Comparing Event Occurrence Across PORs

[whosapopstar?]

The "time dilation" factor is the ratio of the coordinate time between two events in one frame and that between the same events in a different frame which means time dilation is only defined if you have a minimum of two different coordinate systems.

Apparently there is a disagreement here. Please refer to a muon experiment, brought up earlier in this thread.

 

[GeorgeDishman]

The "time dilation" factor is the ratio of the coordinate time between two events in one frame and that between the same events in a different frame

Apparently there is a disagreement here. Please refer to a muon experiment, brought up earlier in this thread.

There are no details in the previous mention but I guess it is referring to the fact that the rest frame lifetime is 2.2us while it is longer if they are moving at high speed. The dilation factor is their lifetime in the lab frame relative to that in their rest frame.

If you are using some alternative definition of "time dilation", please let me know, I'm assuming the usual terminology.

 

[whosapopstar?]

There are no details in the previous mention but I guess it is referring to the fact that the rest frame lifetime is 2.2us while it is longer if they are moving at high speed. The dilation factor is their lifetime in the lab frame relative to that in their rest frame.

If you are using some alternative definition of "time dilation", please let me know, I'm assuming the usual terminology.

i guess, this means there is no need to consider reults of any other measurement lab moving at constant speed, besides your own lab, in order to prove the existence time dilation.

 

[GeorgeDishman]

i guess, this means there is no need to consider reults of any other measurement lab moving at constant speed, besides your own lab, in order to prove the existence time dilation.

If the universe were Galilean invariant, there would be no time dilation effect, the ratio would always be 1, so you do need experiments to confirm it. The definition is based on the relationship between two coordinate systems either way so I think you just need to be clear as to what question you are asking.

 

[ghwellsjr]

The explanation that George gave was indeed very clear.

For the sake of others reading this, the explanation you are referring to is here.

But my question departs from the rest of your explanation, exactly where you show that having a result of light-speed as ∞, is a problem.

i see how this problem that you describe, to measure a numerical value for the one way speed of light, appears.

But on the other hand i ask, why is this not a great opportunity to prove that, although without regard to a specific numerical measurement value, still, a speed measurement of ∞ for light, in that very configuration presented by George, enables us to prove that there is no change in the one way speed of light.

How can it be possible to exclude a change of speed, without regarding a specific numerical value, you might ask? Well, why should it be wrong to say this:

Let us assume that light changes its speed when traveling inside the boundaries of detectors 1 and 2 of spaceship 3. Then, within the boundaries of spaceship 2, we will use the exact same method that George explained with wires and one clock, but using the configuration that gave us ∞ speed (clock always at the end). Now, we will not get an ∞ result any more, as the measurement of light speed made inside the boundaries of detectors 1 and 2 of spaceship 2. When assuming such a scenario, that light changed its speed between the two detectors of spaceship 3, we will measure a negative or a positive result for light speed (depends if we assume faster or slower light speed inside the boundaries of spaceship 3).

But we know from experiments, that we will always get ∞, as a measurement result for the speed of light within the boundaries of spaceship 2. Hence this initial assumption, that the one way speed of light can change, is wrong. Hence there is always an implicit assumption, that light never changes its one way speed, although we cannot measure a numerical value for that one way speed.

Where is the error in this chain of arguments?

Thanks.

Even if the speed of light changed between the two detectors of spaceship 3, we have to assume that the speed of the electrical signal traveling down the cable changes by exactly the same amount (electrical signals and light are both electromagnetic phenomenon obeying the same laws) and that this happens for both spaceships which means they will both still measure ∞ for the speed of light. Remember, a speed of ∞ simply means that the light traveled from detector 1 to detector 2 in the same amount of time that the electrical signal traveled the same distance. It really doesn't matter what the actual speeds are or even if they change as long as they are the same and change the same.

 

[ghwellsjr]

The "time dilation" factor is the ratio of the coordinate time between two events in one frame and that between the same events in a different frame which means time dilation is only defined if you have a minimum of two different coordinate systems.

Apparently there is a disagreement here. Please refer to a muon experiment, brought up earlier in this thread.

There is no disagreement here.

When Einstein defined the meaning of τ (tau, which is Proper Time) in the middle of section 4 of his 1905 paper, he used two coordinate systems. But later in the section, when he applied that definition to his introduction of the Twin Paradox, he used only one coordinate system.

So time dilation is the ratio of t (Coordinate Time) to τ (Proper Time) for a clock moving in a single coordinate system. You can also arrive at the same conclusion by going back to the original definition involving two coordinate systems in which the Proper Time for the clock moving in one coordinate system becomes the Coordinate Time for the clock at rest in the second coordinate system.

But I was making the point in post #37 that time dilation can be proven without establishing any coordinate system, simply by enacting the twin paradox--two synchronized clocks at mutual rest, one takes a trip and comes back with less accumulated time on it.

 

[whosapopstar?]

What i meant was that,
Let's assume that while both the electric cable signal and light aboard spaceship 3, move at the same rate and reach spaceship 3 clock together, the electric signal in the cable on spaceship 2 (regard, another separate cable), always moves at another constant rate, all the way from the detector to the clock on spaceship 2, even when the electric signal is moving 'under' spaceship 3. i assume that its only light that changes its rate, while on a single path- e.g. when in spaceship 2 and outside spaceship 3, its speed is constant, equal in both sides and different from its constant speed between the detector and clock of spaceship 3. Then i prove that this is not possible, and then i conclude that light does not change its speed as a result of the difference of constant speed between spaceship 2 and spaceship 3.

 

[GeorgeDishman]

There is no disagreement here.

True.

So time dilation is the ratio of t (Coordinate Time) to τ (Proper Time) for a clock moving in a single coordinate system. You can also arrive at the same conclusion by going back to the original definition involving two coordinate systems in which the Proper Time for the clock moving in one coordinate system becomes the Coordinate Time for the clock at rest in the second coordinate system.

Exactly, proper time is just coordinate time in the rest frame of the clock (barring acceleration of course).

But I was making the point in post #37 that time dilation can be proven without establishing any coordinate system, simply by enacting the twin paradox--two synchronized clocks at mutual rest, one takes a trip and comes back with less accumulated time on it.

Ah, good point. Given the mention of muons, I was thinking of something like the evidence provided by the Ives-Stilwell experiment but Hafele-Keating (ignoring gravitational effects) can prove the existence of the effect without a coordinate system as such.

 

[GeorgeDishman]

.. i conclude that light does not change its speed as a result of the difference of constant speed between spaceship 2 and spaceship 3.

I've come into this thread late so sorry if I've picked it up wrongly but you seem to be saying that none of the ships are accelerating so no speeds are going to "change" for any ship.

Can I suggest a change to your diagram that might make the meaning of some terms clearer. Replace your light source with a camera flash bulb, and assume the light lasts for a negligible time, i.e. it can be detected at a specific instant but its duration is too short to measure. An "event" is then the flash hitting a ship's detector and the speed of the light is the distance between any two detectors when illuminated by the flash divided by the time between the events. Of course both numbers must be expressed in the same coordinate system to get the speed in that system or "frame".

 

[whosapopstar?]

I've come into this thread late so sorry if I've picked it up wrongly but you seem to be saying that none of the ships are accelerating so no speeds are going to "change" for any ship.

Can I suggest a change to your diagram that might make the meaning of some terms clearer. Replace your light source with a camera flash bulb, and assume the light lasts for a negligible time, i.e. it can be detected at a specific instant but its duration is too short to measure. An "event" is then the flash hitting a ship's detector and the speed of the light is the distance between any two detectors when illuminated by the flash divided by the time between the events. Of course both numbers must be expressed in the same coordinate system to get the speed in that system or "frame".

What i ask is, to assume that light changes its speed, and then to prove this possibility wrong.

i think that i describe clearly what i mean by light changing its speed, isn't it so? If i did not describe very well what I call 'light changing its speed', please let me known and I will try to make it as clear as possible.

Basically what i am describing relies on the fact that according to all experiments, light and electric signal always arrive together to clock. Now if we assume a different speed for light and electric signal in spaceship 3, with respect to the electric signal that moves just under them, in spaceship 2, then in spaceship 2 the physical law that says that light and signal arrive together, will not preserve itself anymore, in contradiction to every possible experiment. Hence it is not possible.

If I have an error in this chain of arguments, where is it? please let me understand. If i need to describe better what i mean by: to assume that there is a difference of speed between light and signal in spaceship 3 and the signal under them in spaceship 2, i think i can, and there will be no need for any angle calculation, since i will put spaceship 3 very close over spaceship 2 floor and electric cable, at a negligible height.

i think that if i describe in an accepted way, what does light changing its speed mean, and then i negate this possibility, what i gain is the definition of light not changing its speed.

Since it took me a lot of effort to get to that scenario, i'd rather not change it and rather try to find an error in it so i will understand things in the way that i think of them, if logically right or wrong.

 

[GeorgeDishman]

What i ask is, to assume that light changes its speed, and then to prove this possibility wrong.

i think that i describe clearly what i mean by light changing its speed, isn't it so? If i did not describe very well what I call 'light changing its speed', please let me known and I will try to make it as clear as possible.

I haven't seen you state it at all which probably means I just missed the message. I've looked at both your diagrams and the associated posts and a few around them and haven't spotted it so can you tell me the message number where you define it.

Basically what i am describing relies on the fact that according to all experiments, light and electric signal always arrive together to clock.

In that case there are two more problems, firstly you haven't shown where there are clocks or cable in your diagram and secondly electrical signals in copper wire travel at about 60% of the speed of light in the rest frame of the wire. The way that transforms between frames will be similar to Fizeau's experiments on light in flowing water.

Now if we assume a different speed for light and electric signal in spaceship 3, with respect to the electric signal that moves just under them, in spaceship 2, then in spaceship 2 the physical law that says that light and signal arrive together, will not preserve itself anymore, in contradiction to every possible experiment. Hence it is not possible.

If I have an error in this chain of arguments, where is it?

Well the obvious point I have to make is that you have not done any calculations to create your argument. What you need to do is define the motion of the individual detectors and calculate where and when the flash (or the leading edge of the light being switched on) hits each. Then transform those into craft coordinates using the Lorentz Transforms. If you have electrical cables going to clocks, do the same for those signals. Then calculate the proper time between each signal arrival at each clock and see if there are any differences.

.. there will be no need for any angle calculation, since i will put spaceship 3 very close over spaceship 2 floor and electric cable, at a negligible height.

No problem, assume the cables are parallel to the direction of motion and ignore lateral displacement.

i think that if i describe in an accepted way, what does light changing its speed mean, and then i negate this possibility, what i gain is the definition of light not changing its speed.

If you apply the Lorentz Transforms properly, you will find that everyone measures the same speed.

Since it took me a lot of effort to get to that scenario, i'd rather not change it and rather try to find an error in it so i will understand things in the way that i think of them, if logically right or wrong.

OK, you can use the rising edge of the light being switched on as equivalent to the flash, you just need something that happens at a well defined instant, not something with a duration.

 

[GeorgeDishman]

I'm just wondering if I have been misreading what you are asking.

Basically what i am describing relies on the fact that according to all experiments, light and electric signal always arrive together to clock. Now if we assume a different speed for light and electric signal in spaceship 3, with respect to the electric signal that moves just under them, in spaceship 2, then in spaceship 2 the physical law that says that light and signal arrive together, will not preserve itself anymore, in contradiction to every possible experiment. Hence it is not possible.

If you first assume that all experiments say that light always has a specific speed in any inertial frame then subsequently assuming two different speeds will contradict what you have assumed about the experimental results. That's an obvious tautology though so I'm not clear on what you are trying to achieve with this.

 

[whosapopstar?]

I'm just wondering if I have been misreading what you are asking.
If you first assume that all experiments say that light always has a specific speed in any inertial frame then subsequently assuming two different speeds will contradict what you have assumed about the experimental results. That's an obvious tautology though so I'm not clear on what you are trying to achieve with this.

This is great! We might be very close to putting the finger on the place that i got it all wrong. If this will not turn out be the case, then i will get back and reply to your previous message.

Let's assume that light and electric signal arrive together, if this will turn out to be the main problem (and that electricity is actually 60% slower), then as said above, i will relate to this later, since it belongs to your previous message.

If you think that, anyway i should add a clearer diagram, let me know and i will draw one.

What i assume, is that light changes its speed when entering spaceship 3. Then i assume that light and signal arrive to clock together aboard spaceship 3, as well, at this point, i assume that the electric signal on spaceship 2 continues all the way at the same speed as light had, before entering spaceship 3, and when light returns to spaceship 2, it returns to its previous speed. Then i prove that this negates the possibility that also aboard spaceship 2, light arrives together with spaceship 2 electric signal to clock. This brings me to the conclusion that there is no change in the speed of light, not only within each frame, but also when moving from one frame (space ship 3) to another (space ship 2).i am aware of the fact, that this is most probably a logical error, but i still don't see the exact details from your explanation, since your write " you first assume that all experiments say that light always has a specific speed in any inertial frame ", but as much as i understand it, this is not what i assume, since i assume something about every frame by its own, and only then arrive at a conclusion that has to do with all the frames together.

Thanks.

 

[GeorgeDishman]

What i assume, is that light changes its speed when entering spaceship 3. Then i assume that light and signal arrive to clock together aboard spaceship 3, as well, at this point, i assume that the electric signal on spaceship 2 continues all the way at the same speed as light had, before entering spaceship 3, and when light returns to spaceship 2, it returns to its previous speed. Then i prove that this negates the possibility that also aboard spaceship 2, light arrives together with spaceship 2 electric signal to clock. This brings me to the conclusion that there is no change in the speed of light, not only within each frame, but also when moving from one frame (space ship 3) to another (space ship 2).

OK, here's another way to help people understand what you're saying. Suppose ship 3 is filled with water. When the light enters it, we know it really will change it's speed. Would your ergument prove that is impossible?

i am aware of the fact, that this is most probably a logical error, but i still don't see the exact details from your explanation ...

My problem is that I don't understand what you are trying to achieve. If the light travels in vacuum everywhere, there is no reason why it should change speed and if it does change as in my question above, your experiment shouldn't prove it doesn't. Again, it appears to be a tautology.

 

[whosapopstar?]

The reason is that i understood, since long ago, that in special relativity, even if the FoRs are moving at constant speed, there is no actual meaning to trying to find a phenomenon that is not dependent on choosing a FoR in advance, furthermore, all this, even if we relate to light, which all special relativity starts from.

That is why i ask about the validity of a way to prove, that actually light speed constancy is a phenomenon that is not dependent on choosing a FoR. It seems that when you are saying that "there is no reason why it should change speed and if it does change as in my question above…" you mean that light cannot change its speed, is true, you only mean that this notion has no meaning or is not defined; therefore it is true only as a vacuous truth.

But i am questioning if there is a possibility to well define a meaning for "light does not change its speed" in a way that will deliver a true meaning of independent FoR definition of light speed constancy, and not just as something that is a result of a vacuous truth. i am asking if, what i propose in the main paragraph of the previous message, do not present a possibility that light does not change its speed, independently of FoRs - as a matter of definition.

You say tautology, but i need you to help me to see these logical details, relating to why this is a tautology or a vacuous truth or any other kind of mistake, to really understand why it is so.

i think that i tried to ask why it is not a tautology, in the main paragraph of my previous message, by repeating the idea, while trying to shed off any redundant words that are not clear. Is it possible somehow to 'dissect', so to speak, that paragraph, in order to show me why it is a tautology or a vacuous truth or any other kind of mistake?

 

[GeorgeDishman]

But i am questioning if there is a possibility to well define a meaning for "light does not change its speed" in a way that will deliver a true meaning of independent FoR definition of light speed constancy, and not just as something that is a result of a vacuous truth. i am asking if, what i propose in the main paragraph of the previous message, do not present a possibility that light does not change its speed, independently of FoRs - as a matter of definition.

It's very difficult to understand what you mean but I'm going to take it as you have said it. Why are you talking about light "changing speed"? What relativity says it that the speed measured by ship 2 has the same numerical value as is measured by ship 3. There is no suggestion of any change of speed seen by either ship but that's not the point. That is unlike Newton's mechanics where you would expect the values to dffer by the speed of one ship as measured by the other.

 

[whosapopstar?]

Can you assure me that it is correct to say (?):

1. That there is no kind of transformation, at constant speed, that says: Yes, we measure light to be 300000kmps in our FoR, but if we transform something from another FoR we conclude that 'his' light is faster or slower the 'our' light?

2. Furthermore, that even numerically, according to SR (at constant speed), the speed of light has the same value for all FoRs, and that this is not something meaningless, true only in a vacuous way, tautological, or just mistake...?

 

[GeorgeDishman]

Can you assure me that it is correct to say (?):

1. That there is no kind of transformation, at constant speed, that says: Yes, we measure light to be 300000kmps in our FoR, but if we transform something from another FoR we conclude that 'his' light is faster or slower the 'our' light?

2. Furthermore, that even numerically, according to SR (at constant speed), the speed of light has the same value for all FoRs, and that this is not something meaningless, true only in a vacuous way, tautological, or just mistake...?

You are close but there are some details that could be clearer. Both ships are measuring the same flash (or rising edge) of light so there is no "his light" or "our light", just "the light".

To be pedantic, the value of c is 299,792,458 m/s and let's suppose that ship 2 is moving past ship 3 at 792,458 m/s. One ship measures the value 299,792,458 m/s. If they then apply the Lorentz transform, they will predict that the other ship will also measure that same numerical value for the speed of the same light. On the other hand, if they apply the Galilean Transform, they will predict that the other ship will measure a speed of 299,000,000 m/s. Experiments are therefore required to distinguish which occurs in reality and the answer is that the Lorentz Transform gives the correct prediction.

For that reason, it is not a tautology. In your previous posts you started by assuming that the speed would be the same and then went on to prove that the speeds would be the same which is just the same as the assumption.

 

[whosapopstar?]

Can anyone please read only the opening message of the thread: "synchronized clocks with respect to rest frame" and answer me this:

When the train returns, we can see that somthing happened, e.g. we have time dilation on the clock, and we agree that at least part of that time dilation was produced by constant speed (CS). There is evidence of say "nature 1" that somthing happened there.

Now regarding the clocks that are not synchronized, although they are both on the same train (but apart from each other): is there an experiment that can be done, which will show us this difference of de-synchroniztion between them, after the clocks will return to the station (nature 1), and not by sending signals when the train is on the move (say we call this kind nature 2)? if not, how come one clock can bring back evidence to the station of a phenomenon (CS time dilation on a single clock of nature 1), while another phenomenon, the de-synchronization of two clocks, is not somthing that can be brought back as evidence (of nature 1 type but only of nature 2 type)? or is such an experiment plausible, after all, for two clocks? or is this de-synchronization, a result of accelerating and de-accelerating and not of constant speed?

Thanks.

 

[ghwellsjr]

Consider two synchronized clocks at rest with respect to each other. Merely accelerating one clock does not de-synchronize it. You could instantly accelerate a clock to some high speed and then just as instantly decelerate it back to its original condition and the time will not have changed on it at all. Accelerating one clock causes it to be at a different speed than the other clock which causes it to tick at a different rate than the other clock but it has to remain at that different speed for some time in order to accumulate a different elapsed time when brought back to the other clock that experienced no acceleration.

I think the easiest way to address your concerns is to think about the Doppler effect and what it would be like if there were no relativity. I encourage you to look up "Doppler effect" in wikipedia. There you will see some formulas to involving the observed frequency f and the emitted frequency f₀. But instead of thinking about frequencies, just think about how each clock views the other one. Specifically, look at this formula where c is the speed of light in a fixed ether medium, v_r is the velocity of the receiver through the ether and v_s is the velocity of the source through the ether:

Just look at the part of the formula inside the parentheses. Let's say, just to get familiar with the formula, that the source clock is moving away from the receiver clock at 10% of c through the medium but the receiver clock is stationary in the medium. That means that the stationary clock will see the moving clock ticking slower than itself by a factor equal to:

c/(c+0.1c) = 1/1.1 = 0.90909

Now let's say instead that the source clock is stationary in the medium but the receiver clock is moving in the other direction at the same speed of 10%c. Now the source clock will see the receiver clock as ticking slower than itself by a factor of:

(c-0.1c)/c = 0.9/1 = 0.9

And you could calculate how the other clock views the first clock in each situation.

Clearly, there is a difference in how each clock sees the other one ticking, based on their speeds relative to the fixed medium, even though the relative speed between them is the same. If there were no relativity, then this difference in the observed tick rates between two clocks in relative motion would change depending on how they are moving through the ether.

But that is not what actually happens. What actually happens is that both clocks see the other one as ticking at the same rate. Please look up the wikipedia article called "Relativistic Doppler effect". Now we have a new formula where f_o is the observed frequency, f_s is the source frequency and β is the relative speed as a fraction of the speed of light:

Just look at the square root part of the formula. For our example of 10%c, β = 0.1 and:

√[(1-0.1)/(1+0.1)] = √[0.9/1.1] = 0.904534

This value is somewhere between the two values that we got before and more importantly, it is the factor that each clock sees the other one ticking at compared to their own. This is really quite an amazing and surprising result because it means that what we observe does not depend on a medium to propagate that observation and any attempt to identify one is doomed to frustration. If we could identify one, then we could take into account the light propagation time to determine the actual time displayed on the remote clock at each location as it moved away from us. Instead, it is not possible to arrive at a conclusion in a determinate way.

Prior to Einstein, scientists believed that the light propagation time was fixed according to an absolutely stationary medium, even if they could not determine its state but Einstein figured out that you could assume any fixed state to be the one in which light propagated at c and this is the basis for Special Relativity.

 

[GeorgeDishman]

Can anyone please read only the opening message of the thread: "synchronized clocks with respect to rest frame" and answer me this:

Answer #2 in that thread is correct but also note that #3 is an important qualifier.

When the train returns, we can see that somthing happened, e.g. we have time dilation on the clock, and we agree that at least part of that time dilation was produced by constant speed (CS). There is evidence of say "nature 1" that somthing happened there.

There is a cumulative time difference between the clocks that went on the journey and an identical clock that remained on the station. That is the essence of the Twins scenario.

Now regarding the clocks that are not synchronized, although they are both on the same train (but apart from each other):

While moving, they are not synchronised as determined by observer "O" but they are synchronised as determined by observer "R". It is important to specify the observer since simultaneity is frame-dependent.

is there an experiment that can be done, which will show us this difference of de-synchroniztion between them, after the clocks will return to the station (nature 1),

Off-hand, I'm not sure if there is one that addresses synchronisation specifically but the cumulative difference between the train clocks and the station clock was famously tested by Hafele and Keating, while the effect on moving "clocks" was first tested by Ives and Stilwell.

http://en.wikipedia.org/wiki/Hafele–Keating_experiment

http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

It is important if you want to understand this stuff to note that this is not indicative of flaws in the clocks, in the thought experiments they are assumed to be working perfectly at all times and in real experiments, the accuracy of the instruments is adequate to demonstrate the results. What you are supposed to understand from them is that the measurement we call "time" is path-dependent, like the mileage reading from odometers in cars taking different paths between two locations.

 

[whosapopstar?]

Please see attached diagram:
Here is an apparatus aboard a train. It is activated once when the train is at bay and once when it is moving at constant speed. Results are the same at both cases.

What would be the reason that while time dilation is influencing clock C, still when the train is on the move, clock A shows X+C (clock C increment) and not X+D (a different clock C increment).

i cannot find the reason to be anyone of the following:
1. Light speed - can't be, always stays the same, either if the apparatus is at station or moving.
2. Clock A and B de-synchronization - can't be, they are aligned at the same vertical line.
3. Length contraction - can't be, the apparatus is symmetric.

 

[ghwellsjr]

If you are saying that clock C introduces a delay of C, then why should moving at any speed have any effect on the result? Remember, time dilation is what another observer moving with respect to the train would see happening to the clocks on board the train.

 

[GeorgeDishman]

What would be the reason that while time dilation is influencing clock C, still when the train is on the move, clock A shows X+C (clock C increment) and not X+D (a different clock C increment).

It doesn't matter where on the train you put the delay so put it at the end, the light pulses then arrive simultaneously and then the delay runs.

The delay will have duration C as measured by some on the train next to it but a longer time as measured by someone on the platform (the clock seems to run too slowly).

 

[whosapopstar?]

If we still don't have the technology to build a Planck clock (a clock which fundamental unit is 1 Planck unit), how can we ever validate the existence of time dilation?

 

[GeorgeDishman]

If we still don't have the technology to build a Planck clock (a clock which fundamental unit is 1 Planck unit), ..

Just multiply the scale of any good clock by the number of Planck units in a second.

how can we ever validate the existence of time dilation?

First done in 1938:

http://en.wikipedia.org/wiki/Ives–Stilwell_experiment

 

[whosapopstar?]

Yes but how can we know that this clock that you take its results and divide them by the Planck unit, gives you always, say, 1 NPU (Not Planck Unit) per 10 Planck units and not, say, once, 1 NPU per 10 Planck units and again, when measuring against a Planck clock, but at different constant velocity conditions, say 1.8 NPU units per 10 Planck units?

 

[GeorgeDishman]

Yes but how can we know that this clock that you take its results and divide them by the Planck unit, gives you always, say, 1 NPU (Not Planck Unit) per 10 Planck units and not, say, once, 1 NPU per 10 Planck units and again, when measuring against a Planck clock, but at different constant velocity conditions, say 1.8 NPU units per 10 Planck units?

Velocity relative to what?

 

[whosapopstar?]

Velocity relative to the station. One pair of NPU clock + Planck clock on the station and another pair of that sort, on the train, moving at constant speed. Should the Planck clock on the train be able to discover that the NPU clock is experiencing time dilation? or only when they retun to station? how come? there is no length contration at a Planck scale. On the other hand, relativity principle has to preserve itself...

 

[GeorgeDishman]

Velocity relative to the station. One pair of NPU clock + Planck clock on the station and another pair of that sort, on the train, moving at constant speed. Should the Planck clock on the train be able to discover that the NPU clock is experiencing time dilation? or only when they retun to station?

Yes, they will behave exactly the same as modern atomic clocks.

how come?

Because the effects of relativity are caused by geometry.

Draw a vertical line on a sheet of paper. Draw another line nearly vertical but crosssing the first near the bottom. Put marks every 1cm starting at the crossing point along each line. Now draw horizontal lines from the marks on the sloping line to the vertical. Those projections will not cross on the 1cm marks on the vertical line.

It doesn't matter whether the scale is 1cm=1 Planck time or 1cm = 1 second, the geometry always produces the same effect. The same is true for distances in space whether the ticks are 1 Planck length or 1 light second of distance.

there is no length contration at a Planck scale.

Geometry applies at all scales.

Perhaps you should learn how SR works before trying to find faults in it, you'll save yourself a lot of wasted time.

 

[whosapopstar?]

Nope. this does not answer my question. If i want to draw on that paper marks, at closer and closer distance, then i need a thinner and thinner pencil, right? Doesn't the Planck scale say that at certain point i will not be able anymore to draw the marks closer, no matter what kind of pencil i use?

 

[GeorgeDishman]

Nope. this does not answer my question.

Maybe you need to give it more thought, it's not difficult. The analogy isn't perfect but if you spot the flaw, I'll explain how to fix it, it doesn't alter the basic understanding.

If i want to draw on that paper marks, at closer and closer distance, then i need a thinner and thinner pencil, right?

No, the ticks represent instants of time so have no width. You also need to remember that GR is a classical theory, not quantum. It is the difference between the spacing of ticks drawn along one line to the projection of those on the other which is called "time dilation".

Doesn't the Planck scale say that at certain point i will not be able anymore to draw the marks closer, no matter what kind of pencil i use?

IMHO it says that at some small distance, the uncertainty principle means nothing can be located well enough to distinguish between being in the same place and being separated but regardless of its interpretation, since there is no preferred frame, the scale must be the same for the clock on the train and that on the station. The operation would be identical to that of standard atomic clocks.

 

[whosapopstar?]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

 

[GeorgeDishman]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

This page has an applet at the top that implements the Lorentz Transforms and is very simple to use though you have to be a little careful as the cursor doesn't snap to the grid. There are other geometries farther down the page for comparison:

http://www.reagenix.com/personal/sci/space_time/test.html

It shows a standard spacetime diagram so an item at rest is a vertical line. A surface joining simultaneous events is a horizontal line. The speed of light is 45 degrees.

The slider at the top allows you to view the whole thing from the point of view of different observers.

To investigate the train and station, draw two vertical lines representing the ends of the platform. Then move the slider a little (so that you view the platform from the point of view of someone on the train) and draw two more vertical lines representing the ends of the train. Now you can add lines at 45 degrees representing the light signals and see how everything transforms.

You can add small dots on any line to represent the ticks of a clock, for example put them on the horizontal gridlines but make sure each line is vertical when adding them to get the same tick frequency for all clocks.

 

[whosapopstar?]

This is not what i meant. i need an animation software where i can draw objects and let them move between two or more points that i draw, and then put clocks and light sources inside and outside these objects, and while the objects are moving, send light beams from within these objects and outside of them to points i draw outside and inside the objects, and then let the whole thing run as animation by itself, while the constancy of speed of light and time dilation and length contraction are kept as rules in that animation, relating to a FoR of one of these objects that i mark in advance. What I need is that sort of educational and flexible tool.

 

[GeorgeDishman]

What I need is that sort of educational and flexible tool.

The applet is precisely what you need. What you asked for would not explain how SR works, it would be nothing more than a toy for making pretty pictures. If you only use a tool that incorporates what you already know, you won't learn anything new.

Try drawing out the train and station, or the twins paradox and see how it works.

 

[whosapopstar?]

No it would not be just a toy. And because such a thing does not exist, now i have to look for some kind of flash animation or graphic expert, only in order to be able to bring to life, some really not too complicated scenarios i have in question.

 

[GeorgeDishman]

No it would not be just a toy. And because such a thing does not exist, now i have to look for some kind of flash animation or graphic expert, only in order to be able to bring to life, some really not too complicated scenarios i have in question.

Here's a suggestion then. Draw your scenario in the applet as I suggest. Then move the slider to select a particular observer frame. The horizontal lines represent observer times so for each horizontal line, note the location of each body and then draw a picture representing that. Now make a movie from the sequence of pictures (there are free applications to create animated gifs). That gives you one observer's view.

Move the slider to a different position and repeat the process for any other observers you want.

If you intend to get someone to do the graphics for you, that is what they would need to do as well.

However, what I expect will happen is that once you draw your scenario in the applet and move the slider, you will immediately see not only what happens but why the various effects occur. That explanation will not be visible in your flash version.

It's your choice of course, but if you want to learn SR, the applet will be of more more use.

 

[whosapopstar?]

If existing educational tools for SR teaching where more flexible, i would draw three points that represent the clocks in the diagram, presented here before, and attach visible time counters to each of them. Then i would change the rate of the common time rate of the clocks, while keeping the two animated advancing lines that represent the light beams, at their former speeds. Then i would play with the common constant speeds of light beams and common rates of clocks (each time changing twice the clocks per one change of light speed), to see that no matter what changes i make with these parameters, both light beams would arrive together at the two clocks, although there is an apparent non-symmetry, in the form of one light beam going through the third clock 'barrier', while the other light beam has no barriers on the way. i would also attach flickering effect of dots to the clocks, so maybe when changing the parameters to extreme values, i would be able to feel the scenario better, only by looking at the flickering rate of dots and light beams 'sprint' to the finish line (extreme enough to make the difference of positions on the screen itself negligible - i hope no one is going to claim a problem of this sort!). Then maybe i would be able at last after many years, to overcome the notorious, counter-intuitive and even frustrating on purpose, in some people hands, thing with SR. The sliders applet would never do the job, since they will not let me the feeling that i built the scenario, according the way my imagination works (of course, as long as physical rules are kept in form, in such a hypothetical 'SR flash animation' tool).

 

[yuiop]

Is there any free and simple geometry animation software where i can build all kinds of scenarios with light beams and moving spaceships and trains and clocks etc...and see with my own eyes that things work in a certain way and not another?

Is this more like the sort of thing you are looking for? http://www.its.caltech.edu/~phys1/java/phys1/Einstein/Einstein.html

You usually have to enter the relative velocity of the other frame before pressing start and then use the switch frames button. It shows motion in space as an animation along with the same motion depicted on a spacetime diagram alongside. It creates animations but I think there only preset scenarios.

 

[whosapopstar?]

Ok, let's go back to static images!
Attached is this diagram, please observe details.

d is a very small distance, especially when comparing with the path that ligth beams take between clocks, even very small comparing to the horizontal difference of position between clock A and clock B.

Clock A will indicate which light beam came first: the one from clock C or the one from clock B.

We know that time dilation exists at constant speed and that when we calibrated the apparatus at a slower constant speed, the C clock hindrance of the light beam was exactly in the order to compensate the horizontal difference between clocks A and B and thus, we had the exact same time indications on these clocks (A and B), and hence, clock B indicated that the light beam from clock C arrived first. As well, the mirror reflection time is very small, comparing to anything else described here.

Now we are at a different and faster constant speed, we do not change the apparatus calibration, but still- we know that according to the principle of relativity, time indication of both beams arriving at the clocks, clock A and B, will be an equal time and also as before, clock A will indicate that light arrived first from clock C and not from clock B.

How come? What is the reason? What effect counteracts time dilation, that we know that takes place at a higher constant speed?

 

[GeorgeDishman]

Your description lacks some details but if I understand you correctly, the first of the attached files shows how you would draw it in the applet. The light is emitted at F, triggers clock C as it passes then reflects from the mirror at B before stopping the clock at A. Clock C sends the delayed pulse at D and if I follow your description, the delay is such that the light arrives at A to start the clock (which I show as event E).

The second file shows what the events look like from another frame, i.e. an observer moving right to left hence the clocks are moving left to right. All I did for that was to move the slider. You should be able to see that the diagram shows length contraction, time dilation and the relativity of simultaneity as you move the slider.

p.s. The short horizontal lines on C-D and E-A are the ticks of the clocks.