Light-speed is infinite, in a certain way?

[Ookke]

Let's call "ideal" space a xyz-space where is no limit for speed. "Real" space is the xyz-space with maximum speed c.

Now, the speed c in real space is in many ways similar to infinite speed in ideal space:

1.
ideal: infinite speed is always observed as infinite, regardless the observer's (finite speed) motion
real: speed c is constant to all observers

2.
i: finite speeds are never constant, but relative
r: sub-c speeds are relative

3.
i: finite speeds can be added, and the results is always finite
r: sub-c speeds can be added (in certain way), and the result is always below c

4.
i: if infinite speed is added to a finite speed, the result is infinite
r: if speed c is added to a sub-c speed, the result is c (light emitting by moving particle)

5.
i: no particle with mass can have infinite speed (it would have infinite kinetic energy)
r: no particle with mass can have speed c

6.
i: kinetic energy of a particle can be arbitrarily large, with large enough speed
r: kinetic energy of a particle can be arbitratily large, with speed close enough to c

7.
i: for any finite distance, the traveling time can be arbitrarily short with large enough speed
r: for any finite distance, the traveling time can be arbitrarily short with speed close enough to c


This is a short list, maybe it could be longer. Anyway, I think I made my point clear. The light speed c has many, most or maybe all the qualities of infinite speed, without actually being infinite.

I have very much difficulty to understand (and accept) the light speed as a universal constant and an upper limit for speed. Of course I'm convinced it's true, but I can't help this. Do you think it's of any use to seek this kind of analogies? Or should we go with "just the facts"?

By the way: Does a wave of light (a photon in vacuum) have a reference frame? What would be actually observed there?

 

[cesiumfrog]

That is a very interesting comparison. Incidentally, nothing can be observed by a photon (time slows to a stop as velocity approaches c, exactly as your "infinite ideal velocity" observer experiences everything for zero time).

But when it comes right down to it, you really can measure the speed of light (even with a fancy stopwatch inside a laboratory) and even though in principle you can easily measure something much faster, you never will (ie. if you do = nobel prize).

Finite "c" also gives a useful distinction between "later" events, "earlier" events and events which cannot be connected by light - even though their spatial separation is finite.

 

[Aether]

I have very much difficulty to understand (and accept) the light speed as a universal constant and an upper limit for speed.

Within inertial frames we define one-way light speed to be isotropic, and in the SI system of units we define the base unit for length (e.g., the meter) as a function of the speed of light. These are not fundamental physical truths at all, but something that is done to simplify practical calculations.

Of course I'm convinced it's true, but I can't help this. Do you think it's of any use to seek this kind of analogies? Or should we go with "just the facts"?

It would be better to learn what the facts really are, and then go with those.

 

[Aether]

But when it comes right down to it, you really can measure the speed of light (even with a fancy stopwatch inside a laboratory)...

We can calibrate our measuring equipment based on certain assumptions as to what we would like for the speed of light to be (e.g., what we have already defined it to be), but we can not really "measure" the speed of light or any other dimensionful constant.

J.P. Uzan, The fundamental constants and their variation: observational and theoretical status, Rev. Mod. Phys. 75, 403, (2003).

 

[robphy]

The notion of RAPIDITY, whose hyperbolic tangent is the essentially the velocity, (see my posts in https://www.physicsforums.com/showthread.php?t=125453 ) captures the ideas of the first post. In particular, the additivity of rapidity implies the relativistic velocity composition formula.

 

[cesiumfrog]

but we can not really "measure" the speed of light or any other dimensionful constant.

Bah. That may be true now, after relativity has taught us to define units in such a manner, but it's irrelevant to someone (like Romer or Bradley, or the average person today) asking how many of their paces light journeys per day. An exact answer exists, and my point was that it is so demonstratably finite.

 

[Aether]

... my point was that it is so demonstratably finite.

Yes, the round-trip speed of light is demonstrably finite.

but we can not really "measure" the speed of light or any other dimensionful constant.

Bah. That may be true now, after relativity has taught us to define units in such a manner, but it's irrelevant to someone (like Romer or Bradley, or the average person today) asking how many of their paces light journeys per day. An exact answer exists...

There are two distinct cases for conducting an experiment to measure the speed of light: 1) round-trip speed, and 2) one-way speed. We have already discussed at length in this forum why it is not possible to "measure" the one-way speed of anything in a coordinate-system independent way, so I will refer you to those discussions for the proof of that. You could really measure the round-trip speed of light in units of paces/day, but such units are rather arbitrary. For example, since the length of the Earth day is steadily increasing (in a few billion years it will be about as long as a month is today) what you have (inadvertently) proposed here is a VSL theory like Joao Magueijo's (neglecting for the moment that "paces" introduce additional problems as well) where virtually all of the fundamental physical constants (speed of light, elementary electric charge, Planck's constant, etc.) are linear functions of the moon's orbital radius. The paper that I cited above discusses this subject in great detail.

 

[Ookke]

Within inertial frames we define one-way light speed to be isotropic, and in the SI system of units we define the base unit for length (e.g., the meter) as a function of the speed of light. These are not fundamental physical truths at all, but something that is done to simplify practical calculations.

I'm a bit confused now (nothing really new about it, though).

When a photon travels from point A to point B, isn't that event well-defined, that is, an observer in any frame will observe the same travel. The distance between A and B is frame-dependent, and the traveling time as well, but the speed calculated will always be c.

 

[Ookke]

robphy, thanks for rapidity hint! It may be just what I've been looking for.

 

[Aether]

I'm a bit confused now (nothing really new about it, though).

When a photon travels from point A to point B, isn't that event well-defined, that is, an observer in any frame will observe the same travel. The distance between A and B is frame-dependent, and the traveling time as well, but the speed calculated will always be c.

Your failure to limit "in any frame" to "in any inertial frame" is the source of your confusion. The one-way speed of light will always be calculated as c in any inertial frame because of the way that inertial frames are defined. Not because there is any experiment that you can do to verify (or falsify) this; there isn't, at least not so far.

 

[Ookke]

Not because there is any experiment that you can do to verify (or falsify) this; there isn't, at least not so far.

So, the constant one-way speed of light is basically a lucky guess, which has been verified indirectly, by consequences?

 

[Aether]

So, the constant one-way speed of light is basically a lucky guess, which has been verified indirectly, by consequences?

No, a constant one-way speed of light has not been verified (or falsified) by any experiment or physical consequences either directly or indirectly. And no, Einstein's postulate that the one-way speed of light is isotropic isn't a lucky guess either. As it turns out, there is presently a freedom to choose how one synchronizes clocks that are located at two different places. If you assume that the one-way speed of light is isotropic, and use either Einstein's clock synchronization convention or slow clock transport to syncrhonize your clocks (which are at rest with respect to one another), then what you have done is constructed an inertial frame. If you allow anyone to construct an inertial frame around themselves, then SR (Lorentz transforms) is a tool for relating these various inertial frames one to another. It is a very convenient assumption for doing many practical calculations, and that is all.

 

[MeJennifer]

And no, Einstein's postulate that the one-way speed of light is isotropic isn't a lucky guess either.

Could you provide a source for that?

As far as I know Einstein never made such claims, I thought he simply made claims concerning the round trip speed of light.

 

[Aether]

And no, Einstein's postulate that the one-way speed of light is isotropic isn't a lucky guess either.

Could you provide a source for that?

As far as I know Einstein never made such claims, I thought he simply made claims concerning the round trip speed of light.

Sure. http://www.fourmilab.ch/etexts/einstein/specrel/www/" is a translation of Einstein's 1905 paper on special relativity.

If at the point A of space there is a clock, an observer at A can determine the time values of events in the immediate proximity of A by finding the positions of the hands which are simultaneous with these events. If there is at the point B of space another clock in all respects resembling the one at A, it is possible for an observer at B to determine the time values of events in the immediate neighbourhood of B. But it is not possible without further assumption to compare, in respect of time, an event at A with an event at B. We have so far defined only an ``A time'' and a ``B time.'' We have not defined a common ``time'' for A and B, for the latter cannot be defined at all unless we establish by definition that the ``time'' required by light to travel from A to B equals the ``time'' it requires to travel from B to A.

 

[Integral]

This thread has been closed for 2 reasons.

Note that our forum guidelines prohibit discussion based on idle speculation. Not only is the original post idle speculation it is pointless idle speculation.

Also the thread has been dominated by the pushing of a members personal pet peeve.

 

[pess5]

No, a constant one-way speed of light has not been verified (or falsified) by any experiment or physical consequences either directly or indirectly.

Well, I am supposing you know this to be true? However, Einstein build his postulates and kinematic model upon Maxwell's theory, which requires light speed to be invariant c in vacuum. Einstein simply accepted it.

Granted though, the Michelson/Morley null result arose from light paths which were reflected & refracted, and hence was not a 1-way light speed test. However, I offer this ... If the 2-way (or more-way) speed of light is always measured to be invariant c no matter how you turn your test apparatus, or no matter what time of the year you test it, it seems very reasonable to assume that the 1-way speed of light is the same as the 2-way speed of light. It would be interesting to see someone show mathematically how a light beam is always c in any and all multi-paths, but not invariant c in a 1-way path.

 

[Aether]

Well, I am supposing you know this to be true? However, Einstein build his postulates and kinematic model upon Maxwell's theory, which requires light speed to be invariant c in vacuum. Einstein simply accepted it.

Granted though, the Michelson/Morley null result arose from light paths which were reflected & refracted, and hence was not a 1-way light speed test. However, I offer this ... If the 2-way (or more-way) speed of light is always measured to be invariant c no matter how you turn your test apparatus, or no matter what time of the year you test it, it seems very reasonable to assume that the 1-way speed of light is the same as the 2-way speed of light. It would be interesting to see someone show mathematically how a light beam is always c in any and all multi-paths, but not invariant c in a 1-way path.

I am sorry, pess5, but since Integral want's this thread closed I will respect his wishes and no longer contribute to it. We have already discussed this subject at length elsewhere in this forum however, and you can simply do a search to find those other threads.