A-wal Posted December 6, 2016 Report Posted December 6, 2016 ''Now here is a question for you. You set out to see Bob from your home, and drive for 1 second at 200,000 kilometers a second as measured by Bob, who is waiting on his porch for you to drive by. Bob's house is 200,000 kilometers from your home. How long before you see Bob? And what will your speedometer show?'' speedometer shows 200,000km a second It takes 1 second to get to Bob, But you see Bob instantly because of the clear line of sight."Light moves past every inertial (non accelerating) observer at the same relative velocity, so... A is moving away from a light source and B is moving in the same direction away from the light source and moving at 0.5c relative to A. C moves past A at c and C moves past B also at c. None of them accelerated. This is what's important to understand...Unlike the first example, C passes A at the same speed that C passes B. From A's perspective C moves past themselves at c and still from A's perspective, C moves past B at 0.5c. From B's perspective C moves past A at 1.5c and moves past themselves at c." The light © passes B at 0.5c in A's frame and passes B at 1c in B's frame. The same light is moving past the same object at different velocities depending on the reference frame. Velocity is a measure of distance in space over distance in time. So in A's frame the light is covering a shorter distance (length contraction) in space over a greater amount of time (time dilation) relative to B than it is in B's frame because it's in A's frame it's overtaking B at half the velocity than it in B's frame (0.5c instead of 1c). Firstly we both must reach an agreement and be sure we understand the definition of subjective and objective. subjectivesəbˈdʒɛktɪv/adjective 1. based on or influenced by personal feelings, tastes, or opinions. objective əbˈdʒɛktɪv/ adjective 1. (of a person or their judgement) not influenced by personal feelings or opinions in considering and representing facts. ObjectiveNot influenced by personal feelings or opinions in considering and representing facts. Examples:A model of velocity addition that includes time dilation and length contraction in order to be consistent with the verified observation that the speed of light is the same in all inertial frames of reference. Light moving at a finite speed rather than magically teleporting from the source to your eye. SubjectiveBased on or influenced by personal feelings, tastes or opinions. Examples:Everything you post. Incorrect. Your speedometer shows 260,000km a second due to time contraction.No. He already specified that it's moving at 200,000 km per second. Objects that are in relative motion are time dilated and length contracted. An object is never time dilated and length contracted from its own perspective. There's no such thing as time contraction. Are you using 'time contraction' as shorthand for time dilation and length contraction? It doesn't work. Time doesn't contract, it dilates. Length in time dilates, length in space contracts. Quote
xyz Posted December 6, 2016 Author Report Posted December 6, 2016 OK I can not quite believe my ears from the posts. Let me put this very very simply for you all to remove your obvious confusion. A twin makes any of the journeys you mention, he arrives at his destination to see the dilated time. He arrives back at Earth to tell the twin brother all about it. He tells the twin he as aged less and explains why. The twin brother looked at him puzzled, he says to his time dilated twin brother, '' how strange you think that, you did not just arrive back here in the past, if time had ran slower for you then how do you explain you just arrived back here in my present, you have spent the same amount of time away from me as I you and you arrived back here in my present''. The end. Quote
billvon Posted December 6, 2016 Report Posted December 6, 2016 OK I can not quite believe my ears from the posts. . . . The twin brother looked at him puzzled, he says to his time dilated twin brother, '' how strange you think that, you did not just arrive back here in the past, if time had ran slower for you then how do you explain you just arrived back here in my present, you have spent the same amount of time away from me as I you and you arrived back here in my present''.Ah. You do not understand the twin paradox, then. It does not involve "arriving back here in the past." Quote
billvon Posted December 6, 2016 Report Posted December 6, 2016 No, the speedometer is in the moving frame of reference and will measure a contracted distance and a dilated time. But the relative velocity measured in the moving frame must agree with the relative velocity measured in the rest frame. In this case, the stationary observer measures a relative velocity of 200,000 km/s and the moving observer must agree on that velocity.Only if the moving person uses his (moving) ruler to compare against passing landmarks. If he knows that his friend lives 200,000km away, he will note that it takes him .745 seconds to get there. If he calculates that velocity, he will deduce it is 260,000 km/s. So from his perspective, compared to the road, he is going faster. Quote
xyz Posted December 6, 2016 Author Report Posted December 6, 2016 (edited) Ah. You do not understand the twin paradox, then. It does not involve "arriving back here in the past."I understand that for time to slow for a person, they would be out of sink in time compared to everyone else. They would arrive back here in the past. Think about why you are so wrong on what I have just said. Think about travelling from A to B and back again, time does not slow down, you arrive back in the same time as me. A rocket travels at 1000 mph to the sun, the clock on board the rocket runs slow, this does not affect the velocity of the rocket. Edited December 6, 2016 by xyz Quote
OceanBreeze Posted December 6, 2016 Report Posted December 6, 2016 Only if the moving person uses his (moving) ruler to compare against passing landmarks. If he knows that his friend lives 200,000km away, he will note that it takes him .745 seconds to get there. If he calculates that velocity, he will deduce it is 260,000 km/s. So from his perspective, compared to the road, he is going faster. You said his speedometer would read 260,000 km/s. That is wrong. Now you are talking about making a comparison with the stationary observer and calculating his velocity. That is a different matter and in fact it is still wrong. His velocity was exactly 200,000 km/s. That is what length contraction and time dilation results in. Quote
OceanBreeze Posted December 6, 2016 Report Posted December 6, 2016 "Light moves past every inertial (non accelerating) observer at the same relative velocity, so... A is moving away from a light source and B is moving in the same direction away from the light source and moving at 0.5c relative to A. C moves past A at c and C moves past B also at c. None of them accelerated. This is what's important to understand...Unlike the first example, C passes A at the same speed that C passes B. From A's perspective C moves past themselves at c and still from A's perspective, C moves past B at 0.5c. From B's perspective C moves past A at 1.5c and moves past themselves at c." The light © passes B at 0.5c in A's frame and passes B at 1c in B's frame. The same light is moving past the same object at different velocities depending on the reference frame. Velocity is a measure of distance in space over distance in time. So in A's frame the light is covering a shorter distance (length contraction) in space over a greater amount of time (time dilation) relative to B than it is in B's frame because it's in A's frame it's overtaking B at half the velocity than it in B's frame (0.5c instead of 1c). The parts in red are wrong. You cannot use simple addition and subtraction to get these relative velocities. Your result of 1.5 c for the relative velocity of C with respect to A, from B’s perspective should alert you that you are doing something wrong. No relative velocity is ever more than c from any reference frame. . Quote
OceanBreeze Posted December 6, 2016 Report Posted December 6, 2016 About the only thing right about this thread is the fact it is located in the “Strange Claims Forum” The amount of wrongness in here is just astonishing. :shocked: Quote
A-wal Posted December 7, 2016 Report Posted December 7, 2016 OK I can not quite believe my ears from the posts. Let me put this very very simply for you all to remove your obvious confusion. A twin makes any of the journeys you mention, he arrives at his destination to see the dilated time. He arrives back at Earth to tell the twin brother all about it. He tells the twin he as aged less and explains why. The twin brother looked at him puzzled, he says to his time dilated twin brother, '' how strange you think that, you did not just arrive back here in the past, if time had ran slower for you then how do you explain you just arrived back here in my present, you have spent the same amount of time away from me as I you and you arrived back here in my present''. The end.WFT! :) Er, no. Time dilation can never cause an object to move backwards on time. It causes objects to move forwards in time at different rates so that if two objects start off in the same frame and then move relative to each each before meeting up in a common frame of reference again, the object that accelerated will have aged less than the one that didn't. Read it again:"Light moves past every inertial (non accelerating) observer at the same relative velocity, so... A is moving away from a light source and B is moving in the same direction away from the light source and moving at 0.5c relative to A. C moves past A at c and C moves past B also at c. None of them accelerated. This is what's important to understand...Unlike the first example, C passes A at the same speed that C passes B. From A's perspective C moves past themselves at c and still from A's perspective, C moves past B at 0.5c. From B's perspective C moves past A at 1.5c and moves past themselves at c." How could two objects possibly observe the same thing moving past the same object at different velocities without time dilation and length contraction??? Velocity is a measure of distance in space over distance in time so if they're measuring the same thing moving at different velocities then they're measuring different lengths in time and space because the object is moving over a different amount of space/time. This is time dilation and length contraction. You cannot have a constant speed of light without objects in motion relative to each other disagreeing of the velocity objects, therefore you cannot have a constant speed of light without length contraction and time dilation! Only if the moving person uses his (moving) ruler to compare against passing landmarks. If he knows that his friend lives 200,000km away, he will note that it takes him .745 seconds to get there. If he calculates that velocity, he will deduce it is 260,000 km/s. So from his perspective, compared to the road, he is going faster.No, you have to apply time dilation and length contraction to the reference object (the road) so that the velocity stays the same but the time taken is dilated and the distance is contracted. The velocity remains the same because it's measured in the frame of reference of the observer. I see what you're saying, you can used the measurement of the distance in space between the starting point and the destination when you at rest relative to those two points but that's not the frame of reference you're in while you're in motion relative to those points so it doesn't apply. What you could do is work out what speed you were going once you've arrived at the destination (and are no at rest relative to it) from this reference frame but that's the reference frame you were in while making the journey. The parts in red are wrong. You cannot use simple addition and subtraction to get these relative velocities. Your result of 1.5 c for the relative velocity of C with respect to A, from B’s perspective should alert you that you are doing something wrong. No relative velocity is ever more than c from any reference frame.:) No they're not. If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame. The rule is that objects can move at or over c relative to you, they can't move at or over 2c relative to each other. If an object is moving away from you at 0.5 and towards a light source as in the example you quoted then that light is moving at 1.5 relative to that object from your perspective. About the only thing right about this thread is the fact it is located in the “Strange Claims Forum” The amount of wrongness in here is just astonishing. :shocked: Stop posting then. That would help a lot. Quote
A-wal Posted December 7, 2016 Report Posted December 7, 2016 Time dilation can never cause an object to move backwards on time. It causes objects to move forwards in time at different rates so that if two objects start off in the same frame and then move relative to each each before meeting up in a common frame of reference again, the object that accelerated will have aged less than the one that didn't.Although this is caused by length contraction just as much as time dilation. The rate the time passed was different for the two objects but so was distance in space that the objects travelled. The combination of both is what accounts for the difference in the amount of proper time that elapsed for them. The parts in red are wrong. You cannot use simple addition and subtraction to get these relative velocities. Your result of 1.5 c for the relative velocity of C with respect to A, from B’s perspective should alert you that you are doing something wrong. No relative velocity is ever more than c from any reference frame.I'm curious, do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object? Quote
CraigD Posted December 7, 2016 Report Posted December 7, 2016 If he knows that his friend lives 200,000km away, he will note that it takes him .745 seconds to get there. If he calculates that velocity, he will deduce it is 260,000 km/s. So from his perspective, compared to the road, he is going faster.You said his speedometer would read 260,000 km/s. That is wrong.This all depends on what you consider a speedometer. The usual definition of “speedometer” is a device that measures instantaneous speed – a literal “speed-meter”. Because, as OceanBreeze pointed out, distance traveled contracts by exactly the same factor as time elapsed, such a device would read an unchanged 200,000 km/s. If you consider a technique like traveling a “know distance” (“known” in the reference frame of Bill’s house) and dividing by elapsed time constitute a speedometer, then, as bilvon says, it would give a higher reading. This can be an interesting technique, because the “speed” (a purist might call them pseudospeed) such a technique measures can be greater than the “universal speed limit” of c, 299792458 m/s. This will happen if the true speed is greater than [math]\sqrt{\frac12} \, \dot= \, 0.7071 \,\mbox{c}[/math]. Here are some other pseudospeed – speed pairs, in units of c: 1 0.7071067811865475245 2 0.8944271909999158785 3 0.9486832980505138 4 0.970142500145331894 5 0.98058067569092016 10 0.995037190209989136 100 0.999950003749687528 216 0.999989283437015773 512 0.999998092656824139 1000 0.999999500000375 8766 0.999999993493205852 The last one, 9766 c, is a nice round 1 lightyear/hour. I threw in 216 and 512 c as a nod to Star Trek fans, as they’re equivalent to the original series’ warp factor 6 and 8. :) This kind of play illustrates a consequence of Special Relativity I think’s unappreciated by many fans of space opera that assume faster-than-light travel is needed to travel interstellar distances quickly enough for human lifetime and patience. Quote
xyz Posted December 7, 2016 Author Report Posted December 7, 2016 This all depends on what you consider a speedometer. The usual definition of “speedometer” is a device that measures instantaneous speed – a literal “speed-meter”. Because, as OceanBreeze pointed out, distance traveled contracts by exactly the same factor as time elapsed, such a device would read an unchanged 200,000 km/s. If you consider a technique like traveling a “know distance” (“known” in the reference frame of Bill’s house) and dividing by elapsed time constitute a speedometer, then, as bilvon says, it would give a higher reading. This can be an interesting technique, because the “speed” (a purist might call them pseudospeed) such a technique measures can be greater than the “universal speed limit” of c, 299792458 m/s. This will happen if the true speed is greater than [math]\sqrt{\frac12} \, \dot= \, 0.7071 \,\mbox{c}[/math]. Here are some other pseudospeed – speed pairs, in units of c: 1 0.7071067811865475245 2 0.8944271909999158785 3 0.9486832980505138 4 0.970142500145331894 5 0.98058067569092016 10 0.995037190209989136 100 0.999950003749687528 216 0.999989283437015773 512 0.999998092656824139 1000 0.999999500000375 8766 0.999999993493205852 The last one, 9766 c, is a nice round 1 lightyear/hour. I threw in 216 and 512 c as a nod to Star Trek fans, as they’re equivalent to the original series’ warp factor 6 and 8. :) This kind of play illustrates a consequence of Special Relativity I think’s unappreciated by many fans of space opera that assume faster-than-light travel is needed to travel interstellar distances quickly enough for human lifetime and patience. I am sorry Craig but you are incorrect. You say - ''distance travelled contracts by exactly the same factor as time elapsed'', Please define distance? Distance can not contract, space has no Aether or solidity, I think you really mean, that the Caesium rate passing through space contracts relative to the length of the measurement unit that is equal to 1 second. Quote
xyz Posted December 7, 2016 Author Report Posted December 7, 2016 (edited) Although this is caused by length contraction just as much as time dilation. The rate the time passed was different for the two objects but so was distance in space that the objects travelled. The combination of both is what accounts for the difference in the amount of proper time that elapsed for them. I'm curious, do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object?''The rate the time passed was different for the two objects but so was distance in space that the objects travelled'' poppycock The time passed for all observers is equal . OMG will you please just listen and take that subjective stick from up your...... Any measurement of time no matter what the rate becomes instantaneous history. Is there anything about that you do not understand? Try counting past 0 at any speed and it does not alter time. Infinite speeds of rate if you like or finite speeds, it does not alter the very fact that any counting after zero at any rate is instantaneous history. A car starts to travel at 1 mph leaving its past position behind A car starts to travel at c leaving its past position behind Edited December 7, 2016 by xyz Quote
OceanBreeze Posted December 7, 2016 Report Posted December 7, 2016 :) No they're not. If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame. The rule is that objects can move at or over c relative to you, they can't move at or over 2c relative to each other. If an object is moving away from you at 0.5 and towards a light source as in the example you quoted then that light is moving at 1.5 relative to that object from your perspective. As I said before, you do not have even a basic understanding of what SR is all about. Simple addition and subtraction cannot be applied to relative velocities when dealing with relativistic situations. Taking your example: “If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame”. Total BOLLOCKS! The relative velocities add this way: Velocity addition: u’ = ( u – v ) / [ 1 – uv/c^2 ] U is the velocity of the first object moving at 0.75c away from you in the positive direction. V is the velocity of the second object, moving at 0.75c away from you in the negative direction. U primed, u’ is the relative velocities of the two objects as seen from your reference frame. U’ = [ (0.75c) – (-0.75c) ] / [ 1 – (0.75c) x (-0.75c)/c^2 = 1.5c / 1.5625 = 0.96c Now you should try to work the equation for your other scenarios and see what you get. You will get the relative velocity of C is always c no matter what FOR you use. Remember, in SR the maximum possible velocity is c and you will never measure any relative velocity higher than c from any inertial FOR. That is the second postulate of SR. The first postulate is the laws of physics are the same for all observers in any FOR. If one observer could measure the relative velocity of light different than another observer, then both postulates are being violated and you have defined an absolute FOR; something that SR forbids. Stop posting then. That would help a lot. If I do, you shall remain ignorant and arrogant for the rest of your life. Is that what you want, or do you want to learn something? Quote
OceanBreeze Posted December 7, 2016 Report Posted December 7, 2016 This all depends on what you consider a speedometer. The usual definition of “speedometer” is a device that measures instantaneous speed – a literal “speed-meter”. Because, as OceanBreeze pointed out, distance traveled contracts by exactly the same factor as time elapsed, such a device would read an unchanged 200,000 km/s. If you consider a technique like traveling a “know distance” (“known” in the reference frame of Bill’s house) and dividing by elapsed time constitute a speedometer, then, as bilvon says, it would give a higher reading. This can be an interesting technique, because the “speed” (a purist might call them pseudospeed) such a technique measures can be greater than the “universal speed limit” of c, 299792458 m/s. This will happen if the true speed is greater than [math]\sqrt{\frac12} \, \dot= \, 0.7071 \,\mbox{c}[/math]. Here are some other pseudospeed – speed pairs, in units of c: 1 0.7071067811865475245 2 0.8944271909999158785 3 0.9486832980505138 4 0.970142500145331894 5 0.98058067569092016 10 0.995037190209989136 100 0.999950003749687528 216 0.999989283437015773 512 0.999998092656824139 1000 0.999999500000375 8766 0.999999993493205852 The last one, 9766 c, is a nice round 1 lightyear/hour. I threw in 216 and 512 c as a nod to Star Trek fans, as they’re equivalent to the original series’ warp factor 6 and 8. :) This kind of play illustrates a consequence of Special Relativity I think’s unappreciated by many fans of space opera that assume faster-than-light travel is needed to travel interstellar distances quickly enough for human lifetime and patience. What you are talking about is not SR, it is some mixture of Galilean relativity and Special Relativity. The postulates of SR are such that the measurements made by different observers moving with respect to each other at constant relative velocity are perfectly valid in their respective FOR. The moving observer measures he travelled a distance of 149,000 km in 0.745 s. 149,000 km is the exact correct distance he travelled with respect to his FOR! His velocity is 200,000 km/s.The observer at rest measured a distance of 200,000 km and a time of 1 second for a velocity of 200,000 km/s.Both observers are RIGHT! There is no preferred frame of reference. When you take the distance measure by the stationary observer and divide it by the time measured by the traveler, you are mixing up your frames and getting a meaningless result. Quote
A-wal Posted December 7, 2016 Report Posted December 7, 2016 (edited) Great, now there's two of them. ''The rate the time passed was different for the two objects but so was distance in space that the objects travelled'' poppycock The time passed for all observers is equal . OMG will you please just listen and take that subjective stick from up your......I'm going to make this as simple as humanly possible for you. 1. Two planets, Planet X and Planet Y.2. Observer A is travelling from Planet X to Planet Y.3. Observer B is making the same journey but faster than observer A.4. Light passes observer A at c from A's frame and they work out how long it takes the light to make the journey.5. The same light passes observer B at c from B's frame and they work out how long it takes the light to make the journey.6. Observer B is moving between the two planets faster than observer A so the light will take less time to make the same journey from B's perspective. How could that be possible without length contraction and/or time dilation? Any measurement of time no matter what the rate becomes instantaneous history. Is there anything about that you do not understand? Try counting past 0 at any speed and it does not alter time. Infinite speeds of rate if you like or finite speeds, it does not alter the very fact that any counting after zero at any rate is instantaneous history. A car starts to travel at 1 mph leaving its past position behind A car starts to travel at c leaving its past position behindWow, you're really up confused creek without a clue. I don't know where to start with that mess. None of that remotely makes anything approaching something that in some way resembles sense. I am sorry Craig but you are incorrect.And you know better? lol! As I said before, you do not have even a basic understanding of what SR is all about. Simple addition and subtraction cannot be applied to relative velocities when dealing with relativistic situations.Yea okay. :) Prepare to feel very stupid! Taking your example: “If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame”. Total BOLLOCKS! The relative velocities add this way: Velocity addition: u’ = ( u – v ) / [ 1 – uv/c^2 ] U is the velocity of the first object moving at 0.75c away from you in the positive direction. V is the velocity of the second object, moving at 0.75c away from you in the negative direction. U primed, u’ is the relative velocities of the two objects as seen from your reference frame. U’ = [ (0.75c) – (-0.75c) ] / [ 1 – (0.75c) x (-0.75c)/c^2 = 1.5c / 1.5625 = 0.96c Now you should try to work the equation for your other scenarios and see what you get. You will get the relative velocity of C is always c no matter what FOR you use. Remember, in SR the maximum possible velocity is c and you will never measure any relative velocity higher than c from any inertial FOR. That is the second postulate of SR. The first postulate is the laws of physics are the same for all observers in any FOR. If one observer could measure the relative velocity of light different than another observer, then both postulates are being violated and you have defined an absolute FOR; something that SR forbids.As I said...If an object is moving away from you at 0.75c and anther object is moving away from you at 0.75c in the opposite direction then those two objects are moving away from each other at 1.5c in your reference frame. The rule is that objects can move at or over c relative to you, they can't move at or over 2c relative to each other. If an object is moving away from you at 0.5 and towards a light source as in the example you quoted then that light is moving at 1.5 relative to that object from your perspective.The velocity addition formula is applied if you want to work out what the velocity of the two objects moving away from is relative to each other in their frames! In your frame they're both moving away from you at 0.75c so of course they're moving away from each other at 1.5c. This kind of fundamental error is exactly what happens when you try to memorise stuff without having any actual understanding of it. If you have trouble with something this basic you stand no chance of understanding the rest of it. If I do, you shall remain ignorant and arrogant for the rest of your life. Is that what you want, or do you want to learn something? :rofl: I'm still curious, do you think that if an object is moving away from you at say 0.75c and another object accelerates away from you in the opposite direction, the first object's velocity relative to you will be slowed down by the relative velocity of the second object and/or the the velocity of the second object relative to you will be in some way restricted by the relative velocity of the first object? What you are talking about is not SR, it is some mixture of Galilean relativity and Special Relativity. The postulates of SR are such that the measurements made by different observers moving with respect to each other at constant relative velocity are perfectly valid in their respective FOR. The moving observer measures he travelled a distance of 149,000 km in 0.745 s. 149,000 km is the exact correct distance he travelled with respect to his FOR! His velocity is 200,000 km/s.The observer at rest measured a distance of 200,000 km and a time of 1 second for a velocity of 200,000 km/s.Both observers are RIGHT! There is no preferred frame of reference. When you take the distance measure by the stationary observer and divide it by the time measured by the traveler, you are mixing up your frames and getting a meaningless result.Well that went completely over your head, it's not meaningless. The idea is is measure the velocity of a journey from the perspective of the frame you start and/or end up in by dividing the distance in that frame by the elapsed proper time of the journey. You need to learn the difference between coordinate time and proper time. For example, you can't get to the moon in less than a second from the Earth/Moon reference frame because it's over 186,000 miles away, but you can from your own perspective. Time dilates and length contracts as you accelerate so that the proper time of the journey is less than one second. Using the proper time to get the velocity over the distance traveled between the two objects in their own reference and you get a velocity >c. This can be thought of as proper velocity with regards to the frame in question and it's how you work out how long a journey would take from your own perspective, hardly meaningless. Learn it before you try teaching it or you'll just carry on making a fool of yourself. Edited December 7, 2016 by A-wal Quote
CraigD Posted December 7, 2016 Report Posted December 7, 2016 What you are talking about is not SR, it is some mixture of Galilean relativity and Special Relativity.No, what I’m talking about is a simple application of SR and an unusual but simply and well-defined alternate definition of “speed” – which, to avoid confusion, I called “pseudospeed”. Rather than the usual [math]v = \frac{\Delta d}{\Delta t}[/math], where [math]\Delta d[/math] is change in position as measured by the moving observer and [math]\Delta t[/math] is change in time as measured by his accurate clock, for pseudospeed [math]v[/math], [math]\Delta d[/math] is change in position as measured by the observer at rest relative to the destination (“Bob’s house” in the original post). Though nonphysical, this pseudospeed is a useful quantity, because it conveniently answers a question commonly of interest to travelers – how long ‘til I get there? If Bob’s house is not a mere 200,000 km away, but on 4.2 lightyears Proxima Centauri B, and I happen to have a vehicle that instantly accelerates to 299792456 m/s in that direction, I’ll get there in 4.2 hrs. For Bob, the wait for my arrival will be slightly more than 4.2 years. The so-unlikely-to-be-possible-it’s-practically-fantasy assumption in this example is its “instantly accelerates” part, but the calculations assuming a finite acceleration are more difficult. The implications of more realistic calculations are similar, though: if you can accelerate greatly enough and long enough, you can travel great distances in small amounts of time. For example, at 9.8 m/s/s (1 gee) acceleration, the 4.2 ly trip to Bob’s at Proxima Centauri would take about 3.55 years (see this Wikipedia page for the formula I used. This page by David Darling has some interesting examples of moving observer times to travel astronomical distances at a constant 1 gee acceleration). One could reasonably argue that a spacecraft that can accelerate at 1 gee for 3.55 years is also unlike to be possible, but its unlikelihood is more of the realm of engineering improbability than physics impossibility. I’m trying to threadjack this thread from its original and IMHO silly “I don’t understand math or modern physics so I deny that SR makes sense” theme to a lighthearted look at how the real science of SR impeaches the common notion that SR places disheartening limits on interstellar travel. It doesn’t. The daunting challenges are of engineering, and were as or more daunting under classical physics as under modern. Quote
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