Contradictions of explanations for the speed of light I've recently started reading the book Biocentrism, by Robert Lanza and Bob Berman, which in its mind-blowing chapters, discusses the perceptions of reality, space, and time. Lanza states that:

If one could travel at lightspeed, one would find oneself everywhere in the universe at once. This indeed is what a photon of light must experience if it were sentient.

Immediately, I was confused. If photons can be everywhere at once, doesn't that mean that their speed is infinite? But if that's so, why does it take about 8 minutes for light from the sun to reach earth?
I did some more research and came upon this question. The answer was final and basically stated that:

If the speed of light was to be infinite, every solid, liquid and gas in the universe would instantaneously turn into super heated plasma soup.If String theory is correct, this would probably cause a tear in the fabric of space-time and could "open up" the universe, exposing it to other universes. Since light has infinite speed,the past and future get merged into the present. Events cannot be distinguished from another. Finally, it will be impossible to determine the location of an object, as light will be bombarding the receiver from every possible direction. Everything will be everywhere.
It's like trying to find your way out of a pitch black ocean, while wearing a scuba diving suit, without a torch.

In other words, the world would end.
However, this answer doesn't provide any evidence, let alone links.
Scientific American states that "Were there an infinite value for the speed of light, light itself would not exist at all. Mathematically, the wave equation that describes light as an electromagnetic wave would lose its time-dependence."
In other discussions about the speed of light, I've seen the explanation that photons exist in all points between two points: A and B.
If that's so, why is the constant of the speed of light in a vacuum 186,000 miles per second, or 300 million meters per second? Why not infinity?
New scientific research done by recent scientists has indicated that light might not have a constant, according to this article.
So can light travel at an infinite speed, or not? If photons can be everywhere in the universe, or everywhere between point A and B, how can their speed not be infinite? If they do occupy every point between A and B, why do photons have a constant and a finite speed?
(And I haven't learned much--if anything--in physics, so if they aren't contradictory, any explanation would suffice. Please understand my inexperience and ignorance!)
 A: 
If one could travel at lightspeed, one would find oneself everywhere in the universe at once. This indeed is what a photon of light must experience if it were sentient.

Well, this is badly worded to the point of being completely misleading. What is true is, that special relativity describes two effects: Length contraction and time dilation.
From the point of view of any non-lightspeed observer, any flying clock ticks too slow (time dilation). The limit of this ticking, when speed approaches the speed of light, is no ticking at all. A physical observer must conclude that the photon experiences its emission and absorption exactly at the same time.
From the point of view of a fast observer, the universe appears compressed in the direction of flight (length contraction). The limit of this contraction, when speed approaches the speed of light, is no length at all. Thus, from the point of view of the photon, there is no distance that it has to travel.
Note that I have said "the limit of ..." two times now. This is not strictly within the realm of what special relativity actually claims to describe. It's just beyond its reach. Mathematically, this reasoning is the same as saying that $lim_{x\rightarrow \infty}\frac{2x + 1}{x} = 2$. Saying $\frac{2\infty + 1}{\infty} = 2$ would be nonsense, I can only say that the function $f(x) = \frac{2x + 1}{x}$ gets ever closer to $2$ as $x$ grows beyond all bounds. Those are very different things to say.
Also note that these two effects are complementatory. What appears as length contraction to one observer appears as time dilation to the other, and vice versa. The photon says: Space is a plane, I exist at a point within it, what is "time"? The physical observer says: Space is vast, but the photon experiences its emission and absorption exactly at the same time, its clock must be broken! Those are alternative descriptions of the same events of photon emission/absorption within space and time.
A: You are facing one of the great challenges of science: the belief in the models themselves.  We choose to describe science using the language of scientific realism and, indeed you can correctly capture science in that sense.  But I find it can cause confusion, especially when an author uses that sort of terminology and then reaches too far.  It can be hard to tell where the line was between the real science and what the author claims.
I find it very helpful to sometimes approach science from the language of insturmentalism, saying that science only describes what the universe does rather than defining it.  If I say "the speed of light is finite" in a scientific realist mindset, that means there really is a thing in the universe called "the speed of light" and it really is finite.  If I say the same thing in the insturmentalist mindset, it means that we can describe how some phenomena in the universe occur using the concept of "light," which is a thing that has speed.
This viewpoint then makes it easy to bring in a truism from engineering: All models are wrong; some are useful.
Light will do what light will do.  It will go as fast as it does, infinitely fast if need be.  However, what we have discovered is that it is very well modeled using a "wave equation," which is a particular sort of differential equation with some nice properties.  We find that if we make predictions about what light will do using these equations, we tend to be right.
If we talk about light being "infinitely fast," we do run into some challenges because those differential equations governing waves break down.  It is not possible for light as we know it to travel infinitely fast.  It would break down the equations.
That's not to say light couldn't be faster.  We just wouldn't have found that a wave function was the right sort of function to use.  We would have had to pick an equation that permits infinite speed without breaking down.  As such, if we talk about what it would be like if light traveled infinitely fast, we not only have to change the speed of light.  We have to fundamentally tear down our entire understanding of how light works in this real world, and construct a different hypothetical world with a new set of useful equations.
The same issue shows up with the quote from Biocentrism.  Our current models state that you cannot travel at the speed of light.  They ask about what would happen if you did travel at that speed, and take the models one step further than they were ever intended to be taken.  It looks like they then put in a dash of quantum mechanics to create uncertainty.  Such works really need to be read as works of fiction.  Useful, perhaps, but they take the equations beyond where they were intended to go.  (by the title, I am guessing they explore what it would mean to be a conscious entity traveling at the speed of light)
Now there is indeed a question whether light travels at a constant speed.  There's questions about interactions between photons and virtual particles, and there's questions about whether the constants that go into the speed of light are really constant.  But those should be thought of as slight variations on a theme.  For anything in your daily life, treating light as having a constant speed will work just fine.  When you are an astrophysicist trying to make difficult predictions about the size of the universe using light waves that have been propagating for billions of years, you have to consider more sources of variation.
A: 
If the speed of light was to be infinite, every solid, liquid and gas in the universe would instantaneously turn into super heated plasma soup.If String theory is correct, this would probably cause a tear in the fabric of space-time and could "open up" the universe, exposing it to other universes. Since light has infinite speed,the past and future get merged into the present. Events cannot be distinguished from another. Finally, it will be impossible to determine the location of an object, as light will be bombarding the receiver from every possible direction. Everything will be everywhere.

This does not make any sense. I think you'd do better to ignore these sources.
Newton described a universe where the speed of gravity was infinite (even though we now know that gravity, like light, propagates at the finite speed $c$). Did Newton's model therefore require all the matter to immediately clump together so that everything was in the same place and gravity bombarded the receiver from every possible direction? No to the first, yes to the second. We are getting gravity from every direction and what we notice is the vector sum. Newton's math worked and described a universe superficially similar to ours.
I'm pretty sure that a universe where light had infinite speed would also be pretty similar to ours. Just, not exactly the same. Different enough that experimental evidence can rule it out.
A: 
So can light travel at an infinite speed, or not?

No, it cannot.
First, Lanza’s claim is based on a self contradiction, and literally anything can be proven from a self-contradiction. The colloquial idea of a “photon’s experience” is based on the mathematical idea of the inertial frame of the photon. Such a frame would require light to both be at rest (since it is the photon’s frame) and to move at c (since light moves at c in all inertial frames) This is a self contradiction, and all conclusions that follow from it are nonsense.
A pulse of light does not have proper time along its worldline. Instead, a pulse of light has an affine parameter. The affine parameter serves the same role as proper time serves for a slower-than-light object, but it is free from the self-contradiction of Lanza’s comment. The events on the pulse of light’s worldline are distinct events each identified by a different affine parameter. They are not “everywhere in the universe at once”. Although the affine parameter is not time, it has a clear ordering and all frames agree that the affine parameter increases to the future and decreases to the past. Causes preceed effects and so forth.
A: I am writing this after there were a few answers, so I will not repeat material already in other answers.
The main reply to your question is to warn you that there is a lot of nonsense out there in the pop science world, and to encourage you to learn to detect it. One way to detect it is to check whether the source you are using tries to explain what it is saying, giving you clarity as to what the reasoning is. Also, any sentence which begins with the phrase "If such and such [some important property of nature] were different then ..." is in danger of becoming nonsensical. For example if someone begins by saying "if light speed were infinite, then ..." the trouble is that they are suggesting a very wide-ranging change in the nature of the physical cosmos, so who knows what things would be like. It is like saying "If there can be action at a distance, then ..." which is not so very far from saying "If there can be magic, then ..." so you see where we end up: not very enlightened.
Coming back to light. In mathematics there is a very important distinction between zero and a small number such as $0.000000000000000000001$. At first sight they might seem similar, but they differ in quite profound ways, because you can multiply that small number by $1000000000000000000000$ and get $1$, but if you multiply zero by that huge number then you still get just zero. So a very small number turns out to be, in some respects, not at all like zero.
The situation with travelling fast is similar. There is a big difference between travelling close to light speed and travelling right at light speed. It does not really make any sense to speak of "the experience of a photon". But if instead we think of something travelling very very close to the speed of light, then it is true that it could pass from one galaxy to another while only aging a little, say by a second or so. This does not mean it is everywhere. It is just passing from one place to another place. And it would experience those places as very thin, and the light emitted from them would appear very high frequency as they approach, and very low frequency as they move away. So really this fast-moving observer is having a very different experience of the universe from the one we have. It would be forever at risk of undergoing a catastrophic collision. And if it moves fast enough it would soon be baked to a crisp by all the high-frequency light hitting it. etc. etc.
I admit I have not explained the reasoning behind the above observations. But perhaps you can find them a bit more credible than "one would find oneself everywhere in the universe at once". That is indeed a nonsense statement.
A: What I think the authors of the book meant was that when you travel at the speed of light there is a speculation that time stops. I say speculation, because our current maths (for determining time) break down at light speed. But as you approach light speed time slows down, and so we say that at light speed time stops entirely.
Thought experiment: A photon is released from some apparatus, and the clock of the lab shows 7:00 when the photon is released. Now, from the photon's perspective, it can travel all the way to the edge of the universe and return to the lab, but still the clock would be showing 7:00, because time itself has stopped. So, you don't need infinite speed to be everywhere, you need extreme time dilation.

Mathematically, the wave equation that describes light as an electromagnetic wave would lose its time-dependence.

Yes, that is current. The wave equation for electromagnetism states that light has to travel at the constant speed we call $c$.

In other discussions about the speed of light, I've seen the explanation that photons exist in all points between two points: A and B.

Our current description of light and electromagnetism is a theory called QED. The maths of QED tells us that when we try and calculate the probability for light going from A to B, we have to take into account the fact that light could go from A to B by taking infinitely many paths. That is why we say that light can be anywhere between the two points. But, when we try and measure where the photon actually is, we see that its is located at one fixed position (or is taking one particular path).

A: 
If photons can be everywhere at once, doesn't that mean that their
speed is infinite? But if that's so, why does it take about 8 minutes
for light from the sun to reach earth?

The most important thing you have to understand, is that time, and distance, is different for everybody.
It takes 8 minutes, on earth's time, but it takes zero time on photon's time.
If the photon were carrying a clock, zero time would pass, but if you carry a clock, here on Earth, your clock would count 8 minutes.
From the photon's viewpoint, he's standing still, but the rest of the universe compresses into a plane, where everything on his path is on the same point, so the photon is at zero distance of everything on his path.
For the photon, no time passes, because Earth is at zero distance from the Sun, but on Earth there is more distance, and more time.
For the photon, Earth is at the same distance than Alpha Centauri, but still Earth is closer than Alpha Centauri. So he will pass Earth before Alpha Centauri, and stop here if it crashes.
Time and rulers are different for each "observer". That's why it's called Relativity. You have your own time, and your own distance. Generally, nobody else has the same time and distances than you.
