{
{
Short
description|Relativity
concept
expressed
as
E
{
{
=
}
}
mc²
}
}
{
{
redirect2|E
{
{
=
}
}
MC²|E
{
{
=
}
}
mc²
}
}
[
[
File
:
M87
jet.jpg|thumb|Mass
near
the
[
[
M87*
]
]
black
hole
is
converted
into
a
very
energetic
[
[
astrophysical
jet
]
]
,
stretching
five
thousand
[
[
Light-year|light
years
]
]
]
]
In
[
[
physics
]
]
,
``
'mass–energy
equivalence
''
'
is
the
relationship
between
[
[
mass
]
]
and
[
[
energy
]
]
in
a
system
's
[
[
rest
frame
]
]
,
where
the
two
quantities
differ
only
by
a
multiplicative
constant
and
the
units
of
measurement.
<
ref
name=Serway1217
>
{
{
Cite
book|last1=Serway
|first1=Raymond
A.|title=Physics
for
scientists
and
engineers
with
modern
physics|last2=Jewett
|first2=John
W.
|last3=Peroomian
|first3=Vahé|date=5
March
2013|isbn=978-1-133-95405-7|edition=9th|location=Boston
,
MA|oclc=802321453|pages=1217–1218
}
}
<
/ref
>
<
ref
name=Günther
>
{
{
Citation|last1=Günther|first1=Helmut|title=Einstein
's
Energy–Mass
Equivalence|date=2019|url=https
:
//doi.org/10.1007/978f=The
Special
Theory
of
Relativity
:
Einstein
’
s
World
in
New
Axiomatics|pages=97–105|editor-last=Günther|editor-first=Helmut|place=Singapore|publisher=Springer|language=en|doi=10.1007/978-981-13-7783-9_7|isbn=978-981-13-7783-9|access-date=2020-10-14|last2=Müller|first2=Volker|s2cid=209978258|editor2-last=Müller|editor2-first=Volker|archive-date=2021-02-21|archive-url=https
:
//web.archive.org/web/20210221080229/https
:
//link.springer.com/chapter/10.1007
%
2F978-981-13-7783-9_7|url-status=live
}
}
<
/ref
>
The
principle
is
described
by
the
physicist
[
[
Albert
Einstein
]
]
's
formula
:
&
nbsp
;
<
math
qid=Q35875
>
E
=
mc^2
<
/math
>
.
<
ref
name=
''
famous
''
>
{
{
cite
book
|title=E=mc
<
sup
>
12
!
<
/sup
>
:
A
Biography
of
the
World
's
Most
Famous
Equation
|edition=illustrated
|first1=David
|last1=Bodanis
|publisher=Bloomsbury
Publishing
|year=2009
|isbn=978-0-8027-1821-1|at=preface|url=https
:
//books.google.com/books
?
id=8TX2tFLZ7gYC
}
}
<
/ref
>
In
a
[
[
reference
frame
]
]
where
the
system
is
moving
,
its
[
[
relativistic
energy
]
]
and
[
[
Mass
in
special
relativity|relativistic
mass
]
]
(
instead
of
[
[
Rest
Mass|rest
mass
]
]
)
obey
the
same
formula
.
The
formula
defines
the
energy
{
{
math|
''
E
''
}
}
of
a
particle
in
its
rest
frame
as
the
product
of
mass
(
{
{
math|
''
m
''
}
}
)
with
the
[
[
speed
of
light
]
]
squared
(
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
)
.
Because
the
speed
of
light
is
a
large
number
in
everyday
units
(
approximately
{
{
cvt|300000|km/s|mi/s|comma=gaps|sigfig=3|disp=x|
or
}
}
)
,
the
formula
implies
that
a
small
amount
of
``
rest
mass
''
,
measured
when
the
system
is
at
rest
,
corresponds
to
an
enormous
amount
of
energy
,
which
is
independent
of
the
composition
of
the
[
[
matter
]
]
.
Rest
mass
,
also
called
[
[
invariant
mass
]
]
,
is
a
fundamental
[
[
physical
property
]
]
that
is
independent
of
[
[
momentum
]
]
,
even
at
extreme
speeds
approaching
the
speed
of
light
.
Its
value
is
the
same
in
all
[
[
inertial
frame
of
reference|inertial
frames
of
reference
]
]
.
[
[
Massless
particle
]
]
s
such
as
[
[
photon
]
]
s
have
zero
invariant
mass
,
but
massless
[
[
free
particle
]
]
s
have
both
momentum
and
energy
.
The
equivalence
principle
implies
that
when
energy
is
lost
in
[
[
chemical
reaction
]
]
s
,
[
[
nuclear
reaction
]
]
s
,
and
other
[
[
energy
transformation
]
]
s
,
the
[
[
Physical
system|system
]
]
will
also
lose
a
corresponding
amount
of
mass
.
The
energy
,
and
mass
,
can
be
released
to
the
environment
as
[
[
radiant
energy
]
]
,
such
as
[
[
light
]
]
,
or
as
[
[
thermal
energy
]
]
.
The
principle
is
fundamental
to
many
fields
of
physics
,
including
[
[
nuclear
physics|nuclear
]
]
and
[
[
particle
physics
]
]
.
Mass–energy
equivalence
arose
from
[
[
special
relativity
]
]
as
a
[
[
paradox
]
]
described
by
the
French
[
[
polymath
]
]
[
[
Henri
Poincaré
]
]
(
1854–1912
)
.
<
ref
name=action
>
{
{
Cite
journal|
author=Poincaré
,
H.
|
year=1900
|
title=La
théorie
de
Lorentz
et
le
principe
de
réaction
|
journal=Archives
Néerlandaises
des
Sciences
Exactes
et
Naturelles
|
volume
=5
|
pages
=252–278|
title-link=s
:
fr
:
La
théorie
de
Lorentz
et
le
principe
de
réaction|language=fr|trans-title=
[
http
:
//physicsinsights.org/poincare-1900.pdf
The
Theory
of
Lorentz
and
The
Principle
of
Reaction
]
}
}
<
/ref
>
Einstein
was
the
first
to
propose
the
equivalence
of
mass
and
energy
as
a
general
principle
and
a
consequence
of
the
[
[
Spacetime
symmetries|symmetries
of
space
and
time
]
]
.
The
principle
first
appeared
in
``
Does
the
inertia
of
a
body
depend
upon
its
energy-content
?
``
,
one
of
his
[
[
annus
mirabilis
papers|
''
annus
mirabilis
''
papers
]
]
,
published
on
21
November
1905.
<
ref
name=
''
inertia
''
>
{
{
Cite
journal|last=Einstein|first=A.|date=1905|title=Ist
die
Trägheit
eines
Körpers
von
seinem
Energieinhalt
abhängig
?
|journal=Annalen
der
Physik|language=de|volume=323|issue=13|pages=639–641|doi=10.1002/andp.19053231314|bibcode=1905AnP
...
323..639E|trans-title=
[
http
:
//www.fourmilab.ch/etexts/einstein/E_mc2/www/
Does
the
Inertia
of
a
Body
Depend
Upon
its
Energy-Content
?
]
|issn=1521-3889|doi-access=free
}
}
<
/ref
>
The
formula
and
its
relationship
to
momentum
,
as
described
by
the
[
[
energy–momentum
relation
]
]
,
were
later
developed
by
other
physicists
.
==Description==
{
{
Special
relativity
sidebar
}
}
Mass–energy
equivalence
states
that
all
objects
having
[
[
mass
]
]
,
or
``
massive
objects
''
,
have
a
corresponding
intrinsic
energy
,
even
when
they
are
stationary
.
In
the
[
[
rest
frame
]
]
of
an
object
,
where
by
definition
it
is
motionless
and
so
has
no
[
[
momentum
]
]
,
the
mass
and
energy
are
equal
or
they
differ
only
by
a
constant
factor
,
the
[
[
speed
of
light
]
]
squared
(
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
)
.
<
ref
name=Serway1217
/
>
<
ref
name=Günther
/
>
In
[
[
Newtonian
mechanics
]
]
,
a
motionless
body
has
no
[
[
kinetic
energy
]
]
,
and
it
may
or
may
not
have
other
amounts
of
internal
stored
energy
,
like
[
[
chemical
energy
]
]
or
[
[
thermal
energy
]
]
,
in
addition
to
any
[
[
potential
energy
]
]
it
may
have
from
its
position
in
a
[
[
field
(
physics
)
|field
of
force
]
]
.
These
energies
tend
to
be
much
smaller
than
the
mass
of
the
object
multiplied
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
,
which
is
on
the
order
of
10
<
sup
>
17
<
/sup
>
&
nbsp
;
[
[
joule
]
]
s
for
a
mass
of
one
kilogram
.
Due
to
this
principle
,
the
mass
of
the
atoms
that
come
out
of
a
[
[
nuclear
reaction
]
]
is
less
than
the
mass
of
the
atoms
that
go
in
,
and
the
difference
in
mass
shows
up
as
heat
and
light
with
the
same
equivalent
energy
as
the
difference
.
In
analyzing
these
explosions
,
Einstein
's
formula
can
be
used
with
{
{
mvar|E
}
}
as
the
energy
released
(
removed
)
,
and
{
{
mvar|m
}
}
as
the
change
in
mass
.
In
[
[
Theory
of
relativity|relativity
]
]
,
all
the
energy
that
moves
with
an
object
(
i.e.
,
the
energy
as
measured
in
the
object
's
rest
frame
)
contributes
to
the
total
mass
of
the
body
,
which
measures
how
much
it
resists
[
[
acceleration
]
]
.
If
an
isolated
box
of
ideal
mirrors
could
contain
light
,
the
individually
massless
photons
would
contribute
to
the
total
mass
of
the
box
by
the
amount
equal
to
their
energy
divided
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
.
<
ref
>
{
{
Cite
book|last1=Puri|first1=H
.
S.|last2=Hans|first2=S
.
P.|url=https
:
//books.google.com/books
?
id=hrBe52GPHrYC|title=Mechanics
,
2E|date=2003-07-01|publisher=Tata
McGraw-Hill
Education|isbn=978-0-07-047360-7|language=en|page=
[
https
:
//books.google.com/books
?
id=hrBe52GPHrYC
&
pg=PA433
433
]
}
}
<
/ref
>
For
an
observer
in
the
rest
frame
,
removing
energy
is
the
same
as
removing
mass
and
the
formula
{
{
math|1=
''
m
''
=
``
E
''
/
''
c
''
<
sup
>
2
<
/sup
>
}
}
indicates
how
much
mass
is
lost
when
energy
is
removed.
<
ref
>
{
{
Cite
book|last=Serway
,
Raymond
A.|url=https
:
//www.worldcat.org/oclc/802321453|title=Physics
for
scientists
and
engineers
with
modern
physics.|others=Jewett
,
John
W.
,
Peroomian
,
Vahé.|date=5
March
2013|isbn=978-1-133-95405-7|edition=Ninth|location=Boston
,
MA|oclc=802321453|page=1386
}
}
<
/ref
>
In
the
same
way
,
when
any
energy
is
added
to
an
isolated
system
,
the
increase
in
the
mass
is
equal
to
the
added
energy
divided
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
.
<
ref
name=griffithsElectro512
>
{
{
Cite
book|last=Griffiths
,
David
J.|url=https
:
//www.worldcat.org/oclc/40251748|title=Introduction
to
electrodynamics|date=1999|publisher=Prentice
Hall|isbn=978-0-13-805326-0|edition=3rd|location=Upper
Saddle
River
,
N.J.|oclc=40251748|page=512|access-date=2020-10-15|archive-date=2021-02-21|archive-url=https
:
//web.archive.org/web/20210221080229/https
:
//www.worldcat.org/title/introduction-to-electrodynamics/oclc/40251748|url-status=live
}
}
<
/ref
>
==Mass
in
special
relativity==
{
{
main|Mass
in
special
relativity
}
}
[
[
File
:
E=mc²-explication.svg|thumb|
{
{
math|1=
''
E
''
=
``
mc
''
{
{
smallsup|2
}
}
}
}
—In
[
[
SI
units
]
]
,
the
energy
{
{
math|
''
E
''
}
}
is
measured
in
[
[
Joules
]
]
,
the
mass
{
{
math|
''
m
''
}
}
is
measured
in
[
[
kilograms
]
]
,
and
the
[
[
speed
of
light
]
]
is
measured
in
[
[
meters
]
]
per
[
[
second
]
]
.
]
]
An
object
moves
at
different
speeds
in
different
[
[
Frame
of
reference|frames
of
reference
]
]
,
depending
on
the
motion
of
the
observer
.
This
implies
the
kinetic
energy
,
in
both
Newtonian
mechanics
and
relativity
,
is
'frame
dependent
'
,
so
that
the
amount
of
relativistic
energy
that
an
object
is
measured
to
have
depends
on
the
observer
.
The
``
relativistic
mass
''
of
an
object
is
given
by
the
relativistic
energy
divided
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
.
<
ref
name=
''
Tipler
''
>
{
{
Cite
book|last1=Tipler|first1=Paul
Allen|last2=Llewellyn|first2=Ralph
A.|url=
https
:
//www.worldcat.org/oclc/49894577|title=Modern
physics.|date=2003|publisher=W.H
.
Freeman|isbn=978-0-7167-4345-3|edition=4th|location=New
York|oclc=49894577|pages=87–88
}
}
<
/ref
>
Because
the
relativistic
mass
is
exactly
proportional
to
the
relativistic
energy
,
relativistic
mass
and
relativistic
energy
are
nearly
[
[
synonym
]
]
ous
;
the
only
difference
between
them
is
the
[
[
unit
of
measurement|units
]
]
.
The
``
rest
mass
''
or
[
[
invariant
mass
]
]
of
an
object
is
defined
as
the
mass
an
object
has
in
its
rest
frame
,
when
it
is
not
moving
with
respect
to
the
observer
.
Physicists
typically
use
the
term
``
mass
''
,
though
experiments
have
shown
an
object
's
gravitational
mass
depends
on
its
total
energy
and
not
just
its
rest
mass
.
{
{
Citation
needed|date=February
2021|reason=experiments
which
specifically
address
this
,
unless
what
was
meant
was
that
the
gravitational
mass
of
a
system
is
the
invariant
mass
of
the
system
as
opposed
to
the
sum
of
the
component
invariant
masses
}
}
The
rest
mass
is
the
same
for
all
[
[
inertial
frame
]
]
s
,
as
it
is
independent
of
the
motion
of
the
observer
,
it
is
the
smallest
possible
value
of
the
relativistic
mass
of
the
object
.
Because
of
the
attraction
between
components
of
a
system
,
which
results
in
potential
energy
,
the
rest
mass
is
almost
never
[
[
Additive
function|additive
]
]
;
in
general
,
the
mass
of
an
object
is
not
the
sum
of
the
masses
of
its
parts.
<
ref
name=
''
griffithsElectro512
''
/
>
The
rest
mass
of
an
object
is
the
total
energy
of
all
the
parts
,
including
kinetic
energy
,
as
observed
from
the
center
of
momentum
frame
,
and
potential
energy
.
The
masses
add
up
only
if
the
constituents
are
at
rest
(
as
observed
from
the
center
of
momentum
frame
)
and
do
not
attract
or
repel
,
so
that
they
do
not
have
any
extra
kinetic
or
potential
energy.
<
ref
group=
''
note
''
>
They
can
also
have
a
positive
kinetic
energy
and
a
negative
potential
energy
that
exactly
cancels.
<
/ref
>
Massless
particles
are
particles
with
no
rest
mass
,
and
therefore
have
no
intrinsic
energy
;
their
energy
is
due
only
to
their
momentum
.
===Relativistic
mass===
Relativistic
mass
depends
on
the
motion
of
the
object
,
so
that
different
observers
in
relative
motion
see
different
values
for
it
.
The
relativistic
mass
of
a
moving
object
is
larger
than
the
relativistic
mass
of
an
object
at
rest
,
because
a
moving
object
has
kinetic
energy
.
If
the
object
moves
slowly
,
the
relativistic
mass
is
nearly
equal
to
the
[
[
rest
mass
]
]
and
both
are
nearly
equal
to
the
classical
inertial
mass
(
as
it
appears
in
[
[
Newton
's
laws
of
motion
]
]
)
.
If
the
object
moves
quickly
,
the
relativistic
mass
is
greater
than
the
rest
mass
by
an
amount
equal
to
the
mass
associated
with
the
kinetic
energy
of
the
object
.
Massless
particles
also
have
relativistic
mass
derived
from
their
kinetic
energy
,
equal
to
their
relativistic
energy
divided
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
,
or
{
{
math|1=
''
m
''
{
{
ssub|rel
}
}
=
``
E
''
/
''
c
''
<
sup
>
2
<
/sup
>
}
}
.
<
ref
>
{
{
Cite
book|last=Mould|first=Richard
A.|url=https
:
//books.google.com/books
?
id=lfGE-wyJYIUC|title=Basic
Relativity|date=2001-11-01|publisher=Springer
Science
&
Business
Media|isbn=978-0-387-95210-9|language=en|page=
[
https
:
//books.google.com/books
?
id=lfGE-wyJYIUC
&
pg=PA126
126
]
}
}
<
/ref
>
<
ref
>
{
{
Cite
book|last=Chow|first=Tai
L.|url=https
:
//books.google.com/books
?
id=dpnpMhw1zo8C|title=Introduction
to
Electromagnetic
Theory
:
A
Modern
Perspective|date=2006|publisher=Jones
&
Bartlett
Learning|isbn=978-0-7637-3827-3|language=en|page=
[
https
:
//books.google.com/books
?
id=dpnpMhw1zo8C
&
pg=PA392
392
]
|access-date=2016-02-22|archive-date=2016-12-02|archive-url=https
:
//web.archive.org/web/20161202172249/https
:
//books.google.com/books
?
id=dpnpMhw1zo8C|url-status=live
}
}
<
/ref
>
The
speed
of
light
is
one
in
a
system
where
length
and
time
are
measured
in
[
[
natural
units
]
]
and
the
relativistic
mass
and
energy
would
be
equal
in
value
and
dimension
.
As
it
is
just
another
name
for
the
energy
,
the
use
of
the
term
``
relativistic
mass
''
is
redundant
and
physicists
generally
reserve
``
mass
''
to
refer
to
rest
mass
,
or
invariant
mass
,
as
opposed
to
relativistic
mass.
<
ref
name=elementaryParticles
>
{
{
Cite
book|last=Griffiths
,
David
J.|title=Introduction
to
elementary
particles|date=2008|publisher=Wiley-VCH|isbn=978-3-527-40601-2|edition=2nd
,
rev.|location=Weinheim
[
Germany
]
|oclc=248969635|page=101
}
}
<
/ref
>
<
ref
name=serway
>
{
{
Cite
book|last=Serway
,
Raymond
A.|title=Physics
for
scientists
and
engineers
with
modern
physics.|others=Jewett
,
John
W.
,
Peroomian
,
Vahé.|date=5
March
2013|isbn=978-1-133-95405-7|edition=Ninth|location=Boston
,
MA|oclc=802321453|page=1219
}
}
<
/ref
>
A
consequence
of
this
terminology
is
that
the
[
[
conservation
of
mass|mass
is
not
conserved
]
]
in
special
relativity
,
whereas
[
[
Momentum
#
Conservation|the
conservation
of
momentum
]
]
and
[
[
conservation
of
energy
]
]
are
both
fundamental
laws.
<
ref
name=elementaryParticles
/
>
===Conservation
of
mass
and
energy===
{
{
Main|Conservation
of
energy|Conservation
of
mass
}
}
The
conservation
of
energy
is
a
universal
principle
in
physics
and
holds
for
any
interaction
,
along
with
the
conservation
of
momentum.
<
ref
name=elementaryParticles
/
>
The
classical
conservation
of
mass
,
in
contrast
,
is
violated
in
certain
relativistic
settings.
<
ref
name=serway
/
>
<
ref
name=elementaryParticles
/
>
This
concept
has
been
experimentally
proven
in
a
number
of
ways
,
including
the
conversion
of
mass
into
kinetic
energy
in
nuclear
reactions
and
other
interactions
between
[
[
elementary
particle
]
]
s.
<
ref
name=serway
/
>
While
modern
physics
has
discarded
the
expression
'conservation
of
mass
'
,
in
older
terminology
a
[
[
relativistic
mass
]
]
can
also
be
defined
to
be
equivalent
to
the
energy
of
a
moving
system
,
allowing
for
a
``
conservation
of
relativistic
mass
''
.
<
ref
name=elementaryParticles
/
>
Mass
conservation
breaks
down
when
the
energy
associated
with
the
mass
of
a
particle
is
converted
into
other
forms
of
energy
,
such
as
kinetic
energy
,
thermal
energy
,
or
[
[
radiant
energy
]
]
.
Similarly
,
kinetic
or
radiant
energy
can
be
used
to
create
particles
that
have
mass
,
always
conserving
the
total
energy
and
momentum.
<
ref
name=elementaryParticles
/
>
===Massless
particles===
Massless
particles
have
zero
rest
mass
.
The
[
[
Planck–Einstein
relation
]
]
for
the
energy
for
[
[
photon
]
]
s
is
given
by
the
equation
{
{
math|1=
''
E
''
=
``
hf
''
}
}
,
where
{
{
mvar|h
}
}
is
the
[
[
Planck
constant
]
]
and
{
{
mvar|f
}
}
is
the
photon
[
[
frequency
]
]
.
This
frequency
and
thus
the
relativistic
energy
are
frame-dependent
.
If
an
observer
runs
away
from
a
photon
in
the
direction
the
photon
travels
from
a
source
,
and
it
catches
up
with
the
observer
,
the
observer
sees
it
as
having
less
energy
than
it
had
at
the
source
.
The
faster
the
observer
is
traveling
with
regard
to
the
source
when
the
photon
catches
up
,
the
less
energy
the
photon
would
be
seen
to
have
.
As
an
observer
approaches
the
speed
of
light
with
regard
to
the
source
,
the
[
[
redshift
]
]
of
the
photon
increases
,
according
to
the
[
[
relativistic
Doppler
effect
]
]
.
The
energy
of
the
photon
is
reduced
and
as
the
wavelength
becomes
arbitrarily
large
,
the
photon
's
energy
approaches
zero
,
due
to
the
massless
nature
of
photons
,
which
does
not
permit
any
intrinsic
energy
.
===Composite
systems===
{
{
see
also|Mass
in
special
relativity
#
The
mass
of
composite
systems
}
}
For
closed
systems
made
up
of
many
parts
,
like
an
[
[
atomic
nucleus
]
]
,
planet
,
or
star
,
the
relativistic
energy
is
given
by
the
sum
of
the
relativistic
energies
of
each
of
the
parts
,
because
energies
are
additive
in
these
systems
.
If
a
system
is
[
[
Binding
energy
#
Mass-energy
relation|
''
bound
''
]
]
by
attractive
forces
,
and
the
energy
gained
in
excess
of
the
work
done
is
removed
from
the
system
,
then
mass
is
lost
with
this
removed
energy
.
The
mass
of
an
atomic
nucleus
is
less
than
the
total
mass
of
the
[
[
proton
]
]
s
and
[
[
neutron
]
]
s
that
make
it
up.
<
ref
name=Serway1386
>
{
{
Cite
book|last=Serway
,
Raymond
A.|url=https
:
//www.worldcat.org/oclc/802321453|title=Physics
for
scientists
and
engineers
with
modern
physics.|others=Jewett
,
John
W.
,
Peroomian
,
Vahé.|date=5
March
2013|isbn=978-1-133-95405-7|edition=Ninth|location=Boston
,
MA|oclc=802321453|page=1386|access-date=15
October
2020|archive-date=21
February
2021|archive-url=https
:
//web.archive.org/web/20210221080236/https
:
//www.worldcat.org/title/physics-for-scientists-and-engineers-with-modern-physics/oclc/802321453|url-status=live
}
}
<
/ref
>
This
mass
decrease
is
also
equivalent
to
the
energy
required
to
break
up
the
nucleus
into
individual
protons
and
neutrons
.
This
effect
can
be
understood
by
looking
at
the
potential
energy
of
the
individual
components
.
The
individual
particles
have
a
force
attracting
them
together
,
and
forcing
them
apart
increases
the
potential
energy
of
the
particles
in
the
same
way
that
lifting
an
object
up
on
earth
does
.
This
energy
is
equal
to
the
work
required
to
split
the
particles
apart
.
The
mass
of
the
[
[
Solar
System
]
]
is
slightly
less
than
the
sum
of
its
individual
masses
.
For
an
isolated
system
of
particles
moving
in
different
directions
,
the
invariant
mass
of
the
system
is
the
analog
of
the
rest
mass
,
and
is
the
same
for
all
observers
,
even
those
in
relative
motion
.
It
is
defined
as
the
total
energy
(
divided
by
{
{
math|
''
c
''
<
sup
>
2
<
/sup
>
}
}
)
in
the
[
[
center
of
momentum
frame
]
]
.
The
``
center
of
momentum
frame
''
is
defined
so
that
the
system
has
zero
total
momentum
;
the
term
[
[
center
of
mass
]
]
frame
is
also
sometimes
used
,
where
the
``
center
of
mass
frame
''
is
a
special
case
of
the
center
of
momentum
frame
where
the
center
of
mass
is
put
at
the
origin
.
A
simple
example
of
an
object
with
moving
parts
but
zero
total
momentum
is
a
container
of
gas
.
In
this
case
,
the
mass
of
the
container
is
given
by
its
total
energy
(
including
the
kinetic
energy
of
the
gas
molecules
)
,
since
the
system
's
total
energy
and
invariant
mass
are
the
same
in
any
reference
frame
where
the
momentum
is
zero
,
and
such
a
reference
frame
is
also
the
only
frame
in
which
the
object
can
be
weighed
.
In
a
similar
way
,
the
theory
of
special
relativity
posits
that
the
thermal
energy
in
all
objects
,
including
solids
,
contributes
to
their
total
masses
,
even
though
this
energy
is
present
as
the
kinetic
and
potential
energies
of
the
atoms
in
the
object
,
and
it
(
in
a
similar
way
to
the
gas
)
is
not
seen
in
the
rest
masses
of
the
atoms
that
make
up
the
object.
<
ref
name=griffithsElectro512
/
>
Similarly
,
even
photons
,
if
trapped
in
an
isolated
container
,
would
contribute
their
energy
to
the
mass
of
the
container
.
Such
extra
mass
,
in
theory
,
could
be
weighed
in
the
same
way
as
any
other
type
of
rest
mass
,
even
though
individually
photons
have
no
rest
mass
.
The
property
that
trapped
energy
in
any
form
adds
weighable
mass
to
systems
that
have
no
net
momentum
is
one
of
the
consequences
of
relativity
.
It
has
no
counterpart
in
classical
Newtonian
physics
,
where
energy
never
exhibits
weighable
mass.
<
ref
name=griffithsElectro512
/
>
===Relation
to
gravity===
Physics
has
two
concepts
of
mass
,
the
gravitational
mass
and
the
inertial
mass
.
The
gravitational
mass
is
the
quantity
that
determines
the
strength
of
the
[
[
gravitational
field
]
]
generated
by
an
object
,
as
well
as
the
gravitational
force
acting
on
the
object
when
it
is
immersed
in
a
gravitational
field
produced
by
other
bodies
.
The
inertial
mass
,
on
the
other
hand
,
quantifies
how
much
an
object
accelerates
if
a
given
force
is
applied
to
it
.
The
mass–energy
equivalence
in
special
relativity
refers
to
the
inertial
mass
.
However
,
already
in
the
context
of
Newton
gravity
,
the
weak
[
[
equivalence
principle
]
]
is
postulated
:
the
gravitational
and
the
inertial
mass
of
every
object
are
the
same
.
Thus
,
the
mass–energy
equivalence
,
combined
with
the
weak
equivalence
principle
,
results
in
the
prediction
that
all
forms
of
energy
contribute
to
the
gravitational
field
generated
by
an
object
.
This
observation
is
one
of
the
pillars
of
the
[
[
general
theory
of
relativity
]
]
.
The
prediction
that
all
forms
of
energy
interact
gravitationally
has
been
subject
to
experimental
tests
.
One
of
the
first
observations
testing
this
prediction
,
called
the
[
[
Eddington
experiment
]
]
,
was
made
during
the
[
[
Solar
eclipse
of
May
29
,
1919
]
]
.
<
ref
>
{
{
Cite
journal|last1=Dyson|first1=F.W.|author2=Eddington
,
A.S.|author3=Davidson
,
C.R.|name-list-style=amp|date=January
1920|title=IX
.
A
determination
of
the
deflection
of
light
by
the
sun
's
gravitational
field
,
from
observations
made
at
the
total
eclipse
of
May
29
,
1919|journal=Philosophical
Transactions
of
the
Royal
Society
of
London
.
Series
A
,
Containing
Papers
of
a
Mathematical
or
Physical
Character|language=en|volume=220|issue=571–581|pages=291–333|doi=10.1098/rsta.1920.0009|bibcode=1920RSPTA.220..291D|issn=0264-3952|doi-access=free
}
}
<
/ref
>
<
ref
>
{
{
Cite
journal|last=Stanley|first=Matthew|date=2003-03-01|title='An
Expedition
to
Heal
the
Wounds
of
War
'
The
1919
Eclipse
and
Eddington
as
Quaker
Adventurer|url=https
:
//www.journals.uchicago.edu/doi/10.1086/376099|journal=Isis|volume=94|issue=1|pages=57–89|doi=10.1086/376099|pmid=12725104|bibcode=2003Isis
...
94
...
57S|s2cid=25615643|issn=0021-1753|access-date=2020-10-22|archive-date=2020-08-05|archive-url=https
:
//web.archive.org/web/20200805053416/https
:
//www.journals.uchicago.edu/doi/10.1086/376099|url-status=live
}
}
<
/ref
>
During
the
[
[
solar
eclipse
]
]
,
the
English
[
[
astronomer
]
]
and
physicist
[
[
Arthur
Eddington
]
]
observed
that
the
light
from
stars
passing
close
to
the
Sun
was
bent
.
The
effect
is
due
to
the
gravitational
attraction
of
light
by
the
Sun
.
The
observation
confirmed
that
the
energy
carried
by
light
indeed
is
equivalent
to
a
gravitational
mass
.
Another
seminal
experiment
,
the
[
[
Pound–Rebka
experiment
]
]
,
was
performed
in
1960.
<
ref
>
{
{
Cite
journal|last1=Pound|first1=R
.
V.|last2=Rebka|first2=G
.
A.|date=1960-04-01|title=Apparent
Weight
of
Photons|journal=Physical
Review
Letters|language=en|volume=4|issue=7|pages=337–341|doi=10.1103/PhysRevLett.4.337|bibcode=1960PhRvL
...
4..337P|issn=0031-9007|doi-access=free
}
}
<
/ref
>
In
this
test
a
beam
of
light
was
emitted
from
the
top
of
a
tower
and
detected
at
the
bottom
.
The
[
[
frequency
]
]
of
the
light
detected
was
higher
than
the
light
emitted
.
This
result
confirms
that
the
energy
of
photons
increases
when
they
fall
in
the
gravitational
field
of
the
Earth
.
The
energy
,
and
therefore
the
gravitational
mass
,
of
photons
is
proportional
to
their
frequency
as
stated
by
the
Planck
's
relation
.
==Efficiency==
In
some
reactions
,
matter
particles
can
be
destroyed
and
their
associated
energy
released
to
the
environment
as
other
forms
of
energy
,
such
as
light
and
heat.
<
ref
name=Serway1217
/
>
One
example
of
such
a
conversion
takes
place
in
elementary
particle
interactions
,
where
the
rest
energy
is
transformed
into
kinetic
energy.
<
ref
name=Serway1217
/
>
Such
conversions
between
types
of
energy
happen
in
nuclear
weapons
,
in
which
the
protons
and
neutrons
in
[
[
atomic
nuclei
]
]
lose
a
small
fraction
of
their
original
mass
,
though
the
mass
lost
is
not
due
to
the
destruction
of
any
smaller
constituents
.
[
[
Nuclear
fission
]
]
allows
a
tiny
fraction
of
the
energy
associated
with
the
mass
to
be
converted
into
usable
energy
such
as
radiation
;
in
the
decay
of
the
[
[
uranium
]
]
,
for
instance
,
about
0.1
%
of
the
mass
of
the
original
atom
is
lost.
<
ref
name=
''
bulletin1950
''
>
{
{
Cite
journal|last=Bethe|first=Hans
A.|date=1950-04-01|title=The
Hydrogen
Bomb|url=https
:
//doi.org/10.1080/00963402.1950.11461231|journal=Bulletin
of
the
Atomic
Scientists|volume=6|issue=4|pages=99–104|doi=10.1080/00963402.1950.11461231|bibcode=1950BuAtS
...
6d..99B|issn=0096-3402
}
}
<
/ref
>
In
theory
,
it
should
be
possible
to
destroy
matter
and
convert
all
of
the
rest-energy
associated
with
matter
into
heat
and
light
,
but
none
of
the
theoretically
known
methods
are
practical
.
One
way
to
harness
all
the
energy
associated
with
mass
is
to
annihilate
matter
with
[
[
antimatter
]
]
.
[
[
baryon
asymmetry|Antimatter
is
rare
in
our
universe
]
]
,
however
,
and
the
known
mechanisms
of
production
require
more
usable
energy
than
would
be
released
in
annihilation
.
[
[
CERN
]
]
estimated
in
2011
that
over
a
billion
times
more
energy
is
required
to
make
and
store