Can the Speed of Light Be Changed and What Does It Mean for Space Exploration?

[Doc Al]

ok let's think about it this way.
...
from the point of view of a, b has moved 44000 lightyears away at .99c.
...
from the point of view of b, a has moved 44000 lightyears away at .99c.

how is that not the same?

You don't seem to be catching on to the fact that the viewpoints are not symmetric. Since the two frames are in relative motion, they measure different distances. So just saying they are "44,000 ly apart" means nothing unless you specific who is measuring what.

Let's try to be very clear as to what's going on. Let's say that exactly 44,000 ly from Earth there is a marker floating in space. The marker is at rest with respect to the earth. The distance is measured from the Earth's frame. Make sense so far? A rocket heading toward Earth at 0.99c passes the marker on its way.

Let's describe the trip from marker to Earth from (1) the Earth frame and (2) the rocket frame. We've analyzed this to death, so I'll summarize:

From the Earth frame:
Distance traveled by rocket: 44,000 ly
Speed of rocket: 0.99c
Time of travel: t = D/v = 44,444 years

From the rocket frame:
Distance traveled by earth: 44,000 x 0.141 = 6204 ly (Lorentz contraction)
Speed of earth: 0.99c
Time of travel: t = D/v = 6,267 years

Note that to the rocket observer, the distance from marker to Earth is only 6204 ly. This is key to understanding what's going on.

Note that having a marker, as I introduced above, is a key to an unambiguous statement of the problem. Just saying "The rocket is a distance X from earth" is not good enough, since it gives a distance without saying who measured what.

 

[bino]

ok. that makes sense to me. but from the frame of the rocket it is at rest and that the marker and the Earth are moving?

 

[Doc Al]

but from the frame of the rocket it is at rest and that the marker and the Earth are moving?

That is correct.

 

[bino]

so then would not the numbers be swiched?

 

[HallsofIvy]

That was exactly what Doc Al did:

From the Earth frame:
Distance traveled by rocket: 44,000 ly
Speed of rocket: 0.99c
Time of travel: t = D/v = 44,444 years

From the rocket frame:
Distance traveled by earth: 44,000 x 0.141 = 6204 ly (Lorentz contraction)
Speed of earth: 0.99c
Time of travel: t = D/v = 6,267 years

 

[bino]

ok so from that. i got that the ship would arrive to Earth 38177 years before anyone on Earth noticed the ship was here. or is it that everyone on the ship is 38177 years younger than what they would be on earth? why would the lorentz contraction take affect only from the ships viewpoint?

 

[Nenad]

ok so from that. i got that the ship would arrive to Earth 38177 years before anyone on Earth noticed the ship was here.

NO

or is it that everyone on the ship is 38177 years younger than what they would be on earth?

YES

why would the lorentz contraction take affect only from the ships viewpoint?

Because the ship is the one in motion, NOT the earth.

 

[bino]

So just saying they are "44,000 ly apart" means nothing unless you specific who is measuring what.

if they both are sitting at rest 44000 lys from each other the distance is the same from both points of view. right? say one of them can instantly go straight to .99c. now as soon as that one starts the distance for that one shrinks. but it stays the same for the one that stays at rest.

 

[Doc Al]

ok so from that. i got that the ship would arrive to Earth 38177 years before anyone on Earth noticed the ship was here.

No. That's kind of silly, isn't it?

or is it that everyone on the ship is 38177 years younger than what they would be on earth?

No. It's not so simple. The rocket and the Earth would disagree as to what time the rocket passed the marker.

why would the lorentz contraction take affect only from the ships viewpoint?

What makes you think that the Lorentz contraction only works from the ship's viewpoint? In this example, only one distance was given: 44,000 km, measured from the earth. So, only the rocket sees that "length" as moving. But the Lorentz transformation certainly works both ways. For example, if the rest length of the rocket was length L, the Earth observers would see it contracted to only (0.141)L.

 

[bino]

Because the ship is the one in motion, NOT the earth.

but from the point of view of the ship the Earth is in motion and not the ship.

 

[Doc Al]

but from the point of view of the ship the Earth is in motion and not the ship.

Of course. From the Earth frame, the rocket moves; from the rocket frame, the Earth moves.

 

[bino]

So, only the rocket sees that "length" as moving. But the Lorentz transformation certainly works both ways. For example, if the rest length of the rocket was length L, the Earth observers would see it contracted to only (0.141)L.

so then from the rockets view everything is shrunk except itself but from Earth's view only the ship is shrunk?

 

[Doc Al]

if it's moving, it's "shrunk"

so then from the rockets view everything is shrunk except itself but from Earth's view only the ship is shrunk?

No. It's simple: Every frame measures anything moving as being shorter that it would be if it wasn't moving. That's true for the rocket, the earth, everybody. So, if you want to know if something is "shrunk" from a certain viewpoint, just ask "Is it moving from that viewpoint?". If the answer is yes, then it is measured to be "shrunk"; if no, then not shrunk. Got it?

 

[bino]

so from the view point from Earth only the ship is moving but from the view point of the ship everything is moving. i think that is what i was not grasping.

 

[h8ter]

An object is hurled towards a another object that has emitted light. The object that is traveling towards the emitting source has a velocity of .5c. Does the wavelength of light shift and become red? I was just wondering. After this is answered, I have another question.

 

[Nereid]

An object is hurled towards a another object that has emitted light. The object that is traveling towards the emitting source has a velocity of .5c. Does the wavelength of light shift and become red? I was just wondering. After this is answered, I have another question.

Observers on each object will record EM emissions (e.g. the yellow sodium D lines) from the object they see as moving towards them as being 'blueshifted' wrt the same emissions at rest wrt themselves.

 

[Nenad]

No. It's not so simple. The rocket and the Earth would disagree as to what time the rocket passed the marker.

Doc Al, I don't understand what you're talking about, it would be this simple. The peson on the rocket would age much less than if he was on Earth during the trip.

 

[Doc Al]

Doc Al, I don't understand what you're talking about, it would be this simple. The peson on the rocket would age much less than if he was on Earth during the trip.

It's certainly true that the Earth observers will measure the time for the trip to be longer (44,444 yrs) than the time measured by the rocket observer (only 6267 yrs). Since the rocket observer carries his clock with him, that 6267 yrs can certainly be thought of as an "age" of someone: imagine that someone (Methuselah?) was born in the rocket at the exact moment that the rocket passed the marker. How old would that person be when the rocket passes earth? Everyone would agree that the person would be 6267 years old (according to his own calendar and biological clock).

But where is the corresponding person (twin?) in the Earth frame? And how old will he be when the rocket passes earth? According to who? Things are tricky now since we first have to agree on when that person was born. Let's be very clear. Let's say that a person is born on Earth exactly at the moment that the rocket passes the marker. But according to who? The two frames will disagree as to when the rocket passed the marker!

Simultaneity of space-separated events is frame-dependent.

Let's work out the details. Let's put a clock on that marker, synchronized with the Earth clock. That's no problem, since they are in the same frame. Let's assume that according to the Earth frame the rocket passes the marker exactly when the clocks read zero. Will the rocket observer agree? No! To the rocket observer the Earth and marker clocks are wildly out of synch! To the rocket observer, the clock (calender, I guess) on Earth reads 43,560 yrs when the rocket passes the marker. Since the rocket arrives when the Earth clock reads 44,444 yrs, the rocket observer would say that Methuselah is only 884 earth-years old. This makes sense, since the rocket sees the Earth clocks as running slow. Of course, the Earth frame will drag out a 44,444 year old geezer and say that he was born exactly the moment that Methuselah was. Of course the rocket guys would laugh--they know that this Earth man was born way before they came anywhere near that marker, long before Methuselah was born.

I hope this makes sense to you. (And that I explained it correctly.)

The moral of this story: There's a reason that the infamous twin "paradoxes" of SR always arrange for the twins to start out together (just like real twins!), then go their merry ways, and then be reunited. After all is said and done, once they are reunited there is no frame-dependent ambiguity. Every observer in every frame will agree as to which twin is older.

 

[bino]

so the if they switch twins and took the older one back to the marker. would they then become the same age if methuselah stayed on earth?

 

[h8ter]

Observers on each object will record EM emissions (e.g. the yellow sodium D lines) from the object they see as moving towards them as being 'blueshifted' wrt the same emissions at rest wrt themselves.

Ok, I can agree with that. Now, throw in an outside observer. He observes the one object headed towards the light source. The object heading towards the light source sees the light as shifted to a different frequency. Does the man see the light as its original frequency and wavelength?

 

[Doc Al]

Now, throw in an outside observer. He observes the one object headed towards the light source. The object heading towards the light source sees the light as shifted to a different frequency. Does the man see the light as its original frequency and wavelength?

The shift in frequency seen by any observer depends on the relative velocity of the source with respect to that observer.

 

[Doc Al]

so the if they switch twins and took the older one back to the marker. would they then become the same age if methuselah stayed on earth?

Sorry, but I really have no idea what you are asking.

 

[bino]

im asking if once the rocket arrived on Earth if the twin that was on Earth then got on the ship and the twin that was on the rocket switched places. then the ship flew back to the marker if the twins would then become the same age again.

 

[Nenad]

It's certainly true that the Earth observers will measure the time for the trip to be longer (44,444 yrs) than the time measured by the rocket observer (only 6267 yrs). Since the rocket observer carries his clock with him, that 6267 yrs can certainly be thought of as an "age" of someone: imagine that someone (Methuselah?) was born in the rocket at the exact moment that the rocket passed the marker. How old would that person be when the rocket passes earth? Everyone would agree that the person would be 6267 years old (according to his own calendar and biological clock).

But where is the corresponding person (twin?) in the Earth frame? And how old will he be when the rocket passes earth? According to who? Things are tricky now since we first have to agree on when that person was born. Let's be very clear. Let's say that a person is born on Earth exactly at the moment that the rocket passes the marker. But according to who? The two frames will disagree as to when the rocket passed the marker!

Simultaneity of space-separated events is frame-dependent.

Let's work out the details. Let's put a clock on that marker, synchronized with the Earth clock. That's no problem, since they are in the same frame. Let's assume that according to the Earth frame the rocket passes the marker exactly when the clocks read zero. Will the rocket observer agree? No! To the rocket observer the Earth and marker clocks are wildly out of synch! To the rocket observer, the clock (calender, I guess) on Earth reads 43,560 yrs when the rocket passes the marker. Since the rocket arrives when the Earth clock reads 44,444 yrs, the rocket observer would say that Methuselah is only 884 earth-years old. This makes sense, since the rocket sees the Earth clocks as running slow. Of course, the Earth frame will drag out a 44,444 year old geezer and say that he was born exactly the moment that Methuselah was. Of course the rocket guys would laugh--they know that this Earth man was born way before they came anywhere near that marker, long before Methuselah was born.

I hope this makes sense to you. (And that I explained it correctly.)

The moral of this story: There's a reason that the infamous twin "paradoxes" of SR always arrange for the twins to start out together (just like real twins!), then go their merry ways, and then be reunited. After all is said and done, once they are reunited there is no frame-dependent ambiguity. Every observer in every frame will agree as to which twin is older.

I still don't get why you chose to make things so compliaced. In the end, the observer on the rocket ages less than the observer on earth. There is not assumptions or ambiguity.

 

[bino]

how do they measure the length of the moving object? i know they have an event happen simultaneously but how do they then measure that?

 

[Nenad]

how do they measure the length of the moving object? i know they have an event happen simultaneously but how do they then measure that?

If you know the moving objects speed and rest length, then you can measure its moving length using:

d_{rest} = d_{moving} \sqrt{1-v^{2} / c^{2}}

 

[quibton]

Bino says "Each claims that the other is shorter, and that nothing is out of the ordinary with regards to their own length. how can it be that the length of an object can get shorter to someone but not to someone else? i could understand it if it only looks shorter to the observer. it is like looking at a barn from 1ft away and looking at it from 200 ft away. the barn is smaller from farther away."

The observer is quantified by a specific physics value when in "motion". This quantity revolves around what the difference means between the ability to "accelarate" in relation to the ability to be in "motion". Either relative view piont could suggest an abstract, illusionary or real effect of the barn or not even if the barn is the same from piont 1 (before calulating what it could be after). Relativity was discovered to exaplain away probably one of the most complex problems in physics i,e were is everything in relation to everything else, considering we know what those things are anyway? Acceleration is not motion. The effects of what could happen due to the "inertia" qualities of space time within an accelerated "body" relative to the outside space time effect is not entirely understood, especially in the subjective, temporal, biological human context, even if we, being a human construct of space time have allready denoted a value of it, for a certain point that represents a certain property that is used in many equations to explain it, in its final terms. Your questions are very clever. Keep asking them

Quibtonite

Claire

 

[bino]

If you know the moving objects speed and rest length, then you can measure its moving length using:

d_{rest} = d_{moving} \sqrt{1-v^{2} / c^{2}}

yes i know this but how was this equation formed? i know that it is some how derived from time dilation. right? don't they do something with the end points.

 

[Chronos]

yes i know this but how was this equation formed? i know that it is some how derived from time dilation. right? don't they do something with the end points.

No. Why would you need to?

 

[Doc Al]

Regarding my analysis of relative "aging" for observers in different frames in the rocket-earth scenario (post #198):

I still don't get why you chose to make things so compliaced.

Get used to it. That's the way SR and the world works. It's only as "complicated" as it needs to be to accurately describe the situation.

In the end, the observer on the rocket ages less than the observer on earth.

Nonsense. You seem to think that the rocket observer is somehow the one who is really moving. Not so. SR "time dilation" works for both frames.

In post #187 you state:

Because the ship is the one in motion, NOT the earth.

Oh really? This leads me to conclude that you are missing the point of SR.

There is not assumptions or ambiguity.

You won't find any ambiguity in my analysis or in what SR states.