What is the Fundamental Microscopic Structure of Space-Time in our Universe?
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00:00
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Transcript: English(auto-generated)
00:05
The research question is, what is the fundamental microscopic structure of space-time? Space-time is the fabric of our universe that everything else exists in. And Einstein's theory of general relativity teaches us that space-time itself is dynamical. It responds to the presence of energy and matter by curving.
00:24
And one of the key predictions of general relativity is if you have two massive astrophysical bodies, for instance neutron stars, that orbit each other, this system will emit ripples in space-time, so-called gravitational waves. An analogy that you can think of for this process is if you have two power boats on the ocean which circle each other,
00:43
they will create surface waves on the ocean. The prediction of general relativity was made about 100 years ago and was confirmed recently, in 2015 actually, by the LIGO collaboration, who for the first time observed gravitational waves and thereby confirmed Einstein's general relativity to very high precision.
01:02
And so the question is, is there anything at all left to understand about space-time? And the answer is yes, there's actually a huge open question. General relativity describes space-time at large scales. It describes how space-time responds to the presence of large bodies like the Earth or astrophysical bodies like stars. But how does space-time respond to an atom or an elementary particle like an electron?
01:25
How do these curve space-time? For these systems, quantum physics becomes important. Therefore, for instance, an electron can be in this very weird superposition state, in a quantum superposition of being in two places at the same time. And space-time has to respond to that and has to also undergo quantum effects.
01:44
It has to go into a quantum superposition. This is very, very tough to describe in a mathematically consistent framework. And therefore, understanding the quantum structure of space-time, developing a quantum theory of gravity, is one of the huge challenges of fundamental physics and has been for at least the last 50 years.
02:02
And so this is the key question that I'm addressing with my research group. What is the fundamental microscopic structure of space-time in our universe? So ideally, what we would like to do would just be to set up an experiment that allows us to zoom in and resolve the microscopic quantum structure of space-time.
02:24
That's actually a huge challenge and currently impossible because the microscopic fabric of space-time becomes visible at scales of about 10 to the minus 35 meters. To put that into context, the LHC, the most powerful machine that has been built to date, only resolves distances of 10 to the minus 18 meters.
02:43
So experimentally, we are still missing 17 orders of magnitude. And so therefore, the research methodology that I'm applying is purely theoretical. We are using what you can think of as the mathematical version of a microscope in order to zoom in on quantum space-time and resolve its microscopic structure. You can think of what we are doing as follows.
03:02
We are starting from a microscopic description that takes into account quantum fluctuations of space-time in the vacuum. From this microscopic description, we average over larger and larger patches to arrive at an effective description that blurs the microscopic details. This is like zooming out, decreasing the zoom factor with a microscope.
03:22
And in this way, using our mathematical microscope, the renormalization group, we can zoom in and zoom out of our picture of space-time. One of the key findings that several research groups around the world have contributed to is the discovery of a regime where as you zoom in further, space-time becomes scale invariant.
03:41
Scale invariant simply means that as you zoom in further, the picture doesn't change anymore. This allows you then to zoom into arbitrarily small distances and understand what the true microstructure is. You can think of the scale invariant regime as similar to a mathematical object called a fractal. A fractal is an object that is self-similar, so this means as you zoom in, you still see the same picture.
04:04
If you want a real-life example, you can think for instance of a broccoli. For a broccoli, the whole vegetable and one of its smaller parts, if you break it off, look exactly the same. For a true mathematical fractal, that continues, so you can zoom in further and further. So this is the picture of space-time in asymptotically safe quantum gravity.
04:24
It's scale invariant beyond a certain minimal scale. Now the key new ingredient that I'm adding with my research group can be captured by the slogan matter matters. So matter already plays a huge role in shaping the dynamics and the structure of space-time at large scales.
04:41
And so what we are arguing, what we are convinced of, is that in particular quantum fluctuations of all of the elementary particles play a huge role in shaping the structure and dynamics of quantum space-time. And so we are arguing that zooming in on a description of pure quantum space-time will actually not help us to understand the quantum structure of space-time in our universe.
05:03
Instead, what we should be doing is zooming in on a joint description of quantum space-time and matter. And so this is the methodology that I'm applying with my research group. We are considering joint descriptions of quantum space-time and matter by elementary particles. And we use our mathematical microscope, the renormalization group, to zoom in and search for an asymptotically safe scale invariant regime
05:28
that provides a microscopic description of all of the fundamental building blocks of our universe. I would like to highlight two key findings.
05:40
They have to do with the fact that the interplay of quantum gravity with matter actually has two sides. One is the impact of matter on the quantum structure of space-time and the other is the effect of quantum gravity on matter. So our first key highlight result is that indeed matter matters. So this means that quantum fluctuations of matter field impact the microscopic structure of space-time.
06:04
Our results indicate that it isn't possible to add too many matter species to this description until the scale-invariant asymptotically safe regime for quantum gravity breaks down. On the other hand, our results suggest that you can add all of the observed species of matter
06:21
and still arrive at such an asymptotically safe description. And I would like to highlight that I'm using the words suggest and indicate very deliberately to mean that we do not have a mathematical proof for these statements. We are doing calculations which are technically rather challenging. And so to make progress, we have to make approximations.
06:40
And so our results hold under these approximations that we are making, and of course we can step-by-step improve on them, but the results at the moment are still achieved with insignificant approximations. The second key result was perhaps a little bit surprising, and it is that quantum gravity impacts the structure of matter
07:00
and actually allows us to predict or explain some of the properties of matter from this new perspective. In a little bit more detail, this asymptotically safe scale-invariant description of a quantum gravity regime restricts some of the interaction strengths of matter, including the interaction of charged particles with the electromagnetic field
07:24
and the interaction of some of the elementary particles with the Higgs field. Let me put that into context. In the standard model of particle physics, there is a mechanism that explains why some elementary particles, such as the quarks, are massive. They are massive because they interact with the Higgs field,
07:40
and the stronger they interact, the more massive they become. On the other hand, the standard model does not predict or explain the values. In order to know how massive, for instance, the top quark is, you have to build an experiment, measure its mass, and from that you can then extract how strongly it interacts with the Higgs field and put that number into the theory.
08:00
And now our results on asymptotically safe gravity and matter indicate that that actually changes within our picture, and that in order to achieve such a scale-invariant, asymptotically safe description, the interaction strength of the top quark with the Higgs is actually restricted to one very particular value. Within our calculations that, as I said, are done within approximations,
08:21
we are then calculating the mass of the top quark from first principles, and we are getting a value that is surprisingly close to the experimental one. Well, in some sense, what we are asking is a very simple question, and one that probably many of us have wondered about at some point or other,
08:40
namely, what are the building blocks of our universe that we and everything around us is made of? And our results are relevant because they open up the possibility of a new paradigm in which we can understand these fundamental building blocks. In particular, the results that we have indicate that there might be a possibility of understanding matter and space-time
09:02
within the asymptotic safety paradigm. So what happens in this picture is that the standard model of particle physics remains a viable description of matter down to the smallest possible scales if you add one new degree of freedom, one new component, namely gravity, and its corresponding force particle, the graviton.
09:23
And our results indicate that then there could be a consistent microscopic description of all of the fundamental building blocks of our universe, including quantum gravity and matter, and then possibly this new paradigm could stand alongside other ideas for the fundamental microstructure of our universe,
09:41
such as, for instance, ideas based on string theory. Of course, at the moment, we are finding indications that such a paradigm could work, but we don't know for sure yet. But it's certainly really, really exciting to try to find out whether the asymptotic safety paradigm can be viable for a description of our universe. In a broader context, you could actually ask,
10:01
well, why are such foundational basic questions actually relevant? Why do we not devote our resources to answering questions which are much more pressing in real-world problems? Why do we really need to understand the microscopic structure of space-time and matter? To this, I would like to respond with a few historical examples that show that basic foundational research was very often unexpectedly
10:24
and quickly converted into new technological applications. One example is quantum mechanics, which was developed to understand the structure of atoms and nobody was thinking about applications, but quantum mechanics actually underlies semiconductor physics, which are important for all modern-day electronics, laptops, mobile phones, and so on.
10:42
The second example is general relativity, which was developed to understand the large-scale structure of space-time, but special and general relativistic effects are key for the GPS to work at the precision that it does. And so these examples show that very often basic foundational research can very quickly lead to technological progress.
11:03
And so even if there is currently no way of seeing that quantum gravity will ever be the basis for any technologies, we shouldn't dismiss the possibility that basic foundational research can very quickly also trigger new ideas and applications that help with real-world problems. So I think the outlook is really exciting because currently we are just taking the very, very first steps
11:28
towards trying to establish the asymptotic safety paradigm as a model for the fundamental building blocks of our universe. And so there's a wealth of exciting open questions and I would like to highlight three of the key challenges.
11:40
The first one is a calculational challenge. So we are working, as I said, within approximations and we are seeing really interesting structures. For instance, we are seeing indications that we can explain and derive the mass of the top quark from this asymptotically safe picture. The question is whether that is actually an artifact of a too simple approximation or whether it will persist as we refine the approximation.
12:03
And so the first key challenge is to step-by-step improve on our approximations and make sure that our results are really robust. The second key challenge is then trying to understand whether as we go towards more and more refined approximations we can also explain more structure.
12:20
So for instance, can we explain more of the properties and dynamics of matter as it is encoded in the standard model? Can we explain and derive more of that from asymptotic safety as we go to more refined approximations? So how many of the open questions of particle physics can we answer from this asymptotically safe point of view?
12:42
That's the second key challenge. The third key challenge is an observational one because we do have indications that the standard model of particle physics does not describe all of the matter in our universe. There is another form of matter out there, dark matter. We see its gravitational pull on ordinary matter both within our own galaxy and in other galaxies.
13:03
And we don't really know what dark matter is. Is it an additional force particle of the gravitational force? Is it a new species of matter? That's an open research question. And for us the key challenge is to understand whether an asymptotically safe point of view as we are developing actually allows us to pin down the structure and nature of dark matter
13:24
in more detail so that we can actually predict and tell experiments where they should be looking for dark matter and what form it will take.