Causality as defined by Einstein’s theory of special relativity via “compression-type” length contraction is truly remarkable – the causality (physical) path for any particular physical body during its present moment in time, corresponds to both past and future events as experienced by any other body that is travelling at a different speed to that particular body.
Past events for one observer existing as future events for another observer (and vice versa), infers that all events (physical states) in time already exist, not just the present moment – a reality that is referred to as the “block universe”... also known as the 'B' theory of time, which many physicists advocate.
Visit “Spatial Grid Resolution” interpretation: “Skipping Spatial Grid Sampling” – An alternative to the “Block Universe” interpretation” (the 'A' theory of time triumphs)
Lorentz transformations... x' = γ(x - βct) ... ct' = γ(ct - βx)
Where... x = distance... β = v / c ... v = relative velocity... c = speed of light... ct = time axis converted to metres such that lightspeed is 45 degrees on the spacetime diagram.
Via this Minkowski spacetime block universe interpretation whereby all time pre-exists, the Lorentz transformations that are stated above, calculate the corresponding distance and time values from one observer to the other within the block universe.
For example, spacetime as in accordance with “compression-type” length contraction, asserts that if the primed (denoted by the apostrophe) observer is travelling through space faster than the unprimed observer, then the primed observer will causally correspond (in principle, i.e., there exists a causal connection) to the unprimed observer's pre-existing future...
In other words, it means that the physical status of an event “x” at time “ct” ... is causally connected to the physical status of “x prime” at an earlier time than that same “ct” time... diagrams to be added soon.
“Causal time paths” as used here refers to a traveller’s “block slice”, i.e., a more descriptive alternative.
Basically, an observer’s block slice represents a path through spacetime, and depending on the observer’s absolute speed (i.e., relative to the CMB; there must be a potentially fastest clock speed), the more or less their slice (path) through spacetime becomes tilted.
This variation in speed is often taught as each observer’s speed being relative to every other observer’s speed... because it is...
But thinking that an observer’s clock (B) slows down relative to some observer (A) that “B” has departed from... can be a mistake – although departing is likely to (depending on the direction) result in travelling at a different speed relative to the “CMB”, the change in clock speed could be faster or slower... if for example “A” is travelling at speed +10 relative to the CMB, and “B” departs from “A” at a speed of 7, it could be +7 or -7, which means B’s clock will just as likely run faster than A’s as opposed to slower...
Therefore, examples which make reference to the CMB are much clearer and intuitive to understand – not being taught about the so-called “global rest reference frame” (GRRF) can easily lead to the whole situation seeming nonsensical...
Earth is travelling through space at speed +10 relative to the CMB radiation, direction right.
You’ve departed from home in your family spaceship and are now heading towards your favourite holiday planet at speed +20 relative to Earth, direction right (total speed is now +30) – your own clock is now running slower than Earth’s clock...
Oh dear... you forgot to put your luggage onboard, so you get into the shuttlecraft and head left back to Earth, travelling at a speed -20 relative to your family ship... your clock is now at the same speed as Earth’s clock, but you’re not making any headway...
You step on the gas and speed up to -30 relative to your family ship (total speed is now 0) – your clock is now running as fast as it possibly can... even faster than Earth’s clock... you arrive at Earth, bring the shuttlecraft to a stop, and your clock is now running at the same speed as Earth’s clock once again.
Conclusion: If your own clock only ever slowed down after departing from another body, then when you arrived back on Earth you would exist in slow motion – in fact, even by just walking around for a while on Earth... your own molecules would eventually stop ticking.
First, consider the type of language used to describe the Einsteinian “block universe” (eternalism... as opposed to presentism).
To speak correctly you’re only allowed to use tenseless words or language, in contrast to how we normally speak about time – it can be tricky to not make a mistake...
“Continuing to explain” ... the act of you reading this sentence from start to finish, already existed. Continuing as used here implies time is flowing, but via a block universe all moments already exist. Notice even the words “reading” and “already” seem to imply that time is flowing.
“Yesterday when I was eating my dinner” ... I’m actually eating yesterday’s dinner; every mouthful; every single moment in fact, constantly – each snapshot simply exists, frozen like a photograph.
“Zeno was born before Aristotle” ... neither came into being in such a timely manner – every moment of their existences simply exists, equally real – the so-called past is no less real than the so-called now; the present.
“Recording holiday activities next summer” ... any so-called future activity, such as someone who is going to use their phone to record something, already exists – there is no future yet to come into physical existence.
The following “Twin paradox example” further down is based on the explanation given in the following article: “How does relativity theory resolve the twin paradox?”
As a point of interest – quote from near the end of the above article: “The Doppler effect and relativity together explain this effect mathematically at any instant.”
Another point of interest – note Philip Wood’s answer in the follow post: “Difference between Doppler effect and relativistic Doppler effect?”
Twin paradox example: Using the moment when the ship reaches the planet as the corresponding reference point. A twin sets off from Earth in his spaceship traveling at 75% lightspeed, and heads to another planet 50 light-years away – time and distance are dilated by a factor of 0.661, and acceleration is assumed to be instantaneous...
Apparent time dilation (slower) on the way to the planet:
Earth’s perspective:
50 / 0.75 = 66.67 -- Earth light-years for the spaceship to reach the planet.
50 + 66.67 = 116.67 -- light from the ship that Earth will eventually see that corresponds to when the ship reaches the planet.
66.67 × 0.661 = 44.07 -- spaceship light-years (its clock is ticking slower than Earth’s) for the ship to reach the planet.
44.07 / 116.67 = 0.378 -- Earth sees the ship’s time to be ticking slow, i.e., 37.8% of Earth’s time.
Ship’s perspective:
66.67 - 50 = 16.67 -- light from Earth that the spaceship sees at the instant the ship reaches the planet.
16.67 / 44.07 = 0.378 -- ship sees Earth’s time to be ticking slow, i.e., 37.8% of the ship’s time.
Apparent time dilation (faster) on the way back to Earth:
Earth’s perspective:
66.67 + 66.67 = 133.34 -- total time past on Earth when the ship reaches Earth.
133.34 – 116.67 = 16.67 -- difference between the light that was seen as emitted by the ship when it was at the planet, and when the ship is back at Earth.
44.07 / 16.67 = 2.64 -- Earth sees the ship’s time to be ticking fast, i.e., 264% (1 / 37.8%) of Earth’s time.
Ship’s perspective:
66.67 + 66.67 = 133.34 -- total time past on Earth when the ship reaches Earth.
133.34 – 16.67 = 116.67 -- difference between the light that was seen as emitted by the ship when it was at the planet, and when the ship is back at Earth.
116.67 / 44.07 = 2.64 -- Earth sees the ship’s time to be ticking fast, i.e., 264% (1 / 37.8%) of Earth’s time.
According to Minkowski spacetime (block universe), both the past and the future exist... just as real as the present exists, i.e., all of time and all physical states of existence are effectively just 1 frozen instant... no time! (tenseless)
For example, if you had some garden secateurs with handles many millions of light-years in length, you could prune a tree (in principle) that already exists in your current slice of the block universe, but which has not started to grow in the block slice that corresponds to another person travelling through space at a different speed to which you are travelling.
Realistically however, but excusing the rather long handles, the transfer of movement from atom-to-atom along the handles cannot travel faster than lightspeed, so as you started to squeeze, it would then take “many millions” of years for the blades to close together, by which time the tree would have long perished.
The temporal difference is not the same effect, whereby an object (such as a person) can be considered to have travelled into the future purely because they have aged slower, i.e., the movement of their own particles (time) ran slower (time dilation) because of travelling through space extremely fast – although metaphysically time dilation is part of the process, and therefore does correspond accordingly.
During being in a constant rate of time dilation relative to the slower, non-comoving observer, the comoving observer really does travel forwards into the non-comoving observer’s future... gradually leaving them behind in their slower progressing present.
In a flat universe, the spaceship would still progressively travel into the future to the same extent as in a closed (i.e., kind of spherical) universe, but it would of course be getting further away unless it changed direction and headed back to the planet.
The temporal difference between causal paths is extremely small at relatively short distances, hence the rather long handles in the previous example.
However, traveling close to lightspeed results in significant “length contraction” (see more detailed description further down), i.e., for a fast-moving observer space exists as being shorter along the direction of travel – however this new relatively shorter distance still corresponds to the initial distance, and therefore counts as that much longer measurement with regards to the temporal difference that exists at any particular location along the causal path.
Therefore, if an alien were travelling through flat space in their spaceship at very close to lightspeed, the front-seated passengers could wind down the windows and prune (in principle) all the trees along the way that pre-exist in your distant future (which has now become their present), spanning the entire length of the universe before their ship finally transmogrifies as it approaches spacetime’s outer limits.
“Length contraction” corresponds between comoving (e.g., a person travelling along inside their spaceship) and non-comoving (e.g., a person watching from Earth) observers, such that they experience each other (but not themselves) to be physically shorter – the faster their motion relative to each other’s location (regardless of whether one is stationary in space relative to the CMB), the more they experience each other to be contracted along that same relative (closing) direction of travel.
Even more interesting is how the tree pruning scenario differs when considering a closed (sort of spherical) universe whilst travelling super-fast.
Relativity Paradoxes – Presented by: Matt O'Dowd (PBS Space Time)
The ship is travelling at the speed required to make its own length span once around the entire cosmos (from its perspective) ... remember this is a closed (spherical) universe.
The spacetime diagram changes from a flat 2D representation to become a cylinder, i.e., the distance axis becomes circular.
The front end of the spaceship exists at the same physical location as the rear, but in the rear-end’s future, conveniently avoiding a bumper-to-bumper crash. In principle this would happen because of the relativistic effects that occur when travelling extremely close to lightspeed.
Therefore, the front-seated passengers can once again wind down the windows and start pruning trees, but this time the trees are in the same location in space as the rear-seated passengers (although outside the ship of course) but in their future, and so for them, the trees haven't even started to grow yet.
As described in the tree pruning gardener example further up, it points out the delay whereby the atom-to-atom transfer of movement along the secateurs would take millions of years to travel the great distance.
Interestingly, even though ultra-fast speed causes length contraction, the initial length still counts (as stated previously) for the time causal path, which therefore gets around the atom-to-atom “great distance” delay problem.
But the price to pay in exchange for normal length secateurs is the corresponding extreme time dilation – everything on board the ship including the gardener and his secateurs will be virtually frozen in time.
In a flat universe when an object travels further or closer away relative to another object, the temporal difference at the relative positions along the “time causal paths” can become smaller or larger depending on:
The current position along each block slice.
The direction of travel along each block slice.
In contrast to their existing just one spacetime copy of a given entity, consider what it would mean if the entire ship’s length fully existed (i.e., multiple separate copies) across the past, present, and future – in that case, multiple, perfectly complete copies of the ship would exist, spanning millions of years through time... but this is not how it works, simply because such supposed copies are instead one and the same physical entity in spacetime.
From the perspective of people on Earth, the spaceship will exist as a thin flat sheet travelling through space as it journeys one lap of the cosmos – the ship along with everything onboard will exist as virtually timeless, i.e., movement through space but no movement within itself.
From the perspective of the passengers onboard, the entire universe has a circumference equal to the length of their own ship... but if the closed universe were instead flat, any planet would then exist as being extremely squashed, i.e., like an extremely squashed ball, or a thin flat disc...
However, in a closed universe the planet would exist as a series of ultra-thin flat discs, joined smoothly at the edges, i.e., as the ship circles the cosmos, numerous discs would exist all at once – each disc would exist as a progression through time – like looking at a very finely segmented ball which has not been parted.
Travelling at 99.999,999% the speed of light causes technical difficulties.
Time dilation for the passengers would mean their own (proper) time slows down approximately 7070 times compared to Earth’s ticking clock, even though everybody could be chatting away normally from the perspective of being onboard.
Each person’s relativistic mass (total energy) would be extremely high and sensitive to change due to “gamma”, which would result in severe relativistic effects for individual passengers trying to move any part of their body.
Hypothetically the round trip could take several thousand billion proper Earth light-years, and even after considering time dilation, e.g., 3000,000,000,000 / 7070... it would still take about 424 million proper spaceship years to circle the universe.
Therefore, quite a few more decimal places would be required after the lightspeed percentage (stated above) for the spaceship to exist as stretched once around the full circumference of the entire cosmos.
Relativity theory presents the picture that all time exists... past, present, and future (i.e., the block universe), all equally real, which follows directly from some of the relativistic physical values it predicts (tested and proven to be true experimentally) and compression-type length contraction.
Causality pre-exists as the single instant of existence... the block universe – however, the term “time” is still convenient for describing causality...
Causality through time is extremely restricted within the block universe as follows:
It would take an extreme amount of time for the causal influence to arrive at the destination in space if travelling at relatively normal speeds.
(a) From any relatively slow-moving perspective, time slows down extremely for matter travelling at the speeds required to bridge (overcome 1 above) the otherwise great distances through space...
(b) But according to the faster comoving perspective, they experience their own time as ticking normally, but they're hampered when it comes to physically interacting with anything else, because everything else is both very compressed and ticking very fast compared to them...
(c) However, even when a massive body travels only very slowly relative to the CMB, it's path through time is steeper compared to any massive body that is at absolute rest, i.e., the moving body literally travels into the pre-existing future such that it really exists there, leaving all the observers that are at rest relative to the CMB... to exist in the moving body's past.
Objects become extremely stretched (as in 2 above) across time whilst travelling ultra-fast in order to physically correspond to past and future events.
Example: a spaceship 15 metres in length is travelling at close to lightspeed, and therefore experiences the entire universe to exist as being extremely squashed up. The ship just happens to be travelling at the correct speed to experience the universe as also existing to be 15 metres in length.
Causality exists as always which corresponds between the ship and the universe...
But the front end of the ship exists millions of years into the future relative to the rear end of the ship, i.e., the ship’s block slice (time causal path) is tilted relative to the rest of the universe, and from the ship’s perspective the ship is effectively stretched out along its own block slice.
Consider the ship to be flying from right to left:
Left side of universe at year 1... corresponds to ship front end... say year 20.
Right side of universe at year 1... corresponds to ship rear end... also year 1.
Spaceship is experienced by individual universe-observers to exist as an ultra-thin flat sheet.
Entire universe is experienced by spaceship to exist as being 15 metres in length.
Question: is the front end of the ship really in the future? ...
Length contracted non-comoving bodies are equivalent to stretched comoving bodies – the spaceship experiences the universe to be contracted, which is equivalent to the ship being stretched... instead.
The terminology “tilted or steeper paths” does not simply refer to plots of distance travelled vs time passed as illustrated via non-relativistic motion graphs... but instead means – a faster steeper tilted path through time, such that everything else in existence ticks more quickly from the perspective of the relatively faster-moving observer, i.e., compression-type length contraction forces the experience of being fast-forwarded through time as explained below...
As any moving body such as a spaceship extends through spacetime, its length effectively becomes increasingly stretched, and therefore its path through space must become steeper the faster it moves – otherwise in the case of a closed universe for example, its own physical existence would end up overlapping with itself, and therefore occupy the same physical space at the same point in time, which would be paradoxical – see the closed universe spaceship (“Relativity Paradoxes”) video by “PBS Spacetime” further up.
(a) In addition to the ship’s physical length through spacetime being at some constant relative angle of tilt for any given speed, its direction of motion through spacetime is treated to be along that same tilted path, i.e., like an arrow travelling through space – if the motion of the tilt was instead horizontal, the metaphysical experience of compression-type length contraction would still have to make sense without there being any displacement into the future relative to all non-comoving observers...
(b) Observers moving at different speeds to one another would somehow have to metaphysically experience full resolution length compression, but purely in an absolute present – the same present as would exist for all the different non-comoving observers, each travelling at their own independent speeds though space – which is paradoxical, and non-conforming as below...
(c) Every particle of a moving body can be considered individually, and therefore if a path still continued to move horizontally after becoming tilted – each individual particle would not be conforming to the initial phenomenon that caused the tilt.
Therefore, it seems to make sense to consider “compression-type” length contraction to be the primary metaphysical phenomenon, and time displacement into the future combined with time dilation (slower ticking clock) to be secondary/consequential.
Therefore, based on length contraction existing as the compressed experience of the full resolution of physical space – the block universe can be considered to be the logical conclusion.
The following video shows how time and distance become increasingly tilted for an object as it moves faster through space. As an object approaches lightspeed its time and distance axis approach each other – ultimately overlapping – meaning that no time, and no distance, are experienced.
Note: spacetime diagrams show each of the observer’s time and distance axes separately to illustrate their relational significance; time dilation and length contraction are represented by both axes tilting at a maximum of 45 degrees towards each other – whereas the block universe illustration uses just a single path for displaying each observer’s journey through spacetime, which becomes steeper as the observer travels faster, tilting from horizontal to 45 degrees.
In contrast to spacetime diagrams (see video below), length contraction via the block universe can be thought of as the physical length of a moving body becoming stretched out along its own block slice as it travels faster.
Spacetime Diagrams – Presented by: Khan Academy
A spaceship measures 15 metres when at rest relative to Earth. The length of the ship from your perspective standing on Earth is 15mm – the ship is flying from right to left...
You fire your 1st bullet at the spaceship as it passes by Earth... it’s a difficult target; ultra-thin; lightning-fast – the bullet penetrates the ship’s hull at the rear end and travels left, through time into the future, as it heads to the front to assassinate the captain...
From Earth's perspective as the bullet pieces through the hull, the bullet contracts along the direction of the ship’s motion, i.e., the bullet’s speed increases by the speed of the ship as it gets swept along by the ship’s momentum – thereby existing via the ship’s block slice instead of Earth’s.
An example – 99.99995% lightspeed from Earth’s perspective (1000 times dilated) – the captain is exactly 30 years old just before the ship starts to accelerate. It takes 2 proper Earth years to reach near-lightspeed travel, at which time you see the ship flash by Earth.
The ship now spans 15,000 metres (9.32 proper Earth miles) through space along its own 15 metre proper length, which exists to be 15mm long from your perspective standing on Earth.
The 15mm long ship and 15,000 metre long ship are not copies of the 15 metre long ship – they are the exact same ship, and exist as the entire length of the ship – they are all one and the same ship.
Due to relativistic time dilation, only 1 proper ship month has passed onboard.
It takes about 8 proper ship seconds to walk the full length of the ship – which corresponds to 8000 proper Earth seconds.
The captain's physical age is 30 years plus 1 month.
The next 1 hour of his life onboard will correspond to 3.6 proper Earth seconds – clock speed is: 1 / 1000 of Earth’s – virtually frozen in time.
At this instant, the ship’s position along its own block slice intersects your position along your own block slice – From the ship’s perspective it is directly overhead from where you are standing on Earth, such that the alignment of the rear end onboard is virtually flush with the rear end from the 15mm perspective on Earth.
You’re standing on a marked ‘X’ – you jump upwards into space and squeeze onboard (in principle; instantaneously) through the rear hatch – the ship appears to expand in length – you turn your head and see the captain 15 metres to the left, dropping his clipboard.
The 15 metre length of the ship corresponds to 15,000 Earth metres, i.e., whilst the captain is looking through his front window, whatever he sees (experiences) happening on Earth at the very moment you squeeze onboard, is whatever exists at some moment in time 15,000 metres to the left of where you were standing on Earth.
The front end of the ship’s stretched existence-span along its own tilted block slice when projected downwards vertically, intersects Earth’s horizontal block slice at 15,000 metres to the left of where you were standing.
An observer Derek is standing on Earth 15,000 metres to the left of where you were standing, timing how long it takes for the ship to fly from overhead above the marked ‘X' to overhead where he’s standing – from Earth’s perspective, the 15mm long ship will reach Derek in: (15,000m / lightspeed: 299,792,458mps) × 99.99995% = 0.05 milliseconds.
The very moment you crawl into the 15mm long ship, you ask the captain what he can see through his front window... “some geezer (Derek) holding a timer that reads 0.05 milliseconds”, he replies. At that very same instant Derek is just about to press the timer’s start button for the very first time.
You contact Derek via your magic block-slice-time-distance tracker situated next to the ‘X' where you were standing and ask why he hasn’t zeroed his timer. “I just reset it this very instant”, he replies – therefore the captain from the perspective inside the ship, literally exists 0.05 milliseconds into Earth’s future, and also experiences the 15,000 Earth metres to be squashed (compressed) to equal 15 proper ship metres.
Therefore, the ship is travelling into the future at a rate of 0.05 Earth milliseconds per 15,000 Earth metres from Earth’s perspective, starting from where the two block slices cross paths with each other as described in step 3.
You now walk to the front of the ship and pick the clipboard up off the floor and hand it back to the captain. By now the ship has travelled significantly along its own block slice – the simultaneity of events is now much more out of alignment than when the ship was just above the Earth. The ship is now passing by a space station that is situated 239.83 trillion metres to Earth’s left.
The ship travelled through space for a further 8000 Earth seconds as you walked to the front: 8000s × lightspeed: 299,792,458mps × 99.99995% = 239.83 trillion Earth metres... / (0.05ms per 15,000m) = 799,433s = 13324 minutes... / 60 = 222 hours further into the future from Earth’s perspective – from the perspective onboard the ship, the distance travelled to reach the space station is only 239.83 billion metres.
From Earth’s perspective after only the first 8 of the total 8000 Earth seconds, the ship had only travelled 239.83 billion metres. By using 8 seconds as a common parameter for both of the observer perspectives, to measure simultaneity, the difference in corresponding physical location in Earth metres at 8 proper seconds is: 239.83 trillion - 239.83 billion = 239.59 trillion metres.
You fire a 2nd bullet that penetrates the ship’s hull at its front end, but this time it travels to the rear of the ship. However, the bullet cannot causally affect the past, even though onboard, the rear of the ship exists 8000 Earth seconds into the past, relative to the front, via walking speed in ship proper time...
Once the bullet is onboard, it gets swept along via the ship’s block slice, and therefore experiences the ship’s time dilation...
Indeed, the bullet heads towards the rear, but every time-step that it makes towards the past is more than counteracted by the ship’s larger time-step towards the future.
When a spaceship first accelerates ultra-rapidly down an ultra-long runway, the front end of the ship will be in the future, significantly more so than its rear end. The ship could collide with any number of obstacles that exist in the future that are also located at the same position in space as the runway – the grass gets mowed on Fridays – you take off on Monday... splat into the mower.
From Earth’s perspective, the relatively small amount of time that it takes for the ship to travel the length of the runway (which from the ship's perspective exists as the ship being displaced into the future), exactly corresponds to how compressed the runway exists to be from the ship’s perspective...
Compressed-type length contraction forces the ship to ramp upwards through block time – or else it would mean that metaphysically, different total lengths of the same physical runway would have to exist along a single path through time, i.e., there would exist the same horizontal one and only block slice, i.e., no block, but different physical lengths of the same space would need to exist in the same one and only present.
The full resolution (i.e., spatial grid detail) of a physical body, cannot exist at different lengths via the same time slice – hence, compression-type length contraction forces space and time to be fused together... but without length “compression”, spacetime can conceptually... almost become separate space and time once again... more details: “Spatial Grid Resolution vs Length Compression”
An intuitive explanation and animation of gravity as can be visualised for general relativity.
Gravity Animation – Presented by: Alessandro Roussel (ScienceClic)
Explains how the theory of gravity as taught in “middle school” and “high school” is merely an approximation, and that it fails when the pull is too strong “such as the path of mercury around the sun”.
The general theory of relativity was proposed in 1915 by Albert Einstein – often thought of as the modern-day theory of gravity which supersedes Isaac Newton’s 200-year-old “theory of mechanics”.
For extremely massive objects and for extremely fast-moving bodies (close to lightspeed), Isaac Newton’s physical theory (which applies to how we intuitively experience reality as described via classical physics/mechanics) becomes increasingly more inaccurate – the results being inadequate for modern-day applications.