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Tags light , speed , half , travel , impossible

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Old 20th February 2006, 01:29 PM   #81
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Originally Posted by ynot View Post
WHY? - Just saying it doesn't make it so.
Well, its experimental data, not an opinion. So, its obvious that what is wrong here are our ideas of what is going on. We tend to think in human terms, our language is prepared to deal with objects, speeds, space and other physical instances of what we call reality, but if we expand our senses to capture things we are not prepared to see (and thus think) we start to confront the limits of our ideas.
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Old 20th February 2006, 01:35 PM   #82
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Sorry if I'm repeating anything but the key here is time.

The velocity of an object is always expressed relative to another object. We define the velocity relative to a fixed, or inertial frame of reference. Let's say the Earth is our inertial frame. If I left Earth and accelerated to 0.99 c (99% the speed of light, theoretically, matter can never reach the speed of light.) time for me passes slower than time for the folks on Earth. Let's say somebody else took off from Earth in the opposite direction and accelerated to 0.99 c relative to Earth. It would seem, at first, that they would be moving at 1.98 c relative to each other, but, remember time.

Velocity is distance per unit time. Since their time slows relative to Earth the same way my time slowed relative to Earth, we are now passing through time at the same rate. He's moving at ~186000 mi/sec away from Earth and I'm moving ~186000 mi/sec away from Earth in the opposite direction but ONLY for people standing still on Earth. From my point of view, he is moving: ~186000 mi/sec away from me.

The time dimension of velocity changes depending upon who is doing the observing.

Last edited by lumos; 20th February 2006 at 01:40 PM.
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Old 20th February 2006, 01:54 PM   #83
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Originally Posted by epepke View Post
Well, as I said, it's not entirely clear to me that light really travels at all.
Light starts at A and ends up at B.

Thought 1) Light doesn’t travel through the distance between A and B, and is “transpositioned” (couldn’t think of a real word) from A to B. It does this with a delay of c, not instantaneously (so we calculate that the process has a “speed” of c). (all a bit too magical for me)

Thought 2) Light does travel through the distance between A and B but the distance is effectively shortened by the speed motion of light. The shortened distance (not 0) is such that the we calculate that light travels at c.

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But that's what makes physics fun. If it were all a bunch of stuff that everybody knew, it wouldn't be any fun. The fun part is in trying to push the envelope of understanding.
Agree entirely
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Old 20th February 2006, 02:41 PM   #84
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Originally Posted by ynot View Post
Light starts at A and ends up at B.

Thought 1) Light doesn’t travel through the distance between A and B, and is “transpositioned” (couldn’t think of a real word) from A to B. It does this with a delay of c, not instantaneously (so we calculate that the process has a “speed” of c). (all a bit too magical for me)

Thought 2) Light does travel through the distance between A and B but the distance is effectively shortened by the speed motion of light. The shortened distance (not 0) is such that the we calculate that light travels at c.
Maybe. Maybe not.

I don't know, and I really do know a hell of a lot about this stuff, a veritable buttload.

I do know that, if a photon were a valid frame of reference, then the distance it traveled would be exactly zero. Which brings up a couple of problems. If the universe, for a photon, is really contracted into a plane with zero thickness, how could something be in front of something else? When I see things, the light hits me in the eye, and not something behind my head. How can this be? I don't know. Also, I know from the relativistic quantum field theories, such as QED, it can't be said that a photon that fails anything really exists. Also, there are a lot of phenomena that can be dealt with using photons or not using them. The virtual photons in Feynman diagrams are often said not to exist at all but are said to be calculation tools. Hawking radiation can be described with virtual particles or without.

To make things even more annoying, a lot of the solutions involving photons work as well with photons going back in time.
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Old 20th February 2006, 02:49 PM   #85
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Alice and Bob

Let's slow down for a second. (forgive the wording there).

Your friends Alice and Bob are training for the Olympics and they want your help. They have painted a starting line and a finish line 186,000 miles to the East. Alice wants to do a time trial, so she gives you a stop watch and tells you to stand at the start line. Instead of starting from a dead stop, she backs up a bit from the startline so she can have a running start. She tells you not to start the watch until she has crossed the start line.

When you are ready, she starts running. She accelerates rapidly, and when she goes by you at the start line, she is moving at .99c (impressive, huh?). You hit the "START" button as she passes. Alice continues running Eastward, holding her speed steady, and when she crosses the finish line, she still seems to be going about .99 c. When you see her cross the finish line, you push "STOP". Your stopwatch reads 2.01 seconds. You subtract 1 second because that's how long it took the "light" of her crossing the finish line to get back to you (it's one light-second away). So her actual time was 1.01 seconds. This means her speed, from your vantage point, was 186,000 miles / 1.01 seconds, or about .99 the speed of light.

So far, no surprises, right?

Now, brace yourself: Alice took a stopwatch with her to doublecheck your results. She pressed "START" as she passed the start line, and she pressed "STOP" just as she crossed the finish line. When she looked down at her watch, though... over 2 seconds had passed (in fact, her time was 2.01 seconds - not 1.01 like on your watch!). So, at the point that Alice had crossed the finish line, she was 186,000 miles away from you... but for her 2.01 seconds has passed, so for her ran the race was done at a pathetic (186,000 miles) / (2.01 seconds) = .49 c.

What happened? Believe it or not, it all had to do with Alice's runway. As she accelerated to .99c, she experienced time dilation... her clock slowed down! So when she passed the start line, her clock was running at about 1/2 the speed of yours. In fact, if she'd been running backwards and watching you as she ran her race, your movement would have seemed to be in slow motion.

Okay - let's bring this all together now, with Bob! It turns out that Bob wanted to do a warmup run at the same time that Alice did her time trial.... but he didn't want to compete with Alice. It turns out he had set up another finish line... 186,000 miles to the WEST of the start line! So, just as Alice backed from the start line and took her running start, Bob did the same thing (but he backed up in the other direction). So, at the same time Alice crossed the start line at .99c going Eastward, Bob crossed it at .99c going Westward.

Not to be bettered, Bob managed to tie Alices' speed exactly - using the eyes on the back of your head, you noticed him cross his finish line at the exact same moment you saw Alice cross hers.

So, to you, Alice ran at .99c Eastward. To you, Bob ran at .99c Westward. Doesn't this mean Alice and Bob were mvoing away from each other at 1.98c?

NO!!!!!!

Remember, Alice's had experienced time dilation! When Alice crossed her finish line, thanks to her clock slowing down, 2.02 seconds had passed since she crossed the startline... Which means to her, it had been 2.02 seconds since she passed Bob. Bob is now at the "West" finish line, which is 472,000 miles West of Alice... Which means, to Alice, Bob had run Westward at (472,000 miles) / (2.01 seconds)... or about .995c!

Does that make it clear how Alice and Bob ran in opposite directions at .99c, but were still only moving from each other at .995c?
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Old 20th February 2006, 03:12 PM   #86
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Originally Posted by kk2796 View Post
When you see her cross the finish line, you push "STOP". Your stopwatch reads 2.01 seconds. You subtract 1 second because that's how long it took the "light" of her crossing the finish line to get back to you (it's one light-second away). So her actual time was 1.01 seconds. This means her speed, from your vantage point, was 186,000 miles / 1.01 seconds, or about .99 the speed of light.

So far, no surprises, right?

Now, brace yourself: Alice took a stopwatch with her to doublecheck your results. She pressed "START" as she passed the start line, and she pressed "STOP" just as she crossed the finish line. When she looked down at her watch, though... over 2 seconds had passed (in fact, her time was 2.01 seconds - not 1.01 like on your watch!).
Uh... no. Alice's stopwatch would show significantly LESS than 1 second in this scenario.

Quote:
What happened? Believe it or not, it all had to do with Alice's runway. As she accelerated to .99c, she experienced time dilation... her clock slowed down! So when she passed the start line, her clock was running at about 1/2 the speed of yours.
Which would mean LESS time should elapse on her stopwatch than on yours, not more.

Quote:
So, to you, Alice ran at .99c Eastward. To you, Bob ran at .99c Westward. Doesn't this mean Alice and Bob were mvoing away from each other at 1.98c?

NO!!!!!!

Remember, Alice's had experienced time dilation! When Alice crossed her finish line, thanks to her clock slowing down, 2.02 seconds had passed since she crossed the startline... Which means to her, it had been 2.02 seconds since she passed Bob. Bob is now at the "West" finish line, which is 472,000 miles West of Alice... Which means, to Alice, Bob had run Westward at (472,000 miles) / (2.01 seconds)... or about .995c!
Sorry, but that's wrong too. First off, as I already mentioned, Alice's stopwatch shows LESS than 1 second elapsing, not more. You forgot an absolutely critical component, which is length contraction. From Alice's moving reference frame, the distance she runs between the start and finish line is significantly shorter than 186,000 miles (which is why she can still see the ground moving past her at 0.99c but complete the course in less than 1 second in her reference frame). Furthermore, when you ask the question of how Alice observes Bob (note, though, that I'm using the word "observe", not "see", and the difference is critical), you have to take into account that although Alice and Bob may have crossed the finish line at the same time in YOUR reference frame, in Alice's moving reference frame Bob would stop running much later than she did, because simultaneity gets screwed up when you change reference frame.

Quote:
Does that make it clear how Alice and Bob ran in opposite directions at .99c, but were still only moving from each other at .995c?
I hate to have to be the one to tell you, but your explanation is way off.
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Old 20th February 2006, 03:18 PM   #87
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Originally Posted by kk2796 View Post
Let's slow down for a second. (forgive the wording there).

. . . . . . . .

Does that make it clear how Alice and Bob ran in opposite directions at .99c, but were still only moving from each other at .995c?
Thanks - Really nice story. Thing is I'm talking specifically about light itself. If we calculate that light travels at c, perhaps it started travelling at 1,000,000c and has been time diluted down to c.
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Old 20th February 2006, 06:21 PM   #88
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In my defense

It's been about 10 years since physics... sorry if my post misled anyone - I'd like to put a disclaimer on it, but I can't find a link to edit it.

Damnit, I knew I remembered relativity stuff being significantly more difficult than what I just laid out!
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Old 20th February 2006, 06:43 PM   #89
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Originally Posted by kk2796 View Post
It's been about 10 years since physics... sorry if my post misled anyone - I'd like to put a disclaimer on it, but I can't find a link to edit it.

Damnit, I knew I remembered relativity stuff being significantly more difficult than what I just laid out!
<monty python skit>

You did physics? . . . Lucky b*rst*rd! . . . I only did detention!

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Old 20th February 2006, 11:53 PM   #90
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Exclamation Relativity is a Clever Commie Plot to Drive You Insane

Originally Posted by ynot View Post
If it is impossible to travel faster then the speed of light, then it must also be impossible to travel faster than half the speed of light because of the following . . .

If A travels away from “static” position B faster than half the speed of light, and C travels away from B faster than half the speed of light, in the exact opposite direction from A, then A and C would be travelling apart from each other faster the speed of light.

Does this make sense, or should I take some more of those pills the nice man in the white coat gave me?

Reminds me of a related problem an old science teacher misled me about years ago when the Earth was young while teaching us his erroneous version of relativity in a general science class.

He told us that for two objects in relative motion in space, I could select either of them as a static reference point and consider that object to be at rest and attribute all the motion to the other object.

He said it wasn't important which object was chosen as the relatively stationary one, since in relativity it didn't matter. Doing so would supposedly simplify subsequent equations of motion between the two objects.

Well, what he taught was not true! He made a big boo-boo.

According to his 'logic', an entire planet or galaxy or anything else with any amount of mass could travel at light speed - if what he was saying was true.

It took me a few years before I finally realized he was wrong.

Grrrrr. A pox on him! May the fleas of 10,000 camels have a birthday party in his drawers!

Which object is considered relatively stationary and which one is considered to be in relative motion does indeed matter very, very much.

Now I realize that if I gave the correct answer on the exam, it would have been considered wrong!

Where do they get these people, from the Discovery Institute ?


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Old 21st February 2006, 01:22 AM   #91
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Originally Posted by JayT View Post
Reminds me of a related problem an old science teacher misled me about years ago when the Earth was young while teaching us his erroneous version of relativity in a general science class.

He told us that for two objects in relative motion in space, I could select either of them as a static reference point and consider that object to be at rest and attribute all the motion to the other object.

He said it wasn't important which object was chosen as the relatively stationary one, since in relativity it didn't matter. Doing so would supposedly simplify subsequent equations of motion between the two objects.

Well, what he taught was not true! He made a big boo-boo.

According to his 'logic', an entire planet or galaxy or anything else with any amount of mass could travel at light speed - if what he was saying was true.

It took me a few years before I finally realized he was wrong.

Grrrrr. A pox on him! May the fleas of 10,000 camels have a birthday party in his drawers!

Which object is considered relatively stationary and which one is considered to be in relative motion does indeed matter very, very much.

Now I realize that if I gave the correct answer on the exam, it would have been considered wrong!

Where do they get these people, from the Discovery Institute ?

I don't see how your science teacher was wrong. Can you explain?

Light is not an "object", so you can't consider it to be stationary; it always moves at c. But you can consider anything else to be stationary that you want, and it doesn't matter at all.
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Old 21st February 2006, 04:43 AM   #92
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Originally Posted by epepke View Post
Well, as I said, it's not entirely clear to me that light really travels at all. What light does may be better described by some notion other than "traveling." I just haven't been smart enough to figure out exactly what it is yet. I'm still doing pretty good, because I at least have some intuition that things may not be as they seem. So, I think, do you, and I encourage you to keep it up.
A question, for 50 points: from the photon's point of reference, is there time at all ?
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Old 21st February 2006, 04:45 AM   #93
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Originally Posted by Bodhi Dharma Zen View Post
Well, its experimental data, not an opinion. So, its obvious that what is wrong here are our ideas of what is going on. We tend to think in human terms, our language is prepared to deal with objects, speeds, space and other physical instances of what we call reality, but if we expand our senses to capture things we are not prepared to see (and thus think) we start to confront the limits of our ideas.
And then we start to lose sanity by the D10.
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Old 21st February 2006, 06:50 AM   #94
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Sorry but whats D10?
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Old 21st February 2006, 07:29 AM   #95
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Originally Posted by Belz... View Post
A question, for 50 points: from the photon's point of reference, is there time at all ?
From the photon's point of view, it travels through space, but not time.

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Old 21st February 2006, 07:43 AM   #96
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Simple Answer.
'A' at 1/2 speed of light.
'C' at 1/2 speed of light.
they travel opposite direction. Starting point B
'A' and 'C' both instantly move at 1/2 speed of light.

will light from 'A' or 'C' reach each other? when initiated from point 'B'. at departure instant?

'A' travelling at speed of 100k/h
'C' travelling at speed of 100k/h

travelling in opposite direction. Starting point B.

will a ball thrown from 'A' or 'C' at 200k/h reach each other? when initiated from point 'B' at the departure instant?
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Old 21st February 2006, 08:18 AM   #97
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Originally Posted by 10001 View Post
Simple Answer.
'A' at 1/2 speed of light.
'C' at 1/2 speed of light.
they travel opposite direction. Starting point B
'A' and 'C' both instantly move at 1/2 speed of light.

will light from 'A' or 'C' reach each other? when initiated from point 'B'. at departure instant?
You need to work on your phrasing. But assuming I understood you properly, yes, light from A will reach C or vice versa.

Quote:
'A' travelling at speed of 100k/h
'C' travelling at speed of 100k/h

travelling in opposite direction. Starting point B.

will a ball thrown from 'A' or 'C' at 200k/h reach each other? when initiated from point 'B' at the departure instant?
Discounting relativistic corrections, the ball will not close the gap between A and C. We can safely discount relativistic corrections as speeds like 200km/h as their effects will be essentially zero. We cannot discount them at the speed of light.
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Old 21st February 2006, 08:24 AM   #98
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Logic is a Two-Edged Sword

Originally Posted by 69dodge View Post
I don't see how your science teacher was wrong. Can you explain?

That was my point. Since he said ANY two objects, and having no understanding of relativity at that time, I took him literally. After all, teacher knows best. So I wondered about a photon being one of the two objects and the Earth being the other, travelling in opposite directions. At least that much is physically possible thus far.

But, if it truly made NO difference, literally, which object we considered to be the static reference frame object, I then considered imagining the photon to be the stationary object and attributing all the motion to the Earth instead. In that scenario, it was the Earth moving away from the photon at the speed of light rather than the other way around Viola! A mass moving at light speed!

All you had to do was choose the right one of the two objects and that solved the problem of a mass moving at light speed.

Isn't logic wonderful?

The rule he overlooked was that his statement was true ONLY if it wasn't the photon being considered static. In relativity, it is invalid to define a photon as stationary.

Every energy field has its fundamental particle to transmit its energy. A photon is pure electromagnetic energy. It is the fundamental energy transmission unit of the electromagnetic field. It may be visualised as the energy of pure motion, independent of mass. This is why it is invalid to define a stationary photon - no speed, no energy. The photon would physically cease to exist, violating the conservation of energy rule by vanishing into nothingness. As such it moves at the 'speed of energy' or the maximum speed of an electromagnetic particle. A photon is a vector boson 'particle'. That is, 100% of the photon's motive energy is vectored in one single direction.

For a mass particle composed of massless particles, 100% of its energy cannot all be vectored in a single direction while they are bound in union, so its speed must be less than light speed.

The total energy of a bound system cannot ALL be vectored in the same direction.

When 2 or more massless photons form a bound union, their combination behaves like a single particle. In the context of this single particle, this combination cannot reach light speed until the elements are somehow ripped apart or decay.

This physical mass is manifested by the property (inertia) that the bound system (treated as a particle) cannot be accelerated to light speed until the union that defines it is broken by some means, perhaps a collision with another mass particle moving at a high velocity or even another free photon which provides the necessary energy needed to break the bond.

What this physically means is that 2 massless photons may possibly combine to produce a compound particle with the characteristic we define as mass.

Conversely, a particle with mass may possibly decay into 2 massless particles that can then move at light speed independently of each other, usually in opposite directions (photon pairing).

This does not violate the conservation of energy rule in any way.
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Old 21st February 2006, 09:03 AM   #99
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Originally Posted by JayT View Post
What this physically means is that 2 massless photons may possibly combine to produce a compound particle with the characteristic we define as mass.

Conversely, a particle with mass may possibly decay into 2 massless particles that can then move at light speed independently of each other, usually in opposite directions (photon pairing).

This does not violate the conservation of energy rule in any way.
Yes. The classical example is the decay of an atom of positronium (well, several things are called positronium, but I mean an electron and a positron), which send off two .511 MeV photons in opposite directions.

Like most of physics, this is time reversible, so two .511 MeV photons can form an atom of positronium. Lotsa luck aiming the photons, though.
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Old 21st February 2006, 09:09 AM   #100
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Originally Posted by drkitten View Post
Discounting relativistic corrections, the ball will not close the gap between A and C. We can safely discount relativistic corrections as speeds like 200km/h as their effects will be essentially zero. We cannot discount them at the speed of light.
If I remember High School well enough, you have to have speeds about 14% of c to get a 1% difference from what you get by using classical Newtonian physics. Back-of-the-envelope calculations seem to confirm this; at 14% of c, gamma is about 1.01.
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Old 21st February 2006, 09:33 AM   #101
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Originally Posted by Belz... View Post
A question, for 50 points: from the photon's point of reference, is there time at all ?
A photon is not a valid point of reference (I think you mean frame of reference, or coordinate system).

However, in this instance we can imagine what life for a photon would be like as a limit. As things get faster, the elapsed time of a moving object shrinks, and so does the size of the universe in the direction of travel. This is why it would be possible, with a sufficiently good spaceship, to get from Earth to Barnard's Star, in five minutes ship time. On the ship, you'd only be moving for five minutes, but you'd measure Barnard's Star as being a little bit less than five light-minutes away.

At the limit, then, time wouldn't pass at all, and there would be no distance to travel.

To test this, we can plug the numbers into the equations for the interval. The interval is a measurement of the spacetime separation between events, such as for example A) a spaceship leaves Earth, and B) the spaceship arrives at Barnard's Star. Or, say, light leaves Earth and arrives at Barnard's Star.

The square of this interval is usually given as

\math{x^2 + y^2 + z^2 - ct^2}

Note that this is just the Pythagorean theorem for the square of the hypotenuse, except that there's a minus sign before ct, which reflects the characteristics of Minkowski space.

For any two events, for all observers, this number is the same. For events separated by light, it's always 0. If we plug in 0 for x, y, z, and t, we do get 0.

I have to warn you, though, that it's a happy accident that this works out. Most of the intuitions don't when they are extrapolated to light.
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Old 21st February 2006, 09:38 AM   #102
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Originally Posted by epepke View Post
Lotsa luck aiming the photons, though.
The trick to that is to use two extremely dense and powerful lasers to increase the odds of observing the desired photon interaction that produces a pair of mass particles. It's still a probabilistic long shot, but possible.

It seems that such interactions always involve pairs on both sides of the interconversion process.
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Old 21st February 2006, 09:44 AM   #103
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Originally Posted by JayT View Post
For a mass particle composed of massless particles, 100% of its energy cannot all be vectored in a single direction while they are bound in union, so its speed must be less than light speed.

The total energy of a bound system cannot ALL be vectored in the same direction.

When 2 or more massless photons form a bound union, their combination behaves like a single particle. In the context of this single particle, this combination cannot reach light speed until the elements are somehow ripped apart or decay.
Ooh ooh... does this inability to be vectored relate to mass in any way ?
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Old 21st February 2006, 09:45 AM   #104
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Originally Posted by Bodhi Dharma Zen View Post
Sorry but whats D10?
10-sided die. It's a Call of Cthulhu joke.
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Old 21st February 2006, 10:32 AM   #105
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Originally Posted by Belz... View Post
A question, for 50 points: from the photon's point of reference, is there time at all ?
In a nutshell - NO.

As an object approaches light speed (a photon can be considered an 'object'), its relative time goes slower and slower according to the relatively stationary observer. At light speed, a photon's proper (local) time over any interval would be zero between any two points in space-time regardless of distance or direction.

A mass particle moves through time and space. A photon only moves through space (from its viewpoint).

From a mathematical photon-eye view, the universe is a sphere of radius zero since it takes the same time (zero time) to reach any point at any distance from its origin of motion independent of direction. This translates to either infinite speed or zero time from its viewpoint.

The physical implication here is that something can be infinite from one viewpoint or finite as viewed from another perspective, both at the same time, including the universe as a whole, depending on the manner in which we decide to visualise it.
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Old 21st February 2006, 11:13 AM   #106
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Vector von Photonstein

Originally Posted by Belz... View Post
Ooh ooh... does this inability to be vectored relate to mass in any way ?

Yes.

But the relationship is still elusive.

The equation e=mc˛ is insufficient in itself to account for everything here because it neglects to account for the gravitational component after the mass-energy conversion. That is, what part of the total energy can be attributed to the gravitational aspect of the original mass, since the energy referred to is totally electromagnetic energy after the conversion? What portion of this energy can be attributed to the gravity of the mass and where did the gravity go during and after the conversion? Those questions are still unresolved.

Physically speaking, the equation specifically refers to the total energy equivalent held in a static mass.

As an analogy, try to imagine one photon so close to another that their mutual bending of space in their vicinity lock them together so that one 'orbits' the other, like a planet orbiting a star.

Can this linked system (mass particle) move as a whole at relative light speed as viewed by an external observer?

Analytically, the answer is 'NO'. Not until the bound system is broken, because as a bound system, they cannot both share a common 'particle' vector velocity unless it is less than light speed. As such a system, the total energy cannot be vectored entirely in one direction. The light speed vector analogy only applies to individual photons, not a compound particle originating from their binding.

The bound system vector velocity, treated as a single particle, must always be less than the vector velocity of the individual photons. This can explain why a mass particle that cannot be accelerated to light speed can possibly decompose into particles that can travel at light speed when separated from their mutual bonding as long as the decomposition products are not also mass particles.

Please bear in mind that this is only an idealized analytical mind experiment used as an aid to concept visualisation. I'm trying to avoid some ugly math here, but math is the language of physics, so it's rather a sticky thing to explain in bare words.
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Old 21st February 2006, 12:07 PM   #107
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Originally Posted by JayT View Post
The equation e=mc˛ is insufficient in itself to account for everything here because it neglects to account for the gravitational component after the mass-energy conversion. That is, what part of the total energy can be attributed to the gravitational aspect of the original mass, since the energy referred to is totally electromagnetic energy after the conversion? What portion of this energy can be attributed to the gravity of the mass and where did the gravity go during and after the conversion? Those questions are still unresolved.
GR, of course, relates gravity not so much to the mass as to the energy/momentum vector. This leads to another form of the E=mc˛ family of equations. I hope I have this right:

\math{E^2 - p^2 c^2 = m^2 c^4}

When the momentum is zero (meaning "at rest,") this reduces to

\math{E^2 = m^2 c^4}

and take the square root of both sides, and you get E=mc˛. Of course, when you take the square root, you have to be careful of the signs. But if, by convention, mass and energy are positive, this is right.

However, you can reduce this another way. Note that the left-hand side of the equation

\math{E^2 - p^2 c^2}

is just the square of the absolute value (sometimes called the norm) of the energy/momentum vector. The absolute value of energy/momentum vector, like the spacetime interval, is invariant. So what the equation says is that this invariant value is the same as the rest mass.

Which explains why Newtonian gravitation works so well, considering only the mass. It also maintains relativity, because a moving observer passing through the Solar System will still see the laws of physics as the same.

(Picky note: Spacetime intervals usually treat time, effectively as imaginary, while energy/momentum vectors usually treat energy as real. This makes it annoying to remember where to put the minus signs. It is one of the reasons I prefer quaternions. Plus, they have the right-hand rule built in, so you don't have to hold your fingers like a gang member when working things out.)
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Old 21st February 2006, 02:09 PM   #108
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Originally Posted by JayT View Post
Analytically, the answer is 'NO'. Not until the bound system is broken, because as a bound system, they cannot both share a common 'particle' vector velocity unless it is less than light speed. As such a system, the total energy cannot be vectored entirely in one direction. The light speed vector analogy only applies to individual photons, not a compound particle originating from their binding.

The bound system vector velocity, treated as a single particle, must always be less than the vector velocity of the individual photons. This can explain why a mass particle that cannot be accelerated to light speed can possibly decompose into particles that can travel at light speed when separated from their mutual bonding as long as the decomposition products are not also mass particles.
... can you name examples of these bound-photon systems ? I must have been falling behind on a number of things.
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Old 21st February 2006, 03:36 PM   #109
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Kinky Photon Bondage

The 'bound-photon' system I referred to was an explanatory analogy to aid in visualising the concept of why anything with mass cannot achieve light speed until the mass disappears by some decomposition (unbinding) process. It shouldn't be taken too literally. Sometimes when describing physical processes at the fundamental level, we simply can't find an everyday life analogy to use as a description.

Einstein did the same thing by describing space-time as bending like a rubber sheet with masses placed on it. It doesn't necessarily mean that space actually bends like that, but provides us with a way to visualise in terms of human experience how gravity seems to attract masses together or bends the path of a massless photon passing by a mass in space.

Gravity effects all objects equally, whether or not the affected objects in question have mass. In other words, even photons leaving a flashlight start to fall to the ground at the same rate as a heavy rock released at the same moment in the same gravitational field.

Things quickly get counterintuitive at the ground floor level of the universe and such simple analogies with everyday physics get more difficult to formulate.

However, it has been observed and proved experimentally (see links below) that matter can indeed be synthesized from light and that matter can be decomposed back into light.

When photons combine to synthesize matter, I referred to it as 'photon binding' for lack of a better analogy. Matter can in turn be decomposed and reduced again to massless photons.

In this context, I meant that when two photons join (or bind) and matter particles result, we might think of the photons as bound together. Once bound, the resulting particle cannot travel at light speed because we now have two vectors whose energies are not both vectored in a single common direction as they were individually before the binding took place. To achieve light speed, ALL the energy must be vectored in the same direction and this cannot happen within such a bound system.

The photons are still deemed to be separate entities, just bound so closely together at such a high energy that they behave together as a single mass particle until separated again. Such mass exists ONLY while the photons remain bound.

In fact, such matter may be created from pure radiation or from an electromagnetic field, neither of which possess mass.


Here are a few reference links that may prove helpful:

http://www.fnal.gov/pub/inquiring/mo...ht_page34.html

http://www.rochester.edu/news/show.php?id=747

http://www.slac.stanford.edu/exp/e144/science1202.html
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Old 21st February 2006, 10:24 PM   #110
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A question, for 50 points: from the photon's point of reference, is there time at all ?

The answers to the question above assume the photon is travelling though a vacuum. However when the photon travels though a substance (like water) it slows down. Does it experience time then? Does the answer matter anyway? Or the answer to the original question?
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Old 22nd February 2006, 02:46 AM   #111
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Originally Posted by rjh01 View Post
The answers to the question above assume the photon is travelling though a vacuum. However when the photon travels though a substance (like water) it slows down. Does it experience time then? Does the answer matter anyway? Or the answer to the original question?

Light does not actually slow down when passing through a medium. This is mostly an illusion.

It's path through a medium is altered by its interaction with the particles of the medium. It's path is bent by countless particle collisions. The electrons in the atoms or molecules of a material medium can alter the path of photons. It's the electrons in the outer shells of atoms that create most of the photons of the visible spectrum that we see every day.

It's analogous to trillions of photons bouncing at random between trillions of tiny particles until the light finally reaches the other side. Each bounce is a separate path. When all these paths are added together like a straight, the speed still works out to normal.

The way a photon path is altered as it passes near an atom is also analogous to the way a photon's path is bent while travelling past a massive body in space. The photon takes longer to reach it destination than it would if the gravitating mass was absent, but still not due to the light actually slowing down.

Some of the photons can also be absorbed and retransmitted, during which there is a slight delay in its progress, but no actual change in the instantaneous light speed. This process could also change the wavelength of a photon, but not its intrinsic speed.

If we could actually account for all of the zigs and zags of its total path, we would see that it actually maintained its normal speed over each of these tiny paths as it worked its way to the other side.

This makes it take more time to pass through the medium, but not because the speed of light along any path has actually slowed down to below normal light speed.

So, the essential reason light takes longer to pass through a medium is because its path is no longer as nearly a perfectly straight line as it would be through the vacuum of space.

In any event, the photon's proper time interval is still zero regardless of any medium it passes through.
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Old 22nd February 2006, 11:40 AM   #112
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Originally Posted by rjh01 View Post
The answers to the question above assume the photon is travelling though a vacuum. However when the photon travels though a substance (like water) it slows down. Does it experience time then? Does the answer matter anyway? Or the answer to the original question?
I thought I mentioned this already, but maybe that was in a different thread.

A material has stuff in it. The light can't go through in a straight line, because then it would hit stuff, and it wouldn't go through. So it goes around and between the stuff. It's a bit like a slalom.

Jay T did a reasonable pseudo-classical explanation of this. But they don't really bounce like a pool ball bounces. To understand it fully, you need to look at Quantum Electrodynamics. The amplitudes of electrons interfere with the amplitude of the light, resulting in a maximum-probability path that is wiggly. A wiggly path is longer than a straight path.

Note: if you have something like a metal, the electrons sort of blob together, so there are no big interstices to get through. So even thin metal foil is opaque. Very high energy photons can still get through, because they're smaller.

To use a pseudo-classical interpretation, consider a fly screen. Throw a raw egg at it. It won't get through. But throw an insect egg at it, or a bacterium, and it will get through.

Again, all of this is pseudo-classical. If that helps, it's good enough. However, you have to go into quantum behavior to get a better understanding.
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Old 22nd February 2006, 03:41 PM   #113
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Originally Posted by epepke View Post
Jay T did a reasonable pseudo-classical explanation of this. But they don't really bounce like a pool ball bounces.
I deliberately avoided the QED concepts. That's a bit sticky. I hoped the light taking a zigzag path analogous to bouncing off particles was sufficient to get the analogy across that the path was not simply straight like in open space. It's more like a warped path between particles than actually bouncing between them.

It's hard to explain QM effects in terms of everyday analogies, since the QM world is grievously counterintuitive in such terms. Like trying to explain photon entanglement in terms of everyday analogies.

If one did have a background in QED, he probably wouldn't be inclined to ask such a question.

You did a very good job of explaining the non-linear path concept too.

I'm not sure if using math would help simplify explanations to someone who doesn't seem to have a background in QM, but still has an interest in the subject, so I've been avoiding it so far.

One's interest has to start somewhere.

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Old 22nd February 2006, 04:48 PM   #114
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Originally Posted by JayT View Post
I deliberately avoided the QED concepts. That's a bit sticky. I hoped the light taking a zigzag path analogous to bouncing off particles was sufficient to get the analogy across that the path was not simply straight like in open space. It's more like a warped path between particles than actually bouncing between them.
What, because of curvature ?
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Old 22nd February 2006, 06:23 PM   #115
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Originally Posted by Belz... View Post
What, because of curvature ?
I wouldn't put it quite that way. That would be misleading.

As EPEPKE stated above, "the amplitudes of electrons interfere with the amplitude of the light"

At the atomic scale, electrons may exhibit properties similar to light waves and they can interfere with each others' paths of motion. It's best described by quantum probabilities and I really don't want to go there, my wounds haven't healed since my last encounter with Schrodinger's wave equation from hell as applied to electron-photon interactions.

This essentially means that the path of light can be randomly deflected or somewhat warped by passing close to electrons in the medium and vice versa resulting in a very zigzag path through the medium, hence giving the illusion of light being slowed down by the time it reaches the other side.

But light cannot slow down unless it stops altogether, in which case it ceases to exist as light and transforms into energy added to or subtracted from the motion of the particle that absorbed it, depending on the relative motion and direction of the particle and direction of the photon. Since a photon is a vector photon, direction becomes important in how its energy is absorbed at the point of contact.

A photon may be visualised as the energy of pure motion (momentum) in the absence of mass, (photons can only exist while in motion) such that when it stops, it ceases to exist as a photon and becomes part of the momentum of the absorbing object. In effect, this increases the mass of the object, preserving the conservation of energy, the Holy Grail of physics.



The most elementary analogy I can derive to explain the apparent slowing down of light is that it takes a zigzag or wobbly path through the medium, even though it may seem like a straight path to the eye. This zigzag path is longer than a straight linear path and produces the illusion of slowing down.

Nevertheless, light has only one speed.
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