squaring that circle seems, uh, fraught.
Also, doesn’t entanglement already punch that hole? …in which case, assuming non-locality is the minimal assumption.
How so?
Eg, anyons carry a non-local quantum number — which is the source of their robustness as qbits.
From the viewpoint of an electron, the moment it is emitted from an antenna as a photon and the moment it is absorbed in another antenna as an electron are the same moment i.e. the photon travels zero distance in zero time.
Somehow our communications equipment still maintains causality.
Radio amplifiers pump electrons into the antenna, which transmits them as photons, and the receiving antenna absorbs them, turning them into electrons, the flow of which then becomes the audible radio signal which gets (demodulated and) amplified by the receiver.
The photons do not travel any distance and they do so in zero time. This can be mathematically proven.
See e.g. https://phys.org/news/2014-05-does-light-experience-time.amp - the relevant parts:
”The closer you get to light speed, the less time you experience and the shorter a distance you experience. You may recall that these numbers begin to approach zero. According to relativity, mass can never move through the Universe at light speed. Mass will increase to infinity, and the amount of energy required to move it any faster will also be infinite. But for light itself, which is already moving at light speed… You guessed it, the photons reach zero distance and zero time.
Photons can take hundreds of thousands of years to travel from the core of the Sun until they reach the surface and fly off into space. And yet, that final journey, that could take it billions of light years across space, was no different from jumping from atom to atom.”
Can we agree that each of the RADAR and the two RADAR-reflecting objects definitely occupy different points in space?
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RADAR images (taken at e.g. Arecibo, here on Earth) of Venus, the Moon, and several other solar system bodies <https://www.naic.edu/~pradar/radarpage.html#venus>
From the frame of reference of a transmitted photon, the transmission is instantaneous, and the spatial distance traveled is zero.
From our perspective, it is a different story. If you are having difficulty grasping this, perhaps you are thinking that photons are like tennis balls but with a very high velocity. Perhaps you even entertain the sci-fi notion of faster than light travel.
However, speed of light in a vacuum is a much more fundamental limit than an inherent velocity limit of some particle.
It is essentially the default propagation speed of all physical information. Interaction of light with matter causes absorption and re-emission of photons, which causes light to both slow down in a medium and pick up some information about whatever it went through.
...
> If you are having difficulty grasping this
I don't think I am. Compare my longer comment in this thread <https://news.ycombinator.com/item?id=32462046> which makes reference to Wald's standard textbook. It's not just Wald - any standard textbook will agree. I can give you chapter references for practically any of them if you like.
What I was wondering was how you reconcile the difference in time at a RADAR station when receiving photons bounced off targets at different spatial distances with, quoting you, "the photons do not travel any distance and they do so in zero time".
Surely time passes at the RADAR transceiver? Otherwise, wouldn't we get instant returns back from the Moon and Venus, instead of having to wait seconds to minutes?
A broader question might be, "is there a 'best' clock for analyzing a RADAR detection, and if so, which clock?".
Finally, you might want to wonder if an in-flight photon changes spin states or frequency. Doesn't a RADAR photon bouncing off a moving target (or returning to a moving transceiver) undergo a doppler shift, and thus change of frequency? How do police RADAR guns work if photons do not feel time?
It strikes me that you didn't care to answer my earlier RADAR questions at all among your five paragraphs in reply. If you don't care to do so, or you don't want think about any of this, that's fine. But I think you should take care in judging how much or how little anyone on hackernews might know about relativity, or what ideas about sci-fi-like-concepts they might entertain.
p != p' are two points on a 3+1 dimensional Lorentzian manifold (M, g), modelling our spacetime.
There is a minimizing geodesic from p to p', the "shortest straight-line path".
In a Lorentzian spacetime, geodesics are classified into three groups: spacelike, null, and timelike. A null geodesic describes the freefall of the massless relativistic wave equation, which applies to e.g. photons (as the Maxwell equations using the Lorenz gauge); and a timelike geodesic describes the massive relativistic wave equation, which applies to e.g. neutrinos (as the Dirac equation) or the Higgs boson (as the Klein-Gordon equation). In a particle paradigm, photons move at c freely falling on null geodesics; neutrinos, electrons and so forth move at less than c freely falling (experiencing no accelerating force) on timelike geodesics.
If p and p' are timelike-separated, they can be connected by a timelike geodesic (e.g., a path that could be taken by a massive particle), then we can calculate a nonzero spacetime interval S in some coordinate basis, and divide by c, giving us the proper time \tau such that d\tau = dS / c in a patch of flat spacetime (the metric g enters into the definition through general curved spacetime: on path P, \Delta \tau = \int_{P} 1/c \sqrt{g_{\mu\nu} dx^\mu dx^\nu (= \int_{P} d\tau), which is invariant under changes in coordinates, and has the same problem with dividing by c.
However, if spacetime points p and p'are lightlike-separated, they cannot be connected by a timelike geodesic, but rather by a null one. The spacetime interval of a lightlike geodesic is defined such that dS = 0 (thus the name "null").
Any path through spacetime can be parametrized by applying arbitrary labels to its points. A geodesic is a species of path. We can label any geodesic from A to B any way we like: Apple Zebra Xray 3.1415 1 86 Xray-again Manitoba Xray Xray-again ... 911. Arbitrary labellings are not widely useful, though, so we will probably want to label every point with a unique value in such a way that there is a total ordering from A to B, and even more ideally so that there is some smooth monotonically non-decreasing function f on the geodesic, mapping all its points to unique values of the parameter.
Proper time is just such a useful function on a timelike geodesic. It is not the only such function.
On a null geodesic, proper time would give us a labelling 0 0 0 0 0 ... 0, which is obviously not useful, as the 0s aren't unique or ordered. However, we can use any monotonic function, setting out labels at every point along the path from p to p' where we would (if we measured) detect the photon.
A good choice for a null geodesic is the affine parameter, as that preserves the photon's tangent vector under parallel transport along the path. There is a unique affine parametrization satisfying the geodesic equation for every geodesic, including every null geodesic.
One of the properties of the affine parameter on a null geodesic is that we can define a momentum k^{\mu} = \dot{X}^{\mu}, the dot representing the derivative with respect to the affine parameter -- the momentum k can be calculated at every point on the null geodesic, and in a curved spacetime k will differ from point to point. This difference in momentum is exactly the gravitational redshift.
So, it might be better to say: proper time is an unsuitable parameter for a photon in free fall, or for labelling points on its path from point A to point B. Instead we can use affine time (== the affine parameter) for a photon and for its path from point A to point B, and see that there is some definite timelike parameter for a photon on its journey that can [a] show where in spacetime it can be found during that journey and [b] what its momentum is at [a] and thus what its frequency, wavelength or energy is at [a] via the E = h{\nu} = \frac{hc}{\lambda} relation, and how those quantities change along the path in the presence of spacetime curvature.
I would not say "no time passes for it", because we can always define such a time. Affine time is one such (useful) definition, but we can use any others we like. Although a proper time can be calculated for such a massless particle, the proper time is 0 everywhere, so not very useful. However that does not strictly speaking mean that there is no passage of time from the point of view of the photon. It just needs to "wear a different sort of wristwatch" than an electron might choose to. However there is an affine parameterization for an electron moving between points I and J, so electrons (and neutrinos and other non-massless waves, particles, or objects) can always "wear the same sort of wristwatch" as a photon. (Some mathematical details in Wald's graduate-level textbook _General Relativity_ §3.3 and see ch. 3, problem 5).
> Consequently, the only way that hidden variables could explain the predictions of quantum physics is if they are "nonlocal", which is to say that somehow the two particles were able to interact instantaneously no matter how widely the two particles are separated.
It's true that with our current theories, instantaneous action at a distance does not seem possible. Yet quantum experiments (wave function collapse over large distances) consistently suggest this might be possible at macro (non-quantum) scales. I think our knowledge is incomplete on this topic.
Gravity is another area where I don't think non-local effects have been fully ruled out. Gravitational waves (energy emitted/thrown off by certain mass/momentum configurations) have been proven to travel at or near the speed of light, but the propagation speed of the first order gravitational effects an open question. This is an area I would love to see more experimentation done. To simultaneously measure the gravitational and optical positions of the Moon or Sun for example.
https://en.wikipedia.org/wiki/Speed_of_gravity