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

[Doc Al]

therefor it just appears contracted from the view of the object at rest.

I still don't understand what you mean by "appears". I can only assume you mean to contrast "appears contracted" with "really is contracted".

Note that Tom does not say the rod "appears" contracted, he says "If a rod is moving, then it is smaller than it is in its own rest frame." (Emphasis mine.)

Perhaps we are arguing semantics, but I think it's important. An analogy: You look into a spherical mirror, your image is distorted. Is the distortion real or apparent? I assume you would agree that you only appear distorted due to how the mirror reflects light. On the other hand, what if I wish to measure the length of my desk? I apply a ruler and get a certain number of centimeters. Is the length of my desk the actual length (in my rest frame, of course) or is it just the apparent length? Again I assume you would agree that it makes sense to say that the measured length is the actual length, not just an illusion or a trick of light.

Now of course there are practical difficulties in measuring the length of desk that is moving past you at an appreciable fraction of light speed--but let's do the thought experiment anyway. Pretend we have incredibly accurate clocks and detectors. We arrange to measure the position of each end of the moving desk at a precise instant of time according to our (stationary) clocks and metersticks. This is what I mean by the measuring the length of the moving desk. We find that its length is smaller compared to what it would measure if it were at rest. I see no justification for saying that the length of the desk merely "appears" smaller: by any normal definition of "length" it really is smaller.

This contraction is a property of space-time; there is no physical force that reaches out and compresses the desk. But it is real nonetheless.

 

[pervect]

I still don't understand what you mean by "appears". I can only assume you mean to contrast "appears contracted" with "really is contracted".

This discussion is starting to get a bit philosophical, but I thought I'd trhow in my $.02, in the hope that it well help more than confuse the issue (we'll have to see how it works out).

If one defines a "real" property of a body as a property that does not depend on the observer, one that is intrinsic only to the body itself, then space and time both fail to be "real" properties. The Lorentz interval, however, which is a mathematical combination of both space and time, does not fail this test, so it qualifies as "real".

This puts space and time in an interesting philosophical situation. Neither one is "real" by itself, but when combined properly, they form a "real" entity.

So one might say that space and time are illusions, as many mystics have done. And to some extent this is correct. On the other hand, it's a bit hard to explain how two illusions, combined together, form something that is real, if one takes this philosophical approach.

Fortunately, however, it usually doesn't matter which quantites one considers to be "real" when doing physics. I will note, however, that it's generally easier to avoid making mistakes by focusing on the quantites which don't change (are invariant) when doing calculations. In relativity, this approach would be to focus on the Lorentz interval.

 

[quantumdude]

therefor it just appears contracted from the view of the object at rest.

The rod is shorter than its proper length in the moving frame.

How many times are you going to make me say it?

 

[Nenad]

This discussion is starting to get a bit philosophical, but I thought I'd trhow in my $.02, in the hope that it well help more than confuse the issue (we'll have to see how it works out).

its not philosophical at all. Its Special Relativity.

 

[h8ter]

The rod is shorter than its proper length in the moving frame.

I thought it had proper length in the moving frame. To an outside observer it is shorter. Relative to it's own frame, the rod is proper length.

 

[quantumdude]

I thought it had proper length in the moving frame.

The rod is its proper length only in a frame that is at rest relative to the rod. When I say that the rod is shorter "in the moving frame", I mean that the rod is moving, and the observer who measures the length is watching it go by.

To an outside observer it is shorter. Relative to it's own frame, the rod is proper length.

That's right.

 

[h8ter]

Ok, I see what you were saying now. I probably just have poor reading comprehension skills.

 

[bino]

the rod is shorter when it is moving but only to the at rest observer. but if we are going the same speed as the rod then we know that it is not actually shorter.

 

[Nenad]

the rod is shorter when it is moving but only to the at rest observer. but if we are going the same speed as the rod then we know that it is not actually shorter.

Be carefull with the word 'actually'. If you do enter the frame of reference of the rod (light speed), you lill measure it to be rest length, but it you do not enter its frame, and you are at rest while iti s moving, the rod is then 'actually' shorter, meaning it is shorter.

 

[quantumdude]

the rod is shorter when it is moving but only to the at rest observer. but if we are going the same speed as the rod then we know that it is not actually shorter.

What is it with you?

DocAI just described how the measurement process would be carried out. You simultaneously record the locations of the endpoints of a rod as it moves by, and subtract the coordinates. The distance between the points is the length of the rod, and that distance varies with speed.

Haven't you looked at that textbook yet?

 

[bino]

if a ship travels from Earth moving at .99c to a destination 44000 lightyears away. from the view of the ship the trip would take 6270 years but from the view of Earth it would take 44468 years. but from the view of the ship the Earth would be moving at .99c. then wouldn't those numbers be switched?

 

[quantumdude]

if a ship travels from Earth moving at .99c to a destination 44000 lightyears away. from the view of the ship the trip would take 6270 years but from the view of Earth it would take 44468 years. but from the view of the ship the Earth would be moving at .99c. then wouldn't those numbers be switched?

No, because the distance between the Earth and the destination is shorter in the ship frame.

 

[bino]

i have no problem saying that the length of the ship will be measured shorter. i completely agree with that. but the length is not physicaly getting smaller.

 

[quantumdude]

i have no problem saying that the length of the ship will be measured shorter. i completely agree with that. but the length is not physicaly getting smaller.

At last, something I can agree with!

The rod is not physically getting smaller--it simply is smaller than it is in its rest frame.

 

[bino]

right
like i said earlier

you have to keep in mind that the length contracts only from the point of view of the stationary object. that's where the disagreement comes from. the ship looks shorter because it is shorter from the point of view of the lattes. the measurements from the equipment are correct from their point a view. the measurement are taken from a point in time. at that point in time the ship will measure to be shorter than its real length. but from the point of view of the ship its length has not changed so the equipment on the ship will say that same thing that it is in fact the same length as when it was stopped. it all matters on the point of view.

onward and forward.

the ship moving at .99c, 44000 lightyears away. and the Earth moving at .99c, 44000 lightyears away. those are the same, the only difference is what is moving from each others perspective.

 

[Doc Al]

the ship moving at .99c, 44000 lightyears away. and the Earth moving at .99c, 44000 lightyears away. those are the same, the only difference is what is moving from each others perspective.

Not true. The two frames will disagree as to the distance, since they are in relative motion.

 

[bino]

i don't mean that they are moving at the same time. sorry. i mean that the ship moving away from Earth is the same as the Earth moving away from the ship.

 

[quantumdude]

right
like i said earlier


onward and forward.

the ship moving at .99c, 44000 lightyears away. and the Earth moving at .99c, 44000 lightyears away. those are the same, the only difference is what is moving from each others perspective.

No, and I already answered that:

No, because the distance between the Earth and the destination is shorter in the ship frame.

 

[pervect]

its not philosophical at all. Its Special Relativity.

Guess my remarks didn't resolve much.

A statement about what is "actually" happening or what is "really happening" tends to be a sign that a philosophical discussion is occurring.

Generally, philosophy is pretty harmless (except for being a potential source of undending debate), and it usually doesn't matter what one thinks is "real", and what one thinks is "appearance". There are a few exceptions, basically they occur when someone does philosophy badly.

An example of bad philosophy would be to insist that lengths don't change with motion, because of some philosphical belief about them being real.

Another example of bad philosophy would be to claim that time and space are illusion, and then to turn around ans inconsistently start talkig about the "true" length, or the "real" time.

 

[bino]

i don't understand how they could be different? one is going .99c for 44000 lightyears while the other is at rest. and the same goes for the other.

 

[quantumdude]

i don't understand how they could be different? one is going .99c for 44000 lightyears while the other is at rest. and the same goes for the other.

The distance between Earth and destination is different for the two observers for the exact same reason the length of a rod is different in different frames: Length contraction.

Look at the Lorentz transformation, and you can derive it for yourself.

 

[Nenad]

hey bino, how many posts do you have on this thread, like 80? lol. Just read the book Tom posted for you earlier, then come with the questions.

 

[bino]

i understand that

The distance between Earth and destination is different for the two observers for the exact same reason the length of a rod is different in different frames: Length contraction.

what i don't understand is in the point of view from the Earth the ship is moving but in the point of view from the ship the Earth is moving. right? so then from the point of view of the ship the Earth would then take 44468 years to go 44000 lightyears. and from the point of view from the Earth the trip only took 6270 years.

 

[Nenad]

i understand that



what i don't understand is in the point of view from the Earth the ship is moving but in the point of view from the ship the Earth is moving. right? so then from the point of view of the ship the Earth would then take 44468 years to go 44000 lightyears. and from the point of view from the Earth the trip only took 6270 years.

no, in both points of wiew, it takes the other 6270 years to do the trip, but one of them is wrong. The person in motion is wrong and finds out he is wrink when the ship stops.

 

[bino]

ok let's think about it this way.

the starting point =
a b
< >

a< --------------------- >b
resting 44000lightyears moving

from the point of view of a, b has moved 44000 lightyears away at .99c.

now back to start =
a b
< >

a< --------------------- >b
moving 44000lightyears resting

from the point of view of b, a has moved 44000 lightyears away at .99c.

how is that not the same?

 

[bino]

nenad what are you talking about?

 

[Nenad]

ok let's think about it this way.

the starting point =
a b
< >

a< --------------------- >b
resting 44000lightyears moving

from the point of view of a, b has moved 44000 lightyears away at .99c.

now back to start =
a b
< >

a< --------------------- >b
moving 44000lightyears resting

from the point of view of b, a has moved 44000 lightyears away at .99c.

how is that not the same?

Oh my God, We have been through this like 1000 times. Do you not listen. To BOTH observers, what you are saying is true, but one of them is WRONG since one of them is not in real motion. Think of it this way: The way time/length/mass knows who is in motion is the one who accelerates. Both observers wee that the other observers time is slowing down, but one of them is Wrong.

Do you understand now?

 

[pervect]

Oh my God, We have been through this like 1000 times.

I dunno, I have a suspicion that bino is pushing is own "hidden" agenda, as opposed to really trying to learn relativity, but I tend to be rather grumpy and suspicious a lot of the time.

 

[bino]

you figured me out, pervect. I am on a secret mission to a hidden planet 44000 lightyears away and i need to tell my wife when to expect me home for dinner.

 

[bino]

oh shoot i guess it's not a secret anymore.

 

[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?