# Does a photon see a 0-D universe?

For a massless particle the spacetime interval between its point of emission and point of absorption is zero: the two points coincide. From the vantage point of such a particle space-time has reduced to a single point.

In the Standard Model, all particles start with zero mass, so does this suggest that our familiar 4-D spacetime is a consequence of the Higgs field or some similar mechanism by which mass is acquired?

Note: if you believe the large-scale 4D structure of spacetime is a pre-existing given, this question makes little sense. In a relational view, where spacetime emerges out of event relationships, then the question suggests that a universe comprised solely of massless particles would have a fundamentally different event-structure.

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Τwo events separated by a time-like interval lie on a 1-D line but it doesn't mean that a particle's space-time has reduced to a 1-D line. –  Andyk Aug 25 '11 at 17:18
We're talking about a light-like interval here. Although the 'line' at 45 degrees on a Minkowski diagram looks like a line it's not really because of the non-Euclidean metric: all the 'points' on that line are identified within the reference frame of a lightlike object. –  Nigel Seel Aug 25 '11 at 17:57
Those points are not identified. There is a topological metric, which tells you which points are the same, so that all physical values are the same at those points, and then there is a physical notion of distance which is also called a metric. A week ago, I would have said the particle can't have a point of view, because it's infinite time dilation means that it can't do any computation. But I just learned that massless particles can decay. –  Ron Maimon Aug 26 '11 at 0:28
Note to OP: Physics is supposed to give predictions testable by infinitely advanced beings. In other words, no prediction of physics is such that the laws of physics prevent it from being verified. Thus, we cannot 'step into the POV of a photon', even hypothetically, as special relativity forbids any measiring device from piggybacking a photon. –  Manishearth Feb 21 '12 at 10:45
@Manishearth: What is to prevent a hypothetical measuring device made of photons that interact via loop diagrams? –  user1247 Feb 21 '12 at 12:29

Per special relativity, no human measurement device can ever reach the speed of light, and thus we can never test what the universe "looks" like in the eyes of photons. In other words, the question of what light would see is unfalsifiable and thus not a scientific question.

And if you force Lorentz transformation onto the frame of photons, you will get a lot of contradictory conclusions. For example, an object is moving at speed $v$ in some normal frame. Then in the frame of a photon that moves in opposite direction, the object is moving at speed $$\frac{v+c}{1+\frac{vc}{c^2}}=c.$$

According to the invariance of speed of light, the object must be moving at speed of light in any frame, which contradicts our premise that it is moving at speed $v$ in some normal frame.

Moreover, in general relativity, the spatial and temporal component of a four-vector as measured by an observer is directly related to the four-velocity of the said observer. For instance, energy $E$ is the temporal component of four-momentum, as in $$E=-p^\mu U_\mu.$$ Since light-like paths does not have a well-defined four-velocity, you can also see it makes no sense for a photon to "see" or measure anything.

For a massless particle the spacetime interval between its point of emission and point of absorption is zero: the two points coincide.

This is not true. The distance in Lorentzian manifold is not postively definite, so zero distance in no way implies the same point.

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What a photon does "see" is funny on the semantics level already :=). This reminds me of the "looking rays" one of my daughters tried to convince me of when she was about 3 or 4. –  Georg Nov 23 '11 at 10:05
What about a measurement device made entirely of photons? It would be able to move at the speed of light, and interact via loop diagrams. –  user1247 Feb 21 '12 at 10:45
@Georg Didn't the old Greeks postulate looking rays? (Some ray tracers actually work that way :-) ). Although ultimately wrong, I guess it was a nice exercise in scientific thinking to make this hypothesis and test it. –  Lagerbaer Feb 21 '12 at 16:16

We see a 3D universe with help of photons.

The "gauge nature" of all particles is an incredible stretch which does not work itself at all. Higgs "mechanism" is a patch of this stretch and mass of Higgs needs another "mechanism" to be explained.

I think starting from phenomenological masses is the only healthy physical way of giving masses to all particles and bodies. Some masses can be calculated from others then.

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Not an answer but a confession of hopelessness following your unhappiness with the Higgs mechanism! –  Nigel Seel Aug 25 '11 at 20:49
No unhappiness, just a common sense. –  Vladimir Kalitvianski Aug 25 '11 at 20:57
-1 Higgs mechanism is just superconductivity, and gauge nature of all particles is not a stretch, but an experimental fact. –  Ron Maimon Aug 26 '11 at 0:55
@Ron Maimon: And how about bare particles and their strong interactions? They are also "needed" in theory to describe experimental facts. It is they who should be considered as the true bricks of nature. And mass of Higgs is certainly given by God. –  Vladimir Kalitvianski Aug 26 '11 at 8:17
Why Higgs mass may be fine tuned but the other masses may not? Who prevents us from writing the right known masses in our equations? –  Vladimir Kalitvianski Aug 26 '11 at 9:09