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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!)

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    $\begingroup$ Related: physics.stackexchange.com/q/54162 $\endgroup$ – Sovereign Inquiry Jul 13 at 21:37
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    $\begingroup$ I am sorry, but you cannot learn about physics by reading sources written by people who have no grasp of physics. Scientific American, which used to be a good magazine when I was at school, gave up reporting on science thirty or forty years ago, and that seems to be your best source. $\endgroup$ – Charles Francis Jul 13 at 21:42
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    $\begingroup$ The answer was final You should not necessarily assume that an accepted answer on this site is a correct answer. There is no mechanism for assuring that incorrect answers don’t get accepted, or upvoted. I recommend paying more attention to answers by members with very high reputations, even if they weren’t accepted. And since you are interested in answers, check that the very high reputation was earned by answering, not asking. $\endgroup$ – G. Smith Jul 13 at 22:14
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    $\begingroup$ The first quoted passage seems to me to be an excellent reason to stop reading this book. $\endgroup$ – WillO Jul 13 at 23:01
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    $\begingroup$ @CharlesFrancis Oof--I had no idea. So really, it's Non-Scientific American... ,':-| $\endgroup$ – Sovereign Inquiry Jul 13 at 23:30
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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.

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    $\begingroup$ The limit of your experience as your speed (measured from Earth) tends towards light speed is that you seem to go everywhere in zero time, right? $\endgroup$ – user253751 Jul 14 at 11:41
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    $\begingroup$ With that said, if you could approach the speed of light you would observe that, by your own clock, your speed through space would appear to increase without bound, so it's not so big a stretch as you might suggest. At 99.999999% the speed of light it would appear to you, the observer, that you could cross vast distances in vanishingly small amounts of time. Other observers would note that it took you much longer to traverse the distance, seeing you stuck near the speed of light, but by your own clock it would seem that your speed was increasing without bound. $\endgroup$ – J... Jul 14 at 12:51
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    $\begingroup$ But only everywhere in a line, not everywhere in space. Each parallel line is similarly compressed, so space is compressed to a plane. $\endgroup$ – user253751 Jul 14 at 13:12
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    $\begingroup$ @J... by your own clocks and rulers your speed is always 0 and never increases. This is important to remember. Regarding your second comment, you again introduce the self-contradictory “photon’s point of view”. There is simply nothing meaningful to be said about a self-contradiction other than to identify it as such and discard it. Do you have a specific recommendation for improving the answer? $\endgroup$ – Dale Jul 14 at 13:14
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    $\begingroup$ @J... do you have a specific suggestion for improving the answer? Comments are not intended for discussion. $\endgroup$ – Dale Jul 14 at 14:11
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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.

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    $\begingroup$ It's rather similar to Zeno's paradox, but in reverse: Light travelling parallel to you on a matching vector must, by definition, travel at lightspeed relative to you. A second has then passed when the displacement between you in the direction of travel has changed by a distance of 1 lightsecond (the rest of the universe being an irrelevant background animation). However, since the speed of light is a fixed maximum, this means that 2 photons are (as measured from any other frame of reference) both travelling at the same velocity, requiring infinite time for them to experience one second. $\endgroup$ – Chronocidal Jul 14 at 11:52
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    $\begingroup$ Re, "badly worded...misleading." IMO it's flat out wrong. There is no reason to think that any photon visits every place in the universe. As far as we know, every photon is created in one, specific place, and then (some time later in our frame of reference) it experiences one interaction in some other specific place, and that's the end of it. We don't even know that the photon "existed" at any other place or time in between those two points. We only imagine it because that's how we get from one place to another. $\endgroup$ – Solomon Slow Jul 14 at 14:22
  • $\begingroup$ "Mathematically this is the same as saying [the limit of 2x on x as x tends to infinity] is equal to 2". No, it's not. 2x/x = 2 for all finite values of x; there's no need to take a limit. Maybe you meant something like "the limit of the sum of 1/2^x from 0 to k, as k tends to infinity" instead? That way, you actually would need to take a limit to get the answer. $\endgroup$ – nick012000 Jul 14 at 14:59
  • $\begingroup$ @SolomonSlow Ok, I fully agree that the statement is wrong the way it is written. I chose to say "badly worded" because I recognize the meaning that the author tried to put into this statement. I detailed this intended meaning with much more precision in my answer to show both, what is correct, and what is hyperbole. The intended meaning is not too far off, so I felt that "badly worded to the point of being completely misleading" was a fair way of putting it. YMMV. $\endgroup$ – cmaster - reinstate monica Jul 14 at 15:04
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    $\begingroup$ @nick012000 Yeah, it was a bad example. I've added a +1 to the nominator now to force $f(x)\neq 2$ everywhere. I hope that makes the meaning clearer. $\endgroup$ – cmaster - reinstate monica Jul 14 at 15:07
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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.

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    $\begingroup$ @SovereignInquiry As for your first comment. Yes, it is possible but it undermines our basic understanding in the sense that 100% of experiments ever done regarding the speed of light have shown it to be finite. The scientific community does not like to theorize in direct opposition to evidence, especially overwhelming evidence. $\endgroup$ – Cort Ammon Jul 13 at 23:55
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    $\begingroup$ As for your second topic, the idea that the universe is created by life (which I think is typically a 'idealist' position) is a fun one, but one which has to be read carefully when invoking science. More than once while exploring the topic myself, I've accidentally formed a infinite descending set, which forced me to depart from all mathematics as you probably know it. Modern science is almost universally built on top of ZFC, implicitly or explicitly, so its math may not be valid when exploring other systems that cannot be constructed with ZFC $\endgroup$ – Cort Ammon Jul 13 at 23:58
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    $\begingroup$ (Edit because I'm too late to change the comment: "100% of experiments ever done regarding the speed of light have shown it to be finite" should be less extreme. We've only found the speed of light to be finite since we had the insturmentation needed to measure it. Hundreds of years ago, we could not discern whether it had a speed or not because it was too fast for our measuring tools) $\endgroup$ – Cort Ammon Jul 14 at 0:04
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    $\begingroup$ Downvoted because we have had evidence of the finite speed of light for 400 years! en.wikipedia.org/wiki/… $\endgroup$ – m4r35n357 Jul 14 at 8:31
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    $\begingroup$ Why can't we take the limit as your speed tends towards light speed? $\endgroup$ – user253751 Jul 14 at 11:42
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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.

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    $\begingroup$ Newtonian mechanics already has infinite speed of light. Turns out the mechanics part is completely incompatible with light (Maxwell's equations). This is why we have Special & General Relativity. Those who neglect history are doomed to repeat it. $\endgroup$ – m4r35n357 Jul 15 at 8:22
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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.

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  • $\begingroup$ Lots of general truths here. Hope the "yes but what if . . .?" community are paying attention ;) $\endgroup$ – m4r35n357 Jul 15 at 8:16
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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).

Light can take many different paths to get from A to B

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  • $\begingroup$ Who can read the mind of a "pop science" author? $\endgroup$ – m4r35n357 Jul 14 at 8:33
  • $\begingroup$ @m4r35n357 I am not mind-reading, I am just providing an explanation of what the author meant, which I don't think is impossible to do. Considering book interpretations and critics everywhere, this seems way to mild to be called 'mind reading' $\endgroup$ – PNS Jul 14 at 9:20
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    $\begingroup$ "from the photon's perspective, ... but still the clock would be showing 7:00" - This is false, by my understanding. It is the photon that experiences no time. If there was a clock attached to the photon (which there cannot be because clocks have mass) that clock would still say 7:00 by the time the photon went around the galaxy and back, even though the scientist's clock would say it's the year 253543697398. $\endgroup$ – user253751 Jul 14 at 11:47
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    $\begingroup$ The "photon" has no POV, please stop saying this! Let me elaborate, A photon reflecting off a mirror at the "boundary of the (observable) universe" would definitely not arrive back at the lab at the same time it left. A "thought experiment" is not physics, it is the precursor to it. $\endgroup$ – m4r35n357 Jul 14 at 13:45
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    $\begingroup$ "Our current maths (for determining time) break down at light speed." Not really. The maths of SR says that there are are 3 types of spacetime interval: timelike, lightlike (aka null) & spacelike, and the character of an interval is Lorentz invariant. So a timelike interval is timelike in all frames, etc. The notion of proper time simply doesn't apply to a null interval, but instead you can use an affine parameter, as Dale mentions, which is perfectly well-behaved. $\endgroup$ – PM 2Ring Jul 14 at 14:12
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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.

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    $\begingroup$ Photons cannot carry a clock. There is no way to assign proper time to a beam of light. $\endgroup$ – m4r35n357 Jul 15 at 8:12
  • $\begingroup$ @m4r35n357 Photons can carry a clock if they bought it on Amazon. You could carry empathy if you buy it on Amazon, or a book explaining metaphors, even when you aren't theoretically capable of empathy. $\endgroup$ – tutizeri Jul 15 at 9:53

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