Recently I came to the realisation that the “block universe” interpretation (i.e., Minkowski spacetime, whereby space and time are fused together), is a situation that arises from length contraction being interpreted as a “length compression” experience, which means that the observer who is experiencing length contraction, effectively becomes stretched.
I’m proposing that “length skipping” (combined with a limited absorption rate) (i.e., missing out spatial grid positions) is the correct metaphysical interpretation of length contraction... In contrast to this proposal, I’ve written about the block universe here: “Special Relativity – Causal Time Paths”
Jump down this page to visit: “Spatial Grid Resolution – Special Relativity Interpretation”
Caution: although time dilation and length contraction are experienced by massive bodies in relation to lightspeed being constant, they do not conversely explain the constancy of lightspeed, even though (mathematically) the light clock derivation method does of course derive gamma correctly... see explanation below the video.
If a body is only travelling slightly faster relative to another body, then the path that the light travels along (as illustrated in the “Lorentz gamma” video below) is only very slightly leaning over – which means that the light only has to travel a tiny bit further.
Incidentally: one way to consider why gamma is such a small value at relatively low speeds, is not simply because such relatively low speeds are only a miniscule percentage of lightspeed – that would still be linear...
Instead, consider the light clock demonstration in the “Lorentz gamma” video below – the percentage increase in length of the hypotenuse relative to the vertical leg of the triangle, increases exponentially as the horizontal leg of the triangle increases, i.e., a faster travelling body is represented by a longer horizontal leg of the triangle.
Via the light clock method, if nothing changes metaphysically, then the women travelling in the railroad car will experience the light as travelling too slow...
Note: the video shows the women’s clock slowing down slightly as a way of compensating for her seeing the light travel along a shorter path...
Also refer to “The Experience of Light Itself – Length Contracted?” further down.
Lorentz Gamma – Presented by: Dr. Don Lincoln
Limitations: although gamma is derived based on the fact that light travels at a constant speed, neither time dilation nor length contraction can explain (via spacetime) why lightspeed is experienced as being constant in all situations.
Point 1) the observer concludes that the clock in the railroad car is ticking slower, based on (evident from the observer's choice of the Pythagorean theorem) the women travelling in the car seeing the light travel along a shorter (i.e., vertical) path than they themselves see the light travel along, i.e., zig-zagged...
Point 2) therefore, the observer must conclude that the clock in the railroad car will tick at the same speed as their own clock if the women can see the same path as they see.
Point 3) therefore, if the observer is once again, at rest, but this time watching the railroad car travelling directly away from them into the distance, they must conclude that the women’s clock is ticking at the same speed as their own clock – but the observer’s conclusion in this case is incorrect, i.e., the women’s clock will still be ticking slower... just as it will be if the railroad car is travelling directly towards the observer.
If the women had multiple sensors along the zig-zagged path that the light travels along, she would realise that the light is not actually travelling vertically...
Therefore, in reality, the women will see the light travelling along the zig-zagged path, which averages out to be a straight-line, and therefore is equivalent to the light travelling in the same direction as the railroad car... but slower than lightspeed – therefore the light clock example is equivalent to list item 3 further down, whereby the Doppler effect incorrectly amounts to 0%.
Although the Pythagorean theorem can be used to derive gamma, it can lead to a misconception – whereby it is incorrectly assumed that light rays themselves are experienced as being length contracted by travelling observers, which is incorrect via spacetime logic.
The light clock method is a very neat trick!
Via spacetime logic, the experience of light itself is not affected by time dilation and length contraction, i.e., light is a phenomenon that exists outside of spatial (and therefore time) existence... albeit light does physically interact with spatial existence.
Although time dilation and length contraction are experienced by massive bodies in relation to lightspeed being constant, those two effects do not conversely explain the constancy of lightspeed... neither do they explain the relativistic Doppler effect.
Imagine the waveforms of some light rays that are continuously being generated, extending from the source, which is at rest, and already having travelled beyond your own position. You see the light rays extending from the source, passing by yourself, and continuing to extend into the distance...
Consider an observer travelling through space relative to the light rays. How would time dilation and length contraction need to affect the observer's experience of the light rays, in order to keep lightspeed constant? ...
Travelling at 90 degrees to the intercepted (i.e., measured) point along the light rays – neither effect is required.
Travelling directly towards the light – purely (100%, not gamma) length contraction is required – Doppler effect 100%, as expected based on zero time dilation.
Travelling directly away from the light – purely (100%, not gamma) time dilation is required – Doppler effect 0%, as expected based on zero length contraction.
Note 1) for light... all three of the above effects effectively occur via spacetime logic, i.e., light's existence exists outside of our spatial experience of the light – light is free (supposedly) from the restrictions of spatial and temporal physical existence...
Note 2) for massive bodies that experience other massive bodies, time dilation and length contraction (via the aspect that is caused by the absolute speed of the co-moving observer relative to the CMB) occur together, which means that they cancel out, i.e., it is never purely one or the other or any of the varying ratios in-between – this cancelling out preserves this aspect of their relative velocities to one another...
The other aspect of length contraction and velocity, is the effect that the non-comoving observer's absolute speed (relative to the CMB) is responsible for, which is also preserved of course, i.e., the co-moving observer experiences the non-comoving observer to be further length contracted due to the velocity of the non-comoving observer...
The overall absolute velocity does increase, but the increase in the relative velocity that each body experiences of the other, is diluted by the fact that they are effectively skipping (i.e., not metaphysically absorbing) more spatial grid positions of each other's physical existence...
A 3rd observer that is at rest relative to where the other two observers will pass by each other, will themselves experience each of the two observers to be less length contracted than they do of each other, because the amount of absorption skipping that occurs between the 3rd observer and each of the other two observers is relatively lower, i.e., less skipped.
The symmetry in the above logic... is that any observer can count as being either the co-moving observer or the non-comoving observer.
Note 3) via this “spatial grid resolution” interpretation of special relativity that I am proposing here, the relativistic Doppler effect can be analysed properly.
How is the Lorentz factor derived? – Link to post by: Unnikrishnan Menon – as derived from the point of view of looking at the spacetime diagram.
Below is a summary of the above linked derivation...
x′ = γ(x − vt) -- Galilean relative distance transformations (with the addition of the unknown “Gamma” scaling factor).
x = γ(x′ + vt′)
xx′ = γ2(x − vt)(x′ + vt′) -- Multiplying the distance transformations together so that gamma belongs to only one equation.
xx′ = γ2(xx′ + xvt′ − vtx′ − v2tt′) -- Multiplication expanded.
tan(45) = (ct / x) = (ct′ / x′) -- Each observer's (time / distance) relationship relative to light being at 45 degrees via the spacetime diagram.
⟹ x = ct... and... x′ = ct′ ... tan(45) = 1 -- therefore, by transposing they become equal to each other.
xx′ = γ2(xx′ + xvt′ − vtx′ − v2tt′)
⟹ ctct′ = γ2(ctct′ + ctvt′ − vtct′ − v2tt′) -- Now substituting in the transposed values ct and ct′ from above.
c2tt′ = γ2(c2tt′ + ctvt′ − ctvt′ − v2tt′) -- And then the algebra continues from here to solve for gamma.
c2tt′ = γ2(c2tt′ − v2tt′)
c2 = γ2(c2 − v2)
⟹ γ2 = c2 / (c2 − v2) -- Dividing the numerator and the denominator by c2 results in...
γ2 = 1 / (1 − (v2 / c2)) -- Where v = relative velocity.
γ = 1 / √ 1 − (v2 / c2) -- Lorentz Gamma.
Lightspeed through a vacuum is the speed limit of the universe, but lightspeed is not an absolute constant ... light knows that spatial existence exists...
All forms of massless energy travel through the vacuum of space at constant 186,282 miles per second.
The constancy of lightspeed varies depending on the medium.
All physical phenomena are experienced as being length contracted by physical bodies that are not at rest relative to that body (or space itself), i.e., physical matter and all forms of massless energy are experienced as being length contracted, via sampling at an otherwise constant sample rate, but which becomes reduced by skipping spatial grid positions.
When a receiving body heads towards the source of some sound waves, the relative (i.e., closing gap) speed is equal to... (the speed of the sound waves + the speed at which the body approaches the source).
Also, sound waves travelling through a given medium are able to travel faster or slower relative to the observer because the medium itself is able to travel... but so does space travel via expansion, e.g., regions of space are thought to be accelerating away from us faster than light, and therefore the light can never reach us.
However, one fundamental difference is that for light, when an observer travels towards or away from the source, light still measures to be travelling at lightspeed (not faster or slower), although the measured frequency does change accordingly.
Physical bodies do not experience light itself to be length contracted via spacetime, simply because length contraction is the experience of space (other than your own proper-space) being “compressed”, and therefore because light does not occupy spatial positions, physical bodies cannot experience light to be length contracted.
Light does not have a ticking clock of its own (i.e., experience time), but neither does it occupy spatial grid positions, as stated above. Therefore, light does not own a speed of its own... light effectively skates in the gaps of a “Rubik’s Cube” (metaphorically speaking) and is also free from logical criticism it seems...
In other words, you cannot truly apply the existence of velocity to something that has zero (i.e., 0) length, i.e., no spatial existence of its own. Therefore, what we measure to exist as massless energy travelling at lightspeed exists as a fundamentally different type of metaphysical interaction.
For more details about the universe’s universal clock ticking process... see: “Spatial Grid Resolution – Special Relativity Interpretation” further down.
Via this spatial grid resolution interpretation of special relativity theory... all physical existence occupies spatial grid positions – including light.
Note 1: physical matter and all forms of massless energy participate in the universal sample rate absorption process, which is possibly 1 Planck unit of spatial existence per 1 Planck unit of time.
Note 2: the minimum amount of time that can be acknowledged as having past from the point of view of there existing only one single massive particle in the entire universe, cannot be quantified unless measured against some other metaphysical phenomenon, such as the gravity ripples that the particle produces which travel through space – a type of self-referencing time-like (restricting) phenomenon.
Related category: Zeno of Elea – Presented by: Professor Angie Hobbs – includes “Movement Logic of a Single Entity”.
Note: physical matter samples massless energy at the universal sample rate... but that otherwise constant rate becomes reduced via gamma.
Light is experienced by physical bodies as actually being length contracted... via this constant sample rate absorption process – resulting in a constant lightspeed experience.
Photons are free to occupy spatial existence either as particles or waves.
Stepping towards an oncoming waveform of light at a constant sample rate results in a shorter wavelength experience.
Stepping away from an oncoming waveform of light at a constant sample rate results in a longer wavelength experience.
A given waveform's absolute rest wavelength is experienced when the receiving body and the source are both at rest relative to the CMB, in which case 50% (hypothetically) of the waveform's photons are absorbed by the receiver.
A waveform's neutral wavelength is experienced to be the same as its rest wavelength (i.e., source and receiver are at rest relative to each other), but the number of photons that are emitted and absorbed by the two bodies depends on the speed of both bodies relative to the CMB... related to “Light Source Tied to Receiver” further down.
For example, as a body travels towards the source of an oncoming waveform, every subsequent photon that is sampled resides at a steeper position along the waveform – the result is a shorter wavelength... less than 50% of the photons are being absorbed...
Likewise, the opposite happens when a body travels away from the source, i.e., every subsequent photon that is sampled resides at a shallower position along the waveform – the result is a longer wavelength... more than 50% of the photons are being absorbed.
Every increment in Planck units that is traversed by a physical body involves both translational and rotational change in position of the body’s own particles...
The rotational aspect represents a given body's proper time. Therefore, a slower rotation occurs via gamma relative to the CMB as a given body travels increasingly faster through space – fewer photons are generated because the body's proper time is ticking slower.
For a more detailed analysis of the source and the receiving body travelling relative to each other – see “Relativistic Doppler Effect...” further down.
Note: physical matter samples mass-type energy at 100% ... i.e., it effectively (i.e., positionally) increases with velocity, because faster speeds mean more spatial grid positions are traversed per unit of time, and therefore it is this otherwise consistent rate of increase that reduces via gamma...
Practically however, physical bodies sample other physical bodies at the same rate as light is sampled, i.e., at the one and only sample rate that exists... but which reduces via gamma, and therefore for relatively slower velocities, spatial grid positions are sampled multiple times before the next grid alignment occurs.
Refer to “Skipping Spatial Grid Positions – Arbitrary Example” further down to see a visual representation.
When an observer travels away from a light source, consider that gamma’s effect is caused by... γ = 1 / √ 1 − (v2 / c2) -- Lorentz Gamma.
γ = 1 / √ 1 − (0.012 / 12) = 1.00005 ..... γ = 1 / √ 1 − (0.32 / 12) = 1.048 ..... γ = 1 / √ 1 − (0.72 / 12) = 1.40 ..... γ = 1 / √ 1 − (0.92 / 12) = 2.29
Even when travelling at 1,862 miles per second (1% (0.01) lightspeed), time dilation only slows time down by: 1 / 1.00005 = 0.99995 (99.995%) normal speed... why? ...
One answer might be that the distance shortfall that time needs to compensate for to maintain a lightspeed experience from the observer’s perspective is minuscule – therefore even just the tiniest minuscule amount of time dilation gives lightspeed plenty of time to travel the distance shortfall...
But then again consider 50% lightspeed travel whereby time ticks at 86.6% normal speed – after any given period of time... light has only travelled half the distance required to maintain a lightspeed experience... the observer’s own clock would need to be ticking at 50% (not 86.6%) the normal rate, because only half the length of the light rays has travelled passed them.
Hence, as stated previously, neither time dilation nor length contraction conversely explain the constancy of lightspeed.
Gamma exists as a variable sample rate which combines translational (travelling) and rotational (proper time) into one positional-type process.
The constancy of lightspeed has already been explained further up... see “Light vs Matter – Sample Rate Types (Spatial Grid)”.
Unlike spacetime... the constancy of lightspeed is not thought of as being directly responsible for time dilation and length contraction.
Refer to “Skipping Spatial Grid Positions – Arbitrary Example” further down.
Lorentz Doppler Shifts – Frequency Symmetry.
The equation below applies to when the observer and the source are travelling away from each other. It shows that for a given frequency... as emitted (measured; experienced) at the source (fem) ... the change in wavelength as experienced by the receiving body is only dependent on the speed of the source relative to the receiver, i.e., it does not matter how much either body is travelling relative to the CMB...
frec = fem√(C − V) / (C + V)
However, alternative insights seem to suggest otherwise, such as described in the following article...
W.W. Engelhardt – JET, Max-Planck-Institut für Plasmaphysik (retired) ... “Apeiron, Vol. 10, No. 4, October 2003 – Relativistic Doppler Effect and the Principle of Relativity”
Quote: Abstract – The frequency shifts predicted by the ‘relativistic’ Doppler effect are derived in the photon picture of light. It turns out that, in general, the results do not depend exclusively on the relative velocity between observer and light source. In this respect, the relativistic Doppler effect is not distinct from the classical one, where the shifts are also different depending on whether the source or the observer moves. The ‘relativistic’ formulae for these two cases have been confirmed by experiment and are described in many text-books. It was, however, not recognized that they are at variance with Einstein’s relativity principle extended to electromagnetic waves.
Consider for example scenarios 1 and 3 below... scenario 1 results in a different wavelength to scenario 3
The following 4 example scenarios are based on the source and the observer both being at rest relative to the CMB, unless stated otherwise. The scenarios are described as experienced from the observer’s perspective. The non-relativistic Doppler effect and the relativistic Doppler effect aspects are both considered independently from each other.
The following illustration shows the wavelengths that are experienced by a receiving body at rest... for (a) when the source is at rest... (b) a moving source but ignoring time dilation... and (c) a moving source including time dilation.
Each dash represents 1 quantity of photons. The constant sample rate is represented by the sets of 4 arrows all being equally spaced. The green waveform consists of more light energy than the amber and red waveforms, for any given time period.
A constant sample rate via the same proper time interval results in a constant lightspeed experience, with either steeper or shallower sample positions along the waveform, depending on the relative velocity.
The above illustration represents “Scenario 1” below... whereby the light’s waveform is stretched by relative velocity and time dilation.
The source is travelling:
If the source is travelling relative to the CMB, then its clock will be ticking slower, and therefore the rate at which it emits light will be slower, i.e., each photon of the waveform will be generated after a longer period of time than if the source was at rest – the waveforms as emitted in all directions will therefore appear more stretched than otherwise (i.e., larger wavelength)
Source sees – the observer is ticking faster.
Observer sees – the source is ticking slower.
Scenario 1: source travelling away from the observer... the waveforms will be stretched by the non-relativistic Doppler effect (+) further stretched by the relativistic Doppler effect.
Scenario 2: source travelling towards the observer... the waveforms will be compressed by the non-relativistic Doppler effect (+) stretched by the relativistic Doppler effect...
The observer is travelling:
Likewise, if the observer is travelling relative to the CMB, then their clock will be ticking slower, and therefore they will acknowledge each photon later than if they were at rest, which means that more of the waveform will have passed by them for each photon that they experience, and therefore the waveforms will appear more compressed than otherwise (i.e., shorter wavelength) ...
Observer sees – the source is ticking faster.
Source sees – the observer is ticking slower.
Scenario 3: observer travelling away from the source... the waveforms will be stretched by the non-relativistic Doppler effect (+) compressed by the relativistic Doppler effect.
Scenario 4: observer travelling towards the source... the waveforms will be compressed by the non-relativistic Doppler effect (+) further compressed by the relativistic Doppler effect.
Conclusion: when considering scenarios 1 and 3 for example, the asymmetry arises because sampling either side of zero on the graph of any waveform, means that a slower ticking receiver absorbs greater (+/-) values of the waveform during any given period of proper time, i.e., compressed by the relativistic Doppler effect as in scenario 3 above.
For example, consider the source to be travelling 10% lightspeed faster than the receiver in the same direction, i.e., the receiver starts off at rest (0% relative to the CMB), and then both the source and the receiver travel increasingly faster, approaching lightspeed... (10%, 20%) ... (20%, 30%) ... (30%, 40%), etc...
Considering the relativistic Doppler effect once again: frec = fem√(C − V) / (C + V)
According to the above equation, if the relative velocity remains constant, it should not make any difference to the frequency that is experienced by the receiver...
However, due to gamma being non-linear, especially when exceeding exceed 50% lightspeed (i.e., gamma’s curve becomes rapidly steeper), then if the source is emitting photons at a rate that is directly dependent on its own clock ticks... the asymmetry as described above (see: “Light Absorption When Considered as Waveforms”) will be different accordingly...
For example, consider the difference in values for gamma at: 0.3 to 0.4 vs... 0.8 to 0.9 along the curve...
Smaller relative difference: 1.091 - 1.048 = 0.043
Larger relative difference: 2.294 - 1.667 = 0.627
Although the relative velocity is 10% lightspeed in both cases – the difference in clock ticking speed is greater, i.e., relatively fewer photons are emitted by the source at 90% lightspeed compared to 40% lightspeed, which means that the receiver will experience an overall increase in red shifting because relatively fewer photons are emitted by the source... slightly lessened by its own relatively smaller amount of time dilation which causes blue shifting.
Similarly, when the receiver shines light back at the source, the source will experience an overall increase in blue shifting because of its relatively greater amount of time dilation... slightly lessened by the relatively fewer photons emitted by the receiver.
In other words, the frequency received by the receiver or the source as either body shines light at the other, changes as the source and the receiver travel equally faster relative to the CMB.
Speed is defined as: distance travelled / time past.
Time is defined as any massive particle’s change in spatial position relative to all other massive particles.
Therefore, conceivably, the greatest speed possible via change in spatial position is to skip from one side of the universe to the other in 1 universal increment of the universe's master clock – and that means there exists a maximum possible speed – the same speed as the 1 universal increment involved via instantaneous quantum entanglement.
But the speed of light (which is also the upper speed limit for physical matter) is nowhere near that fast...
Transitioning along spatial grid positions is to practically transfer energy out (pop out) of spatial existence, and then back into existence (because infinitesimal size increments do not exist). The greater the number of spatial positions traversed (relative to the CMB) in a given period of time, the greater amount of energy is involved (even though the energy is preserved), which is why relativistic mass (total energy) increases with speed via gamma...
If more energy were not involved in travelling faster, the laws of physics would have no mechanism for governing speed control, i.e., things could accelerate indefinitely without restriction.
Finally: light skates (metaphorically speaking) on the threshold of spatial existence; available for immediate physical interaction with physical matter. Therefore, light itself must be putting its feelers out so to speak – so it makes sense that even light-skating has a speed limit – turn on a torch for example... without a speed limit, the light energy would instantaneously become available for physical interaction at the far edges of our finite universe...
In other words: metaphorically speaking light’s “feelers” would snap off.
Length contraction and time dilation exist as part of the same... spatial grid skipping, absorption sampling process...
In other words, as any given body pops in and out of spatial existence, it reflects the following...
Proper time... via the number of times that a physical body has occupied spatial grid positions.
Length acknowledgement (contraction) ... via the number of times a physical body experiences (subject to limited absorption) a unique spatial grid alignment with another body.
Velocity relative to the CMB... travelling faster is to traverse through more spatial grid positions per given number of universal clock ticks. The rate of skipping positions increases with speed via gamma.
Note: continue down the page to “Skipping Spatial Grid Positions...” for an arbitrary example.
The past and the future do not exist, i.e., only the present exists. Therefore, existing in someone else’s past and future and travelling at different angles through time, does not happen, and therefore it does not play a part in the concept of simultaneity, i.e., simultaneity in this sense does not exist... it cannot exist – there exists only the present, and therefore the so-called “now slice” is the same for everyone.
Minkowski's block universe represents the correct relativistic relational values, but it does not metaphysically exist in reality as a tenseless block universe.
To be completed soon... as of 24-04-2021
As a point of interest, simply to help get a feel for relative relationships in general... consider the non-relativistic (but still relative) linear relationship of the following speed-bar for a maximum total speed experience... followed by relativity's “velocity addition formula”.
The following diagram shows the values that are used in example 1 below...
S = Observers own absolute speed relative to being at rest.
R = Remaining absolute speed possible until the speed limit is reached.
E = Extra speed calculated from the combined effect of both absolute speeds.
T = Total relative speed experienced.
E1 = (S2 / (R2 + S2)) × R1 ... T1 = S1 + E1
E2 = (S1 / (R1 + S1)) × R2 ... T2 = S2 + E2
The following two examples are based on a maximum speed of 10:
Example 1:
[S1 = 4... R1 = 10 – 4 = 6]
[S2 = 7... R2 = 10 – 7 = 3]
E1 = (7 / 10) × 6 = 4.2 ... T1 = 4 + 4.2 = 8.20
E2 = (4 / 10) × 3 = 1.2 ... T2 = 7 + 1.2 = 8.20
Example 2:
[S1 = 8... R1 = 10 – 8 = 2]
[S2 = 9... R2 = 10 – 9 = 1]
E1 = (9 / 10) × 2 = 1.8 ... T1 = 8 + 1.8 = 9.80
E2 = (8 / 10) × 1 = 0.8 ... T2 = 9 + 0.8 = 9.80
The above Examples via relativity's “velocity addition formula”... u' = (u+v) / (1+uv / c^2)
Example 1: E = 11 / (1 + (28 / 100)) = 11 / 1.28 = 8.594
Example 2: E = 17 / (1 + (72 / 100)) = 17 / 1.72 = 9.884
The above comparison provides a basic insight into how linear non-relativistic values compare to non-linear relativistic values – the difference in the results between the two methods becomes increasingly less as an observer approaches the maximum value.
An arbitrary example: 100 universal (i.e., universe) clock ticks...
Note: the following example does not use Lorentz transformations. Lorentz transformations are mentioned near the beginning of the “special relativity (block universe)” category, which also includes analysis about what it means for all time to pre-exist.
Slower body travels 3 positions per 10 (of which ≈ 95% are sampled) universe clock ticks...
Travel rate = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 -- (note: only the sampled positions are occupied)
Absolute speed = 30 / 100 = 0.3 -- (maximum 1.0, relative to CMB)
Gamma, slower body to CMB... γ = 1 / √ 1 − (0.32 / c2) = 1.0483 (also... 1 / 0.9539)
Total unique grid positions sampled = 30 / gamma = 28.618
Total grid positions skipped = 30 − 28.618 = 1.382
Average distance travelled per clock tick participation = 30 / 28.618 = 1.0483
Average distance skipped per clock tick participation = 1.382 / 28.618 = 0.0483 (also... gamma - 1)
Universe clock ticks to travel ratio = 100 / 30 = 3.333
Number of times occupying a grid position = 3 * 28.618 = 85.85 (3 is from rounding down 3.333)
Particle positional rotation = 1 per clock tick participation = 1.111 per occupied position = 3.333 per unique position.
Total universe clock ticks skipped percentage = 3.333 * 1.382 = 4.61%
Total universe clock ticks sampled percentage = 100 − 4.61 = 95.39%
Travel distance to skipped universe clock ticks ratio = 30 / 4.61 = 6.51
Accumulative position = 0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, 3.0, 3.3, 3.6, 3.9, etc.
Plotted target value = (26 / 28.618) * 30 = 27.26 (the following 26 samples are plotted in the spatial grid distribution diagram below)
Unique grid positions sampled = 0 to 21 ... 23 to 26 = 26 (target value adjustment = 1 - 1.382 = -0.382) ... 27.26 - 0.382 = 26.89
Faster body travels 9 positions per 10 (of which ≈ 43% are sampled) universe clock ticks...
Travel rate = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90 -- (note: only the sampled positions are occupied)
Absolute speed = 90 / 100 = 0.9 -- (maximum 1.0, relative to CMB)
Gamma, faster body to CMB... γ = 1 / √ 1 − (0.92 / c2) = 2.2942 (also... 1 / 0.4359)
Total unique grid positions sampled = 90 / gamma = 39.23
Total grid positions skipped = 90 − 39.23 = 50.77
Average distance travelled per clock tick participation = 90 / 39.23 = 2.2942
Average distance skipped per clock tick participation = 50.77 / 39.23 = 1.2942 (also... gamma - 1)
Universe clock ticks to travel ratio = 100 / 90 = 1.111
Number of times occupying a grid position = 1 * 39.23 = 39.23 (1 is from rounding down 1.111)
Particle positional rotation = 1 per clock tick participation = 1.111 per unique position.
Total universe clock ticks skipped percentage = 1.111 * 50.77 = 56.41%
Total universe clock ticks sampled percentage = 100 − 56.41 = 43.59%
Travel distance to skipped universe clock ticks ratio = 90 / 56.41 = 1.60
Accumulative position = 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9.0, 9.9, 10.8, 11.7, etc.
Plotted target value = (12 / 39.23) * 90 = 27.53 (the following 12 samples are plotted in the spatial grid distribution diagram below)
Unique grid positions sampled = 0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 25, 27 = 12
Further details to be added soon... as of 24-05-2021
Relativistic results...
Each ship’s relative speed towards the other from: u' = (u−v / (1−uv / c^2)
u−v = 0.3 − −0.9 = 1.2
uv = 0.3 * −0.9 = −0.27
Relative velocity = 1.2 / (1 − (−0.27 / 1) = 1.2 / 1.27 = 94.488% lightspeed...
Gamma, observer to observer... γ = 1 / √ 1 − (0.944882 / c2) = 3.0542
Time dilation for slower body = 1 / 1.0483 = ticking at 95.39% rest speed.
Time dilation for faster body = 1 / 2.2942 = ticking at 43.59% rest speed.
Relative length contraction = 1 / 3.0542 = 32.74% length experience of each other's proper length.
Both ships age at the same rate... which is slower than Earth’s clock ticks as it rests relative to the CMB.
Their absolute velocity relative to the CMB is 75% lightspeed... which exists via occupying and skipping spatial grid positions – every grid position occupied (i.e., potential interaction) is an acknowledgement of spatial existence, and is also an increment in their own (proper) time.
Their velocity relative to each other is 96% lightspeed. Their own clocks are simply ticking at the same speed as they were when considering how their velocity relative to the Earth physically exists... so what is it that’s different? ...
Answer: by experiencing the same speed (proper time) relative to the Earth, but by also experiencing a greater value of spatial grid skipping-type length contraction relative to the other ship, a compromised otherwise absolute closing speed is experienced...
It takes the same amount of proper time for the ships to pass by each other at Earth... but each ship experiences (samples) less physical existence of the other ship's physical existence – as one ship approaches at twice the absolute position (i.e., closing distance) relative to the Earth... then per skip, the other ship also skips by head-on.
Consider a planet that is stationary relative to the CMB, and imagine two spaceships that are many light-seconds away from the planet – one ship is facing one side of the planet and the other is facing the opposite side, i.e., they are flying through space heading directly towards each other, with the planet in-between them – each ship is travelling at 75% lightspeed relative to the planet...
Each ship’s relative speed towards the other from: u' = (u-v / (1-uv / c^2)
Speed = 1.5 / (1 - (-0.5625 / 1) = 1.5 / 1.5625 = 96% lightspeed...
From either ship’s perspective, it is the other ship and the planet that are moving – each ship sees the other ship fly by the planet at the same time as the planet passes by themselves.
The reason why both ships only experience an extra 21% (96% – 75%) lightspeed relative to each other, compared to their speed relative to the planet, is because both ships are travelling along a steeper path through spacetime, compared to the planet which is at rest relative to the CMB – both ships also experience each other to be length contracted to a greater degree than they experience the planet and empty space to be contracted, hence... only 21% extra relative speed increase.
Note: if the spaceships were not being displaced into the future, then due to “compression-type” length contraction, the relativistic differences experienced in speed and distance would be physically contradictory, i.e., both ships would experience two different speeds simultaneously purely in the same time slice – they would be travelling at 75% lightspeed through the exact same space at the exact same moments in time as they are travelling at 96% lightspeed, which would be paradoxical...
However, if the ships are displaced into the future, then the contradiction disappears, i.e., the distance & time relationship of the ships relative to the planet is different to the distance & time relationship of the ships relative to each other, i.e., relativistic speeds in this sense metaphysically exist as the block universe – the block universe is absolutely 100% necessary for “compression-type” length contraction. The spacetime relationships of the ships and the planet can only make sense if the future pre-exists – and if the future pre-exists, the past must also pre-exist.
This section is now a little outdated, as of 23-05-2021 ... will be updated soon.
3D Computer graphics works by multiplying various matrices together per number of physics cycles, e.g., a mesh of vertices being variably rotated and translated per variable number of physics cycles, is equivalent to: proper time... travelling through space... and universal (i.e., universe) clock ticks, respectively.
Via the “compression-type” length contraction experience, physical stretching of faster moving bodies corresponds to relatively different angles of their causal paths through time – zero stretching means zero tilting of the causal path, i.e., block slice – if moving bodies don't stretch... then there's no “block universe”.
To retain the effect of length contraction without effectively stretching the comoving observer, a resolution reduced (pixel-skipping) experience can be used instead. The universe's spatial grid is finite – when grid positions are experienced, regardless of how many have been skipped, the metaphysical experience of each position is such that there are two conceivable possibilities:
Each spatial grid position butts up against the next – i.e., there are no gaps.
Each spatial grid position is metaphysically experienced as being stretched.
Length is simply reduced by omitting every 2nd, 3rd, 4th, etc., quantum (or pixel) of spatial existence from the observer’s metaphysical experience of reality.
Physical existence of a spaceship for example, is equivalent to having a normal resolution ship, but which is layered on top of a variable resolution of everything else that exists – in comparison to computer graphics, the ship simply remains the same size on screen, but it is sitting on top of an increasingly lower resolution background (i.e., universe) as its speed increases relative to the CMB (i.e., background) ... or relative to any other physical bodies that are moving through space.
Although there’s no doubt that spacetime diagrams illustrate the correct relational relativistic values... length contraction is not limited to only one plausible metaphysical interpretation.
Time dilation, length contraction, and relativistic mass (total energy) all still exist, regardless of how length contraction is interpreted metaphysically.
Consider length contraction to be experienced as pixel skipping... instead of pixel squashing (i.e., length compression) ...
If the remaining pixels of the resolution-reduced spatial grid are experienced as being stretch (option 2 further up), then the overall size (outside dimensions) of the universe is experienced as being its normal size, i.e., full size; unchanged...
However, this “spatial grid resolution” interpretation is aimed at option 1 above.
Via compression-type length contraction – lightspeed travel means that 0% length resolution is experienced; but near-lightspeed travel still means that 100% length resolution is experienced – but this spatial grid resolution interpretation utilises a variable (finite) resolution experience...
Consider a spaceship travelling through space at near-lightspeed... a huge percentage of the ship’s length does not causally correspond (effectively exist) from the perspective of any observers that are travelling at typical speeds, i.e., equivalent to the resolution of some computer graphics being lowered, resulting in loss of information... but in this case – loss of interacting causal detail.
Note: the remaining resolution has increased relativistic mass (total energy) accordingly.
From the perspective of any typical observers that are watching a near-lightspeed spaceship travel past, the corresponding causal connection to the ship is nothing more than a 99.9999...% reduction in the physical existence of the ship...
Likewise, from the perspective of the spaceship, the corresponding physical connection to any typical observers is also virtually non-existent.
This spatial grid resolution interpretation means:
Any spaceship travelling at near-lightspeed... does not span across all (virtually) of time... and it does not span the full length of the entire universe.
The ship effectively travels less distance (length contraction) because the physical interaction between the ship and the universe is resolution-reduced, e.g., the ship only experiences (absorbs; samples) a fraction of the universe’s spatial grid, i.e., pixel-skipping.
From the perspective of an observer that is measuring the length of a body travelling relatively close to lightspeed, the measured numerical values would reveal a significant contraction – because any physical information detected would only becoming from the resolution-reduced existence, i.e., the grid (or pixel) alignment is less than a 1 to 1 correspondence as any two objects skip by each other.
“The Richness of Time” – Featuring: Brian Greene, Dean Buonomano, Lera Boroditsky
See: 41:20 to 50:35 – Dean Buonomano explains how the brain has evolved to survive in a world governed by the laws of physics – the domain in which we experience the very nature of time in our everyday lives.
At: 45:03 to 45:18 – quote: “...obviously we know that absolute present doesn't exist because that's been well tested; we know clocks change at different speeds – but that doesn't really say that the present is not fundamentally different from the past or future.”
He also points out that the human brain incorporates various different types of biological clocks, and that “time” (as experienced consciously) seems to play an important role in the evolution of animal life in terms of decision making and planning for the future.
Imagine the various biological clocks that have evolved in human brains as described by Buonomano in the above video, and consider...
A brain stores the information that a seed has been planted.
The brain also records that the seed grows to become a tree which bears fruit.
Some form of a brain-clock evolves, such that it corresponds to the seed developing to become the tree – this helps with all such future decision-making that relates to where and when to plant seeds, and also provides a time-judgement type mechanism for when to harvest the ripened fruit.
Now consider the past, present, and future, all pre-existing in the form of a tenseless block universe, i.e., time exists as solidified causality – all time exists as one single causal instant which obeys the laws of physics – each distinctive individual causal state of existence (slice of the block) effectively resides in a separate dimension of a multi-dimensional spacetime-type reality.
Evolution still has to make sense within this solidified (tenseless) block which incorporates all of causality.
Why would such brain-clocks (or equivalent mechanisms) have evolved if all time pre-exists (is predetermined)?
Ultimately, the brain-clocks question is related to “free will” acting on subjective conscious experiences – sound, colour, touch, smell, taste... time passing, and other conscious types of awareness.
If free will does not exist, then consciousness is just “along for the ride” – it would mean that all of the data received by the senses is used directly by the brain for every single aspect of our behaviour, without ever being influenced by our conscious experiences.
In other words, without “free will” existing to act on conscious experiences... all aspects of behaviour are just consciousness-independent systems acting directly on sensory data and stored information.
If subjective conscious experiences are involved in animal behaviour – then truly free will does exist, even though it cannot have a logical description.
Infinity infers that spatial existence is infinitely divisible (infinitesimal), and therefore the concept of spacetime incorporates the idea of compression-type “length contraction” as opposed to “length absorption rate” (spatial grid skipping), i.e., you cannot skip to another position if the position itself is infinitely divisible... because that would be to effectively skip to arrive at an infinite number of other positions... that are all connected to one another.
Length compression inevitably leads to the block universe interpretation, because the experience of two physically different lengths of the same physical body cannot exist along the same time slice of existence – that would be a physical contradiction.
Simultaneity exists via compression-type “length contraction” – simultaneity via experiencing non-comoving bodies to be length compressed, is a misconception, i.e., simultaneity whereby a given body’s present moment in time, actually exists in the past or future of another body that is travelling at a different speed.
Bodies do not effectively stretch across the entire universe at near lightspeed travel, spanning from the beginning of time to the end of time. Instead, bodies skip spatial grid positions at the rate of near-lightspeed travel... that is all.
Time is not fused together with space.
Time and travelling through space exist as one and the same positional-type mechanism... accompanied by the laws of physics.
Only the present exists. The past and the future do not exist...
Travelling at different speeds through space does not tilt a body’s “time causal path” through a supposedly pre-existing, static (tenseless) existence, i.e., there is only 1 “now slice”, and it is called the present.
Lee Smolin considers the possibility that general relativity might be considered via space and time existing independently from each other, i.e., not existing as “spacetime”. The concept of time and space being fused together, presents great difficulties for quantum gravity theory.
Consider that maybe a theory of quantum gravity should not try to preserve (i.e., incorporate the existence of) the idea of space and time being fused together... such that all time pre-exists... albeit general relativity has proven to be extremely accurate in the predictions that it makes.
Quotes from: 5:16 to 7:53
Robert Lawrence: “...now let’s bring time into it because...”
Lee Smolin: “...but time is already in it because causality is time...”
Robert: “Now can you keep then space and time? ... is that one unit – Einstein’s so-called block universe where every event had a three-dimensional location, and a location in time – so a four-dimensional piece, so you can see the whole history of the universe from beginning to end, supposedly, in this four-dimensional block universe where time is a coordinate?”
Lee: “...from the point of general relativity, classical general relativity, you can have it both ways. You can think of this block universe picture which you mentioned, and you can get away with that, to a certain extent.
When you bring in other questions about how quantum mechanics fits into the whole picture; about how thermodynamics fits into the whole picture, and entropy – I think it gets harder to maintain this block universe picture, and for me this is one of the profound issues...”
Mixed: “...differentiated from space? ... “yes” ... “so you are, teasing apart space and time?”
Mixed: “Because in quantum gravity” ... “sounds quite radical” ... “sure it is, but it’s also, maybe the most conservative solution to a set of conundrums that we face, when we try to bring together quantum theory and gravity...”
Just a quick update: 19/12/2021... YouTube just suggested this video to me (I still fully intend to continue to update, improve, and add more content to this site in the near future and beyond).
I'll add my thoughts about this, here, in the near future, expressing how soothing it is to hear such remarkable people... Dean, Lee, and Fotini, explaining their own thoughts about time.