Why does light have invarient speed?

[Xeinstein]

Another question I had, as posted in the Quantum group, what happens to non-photon particles that are moving at a speed close to c and are moving against each other? Is the relative speed of the two particle beams (whose sum is > c) capped by c? Relativity theory says yes. But what would be the mechanics behind this phenomenon? And would this be called "invarance of upbound of relative speed"?

Yes, the relative speed of the two particle beams (whose sum is > c) capped by c.
This is a result of time dilation. The faster you travel in space, the slower you travel in time. Nevertheless, the length of 4-velocity of any inertial observer is always c

 

[JesseM]

Another question I had, as posted in the Quantum group, what happens to non-photon particles that are moving at a speed close to c and are moving against each other? Is the relative speed of the two particle beams (whose sum is > c) capped by c? Relativity theory says yes. But what would be the mechanics behind this phenomenon? And would this be called "invarance of upbound of relative speed"?

Two particles moving at .999c and -999c relative to one observer still see a relative speed less than c in their own frames.

Yes, the relative speed of the two particle beams (whose sum is > c) capped by c.
This is a result of time dilation. The faster you travel in space, the slower you travel in time. Nevertheless, the length of 4-velocity of any inertial observer is always c

It's worth distinguishing two types of "relative motion" here. In the frame where both particles are moving in opposite directions, each one is moving at less than c, but the distance between them can increase at a rate greater than 1 light-year per year. But in each particle's own rest frame, using rulers and clocks at rest in that frame to measure the distance covered by the other particle in a given time, the other particle's speed in this frame will be less than c.

 

[rbj]

I agree with you. Light doesn't just "happen" to have a speed equal to the apparent "speed limit" of the universe. Something more fundamental is going on. My point was that relativity itself is more fundamental than just a strange consequence of the behavior of light.

i'm glad we agree. i wish i could say the same about Wikipedia when i try to check a little POV over there (i got to do it anonymously now, since they kicked me out).

anyway, i think that the fundamental reason that there is a "speed limit" is because the fundamental interactions are all "instantaneous" in the same way: some cause changes over here and some effect is notices over there. it's not merely the speed limit of such interaction, it's the speed of propagation of the interaction, and since nothing pushes or interacts with anything else, except by way of these fundamental interactions, how can information or any other causal phenomena propagate any faster?

whether the cause and effect are EM, nuclear, or gravitational, it doesn't matter. for an observer that is equidistant from the thing that is the "causal agent" and the other thing that is affected by it, that observer will count some non-zero time between the perturbor and perturbed. that means that this "c" is finite (and real and positive), not infinite, which is the salient physics. it doesn't matter what that finite speed is, whatever it is, our scaling would adapt to it. indeed the scaling of things in the universe depends directly on c, G, and h (as we measure such quantities with our meter, kilogram, and second) and they could be whatever finite, real, and positive values they choose to be and nothing would be perceived to be different on our part. the tick marks of Nature's ruler, clock, and weighing scale would adjust and the quantitative properties of all of the things in Nature would change proportionally with it (lest some dimensionless parameter change which is something that would make a difference) and things would appear the same to us as before. there really is no operational meaning to any particular values for c, G, and h as long as they are real, finite, and postive.

so it's not just c that is invariant. and, if i understand Einstein's sentiment correctly, Nature had little other choice. i don't know how he would have taken it if the M-M experiment came out differently than it had.

 

[JesseM]

so it's not just c that is invariant. and, if i understand Einstein's sentiment correctly, Nature had little other choice. i don't know how he would have taken it if the M-M experiment came out differently than it had.

Why do you think nature had little other choice? There doesn't seem to be anything inherently inconsistent about the Newtonian universe which allows arbitrarily large velocities.

 

[rbj]

so it's not just c that is invariant. and, if i understand Einstein's sentiment correctly, Nature had little other choice. i don't know how he would have taken it if the M-M experiment came out differently than it had.

Why do you think nature had little other choice? There doesn't seem to be anything inherently inconsistent about the Newtonian universe which allows arbitrarily large velocities.

well, i was trying to reflect Einstein's sentiment. here is the quote of Einstein that leads me to believe that he thought that nature had little other choice:

All I have tried to do in my life is ask a few questions. Could God have created the universe in any other way, or had he no choice? And how would I have made the universe if I had the chance?

when i consider that along with other quotes of Einstein, regarding whom or what Albert is referring to when he uses the word "God"

I believe in Spinoza's God, who reveals Himself in the lawful harmony of the world, not in a God Who concerns Himself with the fate and the doings of mankind...I do not believe in a personal God and I have never denied this but have expressed it clearly.

when i put those two together, i think that it's Nature that Einstein means when he referred to "God" in the first quote above. i think that Einstein thought that a universe where the laws of nature were different for two inertial observers was a universe that did not make sense, could not make sense, and to anthropomorphize, that choice of a universe was simply not in the cards. if every inertial observer must have the same laws of nature, every inertial observer must have the same c. and, with the same c, we all know what the consequences of that would be.

i guess this doesn't answer your question about what is inherently wrong with a "universe which allows arbitrarily large velocities". i don't have a good answer for that other than that would mean that the fundamental interactions would have to have instantaneous effect over any arbitrarily large distance (as Newton or Coulomb had modeled for gravity or electrostatics). there is nothing inherently wrong with it that i am aware of, it's only that the physics is different. if c were infinite, there would be no observed magnetic effects. there would only be electrostatics. don't know if there could even be a Planck Length or a Planck Time. don't know how reality could be.

at the very least, things would be qualitatively different with an infinite c vs. a finite c. but once the physics is determined that c is finite, it doesn't matter what finite value it is. we all would adjust to it. may as well call it "1".

 

[mdeng]

I like the way JesseM presents it.

I think the argument of "the laws of nature were different for two inertial observers was a universe that did not make sense" is strong (as it fits what we observed, but remember Newtonian laws were also observed as fits for hundreds of years). However, RBJ's earlier argument assumed that this was sufficient to derive SR. I am glad RBJ adds back the constancy of C to the postulate. I am very curiously though, why without it Einstein's SR would fall apart even though he already had Maxwell's equation? In other words, what's wrong to replace Einstein's 2nd postulate with Maxwell's conclusion of C (which is a theory, not a postulate, though I am not sure what Maxwell's postulate was)?

I keep thinking about the relation between constancy of C and locality principle. Does anyone have an intuitive (or even better, theoretical) explanation why this principle would imply a speed limit (instead of just *finite* speed, but unbounded) and this this limit has to be constancy? And what impact would quantum physics observation of instantaneity would have on locality principle (at a large scale) and SR (and consequently GR)?

 

[rbj]

I think the argument of "[a universe where] the laws of nature were different for two inertial observers was a universe that did not make sense [to Einstein]" is strong (as it fits what we observed, but remember Newtonian laws were also observed as fits for hundreds of years). However, RBJ's earlier argument assumed that this was sufficient to derive SR. I am glad RBJ adds back the constancy of C to the postulate.

be careful how you represent what other people say (or type). i haven't changed my position. the constancy of c (for various inertial observers) is because of the constancy of the laws of nature (for the same inertial observers).

I am very curiously though, why without it Einstein's SR would fall apart even though he already had Maxwell's equation? In other words, what's wrong to replace Einstein's 2nd postulate with Maxwell's conclusion of C (which is a theory, not a postulate, though I am not sure what Maxwell's postulate was)?

i didn't think that Maxwell concluded that c was constant for different inertial observers. if he did, i would like to know of the record of that. i thought that Maxwell (as well as Faraday) understood that c was in reference with the aether. what Maxwell concluded was that

$$c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}$$

for the propagation of electromagnetic waves. and then he figures out that this c that he calculates from the electric and magnetic constants is the very same as the speed of light. then that pretty well nailed down the fact (that was already suspected) that the same visible light we see with, is nothing other than an electromagnetic wave.

 

[mdeng]

be careful how you represent what other people say (or type). i haven't changed my position. the constancy of c (for various inertial observers) is because of the constancy of the laws of nature (for the same inertial observers).

Well, you did add the constancy of C when you mentioned Einstein's view above, which made me think you agreed with him on that postulate. But technically, you did not.

i didn't think that Maxwell concluded that c was constant for different inertial observers. if he did, i would like to know of the record of that. i thought that Maxwell (as well as Faraday) understood that c was in reference with the aether. what Maxwell concluded was that

$$c = \sqrt{\frac{1}{\epsilon_0 \mu_0}}$$

What I meant to say is, why did Einstein have to make the 2nd postulate. All he seemed to have to do was to argue that Maxwell's equation must be true for all inertia systems (I think that was your line of arguments earlier). I believe he could not do that. But I don't truly understand why he could not. IOW, why would he be wrong if he did not have his 2nd postulate?

 

[rbj]

What I meant to say is, why did Einstein have to make the 2nd postulate? All he seemed to have to do was to argue that Maxwell's equation must be true for all inertia systems (I think that was your line of arguments earlier). I believe he could not do that. But I don't truly understand why he could not. IOW, why would he be wrong if he did not have his 2nd postulate?

well, you're basically proving my point. i think the 2^nd postulate was there for clarity and was not strictly needed. acceptance of the 1^st postulate forces one to accept the 2^nd. there is no way for the laws of nature to be precisely the same for every inertial observer yet somehow they have different quantitative values for c. with our meter sticks and clocks, the quantitative value of c is part of the laws of nature. now, if reality were different, if the M-M experiment measured a difference in c (in orthogonal directions) at different times of the year, indicating that there might be an aether, then the 1^st postulate of SR could not be proposed without an immediate refutation. if there is an aether, then inertial observers sharing the same frame of reference with the aether would measure the speed of light the same in all directions, whereas someone moving through the aether at a sufficiently fast speed, would measure the speed of light to be slower in the frontward direction than they would measure in the rearward direction. (edit: actually it would have to be frontward vs. sideward directions, since we would have to measure the speed of light in a round trip., frontward and rearward would be the same.)

but making it a 2^nd and explicit postulate helps nail the coffin shut for argument sake, and if anyone complains about it in 1905, one can point to the M-M experiment which did precede it.

i don't know what it is that you believe Einstein could not do. was that extrapolate the 2^nd postulate from the 1^st?

 

[JesseM]

well, you're basically proving my point. i think the 2^nd postulate was there for clarity and was not strictly needed. acceptance of the 1^st postulate forces one to accept the 2^nd. there is no way for the laws of nature to be precisely the same for every inertial observer yet somehow they have different quantitative values for c.

With quantum field theory I think this is true, but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)? After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).

 

[rbj]

With quantum field theory I think this is true, but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)?

sure, i s'pose. but the expression of this law or description would be different for different inertial observers. i am not saying that the first postulate naturally follows from nothing. the first postulate is a postulate that one has to sort of axiomatically accept (or accept it on the basis that no experiment could show any difference in how the physical reality was different for different inertial frames of reference). i s'pose that they could say that now, that Maxwell's laws are not really fundamental.

After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).

but we have a different experience with sound and air. sound is not as fundamental as a perturbation of a fundamental force like EM, gravity, or nuclear. sound and propagating vibrations in matter requires matter as a medium. there ain't no sound in a vacuum, but there is light (E&M), or gravity waves (if we could only measure them, we better be ready to the next time a supernova that is decently close occurs) in a vacuum. so the basic question is a vacuum devoid of everything, or was this aether left in it, even after we suck all the air molecules out of the jar? so, for sound in air, we are saying that the laws that govern the propagation of sound (i think i can derive the wave equation from continuity, Newton's second law, and the gas law for adiabatic compression) are different for people stationary w.r.t. the air vs. those who are moving through it. we have to do that with wave phenomena that has a medium. it's different when you are moving through a medium than when you aren't.

i don't know even a quarter of the physics you do, Jesse. for me, i am applying epistemology to the physics that i do know (what they teach us Neanderthals in an ABET accredited engineering curriclum). i just do not see how, semantically, the second postulate of SR can be false if the first postulate is true. If the first postulate said that "all laws of physics, with the exception of those that govern E&M, are precisely the same for all inertial observers", then the second postulate would be necessary to go on with SR. but with the broader and simpler expression of the first postulate, i don't see why it would be necessary to add: "just in case you forget, when we say all laws of physics, we mean all laws and every qualitative and quantitative aspect of those laws."

 

[DrGreg]

i think the 2^nd postulate was there for clarity and was not strictly needed.

The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter. This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction. This does not automatically follow from the 1st postulate alone.

Once you've accepted light's independence from the motion of its emitter, the fact that all observers calculate the same numeric speed is a consequence of the 1st postulate. (And you also need to explicitly state that the speed of light is not infinite, otherwise Newtonian theory would satisfy both postulates.)

 

[rbj]

The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter.

i remember that (but forgot it).

This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction.

as if the guy with a flashlight that is whizzing by an observer at 0.9c, that somehow he can give his beam of light a little boost (from the POV of the observer) resulting in a beam of light at 1.9c.

thanks for reminding me of the precise language.

 

[mdeng]

With quantum field theory I think this is true

What are the postulates of QF from which constancy of c is derived?

but back when the only law of nature involving c was Maxwell's laws, couldn't one have argued that Maxwell's laws are not really fundamental, but just a description of the behavior of a certain physical medium filling space (the aether)? After all, no one says that since observers at rest relative to the atmosphere measure sound waves in air to have the same speed in all directions, then this must imply by the first postulate that sound waves in air must have the same speed in all directions in every frame (even in a universe where all of space was filled by such an atmosphere).

Jesse, I am not sure whether your analogy is correct. I believe that Maxwell's law did not say or require the observer must be stationary with respect to the vacuum. So if I factor that into your analogy, I would have said "no one says that since observers at rest or *moving* relative to the atmosphere measure sound waves in air to have the same speed in all directions..." and we know this "since" part is not true.

 

[mdeng]

The important part of the 2nd postulate is that the speed of light does not depend on the speed of the emitter. This might seem "obvious" nowadays, but it was not always so. You could formulate a theory, consistent with the first postulate, in which two light sources moving at different speeds would emit light at different speeds (both speeds relative to a single observer). The 2nd postulate can be paraphrased by saying that it's impossible for any photon to overtake another photon traveling in the same direction. This does not automatically follow from the 1st postulate alone.

Once you've accepted light's independence from the motion of its emitter, the fact that all observers calculate the same numeric speed is a consequence of the 1st postulate. (And you also need to explicitly state that the speed of light is not infinite, otherwise Newtonian theory would satisfy both postulates.)

I am still not clear. Didn't Maxwell's equation say (implicitly, and made explicit by Einstein) that light speed c is regardless whether the observer is flying toward the light or, stated it in another way, the emitter is flying toward us? Therefore, neither overtaking or undertaking ever would happen.

Perhaps Maxwell assumed there was aether and perhaps that was his basis of the equation. However, I believe that his law does not really require this. Perhaps this point can't be proven and thus Einstein just made the 2nd postulate to avoid this sticky issue?

 

[DrGreg]

I am still not clear. Didn't Maxwell's equation say (implicitly, and made explicit by Einstein) that light speed c is regardless whether the observer is flying toward the light or, stated it in another way, the emitter is flying toward us? Therefore, neither overtaking or undertaking ever would happen.

You are right that the second postulate follows from Maxwell's equations. The point is that you don't need the whole of Maxwell's theory to logically develop the theory of relativity; the second postulate (together with the first) is sufficient.

The postulates of any theory are a set of assumptions from which the rest of the theory can be proved without any further assumptions. The development of the theory from the assumptions is a process of logic which doesn't actually depend on any experimental verification.

It's desirable to make the assumptions as simple as possible. You could replace Einstein's second postulate by a postulate that Maxwell's equations are valid in some reference frame (and therefore in all reference frames by the 1st postulate). But Einstein's version is simpler and is all that is necessary for the logic.

If you formulate the 1st postulate as "the laws of physics are the same in every inertial frame", its weakness, from a rigorous mathematical point of view, is that it doesn't actually specify what the laws of physics are. But, ironically, that is its very strength from physical point of view. It is a general framework that you can attempt to apply to any set of physics theories (there aren't really any "laws"); there is no logical requirement that you have to include Maxwell's equations amongst your "laws", so long as nothing breaks the two postulates.

Perhaps Maxwell assumed there was aether and perhaps that was his basis of the equation.

Indeed that was the case when he first formulated them; I believe everything in his equations was measured relative to a postulated aether. However, experiments performed in the years leading up to the formulation of Relativity indicated that Maxwell's equations appeared to be true in moving frames too, which led Lorentz to formulate the Lorentz transformation and later led to Einstein's Special Theory.

The point is, to understand relativity, you don't need to understand Maxwell's equations (partial differential equations which require a moderately advanced knowledge of calculus). It's sufficient to understand the two postulates (no calculus required, until you get to acceleration and gravity).

In essence I'm agreeing with rbj that "2nd postulate was there for clarity and was not strictly needed" provided you accept Maxwell's equations; but if you include the 2nd postulate then you don't need to bring Maxwell into it at all.

 

[DrGreg]

To ressurrect a question implied long ago in this thread (post #24, 5 January):

In calculating this "speed", you're taking the distance traveled as measured in one reference frame, and dividing it by the time as measured in another reference frame. This number is definitely of practical significance to space-travelers, but I think most physicists would resist calling it "speed" because of this mixing of reference frames. Unfortunately, I can't think of a good word to use instead of "speed" here.

This way of measuring motion is called by various authors "proper speed" or "celerity". The celerity of light is infinite. And, for massive objects, momentum = invariant mass * celerity. And celerity = c * sinh(rapidity).

 

[mdeng]

Indeed that was the case when he first formulated them; I believe everything in his equations was measured relative to a postulated aether. However, experiments performed in the years leading up to the formulation of Relativity indicated that Maxwell's equations appeared to be true in moving frames too, which led Lorentz to formulate the Lorentz transformation and later led to Einstein's Special Theory.

Maybe this is it. While Maxwell's equation did not mention motion, we can't just take that as proof that it applies to moving frame as well. The absence of moving does not automatically mean it would hold when motion is involved.

The point is, to understand relativity, you don't need to understand Maxwell's equations (partial differential equations which require a moderately advanced knowledge of calculus). It's sufficient to understand the two postulates (no calculus required, until you get to acceleration and gravity).

In essence I'm agreeing with rbj that "2nd postulate was there for clarity and was not strictly needed" provided you accept Maxwell's equations; but if you include the 2nd postulate then you don't need to bring Maxwell into it at all.

This could be an explanation but I feel it's weak. Einstein himself stated repeatedly that he advocates simplicity. I would speculate that if he could remove a postulate, even if it means more complexity SR must rest upon without it, he would have done that. This is especially so about postulate. We don't make them lightly, they are so fundamental. They should be made not for clarity but for absolute necessity.

 

[rbj]

While Maxwell's equation did not mention motion,

whatever gave you that idea? of course Maxwell's equations (as well as anything describing the magnetic field or force) mention motion.

 

[rbj]

in fact, i knew i mentioned this recently before:$$\oint_C \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 \iint_S \mathbf{J} \cdot \mathrm{d}\mathbf{S} = \mu_0 \iint_S \rho \mathbf{v} \cdot \mathrm{d}\mathbf{S}$$

$$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{(\mathbf{J}\, dV) \times \mathbf{\hat r}}{r^2} = \frac{\mu_0}{4\pi} \frac{(\rho \mathbf{v}\, dV) \times \mathbf{\hat r}}{r^2}$$

$$\mathbf{F} = q \cdot(\mathbf{E} + \mathbf{v} \times \mathbf{B})$$

what do you think they mean by $\mathbf{v}$? what did they measure it against?$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$

$$\nabla \cdot \mathbf{B} = 0$$

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$

$$\nabla \times \mathbf{B} = \frac{1}{c^2} \left( \frac{\partial \mathbf{E}} {\partial t} + \frac{\rho}{\epsilon_0} \mathbf{v} \right)$$more mentions of motion.

 

[mdeng]

in fact, i knew i mentioned this recently before:


$$\oint_C \mathbf{B} \cdot \mathrm{d}\mathbf{l} = \mu_0 \iint_S \mathbf{J} \cdot \mathrm{d}\mathbf{S} = \mu_0 \iint_S \rho \mathbf{v} \cdot \mathrm{d}\mathbf{S}$$

$$d\mathbf{B} = \frac{\mu_0}{4\pi} \frac{(\mathbf{J}\, dV) \times \mathbf{\hat r}}{r^2} = \frac{\mu_0}{4\pi} \frac{(\rho \mathbf{v}\, dV) \times \mathbf{\hat r}}{r^2}$$

$$\mathbf{F} = q \cdot(\mathbf{E} + \mathbf{v} \times \mathbf{B})$$

what do you think they mean by $\mathbf{v}$? what did they measure it against?


$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$

$$\nabla \cdot \mathbf{B} = 0$$

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$

$$\nabla \times \mathbf{B} = \frac{1}{c^2} \left( \frac{\partial \mathbf{E}} {\partial t} + \frac{\rho}{\epsilon_0} \mathbf{v} \right)$$


more mentions of motion.

Is this motion of the EM in "aether", or motion of the observer's frame through aether?

 

[rbj]

Is this motion of the EM in "aether", or motion of the observer's frame through aether?

well, that was the original confusion. when they did experiments it was the motion relative to themselves, the observers. but the theory intended that the velocities were absolute and being that these velocities would be greatly different in greatly different reference frames, then the numbers going into the equations would be different and different results would come out. this was something that they worried about which is why they wanted to get a handle on about how fast (and which direction) we were moving through the aether (so they would know how much to fudge their numbers for velocity). that is, if i am not mistaken, what Michaelson and Morley were trying to determine. in doing the experiment, they got a little surprize.

 

[mdeng]

well, that was the original confusion. when they did experiments it was the motion relative to themselves, the observers. but the theory intended that the velocities were absolute and being that these velocities would be greatly different in greatly different reference frames, then the numbers going into the equations would be different and different results would come out. this was something that they worried about which is why they wanted to get a handle on about how fast (and which direction) we were moving through the aether (so they would know how much to fudge their numbers for velocity). that is, if i am not mistaken, what Michaelson and Morley were trying to determine. in doing the experiment, they got a little surprize.

It seems safe to say that Maxwell's equation did not specify (at least not explicitly) what the reference frame was, whether the frame moves or is stationary (and one question just pops up: does ME say whether the frame has to be inertia?). While all empirical observation suggested that it should hold for moving inertia reference frame as well, the theory does not prove it in the strict mathematical sense. Einstein's great contribution was to postulate that this equation holds for all inertia system.

 

[W.RonG]

Hi everybody. I hope this isn't taken as barging in since I'm brand new here, but I did sign up expressly to offer a solution to mdeng's question. I think rbj provides a key to the answer in mentioning Planck time and Planck distance. These are the smallest units of each respective dimension, so it seems to me that anything (object, force, effect, whatever you want to call it) can only traverse one unit of Lp during one or more units of Tp. The fastest possible speed is therefore based on one unit of Lp per each unit of Tp. To go any faster would require fractional Tp to travel one Lp. The speed of light is simply our calculation based on familiar distance, a large multiple of Lp, divided by familiar time, a large multiple of Tp. Rbj gave equivalent measures of these quantities in an earlier post. To mdeng, does this help to see the "speed limit" of (quantized) space-time?

BTW I hope I will be able to participate in other conversations as well, since I also have some questions and possibly some answers.
Thanks all,
Ron
p.s. is there a place for intros? I didn't see any.

 

[mdeng]

Hi everybody. I hope this isn't taken as barging in since I'm brand new here, but I did sign up expressly to offer a solution to mdeng's question. I think rbj provides a key to the answer in mentioning Planck time and Planck distance. These are the smallest units of each respective dimension, so it seems to me that anything (object, force, effect, whatever you want to call it) can only traverse one unit of Lp during one or more units of Tp. The fastest possible speed is therefore based on one unit of Lp per each unit of Tp. To go any faster would require fractional Tp to travel one Lp. The speed of light is simply our calculation based on familiar distance, a large multiple of Lp, divided by familiar time, a large multiple of Tp. Rbj gave equivalent measures of these quantities in an earlier post. To mdeng, does this help to see the "speed limit" of (quantized) space-time?

BTW I hope I will be able to participate in other conversations as well, since I also have some questions and possibly some answers.
Thanks all,
Ron
p.s. is there a place for intros? I didn't see any.

Hi Ron,

I really appreciate your effort to answer my question. Your answer is new to me. I don't have formal training in physics, just fascinations and intuitions. So please bear with me. How were Tp and Lp decided to be the least unit? What postulates are they based on? Why would Lp/Tp be a constant to all observers (i.e., is constancy a property of Tp/Lp)? Or do Lp/Tp expand/contract when there are relative movement between observers and and the object being observed?

Furthermore, can we use them to claim that there would be nothing in the universe that may travel faster than light? Can they be used to disprove the instantaneity that quantum physics claims to have observed? I understand that while SR says if we travel with a starting speed < c then we can't reach or go over it, SR does not say that nothing can travel faster than light if its starting speed is > c. Perhaps Lp and Tp have the same restriction/allowance?

Thanks again for the reply.

 

[Xeinstein]

Hi everybody. I hope this isn't taken as barging in since I'm brand new here, but I did sign up expressly to offer a solution to mdeng's question. I think rbj provides a key to the answer in mentioning Planck time and Planck distance. These are the smallest units of each respective dimension, so it seems to me that anything (object, force, effect, whatever you want to call it) can only traverse one unit of Lp during one or more units of Tp. The fastest possible speed is therefore based on one unit of Lp per each unit of Tp. To go any faster would require fractional Tp to travel one Lp. The speed of light is simply our calculation based on familiar distance, a large multiple of Lp, divided by familiar time, a large multiple of Tp. Rbj gave equivalent measures of these quantities in an earlier post. To mdeng, does this help to see the "speed limit" of (quantized) space-time?

BTW I hope I will be able to participate in other conversations as well, since I also have some questions and possibly some answers.
Thanks all,
Ron
p.s. is there a place for intros? I didn't see any.

I think Einstein's relativity is a classical theory, so it has nothing to do with Planck

 

[W.RonG]

Thanks for not responding in a violent manner. Some forums (fora?) can get pretty sensitive about new people showing up in the middle of a thread.
I tried to phrase my post carefully so as not to be a specific final answer to the original question. In fact it leads to more questions such as those mdeng posited. I wanted to point the thought process in this particular direction but did not want it to sound circular (Planck constants are defined by c, c is described by Planck units). But this does lead directly to questions of the nature of space (or space-time), propagation of energy through space, and our perceptions of those phenomena. Also the original question was not about SRT directly, but about us measuring c with the same result regardless of our motion relative to any other inertial frame. I think that says more about us and our measurement methods than it says about light (well, electromagnetic energy in general).
IOW space is what it is, e-m propagation takes place independent of us, and we observe/measure/theorize about it all. I like to think of it this way: why are all observers (in their inertial frames) traveling at "the speed of light" less than c? After all, length and time contraction/dilation affect us and our measurement tools, not light.
rg

 

[rbj]

I think Einstein's relativity is a classical theory, so it has nothing to do with Planck

i think that the fact that we don't measure anything except against like-dimensioned quantities means that whether the dimensionful parameter is c or G or $\hbar$ or $\epsilon_0$, any variation of any of these dimensionful parameters is "operationally meaningless" (those are Michael Duff's words) or "observationally indistinguishable" (those are John Barrow's words). and that does have something to do with Planck Units.

if we measure everything in Planck Units, we'll have dimensionless numbers, which are meaningful. but a consequence of that is the speed of light (which is more generally the speed of all fundamental interactions, not just E&M), the gravitational constant, the Coulomb electric constant, and Planck's constant all just go away. they turn into the number 1.

so God decides to turn the knob marked "c" on his control panel from 299792458 m/s (or whatever units he likes) to, say, half that value, and guess what? c still equals 1 (in Planck Units, that is c = 1 Planck Length per Planck Time, no matter what the knob is set to) and if all of the dimensionless parameters remain the same as before (those are the salient parameters), then the number of Planck Lengths per meter remain the same, the number of Planck Times per second remain the same, and then when we get our meter sticks and clocks out to measure c again (after God has twisted the knob marked "c") we still find out that light still travels 299792458 of our new meters in the time elapsed by one of our new seconds. so how are we going to know the difference?

 

[JesseM]

i think that the fact that we don't measure anything except against like-dimensioned quantities means that whether the dimensionful parameter is c or G or $\hbar$ or $\epsilon_0$, any variation of any of these dimensionful parameters is "operationally meaningless" (those are Michael Duff's words) or "observationally indistinguishable" (those are John Barrow's words). and that does have something to do with Planck Units.

I agree with what you say about "changes" in dimensional constants like c being meaningless, but it seems to me that W.RonG's post was about the notion that quantized spacetime was somehow essential to explaining the invariant speed of light, whereas we can certainly use Planck units (which are just based on manipulations of some other constants like G and h) without committing to any notion that space and time are quantized as opposed to infinitely divisible.

 

[W.RonG]

What is the physics answer to the question of why light has an invariant speed
to anyone and everyone, other than this is what light is?

Here's where I'm going - the nature of space is to propagate energy (rbj's interactions) at a fixed rate. The nature of our measurements of space and energy propagation causes them to always get the same result. But we realize that we may be moving relative to another system that got the same answer that we did, and we are puzzled. The answer lies in understanding the nature of our physical existence in natural space-time. That includes our measuring rods and our ticking clocks with which we describe our motions.
I have to get going so if I can put more thoughts into words I'll try to expand on this later. I hope others see the connections between the material in post #15 (too much to quote) and the ultimate answer to the initial question, and can help this process along.
rg

 

[Xeinstein]

i think that the fact that we don't measure anything except against like-dimensioned quantities means that whether the dimensionful parameter is c or G or $\hbar$ or $\epsilon_0$, any variation of any of these dimensionful parameters is "operationally meaningless" (those are Michael Duff's words) or "observationally indistinguishable" (those are John Barrow's words). and that does have something to do with Planck Units.

if we measure everything in Planck Units, we'll have dimensionless numbers, which are meaningful. but a consequence of that is the speed of light (which is more generally the speed of all fundamental interactions, not just E&M), the gravitational constant, the Coulomb electric constant, and Planck's constant all just go away. they turn into the number 1.

so God decides to turn the knob marked "c" on his control panel from 299792458 m/s (or whatever units he likes) to, say, half that value, and guess what? c still equals 1 (in Planck Units, that is c = 1 Planck Length per Planck Time, no matter what the knob is set to) and if all of the dimensionless parameters remain the same as before (those are the salient parameters), then the number of Planck Lengths per meter remain the same, the number of Planck Times per second remain the same, and then when we get our meter sticks and clocks out to measure c again (after God has twisted the knob marked "c") we still find out that light still travels 299792458 of our new meters in the time elapsed by one of our new seconds. so how are we going to know the difference?

If that's the case, how come Einstein never used Planck's constant in relativity?

 

[W.RonG]

... how come Einstein never used Planck's constant in relativity?

Just off the top of my head, I would say it isn't necessary to concern oneself with the granularity/resolution of space and time to develop concepts of relative measurement methodology. Nor would the specific units of measure cause the Theory to change. If I understand correctly, Einstein concerned himself with the overarching concepts and left much of the hard-core mathematics to others (if this really is not true then I apologize in advance).
Quantized space and time answers the ancient conundrum of the arrow shot at a target. In half of the travel time it goes halfway to the target. Half again it is closer and if this is repeated ad infinitum the arrow will never reach the target. But we know it does so there must be a minimum distance unit and a minimum time unit and all speeds are integer ratios thereof.
The inclusion of quantization was meant to describe the speed of light based on the nature of space-time and local interaction which propagates energy. It can only be 1/1=1. Everything else is that or a lower ratio; the only way to propagate faster would be 1/0=?
rg

 

[rbj]

Here's where I'm going - the nature of space is to propagate energy (rbj's interactions) at a fixed rate.

and even if it wasn't a fixed rate from the POV of some god-like observer, if it were to change from this observer's POV (the observer isn't governed by the laws of physics that we are, which is only reason this observer could sense a change in that rate of propagation), we would not sense a difference unless some dimensionless parameter changed. but as far as we're concerned, since we only measure of perceive physical quantities in relationship to other like-dimensioned quantities - we count tick marks on rulers or ticks of a clock. we perceive how long a distance is relative to how big we are, we perceive how long in time some event is in proportion to about how long a fleeting thought is, inverse proportion to how fast our brains can think. so if somehow we think we measured c to be a different number of meters (the pre-1960 definition of the meter) per second, the salient parameter(s) that changed were the number of Planck Lengths per meter (and if the platinum-iridium meter stick is a "good" meter stick, then it doesn't lose or gain any atoms so this would be reflected in the number of Planck Lengths per Bohr radius) and/or the number of Planck Times per second. those are the important numbers.

The nature of our measurements of space and energy propagation causes them to always get the same result. But we realize that we may be moving relative to another system that got the same answer that we did, and we are puzzled. The answer lies in understanding the nature of our physical existence in natural space-time. That includes our measuring rods and our ticking clocks with which we describe our motions.
I have to get going so if I can put more thoughts into words I'll try to expand on this later. I hope others see the connections between the material in post #15 (too much to quote) and the ultimate answer to the initial question, and can help this process along.

Ron, this was pretty close to how i have trying to express this. thanks.

If that's the case, how come Einstein never used Planck's constant in relativity?

it's because, measured with our meters and seconds and kilograms, Planck's constant doesn't affect any of the physical consequences that are addressed in either SR or GR. now, if memory serves, i thought Einstein also wrote a sort of seminal paper about the photoelectric effect, and perhaps he made a reference to the constant of proportionality between the energy of emitted electrons and the frequency of the light onsetting the emittor surface. whether he called it "Planck's constant" or not, that's what it would have been.

 

[JesseM]

Quantized space and time answers the ancient conundrum of the arrow shot at a target. In half of the travel time it goes halfway to the target. Half again it is closer and if this is repeated ad infinitum the arrow will never reach the target. But we know it does so there must be a minimum distance unit and a minimum time unit and all speeds are integer ratios thereof.

But this problem is also simple to resolve in the case of continuous space and time, using calculus. Yes, you can divide the trip into an infinite series of smaller and smaller increments, but the time for the arrow to cross each successive increment will be also be getting smaller and smaller, and in calculus it is quite possible to have an infinite decreasing series which sums to a finite number, like 1/2 + 1/4 + 1/8 + 1/16 + ... = 1

The inclusion of quantization was meant to describe the speed of light based on the nature of space-time and local interaction which propagates energy. It can only be 1/1=1. Everything else is that or a lower ratio; the only way to propagate faster would be 1/0=?
rg

Why couldn't an object move more than one units of space in a single unit of time? After all, for slower-than-light objects, they'd have to move more than one unit of time for each unit of space along their path. In any case, if you think the notion of quantized space and time is established physics you're wrong; it's a speculation that emerges out of some approaches to quantum gravity, and I'm not even sure if it's true if it's technically true in string theory, although something weird does happen when you try to talk about distances smaller than the Planck length in string theory...as http://library.thinkquest.org/27930/stringtheory5.htm says,

A major detail of winding modes involves size. According to string theory, physical processes that take place while the radius of the encircled dimension is below the Planck length and decreasing are exactly identical to those that take place when the radius is longer than the Planck length and increasing. This means that, as the encircled dimension collapses, its radius will hit the Planck length and bounce back again, reexpanding with the radius grater than the Planck length again. In other words, attempts by the encircled dimension to shrink smaller than the Planck length will actually cause expansion.

The Logic Behind Contraction/Expansion Relationships

Wound strings' energy come from two different sources: the familiar vibrational motion and the new winding energy. Vibrational motion can be separated into two categories: ordinary and uniform vibrations. Ordinary vibrations are the usual oscillations discussed in preceding pages; for simplicity, they will temporarily be ignored. Uniform vibrations are the simple motion of a string's sliding from one place to another. There are two important observations related to uniform motion that will lead to the essence of the contraction/expansion relationship.

First, uniform vibrational energies are inversely proportional to the encircled dimension's radius. By the uncertainty principle, a smaller radius confines a string to a smaller area and thus increases the energy of its motion. Second, winding energies are directly proportional to the radius because the radius causes a string to have a minimum mass, which can be translated into energy. These two conclusions show that large radii imply large winding energies and small vibrational energies, and small radii imply small winding energies and large vibrational energies.

This conclusion yields the essential realization: for any large radius there is a corresponding small radius in which the winding energies of the former are the vibrational energies in that latter and vice versa. Since physical properties depend on the total energy of a string, not its individual winding or vibrational energy, there is no observable physical difference between the corresponding radii.

Now consider an example of the preceding principle. Imagine that the radius of the encircled dimension is 5 times the Planck length (R=5). A string can encircle this dimension any number of times; this number is called the winding number. The energy from winding is determined by the product of the radius and the winding number. The uniform vibrational patterns, which are inversely proportional to the radius, are in this case proportional to whole-number multiples (due to the fact that energy comes in discrete packets, or quanta) of the reciprocal of the radius (1/R). This calculation yields the vibration number. If the radius is decreased in size to R=1/10, the winding and vibration numbers simply switch, yielding the same total energy (see table below).

 

[mdeng]

Here's where I'm going - the nature of space is to propagate energy (rbj's interactions) at a fixed rate. The nature of our measurements of space and energy propagation causes them to always get the same result. But we realize that we may be moving relative to another system that got the same answer that we did, and we are puzzled. The answer lies in understanding the nature of our physical existence in natural space-time. That includes our measuring rods and our ticking clocks with which we describe our motions.

I like this view from another angle, though I have yet to see what I may reap from it. How would you think about the relation between this view of nature and the locality principle? Some claims that from that principle, it entails that the propagation speed must be finite, have an upper bound, and must be constant to all observers. If this claim is true, then the locality principle would be a more fundamental feature of the nature.

I think all the answers I have got so far have partially answered my original question. I now see SR as not dependent on some "ad-hoc" feature of light as it might appear, but rather as being built upon a more fundamental assumption of the energy/effect/force propagation speed of the nature. I am not sure whether Einstein thought that way when he presented his SR initially.

My other question, arising from the course of the discussion, was whether the 2nd postulate of SR is necessary (vs. whether it can be derived from Maxwell's equation). At this stage of my understanding, it seems that Maxwell's equation did not prove it was true for all reference frames (stationary, moving, or non-inertial) and its underlying assumption was there was aether in the vacuum. I think Einstein's 2nd postulation effectively says that the equation is assumed to be true for all moving inertial reference frames, regardless whether aether exists or not.