How Does Light Travel So Fast?

[pjlueck]

"Beware, the jabberwock said: Beware of inserting fabulous 'negatives' into physical equations!" At least that's the way I heard it.

 

from above: ".....so past the speed of light, time is going backwards for you..." This arguable premise is then used to assign a negative value to "t" in the equation V = D/T. You can't have it both ways:

 

At 1.1 x the speed of light V=D/T yields 3.3x10 to the 8th meters/second (roughly), if one simply "plugs in numbers." Yet, your conclusion is that the V value would be negative; a concept that that has no basis, and essentially, negates the use of this particular equation. Oh, you can assign a negative number to a vector, but "V" in this sense is not a vector.

 

Better to say...that: "since it requires an infinite amount of energy to get to...the speed of light...all our measurements/considerations of actions above that limit have little or no meaning." (or....we don't understand them!!)

 

And, in passing, the speed of light (in a vacuum) is not "DEFINED," it comes out of Maxwell's equations. Just "pops" up there!

 

I assume that the response above was in response to my little bit of free verse. The last paragraph of my entry is meant to open up the mystery of the photon's speed LIMIT -- not its absolute value. Think of a universe that gave photons an infinite speed...(as they might have....given the value of ZERO mass!!)*** -- wow, what a different universe!!

 

***(See, just use the regular momentum/speed equations and plug in "ZERO" here and there.... You get a lot of infinities!!!)

 

So...why 186,000 miles per second?? The best guess...and best way to start contemplating this puzzle is to re-state the problem:

 

"What is the hidden quality of "space" that slows the possible velocity of a photon to 3.0 x 10 to the 8th m/sec??" And...is this speed an absolute?? Or is it a statistical observation...at some quantum or near-quantum inspection?

 

That is, IF...IF...we could observe the path of a photon at near Planck distance...would the "speed" be constant...or have fluctuations that "add up to" what see as an absolute.???

 

One thing: My mind gets bent out of shape...when someone brings in "virtual" photons!!"

 

My goodness...bring in the string theorists!!!

 

All in good fun...

 

Just sign me: "The Mad Quantum Poet) : ) : ) -- Pat

[pjlueck]

Quoting CraigD here....

 

Though you hear the idea that an object traveling faster than c would travel backward in time quite a bit in science fiction and pop science, it’s not a consequence of any usual physics.

Ah...CraigD, you said it so much nicer than I did! And, with some equations!!! So, what do you think about my re-phrasing of the "cosmic traffic cop" conundrum? Curiously enough...it seems one can look at the question another way:

 

Two possible answers to possible "speed limits of photons:" 1. Infinite. 2. Some fixed value.

 

Option 2 allows us to be in this universe...

 

Another arrow in the quiver of the proponents of the "Antrhropic Universe Theory."

 

(I have always thought that theory was unnecessarily fatalistic!!)

 

Pat

[CraigD]

"Beware, the jabberwock said: Beware of inserting fabulous 'negatives' into physical equations!" At least that's the way I heard it.

The more modern jaberwocks and/or bandersnatches to beware in physics are “infinities”, or more apropos, “theories that predict infinite physical quantities”. This is, from what I’ve read (vs. actually done like a genuine theorist) one of the common banes of string theories (theories in the plural – one of the profound banes of string theories is that there are an infinite number of different ones, with not a lot of criteria for picking the one that’s physical (ie: real)).

 

At 1.1 x the speed of light V=D/T yields 3.3x10 to the 8th meters/second (roughly), if one simply "plugs in numbers." Yet, your conclusion is that the V value would be negative; a concept that that has no basis, and essentially, negates the use of this particular equation. Oh, you can assign a negative number to a vector, but "V" in this sense is not a vector.

Yup – as a rule negative real or complex vector magnitudes are a sign of having done something wrong calculating the unit direction and scalar magnitude part of a vector quantity. Intuitively, traveling due west at 1 m/s is just a ( ;) ab-)normalized way of saying you’re traveling due east at 1 m/s.

 

Better to say...that: "since it requires an infinite amount of energy to get to...the speed of light...all our measurements/considerations of actions above that limit have little or no meaning." (or....we don't understand them!!)

Yes. :thumbs_up Even better to qualify this a bit more to “since it requires an infinite energy to get a body with non-zero invariant mass to the speed of light ... etc.”

 

And, in passing, the speed of light (in a vacuum) is not "DEFINED," it comes out of Maxwell's equations. Just "pops" up there!

:( This gives the impression that the speed of light [imath]c[/imath] is derivable from purely mathematical postulates from Maxwell’s equations, which isn’t true.

 

Maxwell’s equations - this one, for example:

[math]c^2 e_0 u_0 = 1[/math]

Relate [imath]c[/imath], the electric constant [imath]e_0[/imath] and the magnetic constant [imath]u_0[/imath].

 

Three unknowns, 1 constant, and 1 equation, alas, do not a popping out make. You’ve got to experimentally measure 2 of the unknowns to calculate the third.

 

I assume that the response above was in response to my little bit of free verse.

You end a poem with a couple of question marks, you’re gonna get a response, no?

 

What I believe Polymath was noting with

... (about 3 x 10 ^ 8 meters per second [this is defined, not measured, by saying that a meter is the distance that light travels in 1 / c seconds]) ...

is a cool and subtle fact about our physical measurement conventions: [imath]c[/imath] is an exact value: 299792458 m/s. No rounding is involved, and by definition no future experiment can change it, because the meter is defined in terms of the speed of light, not the speed of light in terms of the meter.

 

Both the second and the speed of light are experimentally obtained physical values, but more precise measurements of them result by conventional definition in a more precise value of other lengths, as measured by standard in meters.

 

I find any verse about physics that isn’t in limerick form a pleasant change :), and one about special relativity a special treat, but

Weighing nothing, it takes nothing

to speed them on their way

I cannot abide!

 

Photon’s don’t weigh nothing in the classical approximation. It takes some force to change their velocity, and some energy, if not to speed them on their way, to create them so they can inevitably speed on their way.

 

The relativistic mass of a photon of light of frequency (color) [imath]v[/imath] is

[math]\frac{h v}{c^2}[/math]

Where [imath]h \dot= 6.62606896 \times 10^{-34}\,\mbox{kg}\cdot\mbox{m}^2\mbox{/s}^2 [/imath]

Thus, a photon of [imath]5 \times 10^{14} \,\mbox{cycle/s}[/imath] red light has a mass of about [imath]3.7 \times 10^{-36} \,\mbox{kg}[/imath]

 

Though strictly speaking there’s no practical way I can think of to weigh a photon – support it in a gravitation field and measure the force required – measuring the force required to reflect a stream of them is a delicate but possible task, managed in 1901 using a Nichols radiometer. A easier-to-come-by (I’ve got one as a xmass tree ornament :)) gadget, the Crookes radiometer, was believe by most, for a few months or years, to manage this trick, a few decades before Nichols’s, but actually didn’t.

 

A less subtle, but harder to build and operate, machine that measures the momentum of light, as a side effect to its primary purpose, is a solar sail.

 

That is, IF...IF...we could observe the path of a photon at near Planck distance...would the "speed" be constant...or have fluctuations that "add up to" what see as an absolute.???

Fluctuations, and not necesarily adding up to an absolute.

 

Without getting too formal (a practicality, as it’s a strain possibly beyond my best efforts to get formal enough for this question), what you’d “see” – that is, somehow detect – is what you usually see when you detect things on a small enough scale (or with sufficient patience): a measurement of the speed of light in the classical v=d/t sense would give not a single definite value, but a open-ended probability density. The probability of the photon being detected in a sufficiently large volume where the classical d=vt predicts is nearly 1, but a small but non-zero probability of it being detected in a volume implying a speed of light half, double, or an arbitrarily greater factor of its usual value exists.

 

The catch for aficionados of such weirdness is that there probabilities are so low that to have reasonable expectations of ever catching one requires experiments lasting longer than its likely we, the stars, or perhaps even matter as we know it, will exist. Hence my “sufficient patience” parenthetical above :)

 

One thing: My mind gets bent out of shape...when someone brings in "virtual" photons!!"

Mine, too - though over time, and with help from some of my better-educated friends here at hypography, I’ve got my amateur mind at least reasonably well wrapped around them. I think we’ve enough mind-bendy stuff in this thread – and enough words in this post –without getting into them right now. :edizzy:

[joekgamer]

What I had meant by the 'negative velocity' part of my post was that since V = d / t, and since (theoretically) time will go backwards (the flow of time will be negative) once you exceed the speed of light, then at that point, t will be negative, causing V to be negative.

 

However, CraigD corrected me by showing that time would not go backwards at the speed of light (as far as we can tell as of now anyway; imaginary numberrs are kind of odd), essentially proving my basis (time being ngative) false.