20 Subatomic Stories: Is the Planck length really the smallest?

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Hi there, physics fans! We’ve spent a lot of time talking about black holes, because black holes are undeniably interesting. However, it’s time to return to our roots and talk about tiny things. It’s been said that the Planck length is the smallest possible length, but that’s not the entire tale, as I will tell you in this week’s episode of sub, sub, Subatomic Stories. In episode 15, Divyansh Vishwakarma asked about the Planck length and whether it was proof that loop quantum gravity was real. I promised to answer, and I didn’t forget. It is often said by non-cautious people that the Planck length is the smallest length, the Planck time is the shortest time, and the Planck energy is the highest energy. But that’s not really true. So, just what are these Planck constants? Our story begins in 1899 with Max Planck, a German theoretical physicist, and one of the legends of quantum mechanics – in fact, he was one of the original architects of the first quantum revolution. Here are two pictures of him, one before and one after he made his contributions to quantum mechanics. That’s proof if I ever saw it that quantum mechanics blows your mind. One of the things Planck did was to try to come up with what are called natural units or units on which everyone can agree. This remains a problem even today, as you can see in some of my videos, where people occasionally make snippy comments about whether I use imperial or metric units. Planck reasoned that any scientifically sophisticated society could measure a few quantities in whatever units they used. They are the speed of light, which has units of length per time; the gravitational constant, which has units of length cubed, per mass, per time squared; the reduced Planck constant, which has units of length squared times mass per time; the Boltzmann constant, which has units of length squared times mass per time squared per temperature; and the Coulomb constant of electricity, which has units of length cubed times mass per time squared per charge squared. Planck then took these scientifically measured quantities and made various ratios of them to get a desired unit. For instance, to get a unit of time, he took the reduced Planck constant times the Gravitational constant, divided by the speed of light to the fifth power, and then took the square root of all of that. The result is the Planck time, which has a numerical value of 5.4 times ten to the minus 44 seconds. But some other culture, with different units, could do the same thing and come up with a Planck time of 12 zortblats or something. But since these are the same thing, we now have a way to convert zortblats to seconds and back again. Planck went on and defined the Planck length, mass, temperature, charge, etc. I’ve put some of them here on the screen. Planck was rightfully proud of his accomplishment and wrote in his paper, which was in German, of course, but translated here it said “... it is possible to set up units for length, mass, time and temperature, which…retain their meaning for all times and for all civilizations, including extraterrestrial and non-human ones, which can be called ‘natural units of measure’.” Pretty cool. If we’re ever visited by ET, we’ll at least be able to agree on unit conversions. So, this part of the story is clear. However, in the intervening century and more, the lore has morphed from Planck units being natural units, to being the smallest possible things. How did that happen and is it true? That story stars in 1959 with Alden Mead, who was a chemist at the University of Minnesota. He had an idea connecting gravity and the smallest length. His idea wasn’t popular, and it took him five years of arguing with journal referees, when in 1964 he published his paper entitled “Possible Connection Between Gravitation and Fundamental Length.” I admit I didn’t read it when it came out. I was kinda young. What Mead did was consider the effect of gravity on how light is diffracted when you send it through a very small aperture. Everybody ignores this effect, because it’s so small. But, at small enough scales, the effect of the Heisenberg Uncertainty principle becomes relevant here. The Heisenberg Uncertainty principle says that it is impossible to simultaneously measure an objects position and motion. Mead showed that it is impossible to measure the position of an object to a precision smaller than the Planck length and, from that, we can say similar things about the Planck time. I put a link to his paper in the description. So, what does Mead’s work really mean? It doesn’t say that the Planck length is the smallest possible length. What it says is that at the Planck length, the effect due to gravity is large enough that it can no longer be ignored. What he says is that, at the Planck length, the laws of physics as we know them totally fail and have to be replaced by something better. Perhaps that something will allow for shorter distances. We don’t know. We need a theory of quantum gravity for that, which I talked a bit about in episode 13. I spoke to Mead back in 2013. He was retired by then. He contacted me because he stumbled upon an article I wrote about Planck units, which gave him credit. He filled me in on the decade long conversation about how the scientific community morphed from thinking he was crazy, to accepting he had a point, to saying the Planck scale was the shortest. He even pointed me to a public conversation he had in 2001 with Nobel Prize winning physicist Frank Wilczek. I put a link to the conversation in the description. If you’re interested, it’s worth your time. The bottom line is that the Planck length is >>NOT<< necessarily the shortest length, but it is a length at which existing physics >>HAS<< to fail and needs to be replaced with something better. So, it’s an important size, but it may not be the smallest size. OK, hopefully I taught you something you didn’t know and given you something to ponder. Let’s see what questions we have this week. Questions…questions are always fun. Let’s jump right into it. Duggydo notes that if the expansion of the universe is increasing the wavelength of light, that means that the light’s energy is decreasing. Given that physicists say that energy is conserved, where does the energy go?” Hi Duggydo. So, the answer might surprise you. Conservation of energy isn’t always real. Now, me saying that conservation of energy isn’t really true is pretty staggering and requires some explanation. Bear with me, because this is somewhat technical. The story begins with a theorem created by Emmy Noether, called Noether’s Theorem. This theorem connects conservation laws with mathematical properties of the theories that describe them. According to the theory, a conserved quantity implies that the equations don’t care where you set your zero. For instance, for conservation of energy, the equations can’t care what moment you set as time zero. It could be just over two thousand years ago. It could be the moment you were born, or it could be this very second. If the laws of physics don’t care about that choice, energy will be conserved. But an additional requirement that is never mentioned is that space and time must be static and unchanging. But, of course, in general relativity, that last requirement is not satisfied. Space and time can change and warp and distort. Accordingly, the law of conservation of energy doesn’t necessarily apply. So that’s the reason that it appears that energy is lost. It’s because non-conservation is not only allowed, it’s expected. Now, the description I’ve given here is the gist, but, because of the limited time we have, it’s very brief. So I’ve put links to two more thorough and technical explanations in the video description below. If you want to understand this better, you’re going to have to read those. Cronos804 and many others wants to know why iron is the heaviest element that can be made by fusion. First, let me say that obviously iron isn’t the heaviest element that can be made by fusion, but it >>IS<< the heaviest stable element that can be made by fusion >>AND<< get energy out of it. Let me give you two different explanations. To start out with, two forces govern atomic nuclei – the strong force that holds protons and neutrons together and the electrostatic repulsion pushing the positively charged protons apart. The strong force is basically a contact force like Velcro, while the electrostatic repulsion has an infinite range. As nuclei get bigger, the electrostatic repulsion becomes more important because it applies over larger distances. The strong force of only adjacent nucleons holds it together, while the electrostatic force of all protons pushes it apart. This is the reason that nuclei with more than 120 protons or so don’t exist. But it’s also why iron is the heaviest element that can be made by fusion and have energy come out. For elements lighter than iron, the strong force causes the nuclei to nestle together neatly, and, above iron, electrostatic repulsion starts to become important. This graph shows the energy per nucleon for many elements. The element with the lowest energy is iron. Elements with lower mass release energy as they fuse. Elements with higher energy release energy as they split. In the sun, light elements fuse together, releasing energy until they hit iron. Heavier than that and it takes energy to make them. Elements heavier than iron are made from the energy of a supernova or when neutron stars merge. Heavy element fusion needs energy to proceed. So that’s why iron is the final stage of ordinary stellar fusion. Good question. Nick Fontaine asks if we had a superconducting and super strong wire, could we use it to lower a camera below the event horizon of a black hole and see what is going on. Hi Nick. No. We can’t. And the reason is simple. The event horizon is the point where gravity grows so strong that light cannot escape. Light is, of course, electromagnetism. In your superconducting wire, the information would come out along the wire, using electromagnetism to transmit the signal. Electromagnetism is also what holds the wire together. But we’ve already said that the gravity of the black hole is too strong to let electromagnetism escape. And that’s true, even on a wire. So no go. I’m afraid that the black hole’s secrets are still safe. Mohit Soni notes that I have an unusually great sense of humor for an astrophysicist. Well thank you Mohit. I appreciate that. But it’s entirely understandable that this would be so, because I’m not an astrophysicist. I’m a particle physicist, and we’re known for our clever and dazzling wit. We even have to do a standup comedy routine on our final exams. Astrophysicists, on the other hand, generally aren’t nearly so funny. It’s music that seems to be their thing. Theultrapixel asks if we have enough data to work out a theory of everything if we were smart enough or if we’re missing important pieces. Hi ultra. I guess it’s possible that some smart whiz kid might figure things out, but I totally doubt it. There are many things we don’t understand, like dark energy, dark matter, and a bunch of other things. In fact, this video series is about to pivot to topics exactly like those, which is to say, unsolved mysteries. We talked in this episode about the Planck energy, which is the energy at which the laws of physics as we know them must break down. That energy is about a quadrillion times higher than what the most modern particle accelerator can achieve. It’s inconceivable to me that as we explore higher energies, we won’t encounter phenomena we can’t even imagine now. I think we’re talking thousands of years of research before we can talk about a realistic hope of finding a theory of everything. Sadly, I won’t be here to see it. Naveen James asks me my viewpoint about tachyons, which are particles that go faster than light. Hi Naveen. The answer is simple. I don’t. There is zero evidence that they exist. Of course, it’s possible that they actually do exist, and people should continue to think about ways to look for them. But one thing I’m certain about is that there has been a lot of ridiculous thing written about them. Totally ridiculous. People talk about tachyons as having imaginary mass, or going back in time, or breaking causality, or all sorts of nonsensical things. All of those ideas arise from applying Einstein’s theory of relativity to particles going faster than light. But Einstein’s equations are explicitly valid only for objects moving slower than light. So they just don’t apply. If tachyons do exist, it will require new theories to describe their motion. It’s very much like how Newtonian physics applies fine for the familiar slow and large world we inhabit, but we had to invent relativity and quantum mechanics to describe the world of the fast and the small. If we ever exceed the speed of light, Einstein’s equations will just not apply. People who try to apply them are like those who try to use Newton’s laws to describe a black hole. It’s a foolish endeavor and it just doesn’t work. OK, so that’s all the time we have for questions today. You know the drill. Please like, subscribe, and share. As I just mentioned, after this video, I’m going to turn my focus to mysteries and speculative physics. It’s going to be great fun. I’m sure you agree, because, even at home, physics – both the understood and the speculative – is everything.
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Channel: Fermilab
Views: 207,179
Rating: undefined out of 5
Keywords: Fermilab, Physics, Planck constants, Planck length, Planck time, Planck energy, Max Planck, Alden Mead, Frank Wilczek, smallest distance, shortest time, highest energy, Planck units, Don Lincoln, Ian Krass
Id: rzB2R_qiC28
Channel Id: undefined
Length: 13min 54sec (834 seconds)
Published: Wed Aug 19 2020
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