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I am not a physicist. This is the first question I write in such a forum so if there are remarks on how I wrote it, I'll be happy to edit.

I am originally a mathematician with some interest in physics. I studied the basics of Einstein's formulas in regard to relativity, how space and time changes for an observer looking at an object travelling in a certain speed. The math there breaks down when the speed is c (speed of light).

But I dared, out on being the non physicist that I am, to ask myself what happens if we regard a photon as an observer and ditch calculus for the topology of extended real number line. There we can divide by 0 and have space and time as singular points.

Simply put:

  1. The photon can "measure" all points in space at any given moment.
  2. The photon can measure anything on the timeline.

Example: As I look at the 2-slits experiment and how we "shoot" one particle at a time, this shouldn't matter to a photon because we can't "fool" it by time differences. The photon does not need to interfere with itself but rather it interferes with another photon the will go through the measurement in the future. As soon as we place our own measurement tool to observe, it does not travel in the speed of light and therefore we get a collapsed result because our "observer" is different, as supported by Einstein's relativity.

Obviously, I expect to be wrong. My question is simple:
Why can't we use another topology other than calculus for Einstein's Relativity?
Why isn't physics allowing this?

Tzali
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  • Is it helpful? (I don't know anything of topology so I may not participate in discussion) – Billy Istiak Mar 26 '22 at 07:51
  • In the terms of the link you gave, my question is about removing the time frame limitations as we allow infinity to be a point like any other and time in my question is referring to difference in events. A photon interacts with the world, weather or not we can perceive it. Saying that a photon does not "experience" limits our mind to a new possibility where de-facto, it does (i.e. interference patterns). The post you gave only makes my point. – Tzali Mar 26 '22 at 08:14
  • I can't say much on your post, but your thoughts on "removing time frame limitations" for photons remind me of Roger Penrose's conformal cyclic cosmology model. If all particles decay into photons (I don't think this is verified), then according to this model, our universe will eventually end up as nothing but photons. But since electromagnetism is scale invariant and photons "don't experience time," you can rescale the universe and extend time "past infinity," and what you end up with according to the model is another big bang. It's not accepted by the mainstream, but it is interesting. – Maximal Ideal Mar 26 '22 at 16:40
  • I suggest you read up on quantum electrodynamics. The math is challenging but not formidable. – David Hammen Mar 27 '22 at 13:35

2 Answers2

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Photons as some kind of observer (as if they were like the standard timelike observers in relativity)? As suggested by the discussion linked by @BillyIstiak, there are problems.

  • For example, what does it mean for a photon "to measure"?
    A clear definition needs to be made or proposed.
    For timelike inertial observers, one has (for example) the "radar method" to assign coordinates to all events by sending a radar signal and noting that observer's clock-readings at emission and reception.

Concerning the use of other topological structures in relativity, I'll list some examples below as possible starting points for you. I can't really comment much on them right now... but I merely point out alternatives that have been attempted.

(I hope this list of wikipedia links and DOIs is okay. I could transcribe fuller references, if requested.)

robphy
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  • When I think of "Observing" I naturally thing of "Interaction". A photon that interacts, that is effects or is effected by it's environment, has to "observe" it. I don't know if that is the accepted formal definition, and if no, let us expend the definition to include this. In other words, I cannot be effected in any physical sense by something that I cannot "observe" because in the sense of my question they are both of the same. An thank you very much for the links on topologies! I'll read them in depth I assume you :) – Tzali Mar 28 '22 at 06:54
  • @Tzali Here's the radar method to assign coordinates to events. You want to send a radar signal to a distant event (a specific event on a spacetime diagram). Record the clock-reading t1 when you can send a light-signal to reach the distant event, await the echo and record the clock-reading t2 when it is received. Assign the event to have coordinates T=(t1+t2)/2 and X/c=(t2-t1)/2. This is the radar method. How would a photon carry out this procedure (or a similar procedure) to assign coordinates [presumably a basic measurement of any observer]? – robphy Mar 28 '22 at 23:43
  • for a photon under the terms of the question a radar signal has no distance to travel as immediately it is at the edges of the universe and at the same time in the point of origin. But let's indulge your thought. If the only way something measures (or in the terminology of my question "interacts") with something else is modeled by the radar method, photons wouldn't interacts with anything... and this isn't the case. – Tzali Mar 30 '22 at 14:22
  • @Tzali Interacting and measuring are two different things. I gave a radar method as a procedure that timelike observers would use to measure space and time displacements... i.e. "assign coordinates". It's not the only method... but it gives an operational definition of this "measurement". So, I'm merely asking for an operational definition (by whatever tools available) so that one can say that a photon has measured (here) assigned coordinates to events. [Maybe one can use a set of massive particles... whatever....] Just give an operational definition. – robphy Mar 30 '22 at 17:03
  • This can lead me to understand my problem. If I understand correctly I would describe the interaction itself as a function in space-time which represents all effected particles of a certain event/force. For example, gravity starts as a black hole is created, then in my function, gravity (the force) starts to expand in space-time outwards from the center of the black hole. – Tzali Apr 04 '22 at 07:15
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Photons as observers is an imprecise interpretation of the role of the photon. Photons can only be a means of observation. One can observe their emission and absorption. One can observe the transition of the momentum of the photon to subatomic particles. One can measure the collective behaviour of photons in an electromagnetic wave.

The photon has no ontological properties. And thus no room for interpretation that it reaches any entities because of its speed of light.

HolgerFiedler
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  • When you say photons are a mean to observation I think what it is is terminology. If a photon gives us information about something, it interacted with that something, ergo, it had to "acknowledge" it. I refer to this is "observation" and not necessarily the interpretation of measurement – Tzali Mar 28 '22 at 06:56