# Why is light in vacuum so slow? [duplicate]

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Accepting the speed of light in vacuum and infinite mass and all that, I wonder why light does not have infinite speed?

I know light does not have rest mass, but people use the term infinite mass when taking about the speed of light in vacuum so I am assuming that is kind of correct in this case.

Some background to my question:

I am sure there have been lots of experiments that slow light down. I even believe there was one that used a gas that managed to slow light down to almost 0 for a small fraction of time.

That's all easy to understand (I think) but once the light is free from restriction, i.e. after it makes it though the gas (or whatever is slowing it down) its speed increases back to light speed. So firstly, how is its speed increasing back to light speed? What force is involved in getting it back up to speed? Then, why is it stopping at that speed?

Aside from all the business of slowing light down or speeding it up, why is it so slow in the first place? what is keeping it from going faster?

Is it possibly going faster but we are only able to observe and measure the sub-light part?

Is there something in the universe that makes it difficult for the light to move, some sort of friction if you will?

## marked as duplicate by ACuriousMind♦, Kyle Kanos, Ryan Unger, user36790, Bill NOct 2 '15 at 15:40

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• Please note that correct punctuation, capitalization, spelling, and grammar help make questions easier to understand and therefore more likely to get good answers. I edited this post to correct several issues. In general, please do pay attention to these details. Enjoy the site :-) – DanielSank Oct 1 '15 at 19:46
• An now for the physics. These so-called "slow light" experiments don't actually change the speed of light itself. Rather, they introduce a medium which itself reacts to the electromagnetic radiation (a.k.a. light) and emits its own radiation with phase and amplitude shifts in such a way that the net energy flow is slower than light in a vacuum. I have no idea where you got the "infinite mass" idea, so a reference would be helpful. – DanielSank Oct 1 '15 at 19:48
• Possible duplicate of What is so special about speed of light in vacuum? – Kyle Kanos Oct 1 '15 at 20:16
• Infinite mass comes from the idea that to accelerate past the speed of light is not possible as when your at the speed of light you have an infinite mass. I believe there is some sort of cross over where kinetic energy count as mass when you are travailing very quickly. So even though light it's self has no mass. It has a "mass" from its seed. And in any case the "mass" may not be relevant to my question as i am not suggesting we external need to slow down or speed up the light. – Paul Spain Oct 1 '15 at 20:22
• "Why" is an ambiguous question, but in this case the Anthropic Principle can actually give us an answer: if light had infinite speed then the entire universe would be at the same temperature, and it's hard to see how any complex chemistry could arise in that. – Beta Oct 2 '15 at 4:05

## 4 Answers

I wonder why light does not have infinite speed.

It does not have infinite speed because the experiment of Michelson and Morley has proven that it has the same constant speed in any reference frame. Moreover, any experiment on electromagnetic waves shows the presence of retarded potentials, that is, events need a certain time to propagate in space once they happen somewhere. This is somehow related to the experimental evidence that interactions in the universe cannot propagate instantaneously anywhere.

I know light does not have mass, but people use the term infinite mass when taking about the speed of light so I am assuming that is kind of correct in this case.

There is no such thing as the light. There is the electromagnetic field, whose charge carrier is the photon, indeed massless. Also, there is no such thing as infinite mass either. What happens is that some observable quantities (as energy or momentum) show divergences when $v\to c$, provided the Lorentz transformations are true (and they are).

after it makes it though the gas (or whatever is slowing it down) its speed increases back to light speed.

The velocity of the electromagnetic field depends on the medium the waves propagate into through the dielectric and magnetic permeability. Its value in a medium is always smaller than in the vacuum and for a complete electromagnetic wave different components will travel at different speed; this is somehow due to the interactions and the response of the particles within the material to the incoming wave. When no such particles are present, i. e. in the vacuum, no such effects occur and therefore the electromagnetic wave may propagate at $c$ again.

why is it so slow in the first place? what is keeping it from going faster?

The universe is made such that photons propagate with that velocity, there is no reason why it should be so (it could have been any other) but it is just the way it is. Physics does not explain why things are what they are, rather it explains how to make predictions by using proven models.

• – Kevin Oct 2 '15 at 3:12

The speed of light is determined (in terms of other fundamental constants) by Maxwell's equations. In particular, the speed of light $c$ must satisfy $c^2=1/(\mu_0\epsilon_0)$, where $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of the vacuum. Because neither $\mu_0$ nor $\epsilon_0$ is equal to zero, the speed of light cannot be infinite, and more generally cannot be other than what it is.

If the speed of light were infinite then the laws of physics would be non-local. The way things work in our universe is that the state of a system in the future only depends on the present state of itself an its local neighborhood. E.g., the future state of the Earth one year ahead depends only on the present state inside a bubble of one light year surrounding the Earth. Since specifying the physical state of a finite volume requires only a finite amount of information, one can predict the future, at least to some degree. It is possible to make predictions of the outcome of experiments.

But in the generic non-local case, the laws of physics would not allow one to make predictions. The future state will depend on the present state in an infinitely large volume which will contain an infinite amount of unknown information. It's then doubtful if life could evolve in such an unpredictable universe.

• "Since specifying the physical state of a finite volume requires only a finite amount of information, one can predict the future, at least to some degree." Not to any significant degree, no. Quantum effects and chaotic error propagation are insurmountable confounding factors. "It's then doubtful if life could evolve in such an unpredictable universe." Why do you say that? This sentence came out of left field. – John Kugelman Oct 2 '15 at 3:50
• @JohnKugelman It's not all that difficult to predict the future $10^{-20}$ seconds into the future. The fundamental reason why that's the case is that this time interval corresponds to a very small distance. – Count Iblis Oct 2 '15 at 4:03
• If the physical state of the local environment is inherently unpredictable, the it's difficult to control, so I don't see how life could exist in such a universe, so we couldn't exist. This then explains why we don't live in a universe where c is infinite. – Count Iblis Oct 2 '15 at 4:06

No, there is nothing that is "keeping light from going faster". The local velocity of light in vacuum can not be different than the standard $c=3 \times 10^8{ m\over{sec}}$. There are two parts to my answer.

1) When light passes near you in vacuum, you will always measure the standard $c=3 \times 10^8{ m\over{sec}}$ using your local meter stick and clock.

However, if you are far from a star (a gravitational potential well) and the light passes in vacuum near the star, you will see, using your local meter stick and clock, the light going slower than the standard c (see https://en.wikipedia.org/wiki/Shapiro_delay for experimental proof). In fact if the star were a black hole and the light was near the Schwarzschild radius, the light's velocity would approach zero.

Conversely, if you were near the star and the light passed far away, you would see, using your local meter stick and clock, the light passing at greater than the standard c. In fact if the star were a black hole and you were near the Schwarzschild radius, the far away light's velocity would approach infinity.

So it is possible to view the stuff called light going at different velocities if the light is not local.

2) The notion of being able to change the LOCAL speed of light in vacuum arises from a misconception of what c is. Our historical way of measuring velocity (and the speed of the stuff called light) in meters per second, is based on comparisons to a meter stick and a second stored in the Bureau of Standards. But this was before Special Relativity in 1905 and the non-abelian boosts of the Lorentz Group. We now measure velocity in radians of Lorentz Boost $\lambda$. We can sense how much $\lambda$ a boosted body has by watching a clock riding on the body. The clock will appear $\gamma=cosh(\lambda)$ times slower than an un-boosted clock. Inverting this gives $\lambda = cosh^{-1}(\gamma)$ radians of boost (the modern velocity) for the object. We can relate radians of velocity back to the historical stick per tick velocities by ${v \over c}=tanh(\lambda)$ but this is not necessary to do modern physics. By letting v=c in this formula we see that the stuff called light has a modern velocity of $\lambda=\infty$ radians. These modern velocities add when pointed in the same direction. Historical velocities do not simply add, and you must use for them a special addition formula involving c.

The constant c and other velocities based on a standard stick per tick in the Bureau of Standards are historical artifacts. After 1905, c and v no longer need to appear in physics. Now, objects have dimensionless velocities in units of radians. If your original question referred to changing the constant c, the question is irrelevant because c is not needed in modern physics, and anyway c just depends on what stick and tick are stored in the Bureau of Standards. If your original question referred to changing the velocity of the stuff called light, then it is from changing from $\lambda =\infty$ to something else like what? $\lambda = .8 \times \infty ...or..maybe... \lambda=100+\infty$ ?? ... all of which are still $\infty$.