Really need to interject here - there is no difference between gravitational and inertial mass. Einstein actually said as such, in fact, it's pretty much the fundamental basis of GR.
Read your P/M inbox as far as my source is concerned. There's a dimwit over there too who's pestering me in a different thread, kinda like a couple dimwits on this thread, and I certainly don't want the dimwits here going over there to cause further problems.
I also don't think it's plausible but the poster I identified in my P/M to you does. As far as inertial v. gravitational mass is concerned, they are identical with the exception being that you can have a purely gravitational mass of a certain amount acting on matter in its usual way. Inertial mass, on the other hand, is a function of accelerations impressed on it. Thus we do have a distinction between the two.
Light would bend in an accelerating elevator and a high-power gravitational source. Remove the acceleration of the elevator and you remove the bending of the light. There is no removing the high-power gravitational source; the bending of the light ray always remains.
 
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Cabal

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Read your P/M inbox as far as my source is concerned. There's a dimwit over there too who's pestering me in a different thread, kinda like a couple dimwits on this thread, and I certainly don't want the dimwits here going over there to cause further problems.
I also don't think it's plausible but the poster I identified in my P/M to you does. As far as inertial v. gravitational mass is concerned, they are identical with the exception being that you can have a purely gravitational mass of a certain amount acting on matter in its usual way. Inertial mass, on the other hand, is a function of accelerations impressed on it. Thus we do have a distinction between the two.
Light would bend in an accelerating elevator and a high-power gravitational source. Remove the acceleration of the elevator and you remove the bending of the light. There is no removing the high-power gravitational source; the bending of the light ray always remains.

The response you're talking about, in response to your query whether or not the mass of the reactants goes to infinity was:

"This isn't a case of a sublight particle being accelerated to lightspeed, but of one type of particle being annihilated and another being created, akin to what happens when antimatter and matter annihilates and produces high-energy photons. Particle creation/annihilation is something that is allowed by the rules of quantum field theory."


Well, he does say that fission doesn't involve particles being accelerated to lightspeed, which is the only way that you'd get infinite mass in this way. But anyway, onto the quantum field theory stuff.

My take on this is that he was using annihilation as an analogous process. However, there are no infinities involved with annihilation either, and pair production usually does require the existence of at least the two rest masses' worth of energy floating around. Any more than that goes into kinetic energy. Now, maybe things are different when it comes to near-c speeds. But at this stage my knowledge ends, as I've only just started studying QFT this semester, and we're taking it from the condensed-matter physics approach rather than the particle-physics approach. Interesting, but not really helpful for this discussion....

As for inertial/grav mass, I was under the impression that they were more theoretical constructs than anything else, both describing the same thing.

I still keep coming back to the issue of the Lorentz factor when I think about this discussion - maybe it's different people thinking in different ways, but what is it about mass tending to infinity as v-> c that seems plausible to you (aside from the fact that crunching the numbers can output a mathematical infinity as part of a divide by zero error)? How exactly do you resolve the fact that doing work on an infinite mass requires an input of infinite energy?
 
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Holy Roller

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What is it about mass tending to infinity as v-> c that seems plausible to you (aside from the fact that crunching the numbers can output a mathematical infinity as part of a divide by zero error)? How exactly do you resolve the fact that doing work on an infinite mass requires an input of infinite energy?
I never did resolve it, and I'm in my late 30's.
Ever since I was in my early teens, I always wondered how the E=MC2 in fission played out. I was told that fission was an E=MC2 process, and was also told that this meant the mass of the particles involved (including subatomic ones) turned into energy thru this E=MC2 process.
That necessarily meant that the mass of the particles that will turn into energy has to go to infinity.
The sources I read never explained how that was so. I figured that there was some kind of localized condition that was met that propelled thru acceleration the mass that would ultimately reached infinity. Since this condition was localized on the quantum level I thought, then this infinite mass would never see its effect seen outside its locality, which would be the size of the uranium atom itself.

This is as far as I went with the idea until I started this Infinity thread on CF...
 
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