Solving Paradox of SR & Warning Alpha Centaurians: Passer-by's Perspective

In summary, the conversation discusses Special Relativity and a thought experiment involving a spaceship passing by Earth and Alpha Centauri. The conversation explores the concept of time dilation and the relativity of simultaneity, and how they affect the perceived time on AC relative to the passer-by's ship. The conversation also delves into the Doppler effect and how it plays a role in the perceived time on AC. Ultimately, the conversation seeks to understand why the passer-by will not be able to save the Centaurians despite the apparent time dilation.
  • #1
Pavel
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Hi! Just as I thought I was getting a pretty good grip on relativity, I got thrown back to square one. Please straighten out something for me by taking a role of a passer-by in my thought experiment.

First, I read that according to Special Relativity (SR), observers in two moving inertial frames will perceive time dilation with respect to each other, regardless of the direction of the motion. That is, if I moving at a constant speed towards you, head-on, I will perceive your clock moving slower than mine, and you will perceive my clock to be slower than yours. This is according to SR alone, all other things aside! Correct? Very well. Then I can construct the following thought experiment, which is obviously wrong, but I'd like somebody to explain to me what other relativistic effects are in place and how they solve the "paradox".

I, here on Earth, happen to find out that there's a bomb on Alpha Centaury (AC) that will go off in 3 years, which will kill their civilization. Both Earth and AC are in the same reference frame and it takes 4 years for light to reach AC. Luckily, there's a ship, a passer-by, that happens to fly by Earth tomorrow. This ship flies at a constant speed, almost the speed of light and will fly by both Earth and AC. Being an amateur physicist, I reason: "Hmm, because the passer-by in the ship will literally perceive AC to be much closer and the clock on the bomb on AC will run slower relative to the passer-by (according to SR), if I somehow let the passer-by know about the doomsday of the Alpha Centaurians, the SR's time dilation will allow the passer-by to save them". So, I put a giant billboard on the passer-by's way instructing him to flash the light at Alpha Centaurians to warn them, as he goes by AC. I obviously presume the passer-by always looks in the telescope straight ahead, which will allow him to see the billboard.

Now, please notice, I eliminate any acceleration from the thought experiment: The passer-by flies at a constant speed, both Earth and AC are in the same frame, so I'm talking about inertial frames here moving at a constant speed relative to each other - AC/Earth and the passer-by. You may object by noting that both Earth and AC are in gravitational wells, thus producing acceleration, but I think it's irrelevant - I can always modify the experiment to say that Earth and AC are actually names of the hovering ships, not planets. The "paradox" will still hold.

I know that the passer-by will NOT save the Centaurians, but I don't understand what other effects will make the time on AC to speed up relative to the passer-by. I'm aware of the Doppler effect, but I can't see how that will override time dilation, it has to be some relativistic effect. Is it the mass of the passer-by's ship creating huge mass and therefore gravitational well producing time dilation? But then wouldn't you expect the time dilation of SR be proportional to the GR's dilation from the ship's gravitational well?? So, I'm confused. If you know the answer, please assume the role of the passer-by in the ship and describe what you will perceive starting with looking at the telescope and seeing my warning billboard. In advance thanks, and sorry for being so wordy, just trying to be complete.

Pavel.
 
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  • #2
Pavel said:
I know that the passer-by will NOT save the Centaurians, but I don't understand what other effects will make the time on AC to speed up relative to the passer-by.

Pavel.

Hint: have you considered "relativity of simultaneity"? See for instance the wikipedia article http://en.wikipedia.org/wiki/Relativity_of_simultaneity
 
  • #3
Pavel said:
If you know the answer, please assume the role of the passer-by in the ship and describe what you will perceive starting with looking at the telescope and seeing my warning billboard. In advance thanks, and sorry for being so wordy, just trying to be complete.
By "perceive", do you mean what the ship will actually see as it looks through its telescope as it travels, or how it will reconstruct the timing of events in its own frame once it corrects for the delay between when an event happens and when the light from that event reaches the telescope? In the first case, the answer would lie with the doppler effect, which in relativity says that when you are traveling towards an object, you will see its clock sped up, not slowed down; in the second case, Alpha Centauri's clock will be reconstructed to have been ticking slower than the ship's clock throughout the journey, but as pervect said, the answer has to do with the relativity of simultaneity. If two clocks are at rest with respect to each other and synchronized in their rest frame, and they are a distance x apart in their rest frame, then if in my frame the clocks are moving at speed v along the axis joining them, the relativity of simultaneity implies that in my frame the back clock's time will be ahead of the front clock's time by vx/c^2. So, if Alpha Centauri is 4 light years from Earth in its own frame, and the ship sees the Earth and Alpha Centauri moving at 0.8c, then in the ship's rest frame Alpha Centauri's clock is 3.2 years ahead of Earth's clock at the moment the ship passes Earth (but at that moment the ship will see Alpha Centauri's clock as 4 years behind, just as observers on Earth will at that moment, since the light takes 4 years to cross the distance in the frame where Earth and Alpha Centauri's clock are synchronized).
 
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  • #4
The spaceship traveler moving relative to your frame (the inertial frame of Earth and Alpha Centauri) will indeed measure the Earth-AC distance as shorter and the clocks at Earth and AC as going slower. However, he will not agree that the clocks at the two places are sychronized. When he passes AC he will see that the clock there reads more than 4 years later than your clock did when he passed Earth, even if he measures his own transit time as less than 3 years. The different synchronizations of clocks in different inertial frames always saves you in this type of problem.
 
  • #5
Pavel:
There is no paradox. AC cannot be saved by anyone who depends on info from Earth to do this.

As you point out, a signal from Earth will take at least 4 years to arrive at AC, at least 1 year after AC’s demise.

If a signal is sent from the passer-by ship immediately after it passes Earth, even if the ship is moving at very high speed toward AC, that signal will arrive at AC AFTER Earth’s signal would have arrived at AC, regardless of the choice of frame. You can see this if you draw an SR Minkowski diagram.

Focus on EVENTS and their perceived temporal order, rather than on clock dilation which deals with the transformation of an event’s time-coordinate from one inertial frame to another. The temporal order of 2 events is the same in all frames if the events are timelike-connected, that is if the line joining the events is an allowable worldline (the worldline's absolute speed < c).
 
  • #6
As the object traveled close to the speed of light, it would see the distance light had traveled from the billboard contracted to almost zero for one secound. So it would take a long amount of time for the ship to receive the message as it passed by depending on how close it came to earth. Hopefully not too close, because it would appear to be a black hole unless it was using some sort of "warp drive". They themselves would then need to shoot a signal into a gravity well that they observed Earth and AC being in. For them, Earth and AC wouldn't be very far away but would be more of a matter of the time the signals take for the "rest" frame to travel to the frame traveling close to C.
 
  • #7
Thank you for the insightful replies guys, they were very helpful. Wikipedia seems to have a few good articles on resolving this as well. Looks like the Wiki book on SR might be a very helpful read. But as you indicated, there appears nothing special - I simply need to focus on temporal order of the events from both frames.

I'd like to dive deeper into the passer-by's ship becoming a black hole (due to high speed) story, but I'll review GR and acceleration first. I'm sure it'll change the whole picture.

One more thought occurred to me while reading SR and I'll appreciate any insight. It says there's no preferred (absolute) frame and it's meaningless to talk about who is faster than whom, it's all relative. Well, in pure theory. But practically speaking, at least in this Universe, can't we use CMBR as the kind of ether to measure our direction and speed against? And then use those numbers to compare them with those of some alien civilization, if one exists? Granted, I can't say that the Earth's speed (corresponding to reading 2.7K of blackbody temperature from CMBR) is not absolute, but if I have sensitive enough measuring tools, I should be able to read different temperatures in different directions of the Earth's movement (Doppler effect). On top of that, if an alien civilization reads say 2.2K, then can't I conclude that I'm, in fact, moving faster than the aliens?? Then if we had enough civilizations scattered around, couldn't we come up with some mean temperature that would allow us to agree on the absolute frame, corresponding to some temperature?? What's wrong with this logic?

Pavel.
 
  • #8
Pavel said:
I'd like to dive deeper into the passer-by's ship becoming a black hole (due to high speed) story
That doesn't happen--see If you go too fast do you become a black hole? from the Usenet Physics FAQ.
Pavel said:
One more thought occurred to me while reading SR and I'll appreciate any insight. It says there's no preferred (absolute) frame and it's meaningless to talk about who is faster than whom, it's all relative. Well, in pure theory. But practically speaking, at least in this Universe, can't we use CMBR as the kind of ether to measure our direction and speed against? And then use those numbers to compare them with those of some alien civilization, if one exists? Granted, I can't say that the Earth's speed (corresponding to reading 2.7K of blackbody temperature from CMBR) is not absolute, but if I have sensitive enough measuring tools, I should be able to read different temperatures in different directions of the Earth's movement (Doppler effect). On top of that, if an alien civilization reads say 2.2K, then can't I conclude that I'm, in fact, moving faster than the aliens??
I believe 2.7K is the temperature an observer at rest with respect to the CMBR will measure, any observer in motion relative to it would see a higher temperature, not a lower one. In any case, observations of temperature can tell you something about your speed vs. the aliens' speed relative to the CMBR, but why would you think the CMBR is "at rest" in any absolute sense? The notion that there is "no preferred reference frame" is just saying there is no difference in the laws of physics from one frame to another, there may be differences in observations of particular physical landmarks like the sun, the galaxy or the CMBR. But if you perform a certain experiment in an isolated, windowless room on Earth, and the aliens perform the same experiment in an isolated, windowless room on their planet, you'll both get the same results, because the laws of physics are the same in both frames.
 
  • #9
can't we use CMBR as the kind of ether to measure our direction and speed against?
Yes. There are clear signs of movement in the CMBR measurements. The frame of the CMBR is the frame of the matter in the universe at the time it became transparent. But it's not an absolute frame.

There's a good pic of the dipole anisotropy of the CMBR here

http://antwrp.gsfc.nasa.gov/apod/ap990627.html

On top of that, if an alien civilization reads say 2.2K, then can't I conclude that I'm, in fact, moving faster than the aliens??
You can be sure of one thing, you are moving faster than the aliens WRT the CMBR. Any further deductions at your own risk.
 
  • #10
JesseM said:

I read this post and it is a giant load of crap. E=mc^2 has nothing to do with this idea, and E=mc^2 isn't used to determine relativistic mass.

[tex] m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex]

This equation is what leads people to believe that as V approaches very close to C, your mass would approach infinity. And then you would become a black hole. This would be more of a question of how this mass is distributed from an object as it approaches the speed of light. This equation alone tells nothing of the sort. Now if the speed of an object increases the curvature of space-time as it approaches the speed of light, the curvature of space-time around this moveing object would be relative of the original mass and size of this object. Now if you speaking about a small space craft, the point from which space-time is going to infinity would be rather and small, and I would say yes it could create some sort of singularity like a black hole, given space-time would curve to almost infinite mass around a small object. My experiment to prove this is would come from the expansion of the universe itself. It expands exponentialy the farther out you look. At the edge of the visable universe stars travel close to the speed of light relative to us... and we can not "see" any stars or galaxies from past this point, because light cannot travel from them to us from this relative velocity.
 
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  • #11
As Eli Botkin said, focus on the things that are frame independent. There's probably some frame out there that thinks you're moving close to c. Why aren't you turning into a black hole?
 
  • #12
windscar said:
I read this post and it is a giant load of crap. E=mc^2 has nothing to do with this idea, and E=mc^2 isn't used to determine relativistic mass.

I don't know why you think that, as you don't quote any references of your own, but the sci.physics.faq is a reliable resource (it is however written mainly for a lay audience, which is both a strength and a weakness)

If you want more references look at

http://groups.google.com/group/sci.physics.relativity/msg/64049d344b664ee5 ?dmode=source

which is an actual "post" (as opposed to the FAQ).

Information about Steve Carlip, the author of the above post, (which also cites the FAQ entry and expands a bit on it) can be found at

http://www.physics.ucdavis.edu/Text/Carlip.html#Honors

(If you're really paranoid, I imagine you can verify Steve Carlip's credentials from other sources).
 
  • #13
I wish I were more informed on the subject to jump into the “black hole” debate, but there’s still a lot of basic stuff to conquer. By the way, I do appreciate your time and effort explaining all this.

From what I understand, the formula Windscar posted [tex] m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex] is the time dilation factor, used for both calculating time delay and mass increase. Now, are these two different ways to look at the same effect or are these two completely separate effects? It looks like any way you look at the definition of mass, there’s time involved in one of the factors. So do I deduce increase in mass simply due the time factor changing or does the mass increase regardless of what time does? If the former, then what about accelerated particles producing some damage on the wall they hit. The amount of kinetic energy, using classical physics, should yield a certain amount of damage to the wall the particle hits. If I have a relativistic mass increase, the particle should do more damage, from an observer’s perspective, the only perspective I care about, right?. When I measure the damage, the time factor is out, is it not? Would that be a way to see if time dilation and mass increase are two separate effects?

Thanks,

Pavel.
 
  • #14
windscar said:
I read this post and it is a giant load of crap. E=mc^2 has nothing to do with this idea, and E=mc^2 isn't used to determine relativistic mass.

[tex] m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex]
Are you familiar with the full version of E=mc^2 used for objects that have a nonzero momentum, namely:

[tex]E^2 = {m_0}^2 c^4 + p^2 c^2[/tex]

If you substitute in the formula for relativistic mass that you posted above, along with the formula for relativistic momentum:

[tex]p = \frac{m_0 v}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

...then you'll find that you end up with the formula [tex]E = mc^2[/tex], where m is the relativistic mass rather than the rest mass. So the formula E=mc^2 can in fact be used to determine relativistic mass.
 
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  • #15
Pavel said:
From what I understand, the formula Windscar posted [tex] m = \frac{m_0}{\sqrt{1 - \frac{v^2}{c^2}}} [/tex] is the time dilation factor, used for both calculating time delay and mass increase.
The factor [tex]\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex] appears in many formulas in relativity, it is denoted with the symbol [tex]\gamma[/tex], the greek letter "gamma". Not just in time dilation and relativistic mass, but also in the formula for length contraction, or:

[tex]L = \frac{L_0}{\gamma} = L_0 * \sqrt{1 - \frac{v^2}{c^2}}[/tex]

(L0 is the length of the object in its own rest frame, L is its length in another frame where the object is moving at speed v along the axis whose length is measured)

The relativistic gamma factor also appears in the "Lorentz transformation" which transforms the coordinates of an event in one frame to the coordinates in another. If an event happens at space coordinate x and time coordinate t in my frame, and I want to figure out its coordinates x' and t' in another frame which is moving at speed v along my x-axis, and whose origin (x'=0) passed by my own frame's origin (x=0) at a time coordinate of 0 in both frames (t=t'=0), then the transformation is:

[tex]x' = \gamma (x - vt) = \frac{x - vt}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

[tex]t' = \gamma (t - \frac{vx}{c^2}) = \frac{t - \frac{vx}{c^2}}{\sqrt{1 - \frac{v^2}{c^2}}}[/tex]

The time dilation equation and the length contraction formula can be derived directly from the Lorentz transformation, while the formula for energy/relativistic mass requires slightly more complicated proofs based on the assumption that the laws of physics should work the same way in each of the frames given by the Lorentz transform.
Pavel said:
Now, are these two different ways to look at the same effect or are these two completely separate effects? It looks like any way you look at the definition of mass, there’s time involved in one of the factors. So do I deduce increase in mass simply due the time factor changing or does the mass increase regardless of what time does?
I don't know of any way to deduce an increase in relativistic mass (which as I mentioned in my last post is equivalent to an increase in energy) from time dilation alone. Like I said, the relativistic gamma factor appears in a lot of different places, not just those two equations.
 
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  • #16
JesseM said:
I don't know of any way to deduce an increase in relativistic mass (which as I mentioned in my last post is equivalent to an increase in energy) from time dilation alone. Like I said, the relativistic gamma factor appears in a lot of different places, not just those two equations.


Ok, let me ask you about it this way. I set up an inertial mass between two springs in space, make it oscillate and count ticks per unit of time. The number of ticks obviously depends on the amount of inertial mass. I then speed up the system. Given SR, I should expect the number of ticks to decrease. Does this decrease happen due to time dilation or mass increase? Is it possible to tell? Well, maybe. What if I now calculate the [tex]\gamma[/tex] factor and somehow reduce the inertial mass to adjust for the relativistic mass increase? My question then is, will I now observe the same number of ticks when the system was at rest or will the number still be lower? If it’s the same, then should I conclude that time dilation and relativistic mass increase are the same thing being called two different names depending on the context of measurements? And if the number of ticks is still lower, then should I conclude that time dilation is a separate effect in addition to mass increase? I hope I’m making sense here. If my math was up to speed, I’d figure this out on my own, but until then I have to resort to thought experiments and ask you about the resulting observations. Again, thanks for your help.

Pavel.
 
  • #17
First off, if you assume that you would not observe some kind of black hole effect from observing an object approaching the speed of light, then you would in affect be putting a limit on the amount of curvature of space time as an object approached C. The thing is that Einsteins equation's don't put any such limits on relativity. And if someone discovered a way to prove where these limits take place they would solve a lot of problems faced today in theoretical physics because these equations wouldn't explode into infinities. No one really knows' but based on these equations, it should, because as V approaches C any M or T would approach infinity. Then the real question to answer this would be if as M approached infinity, would the mass be concentrated into a small enough point to create a black hole. Well, the thing is (and think should answer this question and Pavel's question) Special Relativity was not made into a field type of theory. It give no indication of the curvature of space-time near an object that is approaching the speed of light. Time dilation was found by figureing out how much of the hypotenuse of a right traingle should contract to show what an observer at rest should actually observe. Then all these other values were derived from that, when it could very well be the time dilation were sin(theta) =(vt/ct'). As for the matter of using the increase in mass to find further time dialation, I would say no. I don't believe the mass increase is actual increase in the amount of matter inside the atoms of the object. I see it as the objects speed is curving the space time around it relative to an observer at rest. If space-time is indeed one single thing, then the amount of time dilation should be the same even though it has curved the space around it by the same factor, the Lorentz Factor.
 
  • #18
windscar said:
First off, if you assume that you would not observe some kind of black hole effect from observing an object approaching the speed of light, then you would in affect be putting a limit on the amount of curvature of space time as an object approached C.

I'm not sure why you think that - there is in fact no limit on the curvature.

The details can be found in the Aichelburg-sexyl ultraboost

http://en.wikipedia.org/wiki/Aichelburg-Sexl_ultraboost
http://www.citebase.org/abstract?id=oai%3AarXiv.org%3Agr-qc%2F0110032 [Broken]
(online at)
http://arxiv.org/abs/gr-qc/0110032

Components of the curvature tensor increase ("gravitational field") increase without limit, approaching impulse functions in the limit as the velocity approaches c.

Why doesn't the force increase without limit? Basically, because of gravitomagnetism. The "gravitational field" (the curvature tensor, interpretable as tidal gravity) can be decomposed into parts that are somewhat analogous to the electric and magnetic fields of electromagnetism. The magnetic-like parts happen to oppose the electric-like parts in this case. Thus two parallel moving masses appear to have a stronger "electric-like" attrraction, but they also have a "magnetic-like" repulsion. The total force transforms covariantly, as it must.

But there's a much simpler way of describing the situation.
You're missing the most basic point of relativity - Velocity is relative

As other posters have already observed, relative to some observer, you are moving at a high velocity - arbitrarily close to 'c'. You would know if you were a black hole, because you would implode to a singularity. Because you don't implode to a singularity, we know that your scenario must be wrong, even without a more detailed analysis.
 
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  • #19
pervect said:
You would know if you were a black hole, because you would implode to a singularity. Because you don't implode to a singularity, we know that your scenario must be wrong, even without a more detailed analysis.

From what I understand, that's not necessarily the case. The larger the black hole is, the less density it needs to have to shield itself from the rest of the Universe. If I stuff enough stars into a galaxy to create sufficient gravitation thereby making it a black hole to the rest of the Universe, I can still can have a Sun inside such galaxy with planets revolving around it. No implosion necessary. I didn't make this up, is it wrong?

I also would appreciate any insight into my question about time dilation effect vs. mass increase. Is it the same thing or two different effects? In advance, thank you very much.

Pavel.
 
  • #20
Actually an observer falling into a black hole does not necessarily have fall into the singularity, it depends on what kind of black hole.
For instance in the case of a Kerr metric it is not necessarily the case.
 
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  • #21
pervect said:
As other posters have already observed, relative to some observer, you are moving at a high velocity - arbitrarily close to 'c'. You would know if you were a black hole, because you would implode to a singularity. Because you don't implode to a singularity, we know that your scenario must be wrong, even without a more detailed analysis.

Actually according to the twin paradox, both observes would see each other as a black hole at the same time. So being sucked into a singularity would be relative to how far the object's passed by each other. They then wouldn't know which one was the singularity until on accelerated to the speed of the other object. And then this acceleration would allow them to observe themselves being sucked into their own singularity, since acceleration is equal to gravitation.
 
  • #22
Then again, anyone trying to approach the speed of light would have to accelerate and this would separate them from observers traveling at a constant speed, hence allowing them to distinctivly observe themselves becoming a singularity.
 
  • #23
Pavel said:
From what I understand, that's not necessarily the case. The larger the black hole is, the less density it needs to have to shield itself from the rest of the Universe. If I stuff enough stars into a galaxy to create sufficient gravitation thereby making it a black hole to the rest of the Universe, I can still can have a Sun inside such galaxy with planets revolving around it. No implosion necessary. I didn't make this up, is it wrong?

Parts of this seem right - other parts seem wrong, if I am understanding you correctly. I may be misinterpreting what you said.

You can make a black hole by stuffing enough stars into a galaxy. If we imagine a spherical galaxy with a 50,000 light year radius, I estimate that you'll need

(r G ) / 2 c^2 = 10^17 solar masses to form a black hole. But such a mass would still collapse to a black hole in a finite amount of proper time. Using some formulas from an old thread

https://www.physicsforums.com/showpost.php?p=1201638&postcount=20

(unfortunately the homework problem set referenced in this thread is no longer online) the proper time for such a system to collapse (assuming an idealized symmetrical pressureless collapse) should be

[tex]
T = \frac{\sqrt{6 \pi}}{8 \sqrt{\rho G}}
[/tex]

I'm getting rho = 7*10^-16 kg/m^3 for this situation, which means that this system would collapse to a black hole in about 80,000 years.

It's possible I've made some numerical errors here, and any pressure in this situation would change the results slightly, but the point is that the proper time (measured by a clock on one of the stars) from the formation of such a galaxy to its inevitable collapse to a singularity would be finite.

A black hole formed out of the density of something the same as water would collapse in about 35 minutes by this formula.

So if you were large enough to form a black hole, and started with around the same density that you have now (that of water, 1000kg / m^3), you would only live about 35 minutes before you collapsed into a singularity.

I also would appreciate any insight into my question about time dilation effect vs. mass increase. Is it the same thing or two different effects? In advance, thank you very much.

Pavel.

I'll try to give a short answer in another post. I see that this was in fact the originating question of this thread, before the thread got hijacked by some other concerns.
 
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  • #24
Pavel said:
I also would appreciate any insight into my question about time dilation effect vs. mass increase. Is it the same thing or two different effects? In advance, thank you very much.

Pavel.

OK, this is the relevant thread - it just got hijacked.

Pavel said:
Hi! Just as I thought I was getting a pretty good grip on relativity, I got thrown back to square one. Please straighten out something for me by taking a role of a passer-by in my thought experiment.

First, I read that according to Special Relativity (SR), observers in two moving inertial frames will perceive time dilation with respect to each other, regardless of the direction of the motion. That is, if I moving at a constant speed towards you, head-on, I will perceive your clock moving slower than mine, and you will perceive my clock to be slower than yours. This is according to SR alone, all other things aside! Correct? Very well. Then I can construct the following thought experiment, which is obviously wrong, but I'd like somebody to explain to me what other relativistic effects are in place and how they solve the "paradox"

First off, let me say that your understanding is correct. Both observers determine that the other observer's clock is running slow.

As I answered tersely before, the thing you are looking for, the thing that is missing from your analysis s that simultaneity is relative.

When two people at different location compare clocks, they must use some defintion of simultaneity to do so. The defintion of what events are simultaneious are DIFFERENT for two observers moving differently. The wikipedia article I referenced earlier

http://en.wikipedia.org/wiki/Relativity_of_simultaneity

talks about this. This is one of the trickiest aspects of relativity to grasp initially, it is the key to resolving most "paradoxes" of SR.

Let me try and say, very briefly, what relativity of simultaneity menans.

It means that if we have two obsevers, A and B, that are moving relative to each other, that the set of points regarded as simultaneous by observer A is DIFFERENT from the set of points regarded as simultaneous by observer B.

I hope you can see how this complicates your analysis.
 
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  • #25
clarity

Pavel said:
This ship flies at a constant speed, almost the speed of light and will fly by both Earth and AC. Being an amateur physicist, I reason: "Hmm, because the passer-by in the ship will literally perceive AC to be much closer and the clock on the bomb on AC will run slower relative to the passer-by (according to SR), if I somehow let the passer-by know about the doomsday of the Alpha Centaurians, the SR's time dilation will allow the passer-by to save them".
Pavel.

1. part of the explanation is in your quote "PERCEIVE".
perception is not reality.
2. back to first principles: the speed of light is independent of its origin.
it would require 4 yrs from that location.
 
  • #26
phyti said:
1. part of the explanation is in your quote "PERCEIVE".
perception is not reality.
2. back to first principles: the speed of light is independent of its origin.
it would require 4 yrs from that location.

Who are all these people that think that Special Relativity is only some kind of illusion? Who is spreading this garb? If you perceive something, it becomes a part of your reality.
 
  • #27
windscar, you're presenting as fact a lot of totally false information about how relativity works--have you read the Physics Forums Global Guidelines policy on "overly speculative posts", or the IMPORTANT! Read before posting message at the top of this forum? For example:
Actually according to the twin paradox, both observes would see each other as a black hole at the same time. So being sucked into a singularity would be relative to how far the object's passed by each other. They then wouldn't know which one was the singularity until on accelerated to the speed of the other object. And then this acceleration would allow them to observe themselves being sucked into their own singularity, since acceleration is equal to gravitation.
This is nonsense--right now we are traveling at some extremely large fraction of light speed in some frame, so why don't we see ourselves being sucked into a singularity? In any case, if you actually calculate the answer in general relativity instead of just making baseless speculations, the answer you get is that a high relativistic mass due to large velocity does not create a black hole if the object's mass in its own frame is not enough to create one. It is certainly not true that "according to the twin paradox" each twin sees the other one become a black hole!
windscar said:
Then again, anyone trying to approach the speed of light would have to accelerate and this would separate them from observers traveling at a constant speed, hence allowing them to distinctivly observe themselves becoming a singularity.
Again, there are perfectly valid frames in which any object you like--including the Earth--is already moving arbitrarily close to light speed, no acceleration necessary.
 
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  • #28
Pervect and phyti, thank you for your insights. I think I got what I wanted on my original question. JesseM gave me the clue I needed – I didn’t realize that according to my calculations the clocks on AC are actually ahead of similar calculations done on Earth; and that the reason that I see the clocks rolling fast during my journey is due to Doppler effect.

But now, here’s still the mind bending twist. If you can reconcile the following, things would be a lot clearer. I’m going to try to remove the Doppler effect from the picture, by setting up clocks all along my journey to AC and I’ll be “looking” at these clocks as I go by them.

So, AC and Earth are in the same frame. I synchronize all the clocks in this frame and I set a whole bunch of them on the way from Earth to AC. It’s the year 2000 in this frame, it takes light 4 years to reach Earth from AC. I fly by Earth at almost c. You stand on Earth. Both you and I see the image of the clock from AC showing 1996. According to your calculations it’s 2000 on AC, according to my calculations it’s year 2003.9 on AC. So, by the time I reach AC in 0.1 years, the image of the clock I see from AC will go from 1996 to 2004, in 0.1 years of my time. That is due to Doppler effect, as you assert. That’s good; but now, as I fly, instead of looking at the image of the clock from AC, I will be looking at the clocks set up all the way from Earth to AC. They will go from 2000 to 2004 in 0.1 years of my time. THAT is not due to Doppler effect! So, according to SR, the clocks in the AC-Earth frame should be ticking slower, time should dilate. But as I watch these clocks on my journey, they roll a lot faster than mine. Again, these clocks are all synchronized, they show real time of the frame, and since I look at them at very close proximity, there is no need to adjust for delay to receive their images. So, if you ask me, time does not dilate here, it runs faster realtive to my clock. What’s the deal here?

Thanks,

Pavel
 
  • #29
I was using the twin paradox to draw a new conclusion and if the first conconlusion (traveling close to light create's a singularity) was correct than this one would also be correct. Have you read my forum about Delta T > To? I think I understand the basis of relativity and I can show how your change in time just happens to be the inverse of Einsteins origianal equation. Also, we are moveing close to the speed of light relative to other object's in the universe. But, this is due to the expansion of the universe itself. We do not feel any affect from the acceleration due to this expansion.

The expanion of the universe can be described as being on the surface of a balloon that is being blown up. You can draw different points on the balloon and blow it up and watch them get farther and farther away from them. But they all stay on the same points of the balloon. They are moving away from each other with a constant speed in a higher dimension. It is as if they are in constant free fall, traveling a straight line in a dimension, which reduces the force of acceleration felt to zero. That is why we don't feel any forces on ourselves or on the other object with relative acceleration. When looking at the expansion from this stand point, all object's with relative motion due to the expansion of the universe are moveing at a constant velocity relative to each other through a higher dimension. All of these objects are not moveing relative to space-time itself and are at rest relative to the universe itself. (all the point's stay on the same place on the balloon). But, if an object traveling close to the speed of light relative to us in a far away galaxy, started to approach us and their velocity was close to the speed of light relative to the velocity of the expansion of the universe in our area, the object would undergo all the affect's of relativity. Therefore, an object traveling at high velocity due to the expansion of space-time, does not prove anything about the conditions of object's traveling close to the speed of light. Furthermore, the "event horizon" of the universe turns out to be the distance away from us that the expansion of the universe comes out to be the speed of light. As we do not see any objects that are farther out than this.
 
  • #30
Pavel said:
So, AC and Earth are in the same frame. I synchronize all the clocks in this frame and I set a whole bunch of them on the way from Earth to AC. It’s the year 2000 in this frame, it takes light 4 years to reach Earth from AC. I fly by Earth at almost c. You stand on Earth. Both you and I see the image of the clock from AC showing 1996. According to your calculations it’s 2000 on AC, according to my calculations it’s year 2003.9 on AC.
OK, in this case you must be traveling at 0.975c.
Pavel said:
So, by the time I reach AC in 0.1 years, the image of the clock I see from AC will go from 1996 to 2004, in 0.1 years of my time.
Not exactly. If you're going at 0.975c relative to Earth and Alpha Centauri, then the distance between Earth and Alpha Centauri is shrunk from 4 light years to [tex]4 * \sqrt{1 - 0.975^2}[/tex] = 4 * 0.2222 = 0.8888 light years, and since Alpha Centauri is moving towards you at 0.975c, it takes you 0.9116 years to reach it in your frame. However, in your frame Alpha Centauri's clock is also slowed down by a factor of 0.2222, so it only advances forward by 0.9116 years * 0.2222 = 0.2026 years, so it will read 2003.9 + 0.2026 = 2004.1 when you arrive. This matches the prediction of the Earth frame, where you travel 4 light years at 0.975c and therefore take 4.1 years to reach Alpha Centauri, so if you leave in 2000 you'll arrive in 2004.1
Pavel said:
That is due to Doppler effect, as you assert.
Well, the Doppler effect accounts for the fact that if I look through a telescope I'll see the clock at Alpha Centauri ticking fast, going from 1996 to 2004.1 in only 0.9116 years according to my own clock. But the fact that Alpha Centauri's clock reads 2004.1 when I arrive can also be deduced by ignoring what I see and just calculating what is true in my frame, as I did above, where Alpha Centauri's clock was ticking slower than mine throughout the journey but it started off at 2003.9 as I was passing Earth.
Pavel said:
That’s good; but now, as I fly, instead of looking at the image of the clock from AC, I will be looking at the clocks set up all the way from Earth to AC. They will go from 2000 to 2004 in 0.1 years of my time. THAT is not due to Doppler effect!
No, it's due to the fact that each successive clock is ahead of the previous one in my frame, in much the same way that the clock at Alpha Centauri was ahead of the clock at Earth by 3.9 years in my frame. So even though each individual clock is ticking slower than mine, the time I read on each clock as I pass it is farther ahead of the time I read on the previous clock as I passed it than the amount my own clock has advanced in that time. For example, if each clock was only 4 light-seconds apart, then in my frame, each clock is 3.9 seconds ahead of the last one at any given moment. So at the moment I pass a clock reading T=10 seconds, the next clock already reads T=13.9 seconds in my frame "at the same moment". It would take me 0.9116 seconds to reach the next clock, and each clock only advances forward by 0.2026 seconds in my frame due to time dilation, so at the moment I pass the second clock, the first clock reads T = 10+0.2026 = 10.2026 seconds, while the second clock reads T = 13.9 + 0.2026 = 14.1026 seconds. So even though each clock is ticking slow in my frame, it's still true that the time on the second clock as I pass it (T=14.1026 s) is 4.1026 seconds greater than the time on the first clock as I passed it (T=10 s), while my clock has only advanced 0.9116 seconds in that time.

You might like to look at my thread An illustration of relativity with rulers and clocks, where I posted some diagrams of a situation much like this, where two rulers with clocks placed along them at regular intervals were passing alongside each other, and you can see how it's consistent for each ruler to measure the other ruler's clocks as both slowed down closer together relative to its own, as measured in the ruler's own rest frame.
 
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  • #31
Awesome reply, Jesse! This is exactly what I was looking for - a detailed and consistent account of what is going on. I need to go now disect and chew on it for a little until it's all digested in my head. I appreciate your time and effort illustrating the math too.

Pavel.
 
  • #32
a slight correction

quote from jesseM post #30
"However, in your frame Alpha Centauri's clock is also slowed down by a factor of 0.2222, so it only advances forward by 0.9116 years * 0.2222 = 0.2026 years, so it will read 2003.9 + 0.2026 = 2004.1 when you arrive."

Let 'E' be the Earth observer and 'S' be the ship observer.
The trip takes 4/.975=4.10 yrs Earth time.
The S clock reads (4.1)*sqrt(1-.975^2)=.88 yr elapsed time to AC.
S sees the elapsed time of the AC clock from 1996 to 2004.1 as 8.1 yrs.
E calculates the doppler factor as (8.1)/(4.1)=1.975 (=1+v/c)
With time dilation, S calculates the doppler factor as (8.1)/(.88)=9.20.
S perceives the AC clock to be running faster, not slower.
Reasoning if S's clock has slowed, a unit of time on the ship is longer
than the same unit on earth, and will contain more events.
For S world events outside the ship are happening at a faster rate.
Time dilation depends on your speed relative to light.
The doppler effect depends on your speed and direction relative to a light
signal.
 
  • #33
phyti said:
quote from jesseM post #30
"However, in your frame Alpha Centauri's clock is also slowed down by a factor of 0.2222, so it only advances forward by 0.9116 years * 0.2222 = 0.2026 years, so it will read 2003.9 + 0.2026 = 2004.1 when you arrive."

Let 'E' be the Earth observer and 'S' be the ship observer.
The trip takes 4/.975=4.10 yrs Earth time.
The S clock reads (4.1)*sqrt(1-.975^2)=.88 yr elapsed time to AC.
S sees the elapsed time of the AC clock from 1996 to 2004.1 as 8.1 yrs.
E calculates the doppler factor as (8.1)/(4.1)=1.975 (=1+v/c)
With time dilation, S calculates the doppler factor as (8.1)/(.88)=9.20.
S perceives the AC clock to be running faster, not slower.
Yes, but in the sentence you quoted I was referring to how fast Alpha Centauri's clock was ticking in the ship observer's rest frame, which is different from how fast the ship observer sees Alpha Centauri's clock ticking if he's watching it through a telescope. They are two different concepts--what happens in your frame is what you calculate after you have factored out delays due to the finite speed of light (for example, in the Earth observer's frame he sees AC's clock reading 1996 when his own clock reads 2000, but he knows the light took 4 years to reach him, so he concludes that the events he is currently seeing happened at the same time-coordinate of his own clock reading 1996, 4 years in the past).

"Time dilation" in relativity is understood in terms of how fast a clock is calculated to be ticking in your own rest frame--if the clock is moving this is always slower, never faster than your own clock--not based on how fast you see the clock ticking.
 
  • #34
not convinced

S sees the AC clock at 1996 as he leaves earth.
S sees the AC clock at 2004.1 when he arrives at AC.
S sees the elaplsed time on his (S) clock as .88 yrs.
S sees nothing wrong with his clock.
It is running slower only to the other observers but not to him.
Even if S subtracts 4 yrs for the light to reach earth,
there are 4.1 yrs elapsed on the AC clock, which he sees during his trip of .88 yrs. His time dilation increases the doppler effect by a signicant amount.
If he looked back at earth, he would see events moving very slowly because of exteme doppler and time dilation.
Look at the numbers, they tell the story.
 
  • #35
phyti said:
S sees the AC clock at 1996 as he leaves earth.
S sees the AC clock at 2004.1 when he arrives at AC.
S sees the elaplsed time on his (S) clock as .88 yrs.
S sees nothing wrong with his clock.
It is running slower only to the other observers but not to him.
Even if S subtracts 4 yrs for the light to reach earth,
there are 4.1 yrs elapsed on the AC clock, which he sees during his trip of .88 yrs. His time dilation increases the doppler effect by a signicant amount.
If he looked back at earth, he would see events moving very slowly because of exteme doppler and time dilation.
Look at the numbers, they tell the story.
If you do all of the calculations in Earth's rest frame, you will get exactly what Earth's rest frame describes.

Have you tried doing any of the calculations in S's rest frame?
 
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