Exploring the Paradox of Light Traveling at the Speed of Light

[curiouschris]

Hi

This thought has been in my head for a while and I need to resolve it.

If light travels at the speed of light in a vacuum and I am told that it does
AND
time stops when one is traveling at the speed of light, I am also advised this is true
THEN
doesn't that mean for light it is everywhere in its path at the same time.

In other words if I was riding a photonic particle, which was emitted from a torch I would both be leaving the globe and touching the wall AT THE SAME TIME (and everyplace in between).

For me in my time frame there is in fact no time. Of course from an observers frame of reference it took me x seconds to make the journey.

CC

 

[CompuChip]

If light travels at the speed of light in a vacuum and I am told that it does

Yes, it does.

time stops when one is traveling at the speed of light

Time slows down when you approach the speed of light. Note the subtle difference with your statement

In other words if I was riding a photonic particle, which was emitted from a torch I would both be leaving the globe and touching the wall AT THE SAME TIME (and everyplace in between).

Yep, that would be a problem. Luckily (for the theory, that is ) your question becomes void from the moment you say "if I was riding a photonic particle...". That would require you, being massive, to accelerate to the speed of light; which is not possible.

For me in my time frame there is in fact no time. Of course from an observers frame of reference it took me x seconds to make the journey.

Same problem. The frame of a photon and that of a (massive) observer are not equivalent physical frames (in the sense of the postulates of Special Relativity) and this shows that it leads to contradictions.

 

[curiouschris]

Time slows down when you approach the speed of light. Note the subtle difference with your statement

So does time stop AT the speed of light or 'c' or not? and if it does isn't my second postulate accurate, why change it to slows down?

Yep, that would be a problem. Luckily (for the theory, that is ) your question becomes void from the moment you say "if I was riding a photonic particle...". That would require you, being massive, to accelerate to the speed of light; which is not possible.

hairsplitting perhaps?

Let me change the statement to...

In other words if my consciousness was riding a photonic particle, which was emitted from a torch I would both be leaving the globe and touching the wall AT THE SAME TIME (and everyplace in between).

I have it on good authority that consciousness has a zero rest mass.

CC

 

[CompuChip]

It's not hairsplitting. My entire point is that you can't use special relativity to say anything about what space would "look like" "from a photon's perspective". All those formulas of time dilatation, length contraction, energy, etc. only work for massive things <=> objects moving at velocities v < c.
At first attempt it may seem interesting to consider the limit v -> c in special relativity, but such considerations turn out to be useless because massless and massive observers are not equivalent and so laws like time dilation which are derived using that assumption fail.

 

[JesseM]

In other words if my consciousness was riding a photonic particle, which was emitted from a torch I would both be leaving the globe and touching the wall AT THE SAME TIME (and everyplace in between).

I have it on good authority that consciousness has a zero rest mass.

If you think consciousness is the product of a supernatural soul, then physics can tell you nothing about the perceptions of a consciousness moving at different speeds, even sublight speeds, because it only deals with the behavior of physical systems. If you think consciousness is the product of interactions between neurons in the brain as virtually all modern scientists do, then these interactions would be slowed down like any other clock for a brain moving at a large fraction of c, but it would be impossible for the particles that make up neurons to move at exactly c, and you couldn't really construct an equivalent system out of photons since photons don't interact with one another in the same way as massive particles like electrons.

Another point is that in SR when we talk about what would be "perceived" by a given observer, usually we're not talking about what they would actually see visually (which would be influenced by things like the Doppler effect), but rather what they would measure on a system of rulers and synchronized clocks which are at rest relative to themselves...for example, if I see an explosion happen next to the 15-meter mark on my x-axis ruler, and the clock sitting at the 15-meter mark read a time of 8 seconds at the moment the explosion happened next to it, I'd assign this event coordinates x=15 meters, t=8 seconds in my rest frame. It would be impossible to have a similar system of rulers and clocks moving along with a photon, because they couldn't be accelerated to c; and even if we consider the limit of what would happen to rulers and clocks as they got arbitrarily close to c, we'd find that in this limit the rulers approached having a length of zero and the clocks approached being totally stopped, so the limiting case would be useless for assigning coordinates to different events.

 

[Dale]

Hi curiouschris,

See http://www.edu-observatory.org/physics-faq/Relativity/SpeedOfLight/headlights.html" .

 

[Naty1]

So does time stop AT the speed of light or 'c' or not?

In simple terms, yes it does. You can claim "photons don't age" if you like.

The many,many subtlies of relativity kept unfolding for more than 20 years after Einstein's 1915 paper...like black holes, expansion of the universe, etc,etc...there is much to think about in physics.

But after you have thought about the various aspects of relativity, most end up finding the following more accurate:

...you can't use special relativity to say anything about what space would "look like" "from a photon's perspective". All those formulas of time dilatation, length contraction, energy, etc. only work for massive things <=> objects moving at velocities v < c.

and in mathematical terms you can think about lorentz factors becoming indeterminate.

It's akin to thinking, "If I were my Dad (or Mom) I'd be my own relative"...well, yes, you can say that, but you are not, so the conclusion becomes inconclusive...

But it's still fun and "thought experiments" is primarily how Einstein started until he became more well versed in mathematics...

 

[CompuChip]

So does time stop AT the speed of light or 'c' or not?

In simple terms, yes it does. You can claim "photons don't age" if you like.

Actually, I (maybe implicitly) claimed that even that is an ill-defined question. For all speeds v < c we have a formula that works, and that tells us how time keeps slowing down. But it does not say anything about v = c. Now that I think about it, presumably photons would have a proper time like any other observer, we just cannot relate it to the proper time of a subluminally moving observer.

 

[JesseM]

Actually, I (maybe implicitly) claimed that even that is an ill-defined question. For all speeds v < c we have a formula that works, and that tells us how time keeps slowing down. But it does not say anything about v = c. Now that I think about it, presumably photons would have a proper time like any other observer, we just cannot relate it to the proper time of a subluminally moving observer.

Proper times in general aren't meant to be related to one another in the sense of implying any preferred definition of simultaneity though (i.e. you can't ask what my proper time is 'at the same moment' that your proper time has reached some value)--a value for the proper time just tells you how much time has elapsed on a clock between two events that lie along its worldline. For an object moving at constant velocity in SR, proper time is always given by sqrt((delta t)^2 - (delta position / c)^2), where delta t is the difference between the time-coordinate of the first event and the second event in some inertial frame, and delta position is the distance between the position coordinates of the two events in the same inertial frame (the value of the proper time will be the same for a given pair of events no matter what inertial frame you use, despite the fact that delta t and delta position will each individually be different in different inertial frames). This formula does work fine for two events on the worldline of a light ray, and it will always give a value of zero for such events, though of course the physical interpretation of this can't be exactly the same since you can't have a clock moving along with the light ray.

 

[srfriggen]

I have a different question hopefully someone can shed some light on (no pun intended, but noticed).

Say I'm driving a very fast car (close to 'c')and I turn on the headlights. Well, for me it would seem that light is moving at the constant, not faster, because my proper time is slower? So my measurements would show that it is covering the same amount of distance as if I were still...?

What if I am driving toward another fast car and that person shines on their headlights. How would time dilation make it seem the light was not moving faster than c?

 

[JesseM]

What if I am driving toward another fast car and that person shines on their headlights. How would time dilation make it seem the light was not moving faster than c?

If both you and the other person are using rulers and synchronized clocks at rest relative to yourselves to measure distance/time for the light beam, you will both measure the speed of the beam to be c (keep in mind that from your perspective, the rulers of the other guy are shrunk due to length contraction, and his clocks are slowed down due to time dilation, and his clocks are out-of-sync due to the relativity of simultaneity).

Here was a numerical example I gave on another thread:

To measure the speed of anything, you need to measure its position at one time and its position at another time, with the time of each measurement defined in terms of a local reading on a synchronized clock in the same local region as the measurement; then "speed" is just (change in position)/(change in time). So, time dilation, length contraction, and the relativity of simultaneity all come into play. From the stationary observer's perspective, the ruler which the moving observer used to measure the distance was shrunk by a factor of $$\sqrt{1 - v^2/c^2}$$, the time between ticks on the moving clocks is expanded by $$1 / \sqrt{1 - v^2/c^2}$$, and the two clocks are out-of-sync by $$vx/c^2$$ (where x is the distance between the clocks in their own rest frame, where they are synchronized).

Say there's a ruler that's 50 light-seconds long in its own rest frame, moving at 0.6c in my frame. In this case the relativistic gamma-factor (which determines the amount of length contraction and time dilation) is 1.25, so in my frame its length is 50/1.25 = 40 light seconds long. At the front and back of the ruler are clocks which are synchronized in the ruler's rest frame; because of the relativity of simultaneity, this means that in my frame they are out-of-sync, with the front clock's time being behind the back clock's time by vx/c^2 = (0.6c)(50 light-seconds)/c^2 = 30 seconds.

Now, when the back end of the moving ruler is lined up with the 0-light-seconds mark of my own ruler (with my own ruler at rest relative to me), I set up a light flash at that position. Let's say at this moment the clock at the back of the moving ruler reads a time of 0 seconds, and since the clock at the front is always behind it by 30 seconds in my frame, then in my frame the clock at the front must read -30 seconds at that moment. 100 seconds later in my frame, the back end will have moved (100 seconds)*(0.6c) = 60 light-seconds along my ruler, and since the ruler is 40 light-seconds long in my frame, this means the front end will be lined up with the 100-light-seconds mark on my ruler. Since 100 seconds have passed, if the light beam is moving at c in my frame it must have moved 100 light-seconds in that time, so it will also be at the 100-light-seconds mark on my ruler, just having caught up with the front end of the moving ruler.

Since 100 seconds passed in my frame, this means 100/1.25 = 80 seconds have passed on the clocks at the front and back of the moving ruler. Since the clock at the back read 0 seconds when the flash was set off, it now reads 80 seconds; and since the clock at the front read -30 seconds, it now reads 50 seconds. And remember, the ruler was 50 light-seconds long in its own rest frame! So in its frame, where the clock at the front is synchronized with the clock at the back, the light flash was set off at the back when the clock there read 0 seconds, and the light beam passed the clock at the front when its time read 50 seconds, so since the ruler is 50-light-seconds long, the beam must have been moving at 50 light-seconds/50 seconds = c as well! So you can see that everything works out--if I measure distances and times with rulers and clocks at rest in my frame, I conclude the light beam moved at 1 c, and if a moving observer measures distance and times with rulers and clocks at rest in his frame, he also concludes the same light beam moved at 1 c.

If you want to also consider what happens if, after reaching the front end of the moving ruler at 100 seconds in my frame, the light then bounces back towards the back in the opposite direction towards the back end, then at 125 seconds in my frame the light will be at a position of 75 light-seconds on my ruler, and the back end of the moving ruler will be at that position as well. Since 125 seconds have passed in my frame, 125/1.25 = 100 seconds will have passed on the clock at the back of the moving ruler. Now remember that on the clock at the front read 50 seconds when the light reached it, and the ruler is 50 light-seconds long in its own rest frame, so an observer on the moving ruler will have measured the light to take an additional 50 seconds to travel the 50 light-seconds from front end to back end.

 

[atyy]

doesn't that mean for light it is everywhere in its path at the same time.

There is a quantity called the "infinitesimal interval". For massive particles this is non-zero, and it is also called the "infinitesimal proper time" because it is quite directly related to what an atomic clock measures. For photons, the infinitesimal interval is zero, and in this sense, photons experience no time. However, spacetime is characterized by space and time coordinates. These are not zero on the photon's spacetime trajectory, which is why a photon can get emitted and absorbed and travel over spacetime. Freely moving massive particles and photons follow a "straight" line called a geodesic. For massive particle the geodesic equation can be written in terms of the proper time, but for photons, since the proper time is zero, the geodesic equation is written using an "affine parameter".

 

[curiouschris]

My reference to consciousness was to avoid the whole mass massless issue. and I know we could not have our visual cortex or any other organ stimulated at anything close to the speed of light. that's not the point I was simply trying to move into the frame of reference of the photon as opposed to the frame of reference of some observer. I already know the observers frame of reference, I live in it.

This is what I have got. so far.

Because our understanding via the laws of SR break down at the speed of light nobody really knows or can know what happens at the speed of light!

The reason I raised this question in the first place was to try and understand in my own way the seemingly impossible but apparently confirmed enigma of quantum entanglement.

In my mind if time and therefore the other dimensions ceased to exist at the speed of light then a photon is effectively everywhere at once (in its path as we observers measured it).

Now if that's true then entangled photons are not only at distant points in the universe but at the same time (in its reference frame) are in 'contact' with each other so measuring one changes the other.
When we change out to our reference frame. it appears to us that we have "spooky action at a distance" because in our reference frame the photons are incredibly far apart.

CC

 

[Naty1]

Actually, I (maybe implicitly) claimed that even that is an ill-defined question. For all speeds v < c we have a formula that works, and that tells us how time keeps slowing down. But it does not say anything about v = c.

Yes, it is is, but for a novice my answer is a place to start...it's also why I referenced another post here that is accurate...an answer here needs to be tied to the experience of the originator to be understood. I have received answers to my own questions that were technically correct but really, really obscure...so the responder may have looked smart but the answer did not do me much good.

The reason I raised this question in the first place was to try and understand in my own way the seemingly impossible but apparently confirmed enigma of quantum entanglement.

In my mind if time and therefore the other dimensions ceased to exist at the speed of light then a photon is effectively everywhere at once (in its path as we observers measured it).

Posting your question was not the best way to gain insights into entangelement. Light (electromagnetic waves) carries information; entanglement, as it is currently understood, cannot...

 

[curiouschris]

On to JesseM's response to sfriggin with the help of DaleSpam's link

Ahhhh I think I get it!

Because the speed of light is constant, an absolute, THEN everything else must change!

From now on I'll use "c" instead of "the speed of light"

For c to remain constant regardless of your frame of reference TIME MUST CHANGE.

The faster you go the slower time MUST GO so that c is valid for you AND for everyone else regardless of where they are and at what speed they travel.

And getting back to my original question AT the speed of light everything is just absurd so it can't be answered. ;)

Ok another question who determined that TIME and DISTANCE change, isn't it just as valid to say that distances only change. I mean you only need one part of the formula to change to make it valid why change BOTH Time and Distance

$$v = d/t$$

 

[curiouschris]

Posting your question was not the best way to gain insights into entangelement. Light (electromagnetic waves) carries information; entanglement, as it is currently understood, cannot...

I have no interest in the carrying of information or FTL or any of the other questions that arise around entanglement. my only thought was what gives rise to entanglement. as I understand it entanglement is a product of the photon (under special circumstances). as the photon moves at the speed of light then it seemed logical to me understanding the peculiarities of the photon AT THAT SPEED is paramount to any theories about entanglement.

CC

 

[JesseM]

I have no interest in the carrying of information or FTL or any of the other questions that arise around entanglement. my only thought was what gives rise to entanglement. as I understand it entanglement is a product of the photon (under special circumstances). as the photon moves at the speed of light then it seemed logical to me understanding the peculiarities of the photon AT THAT SPEED is paramount to any theories about entanglement.

Entanglement doesn't just concern photons--you can entangle electrons, which have mass and move slower than light, as well.

 

[JesseM]

Ok another question who determined that TIME and DISTANCE change, isn't it just as valid to say that distances only change. I mean you only need one part of the formula to change to make it valid why change BOTH Time and Distance

$$v = d/t$$

Another requirement of relativity is that the laws of physics be totally symmetrical between different inertial observers. So if you're in motion relative to me, and I use my ruler/clock system to measure your own rulers and clocks and find that your rulers seem to have shrunk according to my measurements, then if you use your own ruler/clock system to measure my rulers and clocks, you must find that my rulers have shrunk relative to your own measurements. Mathematically, it's possible to show that if you combine this symmetry requirement with the requirement that every measures light to be moving at c, the only way it can work out is if everyone measures moving clocks to shrink by $$\sqrt{1 - v^2/c^2}$$ and moving clocks to have the length of their ticks expand by $$1/\sqrt{1 - v^2/c^2}$$. (For an illustration of how it works out that both observers measure the other guys' rulers to shrink and the other guys' clocks to slow down, see this thread).

 

[curiouschris]

Entanglement doesn't just concern photons--you can entangle electrons, which have mass and move slower than light, as well.

In that case I have started from an incorrect assumption.

Thanks for the clocks and rulers link. I will need to find time a bit later to read and absorb it.

CC

 

[Anticitizen]

In that case I have started from an incorrect assumption.

Don't feel bad, I went down that same road https://www.physicsforums.com/showthread.php?t=227761"...