Dylan Curious is an bright and enthusiastic fellow, and he has a great YouTube channel focused on what is happening in AI around the world. But Dylan’s curiosity doesn’t stop there. Having read and enjoyed Waves in an Impossible Sea (twice!), he wanted to learn more… so he and I had a great conversation about humans and the universe for about 90 minutes. Don’t let the slightly odd title deter you; we covered a broad set of interesting topics of relevance to 21st century life, including
- In what sense is all motion relative?
- Why haven’t we already encountered intelligent life from other stars?
- Might we live in a simulation?
- Could the universe have glitches akin to what happens in computer games?
- Should the language of science be reconsidered?
- Are the particles we’re made of really waves?
Dylan is fun to talk to and I’m sure you’ll enjoy our discussion. And follow him, as I do, as a way of keeping up with the fast-changing AI landscape!
16 Responses
Dr.Strassler:
Second question:
How would a stationary electron fulfill DeBroglie’s wavelength.
Since the wavelength of a particle is h / p (Planck’s constant divided by momentum). If the stationary electron has zero momentum, the wavelength would be infinite? Or would this be resolved by saying that a stationary electron, has indeterminate momentum?
An exactly stationary particle has momentum exactly zero but its position completely unknown; as a function of space x,y,z and time t the corresponding field then takes the position-independent form Exp[i m c^2 t / hbar]. So De Broglie is correct; the wavelength is infinite.
A stationary particle in a finite region of length L has uncertainty in its position of order L and uncertainty in its momentum of order h/L, so De Broglie is also happy; the field’s shape contains wavelengths that range from infinite to 2L, and the momentum is roughly 0 up to h/2L.
Dr.Strassler:
You may have already answered this question in your above response, I’m not sure. But, momentum is not reference frame invariant. In one frame, the electron may have zero momentum, and the fields shape contains wavelengths stretching to infinite. However, in some other frame, the electron will have momentum, and no longer have wavelengths stretching to infinite?
That’s right. (But the particle’s position is still very uncertain; in fact, in any state with definite momentum, whether zero or not, the particle’s position is completely unknown.)
Dr.Strassler:
Also, just to be clear, wavelength is different than amplitude. Wavelength may be infinite, but the amplitude may be different all along that wavelength. As such, the higher amplitude “area” of the wavelength, would have a higher probability of finding the electron, correct?
It doesn’t work like that.
A wave in space is a sum (really an integral) over waves of definite wavelength, with an amplitude for each wavelength. [For instance, see “Continous Fourier transform in https://en.wikipedia.org/wiki/Fourier_analysis ] You can’t fix the wavelength and then vary the amplitude for that wavelength across space; that doesn’t make sense. The very action of changing the amplitude introduces new and shorter wavelengths into the wave, and you have to go back and do the sum over wavelengths all over again.
Dr.Strassler:
I think I worded my previous question poorly. I was actually implying that the addition of many, many wavelengths, all at specific amplitudes, add together to constructively interfere in some locations, and DESTRUCTIVELY interfere in other locations, in the positions where the wavelengths destructively interfere, the amplitude would be greatly diminished, and the probability of finding an electron there very small. Is that more accurate?
If you add together two bell curves separated from each other by some distance, that’s exactly what happens: you need a wide variety of wavelengths, with many amplitudes, combined together in a particular way. This gives destructive interference in the region between the two bell curves.
In fact, even in one bell curve, the fact that the curve dies off away from the bell also requires destructive interference between many wavelengths with different amplitudes, although the variation in the amplitudes from one frequency to another is less dramatic.
These are standard properties of Fourier Transforms; you need not understand quantum physics to see how this works.
Dr.Strassler:
So the wave packet / wavicle is constructed of many wavelengths of varying amplitudes, what would be considered the DeBroglie wavelength? Would it still be considered the distance between crests, even though the amplitude of the crests is getting smaller in the “tails” of the wave packet?
The DeBroglie wavelength is only defined as the inverse of the momentum, lambda = h/p, where h is Planck’s constant. If the momentum is uncertain, as it is in any state that is constructed from many wavelengths, then the DeBroglie wavelength is uncertain too.
A wave packet is not a wavicle. A wavicle is an object, whereas a wave packet is merely a state that the wavicle may be in — a shape that it may take on.
thanks so much… I am in process of going through a drawing and article response to your paper on deep inelastic scattering and am in an information gathering mode: a constructed element being to relate to your observation on mass generated in proton by independently colliding particle I am resourcing a harmonic over view of various constants in the spirit of Goedel mapping in a way but mapping golden section and Pi and square root of two harmonics over these as they elaborate and will begin with focus on weak thea as a momentum angle so to speak relative then to gravity, the Planck, Higgs, Euler’s,, Feigenbaum, vacuum permittivity,Coulomb, and the masses of the particles all of which speak an involved and musical golden section language to then relate to the light comb statistics of Bjorken you start out with and so that is current status on drawing article per deep inelastic scattering so far… I hope to elaborate the gauge element in the spirity of channelling the Langlands conjecture over string theory which you well understand as essentially a form of deep critique…a kind of analytical continuity on steroids…then to consider the imponderables ie gravity to dark energy and vacuum permitivity in hopes a language of resonance can be resourced from this variation on Goedel mapping to find a cosmogenesis on the numberline as available to analytic continuity as computer simulation for example….
The Fermi Paradox is outmoded.
The SETI AATIP Paradox is more up to date:
“Why do we see signs of ET on Earth but not among the stars?”
In what sense is all motion relative?
Since everything is moving (either forward or backwards) sense of motion can be detected even when two bodies are moving at the same speed. Along with the xpanding Universe, we are all headed somewhere in one of three spheres 9Past-Present or Future) The question can be asked can we be simultaneously in all three. Indeed it is possible but but time and space here is limited to explain
Why haven’t we already encountered intelligent life from other stars?
When you say ‘stars’ those luminous bodies of dynamic heat and light, then such beings would be ‘bright” as opposed to beings coming from planets
Might we live in a simulation? No we are not AI beings, every DNA is NOT simulated
Could the universe have glitches akin to what happens in computer games? There is evil and good, the glitch is the evil but its not a game
Should the language of science be reconsidered? It has to be adapted according to truth and not theory
Are the particles we’re made of really waves? Indeed they are but they are also governed by laws
Thansk for your answers. I think you might get something out of the interview.
Dr.Strassler:
Really good interview, I watched the full podcast.
I often view a wavicle, looking like a wave packet….similar to a wave pulse. If you were to remove the walls, enclosing said wave packet, that is stationary, it would start to spread, however it would never get below a fundamental frequency, as dictated by the rest mass of the particle. One of your blogs talks about this, is my description somewhat accurate?
That’s correct; and if the box is already large. the spread is much slower than if the wavicles mass were zero. I should organize links to those blog posts into one place, but one of them is here: https://profmattstrassler.com/2024/03/19/yes-standing-waves-can-exist-without-walls/