I was going to wait to post this one. But I was just too inspired by another question I just saw. So I will post it now.
We know how Einstein’s theories work on the large scale. Gravity and time. Time dilation and relativity. But do his theories work on the very very small scale?
For example, as I walked to my room to get my smartphone, I was traveling at what? 2-3 miles per hour? Was time still slowing down for me? Was my mass increasing? And my length constricting?
I know if any of those things were happening at all, it had to be on an infinitesimal scale. But was it indeed happening at all?
I also know on such a small scale, almost anything could offset the effect. Gravity. The motion of the earth, and so forth. Also, at some point relativity ends and quantum physics take over. Specifically at what point does that happen?
(Just a quick side note: as I scrolled down to read this reply, I accidentally hit “report this post”. I definitely **DON’T ** want to report this post, and I quickly hit the back button. But if that is not enough [I’ve never reported a post, so I don’t know], please note it was just a mistake. Now carry on :).)
Electrons moving through a wire are, on average, moving at a few centimeters per second or so (the precise speed will depend on the current, size of the wires, etc., but it’s in that ballpark). And yet, relativistic effects from the electrons moving at that speed distort the field around the wire enough that those distortions will cause a compass needle to turn. Magnetism is nothing more nor less than the effect of relativity on electricity.
Yes, though we usually leave mass as a relativistic invariant and talk about energy instead.
As far as we know, relativity holds at all scales. In fact, it’s hard to do quantum physics, even quantum mechanics, without relativity; the objects involved generally behave relativistically. The Dirac equation, for example, is compatible with relativity and dates back to the 20s. For a more familiar example, the interesting particles in cosmic rays and similar sources decay extremely quickly; we’re able to detect them on Earth because of (depending on which frame you choose) the relativistic time dilation or length contraction involved.
But to add to what’s already been stated, GPS satellites offer a startling example of this. Granted, their speed and altitude are a bit out of the norm of everyday things, but they are still moving at an incredibly tiny pace compared to light, and their distance from the earth is pretty minuscule. Yet because they require such incredibly precise clock synchronization, they have to be adjusted for the relativistic effects of both speed and gravity – speed causing the clock speed to lose about 7 microseconds per day relative to a ground clock, and reduced gravity causing the clock to gain about 45 microseconds per day. Because of the required precision, if not compensated for relativity, after 24 hours GPS locations would have an accumulated error of around 10 kilometers, making them useless.
What you may be thinking about with quantum mechanics is that the theory of general relativity, the theory of gravity, is incompatible with quantum mechanics. But even there, that doesn’t mean that one ends and the other takes over. Rather, there are regimes where they’re both relevant. The fact that the theories are incompatible doesn’t mean that the phenomena don’t occur together: It just means that we have no friggin’ idea how they occur together.
We only know how to do Quantum Mechanics in flat spacetime, which occurs when there is negligible gravity over the volume of space we’re considering. Special Relativity (SR) is Relativity in flat spacetime so, yes, we do know how to do Quantum Mechanics taking Relativity into account; we call that Quantum Field Theory (QFT), and we have multiple QFTs, each for different scenarios. A relatively simple example is Quantum Electrodynamics (QED), which describes how electrons and photons interact. QFT is enough to describe all familiar matter down to the quantum level: All chemistry, all biology, all geology, all cooking, baking, and candlestick making is founded on reactions we can take back to QED. QED breaks down when you look inside atomic nuclei or at very extreme scenarios, like deep inside stars or inside degenerate matter, such as neutron stars. We have other QFTs, such as Quantum Chromodynamics, for that.
It also breaks down very close to the singularity in a black hole, but that’s not surprising, because that’s a place where spacetime is not sufficiently flat for SR and, therefore, QFTs to hold.
But, you say, we’re in a gravity field right now! How can a QFT work when my apples fall down and light bends? Well, think of a gently-sloping sheet. If you’re human-size, you see the slope quite clearly, and know the sheet is bent. If you’re ant-sized, you might be able to detect a slight tilt, but not very much. If you’re bacterium-sized, the world is perfectly flat unless you’re a truly advanced physicist. So how flat would it be at the quantum scale?
Suffice to say, the fact you can stand up without your feet being torn away from your legs is proof spacetime around Earth is flat enough for QFTs to be very useful indeed.
Here’s a case I read of some years ago: Playing on old-fashioned vinyl 33-rpm LP record, the outer circumference of the disk moves faster than the innermost track, and thus its time is slowed. This discrepancy is actually measurable, and has been measured.
Relativity works for things that are very very large
Quantum Mechanics works for things that are very very small
For human sized things, Sir Issac Newton is close enough
Actually, we also know how to do relativistic quantum mechanics in a curved background spacetime, and it’s not even particularly more difficult than doing relativistic quantum mechanics in a flat spacetime. Literally all that changes is that you need to turn some commas into semicolons in some of the equations. Well, OK, those semicolons represent some additional math that you have to do that you didn’t have to do with the commas, but it’s all math that we know exactly how to do, and you’re probably getting a computer to do most of it anyway.
What we don’t know how to do, however, is to use matter which is obeying quantum rules as the source for a gravitational field. The best we can do is to do the quantum mechanics, then take a bunch of expected values, and then plug those expected values into the GR equations. For most of the problems we’re studying right now, we’re pretty sure that’s good enough (or at least, we really hope so), but we can come up with problems where we know that it’s not.
All magnetism ultimately gets back to moving charges, for some definition of “moving”. For magnetic materials, whether diamagnetic, paramagnetic, or ferromagnetic, it’s the electrons in the atoms. For diamagnetic materials, it’s due to the orbital motion of the electrons about the nucleus. For paramagnetism and ferromagnetism, it’s due to the quantum-mechanical spin of the electrons, which is a quantum property which isn’t the same thing as what we think of as “spin”, but which does have some similarities to it.
I agree with most of your post, but I’ll point out that we also know how to do quantum mechanics in a fixed background spacetime, even if it’s curved. The event horizon of a black hole, for example, has substantial spacetime curvature; and those curvature effects lead to the prediction of Hawking radiation. It’s only if we try to describe the quantum-mechanical behavior of gravity itself — i.e., how does spacetime evolve in time in terms of a quantum-mechanical picture — that we run into trouble.
I suppose it’s possible that our understanding of QFT in curved spacetimes isn’t accurate; to the best of my knowledge, there haven’t been any experiments or observations that have tested any of these predictions. But that’s a different type of difficulty; in the case of “quantized gravity”, there aren’t even any universally accepted predictions to test.
QFT can be done in curved spacetime too, though it does introduce additional practical and interpretational issues. Quantum fields though have stress-energy and therefore should affect the geometry of the background spacetime, but QFT in curved spacetime does not take this in to account and therefore can only be a low-energy approximation. Semiclassical gravity is a further improvement in that it takes in to account the effect of the quantum field on the background spacetime by relating the geometry of spacetime to the expectation value of the stress energy tensor, but even with this it is easy to construct situations where semiclassical gravity must be wildly incorrect.
We really just have one for all scenarios. Pulling QED out and saying it breaks down in situations where additional phenomena are also relevant is perhaps misleading.
A good approximation, although biology and geology both definitely need the full theory in places (e.g., radiological aspects of geology).
It’s not that QED breaks down in these scenarios. It’s alive and kicking as part of the full QFT of the Standard Model. If you ignore the strong and weak pieces, then yes, you have a theory that doesn’t describe everything in nature. But even in those cases when you need the full theory, the QED piece continues to correctly provide the electromagnetic aspects of the situation. That is, you don’t discard it for something else. You continue to use it, along with the rest of the theory.
To add to Chronos’s reply: A core feature of special relativity is that it gives you the tools to answer “How would this physical system appear to me if I were in a different reference frame?” *i.e *, “…if I were moving with a different velocity relative to the physical system?” If you calculate the forces that one stationary electric charge has on another, you get standard electrostatics. If you apply special relativity to the situation, you can ask how the forces change if some or all of the charges are moving, and you find that the forces take on a different character in the various reference frames involved. The differences are precisely what we call magnetism.
First, to pretty much everyone: Interesting. I didn’t realize how much progress we’d made in quantum mechanics.
True, but if you treat them as black boxes, you can handwave them away by modelling them as point sources which emit particles at random intervals.
My point in emphasizing that was driving at what Frank Wilczek and Sean Carroll call the Core Theory, or the fact we now know the physics behind all interactions in everyday life. I overstated how much QED in specific explains, by neglecting radiation, but Core Theory includes a lot more than QED, so it evens out.
Good post from Carroll: The Laws Underlying The Physics of Everyday Life Are Completely Understood It’s a strong statement because it’s a tonic, an antidote against a pernicious kind of anti-rationalism which even intelligent people can fall prey to: “We don’t understand absolutely everything, therefore we understand absolutely nothing.” That fallacy is the arrogance of a huckster masquerading as the caution of a philosopher, because it renders people unable to immediately reject nonsense. This blog post goes into more detail on this idea.
Worse, it denies us the confidence we’ve rightfully earned, through millennia of patient experimentation and reasoning, by focusing on the fact that all theories can be rejected and ignoring the fact every new theory must explain all the same phenomena the previous theory did, because those phenomena don’t very well stop occurring just because we’ve changed our minds about something.
Right. Looking back, I did explain that wrong.
And I always thought this was just amazing. It emphasizes another aspect of physics in general: Everything is interrelated, so you have multiple ways to get at the same physics. Don’t want to think about space ships going 0.9c relative to you? OK, you can come at SR by way of a needle jumping around due to a current in a wire a few inches away. You can come at it by way of why gold is golden and so resistant to tarnishing. Which just further increases our confidence in the physics we have: There are so many ways of cross-checking the core, the best-known parts, that they’re very unlikely to be wrong.
It reminds me of some speculations I’ve done of Niven’s Ringworld stories. In it, a hyperintelligent character with no previous scientific grounding is able to re-derive the laws of gravitation. It occurred to me that, in the environment that character found itself in, the easiest gravitational phenomenon to study wouldn’t actually be balls falling or pendulums swinging, but deflection of starlight around the local Sun… and that the character would thus go straight to deriving General Relativity, without finding Newtonian gravity first.
