Speaker 1: Hey, Daniel, has particle physics done anything useful lately?
Speaker 2: M you mean other than revealing the fundamental nature of reality?
Speaker 1: Have you done that?
Speaker 2: I mean it's a project.
Speaker 1: I mean that's all nice and cool, but it doesn't
Speaker 1: really help me, you know, with the dishes or you know,
Speaker 1: with my diet.
Speaker 2: I guess we did also invent the World Wide Web.
Speaker 2: That's pretty helpful.
Speaker 1: You mean web surfing. I would say that's not the
Speaker 1: most helpful thing in my life, but that was a
Speaker 1: long time ago. Anyways, what have you done for us recently?
Speaker 2: Yeah, maybe we should be coming up with like a
Speaker 2: fundamental physics diet plan.
Speaker 1: It's just coffee and doughnuts all.
Speaker 2: The time, existential angst about the nature of the universe.
Speaker 1: I guess the problem with physics is that it says
Speaker 1: that the faster you go, the more massive you get. Right,
Speaker 1: that's kind of an anti diet.
Speaker 2: I guess I was thinking, you know, black holes something
Speaker 2: something something liposuction, black holes. I don't know. I didn't
Speaker 2: really have it worked out.
Speaker 1: Quantum cosmetic surgery.
Speaker 2: Whoa, Orange County is definitely the place for.
Speaker 1: That, and you can get a ten to the color bage.
Speaker 1: Hi am jorhammy cartoonist and the creator of PhD comics.
Speaker 2: Hi. I'm Daniel. I'm a particle physicist and a professor
Speaker 2: at UC Irvine, and I was shocked when a pediatrician
Speaker 2: offered my one year old plastic surgery.
Speaker 1: Wait what they do that on one year.
Speaker 2: Old in Orange County? You're never too young for plastic surgery.
Speaker 1: Oh boy. I get to the offer like a subscription service,
Speaker 1: like a membership or something.
Speaker 2: It's a long term relationship. No. Our son had like
Speaker 2: a vein on his eyelid and the doctor was like,
Speaker 2: do you want me to remove that?
Speaker 1: And we were like, no, please, wait the eyelid or
Speaker 1: the vein. You're like, I think my son needs. It's
Speaker 1: his eyelid exactly.
Speaker 2: We were like, I'm pretty sure that's going to be fine,
Speaker 2: And newsflash, he's fine.
Speaker 1: Where You're like, I'm a real doctor, I don't think
Speaker 1: he meets any surgery.
Speaker 2: I'm not a real doctor, but I'm pretty sure he
Speaker 2: didn't need any surgery.
Speaker 1: Like, I'm not a real doctor, I just play one
Speaker 1: in the lab. But anyways, welcome to our podcast. Daniel
Speaker 1: and Jorge Explain the Universe, a production of iHeartRadio.
Speaker 2: In which we try to show you the nature of
Speaker 2: the universe in all of its unvarnished glory. We don't
Speaker 2: want to edit out the ugly bits and smooth over
Speaker 2: the bumps and wrinkles. We want to show you the
Speaker 2: universe the way it actually is, even when it conflicts
Speaker 2: with our intuition and runs aground for our preconceived ideas
Speaker 2: for how things move and flow and dance in the universe.
Speaker 1: That's right, that's because we love the universe just the
Speaker 1: way it is. We love the og universe, the original
Speaker 1: organic version of the universe, untreated, unvarnished, and pretty mysterious.
Speaker 2: That's right. We prefer the granola crunchy Berkeley version, with
Speaker 2: all of its hair and all the original places, even
Speaker 2: on all of its black holes.
Speaker 1: Well, let's not go too far there. I mean, I'm
Speaker 1: a big fan of socks and sandals, but you know,
Speaker 1: there's a time and a place.
Speaker 2: I'm all for accepting people and universes just the way
Speaker 2: they are.
Speaker 1: But it is a wonderful and beautiful universe. It doesn't
Speaker 1: need any cosmic surgery because when we look at it,
Speaker 1: we're just stricken with awe an amazement at how wonderfully
Speaker 1: complex and intriguing it all is.
Speaker 2: And one of my favorite things about the universe is
Speaker 2: that it's surprising. It's not like we look out into
Speaker 2: the universe and we're like, oh, yeah, that's pretty much
Speaker 2: how I expected, or oh yeah, there's nothing new out
Speaker 2: there to discover. Every time we dig deep into something,
Speaker 2: every time we scratch under the surface, we find out, Wow,
Speaker 2: the universe is quite different from the way that we
Speaker 2: imagined it, which is wonderful because it's an opportunity to
Speaker 2: learn to discover the truth instead of just coasting on
Speaker 2: our intuition.
Speaker 1: Yeah, the universe is very different out there in space,
Speaker 1: beyond our galaxy, beyond our cluster of galaxies, and it's
Speaker 1: also very different at the molecular and atomic and particle scills.
Speaker 1: Things are actually very different than our everyday experience.
Speaker 2: And we're tempted when we discover these new weird wrinkles
Speaker 2: in the universe to explain them in terms of things
Speaker 2: that we know, things we understand. It's a very natural
Speaker 2: a way to try to understand the universe, to describe
Speaker 2: it in terms of the language that you already have. Sometimes, though,
Speaker 2: that gets awkward. It's hard to understand how quantum particles
Speaker 2: dance around if you're thinking about them as little dots
Speaker 2: of stuff, And that's because they're not really little dots
Speaker 2: of stuff. And it's hard to think about velocity and
Speaker 2: energy and mass as things approach the speed of life
Speaker 2: because the definitions of those things have to change, and
Speaker 2: the way things move and bounce against each other and
Speaker 2: transfer energy and momentum is really very different at high
Speaker 2: speeds than it is down here in the slow motion
Speaker 2: life on Earth.
Speaker 1: Yeah, things are very weird and awkward in general when
Speaker 1: you talk to physicists, I feel, not just when you
Speaker 1: learn learn what they have to say.
Speaker 2: All right, this is not a therapy podcast. We're talking
Speaker 2: about the nature of the universe here.
Speaker 1: That's right. That's right. In the universe is not awkward
Speaker 1: or weird. It's just the way it is. And I
Speaker 1: guess it's us that are weird and awkward, right, because
Speaker 1: we have this picture of how the world works, but
Speaker 1: that may not be how the universe actually works.
Speaker 2: Yeah, And in physics, our project is to build a
Speaker 2: mathematical description of how things work in the universe, something
Speaker 2: that lets us make predictions and gives us a peek
Speaker 2: at the machinery behind the curtains that's deciding like what
Speaker 2: happens when two balls bounce against each other. But that
Speaker 2: doesn't always translate in an easy or simple way to English,
Speaker 2: the language that most humans speak. So when physicists are
Speaker 2: trying to explain how things work when the universe gets weird,
Speaker 2: they use the terms that we're familiar with, mass and energy, momentum,
Speaker 2: et cetera, and try to translate the weirdness in those terms.
Speaker 2: And so you hear a lot of explanations for what
Speaker 2: happens when things get fast. Some of those explanations are
Speaker 2: bang on, and some of them are a little bit misleading.
Speaker 1: Yeah, because I guess one of the biggest mind bending
Speaker 1: moments and autism and strangest moments in the history of
Speaker 1: science was when we found out that the universe is
Speaker 1: kind of difference once you start are moving really fast exactly.
Speaker 2: We've had Newtonian and Gallean mechanics for centuries, things that
Speaker 2: did a very good job of explaining what happens when
Speaker 2: two balls bounce against each other, and how momentum is transferred,
Speaker 2: and how things look when you're going fast. If you're
Speaker 2: driving in a car at thirty miles an hour, and
Speaker 2: you throw a ball at thirty miles an hour, then
Speaker 2: you know that ball should be moving at sixty miles
Speaker 2: an hour relative to the ground. All that stuff made
Speaker 2: sense for a long time until we started looking at
Speaker 2: things that weren't moving really really fast. We discovered there's
Speaker 2: a speed limit to the universe, and that really changed
Speaker 2: everything we thought about the nature of space and time
Speaker 2: and velocity and gives rise to all sorts of weird
Speaker 2: stuff that's very tricky to unpack.
Speaker 1: Yeah, it gets super tricky. Well, first of all, the
Speaker 1: idea that we have a speed limit in the universe
Speaker 1: is kind of wild. Like, you know, you sort of
Speaker 1: grew up thinking that disguise the limit. The more that
Speaker 1: you push something, the faster you go. But at some
Speaker 1: point the universe says, I think that's fast enough. It
Speaker 1: doesn't let you go faster than a certain speed.
Speaker 2: Yeah, it's a really bizarre feature of our universe, one
Speaker 2: that we've discovered experimentally at the Michaelson Morley. The experiments
Speaker 2: prove that light travels the same speed in every direction
Speaker 2: and effectively demonstrating that there is no absolute reference, framing
Speaker 2: that there is a maximum speed of information and transmission
Speaker 2: in the universe, which leads to all sorts of weird consequences,
Speaker 2: changes what we think about time and the nature of simultaneity.
Speaker 2: Things that happen at the same time for one person
Speaker 2: might happen in a different order for somebody else. The
Speaker 2: whole nature of reality becomes different when there is a
Speaker 2: maximum speed limit to the universe.
Speaker 1: Yeah, and I think it kind of makes people wonder
Speaker 1: what would happen if you try to go faster than
Speaker 1: the speed of light? Does the universe police come and
Speaker 1: flag you down and stop you? Or do you hit
Speaker 1: a wall?
Speaker 2: Or what are you considering trying to break some laws
Speaker 2: of the universe? Be asking for physics legal advice?
Speaker 1: Well, I'm trying to toe the line, you know. I'm
Speaker 1: kind of max out my life here. I need to
Speaker 1: know how far I can go.
Speaker 2: I just don't want to be held responsible if you
Speaker 2: get thrown in physics.
Speaker 1: Jail when I need a physics lawyer.
Speaker 2: I wonder if people who are lawyers are always on
Speaker 2: the look at for like, is this person asking me
Speaker 2: legal advice? I'm not going to get them in trouble
Speaker 2: if I say the wrong thing. I don't usually have
Speaker 2: to worry about that because most people aren't capable of
Speaker 2: trying to break the laws of the universe.
Speaker 1: I think most lawyers don't really care that much.
Speaker 2: But no, there is no physics police that are just
Speaker 2: going to pull you over. It's just that acceleration and
Speaker 2: momentums start working differently at high speeds. So you discover
Speaker 2: that you can pour energy into a particle, it just
Speaker 2: doesn't go much faster. So you can discover that as
Speaker 2: things approach the speed of light, you can keep pouring
Speaker 2: energy into something a rock, a particle of spaceship, whatever,
Speaker 2: it just doesn't go much faster. The same amount of
Speaker 2: energy doesn't get you increases in velocity the same rate.
Speaker 2: It's no longer linear. It becomes asymptotic.
Speaker 1: So today end podcast, we'll be tackling the question do
Speaker 1: things get more massive the faster they move? This is
Speaker 1: kind of like the anti diet, or at least I
Speaker 1: feel like it justifies maybe sitting down on your couch
Speaker 1: all the time, because if I get up up for
Speaker 1: my couch and I move, then I'm just going to
Speaker 1: gain more mass, Right, that's true.
Speaker 2: Well, what we're going to learn on the podcast today
Speaker 2: is that it's a little bit more complicated than that
Speaker 2: this is the kind of popular science thing you hear
Speaker 2: all the time and people write in and ask me about.
Speaker 2: And I think it was wide they taught in textbooks
Speaker 2: until about thirty forty years ago, the feeling that everything
Speaker 2: gets weird as you approach the speed of light, and
Speaker 2: then even your mass might change, things might get like
Speaker 2: infinitely heavy as you approach the speed of light. It's
Speaker 2: an attractive concept for people, I think, because it gives
Speaker 2: you a sense of the strange. But as we'll talk
Speaker 2: about today on the podcast, it's a little bit more
Speaker 2: complicated than that, and it's actually something of an outdated notion.
Speaker 1: Wait, wait, are you saying it's a massive lie.
Speaker 2: You know, there's a lot of different ways you can
Speaker 2: try to translate the crisp mathematics of relativity into English
Speaker 2: and into popular culture. This was one attempt early on
Speaker 2: that I don't think really works very well.
Speaker 1: I see it was just heavily exaggerated. Well, as usual,
Speaker 1: you were wondering how many people had wondered about this
Speaker 1: question at ask this about themselves, about the universe, about
Speaker 1: what happens when you try to go faster and faster,
Speaker 1: And so Daniel went out there into the Internet to
Speaker 1: ask people do you think things get more massive as
Speaker 1: you approach the speed of light?
Speaker 2: I am so grateful to everybody who answers these questions.
Speaker 2: They give me a sense for what people already know,
Speaker 2: and they give listeners a sense of what everybody else
Speaker 2: is thinking. If you would like to participate, please don't
Speaker 2: be shy. You're really very welcome to join the club.
Speaker 2: Just write to me two questions at Danielandjorge dot com.
Speaker 1: So think about it for a second. Do you think
Speaker 1: you should stay in your couch if you don't want
Speaker 1: to gain any mess? Here's what people had to say.
Speaker 3: This question just blows my mind. I'm just stumped. Do
Speaker 3: they get more massive? I guess maybe. I don't know how,
Speaker 3: but maybe something related to quantum mechanics.
Speaker 4: I don't know.
Speaker 2: As you approached the speed of light, I thought Einstein's
Speaker 2: equations told us that you would gain mess, But to
Speaker 2: an outside observer, I don't think you would actually look bigger.
Speaker 5: I mean, at the speed of lighte time was slower.
Speaker 5: Maybe space gets contracted.
Speaker 2: So I'm kind of stormy here.
Speaker 5: Maybe if that is true, then you will have a
Speaker 5: higher density and in that sense, wibly be more massive.
Speaker 2: Not sure.
Speaker 6: I think they do get more massive, but because it's
Speaker 6: it gets harder to move things at that speed, and
Speaker 6: not because they get more the feet.
Speaker 7: My understanding is mass and energy are interchangeable, so the
Speaker 7: more energy you have to pump into something to accelerate
Speaker 7: it closer and closer to the speed of light is
Speaker 7: really no different than making it more massive to begin with.
Speaker 7: So I think, yes, it gets more massive as you
Speaker 7: approach the speed of light, just because mass and energy
Speaker 7: are essentially the same thing.
Speaker 4: I think I remember hearing that they do get more
Speaker 4: massive as they approach the speed of light. I think
Speaker 4: it takes more energy to increase the speed, and like, yeah,
Speaker 4: they just can't really get to the speed of light
Speaker 4: unless it's like, you know, massless.
Speaker 5: I guess so based on the question. I'm not sure
Speaker 5: exactly why, but if has something to do with like
Speaker 5: the kinetic energy of something affecting its mass, then I
Speaker 5: would guess so.
Speaker 8: I think the answer is yes. First I was taught
Speaker 8: it that way. I've since heard that's an old school
Speaker 8: way of thinking about it. But definitely, if we consider
Speaker 8: energy as being mass, you know the way it works relativistically,
Speaker 8: you can concentrate energy as well as matter, and that
Speaker 8: is all mass energy. Then as you add velocity, you're
Speaker 8: adding energy and you become more massive.
Speaker 1: All right, a lot of great answers here. I feel
Speaker 1: like some people were blown away and some people were like, oh,
Speaker 1: I've heard of this. The answer is yes or no.
Speaker 2: Yeah, I thought this was really interesting. There's a lot
Speaker 2: of different ideas here about what energy is and what
Speaker 2: mass is. Very few people mentioned momentum even, but there's
Speaker 2: definitely this understanding that things change as you approach the
Speaker 2: speed of light, and that it's harder to go faster. Yeah.
Speaker 1: Somebody one of the listeners said that it's kind of
Speaker 1: strange that your mass would change, right, And that goes to.
Speaker 2: The heart of what we mean by mass. I think
Speaker 2: a lot of people think of mass is like the
Speaker 2: amount of stuff they have, and so it's really weird
Speaker 2: for them to imagine them getting like more stuff as
Speaker 2: they approach the speed of light. And that's one reason
Speaker 2: why I really don't like this concept of relativistic mass.
Speaker 2: It gives people the impression that something physical is happening,
Speaker 2: which isn't interesting.
Speaker 1: All right, Well, let's dig into it, and I guess
Speaker 1: let's start with the basics. As you said, let's start
Speaker 1: with the concept of mass. Now. I know mass is
Speaker 1: kind of a big mystery. We talked about it in
Speaker 1: our book, like what is mass? Anyways, we have a
Speaker 1: whole chapter about how we don't kind of know what
Speaker 1: mass is. But Daniel maybe step us through it. What
Speaker 1: do we know about what mass is?
Speaker 2: I think in the context of relativity and motion, the
Speaker 2: most important thing to think about is inertia, like the
Speaker 2: fact that it's not easy to change your velocity. You're
Speaker 2: flying through the universe at some speed. In order to
Speaker 2: change that speed, you need a push. Right. That's really
Speaker 2: what F equals is trying to say that to accelerate,
Speaker 2: you need to have a force applied to you, and
Speaker 2: that M in that equation, and F equals MA is
Speaker 2: the mass. It relates how much acceleration you get for
Speaker 2: how much force. We've all heard, for example, that the
Speaker 2: Earth's gravity on you is the same as your gravity
Speaker 2: on the Earth, Right, But we feel a much stronger
Speaker 2: force than the Earth does because the Earth has a
Speaker 2: huge mass. So we feel a much stronger acceleration than
Speaker 2: the Earth does because the Earth has a huge mass,
Speaker 2: and so its acceleration is tiny. Even though the force
Speaker 2: is the same. So really important concept in mass is inertia.
Speaker 2: That's really what mass is about when we're talking about motion,
Speaker 2: and that's connected to this idea of momentum. Right. Another
Speaker 2: way to think about F equals MA is that F
Speaker 2: is actually a change in momentum. When you're flying through
Speaker 2: the universe at a certain velocity, you have a certain momentum.
Speaker 2: In order to change your momentum, you need to have
Speaker 2: a force applied. So mass is this concept that tells
Speaker 2: us basically how hard it is to change your momentum.
Speaker 1: I feel like you're making us go that a rabbit
Speaker 1: hole a little bit, because then it makes me wonder, like,
Speaker 1: what is momentum anyways?
Speaker 2: Yeah, a momentum is something we know is important in
Speaker 2: the universe. It's a quantity that's conserved. Like we look
Speaker 2: at in the universe, we watch stuff, we see things happen,
Speaker 2: and we look for patterns, and a very important pattern
Speaker 2: are conservation laws. Things that don't change. So two balls
Speaker 2: bounce against each other, for example, you calculate all the
Speaker 2: momentum beforehand and all the momentum afterwards, and you notice
Speaker 2: it's the same. It is conserved. We actually know that
Speaker 2: there's a deep reason for why momentum is conserved. It's
Speaker 2: because space is the same everywhere. We did a whole
Speaker 2: fun podcast on Nother's theorem, which tells you that because
Speaker 2: space is the same everywhere, momentum has to be conserved.
Speaker 2: This is deep link there. So momentum is an important
Speaker 2: physical quantity in the universe. It's something that's really powerful
Speaker 2: and it really gives us insight into what's happened. And
Speaker 2: momentum is flowing through a system, right, but it's conserved
Speaker 2: in the universe. The universe at least thinks momentum is important,
Speaker 2: so maybe we should.
Speaker 1: Also well, how is it different from like energy? And
Speaker 1: is momentum the same as energy? Is the momentum of
Speaker 1: a particle or a baseball the same as its kinetic energy?
Speaker 1: How do the two connect?
Speaker 2: Yeah? Great question. First of all, momentum has directionality. You
Speaker 2: can have a momentum in one direction or momentum in
Speaker 2: another direction. It's a vector it points and for example,
Speaker 2: the Earth has a constant magnitude momentum, but the direction
Speaker 2: of its momentum is changing as it goes around the Sun.
Speaker 2: It's like an arrow that tells you which way the
Speaker 2: Earth is headed, and that's constantly changing. So the length
Speaker 2: of that vector isn't changing, but the direction of it is.
Speaker 2: And that's why it takes acceleration to move around the Sun,
Speaker 2: because you're changing the direction of that momentum vector. So
Speaker 2: momentum is a direction, right. Energy doesn't have a direction,
Speaker 2: it's just a number, right. And also, and energy includes
Speaker 2: something else. The energy of an object has two components.
Speaker 2: There's the internal energy what we call it's inertial mass,
Speaker 2: and the energy of its motion, it's kinetic energy. So
Speaker 2: there's two separate components there. So things could have energy
Speaker 2: when they're not moving, like an electron just sitting there
Speaker 2: has some mass, then that corresponds to some energy, and
Speaker 2: there's also energy of motion. Things can have only energy
Speaker 2: of motion, like a photon is just motion energy has
Speaker 2: no mass, or they can have both, like an electron
Speaker 2: flying through the universe has mass and that's energy and
Speaker 2: also has kinetic energy. So energy has two components. There's
Speaker 2: the mass and there's a contribution from the momentum, which
Speaker 2: we also call kinetic energy.
Speaker 1: And so the universe conserves both things, right, like it
Speaker 1: somehow conserves momentum, and it also conserves energy, but not
Speaker 1: necessarily the same way I think, right.
Speaker 2: So there's a little asterisk there in flat space. Yes,
Speaker 2: energy is conserved in the global universe. As space expands,
Speaker 2: actually energy increases, so energy is not strictly conserved in
Speaker 2: the universe. There's a whole podcast episode we did about
Speaker 2: that if you want to dig into it. But let's
Speaker 2: just assume we're like living in flat space and we're
Speaker 2: bouncing balls and particles off each other. We wouldn't notice
Speaker 2: the expansion of the universe. So let's just say for
Speaker 2: the sake of this discussion that, yes, energy is conserved.
Speaker 2: And so you're right, momentum is conserved and energy is conserved,
Speaker 2: and those are actually related. Those are four separate conservation
Speaker 2: laws because energy is one number and momentum is three numbers.
Speaker 2: Because we have three dimensions of space, and momentums can
Speaker 2: serve separately in each of those dimensions. So we have
Speaker 2: four conservation laws, three from momentum and one from energy.
Speaker 2: And in particle physics at least we group energy and
Speaker 2: momentum together into something we call four momentum, like the
Speaker 2: four dimensions of space time, and we say there's conservation
Speaker 2: of form momentum, which combines momentum and energy into one
Speaker 2: conservation law.
Speaker 1: So then mass is related to both things, like mass
Speaker 1: makes your momentum go higher and it makes your energy
Speaker 1: go higher.
Speaker 2: Yeah, that's right. So mass is like your internal stored energy.
Speaker 2: Take a proton, for example, it has a bunch of mass.
Speaker 2: Where does that mass come from. It comes from the
Speaker 2: internal energy of the proton, Like there's the mass of
Speaker 2: the quarks. They get their mass from the Higgs boson.
Speaker 2: Then there's the mass of the binding of those quarks together,
Speaker 2: and that's where most of the mass of the proton
Speaker 2: comes from. So that proton has mass, and you're right,
Speaker 2: that's part of its energy, and the proton could also
Speaker 2: have momentum that's another part of its energy. So we
Speaker 2: think of the mass as the thing that makes it
Speaker 2: hard to push on something or easier to put push
Speaker 2: on something but has low mass, and then there's also
Speaker 2: energy stored in its motion.
Speaker 1: Okay, So then generally speaking, mass is just what makes
Speaker 1: things harder to move, right.
Speaker 2: Basically, that's exactly right. That's the concept of inertial mass
Speaker 2: basically relate to the objects inertia, which tells you how
Speaker 2: hard is it to change its momentum.
Speaker 1: Right, And then there's a concept of gravitational mass, which
Speaker 1: is a different concept, but it's the same number.
Speaker 2: Yeah, And there's a bunch of really fascinating wrinkles here.
Speaker 2: Like in Newton's world, he had F equals maa, which
Speaker 2: tells you about how hard it is to push something.
Speaker 2: And he also had this number m in his gravitational
Speaker 2: law gmm over r square, which tells you the force
Speaker 2: between two objects. And in Newtonian physics, these two things
Speaker 2: are different numbers. They're written in the same way, the
Speaker 2: same letter M in F equals ma and M in
Speaker 2: gmm over r squared. But in principle they could have
Speaker 2: been totally different, right. It was a bit of a
Speaker 2: mystery in Newtonian physics why these two numbers always seem
Speaker 2: to have the same value. Einstein unified these things in
Speaker 2: general relativity and told us that actually inertial gravitational masses
Speaker 2: have to be the same because the corner to Einstein,
Speaker 2: there is no acceleration due to gravity. There is no
Speaker 2: force due to gravity. It's just inertial motion through curved
Speaker 2: space time that when you are having inertial motion, there's
Speaker 2: no forces on you through space time. That's what gravity
Speaker 2: looks like. So motion due to gravity is actually just
Speaker 2: inertial motion and you're just really in free fall.
Speaker 1: Right, So like, for example, the Earth orbiting around the Sun.
Speaker 1: It's not like there's a force pulling the Earth towards
Speaker 1: the Sun, or there's no centripetal force there is, just
Speaker 1: that the space around the Sun for the Earth is
Speaker 1: sort of curved and it's shaped like a circle basically.
Speaker 2: Right, Yeah, that's right. If space were flat, everything we
Speaker 2: just move in what looks to us like straight lines.
Speaker 2: But when space is curved, things move differently and it
Speaker 2: looks like there's a force there bending their paths. But
Speaker 2: really it's just motion through curved space. Because we can't
Speaker 2: see that curvature. You can like look through space and
Speaker 2: see the curvature of space the way you can see
Speaker 2: curvature of a road. It seems like a bit of
Speaker 2: a mystery why things are moving in curves, and of
Speaker 2: course is that space is curved, so there's an apparent
Speaker 2: force there, or.
Speaker 1: More accurately, you mean like space time, right, Like maybe
Speaker 1: space is not curve, but space time is.
Speaker 2: It's definitely more coherent to think about relativity in terms
Speaker 2: of space time because the way like energy and momentum
Speaker 2: are linked, space and time are definitely linked. You can't
Speaker 2: talk about the curvature of space as well and the
Speaker 2: curvature of time separately. They make more sense when you
Speaker 2: think about them together. But yes, space itself can also
Speaker 2: be curved, but space time as well.
Speaker 1: All right, So then that's mess. It's how hard it
Speaker 1: is to push on something, and it's also sort of
Speaker 1: like the effect something has on space time around it.
Speaker 2: Yeah, and this is very intuitive if you're like playing billiards,
Speaker 2: or you're shooting a basketball, or you're rolling rocks down hills,
Speaker 2: and it's aligns with our sense that like things that
Speaker 2: have more stuff to them are harder to push, and
Speaker 2: that all makes sense at low speeds. Things change a
Speaker 2: little bit as you get very high velocity, and then
Speaker 2: you have a question for like, what do you change
Speaker 2: you change momentum, do you change maths, change energy? What's
Speaker 2: the most sensible way to think about these things?
Speaker 1: Yeah, because, as we mentioned, there's the idea out there
Speaker 1: that the faster you go, and as you approach the
Speaker 1: speed of light, your mass starts to get bigger and bigger,
Speaker 1: which is a problem for us who are trying to
Speaker 1: stay slim, and so let's dig into that scenario and
Speaker 1: the problems with that scenario and what it all means
Speaker 1: about the loss of the universe. But first, let's take
Speaker 1: a quick break. All right. We are talking about a
Speaker 1: massive topic here, and it's going by really fast, and
Speaker 1: it's about how really massive things go really fast. Things
Speaker 1: get massive as they go really fast.
Speaker 2: Yeah, things definitely do change as you approach the speed
Speaker 2: of light, and a lot of your intuition goes out
Speaker 2: the window. You can just lean into the mathematics and say, well,
Speaker 2: there are new formulas and I can just use them
Speaker 2: and calculate stuff. But we also want to have like
Speaker 2: an understanding of how the universe works. We want to
Speaker 2: develop a new intuition. So it's important that we make
Speaker 2: sense of what the words mean as things change.
Speaker 1: Okay, so let's talk about change. I guess now, before
Speaker 1: when we just had Newtonian physics, things were kind of simple,
Speaker 1: like if you wanted to change the velocity of something,
Speaker 1: you had to apply a certain force, and a certain
Speaker 1: force would always give you the same amount of velocity change,
Speaker 1: kind of like no matter if you're standing still or
Speaker 1: if you're going fast. If you applied and have you
Speaker 1: always got that change in velocity acceleration.
Speaker 2: Yeah, that's right, F used to equal M in a
Speaker 2: very simple and straightforward way. Or equivalently, we could say
Speaker 2: F is the change in momentum.
Speaker 1: Right, So that's Newtonian physics. But then we sort of
Speaker 1: learned a little bit more about relativity, which says that
Speaker 1: that's not quite true.
Speaker 2: Yeah, because there is a maximum speed to the universe.
Speaker 2: If you pour energy into something trying to get it
Speaker 2: going faster, you don't always get the same amount of
Speaker 2: speed up, which means like it's harder to add velocity
Speaker 2: in the direction something is moving. You have rocket ship
Speaker 2: and it's already going at ninety percent of the speed
Speaker 2: of light, and you fire the engines the same amount
Speaker 2: you did earlier, you're not going to get the same
Speaker 2: amount of speed up even if you're applying the same.
Speaker 1: Force, right, Because I guess under Newtonian physics, you could
Speaker 1: technically go infinitely fast, right, Like if you just kept
Speaker 1: pushing on an object over a long long period of time,
Speaker 1: we just keep going faster and faster and faster because
Speaker 1: F equals ma A And so if I apply a
Speaker 1: constant force to something the velocity is going to keep increasing,
Speaker 1: increasing and increasing, and eventually you would go faster than
Speaker 1: the speed of light in a Newtonian universe.
Speaker 2: Yeah, that's exactly right.
Speaker 1: But we seem to have this speed limit that says
Speaker 1: you can go faster and faster, and so I guess
Speaker 1: my question is what happened then? Did we have to
Speaker 1: adjust our math or does the math tell you why
Speaker 1: you can't go faster than the speed of light.
Speaker 2: We definitely had to adjust our math, right, because those
Speaker 2: formulas are wrong. As you say, they predict you could
Speaker 2: go infinitely fast. So what was wrong about those formulas? Well,
Speaker 2: it turns out our formula form momentum was wrong. We
Speaker 2: thought momentum was just like mass times velocity, and then
Speaker 2: we thought that quantity was conserved in the universe. Turns
Speaker 2: out we were missing a term. There's another term in
Speaker 2: that equation, this thing we call the boost factor. We
Speaker 2: write it as gamma in relativity. It's just a number,
Speaker 2: but if you're going at slow speeds, that number is
Speaker 2: basically one, so it doesn't change your equation. But as
Speaker 2: you approach to the speed of light, that number grows
Speaker 2: to infinity. So what it means is momentum is different
Speaker 2: from what we thought it was. We talked about how
Speaker 2: momentum is this important quantity in the universe that's conserved.
Speaker 2: That's true, but it's not M times V. There's a
Speaker 2: different expression for momentum, and that's the thing that's actually
Speaker 2: conserved in the universe. It turns out M times V
Speaker 2: times this gamma factor. So momentum changes as you approach
Speaker 2: the speed of light, and that's why it's harder to
Speaker 2: increase your velocity as you approach the speed of light,
Speaker 2: because your momentum is changing. It requires a larger force
Speaker 2: to change your momentum.
Speaker 1: I guess this is where it gets kind of confusing, because,
Speaker 1: first of all, all like you're saying that as I
Speaker 1: go faster, my momentum decreases, But doesn't that depend on
Speaker 1: how fast I'm going relative to who or what? Like?
Speaker 1: To me, I'm not going fast at all. If I'm
Speaker 1: going really fast. To me, it just looks like the
Speaker 1: universe is moving around me.
Speaker 2: So, first of all, as you go faster, your momentum
Speaker 2: still increases. That's always true, it's just not a linear increase.
Speaker 2: And you're absolutely right that all of these things depend
Speaker 2: on your frame right, depends on who's watching. Somebody who's
Speaker 2: in a spaceship with you is going to see you
Speaker 2: at zero velocity, and somebody who's on Earth as you
Speaker 2: zip by, it's going to see you moving at very
Speaker 2: high speed. So you're absolutely right. There's no sense of
Speaker 2: talking about, like, what is my velocity in an absolute way.
Speaker 2: It's always measured relative to some observer. So there's an
Speaker 2: important difference between things that are invariant, where everybody agrees
Speaker 2: on them no matter their velocity, and things that are conserved,
Speaker 2: things that don't change in a frame of reference. So momentum,
Speaker 2: for example, is conserved for some observer. You always see
Speaker 2: momentum conserved, like before collision. After collision is the same momentum,
Speaker 2: but momentum is not invariant. Another observer moving at a
Speaker 2: different speed will see a different set of momentum, but
Speaker 2: they will also see momentum conserved. So momentum is conserved,
Speaker 2: meaning for a given observer it doesn't ever disappear or appear,
Speaker 2: but it's not invariant, meaning different people will measure different
Speaker 2: amounts at different velocities.
Speaker 1: Okay, so then I think what you're saying is that
Speaker 1: momentum is not linear. It gets kind of wonky the
Speaker 1: faster you go. And the way it gets wonky is
Speaker 1: that it gets kind of ridiculously big as you get
Speaker 1: closer to the speed of light. Right, you said, momentum
Speaker 1: equals mass time velocity times gamma, and gamma is basically
Speaker 1: one when we're standing still, but it gets to infinity
Speaker 1: as we get closer to the speed of light.
Speaker 2: Exactly. And if you think about force not just as
Speaker 2: mass times acceleration, but as the change in momentum, then
Speaker 2: if your momentum is really really big, then it becomes
Speaker 2: hard to change your momentum. You need to apply a
Speaker 2: really really big force to change your momentum. And your
Speaker 2: momentum grows very very quickly near the speed of light.
Speaker 2: As you say, it approaches infinity as velocity approaches the
Speaker 2: speed of light.
Speaker 1: So I guess I get more concretely, it would mean
Speaker 1: like my couch, me sitting in my couch, my momentum
Speaker 1: would be my mass times my velocity, which in this
Speaker 1: case I guess it's zero, but it would just in
Speaker 1: my mass timeline my velocity. But if I was moving
Speaker 1: at two hundred thousand kilometers per second, then my momentum
Speaker 1: would be not just my mask my velocity, but it'ld
Speaker 1: be mass time my velocity times a really big number,
Speaker 1: which is this adjustment factor that gets bigger the closer
Speaker 1: you move to the speed of light.
Speaker 2: Exactly. This gamma factor is the thing that Newton missed
Speaker 2: in momentum basically, and he missed it because for everything
Speaker 2: he measured and he saw, it was just one, so
Speaker 2: it didn't change any of his calculations. Any number multiplied
Speaker 2: by one is just itself. So you have like a
Speaker 2: hidden factor in your equations that's always one. You can't
Speaker 2: discover it. You can only discover it when it changes
Speaker 2: from one, and it only changes from one as you
Speaker 2: approach the speed of light.
Speaker 1: So I think kind of the message is that the
Speaker 1: universe is kind of like, Okay, if you want to
Speaker 1: move something from your couch to your kitchen, that's fine,
Speaker 1: you can do that. It's going to cost you this much.
Speaker 1: But if you want to move it from you know,
Speaker 1: your couch to almost as to the speed of light
Speaker 1: or super duper fast, it's going to cost you that
Speaker 1: plus an extra like universe tax or something exactly that
Speaker 1: says that, oh, that's going to cost you a lot
Speaker 1: a lot, and somehow the idea is that it that
Speaker 1: kind of lets the universe prevent you from going faster
Speaker 1: than the speed of light.
Speaker 2: Yeah, and the universe tax it's basically zero if you're
Speaker 2: not moving very fast. Even if you're moving at like
Speaker 2: half the speed of light, this gamma factor, this boost,
Speaker 2: this universe tax is like fifteen percent. So even at
Speaker 2: half the speed of light, it's barely noticeable. As you
Speaker 2: get to like ninety percent of the speed of light,
Speaker 2: it's like two point three. And if you get to
Speaker 2: like ninety nine percent of the speed of light, it's
Speaker 2: like seven ninety nine point nine percent of the speed
Speaker 2: of light, it's like twenty two. So it increases very
Speaker 2: very quickly as things get fast.
Speaker 1: Well, I didn't know the universe was so progressive.
Speaker 2: Exactly. Momentum, billionaires, the universe is coming for you. Yeah,
Speaker 2: And so really that's fundamentally what's happening. We like to
Speaker 2: think about momentum because that's something the universe conserves. That's
Speaker 2: something that's important to the universe, energy and momentum, and
Speaker 2: that's really what's driving this experience that it's harder to
Speaker 2: accelerate as you get towards the speed of light. And
Speaker 2: remember that momentum is directional, right, and so adding velocity
Speaker 2: in the direction you're already going takes actually different amounts
Speaker 2: of momentum than adding velocity like perpendicular to your motion.
Speaker 2: It gets very complicated.
Speaker 1: So I think you're saying that momentum is conserved in
Speaker 1: the universe, but there's there's sort of a premium on
Speaker 1: higher momenti momentumus like the bigger momentum has somehow cost
Speaker 1: you more.
Speaker 2: Exactly, And that raises the question like, well, what do
Speaker 2: we do about mass. We used to have this notion
Speaker 2: and that mass told us how hard it is to
Speaker 2: push something, and in the old sense of momentum, it's
Speaker 2: just mass times velocity. Then it all made sense, and
Speaker 2: then you get the equation F equals MA, AND's a
Speaker 2: very natural linear relationship between acceleration and force. That all
Speaker 2: changes when we change the definition of momentum. You no
Speaker 2: longer have F equals M, and so you have to
Speaker 2: think about, like what do you do with mass.
Speaker 1: I think you're saying, like, we have this tax that
Speaker 1: the universe puts on momentum. Now do you take that
Speaker 1: tax and fold it into the definition of mass, or
Speaker 1: is mass still mass, but then you have this extra tax,
Speaker 1: which is not mass exactly.
Speaker 2: And so the modern idea, the one that most physicists use,
Speaker 2: is exactly that to say, let's just leave mass alone.
Speaker 2: Mass is related to your internal stored energy. Let's define
Speaker 2: mass to be something everybody agrees on, no matter what
Speaker 2: their velocity is. And let's just change the definition momentum,
Speaker 2: so mass stays as M whatever it was before, and
Speaker 2: now momentum is M comes v and we conclude the
Speaker 2: gamma factor there in momentum. The other idea, the one
Speaker 2: that leads to this confusion, is this concept of relativistic mass,
Speaker 2: and say, oh, let's redefine mass to be mass times gamma.
Speaker 2: Let's fold that gamma factor into the mass, and that
Speaker 2: lets us keep momentum as mass times velocity because we
Speaker 2: like that equation. And so there's sort of a choice
Speaker 2: to be made there, like do you redefine momentum or
Speaker 2: do you redefine mass?
Speaker 1: Well, I see, it kind of depends on whether you
Speaker 1: define mass as how hard you are to push when
Speaker 1: you're just sitting on your couch, or how hard you
Speaker 1: are to push at any point, or no matter how
Speaker 1: fast you're moving.
Speaker 2: It's definitely a choice, right, It's a definition, and you
Speaker 2: can make one choice or the other, and the equations
Speaker 2: all work. I think it's more coherent. It makes more
Speaker 2: sense if you call mass as you say how hard
Speaker 2: it is to push you when you're sitting on your couch.
Speaker 2: It's tempting to say, well, it makes more sense to
Speaker 2: use masses how hard it is to push when you're
Speaker 2: moving fast as well. But as we can dig into
Speaker 2: in a moment that doesn't actually hang together. You can't
Speaker 2: have just a single number that tells you how hard
Speaker 2: it is to speed up, because that actually depends a
Speaker 2: little bit on the direction of your speed up. So
Speaker 2: relativistic mass is a little bit complicated and problematic. It
Speaker 2: doesn't really do that job. Doesn't let you use F
Speaker 2: equals ma again by redefining m I see.
Speaker 1: So I think maybe for the people who had heard
Speaker 1: that the faster you go, or the closer you get
Speaker 1: to the speed of light, the more mass if you get,
Speaker 1: what they probably heard at that time was that you
Speaker 1: do get harder to push as you get closer to
Speaker 1: the speed of light. But that doesn't mean that your
Speaker 1: mass went up, but that there's an adjustment to your momentum,
Speaker 1: or there's a premium to how much momentum cause, which
Speaker 1: makes it harder for you to push you, but it
Speaker 1: doesn't change how hard you are to get off the couch.
Speaker 2: Yeah, and physics has sort of changed its mind about this.
Speaker 2: Even Einstein for a while used this concept of relativistic mass,
Speaker 2: and it was taught in textbooks. So people who were told, like,
Speaker 2: your mass increases as you approached the speed of light,
Speaker 2: that's not wrong. It just depends on what you mean
Speaker 2: by mass. So it really is our choice what do
Speaker 2: we mean by this word mass. You used to have
Speaker 2: a very crisp and clear definition that everybody agreed about
Speaker 2: at low speeds. At high speeds, it becomes a little
Speaker 2: bit trickier, and you can use the word relativistic mass.
Speaker 2: It's not like it's wrong. It's just a choice for
Speaker 2: how to organize the ideas. And now we think it
Speaker 2: makes more sense to just describe mass as how hard
Speaker 2: it is to push you when you're sitting on your couch,
Speaker 2: and to leave momentum to absorb all the messiness.
Speaker 1: I guess you're saying, like mask can just be how
Speaker 1: hard it is to push you off your couch, but
Speaker 1: we can introduce maybe a constantly called relativistic mass, where
Speaker 1: people did introduce a concept called relativistic mass, which is
Speaker 1: how hard you are to push at all speeds, and
Speaker 1: that changes the faster you go.
Speaker 2: That does change the faster you go, though I would
Speaker 2: say the two choices are not equal. I would say
Speaker 2: there's some problems with relativistic mass. I mean, problem number
Speaker 2: one is that it's just a number, whereas momentum is
Speaker 2: three numbers. It's a direction. And so if you're going
Speaker 2: to talk about how hard it is to change your momentum,
Speaker 2: then if you have a high speed in one direction,
Speaker 2: you basically have a different relativistic mass in each direction,
Speaker 2: because it's harder to push you in the direction you're
Speaker 2: already going fast than it is to push you perpendicular
Speaker 2: to that direction. So then you need like a transverse
Speaker 2: relativistic mass and the longitudinal relativistic mass. It gets messy
Speaker 2: very very quickly.
Speaker 1: Well, I think what you're saying is that it's not
Speaker 1: that it gets message is that the word relativistic mass
Speaker 1: is a vector, like you have to define which way
Speaker 1: you're pointing your li relativistic mass, just like you have
Speaker 1: to define which way you're pointing your momentum.
Speaker 2: Well, we already have that concept of momentum, right, so
Speaker 2: we don't really need a vector of relativistic mass. And
Speaker 2: the formula for relativistic mass, it turns out, is actually
Speaker 2: just energy divided by the speed of light. So relativistic
Speaker 2: mass doesn't actually give you anything new that you don't
Speaker 2: already have for momentum and energy, so sort of unnecessary.
Speaker 2: Whereas invariant mass, your rest mass is actually something independent
Speaker 2: and interesting. It tells you, like what is the thing.
Speaker 2: You know, photons and electrons and protons all have different
Speaker 2: rest masses. That tells you a little bit about like
Speaker 2: what the thing is, what it has to it, which
Speaker 2: I think is more closely connected to like our intuitive
Speaker 2: idea for what mass is that it tells you something
Speaker 2: about like what you're made of.
Speaker 1: And I guess for people who maybe missed it or
Speaker 1: are not super familiar with this idea of directionality, I
Speaker 1: think what you're saying is that, like, if I'm going
Speaker 1: really fast from here to Andromeda, for example, in one
Speaker 1: particular direction, and I'm going at the speed of light,
Speaker 1: then my momentum in the direction from here to Andromeda
Speaker 1: is really high because I'm going really fast, and so
Speaker 1: it's really hard to accelerate be more in the direction
Speaker 1: of Andromeda. But maybe if you're going along with me
Speaker 1: and you try to push me in a direction that's
Speaker 1: perpendicular to the side of the direction from here to Andromeda,
Speaker 1: then you're not going to notice me being super massive
Speaker 1: or having this huge relativistic mass. Is just going to
Speaker 1: feel to you like I'm sitting on the couch, Like
Speaker 1: I'm sitting on the couch in one direction, but I'm
Speaker 1: going really fast in another direction.
Speaker 2: Yeah, that's approximately true, because your motion towards and Drameda
Speaker 2: does change your overall velocity, and the limit is on
Speaker 2: the total velocity in any direction, not just in one direction.
Speaker 2: But for the most part that's true. You know, what
Speaker 2: happens at those very high speeds is like, if you
Speaker 2: push in one direction, you don't get accelerated in the
Speaker 2: direction you were pushing, because the pushing has a different
Speaker 2: impact based on your momentum, right, and so in some
Speaker 2: directions you already have a lot of momentum, and other
Speaker 2: directions you don't have as much momentum, and so the
Speaker 2: pushing changes your momentum differently in those different directions. So
Speaker 2: force and acceleration no longer line up. So F doesn't
Speaker 2: equal ME at very high velocities. Instead, you have to
Speaker 2: use F equals change in momentum. That's the real formula.
Speaker 1: I feel like you're kind of saying, like, just forget
Speaker 1: about mass, like you've seen it on the couch and
Speaker 1: nobody cares about that. Really, what we care about is
Speaker 1: all hard you arc to push in any particular direction.
Speaker 1: Is that kind of what you're saying, right, Like you're saying,
Speaker 1: like res mass, that's just the thing. It doesn't really change,
Speaker 1: nobody cares. What's really happening at these high speeds is
Speaker 1: that weird things are happening with your momentum.
Speaker 2: Yeah, I'm saying, let's talk about what's really important, and
Speaker 2: it's high speeds. It's momentum that's important. Mass is still important.
Speaker 2: It's very interesting and very important, and it tells you,
Speaker 2: like what the thing is. In particle physics, we talk
Speaker 2: about res mass all the time, Like we measure a
Speaker 2: particle where like, oh, what was its mass? Okay, it
Speaker 2: must be an electron or look we found a new
Speaker 2: particle at one hundred and twenty five GeV mass, that's
Speaker 2: got to be something new. We've never seen a particle
Speaker 2: with that mass before. So mass is still very very important,
Speaker 2: but it tells you something different. It's tells you something
Speaker 2: about the character and the nature, the existence, the identity
Speaker 2: of the particle. And what we're talking about here is
Speaker 2: like motion near the speed of light, that's all about momentum.
Speaker 2: And so really, let's talk about momentum when we're talking
Speaker 2: about very high speed motion, and let's talk about mass
Speaker 2: when we're talking about you know, what the thing is
Speaker 2: made out of. I think those are two separate concepts,
Speaker 2: and it's best to disentangle them. Is the point. Not
Speaker 2: that nobody cares about rest mass, it's just it doesn't
Speaker 2: help us understand motion near the speed of light as much.
Speaker 1: No, yeah, I know what you mean. My spouse definitely
Speaker 1: cares if I say to my count all day. But
Speaker 1: I think what you're saying, maybe for listeners, I think
Speaker 1: what you're saying is that if you've heard the phrase
Speaker 1: like your mask gets bigger as you go closer to
Speaker 1: the speed of light, then really what you should hear
Speaker 1: in your head or how you should correct a person
Speaker 1: saying it is that your relativistic mass gets bigger as
Speaker 1: you get closer to the speed of light. And also
Speaker 1: common asterisk. Nobody or modern physicists don't really talk about
Speaker 1: relativistic mass or use that as a concept exactly.
Speaker 2: A relativistic mass is really just another way to say energy.
Speaker 2: Like the relationship in the formula is between relativistic mass
Speaker 2: and energy that have exactly the same value. One is
Speaker 2: just multiplied by the speed of light squared, so they
Speaker 2: change in exactly the same way. So relativistic mass is
Speaker 2: just another way to say, like how much energy does
Speaker 2: something have. It's a way to try to combine the
Speaker 2: rest mass and the kinetic energy together into one like
Speaker 2: overall coherent energy, and then to say, oh, well that's
Speaker 2: all A new kind of mass would just say that
Speaker 2: energy of the particle is kind of like its mass
Speaker 2: of motion. I'm just here to say, like, okay, let's
Speaker 2: just leave mass to be mass of a rest particle
Speaker 2: and to talk about motion. Will leave that as kinetic energy.
Speaker 2: But we have to invent a concept called mass of motion.
Speaker 2: We already have energy of motion. We already have this
Speaker 2: concept described In other words, relativistic mass doesn't really add
Speaker 2: anything if you already have momentum and you have energy.
Speaker 2: So let's leave mass to do its job and tell
Speaker 2: us about like the nature of the object when it's
Speaker 2: sitting on its couch.
Speaker 1: All right, Well, I think we've made that kind of clear,
Speaker 1: and so let's get a little bit deeper into why
Speaker 1: this term is not quite applicable or useful or help
Speaker 1: or even accurate, and what it means about this speed
Speaker 1: limit of the universe and why it exists. But first
Speaker 1: let's take another quick break. All right, we're talking about
Speaker 1: sitting on our couches. Who doesn't enjoy that? And when
Speaker 1: we're sitting in our couch going at zero velocity relative
Speaker 1: to other people, we have a certain amount of mass
Speaker 1: and a certain resistance to movement, which Daniel, I think
Speaker 1: you're saying, that's what we should call mass, not how
Speaker 1: hard you are to push when you're going really.
Speaker 2: Fast, exactly. I think the question you should ask yourself
Speaker 2: is like what are you trying to talk about when
Speaker 2: you talk about mass? And for me, I want to
Speaker 2: talk about, like what is the thing made out of?
Speaker 2: What does it have stored inside of it? And that
Speaker 2: really doesn't change when you go to high velocity. A
Speaker 2: proton moving and high speed doesn't have more stuff to
Speaker 2: it doesn't have more gluons inside of it contributing to
Speaker 2: its mass. It's the same proton. It's just moving faster.
Speaker 2: It has energy of motion, which definitely will affect how
Speaker 2: you accelerate it and how you push it and how
Speaker 2: it responds to those pushes, but doesn't change what it
Speaker 2: is fundamentally. And to me, mass is answering that question
Speaker 2: of like, what is in this thing now?
Speaker 1: I guess the question would be does your gravitational mass
Speaker 1: also change as you go faster or close to the
Speaker 1: speed of light or do you still have the same
Speaker 1: gravity or is that not even relevant in relativity.
Speaker 2: I think that's another reason not to use relativistic mass.
Speaker 2: If you think about relativistic mass of things getting more
Speaker 2: massive as their approach to speed of light and this
Speaker 2: like mass of motion, then you're tempted to think that
Speaker 2: things should have more gravity as they're moving faster. And
Speaker 2: then you might go down the rabbit hole and be like, well,
Speaker 2: if I take a proton and give it a lot
Speaker 2: of speed, why doesn't it turn into a black hole.
Speaker 2: Or if I throw a baseball fast enough, why doesn't
Speaker 2: it collapse into a black hole? If it's gaining more
Speaker 2: relativistic mass, shouldn't that give it also more gravitational mass
Speaker 2: and collapse? Right. We talked about this once on a podcast.
Speaker 2: It's a really interesting and fascinating question because, on one hand,
Speaker 2: the curvature of base time, the thing that could actually
Speaker 2: create a black hole for you, doesn't just depend on mass.
Speaker 2: It also does depend on energy.
Speaker 7: Right.
Speaker 2: General relativity tells us that space bends in response to
Speaker 2: mass and energy, and so you might think, like, oh,
Speaker 2: it doesn't matter if you choose relativistic mass or inertial mass.
Speaker 2: It just depends on the mass and the energy altogether.
Speaker 2: And that's true. But general relativity is a bit more
Speaker 2: complicated than that. You don't just like add up all
Speaker 2: the mass and energy in space and say that tells
Speaker 2: you the curvature. It's a stress energy tensor. There's all
Speaker 2: these components and some ad and some subtract. It's very complicated,
Speaker 2: and the bottom line is that kinetic energy does not
Speaker 2: contribute to the curvature of space. We know this because
Speaker 2: we know that black holes exist for every observer It's
Speaker 2: not like if I'm holding a baseball, I don't see
Speaker 2: a black hole and somebody is zipping by at high
Speaker 2: speed sees it as a black hole. That's not possible.
Speaker 2: Something's a black hole. It's a black hole for everybody,
Speaker 2: And so only the rest mass can contribute to making
Speaker 2: something a black hole, which is a long way of
Speaker 2: saying relativistic mass confuses you because it makes you think
Speaker 2: that you should be adding mass to this object, which
Speaker 2: might lead it to a collapse to a black hole.
Speaker 2: But that definitely doesn't happen, I see.
Speaker 1: So then we just stick to mass as hell hard
Speaker 1: it is to move me on my couch. And when
Speaker 1: we talk about going close to the speed of light,
Speaker 1: then we just just say that momentum gets harder to
Speaker 1: change as you go faster and faster exactly.
Speaker 2: And those calculations in general relativity of like folding in
Speaker 2: kinetic energy, those are a beast And I don't even
Speaker 2: think people have actually been able to do those calculations.
Speaker 2: When they have to do them, they use the trick
Speaker 2: and say, oh, well, if there's a black hole in
Speaker 2: any frame, there's a black hole in every frame, so
Speaker 2: let's do this calculation and the simplest for him, where
Speaker 2: the thing is at rest, where it just depends on
Speaker 2: its mass. I think nobody knows how to do that calculation.
Speaker 2: It's so complicated, but it's just another way of saying
Speaker 2: when we think about gravity also not just like the
Speaker 2: inertial nature of the thing, but also the gravitational nature
Speaker 2: of the thing, how much it bends space time, it
Speaker 2: makes the most sense to think about the rest mass.
Speaker 1: Well, I guess I'll give you that. Maybe it's easier
Speaker 1: to think about it if you don't call something relativistic mass.
Speaker 1: But then I guess my question would be why does
Speaker 1: momentum get harder to change as the faster you go? Yeah,
Speaker 1: that doesn't help you with that quobate question, right, that's
Speaker 1: a very fundamental question about the universe. You're just calling
Speaker 1: things differently. It's still the same question.
Speaker 2: Yeah, it's still the same question. Why does the universe
Speaker 2: conserve this quantity mass times velocity times gamma. The fascinating
Speaker 2: thing is that that's what it conserves. It doesn't conserve
Speaker 2: mass times velocity. Newtonian momentum is not conserved in the universe.
Speaker 2: It's only this Einsteinian momentum. Mass times velocity times this
Speaker 2: gamma factor. That's the thing that's actually conserved in the universe.
Speaker 2: And you can see this if you take a class
Speaker 2: in special relativity and you like think about collisions at
Speaker 2: very very high energies and you try to use like
Speaker 2: normal Galilean velocity edition formulas, and you see the momentum
Speaker 2: is no longer conserved. So the universe conserves this quantity
Speaker 2: mass times velocity times gamma. Why, well, that actually comes
Speaker 2: out of the invariance of space. Right, space is the
Speaker 2: same everywhere in the universe. That tells you that this
Speaker 2: quantity mass times velocity times gamma is the thing that's conserved.
Speaker 2: Why is that. It's because of the invariance of space.
Speaker 2: Space seems to be the same everywhere, and that's why
Speaker 2: momentum is conserved. That's a deep principle in physics.
Speaker 1: Noether's theorem, Well, I think you're creating a causality there
Speaker 1: a little bit, right, Like you don't know that one
Speaker 1: causes the other. It's just that they just both happen
Speaker 1: to be true.
Speaker 2: Well, Notther's theorem tells us that there is a causality.
Speaker 2: It says that for every symmetry in the universe, there
Speaker 2: is a conserved quantity, and so for example, the fact
Speaker 2: that there's no preferred direction in space leads to conservation
Speaker 2: of angular momentum.
Speaker 1: Or maybe the conservation of angular momentum is what space
Speaker 1: it's invariant. Philosophically, I feel like you're making a conclusion there.
Speaker 2: Yeah, I think that conclusion does come from Northern's theorem.
Speaker 2: I understand the point you're making. But this is not
Speaker 2: like an equal sign, right, It's not like a equals B,
Speaker 2: and therefore you can't infer causality. If you follow the
Speaker 2: derivation of Notther's theorem, then it definitely goes in one direction.
Speaker 2: The conservation wills definitely flow from symmetries in the equations.
Speaker 2: If you have a symmet in the laws of physics,
Speaker 2: then it gives you these conservation laws. And it's everywhere,
Speaker 2: like even in quantum mechanics, like local gauge. Symmetry of
Speaker 2: quantum electrodynamics is the reason we have charge conservation in
Speaker 2: the universe. So these things are pretty deep. And what
Speaker 2: it tells us in this case is that it's mass
Speaker 2: times velocity times this gamma factor. That's the thing the
Speaker 2: universe cares about. And even if you don't like others
Speaker 2: theorem and you don't believe in it or whatever, Observationally,
Speaker 2: that's what we've measured Empirically. We're like, look, this is
Speaker 2: the thing the universe seems to care about. This quantity,
Speaker 2: not mass times velocity. So in some sense that's the
Speaker 2: fundamental thing. That's the thing that like the universe is
Speaker 2: telling us it cares about.
Speaker 1: Right, That's what I mean. It's like, that's the thing
Speaker 1: that we know is true. And whether it's caused by
Speaker 1: symmetry or it approves the theory, or whether it enables
Speaker 1: a symmetry that's sort of a philosophical question a little.
Speaker 2: Bit, yeah, a little bit, I mean, or theoretical. Experimentally,
Speaker 2: you're right, this is the thing we measure, and we
Speaker 2: notice the universe cares about absolutely.
Speaker 1: I guess then the question is what does that say
Speaker 1: about the universe that it cares about something doesn't just
Speaker 1: sit in the couch all day.
Speaker 2: I think it tells us a little bit about the
Speaker 2: history of human thoughts. You know, we've been like grappling
Speaker 2: with how to deal with these new discoveries that we've
Speaker 2: made and how to talk about them. One of my
Speaker 2: favorite Cootes from Einstein relates to this. He says, quote,
Speaker 2: the only justification for our concepts and systems of concepts
Speaker 2: is that they serve to represent the complex of our experiences.
Speaker 2: Beyond that, they have no legitimacy, by which he means like,
Speaker 2: you know, what is mass, what is momentum, what is force?
Speaker 2: They only make sense if they're talking about things we experience.
Speaker 2: We put these labels on things we see and experience
Speaker 2: in the universe, and we try to give them meaning.
Speaker 2: And there's actually Einstein originally who created this concept of
Speaker 2: relativistic mass when he was playing around with these equations
Speaker 2: and he was like, hmm, maybe it's useful to have
Speaker 2: this concept of mass that depends on your velocity. Later
Speaker 2: on he abandoned it. He realized, n that's kind of messy.
Speaker 2: And then later he said, it is not good to
Speaker 2: introduce the concept of relativistic mass of a moving body
Speaker 2: for which no clear definition can be He realized it
Speaker 2: was a bit messy. But you know, even geniuses like
Speaker 2: Einstein can't immediately disentangle these discoveries when he makes them.
Speaker 2: It takes a few years, a few decades of thinking
Speaker 2: about how this really lines up with our experience in
Speaker 2: the universe, what's the most sensible way to organize it?
Speaker 2: And the end is just us talking about how humans
Speaker 2: think about these things. The math is very, very clear,
Speaker 2: there's no ambiguity about it. It's really just like, what
Speaker 2: do you mean by this word?
Speaker 1: I think the basic idea is that it is true
Speaker 1: that the faster you move, the harder it is to
Speaker 1: move faster, and so we should think about that as
Speaker 1: just momentum getting more and more expensive the closer you
Speaker 1: get to the speed of light, and not use the
Speaker 1: word mass to think about how hard things are to
Speaker 1: move at those speeds.
Speaker 2: Yep, the universe has a higher tax for momentum millionaires.
Speaker 1: It's a progressive universe. Bernie Sanders and AOC would.
Speaker 2: Be proud until they start their own space company.
Speaker 1: All right, well, we hope you enjoyed that. Thanks for
Speaker 1: joining us, See you next time.
Speaker 2: Thanks for listening, and remember that Daniel and Jorge explain
Speaker 2: the Universe is a production of iHeartRadio. For more podcasts
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