The Theory of Relative Time
Eight explanations, two contradictions, and no mechanism at the bottom of any of them.
Two things are held to cause it and nothing else can. But why either does it has eight different answers in circulation, and they are not the same answer. Some are derivations, some are pictures, and one pair flatly contradicts: light loses energy climbing out of a well, says the textbook heuristic; the light loses nothing and the clocks disagree, says the theory. Both are taught, both give the right number, and they cannot both be what is happening.
Two claims that follow deserve examining on their own. That light experiences no time — a claim that comes from pushing a formula to the one point where it returns no value, for an observer the theory forbids. And that an object falling into a black hole both crosses the boundary and never crosses it, depending who is asked.
This memo examines the reasoning, not the measurements — those are assessed separately, memo by memo. Section 10 states the strongest argument against this series’ own position.
What this memo does and does not do
It sets out the eight explanations given for time dilation and shows that two of them contradict each other, that the formula behind the photon claim returns no value at light speed, and that beneath all of them there is no mechanism — only the statement that the equations require it.
The measurements are assessed in memos E.6, E.8, E.13, E.14 and E.15, not here. The algebra is shared with the alternative reading in section 9.
Draft. A working draft, published for scrutiny rather than as a settled result.
This memo is about explanations, not measurements. That clocks read differently when moved or placed deep in a mass well is established, and the experiments are assessed one by one in memos E.6, E.8, E.13, E.14 and E.15. What is examined here is the reasons given for why it happens.
1. What The Theory Actually Claims
The claim is not that clocks are disturbed. It is stronger than that.
Time itself runs at different rates. It runs slower for things that are moving, and slower again for things deep in a gravitational well. A clock in either situation is working perfectly and reporting faithfully. What has changed is the thing it reports on.
What that means
If a clock merely ran slow — the way a watch runs slow in the cold — there would be nothing remarkable to discuss. Instruments are affected by their surroundings and we correct for it.
The claim being made is different in kind. It is that there is no correction to apply, because nothing has gone wrong with the instrument. Two identical clocks, both perfect, both accurate, reading different amounts of elapsed time — because different amounts of time elapsed.
Everything in this memo turns on whether that is what the evidence shows, or one way of describing what it shows.
2. Two Causes, And No Others
Only two things are held to change the rate: how fast something is moving, and how deep in a mass well it sits.
That is not a summary of what has been looked for and not found. It is structural. The theory describes the world with a set of quantities at each point, and those quantities contain a term for motion and a term for depth. There is no slot in them for anything else. Acceleration, rotation, electric and magnetic fields, direction of travel — none of these appears, and none could be added without rebuilding the theory.
Depth is not the same as pull
The second cause is usually stated wrongly.
What slows a clock is not how hard gravity pulls where it sits. It is how hard it would be to get out from where it sits — the depth of the well, not the steepness of its walls.
Those come apart. At the centre of a planet nothing pulls, because the material around you pulls equally in every direction. But you are as deep as it is possible to be, and a clock there runs slower than anywhere else on that planet. The same is true anywhere inside a hollow sphere: no pull, and slowed clocks throughout.
Mass does three separate things. It makes a depth, which slows clocks. It makes a slope, which makes things fall. And it makes a curvature, which produces tides and half the bending of starlight. The three are linked — each is the rate of change of the one before — and in ordinary situations they rise and fall together, which is why one word gets used for all of them. Only the first affects clocks.
3. Why Moving Is Said To Slow Time
Four explanations are in circulation. They are not the same explanation.
| Account | What it says | Standing |
|---|---|---|
| The geometric picture | Everything moves through the combination of space and time at one fixed total rate. Stand still and all of it goes into moving through time. Move, and some is diverted into space, leaving less for time. | The mainstream picture. Gives the exact formula. |
| The light clock | A clock times something moving inside it. Move the whole clock and that something travels a longer, slanted path, so each tick takes longer. | A real derivation, and it gives the right factor. |
| The medium | Motion through a medium physically alters the forces holding matter together, so every process in a moving object runs slow. | Identical predictions. Proposes a mechanism. |
| Thermodynamic attempts | Various efforts to derive the factor from information or heat. | No accepted result. |
What the first one does not say
The geometric picture is the one usually taught. Everything travels through space-and-time at the same total rate, and moving faster through space leaves less of that rate for moving through time.
Ask what is physically doing the diverting and there is no answer. It is a statement about a four-dimensional geometry, not about anything happening.
4. Why Being Deep Is Said To Slow Time
Again four, and again they differ.
| Account | What it says | Standing |
|---|---|---|
| The sealed room 1907 | A closed room accelerating in empty space cannot be told apart from one standing on a planet. Work out what light does crossing the accelerating room, and the same must happen on the planet. | A genuine derivation, and it came first — eight years before the rest of the theory. |
| Energy paying a toll | Energy has weight, light carries energy, so light climbing out of a well pays for the climb and arrives as a lower note. A clock counting that note counts slower. | Right number. Contradicts the theory it is used to explain. |
| The geometric account 1915 | There is a quantity at each point that sets the local clock rate, and deeper in the well it is smaller. | This is the theory. Exact. |
| The medium | The depth is the local state of a medium — a density, a compression — and a clock in it runs slow because its parts move through a different medium. | Same numbers. The only account that says what the depth is. |
The second one contradicts the third
Both halves of this appear in the same textbooks.
The energy story says light loses energy on the way up, which is why it arrives redder. The theory says the light loses nothing. Its energy is the same all the way along; what differs is that the clocks at the top and the bottom are running at different rates, so they disagree about what note they are looking at.
Those are not two ways of saying one thing. In one, the light changed. In the other, the light did not change and the observers did. Both are taught, both give the right answer, and they cannot both be what is happening.
5. What Each Explanation Covers, And Where It Stops
Set the eight accounts against each other and a pattern appears.
| Kind of account | Gives the right number | Says what is happening |
|---|---|---|
| Geometric | Yes, exactly | No |
| Derivations from a principle | Yes | Establishes that, not what |
| Heuristics | Yes | By contradicting the theory |
| Medium accounts | Yes, by construction | Yes — at the cost of a medium nobody has found |
In both cases — moving and deep — the mainstream account is geometric, exact and silent on mechanism. In both cases the alternative supplies a mechanism and pays for it with something undetected. And in neither case does any measurement separate the two.
6. The Claim That Light Feels No Time
A photon crossing the universe is said to experience no time: for light, none passes between leaving a distant star and arriving in a telescope. Here is where that claim comes from.
The slowing depends on speed through a factor that grows as the speed rises:
| Speed | Slowed by | A year of our time becomes |
|---|---|---|
| Half light speed | 1.2 times | 316 days |
| 0.9 | 2.3 | 159 days |
| 0.999 | 22.4 | 16 days |
| 0.99999 | 223.6 | 39 hours |
| Exactly light speed | — | — |
Why the last row is empty
At exactly the speed of light the sum involves dividing by zero. The formula does not return a large number, or an infinite one. It returns nothing — there is no value to read.
What is true is that as you approach light speed the answer heads toward zero. That is a statement about the approach, not about the destination. A formula that stops working at a point does not tell you what happens at that point.
And there is a second difficulty underneath. The calculation works out how much time passes for the moving thing, which requires standing still alongside it. The theory says nothing can travel alongside light. So the quantity being computed belongs to an observer the theory itself forbids.
The formula gives no value, the theory forbids the observer, and nothing has been measured. The claim is a limit dressed as a fact.
7. An Event That Both Happens And Does Not
The second place the account produces something that cannot be stated as one fact.
Watch an object fall toward a black hole. From a distance it slows, reddens, and freezes at the boundary without ever crossing. The crossing takes forever and does not happen.
Ride with the object and you cross the boundary in a finite time, and nothing remarkable occurs as you do it. The crossing takes a few minutes and happens.
Both descriptions are held to be correct.
What is being asked here
Not whether the arithmetic is right. It is.
The question is what it means for a thing to have happened and not happened at the same moment, depending on who is asked. Either the object is inside or it is not. The standard account declines that question: it says there is no single answer, only answers relative to observers.
On a single universal present there is a plain answer. The object either crossed or it did not, there is one fact about it, and a distant observer cannot see that fact yet, because the light has not reached them. Not being able to see something is a different matter from there being nothing to see.
8. Why Is Never Answered
Follow any of the accounts down and the same thing happens.
Why does a clock deeper in the well run slow? Because the quantity that sets clock rates is smaller there. Why is it smaller there? Because the equations of the theory require it. Why those equations? Because they are the simplest ones that give the right answers.
Where the questions run out
The theory is geometric. It gives the shape of things and calculates what follows from the shape. It does not state what produces the shape, and it does not claim to.
So the chain of why ends after two steps, and it ends in a choice of equations rather than in anything happening.
9. The Other Explanation
There is a second reading of the same equations, worked out before the first and never refuted.
On it, time runs at one rate everywhere and the clocks are what change. A clock moving through the medium runs slow because its parts are moving through something. A clock deep in a well runs slow because the medium around it is in a different state. The clock is a machine, and machines are affected by their surroundings.
Every number comes out the same. Not approximately — identically, by construction. The two accounts use the same mathematics and differ only in what they say the mathematics is about.
What it costs
A medium has a state of rest, and nothing moving relative to it has ever been detected, though the Earth is certainly moving. That is the bill, and it is a large one. It is faced in memo E.8 and it is not paid anywhere in this series.
What it buys is a mechanism. On this reading there is something to point at when asked why a clock slows: its parts are moving through a medium in a particular state.
10. Why Everything Slows By The Same Amount
This is the strongest argument against the reading in section 9, and it belongs here rather than in a footnote.
Clocks are not all alike. One counts an atom flipping a magnetic state. Another counts a particle falling apart under a completely different force. A body ages by chemistry. A lump of uranium decays by something else again.
All of them slow by exactly the same factor.
Why that is hard for a mechanical account
If time itself runs slow, this follows at once. One thing changed, and everything that happens in time follows it. Nothing further needs saying.
If instead each process is being physically hindered, then a medium is somehow interfering with four quite different forces — the one that holds atoms together, the one that makes particles decay, the one that binds nuclei, and the chemistry of a living body — and interfering with each by precisely the same amount, to many decimal places.
Nobody in this series has shown how. It is the reason the standard reading is the standard one, and it is not answered here.
11. What A Clock Can Tell You
A clock measures time the way a thermometer measures temperature: it is an instrument, and it reports on now. No clock has ever gone to the past to check whether it was right.
Every measurement ever made of the effect is a measurement of a clock, or of something behaving like one. The measurements are sound. What they reach is the instrument.
Why this may not be settled
The two readings are not two theories making different predictions. They are two descriptions of the same mathematics, and they agree everywhere by construction. No experiment has separated them and it is not obvious that one could.
What this memo shows is that the standard reading is a reading. It is chosen rather than forced, the explanations offered for it disagree with each other, and at the bottom of all of them there is no mechanism.
12. What Would Settle It
- A mechanism, from either side. Whichever account first explains why a clock deeper in a well runs slow — rather than stating the rate and stopping — would have something the other does not.
- Finding the medium’s state of rest would settle it in favour of section 9. Never finding it is the standing problem, and memo E.8 sets out how severe that is.
- A single account of the deep-well case adopted consistently. At present two contradictory ones are taught side by side, which suggests neither is regarded as the mechanism.
- A process that does not slow by the same factor as the others. This would break the standard reading outright. Every process tested so far follows it exactly.
13. The Numbers
In summary, the figures behind the argument:
- Things held to change the rate of time: two — speed, and depth.
- Explanations in circulation for those two: eight, of which two contradict each other.
- Explanations that say what is physically happening: one, and it requires a medium nobody has found.
- Value the slowing formula returns at exactly light speed: none.
- Different forces that all slow by precisely the same factor: four.
- Experiments that separate the two readings: none.
Terms Used Here
| Word | What it means |
|---|---|
| Aether | The proposed substance filling all space: one kind of particle which light would travel through and which matter would be built from. Not an established entity. |
| Deep space | The Aether far from any matter, at its natural density of about 0.9 kg per cubic metre. |
| “Empty space” | A misleading but unavoidable phrase. The space between the stars is not empty. What is genuinely empty is the void — the room the Aether occupies, which has no properties. |
Every term used across the series is on the terms page.
14. Sources
Reference codes read source.work.passage and resolve on the Master Source Register, which carries every source used across this series.
- A. Einstein. Über das Relativitätsprinzip und die aus demselben gezogenen Folgerungen, Jahrbuch der Radioaktivität (1907). The sealed-room argument in section 4, eight years before the field equations. Carried as reported from secondary sources; the original has not been consulted.
- H. Minkowski. Raum und Zeit (1908). The geometric picture in section 3. Carried as reported; not verified.
- H. A. Lorentz. Electromagnetic phenomena in a system moving with any velocity smaller than that of light (1904). The account in section 9. Carried as reported; not verified.
- On the absence of a local energy density for the gravitational field, and on the two accounts of redshift in section 4: standard in the general relativity literature. Not individually sourced; the points are uncontested.
- The slowing factors in section 6 are computed here from the standard formula, not cited.
Verification register: references 1 to 3 are carried as reported and none has been checked against an original. Reference 1 is load-bearing for section 4 — the claim that the sealed-room derivation preceded the field equations by eight years — and should be read before publication. No measurement is argued in this memo; the experiments are assessed in memos E.6, E.8, E.13, E.14 and E.15.
Ledger — memo T.2.2
- Derived
- That the two accounts of the deep-well case — light losing energy, and clocks disagreeing about frequency — contradict each other, and that both appear in standard teaching
- That the slowing formula returns no value at exactly light speed, and that the quantity it would return belongs to an observer the theory forbids
- That depth, slope and curvature are distinct, that only depth affects clocks, and that the cases which separate them are the centre of a body and the interior of a hollow shell
- Measured
- Nothing in this memo. Every measurement it would rest on is assessed in the experiment memos, and none is argued here
- Assumed
- That describing and explaining are different things. A reader who holds that an exact description is an explanation will find this memo has no force, and the memo does not argue against that position.
- That a mechanism is something a theory ought to have. A geometric theory does not claim one, and the demand can be denied.
- That the mathematics is correct. This memo disputes none of it, and could not — the alternative in section 9 uses the same equations.
- Open
- Why every process slows by the same factor. Immediate on the standard reading, and a serious demand on the alternative. Not answered here or anywhere in this series — section 10
- The state of rest. Required by the account in section 9, undetected, and the bound is severe — memo E.8
- Whether any experiment could separate the two readings. They agree by construction, and no candidate is known
- Whether the postulate the whole theory rests on — that light travels at the same speed for every observer — can be established rather than stipulated. It rests on a convention for setting distant clocks and Einstein called it a stipulation in 1905
- Prior art
- Lorentz (1904) and FitzGerald (1889) — the account in section 9 is theirs, and predates the standard reading. Nothing in it is original here
- Einstein (1907) — the sealed-room derivation, and the observation that it precedes the field equations
- Minkowski (1908) — the geometric picture
- What is added here is only the collection: eight explanations set beside one another, and the observation that two of them contradict