Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Gene Heskett]

On Saturday 05 March 2016 08:11:46 Oscar Benjamin wrote:

> On 5 March 2016 at 02:51, Gregory Ewing  
wrote:
> >  The masslessness of photons comes from an extrapolation
> >
> >> that leads to a divide by infinity: strictly speaking it's just
> >> undefined.
> >
> > No, it's not. The total energy of a particle is given by
> >
> >E**2 == c**2 * p**2 + m**2 * c**4
> >
> > where p is the particle's momentum and m is its mass.
> > For a photon, m == 0. No division by zero involved.
> >
> > For a massive particle at rest, p == 0 and the above
> > reduces to the well-known
> >
> >E == m * c**2
>
> The distinction I'm drawing is between physical fact and mathematical
> convenience. For other particles we can say that the 1st formula above
> holds with m taken to be the mass of the particle at rest. We can
> extend that formula to the case of photons which are never at rest by
> saying that in the case of photons m=0. That's nice and it's
> mathematically convenient in the calculations. It's analogous to
> extending the natural definition of the factorial function by saying
> that 0!=1. We can't prove that 0!=1 but it's useful to define it that
> way. It wouldn't be a disaster to simply leave 0! undefined: it would
> just make some equations a little more complicated.
>
> Since the generally accepted physical fact is that photons are never
> at rest we are free to define their "rest mass" (use any term you
> like) to be anything that is mathematically convenient so we define it
> as zero because that fits with your equation above. Turning full
> circle we can then use the equation above to say that they are
> massless since they would hypothetically be massless in some other
> situation even though genuinely massless photons are not thought to
> exist in physical reality (unless I'm really out of date on this!).
>
> >> Something I don't know is if there's some theoretical reason why
> >> the binding energy could never exceed the sum of the energies of
> >> the constituent particles (resulting in an overall negative mass).
> >
> > Conservation of energy would be one reason. If you
> > put two particles together and got more energy out than
> > went in, where did the extra energy come from?
>
> That's the point: the energy balance would be satisfied by the
> negative energy of the bound particles. The binding energy can be
> defined as the energy required to unbind the particles (other
> definitions such as André's are also possible). From this definition
> we see that the binding energy depends on the binding interaction
> (electromagnetic or whatever) that binds the particles together.
>
> The only examples I know of where the binding energy is computed
> approximately for e.g. a hydrogen atom predict that the binding energy
> is proportional to the (rest) mass of the bound particle(s). If it's
> guaranteed that the binding energy always somehow comes out
> proportional to the mass of the particles with a coefficient
> necessarily smaller than 1/c**2 then you could say that the bound
> product could never have negative energy. I just can't see off the top
> of my head an argument to suggest that this is impossible.
>
> --
> Oscar

I've never heard of a massless photon, and they do exert a push on the 
surface they are reflected from, its even been proposed to use it as a 
space drive.  The push is miniscule indeed at normal illumination levels 
but some have calculated how much laser power it would take to move 
something like a solar sail. Practically, the cost of the energy and the 
size of the laser needed are impractical.

Cheers, Gene Heskett
-- 
"There are four boxes to be used in defense of liberty:
 soap, ballot, jury, and ammo. Please use in that order."
-Ed Howdershelt (Author)
Genes Web page 
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Oscar Benjamin]

On 5 March 2016 at 02:51, Gregory Ewing  wrote:
>  The masslessness of photons comes from an extrapolation
>>
>> that leads to a divide by infinity: strictly speaking it's just
>> undefined.
>
> No, it's not. The total energy of a particle is given by
>
>E**2 == c**2 * p**2 + m**2 * c**4
>
> where p is the particle's momentum and m is its mass.
> For a photon, m == 0. No division by zero involved.
>
> For a massive particle at rest, p == 0 and the above
> reduces to the well-known
>
>E == m * c**2

The distinction I'm drawing is between physical fact and mathematical
convenience. For other particles we can say that the 1st formula above
holds with m taken to be the mass of the particle at rest. We can
extend that formula to the case of photons which are never at rest by
saying that in the case of photons m=0. That's nice and it's
mathematically convenient in the calculations. It's analogous to
extending the natural definition of the factorial function by saying
that 0!=1. We can't prove that 0!=1 but it's useful to define it that
way. It wouldn't be a disaster to simply leave 0! undefined: it would
just make some equations a little more complicated.

Since the generally accepted physical fact is that photons are never
at rest we are free to define their "rest mass" (use any term you
like) to be anything that is mathematically convenient so we define it
as zero because that fits with your equation above. Turning full
circle we can then use the equation above to say that they are
massless since they would hypothetically be massless in some other
situation even though genuinely massless photons are not thought to
exist in physical reality (unless I'm really out of date on this!).

>> Something I don't know is if there's some theoretical reason why the
>> binding energy could never exceed the sum of the energies of the
>> constituent particles (resulting in an overall negative mass).
>
> Conservation of energy would be one reason. If you
> put two particles together and got more energy out than
> went in, where did the extra energy come from?

That's the point: the energy balance would be satisfied by the
negative energy of the bound particles. The binding energy can be
defined as the energy required to unbind the particles (other
definitions such as André's are also possible). From this definition
we see that the binding energy depends on the binding interaction
(electromagnetic or whatever) that binds the particles together.

The only examples I know of where the binding energy is computed
approximately for e.g. a hydrogen atom predict that the binding energy
is proportional to the (rest) mass of the bound particle(s). If it's
guaranteed that the binding energy always somehow comes out
proportional to the mass of the particles with a coefficient
necessarily smaller than 1/c**2 then you could say that the bound
product could never have negative energy. I just can't see off the top
of my head an argument to suggest that this is impossible.

--
Oscar
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Marko Rauhamaa]

Chris Angelico :

> On Sat, Mar 5, 2016 at 1:51 PM, Gregory Ewing
>  wrote:
>> Conservation of energy would be one reason. If you put two particles
>> together and got more energy out than went in, where did the extra
>> energy come from?
>
> You borrowed it from the bank, of course. You have to make loan
> payments periodically, or they'll foreclose on your particles. If
> everyone borrows energy all at once, and then can't make their
> payments, the universe crashes in a "heat death".

Quantum Mechanics works like a corrupt central bank: you have an
unlimited credit line and can borrow energy out of nothing as long as
you repay the loan before the audit.


Marko
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Chris Angelico]

On Sat, Mar 5, 2016 at 1:51 PM, Gregory Ewing
 wrote:
> Conservation of energy would be one reason. If you
> put two particles together and got more energy out than
> went in, where did the extra energy come from?

You borrowed it from the bank, of course. You have to make loan
payments periodically, or they'll foreclose on your particles. If
everyone borrows energy all at once, and then can't make their
payments, the universe crashes in a "heat death".

ChrisA
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Gregory Ewing]

Oscar Benjamin wrote:

If we want to be precise then
it's pointless to even refer to the "rest mass" of something that is
never at rest.


Which just shows that the term "rest mass" is a bit silly.
It came from some confused thinking very early in the
development of relativity. The physicists soon sorted that
out, but unfortunately the textbooks didn't catch up, and
we've ended up with several generations of confused
students as a result. :-(

 The masslessness of photons comes from an extrapolation

that leads to a divide by infinity: strictly speaking it's just
undefined.


No, it's not. The total energy of a particle is given by

   E**2 == c**2 * p**2 + m**2 * c**4

where p is the particle's momentum and m is its mass.
For a photon, m == 0. No division by zero involved.

For a massive particle at rest, p == 0 and the above
reduces to the well-known

   E == m * c**2


Something I don't know is if there's some theoretical reason why the
binding energy could never exceed the sum of the energies of the
constituent particles (resulting in an overall negative mass).


Conservation of energy would be one reason. If you
put two particles together and got more energy out than
went in, where did the extra energy come from?

If you find a way to make that trick work, watch out --
the secret cartel of energy companies that's suppressing
all the free-energy inventions will want to disappear
you...

--
Greg
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[André Roberge]

This discussion about energy and masses of particles has nothing to do with 
Python, and I am hoping that it will be dropped.  That being said, I feel 
compelled to correct what are completely wrong statements.

On Friday, 4 March 2016 13:36:11 UTC-4, Oscar Benjamin  wrote:
> On 4 March 2016 at 10:38, Marko Rauhamaa  wrote:
> > Oscar Benjamin :
> >
...
> 
> That's just a casual use of terminology. If we want to be precise then
> it's pointless to even refer to the "rest mass" of something that is
> never at rest. The masslessness of photons comes from an extrapolation
> that leads to a divide by infinity: strictly speaking it's just
> undefined.

This is simply wrong.  In Quantum Field Theory, particles can have "bare" mass 
term included in the Lagrangian and the measured mass either includes the bare 
mass + quantum corrections OR is a purely dynamically generated term.

In the Standard Model, there is no bare mass term for the photon, nor is there 
any dynamically generated mass.  In fact, to preserve gauge invariance 
symmetry, the mass of the photon MUST be identically equal to zero.

(Of course, the Standard Model could be incorrect but all meausurements done so 
far are completely consistent with a massless photon; see 
http://pdg.lbl.gov/2015/listings/rpp2015-list-photon.pdf for current 
experimental limits.)


> 
> > As for the existence of a negative mass, it is interesting to note that
> > the (rest) mass of an alpha particle is less than the sum of the (rest)
> > masses of its constituents. About 1% of the mass is "missing."
> 
> Since the binding is associated with negative energy it has a negative
> contribution to the energy/mass of the particle as a whole. This is
> true of any bound state.
> 
> Something I don't know is if there's some theoretical reason why the
> binding energy could never exceed the sum of the energies of the
> constituent particles (resulting in an overall negative mass).

The (magnitude of the) binding energy is DEFINED as the difference between the 
(energy equivalent) sums of the individual masses of the consistuents and that 
of the bound state.

===
Now, could we forget about Physics and go back to discussions related to Python?

André Roberge


> 
> --
> Oscar
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Oscar Benjamin]

On 4 March 2016 at 10:38, Marko Rauhamaa  wrote:
> Oscar Benjamin :
>
>> The mass is carried by the new particles. The new particles may have a
>> total *rest mass* which differs from the total rest mass of the
>> previous particles. However the total mass is the rest mass plus the
>> mass associated with the "kinetic energy" of the particles.
>>
>> [...]
>>
>> Mass and energy are not interchangeable in the sense that you can
>> exchange one for the other with e=mc^2 giving the exchange rate.
>> Rather mass and energy are *the same thing*. Although they are
>> different concepts defined in different ways and having different
>> dimensions and units they are inseparable: e=mc^2 gives us the
>> proportion in which the two appear together.
>
> A physicist mentioned to me that the word "mass" has replaced the term
> "rest mass" in modern Physics lingo.

It depends on the context. Rest mass or similar can still be used
where you want to stress the difference (as I was doing).

> That's why you say a photon is
> "massless" even though every observable photon has a relativistic mass.
> It's all in the terminology.

That's just a casual use of terminology. If we want to be precise then
it's pointless to even refer to the "rest mass" of something that is
never at rest. The masslessness of photons comes from an extrapolation
that leads to a divide by infinity: strictly speaking it's just
undefined.

> As for the existence of a negative mass, it is interesting to note that
> the (rest) mass of an alpha particle is less than the sum of the (rest)
> masses of its constituents. About 1% of the mass is "missing."

Since the binding is associated with negative energy it has a negative
contribution to the energy/mass of the particle as a whole. This is
true of any bound state.

Something I don't know is if there's some theoretical reason why the
binding energy could never exceed the sum of the energies of the
constituent particles (resulting in an overall negative mass).

--
Oscar
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Dan Sommers]

On Fri, 04 Mar 2016 12:38:28 +0200, Marko Rauhamaa wrote:

> As for the existence of a negative mass, it is interesting to note
> that the (rest) mass of an alpha particle is less than the sum of the
> (rest) masses of its constituents. About 1% of the mass is "missing."

https://en.wikipedia.org/wiki/Binding_energy
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Marko Rauhamaa]

Oscar Benjamin :

> The mass is carried by the new particles. The new particles may have a
> total *rest mass* which differs from the total rest mass of the
> previous particles. However the total mass is the rest mass plus the
> mass associated with the "kinetic energy" of the particles.
>
> [...]
>
> Mass and energy are not interchangeable in the sense that you can
> exchange one for the other with e=mc^2 giving the exchange rate.
> Rather mass and energy are *the same thing*. Although they are
> different concepts defined in different ways and having different
> dimensions and units they are inseparable: e=mc^2 gives us the
> proportion in which the two appear together.

A physicist mentioned to me that the word "mass" has replaced the term
"rest mass" in modern Physics lingo. That's why you say a photon is
"massless" even though every observable photon has a relativistic mass.
It's all in the terminology.

As for the existence of a negative mass, it is interesting to note that
the (rest) mass of an alpha particle is less than the sum of the (rest)
masses of its constituents. About 1% of the mass is "missing."


Marko
-- 
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Re: [Still off-top] Physics [was Requests author discusses MentalHealthError exception]

[Oscar Benjamin]

On 4 March 2016 at 00:04, Steven D'Aprano  wrote:
> On Fri, 4 Mar 2016 07:20 am, alister wrote:
>
>> On Thu, 03 Mar 2016 11:03:55 -0700, Ian Kelly wrote:
>
>>> Antimatter has positive mass.
>>
>> Are you sure?
>>  mix 1 atom of hydrogen + 1 of anti hydrogen & you end up with 0 mass (+
>> LOTTS of energy)

This is incorrect. Mass and energy are both conserved. In a
particle/antiparticle annihilation new particles are created. See
here:
https://en.wikipedia.org/wiki/Annihilation

The mass is carried by the new particles. The new particles may have a
total *rest mass* which differs from the total rest mass of the
previous particles. However the total mass is the rest mass plus the
mass associated with the "kinetic energy" of the particles.

> As far as the reaction of matter and anti-matter, we've known for about a
> century that mass and energy are related and freely convertible from one to
> the other. That's the famous equation by Einstein: E = m*c**2. Even tiny
> amounts of energy (say, the light and heat released from a burning match)
> involve a correspondingly tiny reduction in mass.

This is also incorrect and suffers from the same misinterpretation as
above. Mass and energy are not interchangeable in the sense that you
can exchange one for the other with e=mc^2 giving the exchange rate.
Rather mass and energy are *the same thing*. Although they are
different concepts defined in different ways and having different
dimensions and units they are inseparable: e=mc^2 gives us the
proportion in which the two appear together.

--
Oscar
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