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As you accelerate away from me you move faster and faster with respect to me. As a result I see your time dilating and so your acceleration diminishes: you see yourself continuing to accelerate with 1 m/s^2 for example but I see your second lasting longer so the amount I see you accelerate in MY second is smaller. There is no need to introduce the concept of relativistic mass to explain this diminished acceleration at higher relative speeds.
I agree. I think relativistic mass has much the same status as Lorentz contraction. It can be a good way of calculating but it doesn’t actually occur. In both cases we can explain completely through time dilation concepts. As you accelerate away from me you move faster and faster with respect to me. As a result I see your time dilating and so your acceleration diminishes: your see yourself continuing to accelerate with 1 m/s^2 for example but I see your second lasting much longer so the amount I see you accelerate in MY second is smaller. There is no need to introduce the concept of relativistic mass to explain this diminished acceleration at higher relative speeds.
I have my doubts about this analysis. Time dilation only occurs along the direction of motion. At the moment the two lances touch there is no time dilation component occurring due to evil George’s horizontal motion so (as far as I can see) both lances have exactly the same vertical speed (but in opposite directions) and so exactly the same vertical momentum (but in opposite directions) due to the equal but opposite push that George respectively evil George give their lances.
Another point is that the bounce off is depicted is from the “stationary” earthbound frame and not George’s frame even though we are talking about how things look from George’s frame. From George’s frame the evil Georges lances comes in from an angle and will strike the top of Georges lance at an angle. George will first see his lance go up vertically (as he pushes it) but will after the collision be pushed down and in the direction of evil Georges motion.
Finally from Georges reference frame his lance only has upward vertical momentum but evil George’s has both a downward and horizontal vertical momentum. This may have no effect on the analysis but I think you would have to explicitly demonstrate that.
What is confusing about the paradox is that if I see your clock run slower and you see my clock run slower how can one of us age faster than the other? Since the frames of reference appear symmetrical (I am moving in your frame of reference and you are moving in my frame of reference) how do you explain an age difference? So where is the asymmetry?
First off, I want to point out that whether acceleration is instantaneous or not doesn’t really matter for the analysis. What is important is who is doing the acceleration and the duration and size of the relative motion.
Suppose you go off in a spaceship and I stay back on earth. To make the analysis simple let’s assume you accelerate instantaneously to the speed of light (with respect to me), you stay at that same relative motion for half a year and then instantaneously decelerate so that you are stationary with respect to me, you stay that way for 5 seconds then instantaneously accelerate to the speed of light to travel back towards me.
Let’s see what you observe.
Since you are travelling at the speed of light you see my clock standing still. The ray of light sent out to you when the second hand om my clock moved (one second after you left) never catches up to you (until you decelerate). Only when you decelerate to stationary (with respect to me) after half a year do you see my clock suddenly start to tick exactly at the same rate that I see it tick. When, after 5 seconds you accelerate and travel back to Earth you see my clock tick at a much faster rate (twice as fast as what I observe to be exact) as you intercept the light rays counting off the seconds on my clock as each of those light rays are travelling shorter and shorter distances to reach you as you head back to Earth.
What do I observe when you stop (with respect to me) after half a year?
Nothing!! I will still see your clock standing still. In fact, I will see your clock stand still as long as there are light rays are travelling to Earth that you sent while moving away from me. This is the missing asymmetry we needed! When you are half a light year away, it will take half a light year before those rays reach Earth (so in total a year after you left). Only after that half a year (so in total 1 year) will I see your clock suddenly start to tick at a (for me) normal rate. But only for 5 seconds because after half a light year and 5 seconds (after you stopped with respect to me) you will have landed back on Earth!
So summarising: you saw my clock stand still for half a year, run at the same rate that I saw my clock run for 5 seconds and then run twice as fast for half a year. Both you and I will have seen my clock measure off 1 year and 5 seconds. I however will only see that your clock has moved forward by 5 seconds when you land. You saw yourself take off, then suddenly see your clock tick for 5 seconds where your ship was a half light year from Earth, then land. Outside those 5 seconds you had no perception of time. Both you and I will have seen that my clock measure off 5 seconds.
If you have a problem with the perception of no time passing whatsoever you can replace light speed with 99.99% of light speed or in fact any other percentage you care to use. Then you will see some time pass on your clock outside the 5 seconds (however small).
This all sounds like a latency issue. Where does time dilation creep in? The answer is that whether I am moving away from you or towards you at light speed the light rays I send off also move at light speed to you due to the constancy of light supposition. In a Newton world those speeds (and the resulting analysis) would yield different results due to the effect of using a Newton based velocity addition instead of a relativistic velocity addition.
This is a bit more speculative but we could explain time dilation as saying when your clock slows you are packing more “physical time” between two clock ticks. Since speed = distance/time and thus distance = speed * time if I can pack more physical time in my time measurement then for any given speed I will have more physical distance. In my view, with Lorentz contraction there is no actual physical distance shortening, it is our metric (the physical length of a meter) that is changed due to a change in time. Meters are defined using time: the distance light travels in 1/299 792 458 of a second second. If I change my duration of a second then clearly the physical distance measured will change too.
What is confusing about the paradox is that if I see your clock run slower and you see my clock run slower how can one of us age faster than the other? Since the frames of reference appear symmetrical (I am moving in your frame of reference and you are moving in my frame of reference) how do you explain an age difference? So where is the asymmetry?
First off, I want to point out that whether acceleration is instantaneous or not doesn’t really matter for the analysis. What is important is who is doing the acceleration and the duration and size of the relative motion.
Suppose you go off in a spaceship and I stay back on earth. To make the analysis simple let’s assume you accelerate instantaneously to the speed of light (with respect to me), you stay at that same relative motion for half a year and then instantaneously decelerate so that you are stationary with respect to me, you stay that way for 5 seconds then instantaneously accelerate to the speed of light to travel back towards me.
Let’s see what you observe.
Since you are travelling at the speed of light you see my clock standing still. The ray of light sent out to you when the second hand om my clock moved (one second after you left) never catches up to you (until you decelerate). Only when you decelerate to stationary (with respect to me) after half a year do you see my clock suddenly start to tick exactly at the same rate that I see it tick. When, after 5 seconds you accelerate and travel back to Earth you see my clock tick at a much faster rate (twice as fast as what I observe to be exact) as you intercept the light rays counting off the seconds on my clock as each of those light rays are travelling shorter and shorter distances to reach you as you head back to Earth.
What do I observe when you stop (with respect to me) after half a year?
Nothing!! I will still see your clock standing still. In fact, I will see your clock stand still as long as there are light rays are travelling to Earth that you sent while moving away from me. This is the missing asymmetry we needed! When you are half a light year away, it will take half a light year before those rays reach Earth (so in total a year after you left). Only after that half a year (so in total 1 year) will I see your clock suddenly start to tick at a (for me) normal rate. But only for 5 seconds because after half a light year and 5 seconds (after you stopped with respect to me) you will have landed back on Earth!
So summarising: you saw my clock stand still for half a year, run at the same rate that I saw my clock run for 5 seconds and then run twice as fast for half a year. Both you and I will have seen my clock measure off 1 year and 5 seconds. I however will only see that your clock has moved forward by 5 seconds when you land. You saw yourself take off, then suddenly see your clock tick for 5 seconds where your ship was a half light year from Earth, then land. Outside those 5 seconds you had no perception of time. Both you and I will have seen that my clock measure off 5 seconds.
If you have a problem with the perception of no time passing whatsoever you can replace light speed with 99.99% of light speed or in fact any other percentage you care to use. Then you will see some time pass on your clock outside the 5 seconds (however small).
This all sounds like a latency issue. Where does time dilation creep in? The answer is that whether I am moving away from you or towards you at light speed the light rays I send off also move at light speed to you due to the constancy of light supposition. In a Newton world those speeds (and the resulting analysis) would yield different results due to the effect of using a Newton based velocity addition instead of a relativistic velocity addition.
This is a bit more speculative but we could explain time dilation as saying when your clock slows you are packing more “physical time” between two clock ticks. Since speed = distance/time and thus distance = speed * time if I can pack more physical time in my time measurement then for any given speed I will have more physical distance. In my view, with Lorentz contraction there is no actual physical distance shortening, it is our metric (the physical length of a meter) that is changed due to a change in time. Meters are defined using time: the distance light travels in 1/299 792 458 of a second second. If I change my duration of a second then clearly the distance measured will change too.
What is confusing about the paradox is that if I see your clock run slower and you see my clock run slower how can one of us age faster than the other? Since the frames of reference appear symmetrical (I am moving in your frame of reference and you are moving in my frame of reference) how do you explain an age difference? So where is the asymmetry?
First off, I want to point out that whether acceleration is instantaneous or not doesn’t really matter for the analysis. What is important is who is doing the acceleration and the duration and size of the relative motion.
Suppose you go off in a spaceship and I stay back on earth. To make the analysis simple let’s assume you accelerate instantaneously to the speed of light (with respect to me), you stay at that same relative motion for half a year and then instantaneously decelerate so that you are stationary with respect to me, you stay that way for 5 seconds then instantaneously accelerate to the speed of light to travel back towards me.
Let’s see what you observe.
Since you are travelling at the speed of light you see my clock standing still. The ray of light sent out to you when the second hand om my clock moved (one second after you left) never catches up to you (until you decelerate). Only when you decelerate to stationary (with respect to me) after half a year do you see my clock suddenly start to tick exactly at the same rate that I see it tick. When, after 5 seconds you accelerate and travel back to Earth you see my clock tick at a much faster rate (twice as fast as what I observe to be exact) as you intercept the light rays counting off the seconds on my clock as each of those light rays are travelling shorter and shorter distances to reach you as you head back to Earth.
What do I observe when you stop (with respect to me) after half a year?
Nothing!! I will still see your clock standing still. In fact, I will see your clock stand still as long as there are light rays are travelling to Earth that you sent while moving away from me. This is the missing asymmetry we needed! When you are half a light year away, it will take half a light year before those rays reach Earth (so in total a year after you left). Only after that half a year (so in total 1 year) will I see your clock suddenly start to tick at a (for me) normal rate. But only for 5 seconds because after half a light year and 5 seconds (after you stopped with respect to me) you will have landed back on Earth!
So summarising: you saw my clock stand still for half a year, run at the same rate that I saw my clock run for 5 seconds and then run twice as fast for half a year. Both you and I will have seen my clock measure off 1 year and 5 seconds. I however will only see that your clock has moved forward by 5 seconds when you land. You saw yourself take off, then suddenly see your clock tick for 5 seconds where your ship was a half light year from Earth, then land. Outside those 5 seconds you had no perception of time. Both you and I will have seen that my clock measure off 5 seconds.
If you have a problem with the perception of no time passing whatsoever you can replace light speed with 99.99% of light speed or in fact any other percentage you care to use. Then you will see some time pass on your clock outside the 5 seconds (however small).
This all sounds like a latency issue. Where does time dilation creep in? The answer is that whether I am moving away from you or towards you at light speed the light rays I send off also move at light speed to you due to the constancy of light supposition. In a Newton world those speeds (and the resulting analysis) would yield different results due to the effect of using a Newton based velocity addition instead of a relativistic velocity addition.
This is a bit more speculative but we could explain time dilation as saying when your clock slows you are packing more “physical time” between two clock ticks. Since speed = distance/time and thus distance = speed * time if I can pack more physical time in my time measurement then for any given speed I will have more physical distance. In my view, with Lorentz contraction there is no actual physical distance shortening it our metric (the physical length of a meter) that is changed due to a change in time. Meters are defined using time: the distance light travels in 1 second. If I change my duration of a second then clearly the distance measured will change too.
What is confusing about the paradox is that if I see your clock run slower and you see my clock run slower how can one of us age faster than the other? Since the frames of reference appear symmetrical (I am moving in your frame of reference and you are moving in my frame of reference) how do you explain an age difference? So where is the asymmetry?
First off, I want to point out that whether acceleration is instantaneous or not doesn’t really matter for the analysis. What is important is who is doing the acceleration and the duration and size of the relative motion.
Suppose you go off in a spaceship and I stay back on earth. To make the analysis simple let’s assume you accelerate instantaneously to the speed of light (with respect to me), you stay at that same relative motion for half a year and then instantaneously decelerate so that you are stationary with respect to me, you stay that way for 5 seconds then instantaneously accelerate to the speed of light to travel back towards me.
Let’s see what you observe.
Since you are travelling at the speed of light you see my clock standing still. The ray of light sent out to you when the second hand om my clock moved (one second after you left) never catches up to you (until you decelerate). Only when you decelerate to stationary (with respect to me) after half a year do you see my clock suddenly start to tick exactly at the same rate that I see it tick. When, after 5 seconds you accelerate and travel back to Earth you see my clock tick at a much faster rate (twice as fast as what I observe to be exact) as you intercept the light rays counting off the seconds on my clock as each of those light rays are travelling shorter and shorter distances to reach you as you head back to Earth.
What do I observe when you stop (with respect to me) after half a year?
Nothing!! I will still see your clock standing still. In fact, I will see your clock stand still as long as the light rays sent when you are moving away from me are travelling to Earth. This is the missing asymmetry we needed! When you are half a light year away, it will take half a light year before those rays reach Earth (so in total a year after you left). Only after that half a year (so in total 1 year) will I see your clock suddenly start to tick at a (for me) normal rate. But only for 5 seconds because after half a light year and 5 seconds (after you stopped with respect to me) you will have landed back on Earth!
So summarising: you saw my clock stand still for half a year, run at the same rate that I saw my clock run for 5 seconds and then run twice as fast for half a year. Both you and I will have seen my clock measure off 1 year and 5 seconds. I however will only see that your clock has moved forward by 5 seconds when you land. You saw yourself take off, then suddenly see your clock tick for 5 seconds where your ship was a half light year from Earth, then land. Outside those 5 seconds you had no perception of time. Both you and I will have seen that my clock measure off 5 seconds.
If you have a problem with the perception of no time passing whatsoever you can replace light speed with 99.99% of light speed or in fact any other percentage you care to use. Then you will see some time pass on your clock outside the 5 seconds (however small).
This all sounds like a latency issue. Where does time dilation creep in? The answer is that whether I am moving away from you or towards you at light speed the light rays I send off also move at light speed to you due to the constancy of light supposition. In a Newton world those speeds (and the resulting analysis) would yield different results due to the effect of using a Newton based velocity addition instead of a relativistic velocity addition.
This is a bit more speculative but we could explain time dilation as saying when your clock slows you are packing more “physical time” between two clock ticks. Since speed = distance/time and thus distance = speed * time if I can pack more physical time in my time measurement then for any given speed I will have more physical distance. In my view, with Lorentz contraction there is no actual physical distance shortening it our metric (the physical length of a meter) that is changed due to a change in time. Meters are defined using time: the distance light travels in 1 second. If I change my duration of a second then clearly the distance measured will change too.
What is confusing about the paradox is that if I see your clock run slower and you see my clock run slower how can one of us age faster than the other? Since the frames of reference appear symmetrical (I am moving in your frame of reference and you are moving in my frame of reference) how do you explain an age difference? So where is the asymmetry?
First off, I want to point out that whether acceleration is instantaneous or not doesn’t really matter for the analysis. What is important is who is doing the acceleration and the duration and size of the relative motion.
Suppose you go off in a spaceship and I stay back on earth. To make the analysis simple let’s assume you accelerate instantaneously to the speed of light (with respect to me), you stay at that same relative motion for half a year and then instantaneously decelerate so that you are stationary with respect to me, you stay that way for 5 seconds then instantaneously accelerate to the speed of light to travel back towards me.
Let’s see what you observe.
Since you are travelling at the speed of light you see my clock standing still. The ray of light sent out to you when the second hand om my clock moved (one second after you left) never catches up to you (until you decelerate). Only when you decelerate to stationary (with respect to me) after half a year do you see my clock suddenly start to tick exactly at the same rate that I see it tick. When, after 5 seconds you accelerate and travel back to Earth you see my clock tick at a much faster rate (twice as fast as what I observe to be exact) as you intercept the light rays counting off the seconds on my clock as each of those light rays are travelling shorter and shorter distances to reach you as you head back to Earth.
What do I observe when you stop (with respect to me) after half a year?
Nothing!! You will still se my clock standing still. In fact, you will see my clock stand still as long as the light rays sent when you are moving away from me are travelling to Earth. This is the missing asymmetry we needed! When you are half a light year away, it will take half a light year before those rays reach Earth (so in total a year after you left). Only after that half a year (so in total 1 year) will I see your clock suddenly start to tick at a (for me) normal rate. But only for 5 seconds because after half a light year and 5 seconds (after you stopped with respect to me) you will have landed back on Earth!
So summarising: you saw my clock stand still for half a year, run at the same rate that I saw my clock run for 5 seconds and then run twice as fast for half a year. Both you and I will have seen my clock measure off 1 year and 5 seconds. I however will only see that your clock has moved forward by 5 seconds when you land. You saw yourself take off, then suddenly see your clock tick for 5 seconds where your ship was a half light year from Earth, then land. Outside those 5 seconds you had no perception of time. Both you and I will have seen that my clock measure off 5 seconds.
If you have a problem with the perception of no time passing whatsoever you can replace light speed with 99.99% of light speed or in fact any other percentage you care to use. Then you will see some time pass on your clock outside the 5 seconds (however small).
This all sounds like a latency issue. Where does time dilation creep in? The answer is that whether I am moving away from you or towards you at light speed the light rays I send off also move at light speed to you due to the constancy of light supposition. In a Newton world those speeds (and the resulting analysis) would yield different results due to the effect of using a Newton based velocity addition instead of a relativistic velocity addition.
This is a bit more speculative but we could explain time dilation as saying when your clock slows you are packing more “physical time” between two clock ticks. Since speed = distance/time and thus distance = speed * time if I can pack more physical time in my time measurement then for any given speed I will have more physical distance. In my view, with Lorentz contraction there is no actual physical distance shortening it our metric (the physical length of a meter) that is changed due to a change in time. Meters are defined using time: the distance light travels in 1 second. If I change my duration of a second then clearly the distance measured will change too.
If you measure in the same frame of reference as the pole (that is using the same now slice) you will get the correct value for the length (the so called “proper” length). The measurement is coupling two events (location front and back of the pole at this moment). However if you measure using a different now slice (which is the case if you are moving with respect to the pole) you will measure a different incorrect value. NOTHING HAS HAPPENED TO THE POLE IT HAS NOT CONTRACTED OR EXPANDED. The value measured is different but no physical contraction is taking place – we are simply using a different now time slice to carry out are measurements.
It really is this simple. You are measuring using an invalid now time slice. The Lorentz contraction simply gives you a way of calculating how far you are off in your measurement. No genuine physical contraction takes place.
Besides the fact that it is difficult to intuitively accept that objects are being physically squeezed there are other phenomena which are difficult to accept presented below which would take effect if distance is physically shortened.
There is a lot of discussion about what Loentz contraction really is, with a significant group claiming that actual contraction of distance takes place (it is a space-like phenonemon) and another significant group stating that what is really happening (and being described) is that time dilation is taking place (it is a time-like phenomenon).
Speed = Distance/Time is something everyone agrees on. What is apparently up for grabs is whether it is valid to invert the expression in order to define distance as Distance = Speed x Time or whether this inversion breaks down in a relativistic context where time is dilating.
If it really is distance then one would need to account for apparent size. Apparent size is a property of distance: when you get closer to an object that object will appear larger. If Lorentz contraction really shortens distance (that is, it is a space like phenomenon and not a time-like phenomenon) then as Lorentz contraction takes place we would get physically closer to the object. By travelling ever closer to the speed of light we could get arbitrarily close. We should then see the object at the distance dictated by the Lorentz contraction. If Lorentz contraction really equates to shorter distances then theoretically, we could even observe a star as being a mile away or even closer (with all its detail!) that is a billion years distant in the rest frame. I do not accept that this is possible so I do not accept that length contraction equates to physical distance shortening.
There are also other properties affected by (true) distance. Radiation intensity and gravitational pull to name two. If we are truly at just 1 mile distance from a star if we accelerate to the appropriate velocity then if we believe the space-like interpretation of Lorentz contraction we will experience the star just as if it were 1 mile away in a non-accelerated situation. We would be both fried and experience an extremely strongly gravitational pull.
Note that the apparent size phenomenon is not the same as magnification. A space-like interpretation of the Lorentz contraction postulates that at the right velocity (very close to light) the distance will really be one mile and the observer (in the rocket presumably) will observe exactly the same thing as we would here on Earth if the star were 1 mile away. Magnification presents resolution issues which do not play a role in the apparent size case. If resolution issues are raised to prevent being able to see the star up close then the Lorentz contraction cannot be true distance shortening.
In my view, Lorentz contraction is a (highly) useful mathematical method for manipulating time dilation (which is a real physical phenomenon) but the Lorentz contraction does not result in actual shortening of the physical distance. Objects and distances do not physically shrink (in the direction of motion or any other direction), a photon is not “everywhere in the universe” and we cannot define Distance to be Speed x Time in a relativistic context.
I think this story is missing a fundamental observation which makes it completely invalid. When the first person grabs the pole and stops it, a deceleration force is transferred along the pole. If that force moves (to the right) along the pole faster than that the pole is moving to the left then the end of the pole (to the right) will take longer to get to the barn or not even get to the barn at all if the decelerating force is acting long enough. This explanation is, in my view, completely incorrect.
There is a lot of discussion about what Loentz contraction really is, with a significant group claiming that actual contraction of distance takes place (it is a space-like phenonemon) and another significant group stating that what is really happening (and being described) is that time dilation is taking place (it is a time-like phenomenon).
Speed = Distance/Time is something everyone agrees on. What is apparently up for grabs is whether it is valid to invert the expression in order to define distance as Distance = Speed x Time or whether this inversion breaks down in a relativistic context where time is dilating.
If it really is distance then one would need to account for apparent size. Apparent size is a property of distance: when you get closer to an object that object will appear larger. If Lorentz contraction really shortens distance (that is, it is a space like phenomenon and not a time-like phenomenon) then as Lorentz contraction takes place we would get physically closer to the object. By travelling ever closer to the speed of light we could get arbitrarily close. We should then see the object at the distance dictated by the Lorentz contraction. If Lorentz contraction really equates to shorter distances then theoretically, we could even observe a star as being a mile away or even closer (with all its detail!) that is a billion years distant in the rest frame. I do not accept that this is possible so I do not accept that length contraction equates to physical distance shortening.
There are also other properties affected by (true) distance. Radiation intensity and gravitational pull to name two. If we are truly at just 1 mile distance from a star if we accelerate to the appropriate velocity then if we believe the space-like interpretation of Lorentz contraction we will experience the star just as if it were 1 mile away in a non-accelerated situation. We would be both fried and experience an extremely strongly gravitational pull.
Note that the apparent size phenomenon is not the same as magnification. A space-like interpretation of the Lorentz contraction postulates that at the right velocity (very close to light) the distance will really be one mile and the observer (in the rocket presumably) will observe exactly the same thing as we would here on Earth if the star were 1 mile away. Magnification presents resolution issues which do not play a role in the apparent size case. If resolution issues are raised to prevent being able to see the star up close then the Lorentz contraction cannot be true distance shortening.
In my view, Lorentz contraction is a (highly) useful mathematical method for manipulating time dilation (which is a real physical phenomenon) but the Lorentz contraction does not result in actual shortening of the physical distance. Objects and distances do not physically shrink (in the direction of motion or any other direction), a photon is not “everywhere in the universe” and we cannot define Distance to be Speed x Time in a relativistic context.
These paradoxes don’t occur because no physical contraction is taking place.