The Real Meaning of E=mc² | Space Time | PBS Digital Studios


A hydrogen atom has less
mass than the combined masses of the proton and the
electron that make it up. That’s right, less. How can something weigh less
than the sum of its parts? Because of this. And today, we’re
going to clarify what the most famous equation
in physics really says. [MUSIC PLAYING] E equals mc squared is probably
the most famous equation in all of physics, but in his
original 1905 paper, Einstein actually wrote
it down differently, as m equals E
divided by c squared. That’s because at its core,
this cornerstone of physics is really a lesson in how
to think about what mass is. You’ll often see statements
like “mass is a form of energy” or “mass is frozen
energy” or “mass can be converted to energy.” That’s the worst one. Unfortunately, none of these
statements is quite correct, so trying to make sense of
them can be frustrating. I think instead we can
get a better sense of what m equals E over c squared means
if we start with some things that it implies
that seem at odds with our everyday
experience of mass. Here’s a pretty
mind blowing one. Even if two objects are made
up of identical constituents, those objects will not in
general have equal masses. The mass of something that’s
made out of smaller parts is not just the sum of
the masses of those parts. Instead, the total mass
of the composite object also depends on, one, how
it’s parts are arranged, and two, how those parts move
within the bigger object. Here’s a concrete example. Imagine two windup watches that
are identical atom for atom except that one of them is
fully wound up and running, but the other one has stopped. According to Einstein,
the watch that’s running has a greater mass. Why? Well, the hands and gears in
the running watch are moving, so they have some
kinetic energy. There are also wound up springs
in the running watch that have potential
energy, and there’s a little bit of friction
between the moving parts of that watch that
heats them up ever so slightly so that its atoms start
jiggling a little bit. That’s thermal energy,
or equivalently, randomized kinetic energy
on a more microscopic level. OK, got it? Now, what M equals E
over c squared says is that all of that kinetic
energy and potential energy and thermal energy that
resides in the watch’s parts manifests itself as part
of the watch’s mass. You just add up all
that energy, divide it by the speed of light
squared, and that’s how much extra mass
the kinetic and potential and thermal
energies of the parts contribute to the whole. Now since the speed
of light is so huge, this extra mass is tiny,
only about a billionth of a billionth of a percent of
the total mass of the watch. That’s why, according
to Einstein, most of us have always incorrectly
believed that mass is an indicator of the amount
of matter in an object. In everyday life, we just
don’t notice the discrepancy because it’s so small,
but it’s not zero. And if you had perfectly
sensitive scales, you could measure it. So wait a second. Am I saying that individually,
the mass of the minute hand is bigger because the
minute hand is moving? No. That’s an outdated viewpoint. Most contemporary physicists
mean mass while at rest, or “rest mass,” when
they talk about mass. In modern parlance, the phrase
“rest mass” is redundant. There are lots of good
reasons for talking this way, among them
that rest mass is a property all
observers agree about, much like the
space-time interval that we discussed in
a previous episode. This all gets a little
bit more complicated in general relativity, but we’ll
deal with that another time. For us, today, the m in m equals
E over c squared is rest mass. You can think of
it as an indicator of how hard it is to accelerate
an object or an indicator of how much gravitational
force an object will feel. But either way, a ticking
watch simply has more of it than an otherwise
identical stop watch. So more examples might help to
clarify what’s going on here. Whenever you turn
on a flashlight, its math starts to
drop immediately. Think about it. The light carries
energy, and that energy was previously stored as
electrochemical energy inside the battery, and
thus manifesting as part of the flashlight’s total mass. Once that energy escapes,
you’re not weighing it anymore. And yes, since the
sun is basically an enormous flashlight,
its mass drops just by virtue of the fact
that it shines by about 4 billion kilograms every second. Don’t worry, Earth’s
orbit is going to be fine. That’s just a billionth of a
trillionth of the sun’s mass, and only 0.07% of the sun’s
mass over its entire 10 billion year lifespan. So does this mean that the
sun converts mass to energy? No. This isn’t alchemy. All the energy in sunlight came
at the expense of other energy, kinetic and potential
energy, of the particles that make up the sun. Before that light was emitted,
there was simply more kinetic and potential energy contained
within the volume of the sun manifesting as part
of the sun’s mass. Those 4 billion kilograms that
the sun loses every second is really a reduction in the
kinetic and potential energies of its constituent particles. What we’ve been
weighing is the energies of the particles in
objects all along. We just never noticed it. Another example. Suppose that I stand
with a flashlight inside a closed box
that has mirrored walls and is resting on a scale. Will the reading
on the scale change if I turn on the flashlight? Interestingly, no. The flashlight alone
will lose mass, but the mass of the whole
box and its contents will stay fixed. Yes, it’s true that the
scale is registering less electrochemical
energy, but it’s also registering an exactly equal
amount of extra light energy that we’re not allowing
to escape this time. That’s right, even though
light itself is massless, if you confine it
in a box, its energy still contributes to the
total mass of that box via m equals E over c squared. That’s why the reading on
the scale doesn’t change. OK, here’s the really fun part. In every example
we’ve done so far, things have weighed
more than the sum of the parts that make it up. But at the top of
the episode, I stated that the mass of a
hydrogen atom is less than the combined masses of the
electron and the proton that make it up. How does that work? It’s because potential
energy can be negative. Suppose we call the
potential energy of a proton and electron zero when
they’re infinitely far apart. Since they attract each other,
their electric potential energy will drop when they get
closer together, just like your gravitational
potential energy drops when you get closer to the
surface of Earth, which is also attracting you. So the potential energy
of the electron and proton in a hydrogen atom is negative. Now the electron in
hydrogen also has kinetic energy, which is always
positive, due to its movement around the product proton. But as it turns out,
the potential energy is negative enough that the sum
of the kinetic and potential energies still
comes out negative, and therefore m equals
E over c squared also comes out negative,
and a hydrogen atom weighs less than the
combined masses of its parts. Booyah. In fact, barring
weird circumstances, all atoms on the periodic table
weigh less than the combined masses of the protons,
neutrons, and electrons that make them up. The same is true for molecules. An oxygen molecule weighs
less than two oxygen atoms because the combined kinetic
and potential energies of those atoms once they form
a chemical bond is negative. What about protons and
neutrons themselves? They’re made of particles called
quarks, whose combine mass is about 2,000 to 3,000
times smaller than a proton’s or neutron’s mass. So where does the
proton’s mass come from? Basically, quark
potential energy. Veritasium did a
nice episode on this that you can click
over here to view. Every time he says
“gluons” in that video, just substitute “quark
potential energy,” and you’ll have a
roughly correct picture of what’s going on. All right, what about the
masses of electrons and quarks? At least in the standard
model of particle physics, they’re not made up
of smaller parts, so where does their
mass come from? Is it some kind of baseline
mass in the pre-Einstein sense of the word? Well, that’s a subtle question,
but crudely speaking, you can think even of
this mass as being a reflection of various
kinds of potential energies. For instance, there’s
the potential energy associated with the interactions
of electrons and quarks with the Higgs field. And there’s also
potential energy that electrons and quarks
have from interacting with the electric fields
that they themselves produce, or in the case of quarks,
also with the gluon fields that they themselves produce. OK, what about
matter-antimatter annihilation? Doesn’t that have to
be thought of as mass being converted into energy? Interestingly, no. There’s a way to conceptualize
even this process as simple conversions
of one kind of energy to another– kinetic,
potential, light, and so forth. You never need mass
to energy alchemy. But please take my
word for it, you don’t actually have to talk
about converting mass to energy ever. Instead, the punchline
of this episode has been that mass isn’t
really anything at all. It’s a property, a property
that all energy exhibits. And in that sense,
even though it’s not correct to think of mass is an
indicator of amount of stuff in the material sense,
you can think of it as an indicator of
amount of energy. So without realizing
it, you’ve really been measuring the cumulative
energy content of objects every time you’ve
ever used a scale. I’m going to wrap up
with two comments. First, Einstein’s original
paper on this topic is only three pages long
and not that hard to read. We’ve linked to an English
translation of it down in the description,
and I strongly encourage you to check it out. Second, I want to leave you
with a challenge question to test your understanding. First, some background. Suppose you put two identical
blocks side by side on a scale and weigh the combo, then stack
them one on top of each other and weigh them again. The second configuration
has more gravitational potential energy than the
first because the second block is higher up, so it will have
more mass than the first. Keep that in mind for the
following challenge question. Suppose that every
person on Earth simultaneously picks up
a hammer from the ground. Would the total
mass of the planet increase, and if so by how much? Do not put answers in
the comments section. That, as always, is
for your questions. Instead, submit your
responses by email to [email protected]
with the subject line “E=MC2 Challenge.” Submit your answers no earlier
than 5:00 PM New York City local time on this date. I want to give everyone a chance
to think about it and everyone a chance to respond, because
we’re going to shout out the first five correct
answers, which must also have correct
explanations to count, on the next episode
of “Space Time.” Last week we talked
about NASA spinoffs. First off, you guys
mentioned some things, to set the record
straight, that are not NASA spinoffs– microwave ovens,
Tang, Velcro, cordless power tools, the space pen, MRI
machines– none of those are NASA spinoffs. But you did mention some
NASA spinoffs that we missed. Ryan Brown brought
up space blankets, David Shi brought up oxygen
permeable contact lenses, and UndamagedLama2 brought up
robotic endoscopic surgery. Nice finds. Jay Perrin, who’s an
airline dispatcher and former firefighter,
vouched for the importance of being able to see
through smoke and fog. Great to hear from someone
with first hand experience with NASA tech. jancultis, or “yawn”-cultis,
points out the NASA is great but inefficient and has lots
of room for improvement. I agree, and I think
NASA does, too. And finally, to Ms.
Croco’s fourth grade class at Dunbar Hill Elementary
in Hamden, Connecticut, thanks a lot for
watching the show. And yes, Ms. Croco and
I really are friends. Stop saying she’s making it up. [MUSIC PLAYING]

100 thoughts on “The Real Meaning of E=mc² | Space Time | PBS Digital Studios

  1. The deep mening is….a mason with his tounge out of his mouth…learn to read their foolish signs……..sheeple

  2. Tanks for the information.
    And if an energy come from a mass like battery……..
    So my question is does the sun energy end .

  3. This guy and the long haired guy have no interest in teaching you anything, they just want to sound smart. If you’re a physicist, especially a teacher, you would clearly know and have enough sense to realize that you’re not explaining anything in a way to teach.

  4. See people always think Physicists talk really fast. In reality, its the world that is moving really slowly around them as they have so much energy and are experiencing the relativistic effects of Special Relativity.

  5. Unable to understand how these electrons revolve around protons….when everything about a stationary piece of metal looks quite still from outside and there is no trace of the slightest movement apparently….

  6. I have two questions:
    First, at around 5:28, could you take the comparison of gravitational potential energy and electrical potential energy so far as to state that the negative potential energy decreases to infinity as the distance of the electron and proton nears 0?
    Second question, at 6:20, a comparison on a balance scale is made between two individual oxygen atoms and two oxygen atoms in a chemical bond. The observation that the side with the bonded atoms has two less electrons(14 vs 16), would seem to imply that it would be lighter simply due to this fact, but that seems to contradict the theme. Are the number of electrons shown supposed to be 16 on both sides, or am I missing something about chemical bonding?
    Lastly, after viewing the comments to see if these questions had been asked, I would like to apologize for myself and my fellow humans who seem to have not heard him say that the comments section is for questions, and state my personal opinion that this episode is more than could be hoped for in a 10 minute video, its the reason I subscribed to the channel, and to everyone involved in making it, thank you.

  7. Sounds like he's saying mass is a property that energy manifests. But, to begin with, there is only energy.

  8. Einstein was pretty shrewd…

    he didn't acknowledge that others before him had shown energy mass equivalence equation…1881 JJ Thompson… Heaveside 1889, Poynting 1884… even Poincare 1900, again book by Thomson 1904, where e=mc2 (squared) was shown…Hasenörhl published papers in 1904 mentioning the equation…even de Pretto a relatively unknown geologist published the equation in 1903 and speculated that classical mechanics kinetic energy formula e=1/2 mv2 could also be equal to e=mc2… if something moved at speed of light…

    Moreover, others did measurements on it in lab to arrive at a very accurate level more than 20 yrs prior to Einstein publication in 1905… while Einstein never did any scientific experiments in lab to prove it.

    So, Einstein was not the first one in 1905 and shouldn't be credited solely for this famous equation..

  9. So it doesn' t matter the effect aka luminens the flashlight omitts for the total weight? How about efficency then, how does that play into the equation?

  10. U have alot of amazing content but prblm is u r not explaning slowly.ur motive should be to make us clear in what u say .right?

  11. Space is Stationary or in motion ?
    if space is stationary , the then what is the movement of time of space .
    also know reference Clock of Space .
    in which clock reference , space clock getting slow or fast .
    if space is stationery like bend . what is the velocity of space at this bending point .
    Space need motion to live the time .

    if space velocity =0 time will T = infinitive if time = infinitive then what is the speed of space clock .

    because space living with time but here T=infinitive.

  12. m = E/ c2 , means that Contraction of Energy ( space ) with the speed of Light its form mass . space it self is energy . ( passing of time will be Zero )

    E= mc2 Expansion of mass with the speed of light form Energy. mass will Convert in space .

  13. How is this more than just semantics? The punchline was a let down for me. Its like saying to objects never touch. Yes they do the atomic forces are what define touching. The sun does in fact do alchemy changing hydrogen into helium. So what is the point of saying it doesn't? I get really annoyed when the emphasis is on "weird factor" while glazing over any practical point.

  14. The speed of light c2 is an aberration. An eccentricity. A departure from the "truth". Light speed can not be measured in "space". The heaven is not a vaccum! The heavens can not be measured. See Jeremiah 31:37. Psalms 103:12 says Yahusha removed the transgressions of his people "black israel" as far as the East is from the West. The heavens are filled with water – and we do not know what else? See Genesis 1:1-8. Messengers are in the heavens. Yahuah's charriots are in the heavens. His throne sits above the firmament.
    Space (the firmament) is not a measurable object. It has no starting nor ending. It was there in the beginning (Genesis1:1 & John 1:1). There are no vacuum tubes big enough to measure (what light is or is not). Light is a word, a vibration, a spirit that obeys the command of the living Yahuah. What is called light particles, is in fact, the imagination and will, manifest (made known) and are parts of the expanded substance of the black creator – Yahuah. Yes, I know he is spirit. His son, Yahusha, came and dwelt among his kin folk. They were so called black Hebrews. See John 1:1. This is where black Yahusha came from – the beginning. See John 1:11-14 – black Messiah lived among his black kin folk.
    We, (so called black people) DOS have been lied too about EVERYTHING we were forced to learn, believe and accept by the nations who used terrorist, and terrorism to indoctrinate and enslave us. E=mc2 does not work when put into proper perspective of reality. Neither does Planks law of black body radiation. Planks law uses substitute materials that are earthly. If I remember, he uses carbon fiber in his experiments. However, the heavens are water. The so called ether is a supernatural fluid that Yahuah called in the language of creation, mayim, from the root mem, or chaos. If you can measure anything in chaos, let me know and I will have some fries with that delicious car battery. Yum! All that praise heaped on these men who created fake news long before DJ T. To the Twelve Tribes Scattered Abroad.

  15. Sound too varied as to elements and properties discussed. I believe Einstein's original equation was much simpler and meant to be simpler. Most physicists tend to spin and twist things to make them more complicated and then they look smarter.
    I simply see energy, in general, as mass times weight to the 2nd power. This 2nd power was simply used as a modem or illustration to express the open, infinate property of energy. In other words, energy, in a general sense, has no limits. It is open ended and infinate power. This can apply to a small ball versus a hugh planet. The planet would have more energy unless the small ball's mass times it's weight would be greater than the planet. Extreme example but never the less true. This is how I read his equation in a simple and understandable form.

  16. C'mon guys, you're complaining about the speed at which this wonderful information is said to you? I expected better comments from the pbs group. There is no fluff here, it's all raw info that you can take to the bank with you.

    Beautifully done pbs, thank you.

  17. Ok let’s suppose an object has only kinetic energy and its moving at speed of light. So Etotal= 0.5mc^2 (because KE=0.5mv^2). Then by m(extra)=Etotal/c^2, m(extra)=0.5m………. meaning that when an object is running at speed of light, its mass only multiplied by 1.5? What did I do wrong?……. help!

  18. Interesting, I always understood invertedly what the equation meant: It is not energy that is mass in movement, but mass that is energy limited in its movements that create mass.

  19. This is ALL Bullshit. E=MC2 Means, Einstein = Murder Chinese TWICE. Once with the A bomb and again with its side effects (cancer). Only problem was that the Japanese got in the way LOL. FK U Einstein!

  20. 1:37 It has more mass due to kinetic energy.
    2:44 It doesn't have more mass due to kinetic energy.
    What? Was it an outdated viewpoint after 1 minute and 7 seconds?

  21. The other chap (Matt) that does these videos is much easier to follow as he has a more subdued tone. & doesn’t feel like he’s trying to get through the subject as fast as possible to get home

  22. If i have a box full of equal amounts of individual electrons and protons, then combine them to form an equal number of hydrogen atoms. The mass of the hydrogen atoms is less than that of the the electrons and protons. Has the closed box decreased in mass? (obviously not but, 5:22 since their combined mass is less, why? Is it because the electrical potential energy between a pair of an individual electron and proton, which extends infinitely by definition, is actually just ignored before their combination?)

  23. If we were to cool an object to absolute zero would it have a mass of zero? If not, what energy does it have? The particles have no kinetic energy themselves.

  24. Mass velocity equals resting mass divided by the square root of 1 minus velocity squared divided by the speed of light squared. M v = Mr/ (1-v^2/C^2) ^1/2

  25. The best way to make this understood is to say like 99.9% of your mass is NOT from the protons or neurtrons or electrons, or any "matter", that makes up your body. The VAST majority of your mass comes from the electric fields that surround your atoms.

  26. if everyone picked up a hammer then the mass of the earth would increase as the gravitational potential energy increases simultaneously. thank me later

  27. I feel like I’m reasonably intelligent but I couldn’t follow this video at ALL. I’m honestly more confused than I was before I watched it. I don’t understand the true meaning of the equation at ALL

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