# Why does light have a speed at all?

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1. Sep 21, 2015

### RUKiddin

I appreciate that this may be the 100th time this is asked but I am yet to see an answer which addresses the question head on.

Given that reaching light speed creates both a length and time singularity; both length and time amount to zero for the propagating wave/photon. Why does that photon nevertheless require (around) 8 minutes to travel from the sun to our eyes? (or perhaps a more correct way to phrase that would be, why do we require 8 minutes of our perception of time for the light to travel the distance which we perceive as being between the sun and the earth?)

Basically I am asking why is such travel not simply instantaneous from all perspectives rather than 'c' from all perspectives?

And as an afterthought, if 'c' is constant from all perspectives, is it also constant relative to the wave/photon itself?

2. Sep 21, 2015

### andrewkirk

The problem with the question is that, as Einstein identified in 1905, there is no such thing as 'instantaneous from all perspectives'. Whether two events happen at the same time depends on your frame of reference, which depends in particular on how fast you are travelling. So two events A and B that are considered to be simultaneous by one observer will happen A before B to a second observer and B before A to a third.

This is called 'relativity of simultaneity'.

There is no perspective of the photon. A frame of reference cannot 'travel at light speed'. If it could, space would collapse to a point in the direction of travel. People often ask what things look like from the photon's point of view. The answer is that there is no such point of view.

3. Sep 21, 2015

### BvU

Hello RU, welcome to PF !

Light is an electromagnetic wave phenomenon. Like all disturbances, a disturbance in the electromagnetic field needs time to propagate through space. "Reaching light speed" sounds like something that can be done. But it can't. Light doesn't come up to speed by accelerating or anything. And you are right that for a photon there is no time or length. So clearly your last afterthought question is something that you can wonder about, but you can't ask...

4. Sep 21, 2015

### Boing3000

That's not correct. Nothing reach light speed. Massless particles and gravitational wave (supposedly) travel at cosmic speed limit. They are born this way, they do not reach it.

Actually a photon cannot record time nor length. The frame of the photon is something quite esoteric.

Nobody knows why. But that's the way nature works... so we measure it, and more spectacularly, everybody will agree with this (not the 8 minutes, but speed C), whatever the frame.

That one is easy. That's because it is impossible to define instantaneity.
From a logical perspective alone, it make sense. If two event where instantaneous, nobody could pretend anymore one is the causer of the other (and not the other the cause of the one)

5. Sep 21, 2015

### Staff: Mentor

The direct head on answer to your question is that the question itself contains a false premise/assumption. It is false that "reaching light speed creates both a length and time singularity". Any question that starts with that as a given is wrong. That is the direct answer to the question, which is always provided.

Here is a brief explanation about why "relative to the wave itself" simply doesn't work.

The other aspect, which is not always addressed, is the fact that even though the spacetime interval is 0 along the worldline of a pulse of light, there always exists a valid affine parameter along that worldline. That affine parameter varies from event to event along the worldline and ensures that the points on the worldline are distinct.

6. Sep 21, 2015

### RUKiddin

What I mean is that quite often the response is that light has no frame of reference or that nothing of mass can achieve the speed of light so there is nothing to answer.

Given that light travels at lightspeed such a condition does exist for -something- in the Universe; allbeit a massless energy. Given that this massless energy itself fits within a frame of reference for observers within the Universe it is natural to ask -hypothetically- what must the conditions be for that massless energy. And I understand the point made that there is no frame of reference because by virtue of the nature of lightravel, a frame of reference is meaningless within the traditional definition of a spacetime reference, but it does strike me as odd that whilst the conditions are undefinable by their nature, they are clearly perceivable within the Universe and indeed have a maximum value; the cosmic speed limit.

Yes, I think this expresses precisely the aspect which I find strange; that the spacetime interval is 0 but that there nevertheless exists a valid affine parameter which itself varies from event to event. Its like the affine parameter itself has a speed.

7. Sep 21, 2015

### BvU

8. Sep 21, 2015

### Staff: Mentor

There's a sensible reason for that. Disturbances of the gravitational field are described by a theory that says the propagation speed should be the same for all observers. Disturbances in the electromagnetic field (that is, light) are described by a theory that says that the propagation speed should be the same for all observers. It turns out that mathematically there can only be one such invariant speed. Therefore, either the theories are wrong or they both have to move at the same speed, the one and only invariant speed that we're allowed.

It only seems baffling because we call the invariant speed "the speed of light" because of the historical acciden that we discovered and measured the speed of light long before we discovered gravitational radiation. If we could just get in the habit of calling $c$ "The invariant speed that light and a bunch of other stuff has to move at" it wouldn't be so baffling.

9. Sep 21, 2015

### Staff: Mentor

What condition are you talking about?

All geodesics have an affine parameter. For timelike geodesics the proper time is an affine parameter, but not for spacelike geodesics. For spacelike geodesics the proper distance is an affine parameter, but not for timelike geodesics. For null geodesics neither proper distance nor proper time is an affine parameter. So their affine parameter is different in that sense. But it nonetheless exists, and therefore the worldline cannot be mapped to a point in any valid coordinate chart.

Last edited: Sep 21, 2015
10. Sep 22, 2015

### RUKiddin

Thanks.

I understand this from the responses; which I express with less than 100% accuracy in laymans terms, but I believe this is the jist:

Light exists validly from the relativistic perspective of others but has no valid relativistic perspective itself within a spacetime frame of reference.

From the -hypothetical- perspective of a photon it is both nowhere and everywhere, both always and never; it has no valid location value within its frame of reference (there exists no frame from which to reference). Trying to ascertain its frame of reference is tantamount to asking what exists beyond the Universe, which by definition incorporates all that exists. Instead, all that we can say exists in a valid sense is the spacetime location of that light from the relativistic perspective of observers / other valid spacetime locations.

11. Sep 22, 2015

### Staff: Mentor

Yes, assuming that by "perspective" you mean "rest frame", which is the usual convention in such discussions.

Which theory of physics are you thinking of using to answer the rest of the question? It cannot be relativity because your hypothetical is incompatible with relativity. I don't know of any standard theory which is compatible, so you probably should post a peer reviewed reference so that I can study it before responding.

12. Sep 22, 2015

### RUKiddin

I wasn't theorizing and was trying to reference you...

and yet relativity has no beef with the fact that my hypothetical photon exists.

I think my hypothetical was simply an attempt to ask what the affine parameter you refer to is a parameter of if it is not a time geodesic nor a space geodesic. My original question was why should light interact with a finite, valid value if light speed travel renders time and space null values. As far as I understand the response it is something like; because light exists it has to obey the timespace parameters of the Universe even if time and space are null values within its own worldline.

Without passing a degree in mathematics it's probably as close as I am going to get to understanding; if incorrectly formulating, the concept.

13. Sep 22, 2015

### pervect

Staff Emeritus
I think it's worthwhile to point out that "why" isn't a scientific question. Science starts with the observations, and the observation are that, in a vacuum, light has a constant speed for all observers.

The idea of a constant speed does depend on having some notion of how to be able to measure time, and how to be able to measure distance. We could spend a lot of time getting into the details of how we do this, but for the purposes of this thread I would simply propose to say that operationally, we measure distances with rulers, and time with clocks, and that the readers have enough experience with both rulers and clocks to have some general agreement as to what they are.

Additionally, besides distance and time, one needs some notion of "simultaneity", or how to synchronize distant clocks. This apparently simple issue is most likely the underlying source of the confusion, but it would be too much of a diversion from the main point I want to make to go further into it. And there are plenty of threads on that topic as well.

The main point I want to make is this. The observation that the speed of light comes constant come first, it is a well-documented experimental observation. The theories have to fit the observations, the observations are not mangled to fit the theories.

So the most important thing to note is thing to note is that if your theories and theoretical constructs do not agree with experiment, than your theories (or perhaps your understanding of them) is wrong.

The second most important thing to note is that relativity, as it is taught in classes and explained in the literature, IS consistent with experiment, and DOES predict the fact that the speed of light (in a vacuum) is a constant for all observers. In fact this idea of constancy of the speed of light (in a vacuum) is one of the postulates of special relativity in Einstein's original papers.

So, applying some ligic, we can conclude that there is something wrong with your understanding of special relativity, given that it apparently doesn't agree with either experiment or with the literature on the topic.

Once we've gotten this far, we can perhaps usefully get into more of the specifics of "what went wrong". Until then, I don't think there's much more to say.

This has been discussed a lot, the basic answer is that photons do not have "perspectives". One thing I did notice is that some of the relevant FAQ entries appeared to be missing, i.e. https://www.physicsforums.com/threads/why-is-the-speed-of-light-the-same-in-all-frames-of-reference.534862/ [Broken] wasn't found. Also it seems to me we had at least one thread that was more relevant to the issue of photons not having a perspective, which is subtly different than the above.

https://www.physicsforums.com/threads/relativity-faq-list.807523/ is the FAQ list, "rest frame of a photon" is very short but perhaps the best answer, as long as one identifies "perspective" with "rest frame".

Last edited by a moderator: May 7, 2017
14. Sep 22, 2015

### Staff: Mentor

You have already been told, in unambiguous terms, that there is no such thing as a photon's perspective. The concept is contradictory to the postulates of relativity.

The word "hypothetical" is not a free pass that lets you escape logic. You simply cannot perform any valid analysis from a mutually inconsistent set of premises. Your hypothetical is inconsistent with relativity, so you cannot do even a hypothetical analysis with it.

Relativity has no problem with the existence of hypothetical or even non-hypothetical photons. It is only their "perspective" that doesn't exist. There is no reason to believe that everything which exists must have a perspective, and light is one thing which doesn't

The affine parameter is any parameter, $\lambda$ such that:
$$\frac{d^2 x^{\mu}}{d\lambda^2}=\Gamma^{\mu}_{\alpha\beta} \frac{dx^{\alpha}}{d\lambda}\frac{dx^{\beta}}{d\lambda}$$
For a timelike worldline the proper time is one such parameter. Once you have one affine parameter you can get any other affine parameter by the transform $\lambda \mapsto a \lambda + b$.

An affine parameter is a pretty interesting geometrical quantity. If you have an affine parameter of $\lambda_A$ at event A and an affine paramter of $\lambda_B$ at event B then the average of the two gives the affine parameter of the event which is "midway" along that path between A and B. It singles out that same event regardless of which reference frame you use to perform the calculation. Similarly for other affine parameter values between $\lambda_A$ and $\lambda_B$.

Last edited: Sep 22, 2015
15. Sep 23, 2015

### RUKiddin

Thanks. This is clear to me now. I did not realize it before I posted my initial question. Is there anything else which doesn't have a perspective?

I don't think I was escaping logic, I did after all highlight why the perspective cannot exist. Hypothetical scenarios are used all the time to demonstrate why such scenarios cannot arise including in the realms of relativity. For example the grandfather paradox or perhaps more correctly, just the causation issues that would result if information could -hypothetically- travel faster than light. Nobody says, "stop right there, you're not allowed to hypothesize about this".

Many of these FAQ links don't work. I did try them before I posted the initial question.

I think I need to learn a bit more about affine parameters... If the timelike worldline is null and the spacelike worldline is null, the proper time and proper space are not parameters what other parameter exists? I understand that mathematically there are infinite parameters, you can simply assign them but in my mind this seems equivalent to hypothesizing the existence of additional dimensions. Do I need to be corrected?

Last edited: Sep 23, 2015
16. Sep 23, 2015

### Staff: Mentor

17. Sep 23, 2015

### BvU

Greg knows. And that one does work.

18. Sep 23, 2015

### Staff: Mentor

Relativity is based on two premises, called postulates, the second of which says that light has a speed of c in all frames.

The "perspective of X" is the frame where X has speed 0.

So the perspective of a pulse of light is a frame where the pulse of light has speed 0, but that contradicts the premise that light has a speed of c in all frames. Hence it is the logical fallacy of contradictory premises.

This is fundamentally different from a "hypothetical" which is used to introduce something that is technologically or economically infeasible. It is also different from a "hypothetical" which is used to introduce something which we have no evidence for but which is compatible with the known laws of physics. It is even different from a "hypothetical" which is used to introduce different laws of physics. All of those can be done in a self-consistent manner so that you can make valid conclusions from the hypothetical premises. But when your premises are self contradictory you cannot form any valid conclusions (other than identifying the contradiction).

Last edited: Sep 23, 2015
19. Sep 23, 2015

### jbriggs444

A "timelike worldline" is a path through spacetime such that all events on that path are separated by a metric distance that is an imaginary number.

A "spacelike worldline" is a path through spacetime such that all events on that path are separated by a metric distance that is a positive real number.

A "null worldline" is a path through spacetime such that all events on that path are separated by a metric distance that is zero.

There is no such thing as a null timelike worldline or a null spacelike worldline.

The metric distance between two events, (x1, y1, z1, t1) and (x2, y2, z2, t2) is given by $\sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2 - (t_1-t_2)^2}$. Note that this is almost the same as the classical Euclidean metric, except that the sign on the time term has been inverted.

Edit: the above is ok for special relativity. I suspect that for general relativity, the definitions need to be tweaked to make them local.

20. Sep 23, 2015

### Staff: Mentor

Pedantic note: it's more usual to state this in terms of squared intervals (a timelike squared interval is negative, a spacelike one is positive--note that this also depends on the metric sign convention we adopt, what you describe is the "spacelike convention", but there is also a "timelike convention" where timelike squared intervals are positive and spacelike ones are negative), in order to avoid any mention of imaginary numbers (since some people have hangups about using an "imaginary" number to describe real measurements).

(Also, note that the term "worldline" is standardly used only for timelike or null curves, on the theory that tachyons aren't physically reasonable so no real object can travel along a spacelike curve.)

Yes, the local version replaces intervals with tangent vectors and their squared norms: a timelike curve is a curve whose tangent vector at every point has negative squared norm (again, this assumes the spacelike sign convention); a spacelike curve's tangent vector at every point has positive squared norm; and a null curve's tangent vector at every point has zero squared norm.

21. Sep 23, 2015

### Maxila

It might help with your reasoning to know that photon is a massless, elementary point particle. Among other things, it means it has no size and no internal structure, in addition to zero mass. If you take that to view the photon more as a disturbance in the EM field rather than as an object, DaleSpam’s, and the other reply’s might make more sense to you. Take a second look at what BvU said in post #3.

Last edited: Sep 23, 2015
22. Sep 24, 2015

### vanhees71

I hate to always repeat this: A photon is NOT a massless elementary point particle, it is a one-particle Fock state of a massless vector field. I hope this statement is allowed even in a B-tagged posting ;-).

23. Sep 24, 2015

### Staff: Mentor

This is true as far as the quantum mechanical model of a photon is concerned. However, for this discussion, "photon" is really being used as a sloppy shorthand term for "a pulse of classical EM radiation of very short duration, which can be treated, for most purposes, as a massless object traveling on a null worldline". Misner, Thorne, and Wheeler, IIRC, have a good discussion of the usefulness and limitations of this point of view.

(Note that I said "object", not "particle", to make it clear that we are not adopting any particular model of the object itself--we're just treating it as a thing that moves on a null worldline.)

24. Sep 24, 2015

### vanhees71

Well, and I thought that MTW is an exceptionally good textbook :-((((. Your "object" is a coherent state, not a photon.

25. Sep 24, 2015

### Staff: Mentor

I agree that "coherent state" would be a better quantum mechanical description of the object I referred to. (It certainly isn't a Fock state of the EM field with a photon number of 1.) But if we're just talking about SR, not quantum field theory, we aren't using quantum mechanical descriptions anyway; we're using classical ones, and the more precise classical description of the object in question is what I said in my previous post.

However, as a matter of custom, the term "photon" is very commonly used to refer to this object. You may not like the sloppiness of this custom, but it certainly exists. MTW uses it; but at least they go to the trouble of explaining that it is a custom, they admit it's sloppy, and they discuss the more precise ways of describing EM states and what their limitations are.

If you could get all physics textbooks and papers to stop using the term "photon" when they should be saying "coherent state" (in a QM discussion) or "a pulse of classical EM radiation of very short duration that, for most purposes, can be treated as an object moving on a null worldline" (in a classical SR discussion), that would be great. But I don't think you're going to accomplish that any time soon. (And even then there would still be all the pop science discussions that don't even bother with the subtleties at all.)