Does the wave function change from the viewpoint of the photon?

[Martian2020]

TL;DR Summary

Does wave function changes when photon going through two slits from view point of a photon?

The question arose when watching Sean Carroll video: The Biggest Ideas in the Universe _ Q&A 6 - Spacetime 3:50 - 13:30
Because photons follow null geodesic in spacetime the question arose from viewers:
"photons do they really
experience no time this is a question"

And in the answer:
"but if you just follow along the crest
of that wave nothing is changing no time
is passing from that point of view"
The above was about photon moving through space.

But how about more complex things, like going through two slits, reflection from a mirror, going through interferometer? Does wave function also same from photon viewpoint?
P.S. I recall reflection is sometimes explained by re-emission, but e.g. for two slits I do not recall similar things.

 

[atyy]

There is no such thing as a wave function from the point of view of a photon. The wave function is written from the point of view of an observer and a choice of reference frame.

 

[weirdoguy]

And there is no such thing as a "point of view of a photon" since there is no reference frame in which photon is at rest.

 

[Martian2020]

And there is no such thing as a "point of view of a photon" since there is no reference frame in which photon is at rest.

Why is that? Why can't we think/imagine such frame?

 

[weirdoguy]

Because photons move with speed c in every inertial frame. So in the frame of photon it would be at rest and at the same time it would be moving with c. That's a contradiction, hence there is no raference frame in which photon is at rest.

 

[vanhees71]

Last but not least there is no wave function for a photon. There's not even a position observable for a photon to begin with! I'm a bit surprised that Carroll makes such misleading statements in a movie (I've not watched it though to see myself, what's really claimed).

 

[Motore]

And in the answer:
"but if you just follow along the crest
of that wave nothing is changing no time
is passing from that point of view"
The above was about photon moving through space.

Watch that segment again. He wasn't talking about the wave function, but about the electromagnetic wave.
Of course, this is a pop sci web series from Carroll, albeit more serious than a normal pop sci.

 

[atyy]

Suppose one changes replaces "photon" with "electron", and "wave function" with "quantum state", it is still the case that there is no such thing as a wave function from the point of view of an electron, because the quantum state is written from the point of view of an observer and a choice of reference frame.

 

[Martian2020]

He wasn't talking about the wave function, but about the electromagnetic wave

Kind of yes. But isn't electromagnetic wave a measurement result of a wave function? We cannot observe electromagnetic wave w/out making observation of a photon as far as I understand.

 

[weirdoguy]

But isn't electromagnetic wave a measurement result of a wave function?

No and unfortunately I think this sentence is just a word salad

 

[Martian2020]

Last but not least there is no wave function for a photon. There's not even a position observable for a photon to begin with!

Elementary particles (if not entangled) are wave functions in Hilbert space. At least Sean said so (I've understood that way). Google finds lots of links for "quantum wave function for photon". Why do you say the opposite?

 

[phinds]

@Martian2020, you should keep in mind that pop-sci presentations, even when given by a serious physicist like Carroll, are entertainment, not education. They can be great for engaging/entertaining folks and creating enthusiasm for science but if you want to LEARN science, get a textbook.

 

[Demystifier]

Suppose one changes replaces "photon" with "electron", and "wave function" with "quantum state", it is still the case that there is no such thing as a wave function from the point of view of an electron, because the quantum state is written from the point of view of an observer and a choice of reference frame.

In ontological interpretations (Bohmian, GRW, many worlds), quantum state makes sense even without an observer. Furthermore, the photon can be described in light-cone coordinates. Does the original question make sense from that point of view?

 

[Martian2020]

@Martian2020, you should keep in mind that pop-sci presentations, even when given by a serious physicist like Carroll, are entertainment, not education. They can be great for engaging/entertaining folks and creating enthusiasm for science but if you want to LEARN science, get a textbook.

As per Sean, textbooks contain Copenhagen interpretation only, wave function collapse. Do you confirm that? If yes, where do I learn other quantum theories?

 

[Demystifier]

If yes, where do I learn other quantum theories?

Norsen's textbook
https://www.amazon.com/dp/3319658662/?tag=pfamazon01-20

 

[vanhees71]

Suppose one changes replaces "photon" with "electron", and "wave function" with "quantum state", it is still the case that there is no such thing as a wave function from the point of view of an electron, because the quantum state is written from the point of view of an observer and a choice of reference frame.

Well yes, but for an electron as a massive particle, there's a non-relativistic approximation, nicely valid in the corresponding realm of applicability, and then the pure state of a single electron can be described by a (Pauli-spinor valued) wave function.

Of course it never makes sense to say "from the point of view of an electron". Everything in physics refers to measurable quantities, being measurable by an "observer".

 

[vanhees71]

As per Sean, textbooks contain Copenhagen interpretation only, wave function collapse. Do you confirm that? If yes, where do I learn other quantum theories?

Fortunately not. There are also more careful textbooks, which just teach the "orthodox" version of the Copenhagen interpretation, which has no collapse.

For me the most convincing interpretation, stripping this issue from all philosophical quibbles that are unnecessary for understanding the theory as a physical theory, is the minimal statistical interpretation. This is treated carefully in Ballentine's textbook.

If you want to learn about the de Broglie-Bohm pilot-wave interpretation (applicable only to non-relativistic QT though) as well as one alternative theory (GRB theory), altering the standard quantum theory by implementing mathematically a kind of collapse, see

Duerr, Lazarovici, Understanding Quantum Mechanics

 

[PeterDonis]

Elementary particles (if not entangled) are wave functions in Hilbert space.

No, this is not correct. If you have a system containing multiple particles, whether they are entangled or not, there is one wave function that contains all the particles. Even if the particles are not entangled, there are not separate wave functions for each particle.

If you have a case where you can treat a single particle as having its own wave function, what you are doing is ignoring the Hilbert space of the total system, and instead using an approximation where you only use the Hilbert space for the system containing just that single particle. In that approximation, you can view the particle as having its own wave function. But cases where this works are rare and usually not very interesting.

 

[atyy]

In ontological interpretations (Bohmian, GRW, many worlds), quantum state makes sense even without an observer. Furthermore, the photon can be described in light-cone coordinates. Does the original question make sense from that point of view?

Yes. But that is interpretation (from the reference frame of this forum)

 

[PeterDonis]

In ontological interpretations (Bohmian, GRW, many worlds), quantum state makes sense even without an observer. Furthermore, the photon can be described in light-cone coordinates. Does the original question make sense from that point of view?

Yes. But that is interpretation (from the reference frame of this forum)

Indeed. Thread participants, please be aware that discussions of QM interpretations belong in the interpretations forum, not this one. Discussion in this thread is to be limited to basic QM.

 

[Demystifier]

Duerr, Lazarovici, Understanding Quantum Mechanics

I didn't know about this, thanks for pointing out!

 

[Demystifier]

Last but not least there is no wave function for a photon.

How do you call the photon probability amplitude in the momentum space? And how do you call the Fourier transform of that?

 

[vanhees71]

I'd call it photon probability amplitude. What you measure are field-correlation functions, which can be derived within linear-response theory assuming, e.g., a detector based on the photo-electric effect. You don't need the errornous idee of a "photon wave function" to describe detection probabilities for photons. See standard textbooks on quantum optics, e.g.,

J. Garrison and R. Chiao, Quantum optics, Oxford University
Press, New York (2008),
https://doi.org/10.1093/acprof:oso/9780198508861.001.0001

 

[Demystifier]

I'd call it photon probability amplitude.

You didn't answer my second question. How do you call its Fourier transform?

 

[vanhees71]

It's the electric-field autocorrelation function in momentum space, or about which quantity are we talking?