# Thread: Relativistic Length Elongation and Why C is the Limit

1. I'd like to examine the apparent length of a space craft at speeds near, at, and exceeding the speed of light.

Let's say I am on a space craft that is capable of incredibly fast speeds. The craft is 300,000 kilometers long from nose to tail, and I am at the halfway point, 150,000 kilometers from the nose and the tail of the craft. At my location I am in possession of a radio receiver. This craft moves at a constant speed and direction through space. On its axis of motion are two radio transmitters positioned 300,000 kilometers apart. The nearer transmitter detects the tail of my space craft and upon detection transmits a radio signal which travels at the speed of light to my receiver. The far transmitter is the same as the other transmitter except that it detects the nose of my space craft.

At slower speeds, my space craft will trip both radio-transmitter detectors almost simultaneously. I will receive both signals on my receiver at the same time or so close to the same time that I can conclude that the signals are simultaneous. The reception of the two signals this way tells me that my space craft's length is the distance between the transmitters, 300,000 kilometers.

At 90 percent of the speed of light (270,000 km / s) things change noticeably. Let's call the time at which I reach the halfway point between the radio transmitters, t = 0. The time at which I receive the signal from the nose transmitter is the solution to the equation:

270,000 t = -300,000 t + 150,000; t = 5 /19 seconds

Similarly, the solution to the following equation provides the time for the tail-transmitter signal to arrive:

270,000 t = 300,000 t - 150,000; t = 5 seconds

The difference in the arrival times, about 4.74 seconds, indicates to me that the nose of the space craft has gone beyond its transmitter-detector before the tail has gone past its detector which can only happen if the craft is longer than 300,000 kilometers. In fact, to me, the space craft's length has increased to 1,578,947 kilometers!

What happens if my space craft travels at the speed of light? Simply put, the signal from the tail transmitter can never catch up with me. I will wait forever to receive it, and the space craft might seem to be infinitely long which is impossible.

If I set the speed of the space craft at 400,000 kilometers per hour, the signal from the nose transmitter would take time equal to the solution of the following equation:

400,000 t = -300,000 t + 150,000; t = 3 / 14 seconds.

I'm not sure what significance this time may have beyond what calculations I've already performed.

Conclusion 1: Lengths of objects near the speed of light seem to elongate from the perspective of a person moving with them.
Conclusion 2: It is impossible for any object to move at the speed of light because its length would be infinite from the perspective of a person moving with it.

Jagella

2.

3. Your own frame of reference is invariant - it is what you measure time and length in relation to.

Time-dilation and length contraction are what happens to whatever else is in motion, in relation to you.

This means...

Conclusion 4: The universe contracts along the axis of motion.

That is how, travelling at only 86.6% of c, you can reach Alpha Centauri in under two and a half years! The distance to Alpha Centauri is around 4.2 light-years. If you travelled at 86.6% of c, that journey would take 4.84 years when calculated from Earth, but from the frame of the spaceship it would only take 2.42 years, as the distance to Alpha Centauri has contracted in your direction of travel, and it is now only 2.1 light-years away!

We calculate the spaceship to be length contracted in its direction of travel, and the spaceship calculates the universe around it to be contracted in its direction of travel.

4. Originally Posted by Jagella
I'd like to examine the apparent length of a space craft at speeds near, at, and exceeding the speed of light.

Let's say I am on a space craft that is capable of incredibly fast speeds. The craft is 300,000 kilometers long from nose to tail, and I am at the halfway point, 150,000 kilometers from the nose and the tail of the craft. At my location I am in possession of a radio receiver. This craft moves at a constant speed and direction through space. On its axis of motion are two radio transmitters positioned 300,000 kilometers apart. The nearer transmitter detects the tail of my space craft and upon detection transmits a radio signal which travels at the speed of light to my receiver. The far transmitter is the same as the other transmitter except that it detects the nose of my space craft.

At slower speeds, my space craft will trip both radio-transmitter detectors almost simultaneously. I will receive both signals on my receiver at the same time or so close to the same time that I can conclude that the signals are simultaneous. The reception of the two signals this way tells me that my space craft's length is the distance between the transmitters, 300,000 kilometers.

At 90 percent of the speed of light (270,000 km / s) things change noticeably. Let's call the time at which I reach the halfway point between the radio transmitters, t = 0. The time at which I receive the signal from the nose transmitter is the solution to the equation:

270,000 t = -300,000 t + 150,000; t = 5 /19 seconds

Similarly, the solution to the following equation provides the time for the tail-transmitter signal to arrive:

270,000 t = 300,000 t - 150,000; t = 5 seconds

The difference in the arrival times, about 4.74 seconds, indicates to me that the nose of the space craft has gone beyond its transmitter-detector before the tail has gone past its detector which can only happen if the craft is longer than 300,000 kilometers. In fact, to me, the space craft's length has increased to 1,578,947 kilometers!

What happens if my space craft travels at the speed of light? Simply put, the signal from the tail transmitter can never catch up with me. I will wait forever to receive it, and the space craft might seem to be infinitely long which is impossible.

If I set the speed of the space craft at 400,000 kilometers per hour, 33 percent faster than light, things get even stranger. At that speed, the signal from the nose transmitter would take time equal to the solution of the following equation:

400,000 t = -300,000 t + 150,000; t = -3 / 8 seconds.

In other words, the signal from the transmitter would arrive 3 / 8 seconds before it is transmitted! Which, as far as any of us can tell, is impossible.

Conclusion 1: Lengths of objects near the speed of light seem to elongate from the perspective of a person moving with them.
Conclusion 2: It is impossible for any object to move at the speed of light because its length would be infinite from the perspective of a person moving with it.
Conclusion 3: No object can exceed the speed of light because the sequence of cause and effect would be reversed.

Jagella
Completely, totally, utteerly wrong.

First, length in the rest frame of the ship does not change at all.

Second, length is maximun in the rest frame. Any observer in a different frame will see the ship as shorter than its rest length.

5. Originally Posted by SpeedFreek
Your own frame of reference is invariant - it is what you measure time and length in relation to.

We calculate the spaceship to be length contracted in its direction of travel, and the spaceship calculates the universe around it to be contracted in its direction of travel.
OK, if I assume that both of these statements are true, then possibly lengths in one's frame of reference would seem to elongate relative to the contraction of the universe in its direction of travel. In my thought experiment, the distance between the detector-transmitters would lessen resulting in my space craft seeming to get longer by comparison. Or at least that's one way to look at it. I could just as easily think of the distance between the detector-transmitters as staying the same and my space craft elongating.

Originally Posted by SpeedFreek
Conclusion 4: The universe contracts along the axis of motion.

That is how, travelling at only 86.6% of c, you can reach Alpha Centauri in under two and a half years! The distance to Alpha Centauri is around 4.2 light-years. If you travelled at 86.6% of c, that journey would take 4.84 years when calculated from Earth, but from the frame of the spaceship it would only take 2.42 years, as the distance to Alpha Centauri has contracted in your direction of travel, and it is now only 2.1 light-years away!
Is it safe to assume that if one's speed is sufficiently close to the speed of light, then distances can become as small as you like? Could the diameter of the observable universe shrink to one mile? At the speed of light, would distances shrink to zero? If you move faster than the speed of light, would distances become negative meaning you'd arrive at your destination before you set out?

Jagella

6. jagella, stop posting. My IQ is dropping every time I read a post of yours

7. Originally Posted by SpeedFreek
...This means...

Conclusion 4: The universe contracts along the axis of motion.

That is how, travelling at only 86.6% of c, you can reach Alpha Centauri in under two and a half years! The distance to Alpha Centauri is around 4.2 light-years. If you travelled at 86.6% of c, that journey would take 4.84 years when calculated from Earth, but from the frame of the spaceship it would only take 2.42 years, as the distance to Alpha Centauri has contracted in your direction of travel, and it is now only 2.1 light-years away!

We calculate the spaceship to be length contracted in its direction of travel, and the spaceship calculates the universe around it to be contracted in its direction of travel.
The universe doesn't change when a spaceship is travelling through it. The fast-moving observer sees it as being length-contracted because he's changed.

Jagella, IMHO you're on the right lines here but your conclusions need a bit more work:

Conclusion 1: Lengths of objects near the speed of light seem to elongate from the perspective of a person moving with them.

The observer is elongated or "smeared out" too. So he doesn't notice any change to his spaceship.

Conclusion 2: It is impossible for any object to move at the speed of light because its length would be infinite from the perspective of a person moving with it.

Check out pair production, where a +1022keV photon interacts with a nucleus to create an electron and a positron. You can diffract an electron, it has a wave nature, along with spin angular momentum and magnetic dipole moment. You can annihilate it with a positron and what you get is light. So think of the electron as being a light wave going round and round. No way can this thing go faster than light.

Conclusion 3: No object can exceed the speed of light because the sequence of cause and effect would be reversed.

As above.

8. Originally Posted by Jagella
Originally Posted by SpeedFreek
Your own frame of reference is invariant - it is what you measure time and length in relation to.

We calculate the spaceship to be length contracted in its direction of travel, and the spaceship calculates the universe around it to be contracted in its direction of travel.
I could just as easily think of the distance between the detector-transmitters as staying the same and my space craft elongating.

Jagella
No, as demonstrated by the following simple experiment:

From your position in the middle of the craft, sent a signal to each end of the ship, which is then reflected back to you. You will always get the same result, indicating that the length of the ship remains unchanged.

9. Originally Posted by Janus
No, as demonstrated by the following simple experiment:

From your position in the middle of the craft, sent a signal to each end of the ship, which is then reflected back to you. You will always get the same result, indicating that the length of the ship remains unchanged.
That's a very good point and well taken. So let's review our options in measuring the length of the space craft:

• 1. We can measure the length of the craft by comparing it to the distance between the transmitter-detectors.
2. We can send two simultaneous radio signals from the middle of the craft to each end, reflect them back to the middle, and use a receiver to detect the signals and record and compare their arrival times.

Now, at this point we need to decide which method of measuring the ship's length gives us the correct result. You evidently believe that your method is the better method, but why? Isn't it possible that the equipment is faulty and providing errant results? Might there be some quirk of physics hitherto unknown to science that might make your method appear to be giving the right measurement while the ship's length has actually changed?

Actually, like I mentioned on another thread, I think it's fair to say that distance is absolute in one's own frame of reference, so I basically agree with you and your method of measuring the craft's length from that frame of reference, the moving space craft. To me or anybody else on board that space craft, it would appear to be the same length if we ignore the space we are moving through. However, relative to the distance contraction in that region of space along our axis of travel, our ship would seem to elongate.

Please remember that we are discussing relativity. You seem to be thinking in terms of absolutes.

Who says you need a doctorate in physics? Just give me a PC, spreadsheet software, a calculator, and some good books, and I'll do just fine.

Jagella

10. Originally Posted by Farsight
Originally Posted by SpeedFreek
...This means...

Conclusion 4: The universe contracts along the axis of motion.

That is how, travelling at only 86.6% of c, you can reach Alpha Centauri in under two and a half years! The distance to Alpha Centauri is around 4.2 light-years. If you travelled at 86.6% of c, that journey would take 4.84 years when calculated from Earth, but from the frame of the spaceship it would only take 2.42 years, as the distance to Alpha Centauri has contracted in your direction of travel, and it is now only 2.1 light-years away!

We calculate the spaceship to be length contracted in its direction of travel, and the spaceship calculates the universe around it to be contracted in its direction of travel.
The universe doesn't change when a spaceship is travelling through it. The fast-moving observer sees it as being length-contracted because he's changed.

Jagella, IMHO you're on the right lines here but your conclusions need a bit more work:

Conclusion 1: Lengths of objects near the speed of light seem to elongate from the perspective of a person moving with them.

The observer is elongated or "smeared out" too. So he doesn't notice any change to his spaceship.

Conclusion 2: It is impossible for any object to move at the speed of light because its length would be infinite from the perspective of a person moving with it.

Check out pair production, where a +1022keV photon interacts with a nucleus to create an electron and a positron. You can diffract an electron, it has a wave nature, along with spin angular momentum and magnetic dipole moment. You can annihilate it with a positron and what you get is light. So think of the electron as being a light wave going round and round. No way can this thing go faster than light.

Conclusion 3: No object can exceed the speed of light because the sequence of cause and effect would be reversed.

As above.
Absolute rubbish.

The internet crank strikes again and once more proves that he is absolutely clueless regarding relativity.

11. If I may jump in,
Originally Posted by Jagella
So let's review our options in measuring the length of the space craft:

• 1. We can measure the length of the craft by comparing it to the distance between the transmitter-detectors.
2. We can send two simultaneous radio signals from the middle of the craft to each end, reflect them back to the middle, and use a receiver to detect the signals and record and compare their arrival times.
Yes. We have the option of measuring the length of the space craft in its own frame of reference - its "rest frame" - any frame that is at rest in relation to the spacecraft. Or, we can try to measure the space craft using a different frame of reference, one that is in motion in relation to it, which is far more difficult.

Originally Posted by Jagella
Now, at this point we need to decide which method of measuring the ship's length gives us the correct result. You evidently believe that your method is the better method, but why?
Because it makes sense to physically put a ruler on the spacecraft you want to measure, rather than try to measure it as it passes a ruler at speed!

No, that was not "my final answer", but there is a ring of truth to it. The "correct result" is that whilst the length of the ship never changes in it's own frame, a different frame will conclude that the ship is shorter in length. Both are correct!

Originally Posted by Jagella
Isn't it possible that the equipment is faulty and providing errant results? Might there be some quirk of physics hitherto unknown to science that might make your method appear to be giving the right measurement while the ship's length has actually changed?
Not a lot can go wrong with a light clock. This whole scenario is designed to deal with a quirk of physics previously unknown to science - the constancy of c to all inertial frames of reference, whatever their relative motions, coupled with the evidence that light does not propagate relative to any absolute frame of reference.

If there were some absolute frame of reference against which light propagated, and objects in the universe were time-dilated and length contracted when in motion relative to that absolute frame, so they always measure light to have the same speed, then you might have a point.

Originally Posted by Jagella
Actually, like I mentioned on another thread, I think it's fair to say that distance is absolute in one's own frame of reference, so I basically agree with you and your method of measuring the craft's length from that frame of reference, the moving space craft. To me or anybody else on board that space craft, it would appear to be the same length if we ignore the space we are moving through. However, relative to the distance contraction in that region of space along our axis of travel, our ship would seem to elongate.
Using Special Relativity, nobody in the universe, with any ruler in the universe, positioned anywhere in the universe, ever measures any object to relativistically elongate. You are mixing reference frames here.

Originally Posted by Jagella
Please remember that we are discussing relativity.
And with relativity, everything is relative to you. There is no preferred frame of reference.

12. Originally Posted by SpeedFreek
If there were some absolute frame of reference against which light propagated, and objects in the universe were time-dilated and length contracted when in motion relative to that absolute frame, so they always measure light to have the same speed, then you might have a point.
There is. You can put ANY inertial reference frame in that role. Refer everything to that arbitrarirly selected frame and use Lorentz transformations to relate to other inertial reference frames.

This is called the Lorentz Ether Theory. It may seem less natural than special relativity, but it is equivalent to it. It is not well known because it offers nothing that special relativity does not, and is rather awkward from a philosophical perspective.

13. Originally Posted by DrRocket
Originally Posted by SpeedFreek
If there were some absolute frame of reference against which light propagated, and objects in the universe were time-dilated and length contracted when in motion relative to that absolute frame, so they always measure light to have the same speed, then you might have a point.
There is. You can put ANY inertial reference frame in that role. Refer everything to that arbitrarirly selected frame and use Lorentz transformations to relate to other inertial reference frames.

This is called the Lorentz Ether Theory. It may seem less natural than special relativity, but it is equivalent to it. It is not well known because it offers nothing that special relativity does not, and is rather awkward from a philosophical perspective.
Yes, of course (I know a little about LET, and Neo-Lorentzian theory), but if you can put ANY inertial reference frame in that role, then as you say that frame is arbitrarily selected, which means that frame cannot be considered to be an absolute frame against which light propagates.

I was trying to rid Jagella of the notion that there might be a frame where measurements are absolute.

14. Originally Posted by Farsight
The observer is elongated or "smeared out" too. So he doesn't notice any change to his spaceship.
That's correct. The space craft in my thought experiment seems to elongate relative to the passing space, in particular the detector-transmitters located in the stationary frame of reference. It does not seem to elongate relative to itself, of course. I'm sorry if I did not make that clear.

Originally Posted by Farsight
Check out pair production, where a +1022keV photon interacts with a nucleus to create an electron and a positron. You can diffract an electron, it has a wave nature, along with spin angular momentum and magnetic dipole moment. You can annihilate it with a positron and what you get is light. So think of the electron as being a light wave going round and round. No way can this thing go faster than light.
Thanks for that explanation. Are you saying that since the electron is converted to light, it cannot go faster than light because it is light? What about the electron prior to its annihilation? It's not light then, so why can't it go faster than light at that time?

By the way, I came up with what I hope is a good rationale for why only light can travel as fast as itself and nothing can move faster. I will post it soon on a new thread. Stay tuned!

Originally Posted by Farsight
Conclusion 3: No object can exceed the speed of light because the sequence of cause and effect would be reversed.

As above.
I understand that Einstein said that nothing can travel faster than light by saying that a tennis ball traveling faster than light would arrive before it is served. Cause and effect would then be reversed. However, I found a mistake in one of my calculations, so I edited out that conclusion in my opening post. I won't come to a conclusion just because Einstein said so. I need to see the logic for myself.

Jagella

15. Originally Posted by Jagella
Originally Posted by Farsight
The observer is elongated or "smeared out" too. So he doesn't notice any change to his spaceship.
That's correct. The space craft in my thought experiment seems to elongate relative to the passing space, in particular the detector-transmitters located in the stationary frame of reference. It does not seem to elongate relative to itself, of course. I'm sorry if I did not make that clear.

Originally Posted by Farsight
Check out pair production, where a +1022keV photon interacts with a nucleus to create an electron and a positron. You can diffract an electron, it has a wave nature, along with spin angular momentum and magnetic dipole moment. You can annihilate it with a positron and what you get is light. So think of the electron as being a light wave going round and round. No way can this thing go faster than light.
Thanks for that explanation. Are you saying that since the electron is converted to light, it cannot go faster than light because it is light? What about the electron prior to its annihilation? It's not light then, so why can't it go faster than light at that time?

By the way, I came up with what I hope is a good rationale for why only light can travel as fast as itself and nothing can move faster. I will post it soon on a new thread. Stay tuned!

Originally Posted by Farsight
Conclusion 3: No object can exceed the speed of light because the sequence of cause and effect would be reversed.

As above.
I understand that Einstein said that nothing can travel faster than light by saying that a tennis ball traveling faster than light would arrive before it is served. Cause and effect would then be reversed. However, I found a mistake in one of my calculations, so I edited out that conclusion in my opening post. I won't come to a conclusion just because Einstein said so. I need to see the logic for myself.

Jagella
You two nut balls deserve one another. Unfortunately you are likely to damage some innocent neophyte who reads your crap.

There is no such thing as length elongation. The length of any object is a maximum in the rest frame of that object.

16. Originally Posted by SpeedFreek
Using Special Relativity, nobody in the universe, with any ruler in the universe, positioned anywhere in the universe, ever measures any object to relativistically elongate. You are mixing reference frames here.
But in my thought experiment, the “ruler” is the radio-transmitter-detectors located on my space craft's axis of motion. At slower speeds that measuring stick tells me that my vessel is 300,000 kilometers long. At faster speeds near the speed of light, the same measuring system indicates that my vessel is significantly longer than 300,000 kilometers.

I'd strongly recommend that you look for a copy of Voyage Through the Universe: The Cosmos. It includes some nice illustrations that help you picture what happens to length when a vessel approaches the speed of light. It explains that for a person on board a vessel approaching the speed of light through a tunnel of known length: “His estimate of the vehicle's length increases; the growing pause between (light) signals is an indication of how much longer it is than the tunnel.” (1)

(Emphasis Mine)

I have used the same reasoning in my thought experiment, but I have changed the measuring system to radio signals rather than light because radio signals would be easier to detect at enormous speeds and distances. I've also added some numbers and basic calculations so that the differences in the space craft's apparent lengths would be more explicit.

Jagella

(1) “The Variability of Length in Motion;” Voyage Through the Universe; Time-Life Books; 1988; pp 44-45

17. Originally Posted by Jagella
But in my thought experiment, the “ruler” is the radio-transmitter-detectors located on my space craft's axis of motion. At slower speeds that measuring stick tells me that my vessel is 300,000 kilometers long. At faster speeds near the speed of light, the same measuring system indicates that my vessel is significantly longer than 300,000 kilometers.
In your thought experiment, everything is acting in the same frame. Regardless of the velocity of this frame with regard to some arbitrarily selected 'absolute' frame, the results will always be the same because there is no relative motion between the observed vessel and the observer.

Or, to rephrase this into a question for you: how would you know how fast you are moving? Why would the results be different at 0.99999999c compared to 0, when within your reference frame, both are exactly the same?

In special relativity, length is observed to be contracted along the direction of motion between different inertial frames of reference.

Within a single frame, there is no relative velocity, so the length is contracted by a ratio of 1/1 - i.e. it does not change. Nor does time dilate.

18. Someone travelling in that spaceship wouldn,t measure a longer spaceship with a ruler that,s for certain. He would have to keep the ruler lengthwise to the spaceship in the same travelling direction. The person and the ruler and the ship for people outside the travelling objekt (looking at it from where it was build and launched and all meassured) change length including the meassuring device if that would stay visible from the outside. If they had a similar meassuring devoce left at the launching platform they are no longer ecqual length only both show there length as one meter because those are the numbers we put on lengths. Nature doesn,t care too much for that strange habit.

Length contraction doesn,t mean that it also counts for the diameter of the ship or the width. On the contrary I expect that when this spaceship would approach lightspeed not only would it approach infinite length but also it,s diameter would appoach a mathematical line same time. Not only the ship but also what - or whoever is inside it.

19. Originally Posted by Ghrasp
Length contraction doesn,t mean that it also counts for the diameter of the ship or the width. On the contrary I expect that when this spaceship would approach lightspeed not only would it approach infinite length but also it,s diameter would appoach a mathematical line same time. Not only the ship but also what - or whoever is inside it.
The word you are overlooking here is 'contraction' - length is contracted as velocity increases, not elongated.

And the observed width and height of the ship would remain unchanged because they are measured perpendicular to the direction of motion.

20. Originally Posted by Jagella

What happens if my space craft travels at the speed of light? Simply put, the signal from the tail transmitter can never catch up with me. I will wait forever to receive it, and the space craft might seem to be infinitely long which is impossible.
So, this is our chance to clarify. Janus was kind enough to clear this up for me in this thread:

http://www.thescienceforum.com/Confu...on.-29863t.php

If you're on the spaceship and it's moving at nearly C, then you perceive the 2 transmitters to be right next to each other, in the same spot.

If you're the rear transmitter, then you perceive the space ship coming toward you to be infinitely short. As far as the transmitter can tell, the front and rear of the space ship arrived simultaneously. This is also true for the front transmitter.

If the transmitters actually wait until you arrive to broadcast their signals, then neither signal will ever catch up with you, and the whole experiment simply fails. If they wait until the last moment before the signal would fail to reach you before sending it, well, your perception of time being what it is (time standing still and all), you would still think the signals had reached you simultaneously.

21. Well thanks for an intelligent and polite response! It's about time more of the members in this forum started acting like professionals rather than claiming to be professionals.

Originally Posted by drowsy turtle
In your thought experiment, everything is acting in the same frame.
I'm sorry if I confused you. What do you mean by “everything is acting in the same frame”? There are two frames of reference in my thought experiment: the space craft in motion and the two transmitter-detectors lying along the space craft's axis of motion.

Originally Posted by drowsy turtle
Regardless of the velocity of this frame with regard to some arbitrarily selected 'absolute' frame, the results will always be the same because there is no relative motion between the observed vessel and the observer.
Yes, but the observer on board the space craft observes the stationary detector-transmitters using a radio-receiver. You seem to be thinking that I'm saying that within the space craft's frame of reference the observer measures the length of the ship. That's not what I'm saying. He's comparing the length of the moving ship to the distance between the transmitter-detectors which are in a different frame of reference. Measuring the craft's length this way works fine at slower speeds, but at speeds near the speed of light the space craft seems to be longer as a result of the difference in the radio signals' arrival at the observer's location on board the craft. If he were to measure the craft's length within its frame of reference, then it would seem to be the same length at the slower speed, 300,000 kilometers.

Anyway, my point is that by using the transmitters as a measuring stick, the results will vary depending on the speed of the space craft. If the observer sticks with this method of measurement, then he'd be compelled to believe the craft has gotten longer at speeds close to the speed of light.

Originally Posted by drowsy turtle
how would you know how fast you are moving?
Good question. One way to determine the craft's speed might be for the observer on board the craft to set his receiver to receive signals from both transmitters as he passes them. The speed of the craft would then be 300,000 kilometers / (time between the two signals). If the signals were two seconds apart, for instance, the the speed of the space craft would be 300,000 kilometers / 2 seconds = 150,000 kilometers per second.

Originally Posted by drowsy turtle
Why would the results be different at 0.99999999c compared to 0, when within your reference frame, both are exactly the same?
I'm not sure what you're asking here. What “results” are you asking about? The length of the space craft? Using the method of measurement I've described in my thought experiment, there would be a big difference in the observed length of the ship at those different speeds.

Originally Posted by drowsy turtle
In special relativity, length is observed to be contracted along the direction of motion between different inertial frames of reference.
That's not worded clearly. The length of a moving object is observed to be contracted for the stationary observer. The stationary observer, though, could just as easily believe that the moving object's length is the same and the distances in the stationary frame have elongated. Which view is “correct”? It's impossible to say.

Originally Posted by drowsy turtle
Within a single frame, there is no relative velocity, so the length is contracted by a ratio of 1/1 - i.e. it does not change. Nor does time dilate.
That's correct, but my observer is not measuring his space craft that way—he's using a system of measurement that involves both frames of reference. You are arguing that using a different method of measurement, using only the moving frame of reference, would not indicate any difference in the length of the craft. What you are arguing is true but irrelevant to my thought experiment.

Got it?

Jagella

22. Originally Posted by Jagella
Well thanks for an intelligent and polite response! It's about time more of the members in this forum started acting like professionals rather than claiming to be professionals.

Jagella
You two deserve each other.

23. Originally Posted by Jagella

Originally Posted by drowsy turtle
Regardless of the velocity of this frame with regard to some arbitrarily selected 'absolute' frame, the results will always be the same because there is no relative motion between the observed vessel and the observer.
Yes, but the observer on board the space craft observes the stationary detector-transmitters using a radio-receiver. You seem to be thinking that I'm saying that within the space craft's frame of reference the observer measures the length of the ship. That's not what I'm saying. He's comparing the length of the moving ship to the distance between the transmitter-detectors which are in a different frame of reference. Measuring the craft's length this way works fine at slower speeds, but at speeds near the speed of light the space craft seems to be longer as a result of the difference in the radio signals' arrival at the observer's location on board the craft. If he were to measure the craft's length within its frame of reference, then it would seem to be the same length at the slower speed, 300,000 kilometers.

Anyway, my point is that by using the transmitters as a measuring stick, the results will vary depending on the speed of the space craft. If the observer sticks with this method of measurement, then he'd be compelled to believe the craft has gotten longer at speeds close to the speed of light.
It depends how you look at it. As I was mentioning before, if the spaceship is traveling at nearly C, then the observer observes the distance between the two transmitters to be nearly zero.

Originally Posted by drowsy turtle
how would you know how fast you are moving?
Good question. One way to determine the craft's speed might be for the observer on board the craft to set his receiver to receive signals from both transmitters as he passes them. The speed of the craft would then be 300,000 kilometers / (time between the two signals). If the signals were two seconds apart, for instance, the the speed of the space craft would be 300,000 kilometers / 2 seconds = 150,000 kilometers per second.
But time dilation would confuse that. At speeds near C, the two signals would appear to arrive almost simultaneously. (As well as the transmitters appearing to be right next to each other.)

A more reliable way to measure your relative speed to the transmitters would be to have a mirror attached to one of them, then bounce a signal off of the mirror and see how much it is blue shifted before it returns to you.

Originally Posted by drowsy turtle
In special relativity, length is observed to be contracted along the direction of motion between different inertial frames of reference.
That's not worded clearly. The length of a moving object is observed to be contracted for the stationary observer. The stationary observer, though, could just as easily believe that the moving object's length is the same and the distances in the stationary frame have elongated. Which view is “correct”? It's impossible to say.
That is true. There is no way to know whether you have elongated, or the object you're looking at has shrunk.

Originally Posted by drowsy turtle
Within a single frame, there is no relative velocity, so the length is contracted by a ratio of 1/1 - i.e. it does not change. Nor does time dilate.
That's correct, but my observer is not measuring his space craft that way—he's using a system of measurement that involves both frames of reference. You are arguing that using a different method of measurement, using only the moving frame of reference, would not indicate any difference in the length of the craft. What you are arguing is true but irrelevant to my thought experiment.

Got it?

Jagella
The thing you're not allowed to do in relativity (or all of its predictions break down) is to know how long something is on the basis of simply knowing. This is counterintuitive, of course.

If you see a meter stick off in the distance, and are approaching it at relativistic speed, it looks shorter than a meter to you. But..... you know it's a meter long because it says "meter stick" on it. Be that as it may, it is considered cheating to know that. Relativity assumes you don't have any of this sort of insider knowledge and you're trying to tell just by looking.

24. Originally Posted by kojax
If you see a meter stick off in the distance, and are approaching it at relativistic speed, it looks shorter than a meter to you. But..... you know it's a meter long because it says "meter stick" on it. Be that as it may, it is considered cheating to know that. Relativity assumes you don't have any of this sort of insider knowledge and you're trying to tell just by looking.
What have you been smoking ?

25. Originally Posted by Jagella
I'm sorry if I confused you. What do you mean by “everything is acting in the same frame”? There are two frames of reference in my thought experiment: the space craft in motion and the two transmitter-detectors lying along the space craft's axis of motion.
Sorry, it seems I misread the OP :P

Actually I think I was drunk when I replied lol

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