Cubic Time Dilation - Corrected Lorentz Factor

[James_S_Saint]

The universe is made of spinning things, not bouncing things. Although that is not 100% true, when it comes to sub-atomic particles and atoms, it is certainly true. The Lorentz time dilation factor assumes the opposite. Considering a space ship traveling through space at 50,000 mph, how many particles and activities within the ship are spinning versus bouncing up and down?

If you are not familiar with the Lorentz factor for time dilation, Wiki has an accurate article on it (warning: not everything in Wiki is).

Time is merely the measure of relative change but an accurate measure of it can be tricky. It has always been assumed that it doesn’t matter in what manner something is changing, but merely how fast. The problem is that change comes with directions of change as an inherent property. Thus when someone speaks of traveling in a direction, the relative changing within the object involves that direction of travel.

The Lorentz transformation concerning time dilation for traveling objects assumes a photon bouncing between two mirrors. It is assumed that the speed of the light must be measured as the same for both an observer watching the traveling mirrors pass by as well as any observer on or in the traveling object. The issue is simply that the total distance of travel for the light will be perceived as different. The observer on the traveling object merely sees light bouncing directly up and down whereas the observer watching the object pass by sees that same light zigzagging up and down.

Speed is merely distance over time. And due to the presumption that light must be observed as traveling at the same speed regardless of one’s travel and the distance being traveled is seen as different, the measurement of time itself must change in order to compensate the distance difference and yield the same speed. The Lorentz factor was derived merely by calculating a factor that would provide such compensation. And a reflecting photon was used to produce that factor. If the universe was made of bouncing photons, it would have been a good model.

But if one realizes that the universe is much more accurately modeled by spinning things rather than bouncing things, that compensating factor changes. In the following, I use a “square clock” to represent a spin rather than a round clock merely to simplify the mathematics. Whether round or square should not alter the compensation factor. What is important is that complete rotations are considered rather than linear reflections.

Fig 1. Square Clock versus Lorentz Clock

In figure 1, a comparison is made concerning the observed distance of travel for the photon in a linear light-clock and a square light-clock. The green dot represents a photon traveling. If the square clock is observed passing by and the speed of that photon is to be constant, one revolution of the traveling clock must take longer than a stationary clock would have taken. The same is true for the linear clock. But the dilation factors for the two types of clocks are different.

Linear, Lorentz Light-Clock Dilation Factor;

Square Light-Clock Dilation Factor;

But the story doesn’t stop there. Note that the square clock is turning in one particular orientation with respect to its travel. All rotations aren’t aligned to the direction of travel. And given any spaceship type of scenario, within the ship, particles and atoms will involve rotations in all three dimensions regardless of the direction of motion.

If a square-clock is facing the direction of travel, its dilation will be the same as the linear clock because there is no forward and back motion for the photon. And for any one direction of travel, two out of three orthogonal clocks will have square-clock dilation while one remains with linear dilation. Simply by taking the average of the dilation factors for each of the three directions so as to account for any direction of travel, we get;

Cubic Light-Clock Dilation Factor;

So for example, the Lorentz time dilation factor for an object traveling at 0.5 the speed of light is 0.8660. The Cubic dilation factor yields 0.8236 as a more accurate figure for real applications.

For extremely precise calculations, the exact method for measuring time must be considered along with the direction of motion.

So next time you go to buy a new watch, make sure it is properly Cubic Dilated.

[PhysBang]

@James S Saint

The Lorentz transformation concerning time dilation for traveling objects assumes a photon bouncing between two mirrors.

No, this is merely one very useful model for representing the difference between timing events in different systems of coordinates.

It is assumed that the speed of the light must be measured as the same for both an observer watching the traveling mirrors pass by as well as any observer on or in the traveling object. The issue is simply that the total distance of travel for the light will be perceived as different.

It depends on how one measures “distance”.

If one measures distance in terms of spatial coordinates and a time coordinate, then the distance that a beam of light (so to speak) travels can vary from one system of coordinates. There is an invariant way of measuring this path, however, that is the same in all valid systems of coordinates.

The observer on the traveling object merely sees light bouncing directly up and down whereas the observer watching the object pass by sees that same light zigzagging up and down.

This is a simplified description of a possible scenario.

Speed is merely distance over time. And due to the presumption that light must be observed as traveling at the same speed regardless of one’s travel and the distance being traveled is seen as different, the measurement of time itself must change in order to compensate the distance difference and yield the same speed.

This is not strictly correct; one needs to take two different corrections to time into account: changes in duration and changes of what events are considered to be simultaneous. Often people forget one or the other, do simplistic calculations, and come up with mistaken conclusions.

But if one realizes that the universe is much more accurately modeled by spinning things rather than bouncing things, that compensating factor changes. In the following, I use a “square clock” to represent a spin rather than a round clock merely to simplify the mathematics. Whether round or square should not alter the compensation factor. What is important is that complete rotations are considered rather than linear reflections.

This prima facie does not make sense for two reasons. Reason one: square paths are not circular paths and circular paths are not rotations. If one is concerned with rotations, then one should look to rotations, not things that are not rotations. Reason two: an aesthetic preference for rotations does not matter to the science. Though claiming that special relativity is based on reflection is a straw man, even if it was, if special relativity works (as it appears to), then there is a burden on supposedly rotational relativity to show that it works better than special relativity. I suspect that it cannot even match existing observations.

So let’s see a single observation that this cubic dilation can match.

So next time you go to buy a new watch, make sure it is properly Cubic Dilated.

Yes. You might want to get one from the following website of equal quality: timecube.com/

[James_S_Saint]

@PhysBang

@James S Saint

The Lorentz transformation concerning time dilation for traveling objects assumes a photon bouncing between two mirrors.

No, this is merely one very useful model for representing the difference between timing events in different systems of coordinates.

Explain.

…not that I agree with any of the rest of what you posted.

[PhysBang]

@James S Saint

@PhysBang

@James S Saint

The Lorentz transformation concerning time dilation for traveling objects assumes a photon bouncing between two mirrors.

No, this is merely one very useful model for representing the difference between timing events in different systems of coordinates.

Explain.

There are many ways to derive the Lorentz transformations. Perhaps the most famous is that in Einstein’s 1905 paper. One can read that in the following llink: fourmilab.ch/etexts/einstein/specrel/www/

In that paper, mirrors come up only in section nine out of ten sections, well after the Lorentz transformations have been established.

A famous unstated premise of the paper is that the speed of light is isotropic, that is, that the speed of light is the same in every direction. However, the paper does not use this in reflection, the paper merely assumes that there are such things as clocks (physical systems or sub-systems that can be counted upon for their regularity), that these clocks can be reset to match each other using a procedure that relies on the constant speed of light, and that it is possible that there are clocks that stay synchronized using that procedure.

One would think, James, that if you were serious, you would have read that paper and addressed it rather than make up claims about special relativity from fantasy.

…not that I agree with any of the rest of what you posted.

Of course not: it’s in straightforward, honest English.

[James_S_Saint]

Son, I read that paper when you were in your diapers. So you can stuff that childishly egocentric “I am the super intelligent and you are shit” attitude of yours.

And regardless of the conflation of what you have presented, you haven’t explained your “No” sufficiently.

For the Lorentz factor to be accurate, that bouncing photon must be able to bounce in any direction and produce the same results. The Lorentz factor exactly reflects that bouncing photon. If the photon is traveling forward and back relative to the motion of the moving object that it is within, the Lorentz factor will be incorrect at calculating the time differential.

The real problem with that is that items, such as photons, within the structure of the object really are traveling forward and back. Every atom has its electrons circling in every direction, including forward and back. Thus if Lorentz were to try to count the number of orbitals based upon his factor, he would come up with the wrong number.

SP requires that any light traveling in any direction within a moving object must calculate back to the exact same velocity and the Lorentz factor is being used for that purpose. They have noted that their calculations don’t work exactly on target. They wouldn’t for other reasons, but for now, one reason would be that the Lorentz factor would predict the wrong number to begin with.

I don’t disagree that using it makes for closer predictions that the older “constant light” notion from Galileo/Newtonian days. I am just showing why it isn’t as accurate as it could be.

[PhysBang]

@James S Saint

Son, I read that paper when you were in your diapers. So you can stuff that childishly egocentric “I am the super intelligent and you are shit” attitude of yours.

I had not notices that I was the person claiming, a priori without any empirical evidence presented, that an entire physics of field is incorrect. So, yes, I will stop that attitude.

And regardless of the conflation of what you have presented, you haven’t explained your “No” sufficiently.

Perhaps you should stop the “I am too willfully obtuse to read” attitude. You made a claim that the Lorentz factor was about mirrors, any idiot can read a great derivation without mirrors.

For the Lorentz factor to be accurate, that bouncing photon must be able to bounce in any direction and produce the same results.

It is true that if the Lorentz transformation is correct, then it will apply equally to a photon traveling in any direction. That is, there will be no difference to a photon based on direction.

The Lorentz factor exactly reflects that bouncing photon. If the photon is traveling forward and back relative to the motion of the moving object that it is within, the Lorentz factor will be incorrect at calculating the time differential.

You are, as usual, simply making things up here. I might be willing to admit that you might not be able to work things out if you tried to apply the transformation to a simple physical system in which objects were moving. However, I see no evidence anywhere of any internal inconsistency in Lorentz transformations applied to moving objects.

I don’t disagree that using it makes for closer predictions that the older “constant light” notion from Galileo/Newtonian days. I am just showing why it isn’t as accurate as it could be.

So far, you have shown nothing. Are you claiming that you can make a prediction of a systematic deviation in particular physical systems? If so, let’s see this.

[Ed3]

Hi Guys,

I had prepared my remarks before PhysBang’s comments, and hope that they do not seem out of place now.

As I have done before, I will dispute the whole concept of time dilation generally, and the Wiki article on this subject specifically.

Moving clocks, in inertial reference frames, run slow – NOT fast. This has been experimentally verified.

Much of the mathematics in the Wiki article is based on the Euclidean metric which is not valid when comparing moving reference frames. Particularly the use of the Pythagorean Theorem is not valid in this situation.

I first discussed this on ILP at:

viewtopic.php?f=4&t=179472

I have discussed this with one of the moderators, DVdm, at Wiki and he acknowledges that the article assumes that the problem can be analyzed in the spatial coordinates alone.

Once someone announces that the sky is green I just stop communicating.

You can see my Wiki comments at:

en.wikipedia.org/wiki/Talk:Time_ … chive_2012

It is located in the section entitled “Analysis - Simple inference of time dilation due to relative velocity”

Thanks

Ed

[James_S_Saint]

I can’t discern your point Ed. Are you saying that the stated Lorentz factor in Wiki is wrong? Or merely that the bouncing photon concept is a bad model? Or…?

My concern in this is that the Lorentz factor is what is being used and that factor exactly reflects the model of the bouncing photon. If the bouncing photon doesn’t fit reality, then neither does the Lorentz factor. And if you want t use something like the bouncing photon concept, then use a “square clock” concept, “Cubic Dilation” to get closer to a real model. The difference in accuracy is small, but then so are the errors that they report using Lorentz.

[Ed3]

Hi James,

My responses relate only to the Wiki article. I find your concept interesting.

The Wiki article, “Simple inference of time dilation due to relative velocity”, concludes:

∆t’ = ∆t / √(1 – (v/c)(v/c))

Using standard notation (t’ is the time in the moving reference frame and t is the time in the rest frame) a reader that is casually acquainted with Special Relativity might conclude that ∆t’ is greater than ∆t. Equivalently a casual reader might conclude that time is dilating (running faster) in moving reference frames.

This is wrong!

The conventional equation reverses ∆t’ and ∆t and should read:

∆t = ∆t’/ √(1 – (v/c)(v/c)) Or ∆t’ = ∆t(√(1 – (v/c)(v/c)))

There is more to this story, and it is possible to understand the Wiki equation, but it is complex and requires a flawed assumption.

Anyway to answer your question, the Lorentz factor is correct, but the Wiki equation using it is wrong.

Relative to the mirrors:

The simple answer is that if we consider the bottom drawing with an observer O centered on the mirror B, and O observes that the mirrors are parallel, then the moving observer, O’, will not see these mirrors as parallel.

From a mathematical view point this is because the Lorentz transform is not a conformal map.

Thanks Ed

[James_S_Saint]

I don’t think that the Lorentz requires that the mirrors be actually “parallel”, as in parallel lines (although that was an interesting thought). It is the distance from one reflection point to another that matters. The “mirrors” could be taken merely as “points of reflection” rather than parallel lines of reflection. Only one point on each mirror is ever used.

[James_S_Saint]

@Ed3

∆t’ = ∆t / √(1 – (v/c)(v/c))

Using standard notation (t’ is the time in the moving reference frame and t is the time in the rest frame) a reader that is casually acquainted with Special Relativity might conclude that ∆t’ is greater than ∆t. Equivalently a casual reader might conclude that time is dilating (running faster) in moving reference frames.

This is wrong!

The conventional equation reverses ∆t’ and ∆t and should read:

∆t = ∆t’/ √(1 – (v/c)(v/c)) Or ∆t’ = ∆t(√(1 – (v/c)(v/c)))

An interesting point because when I first revued that article, I stopped at that exact same point, a little puzzled. But then reading on a bit, I just assumed that they had yet again adopted a different convention, keeping people hopping and confused (t = “your inertial time passage” compared to t’ = “his motion time passage” (our way) rather than t = “amount of inertial light distance per tic” compared to t’ = “amount of motion’s light distance per tic” (I presumed to be their new convention). And that is exactly why I didn’t use the x’ and t’ in my presentation.

But after I had made the anime, I realized that I really shouldn’t have used the “d”. I should have used an “f” for “factor”, not “d”, implying “distance”. The factor is the only concern. Sometimes when I catch something like that after the fact, I go ahead and leave it in just to see if anyone actually reads these things. But in this case, I didn’t want to remake the entire anime (a pain in the butt).

On this site, math seems to merely scare people into silence and presumption. If they like you they presume your math is right and proof of your brilliance. If they don’t like you they presume it is wrong and being used solely to try to impress them (people gauge others by their own sense of value, not accepting that other don’t have the same values).

When I presented a small amount of math (a little trig), Eugene immediately accused me of trying to bluff the “audience” (that he imagines is watching the thread). But he had said that he had a math degree. I seriously didn’t expect him to not be able to add sine functions such as to conclude that I was just trying to fake out an audience. So I stopped using math on that thread (I seldom use it on these threads anyway. It leads to confusion. And I tend to make attention errors too often… such as the “d”). I prefer straight forward reasoning and logic (not symbolic syllogisms to be misinterpreted and obfuscated, although I can understand its use for professionals).

And then even on top of that, math reductions and presumed symbols tend to get misinterpreted into who knows what, so I am never really certain what other people really meant by their presentation, so why should they know what I really mean by mine. Properly translating reality into math and BACK is something that people seem to have a really hard time keeping straight (especially around here, but even in real physics).

Long ago, I noticed a couple of your threads and started to comment. Then I realized that it was all math and no one had said a word even though the thread was perhaps a year old or more. And I hadn’t seen you around at all at that time. I wanted to ask you how you were representing which things so that I could follow it better. I hadn’t used any but relatively simple math for around 15 years (then had to jump up into vector analysis for my own project), so I need explanation when anyone posts things. I don’t trust that they mean what I read (even without math).

Math might be a universal language, but only if you get an interpretation manual along with it (and hopefully the sender read the same manual).

[phyllo]

The Wiki article, “Simple inference of time dilation due to relative velocity”, concludes:

∆t’ = ∆t / √(1 – (v/c)(v/c))

Using standard notation (t’ is the time in the moving reference frame and t is the time in the rest frame) a reader that is casually acquainted with Special Relativity might conclude that ∆t’ is greater than ∆t. Equivalently a casual reader might conclude that time is dilating (running faster) in moving reference frames.

This is wrong!

The conventional equation reverses ∆t’ and ∆t and should read:

∆t = ∆t’/ √(1 – (v/c)(v/c)) Or ∆t’ = ∆t(√(1 – (v/c)(v/c)))

There is more to this story, and it is possible to understand the Wiki equation, but it is complex and requires a flawed assumption.

Time dilation is confusing because there is always some kind of relative measurement taking place and it’s easy to lose track of what is relative to what.

The Lorentz transformation calculates how long an event will take, when in motion, but expressed in ‘standard stationary’ time.

Let’s say that an event takes 1 second to complete when not moving.
That same event will also take 1 second to complete when moving at high speed as measured by the mover.
However comparing the events, it does not take the same amount of time to complete that event when measured by a standard stationary time measure.

For example:
A person runs an experiment on the ground (not moving) and finds that it takes 1 hour to complete.
A second person then performs the experiment in a spaceship at a speed giving a Lorentz factor of 1.2 . Timing within the spaceship shows that it takes 1 hour to complete.
But let’s say that the person, on the ground, stops the spaceship after 1 hour, believing that the experiment is complete. He will find that the experiment has not had sufficient time to finish.
One can use the Lorentz transformation to calculate that a person on the ground will have to wait 1.2 hours for the moving experiment to finish.

Therefore we say that time is running more slowly for the mover. It takes longer for things to happen.

[Ed3]

Hi James,

Since the angles are not preserved, I think it is not likely that the argument about the mirrors will work, but I don’t want to put the effort into proving my statement.

I did provide a derivation of the Lorentz transform, based extensively on the book of “Introduction To Special Relativity” by Robert Resnick and it is located at

viewtopic.php?f=1&t=173286

However, after the derivation, I did regretfully reference the Wiki article on time dilation that we have been discussing. IMHO the transform derivation itself is still valid.

A cleaner, more elegant, derivation not requiring the constancy of the speed of light, is at:

en.wikipedia.org/wiki/Derivation … formations

In any case I think that the relation between ∆t and ∆t’ might be proven by a straight forward substitution.

From the transforms we have:

t2 = (t2’ + (v/(cc))x2’)L
t1 = (t1’ + (v/cc)x1’)L
where L is the Lorentz factor.

Then t2 – t1 = ((t2’ + (v/(cc))x2’ – (t1’ + (v/(cc))x1’)L. Since we can assume that x2’ = x1’ because the clock in t’ is positioned at a fixed position we get:

t2 – t1 = (t2’ – t1’)L and we are done.

Thanks Ed

Hi phyllo,

That’s the best explanation of time dilation that I have ever seen.

Thanks Ed

[James_S_Saint]

@Ed3

t2 = (t2’ + (v/(cc))x2’)L
t1 = (t1’ + (v/cc)x1’)L
where L is the Lorentz factor.

Then t2 – t1 = ((t2’ + (v/(cc))x2’ – (t1’ + (v/(cc))x1’)L. Since we can assume that x2’ = x1’ because the clock in t’ is positioned at a fixed position we get:

t2 – t1 = (t2’ – t1’)L and we are done.

Hey Ed,
I’m not following that line in red. What do you mean by it?
Why is "the clock in t’ " positioned at a fixed position?

[Ed3]

Hi James,

I should have said the clock in the moving reference frame is located at a fixed poition.

Maybe the drawing below will help make more sense.

Hope this makes more sense.

Thanks Ed

[James_S_Saint]

Okay, I see what you had meant.

But this relates to something else being discussed and I’m curious about your opinion on this;

[Ed3]

Hi James,

Can we assume that the grey object marked “Stationary” is an idealized rigid body with a single Force? (If it is not a rigid body then the motion will be a mess). Additionally can we assume that the Force is an Impulse Force exerted only over an exceedingly small range of what I assume we can call the x dimension?

Thanks Ed

[James_S_Saint]

@Ed3

Hi James,

Can we assume that the grey object marked “Stationary” is an idealized rigid body with a single Force? (If it is not a rigid body then the motion will be a mess). Additionally can we assume that the Force is an Impulse Force exerted only over an exceedingly small range of what I assume we can call the x dimension?

Thanks Ed

A rigid body, yes. But not a “single force”.
Perhaps think of it as a train with an engine both pulling from the front and another pushing from the back. Both have a tension monitor to ensure that they each apply identical force.

Unless I’m missing something, as the train accelerates to become a classic Einstein train, the train must become shorter relative to the station or ground. If that is the case, then the front and the rear could not have accelerated at the same rate even though each had the exact same force applied, defying an even more fundamental law than the constancy of the speed of light.

[PhysBang]

@James S Saint

Unless I’m missing something, as the train accelerates to become a classic Einstein train, the train must become shorter relative to the station or ground. If that is the case, then the front and the rear could not have accelerated at the same rate even though each had the exact same force applied, defying an even more fundamental law than the constancy of the speed of light.

You are missing something: there is not the same force applied at the same time in a train that will keep the same length in a reference frame in which the train is stationary. It’s simultaneity that one has to consider carefully.

If one was to work carefully through an example where a train was pushed and pulled, one begins to find that if the different train cars are pushing and pulling with the same force in the frame co-moving with the train, then because of the relativity of simultaneity, they are pushing and pulling with different forces in a frame co-moving with the train track. The trailing car begins to push with more and more force relative to the leading car when judged from a frame co-moving with the tracks.

If one was to see a train where the forces were always the same in a frame co-moving with the track, then one would see that the train breaks at some point, as the cars get smaller while the leading and trailing cars stay the same distance apart.

That latter case would be an example of the Bell’s spaceship scenario. en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

[James_S_Saint]

@PhysBang

@James S Saint

Unless I’m missing something, as the train accelerates to become a classic Einstein train, the train must become shorter relative to the station or ground. If that is the case, then the front and the rear could not have accelerated at the same rate even though each had the exact same force applied, defying an even more fundamental law than the constancy of the speed of light.

You are missing something: there is not the same force applied at the same time in a train that will keep the same length in a reference frame in which the train is stationary. It’s simultaneity that one has to consider carefully.

If one was to work carefully through an example where a train was pushed and pulled, one begins to find that if the different train cars are pushing and pulling with the same force in the frame co-moving with the train, then because of the relativity of simultaneity, they are pushing and pulling with different forces in a frame co-moving with the train track. The trailing car begins to push with more and more force relative to the leading car when judged from a frame co-moving with the tracks.

If one was to see a train where the forces were always the same in a frame co-moving with the track, then one would see that the train breaks at some point, as the cars get smaller while the leading and trailing cars stay the same distance apart.

That latter case would be an example of the Bell’s spaceship scenario. en.wikipedia.org/wiki/Bell%27s_spaceship_paradox

A) It is a “rigid body” thus there is no “pulling apart” (the “train” thought would have merely a single car).
B) Pulling apart requires forces in opposing directions. The only forces are in the same direction.
C) It is a constant force creating a gradual acceleration. The force is never any greater than when it started. If it didn’t pull it apart initially, it never will.
D) Although not required, you are permitted to use your light sphere to establish relative simultaneity to initiate the event. The forces are not changing, so even if you miss your timing, the difference is immediately corrected.
E) The entropy established by “pulling apart” anything requires energy. Where did the extra energy come from?
F) If you look at the time issue, the front and rear have become out of sync even though always in the same reference frame.

G) You seem to be missing the point. There is a body either out or under accelerating the force being applied to it. This breaks two ontological principles;
a) SS+ST=SR (SameState + SameTreatment => SameResult).
– The front and rear of the car are at all times in the same state and being treated equally, yet differ in result.
b) definition of “force” requires only the amount of acceleration accomplished.
– how is an acceleration accomplished if not by the applied force? Where did the extra energy come from or go to?

In short, it is breaking not only the principle of causality, but also the definitions of its own ontology.
It is a “broken ontology”.
Show us some general equations that account for all of that (with example calculations).

So it is not entirely like Bell’s breaking string. This “string” has no means to break, and doesn’t. So how is the result explained?