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Why can light "push" but not be "pushed?"


owl

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First, on the mechanics of light pushing on things...

say on a solar sail just to keep it simple: How does the energy of its momentum transfer force to the sail with no mass to push against the matter of the sail? The sail absorbs the light, no doubt, but how does the "push" manifest?

 

Photons have momentum. The momentum changes when the reflection occurs. That's a push.

 

As to "distance":

I said that the distance between buoys must be 186,000 in earth miles, not contracted "miles" as measured from the speeding ship... requiring the adjustment to compensate as already discussed. Also I already specified that there is, as you said "a difference of 5,580,000 miles between the light and the ship, because one moved at c and one moved at c/2." I laid that out already. Do you have a point in repeating it all?

 

The question remains, why are there only 5,580,000 earth-frame miles between the ship and the far end of the light beam if the light traveled at 'c' ahead relative to the ship as well as relative to the buoys during that minute?

 

The light travels at c relative to the spaceship from the spaceship's point of view. You are analyzing it from the earth's point of view. In that frame, you get 5,580,000 miles between them because light traveled at c and the ship at c/2.

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This not be really correct, but the way I understand it is that the momentum gained from light with solar sails is similar to the gravitational effects of dark matter on galaxies, though in reverse. What I mean by that is that even though photons have no mass they still interact with things electromagnetically, the same way dark matter can interact with things with their mass but they have no interaction from EM. Since the momentum exchange is EM driven there would be no need for mass so long as enough energy is there. I think this is almost close to being vaguely right, but I'm not very knowledgeable about this sort of thing.

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I apologise owl, it was my fault. Your questions were fine and on subject. Mine were simply unmindful questions on the issues. DHs answers were offensive, but hopefully he will eventually get over his arrogance. I wonder, does he even play chess?

 

!

Moderator Note

Come on, rigney, really? Don't insult other members, please.

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This not be really correct, but the way I understand it is that the momentum gained from light with solar sails is similar to the gravitational effects of dark matter on galaxies, though in reverse. What I mean by that is that even though photons have no mass they still interact with things electromagnetically, the same way dark matter can interact with things with their mass but they have no interaction from EM. Since the momentum exchange is EM driven there would be no need for mass so long as enough energy is there. I think this is almost close to being vaguely right, but I'm not very knowledgeable about this sort of thing.

 

The basic idea that they have energy and interact means that they have momentum, and thus can exert a force, is fine.

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Newtonian mechanics implies that massless objects can't have momentum. You are once again showing your Newtonian biases. You need to drop this. If you cannot do that you will not understand.

 

Again, I am not interested in what Newton thought about it. This is my own attempt to clarify questions in my mind, and I am not a stupid person.

You seem to "need" me to "drop this." I am not interested in your needs. If I do not pursue this inquiry I will not understand the answers to what I am asking.

 

The answer is simple: Massless objects can and do have momentum. Even though photons are massless, they do have momentum and energy
.

 

That may be true and I do not deny it. But just stating it as fact doesn't address my inquiry, last stated as:

"How does the energy of its momentum transfer force to the sail with no mass to push against the matter of the sail? The sail absorbs the light, no doubt, but how does the 'push' manifest?"

 

I. Give. Up.

 

Thank you.

 

Photons have momentum. The momentum changes when the reflection occurs. That's a push.

 

I don't dispute those facts, but I still don't understand how a mass-less particle imparts force against (pushes) a mass (like the solar sail.) Momentum acting like mass without having mass still makes no sense to me.

Edit; probably a silly question, but...

Since we can't make photons sit still, we have no way of measuring them "at rest." So how can we be sure they they don't have an infinitesimal amount of mass?

 

The light travels at c relative to the spaceship from the spaceship's point of view. You are analyzing it from the earth's point of view. In that frame, you get 5,580,000 miles between them because light traveled at c and the ship at c/2.

 

My thought experiment is based on "seeing" what goes on here from Earth's frame. I know that the high speed frame will see it differently. That's why I said that I'm not interested in the fact (probability?) that the ship will see less than 186, 000 miles between buoys. Not disputing what the crew would see. Asking what earth based observation would see.

The earth-based mission was to place the buoys 186,000 earth-frame miles apart. So the crew would have compensated for apparent contraction, placing them more than 186,000 earth miles apart as seen from their frame.

So the stage is set.

In one minute the ship travels 5,580,000 earth-frame miles (to the 30th buoy) and its light beam travels 11,160,000 earth-frame miles (to the 60th buoy.) As earth sees it then, the light beam has only traveled 5,580,000 miles further than the ship.

Yet relativity insists that the light has traveled, at constant 'c' 11,160,000 earth-frame miles from the ship in that minute?

 

Or does constant 'c' relative to the seeding ship only hold true for length contracted "miles", i.e, "miles" as seen from the ship?

It doesn't make sense if we use "a mile" defined by earth's frame, as it originated, as the standard of length.

 

Edit: Gone for the weekend. Carry on.

Edited by owl
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This not be really correct, but the way I understand it is that the momentum gained from light with solar sails is similar to the gravitational effects of dark matter on galaxies, though in reverse. What I mean by that is that even though photons have no mass they still interact with things electromagnetically, the same way dark matter can interact with things with their mass but they have no interaction from EM. Since the momentum exchange is EM driven there would be no need for mass so long as enough energy is there. I think this is almost close to being vaguely right, but I'm not very knowledgeable about this sort of thing.

There's no need to invoke dark matter here. That last bit, " Since the momentum exchange is EM driven there would be no need for mass so long as enough energy is there" says it all. Light has energy, so it necessarily also has momentum. Mass is not needed. Light must necessarily transform momentum when it is absorbed or reflected because of conservation of momentum.

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This is my own attempt to clarify questions in my mind, and I am not a stupid person.

Well, keep at it, you'll get it eventually! Even if you have to shun every single answer given to you. This is difficult stuff, even for geniuses. I remember I didn't get it either, when I was first taught it in high school.

 

 

The earliest explanation of these concepts that I remember being taught involves Einstein's thought experiment of emitting photons from one side of a box and absorbing them at the other side.

http://www.adamauton.com/warp/emc2.html

In that experiment, you see that it is accepted that both the emission and absorption of photons involves a "push" on the box.

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A steady beam of light is not like a solid steel beam, it's more akin to a rapid stream of bullets from a machine gun.

 

If a spaceship with a machine gun mounted in the front would continuously fire a stream of bullets ahead of the ship, then the ship would not catch up with the bullets and as such not travel into the stream it is fireing either. Photons in the beam are also increasing their distance from the ship.

 

exactly.

Note: if considered thread hijacking please split or ignore:

on the spaceship with the machine gun, at any ship's velocity, the measured velocity of the bullets will remain constant (as measured from the spaceship). If you put a "mirror" tied at the front of the spaceship, the mirrored bullets will come back at constant speed. No matter the speed of the spaceship. From this POV there is no difference between bullets and photons.

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I don't dispute those facts, but I still don't understand how a mass-less particle imparts force against (pushes) a mass (like the solar sail.) Momentum acting like mass without having mass still makes no sense to me.

 

Because the idea that mass is required to have momentum is not correct. That's a Newtonian view, and the universe isn't Newtonian. It's an issue of having a preconceived notion that almost everybody has to deal with when introduced to relativity.

 

Edit; probably a silly question, but...

Since we can't make photons sit still, we have no way of measuring them "at rest." So how can we be sure they they don't have an infinitesimal amount of mass?

 

Photons having mass would have repercussions in electromagnetism, such as Coulomb's law not working right. So you look for deviations from the expected behavior. This puts limits on the mass. You can't measure zero, because there will always be experimental error, but these limits are incredibly small.

 

My thought experiment is based on "seeing" what goes on here from Earth's frame. I know that the high speed frame will see it differently. That's why I said that I'm not interested in the fact (probability?) that the ship will see less than 186, 000 miles between buoys. Not disputing what the crew would see. Asking what earth based observation would see.

 

But the question of the ship seeing light move at c can only be analyzed from the ship's frame of reference. Light moves at c relative to the observer. Not relative to other things.

 

The earth-based mission was to place the buoys 186,000 earth-frame miles apart. So the crew would have compensated for apparent contraction, placing them more than 186,000 earth miles apart as seen from their frame.

So the stage is set.

In one minute the ship travels 5,580,000 earth-frame miles (to the 30th buoy) and its light beam travels 11,160,000 earth-frame miles (to the 60th buoy.) As earth sees it then, the light beam has only traveled 5,580,000 miles further than the ship.

Yet relativity insists that the light has traveled, at constant 'c' 11,160,000 earth-frame miles from the ship in that minute?

 

Relativity does not insist on this. As I stated above, it says that light moves at c relative to the observer, not relative to some other object.

 

Or does constant 'c' relative to the seeding ship only hold true for length contracted "miles", i.e, "miles" as seen from the ship?

It doesn't make sense if we use "a mile" defined by earth's frame, as it originated, as the standard of length.

 

There is no such thing as a universal standard length.

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"How does the energy of its momentum transfer force to the sail with no mass to push against the matter of the sail? The sail absorbs the light, no doubt, but how does the 'push' manifest?"

(...)

I don't dispute those facts, but I still don't understand how a mass-less particle imparts force against (pushes) a mass (like the solar sail.) Momentum acting like mass without having mass still makes no sense to me.

I think it might help to understand that even objects with mass doesn't physically bump their atoms together when momentum is transferred, the electromagnetic repulsion between electrons keeps them apart during the interaction and electromagnetic forces are meditiated by photons, so a transfer of momentum between objects with mass could be said to happen with a cushion of photons meditiating the "push".

 

 

 

My thought experiment is based on "seeing" what goes on here from Earth's frame.

(...)

In one minute the ship travels 5,580,000 earth-frame miles (to the 30th buoy) and its light beam travels 11,160,000 earth-frame miles (to the 60th buoy.) As earth sees it then, the light beam has only traveled 5,580,000 miles further than the ship.

If you only stick to Earth's frame of view then nothing special happens, from Earth the ship travels with half c relative the buoys, light travels with c relative the buoys and light travels with half c relative the ship. From Earth's view there is nothing wrong with the fact that the lightbeam has only traveled 5,580,000 miles further than the ship after one minute.

 

Yet relativity insists that the light has traveled, at constant 'c' 11,160,000 earth-frame miles from the ship in that minute?

This is wrong, relativity says that light has traveled 11,160,000 ship-framed miles from the ship, in a ship-framed minute.

 

Or does constant 'c' relative to the seeding ship only hold true for length contracted "miles", i.e, "miles" as seen from the ship?

Yes, relativity claims that constant 'c' only holds true for the observers length contracted miles and time dilated minutes.

 

 

Neither the crew on the ship or the observers on Earth notices anything strange or contradictory when they measure distance, time or speed of objects. It is when they compare their measurements that they find inconsistencies and start to disagree on measurements, this is the core of the 'mystery'.

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swansont:

“There is no such thing as a universal standard length.”

 

I am not claiming and have never claimed that there is.

“A mile”, however is derived from earth’s frame of reference... you know, 5280 feet... around 1/25,000the of earth’s circumference, etc.

That is why I went into some detail on the set up, so that the layout of the buoys would be 186,000 earth-frame miles apart and then the ship & its beam would be observed from earth’s frame (taking into account, of course, the time for light to bring the “observation” back to earth.)

 

My thought experiment is based on "seeing" what goes on here from Earth's frame. I know that the high speed frame will see it differently. Likewise a ship traveling at very high speed past the earth would probably see its diameter as length contracted, but that observation does not mean that earth's diameter does in fact become shorter, as we belabored to death in my previous threads.

 

md:

Well, keep at it, you'll get it eventually! Even if you have to shun every single answer given to you. This is difficult stuff, even for geniuses. I remember I didn't get it either, when I was first taught it in high school.

 

No need for your usual insulting condescension. My concern has always been with the distances between “things” (and object’s lengths) as they actually, intrinsically are, as contrasted with how they are observed (how they might appear) from relativistic speeds.

That is why I said above:

My thought experiment is based on "seeing" what goes on here from Earth's frame. I know that the high speed frame will see it differently.
(Bold added.)

 

swansont:

But the question of the ship seeing light move at c can only be analyzed from the ship's frame of reference. Light moves at c relative to the observer. Not relative to other things.

 

To the first sentence, of course... obvious.

 

In this thought experiment, light moves at ‘c’ relative to the earth and relative to the buoys. Your last sentence is false.

 

Again, I do not dispute that a high speed frame will see it all differently, i.e, contracted.

But “a mile” remains an earth-frame standard of length... Note: not a "universal standard of length."

I think that “a mile” as seen from the ship should be called a length contracted 'mile' (l.c.'m.') and recognized as a relativistic distortion of the actual distance “a mile” as earth-frame derived. That l.c.'m.' will vary with the ship's velocity, but the standard earth mile will remain the same length.

 

This recognizes the intrinsic lengths of objects as naturally formed and distances between them as, for instance between sun and planets as naturally spaced when the solar system was formed. No problem with "seeing" those distances differently as per relativistic effects.

That is what my thought experiment was meant to advocate.

 

I think it might help to understand that even objects with mass doesn't physically bump their atoms together when momentum is transferred, the electromagnetic repulsion between electrons keeps them apart during the interaction and electromagnetic forces are meditiated by photons, so a transfer of momentum between objects with mass could be said to happen with a cushion of photons meditiating the "push".

 

If you only stick to Earth's frame of view then nothing special happens, from Earth the ship travels with half c relative the buoys, light travels with c relative the buoys and light travels with half c relative the ship. From Earth's view there is nothing wrong with the fact that the lightbeam has only traveled 5,580,000 miles further than the ship after one minute.

 

This is wrong, relativity says that light has traveled 11,160,000 ship-framed miles from the ship, in a ship-framed minute.

 

Yes, relativity claims that constant 'c' only holds true for the observers length contracted miles and time dilated minutes.

 

Neither the crew on the ship or the observers on Earth notices anything strange or contradictory when they measure distance, time or speed of objects. It is when they compare their measurements that they find inconsistencies and start to disagree on measurements, this is the core of the 'mystery'.

Spyman,

I find this post very helpful! Thank you. (I'd give you an approval point in the margin but for my belief that the popularity contest here is bogus anti-science.)

 

My confusion about SR was the belief that it claims constant 'c' relative to any moving source or any observer, moving or not. Your statement above clarifies that:

"From Earth's view there is nothing wrong with the fact that the lightbeam has only traveled 5,580,000 miles further than the ship after one minute." I had thought that the above dictum required the light to have traveled 11,160,000 from the ship, period, even as seen from earth.

Again, thanks.

Edited by owl
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swansont:

“There is no such thing as a universal standard length.”

 

I am not claiming and have never claimed that there is.

“A mile”, however is derived from earth’s frame of reference... you know, 5280 feet... around 1/25,000the of earth’s circumference, etc.

That is why I went into some detail on the set up, so that the layout of the buoys would be 186,000 earth-frame miles apart and then the ship & its beam would be observed from earth’s frame (taking into account, of course, the time for light to bring the “observation” back to earth.)

 

But you use phrases like "length-contracted miles". There is no such thing — there is no "asterisk" to be placed on a mile, since every frame's measurement is valid. There are miles, and there is the frame of reference in which the mile is measured.

 

My thought experiment is based on "seeing" what goes on here from Earth's frame. I know that the high speed frame will see it differently. Likewise a ship traveling at very high speed past the earth would probably see its diameter as length contracted, but that observation does not mean that earth's diameter does in fact become shorter, as we belabored to death in my previous threads.

 

My point is the you cannot ask about the speed of light relative to the ship being c if you do your analysis in the earth's frame. SR does not claim that you will get the answer of c in that case. In the earth's frame, the light moves away from the ship at c/2, because the ship is moving at c/2.

 

To the first sentence, of course... obvious.

 

In this thought experiment, light moves at ‘c’ relative to the earth and relative to the buoys. Your last sentence is false.

 

Light will not move at c relative to objects that are moving, only to objects that are at rest in that frame, i.e. the observer's frame.

 

 

Again, I do not dispute that a high speed frame will see it all differently, i.e, contracted.

But “a mile” remains an earth-frame standard of length... Note: not a "universal standard of length."

I think that “a mile” as seen from the ship should be called a length contracted 'mile' (l.c.'m.') and recognized as a relativistic distortion of the actual distance “a mile” as earth-frame derived. That l.c.'m.' will vary with the ship's velocity, but the standard earth mile will remain the same length.

 

A mile is a defined length. It can be used in any inertial frame of reference, since you cannot distinguish between them. In the spaceship's frame, the spaceship is not moving. And there is no physics test one can do that will show that it is.

 

 

This recognizes the intrinsic lengths of objects as naturally formed and distances between them as, for instance between sun and planets as naturally spaced when the solar system was formed. No problem with "seeing" those distances differently as per relativistic effects.

That is what my thought experiment was meant to advocate.

 

There is no such thing as an intrinsic length. There is the length as observed in a particular frame.

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Swansont:

There is no such thing as an intrinsic length. There is the length as observed in a particular frame.

 

I ask the forum whether this is swansont's opinion, as a well educated physicist, or an indisputable fact.

 

I will go with the former.

The solar system was formed quite a long time before we came along and started observing it.

The shape of earth and the distances between planets and the sun were well established long before intelligent life evolved on earth.

Our observations and measurements don't change any of that.

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Swansont:

 

 

I ask the forum whether this is swansont's opinion, as a well educated physicist, or an indisputable fact.

 

I will go with the former.

And will be mistaken for doing so.

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!

Moderator Note

Owl - this thread was on whether light can push/be pushed - the meandering into measurement of the speed of light from various frames was acceptable; a rehashing of your own personal inability to accept the validity of Special Relativity is not acceptable. Thanks

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But you use phrases like "length-contracted miles". There is no such thing — there is no "asterisk" to be placed on a mile, since every frame's measurement is valid. There are miles, and there is the frame of reference in which the mile is measured. [/Quote]

 

This is an impossible situation to argue from my point of view because you can make your argument, "no such thing (as) length-contracted miles," but the gag rule is again imposed on me forbidding my argument for length contraction being an "apparent contraction" of naturally occurring lengths/distances between things.

Refer again to my post yesterday specifically replying to your statement, "There is no such thing as an intrinsic length."

 

My point is the you cannot ask about the speed of light relative to the ship being c if you do your analysis in the earth's frame. SR does not claim that you will get the answer of c in that case. In the earth's frame, the light moves away from the ship at c/2, because the ship is moving at c/2.

 

I can and did ask "about the speed of light relative to the ship..." and also how it would look from earth's frame with the buoys place to preserve earth-frame miles between them. Earth sees the ship going 5,580,000 earth-miles and the light beam going 11,160,000 earth-miles in a minute of travel.

My confusion, as already explained, was clarified by Spyman's explanation comparing the ship's frame to the frame of earth and the buoys at rest relative to earth and the ship.

 

Light will not move at c relative to objects that are moving, only to objects that are at rest in that frame, i.e. the observer's frame.

 

Light moves at 'c' relative to the buoys, which were 'brought to rest' relative to the ship dropping them. Review the part where the buoys' retros were fired until they lost 1/2 'c' of velocity, to be at rest relative to both ships (going the same velocity.)

 

A mile is a defined length. It can be used in any inertial frame of reference, since you cannot distinguish between them. In the spaceship's frame, the spaceship is not moving. And there is no physics test one can do that will show that it is.

 

The buoys were placed to the specs of earth-frame miles as explained already in detail. I distinguished between that and length contracted miles in detail also. The ship was instructed to compensate for the difference, dropping them further apart than the length contracted 'miles' its frame would "see" at 1/2 'c' velocity.

The spaceship was moving at 1/2 'c' relative to earth and the buoys. They had been 'brought to rest' relative to the ship, as I keep repeating.

 

There is no such thing as an intrinsic length. There is the length as observed in a particular frame.

 

See above.

 

owl seems to believe there is an absolute frame of reference, in which all lengths are fixed.

...

Maybe you should read the thread before posting. I already addressed that. Here it is again from yesterday's post:

'

But “a mile” remains an earth-frame standard of length... Note: not a "universal standard of length."

 

No. No absolute frame. Ironically, the relativity of varying contracted dimensions is not absolute either. Things and the space between them are as they were naturally formed, not fluctuating with every different frame observing them.

 

This, from Spyman on the 15th answered my basic question about the "push" of light:

 

I think it might help to understand that even objects with mass doesn't physically bump their atoms together when momentum is transferred, the electromagnetic repulsion between electrons keeps them apart during the interaction and electromagnetic forces are meditiated by photons, so a transfer of momentum between objects with mass could be said to happen with a cushion of photons meditiating the "push".

 

And this was very helpful in clarifying my misconception about SR:

...relativity says that light has traveled 11,160,000 ship-framed miles from the ship, in a ship-framed minute.

 

Yes, relativity claims that constant 'c' only holds true for the observers length contracted miles and time dilated minutes.

 

It's just very ironic for me that the "everything is relative" dictum is so absolute that the world/cosmos and all its relationships/distances between bodies loses its intrinsic reality... that things are as they are independent of observational frames.

 

I'm done with this topic now.

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Swansont:

 

 

I ask the forum whether this is swansont's opinion, as a well educated physicist, or an indisputable fact.

 

I will go with the former.

The solar system was formed quite a long time before we came along and started observing it.

The shape of earth and the distances between planets and the sun were well established long before intelligent life evolved on earth.

Our observations and measurements don't change any of that.

 

Relativity is a well-supported theory, and the lack of a preferred frame of reference is, at this point, a scientific fact. If you want to dispute it you are going to struggle against the weight of 100+ years of evidence relativity has in its favor. You will have to find actual experiments which do not agree with the theory or come up with an entirely new theory that supplants it. That "no absolute frame" is part of relativity is an indisputable fact; it's spelled out in the original paper on the subject.

 

Further, as has been pointed out, this is in the context of a question about relativity, not a question of the validity of relativity. You implicitly accepted relativity in framing the question.

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Relativity is a well-supported theory, and the lack of a preferred frame of reference is, at this point, a scientific fact. If you want to dispute it you are going to struggle against the weight of 100+ years of evidence relativity has in its favor. You will have to find actual experiments which do not agree with the theory or come up with an entirely new theory that supplants it. That "no absolute frame" is part of relativity is an indisputable fact; it's spelled out in the original paper on the subject.

 

Further, as has been pointed out, this is in the context of a question about relativity, not a question of the validity of relativity. You implicitly accepted relativity in framing the question.

If you must have the last word, please address my last comment which you quoted:

 

The solar system was formed quite a long time before we came along and started observing it.

The shape of earth and the distances between planets and the sun were well established long before intelligent life evolved on earth.

Our observations and measurements don't change any of that.

 

Edit; Ps: My thought experiment spontaneously emerged from considering the OP question about the ship traveling into the tail end of the light beam it was projecting... with no "pushing" it faster. I was corrected on that misconception.

 

But meanwhile I had set up a scenario by which to compare what earth and the buoys would observe, both at rest relative to the test ship, with what the ship would observe, i.e., "contracted miles," for which it compensated to maintain earth-frame miles, which defines "miles" in the first place.

I do accept that 'c' is constant in and of itself. It provides a constant standard for distance in light years. (The Alpha Centauri complex is 4+ light years away, and the sun is 8+ light minutes away. That remains constant.) Speeding frames of observation do not change that, "in the real world."

 

My question concerned the discrepancy with what the ship would see with light traveling at 'c' relative to itself.

From the ship's position at the 30th buoy (after a minute,) if it observed light traveling at 'c', it should have appeared to travel beyond the 60th bouy to a virtual 90th buoy, though it could only have gone 11,160,000 (to the 60th buoy) miles in a minute.

So "apparent" miles are contracted "for the ship" as its "minutes" are expanded via its clock slowing down. I get it. You just hate to call earth-frame miles "length contracted miles", as seen from the ship.

Oh well.

Pps:

You nailed it here:

In the earth's frame, the light moves away from the ship at c/2, because the ship is moving at c/2.

So did Spyman in his own words, previously quoted.

My misconception was that constant 'c' meant that light should be observed from earth moving away from the ship at 'c' too.

I was mixing frames in error.

Edited by owl
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Speeding frames of observation do not change that, "in the real world."

 

I'm not going through this again. You've been told, repeatedly, not to go through this again. You got the answer to your original question. Drop it, already.

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Me:

"Speeding frames of observation do not change that, "in the real world.""

 

I'm not going through this again. You've been told, repeatedly, not to go through this again. You got the answer to your original question. Drop it, already.

So do speeding frames of reference change the naturally occurring cosmos and all of its properties or not?

 

All this about what I have been told repeatedly... the authoritarian "argument"... does not answer this question. It requires rational thought and then a straight answer.

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It is dropped.

I wonder if there is anyplace in this forum where I can challenge "length contraction" on macro-scale without continuing censorship. Just wondering.

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Telling you to please stop asking the exact same question that has already been answered very robustly is not equivalent to censorship. You should avoid conflating the two.

 

a: What is 1+1?

b: 2

a: What is 1+1?

b: 2

a: What is 1+1?

b: 2

a: What is 1+1?

b: 2

a: What is 1+1?

b: 2

a: What is 1+1?

b: STFU already!! You've been told. It's not our fault you're too obtuse to get it.

a: I'm being censored!

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