Faster than light relative speeds (I know it's impossible)

[coktail]

We have particle accelerators on Earth that can speed up particles to near the speed of light. Earth itself is hurtling through space, as is the solar system and galaxy that its a part of.

If an observer were to float outside of our galaxy and observe those speeding particles in the accelerator on Earth, how would the cumulative movement of the particles, Earth, the solar system, and the galaxy not add up to more than the speed of light (Aside from the fact that the velocities might not add up)?

Time dilation?

I know that FTL travel is impossible, so I'm not trying disprove it or anything futile like that. I just can't wrap my head around how this works, and I couldn't find a thread that addressed this question.

Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?"

Phewph! Thanks for your help.

 

[Whovian]

Simple. Speed doesn't add up like normal. If an observer sees a train moving at velocity $\vec{v}_1$ and you're walking on it at velocity $\vec{v}_2$ (relative to the train), your speed as observed from the observer is not $\vec{v}_1+\vec{v}_2$. It's a bit different, and supported by time dilation.

 

[coktail]

My time as an observer dilates as the train passes me? I thought it would be the train's time that would dilate...

So close to understanding, and yet so far.

 

[Mentz114]

I know that FTL travel is impossible,...

Good. Also, nothing with mass can even reach light speed.

... "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?"

Impossible. The train cannot travel at the speed of light.

Please look up the relativistic velocity addition rule, e.g.

http://en.wikipedia.org/wiki/Velocity-addition_formula

As Whovian said, you can't add velocities with v₁ + v₂.

 

[Nugatory]

Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?"

Yes, it is basically the same, and the answer is:

First, you can't ask any question about "a train moving at the speed of light", because, as you say, that's impossible so there is no such thing. But you can pose the same general problem by asking about a train that is moving at 99.99999999999999999% of the speed of light.

If you are on that train and walking forward at speed v, your speed relative to the train will be v.

However an observer watching the train pass at speed u, very close to the speed of light, will NOT measure your speed as u+v, but rather as (u+v)/(1+uv).

Here I'm measuring distances in light-seconds and time in seconds, so the speed of light is equal to 1; if I used some other units there'd have to be a c^2 in there somewhere.

 

[Whovian]

My time as an observer dilates as the train passes me? I thought it would be the train's time that would dilate...

So close to understanding, and yet so far.

From your reference frame, no, you count quite well as an inertial observer.

From the person off the train's reference frame, yes, both you and the train are severely time-dilated.

 

[coktail]

So in my galaxy, solar system, Earth, particle accelerator thought experiment, which is admittedly overly-complex, the same principal of the train applies, and the magical floating observer measuring the velocity of the particles in the accelerator from outside the galaxy would see them as moving slower than the speed of light because he would be time-dilated because of his movement relative to the galaxy etc... that he's observing?

Is there a maximum time dilation? It seems to me (incorrectly?) that the more movement you add on top of other movement, the more time has to dilate to accommodate.

 

[Nugatory]

Is there a maximum time dilation? It seems to me (incorrectly?) that the more movement you add on top of other movement, the more time has to dilate to accommodate.

Actually, that's pretty much about right... no maximum time dilation. The amount of time dilation is given by:

$1/ \sqrt{1-v^{2}}$

and that becomes infinite as v approaches 1 (the speed of light in my seconds and light-seconds units). So the more velocity you add, the more time dilation and length contraction you get, and these effects become arbitrarily large as you get arbitrarily close to the speed of light.

 

[coktail]

Yussss. I've heard and read people say things like, "70% time dilation." Is that relative to a reference frame? As in, you're time is dilated 70% relative to mine?

 

[The_Duck]

If an observer were to float outside of our galaxy and observe those speeding particles in the accelerator on Earth, how would the cumulative movement of the particles, Earth, the solar system, and the galaxy not add up to more than the speed of light (Aside from the fact that the velocities might not add up)?

Time dilation?

Yes. The accelerator physicists sitting next to the accelerator measure their particles to have some velocity relative to the earth. They do this using some sort of generalized meter-sticks and stopwatches, recording how far the particles travel in some amount of time, and then calculating speed = distance / time.

Now, from the perspective of the distant observer the Earth has some large velocity through space. As a result, the observer perceives all the meter-sticks on Earth to be length-contracted along the Earth's direction of motion, and all the stopwatches on Earth to be slow. As a result the distant observer does not agree with the speed calculation performed by the accelerator physicists on Earth. If he does his own calculation of the speed of the particles relative to the Earth, using his own meter-sticks and his own stopwatches, he will get a smaller value than the accelerator physicists. Then when he adds in the velocity of the Earth, he will always get a value less than c, no matter how fast the accelerator physicists observe the particles to be traveling in their reference frame.

 

[HallsofIvy]

So in my galaxy, solar system, Earth, particle accelerator thought experiment, which is admittedly overly-complex, the same principal of the train applies, and the magical floating observer measuring the velocity of the particles in the accelerator from outside the galaxy would see them as moving slower than the speed of light because he would be time-dilated because of his movement relative to the galaxy etc... that he's observing?

Is there a maximum time dilation? It seems to me (incorrectly?) that the more movement you add on top of other movement, the more time has to dilate to accommodate.

No, he would see them as moving slower than the speed of light because speeds do not combine just as "u+ v" (Whovian says "Speed doesn't add up like normal". I would say, rather, that "combining speeds do not add".) For any u and v less than c, (u+ v)/(1+ (uv/c^2))) is still less than c.

People with respect to whom the observer is moving would see him "time dilated" with respect to them, he would see them "time dilated" with respect to him. There is no "maximum time dilation" (nor "minimum time rate") the closer the speed of an object, relative to me, is to c, the slower I would observe their timer rate. Since the speed of an object, relative to me, can be arbitrarily close to c, but not equal to c, the time rate I observe could be arbitrarily close to 0 but not equal to 0.

 

[xlines]

Time dilation?
...
Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?"

Phewph! Thanks for your help.

In essence - yes. Maybe this mental image will help you. Photon (quanta of light) and proton (a baryon, nucleus of hydrogen) are racing across the galaxy. Let's say that proton has so much energy and it's so fast that after 100 years of racing, it's only 1nm behind photon. Let us also assume that one of the postulates of STR, velocity of light is the same in all inertial systems, is true. So, if light always has the same speed for all observers, how come photon managed to run away only 1nm in 100 years?

TIME DILATATION. Having so much kinetic energy, while we spent entire lifetime, proton saw only 10^(-17) seconds of action. So, that's what happens and when you lay that on a paper, you get neat velocity addition formulas you can find on wiki or somewhere.

 

[coktail]

Would it be totally off base to say that the farther you zoom out in the universe, the greater the level of time dilation since movement compounds on top of movement at the smaller levels relative your zoomed out reference frame?

 

[dkong]

Would it be totally off base to say that the farther you zoom out in the universe, the greater the level of time dilation since movement compounds on top of movement at the smaller levels relative your zoomed out reference frame?

Time dilation doesn't depend on position or separation, only relative velocities. If you add up all the velocities at the smaller levels (using the non-classical velocity addition formula, of course), then you'll find a net relative velocity between you and what you're observing, and that is what time dilation will depend on.

 

[solarflare]

Yes, it is basically the same, and the answer is:

First, you can't ask any question about "a train moving at the speed of light", because, as you say, that's impossible so there is no such thing. But you can pose the same general problem by asking about a train that is moving at 99.99999999999999999% of the speed of light.

If you are on that train and walking forward at speed v, your speed relative to the train will be v.

However an observer watching the train pass at speed u, very close to the speed of light, will NOT measure your speed as u+v, but rather as (u+v)/(1+uv).

Here I'm measuring distances in light-seconds and time in seconds, so the speed of light is equal to 1; if I used some other units there'd have to be a c^2 in there somewhere.

Didnt Einstein himself imagine himself speeding through space on a beam of light? if light can not travel less than the speed of light then he must have been traveling at the speed of light.
Its people like you that tell others something can't be true, without any real evidence, that keep our civilisation static. Its good job Einstein was able to think like that without having to endure critisism because we might not have the theory in the first place.

 

[QuantumHop]

Didnt Einstein himself imagine himself speeding through space on a beam of light? if light can not travel less than the speed of light then he must have been traveling at the speed of light.
Its people like you that tell others something can't be true, without any real evidence, that keep our civilisation static. Its good job Einstein was able to think like that without having to endure critisism because we might not have the theory in the first place.

Funniest trolling I've seen in a long time, keep up the good work :)

 

[Doc Al]

Didnt Einstein himself imagine himself speeding through space on a beam of light? if light can not travel less than the speed of light then he must have been traveling at the speed of light.
Its people like you that tell others something can't be true, without any real evidence, that keep our civilisation static. Its good job Einstein was able to think like that without having to endure critisism because we might not have the theory in the first place.

Note that it is Einstein's own theory--for which there is ample evidence--that prohibits trains and other massive objects from moving at light speed.

 

[solarflare]

the point is that he imagined himself on a beam of light, and came up with a theory that says it is impossiple to do what he imagined. People claim his theory explains how the universe works. (which i find amusing due to the fact that Einstein himself said that his theory was not complete and didnt explain everything)

Here is a question that i hope i can get an answer to. Why is it not possible for GPS to give exact results when we use GR. it gives results to within a few metres but if GR is precise then using it would surly give precise results.

 

[Doc Al]

Here is a question that i hope i can get an answer to. Why is it not possible for GPS to give exact results when we use GR. it gives results to within a few metres but if GR is precise then using it would surly give precise results.

Do you seriously think that the only thing affecting GPS accuracy is GR? Many other factors are involved. (The point for this forum is that SR and GR must be accounted for in GPS systems.)

 

[solarflare]

Do you seriously think that the only thing affecting GPS accuracy is GR? Many other factors are involved. (The point for this forum is that SR and GR must be accounted for in GPS systems.)

actually i don't think that at all - i think that there is a lot we don't know - for example light travels at the speed of light but only in a vacuum. so how is that revelent when the signals have to pass through an atmosphere?

 

[solarflare]

all i was trying to point out is that Einstein used his imagination and that made him come up with his theory. if you think Einstein is right then how you can you discourage others from doing the same thing as him. i say imagine anything you like and you might be able to fill in a few of the holes GR currently has.

 

[QuantumHop]

Here is a question that i hope i can get an answer to. Why is it not possible for GPS to give exact results when we use GR. it gives results to within a few metres but if GR is precise then using it would surly give precise results.

GPS systems are made DELIBERATLY innacurate to prevent them being used as guided missile systems, if they wanted to they could pinpoint you to the nearest inch.

GPS has been used to monitor continental drift.

 

[solarflare]

i doubt anyone needing to use a sat nav as a missile guidance system would care about a few metres. aim it the centre of the a large complex and you will still hit it. and i heard it was a few metres from many sources including those that are explaining how GR is needed for GPS. So what you are saying is that are telling us lies and saying it is true. why don't they say GPS is accurate to an inch but purposfully make it inaccurate.

after all the truth is what science is about - or at least i thought it was.

 

[jbriggs444]

Google for GPS selective availability, to learn that the intentionally induced fuzziness in the GPS system was turned off over a decade ago.

i.e. http://en.wikipedia.org/wiki/Global_Positioning_System

Google for GPS accuracy, to learn of the various problems that prevent vanilla GPS from obtaining accuracies approaching one inch and of the various approaches that can be used with GPS to obtain improved results.

i.e. http://earthmeasurement.com/GPS_accuracy.html

 

[jtbell]

Didnt Einstein himself imagine himself speeding through space on a beam of light?

And he realized that this line of thought led to logical/mathematical contradictions. This was one of the things that led him to his theory of relativity, which avoids the contradictions by eliminating reference frames that travel at the speed of light with respect to each other.

 

[QuantumHop]

i doubt anyone needing to use a sat nav as a missile guidance system would care about a few metres. aim it the centre of the a large complex and you will still hit it. and i heard it was a few metres from many sources including those that are explaining how GR is needed for GPS. So what you are saying is that are telling us lies and saying it is true. why don't they say GPS is accurate to an inch but purposfully make it inaccurate.

after all the truth is what science is about - or at least i thought it was.

This may be true if your ambling along in your car and you want to crash it into the local post office but when a missile is traveling a kilometre a second and your sat nav only updates every half a second the inaccuracies become huge.

The faster you go the more inaccurate GPS becomes because of the speed it updates.

*edit*

copy and pasted from the link posted above
http://en.wikipedia.org/wiki/Global_Positioning_System

Restrictions on civilian use

The U.S. Government controls the export of some civilian receivers. All GPS receivers capable of functioning above 18 kilometres (11 mi) altitude and 515 metres per second (1,001 kn)[61] are classified as munitions (weapons) for which State Department export licenses are required. These limits attempt to prevent use of a receiver in a ballistic missile. They would not prevent use in a cruise missile because their altitudes and speeds are similar to those of ordinary aircraft.

*and another edit*
http://news.bbc.co.uk/1/hi/england/nottinghamshire/2956026.stm

This link explains how GPS is used to monitor continental drift and measure the rise and fall of land mass to just a few millimetres.

 

[I_am_learning]

We have particle accelerators on Earth that can speed up particles to near the speed of light. Earth itself is hurtling through space, as is the solar system and galaxy that its a part of.

If an observer were to float outside of our galaxy and observe those speeding particles in the accelerator on Earth, how would the cumulative movement of the particles, Earth, the solar system, and the galaxy not add up to more than the speed of light (Aside from the fact that the velocities might not add up)?

Time dilation?

I know that FTL travel is impossible, so I'm not trying disprove it or anything futile like that. I just can't wrap my head around how this works, and I couldn't find a thread that addressed this question.

Is this question basically the same thing as, "If I walk forward on a train moving at the speed of light, how do I not travel faster than light?" Would that answer to THAT question change from the perspective of an observer watching that person walk to the front of the light speed train from the ground as the train passes?"

Phewph! Thanks for your help.

haha, You don't need to be so defensive to prove that you aren't a crackpot. You can simply say "I have read that FTL travel is impossible, I just can't wrap my head around."
But perhaps, its only me, who considers 'knowing' something only if I understand it.
Or may be its your way of showing respect and trust to the main stream science. Either way its your choice.

 

[solarflare]

This may be true if your ambling along in your car and you want to crash it into the local post office but when a missile is traveling a kilometre a second and your sat nav only updates every half a second the inaccuracies become huge.

The faster you go the more inaccurate GPS becomes because of the speed it updates.

*edit*

copy and pasted from the link posted above
http://en.wikipedia.org/wiki/Global_Positioning_System

Restrictions on civilian use

The U.S. Government controls the export of some civilian receivers. All GPS receivers capable of functioning above 18 kilometres (11 mi) altitude and 515 metres per second (1,001 kn)[61] are classified as munitions (weapons) for which State Department export licenses are required. These limits attempt to prevent use of a receiver in a ballistic missile. They would not prevent use in a cruise missile because their altitudes and speeds are similar to those of ordinary aircraft.

*and another edit*
http://news.bbc.co.uk/1/hi/england/nottinghamshire/2956026.stm

This link explains how GPS is used to monitor continental drift and measure the rise and fall of land mass to just a few millimetres.

I hate to burst your bubble but the USA is not the centre of the universe and there are other nations that make similar devices. If that was not the case then the USA would not be at all worried that Iran might be capable of firing a nuclear weapon.

Einstein used a lot of other peoples work and put then altogether and then used his imagination to fill in the gaps. I am not saying he is wrong but i think its ridiculous to say that he is definitely right on these forums when even the experts say he is probably wrong but like Newton its a good approximation for day to day practice.

 

[solarflare]

and just incase people reading this think in anti - relativity i am not. i just don't think that it should be used as a fact when the creator said himself that it had flaws. if he can say it has flaws i can't see how others can say now that it dont.

 

[Dale]

if you think Einstein is right then how you can you discourage others from doing the same thing as him. i say imagine anything you like and you might be able to fill in a few of the holes GR currently has.

Regardless of what Einstein did, this site is not designed for speculation nor for advancing the state of the art in science. It's mission is primarily educational, for discussing and learning current mainstream science, not developing new science.

and just incase people reading this think in anti - relativity i am not. i just don't think that it should be used as a fact when the creator said himself that it had flaws. if he can say it has flaws i can't see how others can say now that it dont.

Can you provide a specific reference for the supposed flaws?

AFAIK, SR is self consistent and is consistent with all experimental evidence today within it's domain of applicability.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

 

[coktail]

haha, You don't need to be so defensive to prove that you aren't a crackpot. You can simply say "I have read that FTL travel is impossible, I just can't wrap my head around."
But perhaps, its only me, who considers 'knowing' something only if I understand it.
Or may be its your way of showing respect and trust to the main stream science. Either way its your choice.

Both. I was being respectful to the mainstream science, and also trying to explain that I am not a crackpot.

 

[solarflare]

Regardless of what Einstein did, this site is not designed for speculation nor for advancing the state of the art in science. It's mission is primarily educational, for discussing and learning current mainstream science, not developing new science.

Can you provide a specific reference for the supposed flaws?

AFAIK, SR is self consistent and is consistent with all experimental evidence today within it's domain of applicability.

http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html

https://www.physicsforums.com/showthread.php?t=430554

 

[Dale]

https://www.physicsforums.com/showthread.php?t=430554

I didn't see anything in that thread about Einstein asserting a breakdown of relativity at the Planck scale.

 

[solarflare]

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

According to general relativity, the initial state of the universe, at the beginning of the Big Bang, was a singularity. Both general relativity and quantum mechanics break down in describing the Big Bang, but in general, quantum mechanics does not permit particles to inhabit a space smaller than their wavelengths. Another type of singularity predicted by general relativity is inside a black hole: any star collapsing beyond a certain point (the Schwarzschild radius) would form a black hole, inside which a singularity (covered by an event horizon) would be formed, as all the matter would flow into a certain point (or a circular line, if the black hole is rotating). This is again according to general relativity without quantum mechanics, which forbids wavelike particles entering a space smaller than their wavelength. These hypothetical singularities are also known as curvature singularities.

 

[DennisN]

and just incase people reading this think in anti - relativity i am not.

Ok.

i just don't think that it should be used as a fact when the creator said himself that it had flaws.

But now you seem to be arguing against relativity in a way I do not understand. Do you think SR and GR should not be taught, or what's your point? Science is based on models. SR and GR are two very good models. The best models are used, until better models are available. On this forum mainstream models (and some emerging models like e.g. Loop Quantum Gravity & String Theory) are discussed/used here.

if he can say it has flaws i can't see how others can say now that it dont.

I don't know/remember everything Einstein said, we will need some references for that. Further, I have personally never heard anyone claiming that SR or GR are Theories of Everything. They are however very successful theories within their domain (1, 2, 3). I do not know/understand who/what you are arguing against. But you could start a thread about it and perhaps find out?