# Must time pass in order for causality to operate?

Motivation; It is perhaps quite well known that things in a faster moving frame of reference perceive time as passing slower. (This is in fact special relativity and it doesn't account for behavior during acceleration or in gravity wells. Let's ignore those situations for now though.) This scales such that as you get closer to the speed of light time moves slower and slower and the mathematics predicts that for a photon time does not move at all.

If the mathematics are to be trusted photons perceive the entire universe in a single instant. Yet they still appear to behave causally.

It seems to be that one of three things could be true;

1. The maths is wrong, or somehow oversimplified.
2. The maths is correct but the passage is time is not required for causal behavior.
3. The universe is illogical.

Question; Is number 2 possible? Is it possible that the passage is time is not required for causal behavior?

• If, for a photon, time does not move at all - what is a light year? – Ron Royston Jul 11 '15 at 2:13
• @RonRoyston, a light year is the distance a photon would travel in empty space, while the earth orbits the sun once. – nir Jul 11 '15 at 10:50
• @RonRoyston One has to distinguish "our" time and the photon's proper time. – Atamiri Jul 11 '15 at 13:49
• @royston: there are two contexts: consider a man watching a photon go past, then 1) time for the photon doesn't pass; but 2) time for the man does pass. This sounds strange because we expect time to flow at the same rate everywhere, a minute passing on a clock on a photon should take the 'same time' as a minute that passes on the clock held by the man. – Mozibur Ullah Jul 12 '15 at 8:54
• This is what is generally called Newtons notion of absolute time; but in Einsteins notion the clock on the photon is slowed down until it actually freezes; whilst the mans clock is left as it is. – Mozibur Ullah Jul 12 '15 at 8:56

(Personally, I agree with the idea that time is an aspect of change, and not the other way around. But the physics does not presume that, and still allows for a consistent interpretations.)

None of the above. You can anthropomorphize the happy photon, but you have to bring the rest of relativity along with you. And relativity presents an interpretation in which time does stop for the photon, causation is temporal, and events are predictable.

Even if we imagine a the photon has a sense of time of its own, there is still no spatial movement seen by the photon relative to our perceived space.

Taking the same limit that reduces the passage of time to zero, also affects space. The photon sees our length completely compressed to zero in whatever direction it is travelling relative to us.

We are always completely in its peripheral vision, whenever it might rotate to look at us, we disappear. (We are like Carlos Casteneda's death, always straight left of its line of sight, even when it turns its gaze.) Whatever direction it might choose to move in our space, the space won't let it. In effect, then, our whole space is reduced to a single point. And for it to bounce around our point-sized universe does not ever require, or even allow for, motion with velocity.

To the extent it might perceive the remaining dimensions of our space perpendicular to the one in which it is traveling, there is still no real causal sense. Things in our universe might cause it to turn, relative to us, but the photon sees this as other things moving around it, and not as causal effects upon it.

Further, those things moving around it are stuck where they are relative to one another, and in some ways relative to it. They cannot get closer or farther, or change their other effects upon it in any way. From the photon's point of view, our time is frozen, because when the photon's time passage relative to us became zero, so did our time passage relative to it. That is what is relative about relativity. And the bizarre view available to it of our frozen time would have to be one in which everything we see as successive, is actually happening at once.

This does not mean, necessarily, that the photon does not experience causation, but that the causation is independent of anything we might perceive. It gets its own frame of reference, in which it can be affected by gravity, etc., in ways we would not perceive, just as it sees no effects on or from us, because our timelines are independent. It sees as static what we see as changing, and vice versus, with each of us having a complete map of the other's timeline embedded in its view of space.

Rudy Rucker imagines extra spatial dimensions in which we might be extended and participate, but never perceive. Our space would be like that to the photon. Except that additionally, since our timelines are perpendicular, all side-effects of its participation in our space are frozen, still pending but already done, so there will never be real evidence to the photon that we exist or at least that what happens/ed here ever affects/ed it in any way.

Another way of looking at this is proposed by Wheeler and Dyson. The slickest way to formulate the change of frames of reference is as four-dimensional rotation in a hyperbolic space. As we speed up, time rotates (rotatesh ?) relative to space. Attaining the speed of light relative to us, then, is a (hyperbolically) perpendicular rotation, which takes its time dimension into (a bizarre reshaping of) one of our spatial dimensions. This indicates all the same effects but is far harder to interpret anthropomorphically.

• This physical description is intriguing, and slightly headache-inducing. Would the "things moving around it [that] are stuck where they are relative to one another" not also appear to be in several places at once? – Jekowl Jul 13 '15 at 18:45
• Right, by the rotation analogy, our time his their space. So there would have to be a spatial configuration that traced our history in some way. The only thing that I can imagine is a smear of superpositions. It is more likely that there is no view from them into our space, but the physics does not explicitly rule it out, just makes it bizarre. – jobermark Jul 13 '15 at 21:39

For statement #2, the math is correct. Also, the passage of time is required for causal behavior. You are being misled by your statement, "they (photons) appear to behave causally." I believe this is caused by you not differentiating between "photon causality" and "observer causality." Even if the photon had a "brain," it would not be "aware" of causing anything (time is zero, motion is zero). It is the observer (moving at a speed < c) that is/becomes aware of any photon causality.

For your specific reasoning the answer is close to option 1: photon does not have any reference frame associated to it, and "photons perceive the entire universe in a single instant" is meaningless even if photons were somehow intelligent. Most relativistic quantities become meaningless in the limit v=c, so what happens in the limit is not the limit of what happens when it is approached. It takes infinite energy to accelerate any massive object to the speed of light and photons can never be decelerated down from it, so neither can ever "approach" what happens to the other. See If a photon is in a 'timeless' state, how can objects around it move?

But irrespective of special relativity atemporal causation is perfectly possible, e.g. in theology God causes the world to exist from outside of time. Recall also that in classical mechanics gravity of one body caused another one to accelerate across arbitrary distances without any passage of time. So option 2 is logically available, albeit unnecessary.

• "photons can never be decelerated down from it" - Sort of not true, light considered as a wave will slow down. See refractive indices. In your gravitational example you imply an asymmetry that isn't present. Both bodies act on each other simultaneously and symmetrically. Causality implies a reaction that is in some way asymmetric because it would look wrong played backwards. – Jekowl Jul 11 '15 at 15:48
• @jekowl: the implied context is that this is in a vacuum; and light maintains a constant speed there; there are theories in which light speed is variable - but they are speculative. – Mozibur Ullah Jul 12 '15 at 8:50
• @MoziburUllah I did not mean to imply that I am only interested in theoretical vacuum behavior, sorry for the confusion. If the question was set in an impossible perfect vacuum then there would be no interactions and the word 'causality' would be a bit meaningless. Unfortunately if we consider light both in and out of the vacuum this means that it can approach its full speed from a speed less that c. So The idea of "taking a limit" is back on the table. – Jekowl Jul 12 '15 at 10:10
• @jekowl Light in a medium is a "superposition of excited matter states and pure photons, and the latter always move at the speed of light c", slowdown is only a macroscopic appearance for the classical wave. Vacuum or not, photons either move at speed c or do not exist physics.stackexchange.com/questions/153904/… In the gravity example the symmetry makes no difference for causation, each body exerts a force that causes the other to accelerate, in zero time. – Conifold Jul 13 '15 at 17:45
• @jekowl Well, classical notion of velocity is meaningless in quantum theory, but in the system light+medium you will not find an eigenstate where photons "slow down". Something like a hybrid explanation is that photons get scattered and/or absorbed and re-emitted, creating the illusion of slowdown, but this relies too heavily on classical intuitions to represent the QFT picture correctly. – Conifold Jul 13 '15 at 19:18

One answer has been already been elaborated - that there is no inertial frame associated with the photon.

Another answer is to take this seriously and attempt to interpret what this may mean. One observation is that this means that the photon is out of time (and space); ie timeless.

This is reminiscent of Parmenides conclusion two Millenia ago that reality is without time; which has been resuscitated by the 'neo-parmenidians' Barbour and Rovelli.

But your objection is how do we explain causality here; well, even in Relativity with the above interpretation we have a timeless entity (the photon, in its timeless frame) which still has an effect (in the frame of the world) ie causality, in a sense.

There is another option, which goes back to Aristotle, and then via Mach; which is that 'time is an aspect of change' (Aristotle) and then Mach, time is exactly the change in the motion of the stars; part of Barbours work shows that time in classical mechanics as an independent parameter 'falls out' which is good evidence for the Machian view.

• This seems like it's talking about your last paragraph. physicsforums.com/threads/… It seems to be second hand though, and heavly abridged, would you know where I might find the orignial in a more complete form? – Jekowl Jul 12 '15 at 10:29
• the essay on Barbour is here; and a discussion of this is Huggets essay in the Blackwells companion to the Philosophy of Time. – Mozibur Ullah Jul 12 '15 at 11:02
• The essay by Hugget is available here on the arxiv – Mozibur Ullah Jul 12 '15 at 11:10
• Boltzmann's evasion of Loschmidt produces the same notion. Look up Boltzmann Brains or the related background material. In that sense entropy is an aspect of change, and time is the accumulation of entropy, so time is an aspect of change, even if there is some underlying, "more real",time against which entropy increases or decreases. – jobermark Jul 13 '15 at 14:21