I Real life example of the energy contained at E=γmc^2

[ZapperZ]

Do you agree that "rest energy" $E_0$ is "already energy"?

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

 

[Orodruin]

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

No. It is just a matter of unit conversion in terms of the actual SR definitions, which defines mass as the rest energy up to the unit conversion factor $c^2$. That the rest mass then happens to be the inertia in the rest frame is the mass-energy equivalence.

 

[SiennaTheGr8]

Yes, and do you agree that this is not mathematically equal to the rest mass?

Zz.

Yes, but the $c^2$ in the equation $E_0 = mc^2$ is no more than a unit-conversion factor, which we're free to set equal to $1$. The distinction between mass and rest energy is merely an artifact of unnecessarily using different units for energy and mass in the first place. There is no conceptual difference between the quantities at all. They are one and the same property, measured in different units.

 

[Orodruin]

The mass of an electron is more than just an energy content.

It really isn't in terms of how mass is defined in SR.

 

[ZapperZ]

No. It is just a matter of unit conversion in terms of the actual SR definitions, which defines mass as the rest energy up to the unit conversion factor $c^2$. That the rest mass then happens to be the inertia in the rest frame is the mass-energy equivalence.

Yes, but the $c^2$ in the equation $E_0 = mc^2$ is no more than a unit-conversion factor, which we're free to set equal to $1$. The distinction between mass and rest energy is merely an artifact of unnecessarily using different units for energy and mass in the first place. There is no conceptual difference between the quantities at all. They are one and the same property, measured in different units.

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c² "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Please keep in mind that you're talking to someone who is very familiar with calling "ω" or "1/k" as "binding energy". So I get it! But how this fits into the thread at the level that the OP is asking is puzzling, and invoking advanced ideas of mass and energy into something like this is very confusing.

Zz.

 

[SiennaTheGr8]

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c² "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Then are $v$ and $\beta=v/c$ physically different quantities? Are $t$ and $ct$? $p$ and $pc$?

But how this fits into the thread at the level that the OP is asking is puzzling, and invoking advanced ideas of mass and energy into something like this is very confusing.

Yes, this conversation might be better suited for another thread. Cheers.

 

[Orodruin]

Then we are at a disagreement with what is meant by "conversion", because there is a physical difference between "energy" and "mass" from my perspective. Simply calling c2 "merely" a conversion factor doesn't remove the fact that there IS a "conversion" between mass and energy.

Do you also consider time and length to have different dimension? In that case you are missing out on one of the greatest insights of SR. The entire point is that length and time depend on perspective and intrinsically are just a matter of defining directions in a Lorentzian manifold.

To me $c$ in relativity is nothing but a unit conversion factor between things that have the same dimension, just as $k = 2.54$ cm/inch is a conversion factor between different length units.

 

[PeterDonis]

there is a physical difference between "energy" and "mass" from my perspective.

I'm not sure what you think the difference is. For example, when you say:

Take the individual mass of an electron, a proton, a neutron, and then add them all together in the appropriate amount to form all the various elements in the periodic table. Then compare those masses that you have added to the actual masses of each individual element. They are not identical!

This is true, but it leaves out something: where did the difference in mass go? There is still a conservation law involved, so it couldn't just disappear.

In a typical process of this sort--individual constituents coming together to form a bound system--the difference ends up in radiation that is emitted by the system. But "energy" is not synonymous with "radiation": it's a property of radiation (for example, a bunch of photons) just as much as it's a property of "matter" (stuff like electrons, protons, and neutrons). So what is the difference?

The mass of an electron is more than just an energy content. It's presence in itself immediately puts a limit to how fast it can move in any frame.

Here it seems like the key difference is that the electron has nonzero rest mass, while the photon has zero rest mass. (Or, to put it in more fundamental terms, an electron has a timelike 4-momentum, while a photon has a null 4-momentum.) I'll agree that this is a physical difference, but I'm not sure it lines up with the difference between "mass" and "energy".

 

[ZapperZ]

This is true, but it leaves out something: where did the difference in mass go? There is still a conservation law involved, so it couldn't just disappear.

In a typical process of this sort--individual constituents coming together to form a bound system--the difference ends up in radiation that is emitted by the system. But "energy" is not synonymous with "radiation": it's a property of radiation (for example, a bunch of photons) just as much as it's a property of "matter" (stuff like electrons, protons, and neutrons). So what is the difference?

I didn't say there isn't a conservation law here. The "mass difference" is the example I was giving the OP that the missing mass goes into the nuclear binding energy of the atom, i.e. a "real life example" (remember the original title?).

I'm surprised I'm being given a lesson in this. This is a standard General Physics material in an undergraduate textbook.

Zz.

 

[PeterDonis]

The "mass difference" is the example I was giving the OP that the missing mass goes into the nuclear binding energy of the atom.

But it doesn't; the binding energy is negative* (because the mass of the nucleus is less than the sum of the masses of the constituents). So, heuristically, the binding energy gets "taken out" of the constituents, and has to go somewhere else. Where does it go? That's the question I asked (and answered for a typical process), and which has to be answered to see how conservation laws are satisfied.

[*Edit: Negative if we're using the implicit sign convention we've been using, which is different from the sign convention that is often used for binding energy in textbooks.]

I'm surprised I'm being given a lesson in this. This is a standard General Physics material in an undergraduate textbook.

The process itself is, yes. But I'm trying to understand what, specifically, you think the physical difference between "energy" and "mass" is. I don't think that specific question is treated in undergraduate textbooks (and as you can see, I'm not the only one in this thread who is asking it).

 

[ZapperZ]

But it doesn't; the binding energy is negative* (because the mass of the nucleus is less than the sum of the masses of the constituents). So, heuristically, the binding energy gets "taken out" of the constituents, and has to go somewhere else. Where does it go? That's the question I asked (and answered for a typical process), and which has to be answered to see how conservation laws are satisfied.

[*Edit: Negative if we're using the implicit sign convention we've been using, which is different from the sign convention that is often used for binding energy in textbooks.]

OK... I do not see why this is an issue. This is the reason why the mass of the atom is less than the mass of the individual constituents added together. Isn't this a clear example of E=mc² that the OP was asking waaaaaaaay back in Post #1? I gave that example not to show the difference between mass and energy, but to provide a simple example that the OP might be able to understand.

The process itself is, yes. But I'm trying to understand what, specifically, you think the physical difference between "energy" and "mass" is. I don't think that specific question is treated in undergraduate textbooks (and as you can see, I'm not the only one in this thread who is asking it).

But I've already stated earlier about the specific limits to speed in mass, etc., which Orodruin disagreed. But go back to why I got into this in the first place. It was because of the semantic reason that somehow describing the process that energy and mass can be converted into another becomes a "pet peeve"! Considering the level of this thread, I argued that it should not be! Trying to get e-p pair out of gamma photons is a painful "conversion"! And in the back of my mind, I'm reminded of all the threads that we've had on this forum of people claiming that electrons, etc. are nothing more than just clumps of energy, while ignoring all the other attributes associated with these particles beyond just the energy content. Maybe it is silly to think about what someone could use this thread for later on, but it won't be the first time that someone misunderstands a thread on here.

Zz.

 

[PeterDonis]

Trying to get e-p pair out of gamma photons is a painful "conversion"!

Sure. But is it a conversion of "mass" to "energy"? Or is it a conversion of, well, an e-p pair into a pair of gamma photons? The latter description seems to me to be much less subjective, as well as less likely to be misunderstood.

 

[ZapperZ]

Sure. But is it a conversion of "mass" to "energy"? Or is it a conversion of, well, an e-p pair into a pair of gamma photons? The latter description seems to me to be much less subjective, as well as less likely to be misunderstood.

But that plays right into what I said earlier that the conservation laws with these "mass-energy conversion" process involves more than just mass-energy conservation. Certainly, for e-p to gamma, you have charge and momentum conservations to take care of as well. I know that these are external issues to the mass-energy equivalent, but I'm looking at the entire process and consider that, semantically, I do not see why calling this a "conversion" is wrong or make it someone's pet peeve. I mean, I don't go around and announcing that it is my pet peeve when someone claims that photon energy less than a work function cannot emit a photoelectron, even though I have done it numerous times! At some point, the level of the discussion (and the OP) requires us to hold back the whole, advanced picture.

Zz.

 

[SiennaTheGr8]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

 

[ZapperZ]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

 

[Orodruin]

I dislike "mass is converted to energy" because it suggests that the energy wasn't there in the first place. Really it's always a conversion of one type of energy to another.

The big problem is that "energy" in many layman conversations refer to "usable energy" in the sense of energy available to do work on something I need to do work on. This often translates into laymen thinking that energy is some sort of substance that can be produced.

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

I do not think it is to be overly picky. The misconception that energy is some form of substance is a something that it takes years to pull out of many university students.

 

[SiennaTheGr8]

I'm glad you said that. Next time someone accuses me of being overly picky, I'll point to this one.

Zz.

Please do! It might help someone who's struggling to understand this stuff.

 

[Sorcerer]

their statement wasn't wrong at all, the interpretation of the question was. Mister T has allot of great replies to questions and has enlightened me a number of times.

To be even more clear, surely the OP is, like the vast majority of people, used to "chemical energy", and in turn the concept of energy density.

They are not "one and the same", they are equivalent...clearly on opposite sides of the equation.

Well, in terms of the equation. What is mass? Energy ultimately is just a concept, but so is mass. It's mostly space, made up of little sub-atomic particles, and of course, energy, and what are those exactly? What are they made of? Quarks, etc?

Obviously that's unanswered at the moment. But I mean, point is, why and how could one be larger than the other? What does "larger" even mean in that context? Magnitude? (mc²)² literally IS the magnitude of the energy-momentum equation, isn't it?
E² - (pc)² = (mc²)², right?

 

[nitsuj]

Well, in terms of the equation. What is mass? Energy ultimately is just a concept, but so is mass. It's mostly space, made up of little sub-atomic particles, and of course, energy, and what are those exactly? What are they made of? Quarks, etc?

Obviously that's unanswered at the moment. But I mean, point is, why and how could one be larger than the other? What does "larger" even mean in that context? Magnitude? (mc²)² literally IS the magnitude of the energy-momentum equation, isn't it?
E² - (pc)² = (mc²)², right?

 

[sweet springs]

As a real life example nuclear fuel get lighter after spent in power station.

 

[Orodruin]

The big problem is that "energy" in many layman conversations refer to "usable energy" in the sense of energy available to do work on something I need to do work on.

To add to this, I believe this is exactly what the OP has run into based on this:

But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

In the colloquial use, energy is what is "produced by power plants" and it therefore becomes a barrier when laymen are faced with energy as being a property of things and certainly not being something that can be produced.

 

[Herman Trivilino]

Matter is just an informal word meaning stuff that has mass, isn't it?

If so then a pair of photons could be called matter in some reference frames but not in others. A single photon would not be matter in any reference frame.

In any case, the Einstein mass-energy equivalence teaches us that mass is not a measure of the quantity of matter.

 

[Orodruin]

If so then a pair of photons could be called matter in some reference frames but not in others.

The square of the total 4-momentum of the photons is invariant.

 

[Herman Trivilino]

The square of the total 4-momentum of the photons is invariant.

Ahhh... yes. I didn't explain my thoughts correctly. If the pair of photons are co-moving their mass is zero (in all frames) but if not then they have a nonzero mass (which has the same value in all frames). So what I should have said is that a pair of photons may or may not have mass, depending on how they are moving. Not on the reference frame.

 

[gnnmartin]

I think the equation e=mc^2 should be interpreted as telling us that energy has mass, not that mass is energy. Mass is the unambiguous term, defined by Newton's laws. Energy is ambiguous, since it implies something usable, but its usability depends on the state of our technology and our intentions, and anyhow the usability is limited by the laws of thermodynamics.

 

[weirdoguy]

Mass is the unambiguous term, defined by Newton's laws.

You are mixing non-relativistic and relativistic mechanics. Mass (squared) in relativity is defined as a norm of momentum 4-vector. It has nothing to do with Newton's laws.

Energy is ambiguous

No it's not.

 

[SiennaTheGr8]

Energy is ambiguous, since it implies something usable

As @Orodruin pointed out earlier in this thread, this is a common misconception. "Usability" is a red herring. Conservation is the ticket.

 

[Philip Koeck]

We've just begun studying about relativity, and I find it amazing that bodies have the energy of E=γmc^2. Even at rest they have E=mc^2.
But where exactly is this energy present in real life? For example the keyboard I am currently typing this post with has a huge amount of energy, according to this equation, but how is it usable?

Hi Foruer. I'm not sure if anyone has given similar answers since I haven't looked through the list. Anyway: One example is something I calculated in a University course. We were given some information about the total radiation from the sun and asked to calculate how much lighter the sun gets per year. This is quite an everyday thing I would say. All the energy radiated off by the sun leads to a tremendous mass loss. Another example is of course particle-antiparticle annihilation. There the energy of the photons produced is equal to the sum of relativistiv masses times c squared.Hope that helps.

 

[Ibix]

Mass is the unambiguous term, defined by Newton's laws.

Defining the concepts of a more precise theory in terms of the concepts of a less general, less precise, theory seems back to front. Relating the terms is fine (e.g. $(\gamma-1) mc^2\simeq mv^2/2$ implying that this is the correct expression for KE) is fine, but don't mistake that for definition.

I think that $E=mc^2$ is effectively the definition of mass in relativistic terms. It's the modulus of the energy-momentum four-vector, which is a conserved quantity you can relate directly to experiment. It happens to be interpretable as a generalisation of what Newton would call mass.

 

[Ibix]

There the energy of the photons produced is equal to the sum of relativistiv masses times c squared.

...or equal to the sum of the total energies of the particles, if you are trying to avoid the term "relativistic mass" (which is the modern convention).