Light Speed

¿where is my error, if any?

When you said Einstein theories say that is not possible.

Einstein never said that. He said that matter could not travel at the speed of light. He also said that we (material beings) would always measure the same value for the speed of light moving in a vacuum.

Many thanks.

Forget Einstein. There are many misinterpretations of his theories: What changes with the speed is the movement of the clock or the biological development, not the time. Time is not any entity as distance or mass. Time is not measured by a unit of time but by the comparison of two movements. For the "time" being, distance is measured with a distance and mass with a mass.

What I see is that there are two things (light=energy+matter, or what) moving one with respect to the other at double the speed of light.

Then the light speed is not any unattainable speed limit.

Best regards,

Arturo

I know the speed of light is not increased when the emitter focus moves in the same vector direction of the light speed (I do not know how to say "sentido" in English: on a straight line there are two opposite "sentidos").

For an observer, let us say, placed on the Earth, the "point" of each of the two beams are increasing their relative distance at two times the speed of light.

Irrelevant the movement of the Earth.

Best regards,

Arturo

What you say makes sense and does not contradict my proposal.

I I take as reference system the point of one beam, the point of the other is travelling at 2C with respect to the point of the first beam, considered at still stand.

I think that the inertial reference system I have considered is valid, because the speed of light is always C, there is not any acceleration.

Question could be: can we consider the two front points of the beams being "mass" or what?

Scientists say light is mass + oscillation.

Thanks,

Arturo

El 'sentido opuesto' es lo mismo que 'opposite direction".

no the speed of light is not increased but what you may experience is a red shift. This is where if you are traveling in the opposite direction of the light, the wave length of light is longer, hence a red shift. Or if the light is approaching you from the source and towards your direction while you are approaching the light source the wave length of the light will be shorter or have a blue shift. p911

A few points of discussion. First off let us bring everything to usable terms. 400mph works out to a bit less than 178 meters per second, which is pretty damned slow I might add. Even the old .45ACP with a 230 grain bullet moved at almost 260m/s. The train is moving at mere 22m/s. However, the speed of light is 299,792,458m/s.

Just looking at these numbers tells us that, relative to the speed of light, the speed of the train, or even the speed of the pistol bullet, is quite insignificant. Considering the magnitudes of the speeds involved, it is virtually impossible to get meaningful experimental results with our present capabilities. Even present orbital velocities are insignificant compared to c.

However, let us suppose that we are on the bridge of a starship in sub-light combat against two other ships, with a fourth, neutral vessel acting as an observer and stationary relative to the rest of us. Let us further suppose that we are moving at .9c, one enemy combatant is directly astern and stationary, and the other ship is dead ahead and closing, and his velocity is .9c, all relative to observer. Now, all three ships open fire with energy weapons at the exact same instant, our ship firing at both enemy ships, and both of them firing at us, and at that instant where the enemy ships are exactly equidistant from our ship. For the purpose of this action, the fourth ship acts as a privileged frame of reference. So, what happens? Will all four beams strike at the exact same moment?

The point here is that, while Relativity makes certain predictions about what will happen, there is just no way to know for certain until we can actually conduct experiments, and I strongly suspect that the actual results from such experiments will be very interesting.

I think you got lost in the minutia and details that are not important to the concept I was trying to state.

It really is not important if the speed of the bullets is not grounded in reality, but the concept is.

The same applies with the laser pistols. While technically they don't exist and we don't know if they will in 100 years, the fact is that if both lasers are fired at the exact same instant and are equidistant from the target, any relative velocity between the moving target and the stationary laser is not a contributor to the final velocity of the laser.

The concept is valid in both examples.

"Considering the magnitudes of the speeds involved, it is virtually impossible to get meaningful experimental results with our present capabilities."

I think that is absolutely false. 1983, scientists have determined the distance light travels in one second more accurately than the definition of the standard meter.

We know the speed of light to an accuracy better than 1 meter per second, so a 22 meter per second change is quite significant.

Considering the magnitudes of the speeds involved, it is virtually impossible to get meaningful experimental results with our present capabilities.

GPS relies on the TOR, accurate measurement of the speed of light, etc. This stuff is not anywhere as magic as you seem to think it is.

The point here is that, while Relativity makes certain predictions about what will happen, there is just no way to know for certain until we can actually conduct experiments

We've done the experiments. So far, relativity is as certain as the effects of gravity or F=MA.

Good explanation. If my facility for giving you a GA worked, I would do so.

Since sunlight travels on the " fabric of time", and is curved around any mass (including black holes) embedded in it, would not the speed of light be pushed outwards a bit and take more time A to B. Is the shortest distance between two points a straight line?.

Oh, Anonymous Hero,

I agree with your example:

I a focus of light (the laser pistol of the cop on the train) is moving at v speed, this v speed does not add to the speed of light, C, of the laser pistol.

I am reviewing the relativity formulas. It will take some time, I must be careful.

But I think that the relativity theories are tautological. And the formulas, indeed.

I will see.

One remark:

Cesium (or quartz) oscillations are movements, more precise than these of a mechanical clock, but movements:

What we call time is not measured by a unit of time, but by a comparison of movements:

While the clock turns the minute arrow 360 º, the cesium atom makes b oscillations or movements. (I do not remember b)

Buenas noches.

Good night,

Arturo

I am interested in your post about the photon/s from the sun. It leaves the sun, travels, and gets to our eye in about 8 minutes. The same photon (am I mistaken) leaves a distant sun, travels, and gets to our eye in about, lets say, 8 years. I have been looking directly into the morning and evening sun, (20 minutes or so) and can feel the photons absorbing into my optic nerve. During the day when my eyes are always away from the sun (don't want to burn them), the same photons come from a direction other than the sun, and affect me differently. When I look at that distant star, the photon still hits my optic nerve and gives me the same energetic and amazing feeling, and I have come to the conclusion that our ancestors used this energy, morning and evening and night, to keep themselves "energized" for each day. Then, in the not to distant past, the sun "God" RA, etc. was wiped clean from any tabloids, and replaced. The photon must be a true energy from the universe, and, except for the energy of the heat, it goes unnoticed as an "energizer", in this day and age. We all talk about saving energy, why not save it, by letting more direct sun/star light into our optic nerves? I am interested in your opinion about these photons traveling at the "speed of light", and their affect, other than heat.

The error is in saying that the source of one is twice the speed of light relative to the other. The speed of light is always measured to be the speed of light. If there were something moving faster than the speed of light, we could not know it since we could not measure it. It just cannot be.

"If there were something moving faster than the speed of light, we could not know it since we could not measure it. It just cannot be."

Ummmm - well we could, and do (in one direction), and "it can be" if one applies some "falling apple" logic to observed events in astrophysics.

"cannot usefully be" or "energy affordability be" might be closer.

'jus' sayn' - not pickin'- only lurkin'

What do we measure as moving faster than the speed of light? In vacuum, of course; I know we can do it in other media. We might infer it, but I don't know what we measure. I haven't kept up on cosmology after people starting making fun of my BF theory.

Sorry missed this earlier - one thing we measure that is faster than light is time.

No, I am not being flippant - time is an underpinning of the whole concept - and is often "assumed" another 'constant' by folks dealing in BS deductions like mass or energy become 'infinite' at C - as opposed to C² - there is quite a gap between those values.

Mr E also 'pondered' the impacts of the time as a constant concept.

Actually, not. Time moves at the speed of light. It's easy to see; just set your watch on the table and let it be. It'll move forward through time at the speed of light.

Yes ¡¡

Arturo

If Einstein North (running along the light) collides with Einstein South - We will have an Einstain.

Yes.

ArthurEinstein

You sort of summed it up in your OP. If there are two beams of light, each one is traveling at the speed of light. Just because they are going in the opposite direction, doesn't make the speed of light faster.

If two cars pass each other, each going 60 mph, their speed is not increased just because they are going in opposite directions.

But the relative speed of one vehicle with respect to the other is 2 times 60 mph= 120 mph.

Does the same occur when talking of two beams of light?

Please read again my first proposition.

Thanks,

Arturo

I would think so, of course, I may not be smart enough to even be commenting in this thread.

If two beams of light aimed directly at each other collided, the relative speed of the collision would 2x the speed of light. But, since light has no mass, that collision could never take place. So the speed of light is always the speed of light.

I'm going out on a limb here, and am totally prepared to be publicly shot down if I'm not making sense.

The idea in this thread simple, but interesting. If there are two stars shining on opposite sides of the earth, the light from them both covers a distance twice as great over time than from just one does. This can be done repeatedly for any number of light sources regardless of the direction of travel. The total distances covered by the beams emitted from all sources under consideration will equal the sum of the distances of the individual light beams.

Thanks.

"Time" is not any entity.

When a clock is onboard, it is the movement (or vibration) of the clock what becomes slower.

If you eliminate the variable T (for time) in the physical equations, you will find the surprising results I have found.

Best regards,

Arturo

I gave you a GA because our way of looking at things depends on the conventions that we set up. It's relative!

Please, what is a GA?

Never mind whether it is polite for me or not.

I only wish to learn.

Thanks,

Arturo

Oh no worry, that is short for good answer. We write it as GA, but the proper abbreviation is actually g.a.

Thanks, many thanks.

I agree.

The speed of the forefront of one beam al light with respect to the forefront of other beam going opposite, is two times "c".

Obviously, it is relative speed.

Then...

Arturo

The Doppler effect is used to quantify the relative velocity of a light source with respect to the observer. The result is a shift either toward red or toward blue depending on the sign of the relative velocity. This is possible because light has a constant speed but frequency changes.

Dr. Moose said: What Prof. Einstein actually said was that, if you measure the speed of light in a vacuum, "c", the value you observe will always, always, always be the same, thus making "c" a constant. In a way, this made the speed of light the only (sort of) privileged frame of reference.

I agree, but I'd cast a slightly different light on it, that might help others (or not). Let me say it this way:

All the experimental evidence of the previous 20 to 30 years said that the speed of light could not be exceeded. So, then Einstein (and others) set out to figure out why and develop a theory that could explain the results found so far and then predict further results based on that theory.

That is when Einstein developed his theory, which, to fit reality, had to say "if you measure the speed of light in a vacuum, "c", the value you observe will always, always, always be the same, thus making "c" a constant. In a way, this made the speed of light the only (sort of) privileged frame of reference."

I hope this helps!

Velocity is measured in terms of distance per unit time; miles per hour, meters per second furlongs per fortnight, etc.

Consider the problem another way. Imagine you are on a space ship traveling toward a star.

Before ignition, you are at a relative velocity of zero and the photons that strike your retina from your destination star do so at the speed of light, C.

As you propel towards your destination your velocity increases and your science officer, Mr. Spook (you are leaving on Halloween) begins measuring the speeds of the incoming photons from your destination star.

As you approach light speed you ask for the data your science officer has been collecting and notice that each photon, regardless of the ship's velocity, has the same velocity that the first measured photon did before ignition of the impulse drive.

You smile as you have confirmed, once again, that Einstein has not been proven wrong yet.

Einstein predicted that effect in 1905 and it has to do with one's inertial frame of reference. Yes, everything is relative and it's called the Special Theory of Relativity or STR. Essentially, the speed of light is constant in all frames of reference.

You can wade through all of the information HERE on the theory. It is more than I can explain in brevity.

This of course will not be proven to be true until we are able to take measurements from the deck of a starship, though for now, this is the accepted theoretical belief. That was my whole point. We will not actually know for sure until we go out and do it. And, what we observe when we do will quite possibly yank the rug right out from under Relativity. Who knows? I certainly don't, and anyone who says he or she does is making too much soup from one bone (so to speak).

I think there is proof. There have been numerous experiments concerning the speed of light and some have been performed on spacecraft, all confirming Special Relativity's theories.

We haven't been able to test this at speeds close to C, but our discrimination ability with our instruments allows us to confirm the results at much slower speeds with a very high degree of precision.

The long and short of it is, no holes have been found in the theory, to date, and a lot of work has been done to try to poke holes in it.

But, but....The Earth IS a starship, and we have taken all kinds of measurements from it.

:O

So there is an speed higher than the light speed.

Einstein theories say that is not possible.

¿where is my error, if any?

Your error is in your understanding of the theory of relativity. Two photons moving in the same direction in parallel beams have a relative speed of 0. Two photons converging have a speed relative to one another of 2C. Which of Einstein's theories says that a closing speed of 2C is impossible? (The observer is is between the light sources, and the light sources are not moving relative to the observer.)

Thanks.

You say:

"Two photons converging have a speed relative to one another of 2C."

Thanks, that is mi first proposal, written in other terms.

Some scientists say that light is vibration and mass.

I have not read all the Einstein´s physical theories, then when I say that the max. speed accordingly with Einstein´s writings is C, it is because i have read that from comments made to Relativity, and it is said very often.

But it is for the first time that anybody (myself) tells of an example of speed, although theoretically considered, higher that C.

Best regards,

Arturo

Velocities do not add by simple (Euclidean) addition. It has been too long since I studied this to remember the formula, but it relates to the Lorentz contraction, involving a factor of √(1-v²/c²). Lancelot Hogben's Relativity for the Million, or Martin Gardner's Relativity [I think that's the title, but there might be more words in it], might be helpful, or any modern physics textbook.

Einstein theories state about absolute speed of light & not about relative.

This thread has become a little confusing and from what I see a bit off track on the original question.

From what I understand Arturo states "The light of the Sun takes 8 minutes to reach the Earth. Therefore there is an starting point of the Sun light beam travelling in the space."

Assuming that this is a statement of fact.

He then states "Imaging two beams of light, parallel, traveling one opposite to the other."

So, imagine the sun giving out a beam of light 180 degrees to each other (I know the sun is a sphere and emits light from it's whole surface before any comments).

What Arturo is asking if I am correct in his question is -

If you turned off the sun (impossible I know, ok not impossible, but for now) and then turned it back on again, if you were to sat something on the start of each light 'beam' the opposing distance of the two objects would be twice the speed of light.

The problem is that the speed of light is a measurement of time that light takes to travel so it is what it is, there is no such thing as twice the speed of light. Although both objects would be moving away from each other at 599,584,916 m/s.

Twice light speed is just a term but in reality is not possible.

It's like saying the max speed of a Buggati Veyron is say 220 mph and instead of saying a plane travels at 440 mph it is actually travelling at twice the speed of a Bugatti Veyron, not a true terminology of speed.

Thanks for having well interpreted my proposal.

It is more clear like that:

One light beam starts from the Sun. "At the same moment" other one starts from the Earth towards the Sun, directed to the starting point of the beam coming from the Sun. (we must assume that for several minutes the sun and the Earth do no move)

The two front points of the light beams will travel, one with respect to the other, at 2C. It will take approximately 4 minutes to meet each other.

And for an exterior observer, the two front points of the beams are approaching each

other at 2C.

Scientists say that light is vibration and mass.

Then...

Best regards,

Arturo

Then... what?

Anonymous Hero ¡

...then, taking the point of one beam, as reference system (valid because the speed of light is invariant) the front point of the other beam is moving at 2C, unless you apply the relativity formulas and calculate that this speed is not 2C.

It is a very simple case.

Thanks,

Arturo

May I try an explanation although after so many it will not bring some thing very new.

Let assume a source in a space free from mass distortions so that light travels straight. Let assume that from this source 2 photons are issued at exactly same time and start their trip at an angle 2θ.

The distance between the 2 photons versus time will be D= t * c* 2* sinθ where t= time, c= light speed.

Both photons travel at "c" only the "distance " between them will increase with a "time rate" 2*c*sinθ". This increase rate has noting to do with the movement it self. If θ=90° then the rate with which the distance grows will be 2*c. But again this NOT a particle speed since both particles continue to progress with their initial speed ="c". The confusion is between particle speed and distance rate of change.

The relative amount of confusion on this subject is demonstrating that a number of people are in the dark when it comes to the properties of light.

To be sure!

Yes ¡

And also in many other fields.

Best regards,

Arturo

The speed of light observed at any particular point of reference (coordinate system) is always "c". The speed of light in invariant.

Note that if a point of reference is in motion relative to another point of reference, then an observer will notice the peculiar phenomena of time dilation and dimensional changes that cause the first point of reference to measure the speed of light as a constant.

At any particular point of reference (coordiante system), everything always looks "normal", i.e. the speed of light in any direction is always a constant. Other characteristics of light, such as the wavelength, however, will vary depending upon the relative motion with regard to the source of light.

Your explanation seems to reflect what the Relativity says, and is very clear.

But for an exterior observer looking at the two beams, at what speed and why, explained in a simple way, will he see the two front points approaching each other?

Thanks,

Arturo

Arturo:

An observer will always see light traveling at speed c no matter what. Light coming in from any direction will be measured as speed c.

Remember that to see light and assuming a vacuum, you have to be in the light beams. If you are observing two light beams, they are both pointed at you.

Each beam will be measured at speed c. If they are arriving 180 degrees from one another along the "x" axis, for example, beam 1 will be moving at speed c to the left and beam 2 will be moving at speed c to the right. Therefore, the observer will say that the relative speed of the two beams is twice the speed of light, or 2c.

Note that this does not violate the theory of relativity. Both beams are still moving at speed c in the coordinate system of the observer.

Thanks, many thanks.

That is what I say from the beginning.

I never said the light to travel at more than C, but that the relative speed of the two front points of two beams of light traveling opposite on parallel rectilinear paths, is 2C, as seen by an exterior observer.

With respect to the point of one beam, taken as reference system, the other point of light is travelling at 2C? I think yes, but maybe I am wrong.

Do the relativity formulas, applied to this case, show that it is not so?.

Please, anyone who knows how to calculate this speed, send the calculus.

It is very simple case.

Best regards,

Arturo

Arturo:

An interesting "factoid": There is no way that you can observe or measure anything about a light photon moving directly towards you until it hits you. You would not know a thing until it hit you, a big hit coming out of nowhere. You cannot "see" the photon before it hits because it is moving at the speed of light. Intelligence about it cannot get to you before the photon strikes.

If you ride on a photon, you cannot be seen by anything that is in its path. In other words, no one is going to get out of the way because they cannot see it coming until suddenly -- ZAP.

Once again, in all frames of reference, the speed of light does not change. No matter what, in any coordinate system, you will never measure anything going faster than the speed of light.

It makes no practical sense to talk about an observer traveling on a light photon. That is clearly impossible.

The formulas were provided to you in one of the previous posts concerning how to calculate what an observer will see. They are correct and will give you the right answer for any problem dealing with Special Relativity.

It is better to think about your original postulation of two coordinate systems moving at 0.75c towards each other as measured by an observer in a "stationary" coordiate system sitting between these two "moving" coordinate systems.

As noted before, the "stationary" observer will measure the relative velocity of the two "moving" coordiate systems as 1.5c, with each moving at a speed of 0.75c.

Use the equations previously provided, and you will find out that from the perspective of one of the "moving" coordinate systems, the stationary observer is approaching at 0.75c and the other "moving" coordinate system is approaching at a speed less than c. In any coordinate system, you will never measure any object or light beam moving towards you or away from you at a speed greater than c.

I know that this is not intuitive, but it has to be the case or else the universe falls apart. There is a limit to how fast things can propagate in the universe. No one can receive information or observe events faster than the speed of light with the possible exception of God. Creators tend to give themselves Superuser rights.

Actually, once you get used to the "simple" fact that nothing is measured as moving faster than the speed of light in any coordicate system, things fall into place very logically after that. You just have to think about it long enough and play with the equations until you get the physical feel for it. The Divine Intelligence is awesome the way it all fits together. Wow.

I will do so.

Many thanks.

They say for God time is irrelevant, so speed. No problem.

I say that God creates the Universe, and all its innumerous configurations are known (and loved) by Him.

Arturo.

Arturo:

Such incredible effort to tie up the loose ends in such a magificent way seems to have a lot of passion behind it. God's creation from sub-atomic particles to rainbows and butterflys and galaxies is vastly beyond incredible. It humbles all thoughtful people.

The more I know, the more I know I don't know, and the more amazing and awesome all creation becomes.

I agree.

Creation is one of the revelations of God.

The god we think of, is not the God who is: Yahweh.

Best regards,

Arturo

Arturo wrote: With respect to the point of one beam, taken as reference system, the other point of light is travelling at 2C? I think yes, but maybe I am wrong.

Here you are wrong, and this is the surprising thing which made Einsteins hair stick out like you see it in pictures ;-)

It is c, not 2c.

This was demonstrated by things like the Michelson-Morley experiment. This was explained (somewhat) by the Lorentz contractions and more thoroughly by Einstein's theories of relativity.

If you follow the math (that comes from the Lorentz contractions / Einstein's theories), you will find this formula for speed contraction, where, for our purposes, u is the speed of the observer, and v is the speed of what is being observed--in this case, the observer, in the head of one beam of light, is traveling at c, and the beam of light that he is observing, is also c (in its, and, in fact, all frames of reference):

Here is the formula for the observed speed in the case described:

Oops, I need to find the formula, and I need to stop using my eyes for a while--I'll try again later--if you want to, look for it yourself on:

http://www.relativitycalculator.com/addition_relativistic_velocities.shtml

I hope this helps!

Ok, here is the formula I was looking for... the relative speed in the situation where the observer is on one beam of light (moving, obviously, at c) and is watching a beam of light approaching him (at speed c) is calculated as follows:

= (u + v) / (1 + (u x v)/c^2)

In this scenario, both u and v are c, so:

= (c + c) / (1 + (c x c)/c^2)

= 2c / 1 + c^2/c^2)

= 2c / 1+1 = 2c / 2 = c

Hope this helps. Depending on what you're thinking (or what I think you might be thinking ;-), I'll write more later.

Like I mentioned in #42, one of the other very convincing arguments / experiments for me is the muon decay experiment, which does a pretty good job of proving that time really does slow down as the speed of light is approached. Read up on that, if you don't understand it, ask questions.

The place I found a good description of that was:

http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

... near the end of the page, in a section called "Experimental Evidence for Time Dilation: Dying Muons"

Hope that helps!

Many, many thanks, I thought my case of light speed was very simple to calculate.

But you are the only who has given all of us a mathematical response, in agreement with relativity theories.

I see:

When u and v are very small with respect to c, u/c and v/c become negligible and

V relative=u+v, in the limit.

"... near the end of the page, in a section called "Experimental Evidence for Time Dilation: Dying Muons".

Many thanks for that, also.

In due time I could come back to you. It seems to me that you know many things. Congratulations.

Arturo

You are welcome! I am happy if I have helped!

(I just hope I haven't made any silly math mistakes!)

You are welcome to come back with more questions at any time--I am sure they will help me to learn--either to learn more about relativity, or to learn more about how to teach relativity. (I won't guarantee that I will always be "monitoring" this forum (or even any part of cr4)--you may have to track me down elsewhere if I don't respond. (OTOH, I know that any of the others here can answer your questions also.)

I would point out two things:

* Remember that the problem with the speed of light came first, the theory to explain it (along with the math) came second; hence my thought of focusing on the problem first, and the math later. But, I was exposed to theory and math first (before I knew the problem--I might have been asleep in that class ;-)--it worked for me, but took 40 to 50 years. ;-)

* Those links I gave to the physics lectures--there are other lectures in that series that are also very helpful--look at the few just after the one on the Michelson-Morley experiment. (The one about the light and mirrors on a (big) train is a good one--can't recall any more details atm--you'll recognize it.)

rhkramer, have a good day.

Many thanks.

I will review the Lorentz concepts and formulas, and the Michelson-Morley experiments and others. I will look for them in the address you gave me. Thanks.

Best regards,

Arturo

Albert Einstein also said "For the rest of my life I want to reflect on what light is".

Light has always remained a great mystery.

Rajan

Interesting discussion, and of particular interest to me as I have a desire to teach relativity to pre-schoolers. (I may have to settle for teaching kindergartners, but I can live with partial success ;-) Also, I really shouldn't be taking the time to respond to this right now, because I have some other things I must do, but I thought I'd make an attempt--I'll edit it or replace it some time in the future.

There are a few ways I might approach this, but let me start here...

I'm going to say that Einstein didn't predict that the speed of light could not be exceeded--he tried to explain how to make sense of that fact...

Read up on some of the Michelson-Morley experiments, especially the one where they tried to measure the speed of light with and against (or crosswise) to the "aether wind". They devised and executed an experiment to measure the speed of light along the path (in the direction of the path) of the earth's travel (what is that--900,000 m/sec or more (according to http://curious.astro.cornell.edu/question.php?number=507--they say 900 km/sec), and crosswise (at right angles) to the path of the earth's travel.

Aside: maybe I shouldn't count the entire velocity of the earth, maybe the only important part for this narrative is the 30 km/sec (30,000 m/sec) representing the speed of the earth in its orbit around the sun--so let's just consider that...

(Here's one page discussing the Michelson-Morley experiments, picked almost at random (after a google search)--the first experiment (measuring the speed of light) is not the interesting one--the second one (measuring the speed of light in the direction of and across the "aether wind") is the one you want to pay attention to:

http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html

)

Someone familiar with Newton's physics would have expected the speed of light in those two directions to be different, but, to a very great level of precision, it was the same in both directions. (I think their experimental error was in the range of 30 m/sec (nowhere near the 30,000 m/sec representing the velocity of the earth in its orbit around the sun)). (I don't know if they did their experiment in metric or English units.)

That 30 m/sec margin of error can't explain why there is not a difference of 30,000 m/sec due to the earth's speed in its orbit around the sun.

Anyway, this was the big surprise--the speed of light was measured, to a great level of precision, to be the same whether initiated along the path with what could be considered a speed boost (head start) of 30,000 m/sec or without that speed boost.

(I know, my description above isn't completely accurate or convincing (nor worded very well--I need to edit more)--I should explain and, obviously, understand this better--I guess the better way to understand / explain it is that in one case, they shot their beam of light out in the direction of the path of the earth (presumably getting a 30,000 m/sec speed boost) and in the other case they shot the beam of light out at right angles to that path (not getting the advantage of that speed boost) and, to within 30 m/sec, they measured the same speed for both beams.

But, in a way it doesn't matter what I understand or can explain--really, the great physicists / scientists at the time (Michelson, Morley, Lorentz, Einstein) realized that there was a problem--the speed of light was measured to be the same in two frames of reference moving at different speeds.

Newton had to be turning over in his grave.

Lorentz came up with formulae to describe things like a length contraction to explain the puzzle.

Einstein carried it a bit further, developing his special and general theories of relativity. (Which I am tempted to rename theories of non-relativity--speeds were relative in Newton's world--in Einstein's world they were not, or at least the speed of light (in a vacuum) was absolute, not relative.)

So--well, I'm leaving out some things I meant to say (because I'm old and forgetful), but let's now go to the original question, and let me phrase it this way:

Suppose there is an observer between two sources of light, aimed towards him.

But let us also add two other observers, one at the head of each of those two light beams--let's figure out what they each see.

Let's assume the observer between the two sources of light is at rest (not necessary, it just gives me one less point to be confused about). As at least one other person on this thread has stated, that observer will (or could) measure the speed of each light beam, and he'd find that each light beam (assuming we're all in a vacuum here) is traveling at c.

Also, as someone else has stated, if that observer did a calculation to find how fast the two light beams are approaching each other, he'd find that to be 2 times the speed of light. (As others have stated, neither beam is traveling faster than c, but, from the point of view of that observer, the head ends of the two beams are approaching each other at a "calculated" speed of 2c.)

Ok, now what about an observer traveling at the speed of light (impossible though that may be) at the head of the first beam, call it beam A? According to Einstein (and as demonstrated by the (2nd) Michelson-Morley experiment), that observer will see the other beam (beam B) traveling at the speed of light, c. And likewise, the observer at the head of beam B, traveling at the speed of light, will likewise measure the speed of beam A as being c.

Scratch your head--Michelson, Morley, Lorentz, Einstein and others all did the same thing--you're in good company.

Now I'm hesitant to say what the observers at the head of beams A and B see when they look at the observer in between them. Maybe I should wait until I think about it some more, but that rarely stops me... ;-)

Digression: There is (theoretically) no beam of light coming from that observer in the middle (but, if I understand Heisenberg at all, that statement is incorrect--the only way an observer anywhere else could observe the observer between the two beams is if that observer is emitting (or, at least, reflecting) photons.

The root of the Heisenberg uncertainty principle, is, iiuc, those photons used to observe the observer (or anything else) carry momentum--and, to observe something, that something has to be struck by one or more photons. Those photons carry momentum which will change the momentum (i.e., the speed or position) of what you are observing, thus resulting in the uncertainty.

/Digression

Back to what the observers in the beam of light see of the observer in the middle--hmm, I'm hesitant about that, but I want to say that they'd appear to be approaching that observer at the speed of light. (But they wouldn't see a beam of light whose speed they could measure.)

So, they'd measure the speed of light for the other beam to be c, *and* they'd calculate that they are approaching the observer in the middle of the two beams at c. (Like I suggested earlier, scratch your head ...)

It's a little like that old adage that I won't quote quite correctly--when you've eliminated the impossible, what remains, however improbable, must be the truth. They found that the speed of light didn't vary based on the speed of its frame of reference, and now they had to explain it... So, they came up with an explanation that has stood the test of time.

So far as I know, none of the other theories of advanced physics (quantum physics, the multiple dimension theories, and so forth), have disproved any of Einstein's theories. Nor have any more recent experiments disproved that the speed of light is the same in all frames of reference.

If I could edit my previous comment (which, it seems, I can't now that somebody else has commented after me), I'd change the following paragraph, somewhat:

Ok, now what about an observer traveling at the speed of light (impossible though that may be) at the head of the first beam, call it beam A? According to Einstein (and as demonstrated by the (2nd) Michelson-Morley experiment), that observer will see the other beam (beam B) traveling at the speed of light, c. And likewise, the observer at the head of beam B, traveling at the speed of light, will likewise measure the speed of beam A as being c.

Maybe to read like this:

Ok, now what about an observer traveling at the speed of light (impossible though that may be) at the head of the first beam, call it beam A? According to Einstein (and as demonstrated by the (2nd) Michelson-Morley experiment), that observer will see the other beam (beam B) traveling at the speed of light, c (not 2c as Newton and a host of others would have expected). And likewise, the observer at the head of beam B, traveling at the speed of light, will likewise measure the speed of beam A as being c (again, not 2c).

And you are going to try to teach all this to pre-schoolers!? These concepts are not understandable by any but a few of the brightest high school seniors (at least here in the USA).

More power to you if you can do it!

Thanks!

I'm quite certain it can be done, I'm also quite certain I won't accomplish it alone, but I can start...

Ok, I've now learned that I can edit one of my previous comments for only 15 minutes after posting it (and I didn't make it in this case)--I meant to add:

The lecture series by Michael Fowler, titled "Galileo and Einstein", is particularly helpful (imho). The home page is at:

http://galileoandeinstein.physics.virginia.edu/.

I haven't seen or read any physics lectures in a long time--quite possibly there are others that are just as good or even better.

I think it's good for at least two reasons:

* the seemingly irrelevant beginnings of the series: on Babylonian number systems, the Pythagorean's problems with irrational numbers, and such, do provide a storyline to introduce the scientific method: people trying to figure out the world around them, making theories, disproving them, making better theories, ...

* the few lectures after the one on the Michelson-Morley experiments give some solved examples of the conundrums that stem from the theories of relativity. He (Martin Fowler) lets you see how confusing and possibly contradictory some of the results can be, then goes through and clarifies the situation and shows that there is no contradiction after all.

I found the experiment with the moving and stationary Einstein light clock and the decaying muons to be especially helpful:

http://galileoandeinstein.physics.virginia.edu/lectures/srelwhat.html

Please, an observer who were looking at the two beams, would not compute the two points of the beams approaching each other at 2C?.

Thanks.

Arturo

Arturo wrote: Please, an observer who were looking at the two beams, would not compute the two points of the beams approaching each other at 2C?.

Yes, you are 100% correct! Well, I think you are...read on.

Thank you for reading my comment #44. I hope you also read my comment #42, as the comment in #44 was only a small clarification or added emphasis to what I said in my long-winded comment #42.

I hope it was very clear in #42 that I am considering three different observers--one observer (not moving) in between the two beams of light, and two additional observers, one in the head of each beam of light (and moving at the speed of light).

I hope it was very clear in #42 that I agreed with you, for the case of the stationary observer between the two beams of light. That observer can calculate that the two beams are approaching each other at 2c. (But, note that neither light beam nor is anything else traveling at anything over 1c.)

Now, for the observers in the head of the light beams, they will see that they are approaching the center position (the central observer) at c, but they will also measure the speed of light in/from the other beam as c (not 2c).

I would like to write more, and I will, because I think I can help you understand the theory of relativity. Unfortunately, I have a headache (for several days) that makes it hard to write the way I want to write. When that clears up, I will write again.

Maybe I'll try to say a little more now, and try to say it a little more clearly later. The page that, iirc, Anonymous Hero mentioned on calculating relativistic velocities in parallel is quite useful, especially if you want to follow the math.

http://www.relativitycalculator.com/addition_relativistic_velocities.shtml

However, I wouldn't start with the math--as it happens, I got a pretty good grounding in math and the math associated with Lorentz contractions before I felt I had an understanding of relativity. (And, for reference, the biggest kick start I got to understanding relativity was reading Stephen Hawking's book, "A Brief History of Time" (which I'm currently re-reading).)

The key for me was finally understanding (and maybe accepting at a gut level) what the (2nd) Michelson-Morley experiment showed--that we (that is nobody) could find any evidence that light ever exceeded c, even when it sure seemed like it should. Again--when light was "shot out" in the same direction the earth was moving (and the earth was moving at 900,000 m/sec) it was no faster than light shot out at right angles to the path of the earth (i.e., without the speed boost of 900,000 m/sec).

So, after lots of anguish over trying to decide whether to believe this or not, Einstein (and lots of others) set out to try to find an explanation.

It might help you to try to find a theory/explanation for yourself. I can think of two right off the bat (because my mind has been conditioned--just like Einstein's was--more below):

Theory one: light and other objects can move freely up to the speed of light, but there is some sort of speed barrier at the speed of light which nothing can exceed. You can move anything at .75c, .90c, .99c, .9999c, even 1.0c with no problems or consequences, but nothing beyond 1.0c. (and no sort of "friction" or other opposing force before you get to 1.0c+).

Theory 2: There is some force, or friction, or something that opposes motion the closer you get to the speed of light, until, at the speed of light, that opposing something is infinite, and you can't get past the speed of light.

Einstein and others already had clues that would make the 2nd theory fit with other things that had been discovered, like the Lorentz contractions that occurred as you approach the speed of light.

I'll just about stop here--right now I'm trying to read a little more about Lorentz and how he discovered the Lorentz contraction. It sounds like I'm going to read about the field around some thing that was distorted because of its high speed...

I hope this helps!

You are very brilliant and didactic ¡

Best regards,

Arturo

Arturo wrote: You are very brilliant and didactic

Thank you! I'm afraid that I might write a long-winded reply here, and I don't think I want to do that. In short, I flatter myself to think that I am a human of about average intelligence (by intelligence, I mean learning ability), I have been exposed to a lot of knowledge, I have absorbed some, and I am still capable of learning.

Your question(s) give me an opportunity to expand my learning, and to head in the direction of one of my goals (teaching relativity to very young children), and I take particular pride in your use of the word didactic--hopefully I am occasionally able to teach (when I apply myself to that).

BTW, I'd like to clarify my goal of teaching relativity to very young children--and I won't do it completely here, but it is not because I think that relativity is the most important thing for children to learn. On the contrary, there are many things that are far more important (for example, helping discover or implement the policies (or attitudes) that can help us all to live good lives on the planet earth and beyond).

Among other things, understanding relativity can help with their self esteem. Around the time I was in college, there was (iirc) the statement still floating around that there were only a very few people capable of understanding relativity (and, btw, I don't claim a full understanding of relativity--I understand a lot more than I used to, and hope to understand the rest--but even with what some might judge as an almost complete understanding of relativity, there are, in many things, different perspectives / details that a person with a good overall understanding of relativity, might be surprised by.

I've been trying to understand relativity for 40 or 50 years, and only in the last 10 years started to get a decent handle on it (with the reading of Stephen Hawking's "A Brief History of Time"--more specifically, the insight that Einstein didn't just wake up one morning and invent those theories, but instead, that Einstein and others found a problem--(the speed of) light just didn't behave according to the current theories at that time, so Einstein, and others, tried to figure out more correct theories). And furthermore, Einstein had quite a bit to build on, for example, things like the Lorentz contractions were something he was exposed to.

Now that Einstein and others have figured out the best current explanation (of why the speed of light cannot be exceeded), why should not all of us have at least a general understanding of that explanation? It's part of our human culture--it's an achievement of man that we can take at least some pride in. It's a shared insight about the universe. ....

And maybe the next Einstein, the one that is going to create the next "current best explanation" (or the one that is going to find the error in Einstein's theories) is out there, but hasn't been taught physics. (I'm ignoring that there are other theories out there already, that might be that next step--I won't go into those--but, iiuc, the current main puzzle is how to combine relativity with quantum theory, and theories have been advanced in that direction.)

And, maybe learning relativity is a little bit valuable in the same way that learning the alphabet is--a bit of background that may be useful in all kinds of ways which we don't yet foresee.

(BTW, I'd like to teach lots of similar subjects to pre-schoolers--calculus, maybe thermodynamics, and then try to move on to things like psychology, sociology, economics, politics, ....)

Although I started to get a good handle on relativity maybe 10 years or so ago, in the last few months I made some renewed progress. (In defense of my having taken 40 to 50 years to get to the level of understanding I currently have, it is not my day job. ;-)

Your questions come at a good time for me.

Like I hinted at in some of my other comments, in some ways, my learning is only barely ahead of yours (and I hope and trust you will catch up and exceed mine).

For example, I can see that Einstein benefited greatly from the contributions of Lorentz (the contractions)--but I don't understand what drove Lorentz to come up with those. I'm now reading to try to learn how that came about--I think it has something to do with Oliver Heaviside and what he called (iiuc) ellipsoids--the distortion of the (electromagnetic) field around an object moving at high speed (maybe it was an electron, or something like an alpha particle (a hydrogen or helium nucleus))--maybe by the time you ask your next question, I will have learned enough to answer it--or maybe your question will provoke me to learn something else.

And nothing I say here is intended to reflect at all on any of the others who have responded to this thread--I suspect they all understand relativity better than I do--maybe in a few cases I've found a way of thinking that happens to match your way of thinking so that you may more easily understand.

As is often the case, I wrote too much, and didn't carefully plan what I was going to write. Thus, I'm sure that the above needs editing to come closer to what I really want to say. But, to keep it simple, thank you for your compliments, I know I'm not a genius, and I hope I always remember that...

Sometimes I like to think that "I'm just a man whose intentions are good (I hope, or at least usually), ..., please don't let me be misunderstood" (Benny Benjamin, iirc). ;-)

I may make some brief comments to some of your other recent comments, but only where I want to point out something else that may help you. (And, with that, I'll try not to revisit this subject again, at least not on this thread.)

I'd like to correct the quote and the attribution from the previous post (as well as my modification of it)--I'd like it to read:

"I'm just a soul whose intentions are (usually, I hope,) good, ..., please don't let me be misunderstood" --Horace Ott (but I'd like to also credit Benny Benjamin and Eric Burdon)

When observed from one of the other beams of light, the other beam of light would be meaasured to be traveling at the speed of light. You however, are probably stuck in the same moment of time for enternity as time has stopped for you. Pray for a black hole to suck you and end your spacely veil of tears ......

In your frame of reference, everything is normal. Remember that we are talking about relative motion. All motion is relative to a coordinate system. Any coordinate system that is not experiencing acceleration can be considered "stationary".

Let's say that we are in coordinate system A and we consider ourselves stationary. Then we count all motion of other coordinate systems as not stationary. For example, the people in coordinate system B might consider that they are stationary but that system A, our "stationary" coordinate system is in motion compared to them.

If coordinate system A is moving at nearly the speed of light relative to B, then A thinks that B is just about stuck in the same moment of time, and B thinks that A is just about stuck in the same moment in time also!

Interestingly, if B were to "take off" from A and accelerate away and then accelerate to return and land back on A, the clocks on B would say that less time has expired while they were gone than the clocks on A measure.

Galileo Galilei was beaten by sentence of the Church officers, who said the Sun turned around the Earth.

Both were right:

The Sun (And the whole Universe) takes 24 hours (Tautology) to make one turn around the Earth. The Church was right.

The Earth takes 365, etc. days to make a turn around the Sun. Galileo was right.

Relativity of the movement.

I say time can not expand or shrink because time is not a thing, it is the result of the comparison of two movements, a ratio:

Einstein says: A clock (mechanical or oscillation type) slow down when the clock moves at a speed u with respect to other clock.

The other clock, synchronized with the first when this one started to move, keeps its pace.

Then, when you compare the two clocks, when the first returns from its trip, they show different hours.

If you are on the ship of the travelling clock, theoretically you grow up one year, when your clock has turned 365 times the arrow which shows the days. I you were able to see one person who had stayed near the other clock, this person would be older than you, in the hypothesis the two person were of the same age when the trip started, because the movement of the "static" clock and the physiological development "go" faster, than the ones on the ship.

What I say is that all that has nothing to do with time, but with two movements, in this case, which are submitted to different speeds. And with the physiological development (also a movement) of two persons of the same age at the beginning of the experiment, for example.

I am not against the relativity theories, poor of me ¡, but I see things from a different point of view, as the Church and Galileo, when looking at the same phenomenon.

The Lorentz and the relativity formulas allow us to calculate the number of turns of the arrow of the flying clock, but they do not tell us why and how that happens.

I do not mind if you think I have an illusious mind. I accept, in principle, the value of the relativity formulas to make useful calculus. What I say is that time is not an entity comparable to a movement. It is a ratio.

I like humor, and fun.

I always think I can be wrong. And that other could be wrong. Who knows?

Best regards,

Arturo

The main reason for this seeming to be paradoxical is that adding the velocities of two photons moving in space and headed in opposite directions should intuitively result in one photon seeming to move at twice the speed of light as seen from the other. Instead, what we'd see from one of the photons headed towards Earth and the other photon headed toward the first would be: Earth moving towards the first photon at the speed of light; and the second photon ALSO moving towards the first at the speed of light. The key to solving this paradox is 'MOVING IN SPACE'. According to Mr. Einstein's theories of relativity, the Universe doesn't exist in space; it exists in SPACETIME. What happens in spacetime is that, for the first photon, time for everything outside itself is halted. What this means is that the first photon will see both the Earth and the second photon headed toward itself at the speed of light. What that means is that the Earth and the second photon will appear fixed (as in they won't be moving) in relation to each other. In other words, even if the second photon is actually moving at the speed of light in relation to the Earth, it's change in position in relation to the Earth will be zero since speed times (change in time) = displacement (change in position). If time stops (that is, it never changes) for things outside the first photon (as seen by the first photon), then displacement of objects between themselves outside the first photon will always be zero ... as seen by the first photon. Note that all of the above applies only for objects moving towards another (the first photon) at the speed of light in spacetime. If the photons are replaced by other objects necessarily moving at less than the speed of light, then the first object will see the second one and the Earth diverge from each other since time won't be completely stopped. In the limit case, where speeds are but very small fractions of that of light, time will flow at the same rate in different objects moving 'slowly' in relation to each other, and relative speeds become additive (e.g., 50 miles per hour in one direction plus 50 miles per hour in the opposite equals 100 mph for one object in relation to the other). For objects moving at low speed in relation to another, spacetime for the latter object is equivalent to mere space; there is no time dilation. Cheers! DZ

Good invention ( to invent = to find something that was occult) of M. Einstein:

Space-time.

If you eliminate "mathematically" the time in relativity equations, What will you find?

Time and space are considered bay M. Kant as structures of the human knowledge, not as entities.

I have got to eliminate the variable time, but not the variable space, from my mind.

It is really very difficult even to speak without using the time.

I think that it is the movement what counts:

When you compare two movements you find the time:

Indeed our clocks, even the most modern (cesium, etc.) compare the vibrations=movement, with, for example, the movement of the Earth on its axis.

You never measure a "time" with a unit of time: it does not exist.

But you measure a distance with a unit of distance: inch, cm. etc.

For me, time is really an structure of our mind.

Beware of the time ¡

Thanks,

Arturo

The Original Poster,show great insight and should be commended for the thinking behind the question,,regardless that it is in-correct,

This is evidenced here by the amount and depth of the replies.

Keep on thinking Arturo,,but be prepared to be wrong.

You may not be wrong always,with other questions/thoughts.

Joe in Texas

Joe, I am always thinking and working and enjoying life.

I keep to my original statement: Two trains running opposite on parallel railways at 0,75 C would approach each other at 1,5 C, relative speed.

0,75 C is an attainable speed, accordingly to the in vigor physical theories.

If I take one train as reference system, the other train is moving at 1,5 C.

Maybe I am wrong.

In one thing I am not wrong:

I have designed and tested an automotive alternator which has more then double power output than the conventional one of the same volume, at the critical speed of 1500 rpm (corresponding to idle speed of the IC engine of 750 rpm).

That has nothing to do with relative speeds, but some engineers told me it was impossible.

They were wrong.

Best regards.

Arturo

Arturo:

If you are an observer standing next to the very high speed railroad track, each train would be approaching you at 0.75 c relative speeds from opposite directions. This observer would say that the trains are indeed going towards one another at 1.5 c as measured in your "stationary" coordinate system.

However, if you are on one of the trains, you will say that the other train is approaching you at less than the speed of light, and you will say that the observer next to the tracks is approaching you at 0.75 c.

If the other train were actually approaching you at 1.5 c in your frame of reference, it would hit you before you ever saw the headlight! Clearly, light emitted by the other train will reach you before the train arrives, and this light will be measured as moving at speed c. The other train will appear to move at less than c.

Light can move at a relative speed of c, but everything else is measured to move at speeds less than c. Only light can move at c because any object with mass at rest would require an infinite amount of energy to get very close to the speed of light.

If indeed there was a train approaching you at 1.5 c, it wouldn't hit you. Nobody knows what it would it would do, but hitting you would convey information and that (in the conventional sense) can't travel faster than c.

I like the last bit;

"Aside from the philosophic questions of time and mass dilations arising from relativistic addition of velocities, we also observe from the above examples that there exists a "pseudo - rotation" in spacetime geometry of the velocities observed in as compared to relatively stationary . For this and other geometries being shown here, please go to Minkowski's "Light Cone" wherein it's also shown that we humans live in a "45^° physical reality of knowing" beyond which there is cosmological Elsewhere."

Oh, Anonymous Hero, I can not take on faith what men say, and scientists are men.

Euclid's Geometry was during millenniums a rock, until the Non Euclidean Geometries arrived. But you can not build a brick wall following the non Euclidean Geometries.

Newton was replaced by Einstein, Einstein will be replaced by another "team" of mathematicians and scientists which will elaborate a new theory to explain during several years, the physical phenomena.

I could follow the math, because I have very good theoretical preparation, but I will not spend my time in math formulations in this case, for the time being. I wish to learn from other people direct explanations.

In the case of the trains, I follow Einstein´s examples. The only difference is the speed of the trains:

When I say 100.000 Km/s (1/3 C), there is no problem, because 1/3C+ 1/3C = 2/3 C.< C. When I put on the table 0,75 C (3/4 C) it seems to be a problem, because 3/4+3/4=1,5C>C. Not for me.

My statement is not against the in-variation of the light speed, which seems to correspond to the "reality". (Nobody knows "what" is the light).

I am talking of trains, which are made of materials of different structure than the light, but at the end, of mass and energy= What? (The physical world has not neither start nor end, as Aristotle said). After the two trains encounter on the parallel railways, they get apart at 1,5 C.

But maybe I am wrong, I am humble.

Best regards,

Arturo

Have they not flown airplanes from New York to Dublin? Bet you money they used non-Euclidean geometry.

"Greater Circle Navigation"?

Back in the early days, all pilots were trained to use Euclidean geometry. They'd take off from San Francisco, turn east and fly straight into the Sierras. It got so bad, the FAA built Altamont Pass just to let the little Fokkers (that was the earliest passenger planes) get through.

Ha!

Actually, Altamont Pass (1009 ft, plus the height of the overpass) just lets them get from the Bay area (San Francisco etc.) over the East Bay hills into the San Joaquin Valley. The lowest passes over the Sierra (Echo Summit, Donner Pass, Yuba Pass) are around 7000 ft.

Are you sure? Back in the day I knew a ton of people who told me they got high when they went to Altamont, so I just assumed... _oh

I admire the non euclidean Geometries, as I admire the Hiperbolean trigonometric functions.

Both of them are used in their fields.

When using Hiperbolean trigonometric functions, you always makes the difference by using the letter H.

When talking of non euclidean geometries we should do the same. Both functions, and many others, apply to non intuitive fields.

At first instance, I would say that H and NEG are complex algorithms to deal with calculations that would take much more "time" with the conventional Geometry.

Maybe the Einstein´s theories are the like.

Welcome to the new use-full discoveries.

Best regards,

Arturo

"I could follow the math, because I have very good theoretical preparation, but I will not spend my time in math formulations in this case, for the time being. I wish to learn from other people direct explanations."

It is wise to doubt, but unless you are willing to invest the time and effort to understand this, you will never gain an understanding.

This is not a trivial subject and requires lots of work; work that only you must do. Others might help illuminate the way for you, but it will also require a lot of time on their behalf.

Mathematics is the only way to understand the problem space. If you want to understand the problem and you want proof of the explanations, you have no other recourse. Since you have ruled out that route, I am at a loss as to what to suggest for you.

Thanks, Anonymous Hero.

I will study the maths involved and I hope I will see the Light.

Best regards,

Arturo