I am not sure there’s any breakthrough here, but this article is about a different QM interpretation (as opposed to Copenhagen or Many Worlds). Interesting but seems irrelevant to the discussion here of particles and fields.
Letter to John Lighton Synge (9 November 1959), as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679
It is not a breakthrough, it is just something we refuse to see, something that was known for a century.
"All is a wave" is the unifying principle. I am no mathematician, but the math needs to start with that fundamental principle.
The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."
And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
> It is not a breakthrough, it is just something we refuse to see, something that was known for a century.
This sounds like you're about to try selling me a crystal and a magic ritual. The wording here is far too grandiose, and I assure you physicists are not "refusing to see" that "everything is a wave". Whatever you imagine that might mean.
> The very notion of calling it "qunatum" physics is probably wrong since quantum is "a discrete quantity of energy proportional in magnitude to the frequency of the radiation it represents."
> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
Mumbo-jumbo.
It's called "quantum" physics because of the discovery that many parts of nature do indeed exist in discrete steps. Yes, electron orbitals are described with wave functions - that is, the electron exists as a probability cloud, but the functions themselves are still discrete! When an electron gains energy, it jumps from one orbital to another without passing through a continuous state in the middle. That is the fundamental insight of Quantum Mechanics - energy, momentum, etc are all quantized and not actually continuous.
Isn’t the wave function only discrete when we measure it?
The field is the continuous state so nothing has to jump through anything.
For example the hydrogen wave function does not tell us where the electron will be located, only where most likely will be located. What is discrete about that?
> Isn’t the wave function only discrete when we measure it?
No.
> The field is the continuous state so nothing has to jump through anything.
No.
> For example the hydrogen wave function does not tell us where the electron will be located, only where most likely will be located. What is discrete about that?
Read what I wrote again. The wave function itself is continuous but the jump between states (aka between wave functions) is discrete. This is because energy is quantized and does not exist in continuous quantities. The transfer of energy in quantum systems is therefore discrete, which is the whole reason it is called quantum mechanics.
> The wave function itself is continuous but the jump between states (aka between wave functions) is discrete.
What exists between the wave functions?
> This is because energy is quantized and does not exist in continuous quantities.
"Quantized" in quantum mechanics means that a physical quantity can take only a discrete set of values rather than any value from a continuous range.
Yes, energy is quantized because we see it separate from a continuum. Because we SEE it as separate from a continuum does not mean it is separate from any continuum. This is the theory of everything is wave in a nutshell.
Since you have another theory, that the wave function can have properties of a particle and a wave, so you disagree with me. To me, the wave function only shows the properties of a wave, after you have made a measurement, the probability of what you have measured suddenly changes to 1, and the wave function appears as a particle, but still has the properties of a wave, which are there, but ignored.
> I am no mathematician, but the math needs to start with that fundamental principle.
This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”
> And if everything is a wave there are no discrete quantities beyond our definition of what constitutes the end, or borders, of the wave.
This is not true in multiple ways. First, it’s known that these particles exhibit quantum behavior. This is measured and confirmed over and over. Many measures are in fact quantized.
Second, existing as a wave does not mean no discrete quantities. Even in everyday materials we observe situations like standing waves that are effectively quantized.
> This is a weird sort of hubris. “I’m not qualified to do this job but I can certainly tell you how it needs to be done.”
A quantum state is a mathematical entity that represents a physical system. Since waves are not physical can you see where I can assume that the math needs to start from a different place? If it is even useful at all?
> it’s known that these particles exhibit quantum behavior. Many measures are in fact quantized.
To measure is to quantize, so this is circular reasoning. If particles are always waves we would still see the quantum behavior.
> Second, existing as a wave does not mean no discrete quantities.
Where is the precise point a standing wave ends and begins? The best we can do is guess with calculus and differential equations. Again, yoiu are quantifying things that in and of themselves are not quantized outside of our conception.
> To measure is to quantize, so this is circular reasoning.
This is a fundamental misunderstanding. Measurement (which is a precisely defined mathematical concept) is not the same thing as quantization. For a very basic example, in all known physics theories, including QFT, SR, and GR, space and time can be measured, and they are not quantized. In fact, there is no theory compatible with SR in which space and time can be quantized, given the nature of the Lorenz transform: SR predicts continuous length contraction from the PoV of observers moving at any velocity relative to each other; for any distance of length 1, some other observer can exist for which the length would be 1/x, with x as a real number.
Again, our current theories all agree that space and time are continuous, not quantized. Quantized space or time are not consistent with either QFT or GR.
Now, we do know that QFT and GR are not consistent with each other, so at least one new theory is necessary, at least one of them must be wrong. So the new theory could involve quantized space or time - but it could very well not. We don't know at the moment, and all we know is that our best theories, limited as they may be, require continuous space and time (and other quantities).
Either you understand this stuff at a level so much deeper than me that I can’t comprehend what you’re getting at or you are way out of your depth because none of this makes any sense to me.
Waves aren’t physical but everything is waves? We can’t measure standing waves but have to “guess” with calculus and differential equations?
Let’s take calculating the area of a circle. Since pi is in an irrational number that goes on forever, we can only get a closer approximation to an area circle by extending the decimals of pi. But since pi goes on forever, we can never know the exact area of aLet’s take calculating the area of a circle. Since pi is in a irrational number that goes on forever, we can only get a closer approximation to an area circle by extending the decimals of pi. But since pi goes on forever, we can never know the exact area of a circle.
Hard pass. The exact area of a circle is pi*r^2. We can calculate decimals of pi arbitrarily far, certainly further than our ability to measure. “Exact area” means we use symbolic math, not that we quibble about significant digits.
In quantum physics, "quantized" means that a field has a smallest possible excitation, called a quantum, rather than being able to vary continuously.
For example, the quantum of the electromagnetic field is the photon.
A quantum field is fundamentally quantized, so the waves that arise in quantum fields are similarly quantized.
> Again, you are quantifying things that in and of themselves are not quantized outside of our conception.
No, we have extremely strong evidence that the physical fields themselves are quantized. If you try to model physics using classical waves - which we do, e.g. in semiclassical electrodynamics, which models the electromagnetic field as continuous instead of quantized field - you find there are limits to what can accurately be modeled. To get an accurate model, you need to quantize the field.