A Implications of quantum foundations on interpretations of relativity

[Demystifier]

In which case you don't have a different interpretation of GR, you have a different theory. In standard GR the locus $r = 2m$ in Schwarzschild coordinates is not a physical singularity, since all curvature invariants are finite.

I agree that it's a different theory. I just use the word "interpretation" differently. In most of science, interpretation is not necessarily something that cannot be falsified.

 

[Demystifier]

Are there solutions like those?

Sure, why not? In the paper I write about cosmological solutions explicitly.

 

[martinbn]

Sure, why not? In the paper I write about cosmological solutions explicitly.

The coordinate $t$ you use belongs to an interval of the form $(t_0,\infty)$. For Minkowski it is $(-\infty,\infty)$. You clearly have more events than in the cosmological model.

 

[Demystifier]

The coordinate $t$ you use belongs to an interval of the form $(t_0,\infty)$. For Minkowski it is $(-\infty,\infty)$. You clearly have more events than in the cosmological model.

You are right about that. But it doesn't mean that there is no big bang in the nongeometric interpretation. It means that there is big bang, but also that there is time before big bang.

 

[AnssiH]

The important part of course being that the QM correlation does not represent an actual detection, but the probability of a detection.

No, the "QM correlation" is a prediction of what the correlation will be after the measurements are made and the results are known. It is not a prediction of a probability of anything.

It is true that QM cannot predict what the individual measurement results will be, it can only predict probabilities. But that does not mean its prediction of the correlation between results is probabilistic. It isn't. QM predicts that the correlation will be exactly cos⁡θ. It does not predict that the correlation has probability p of being one value and probability q of being another value.

Yup, good correction, and I would rephrase my sentence as "The important part of course being that the QM correlation does not represent an actual detection, but the probability of a detection of an entangled pair."

Because it's still good idea to view this as arising as a direct consequence of the from the concept of a probabilistic wave. When we change the angle of one filter, we reduce the probability of any entangled pair getting detected through both filters. And as per standard wave mechanics, that probability / "wave energy" (if you will) reduces by cos^2(angle)

 

[PeterDonis]

I would rephrase my sentence as "The important part of course being that the QM correlation does not represent an actual detection, but the probability of a detection of an entangled pair."

This is still wrong. As I said, the QM correlation is not a probability of anything. It is an exact prediction of what the correlation will be when you run a large number of experiments on identically prepared entangled pairs.

When we change the angle of one filter, we reduce the probability of any entangled pair getting detected through both filters.

No, you don't. You change the correlation between the results. In an ideal experiment of this type, there are no filters; every entangled pair gets detected, so for each pair there is a pair of results, which can be either the same or opposite. The correlation is just the fraction of pairs for which the results are the same; the QM prediction is a prediction of that fraction.

 

[AnssiH]

I wasn't just asking for experiments, I was asking for models. Before you can even think about doing an experiment to compare the predictions of models, you have to have models to compare.

The same answer applies - the difference between these flavors seems to be philosophical to me, i.e. a matter of interpretation.

There was some discussion in this thread about the difference between theories / models / interpretations, and to me it's pretty simple; interpretation operates beyond the observational limits, and will be a subject to everyone's philosophical / ideological bias. I don't personally find it interesting or meaningful to debate which one might be correct, but I find it interesting to discuss the actual ideological differences between interpretations, and to draw attention to the cases where people confuse their interpretation of a theory with reality itself. It will never be possible to conclusively find how reality is, because infinite number of observationally identical interpretations can always be derived from any model or theory (the fundamental reason being that any theory is always based on some finite set of data).

The important part of Bell's Theorem to me is that it implies strongly that at least one of the following concepts must be relaxed by any self-consistent theory / model / interpretation - 1. realism (relating to consciousness effect), 2. localism, or 3. the idea that information propagates literally as particles.

I don't care to debate which choices are somehow "more correct" - we can't know and I can easily form all sorts of models based on these ideas. But it is interesting that the last possibility is not very commonly discussed, while it does open a very real possibility for a local realist interpretation, which ought to have utility, even if you can never prove it over the other choices.

If you think about it, really it only involves establishing a clear boundary to wave-like information propagation - which quite easily lands on the quantized energy absorption event of atoms. Meaning, that interaction would represent the "collapse of a wave function" - only it represents it by absorbing some amount of wave energy out from the system.

It might be that the reason why this route is not very well explored is that it - at least superficially - represent a philosophy that is not commonly very well liked in physics - the idea that there "exists unobservable things". In this model, wave-like energy levels that fall below an absorption threshold (e.g. anything left over from a quantized absorption) may feel to some like an unobservable thing that ought to not exist in a model. So it might feel philosophically cumbersome idea. But actually if you follow this line of thought through, it would have to represent the noise from the rest of the universe, that would invisibly impact all of our measurements, making energy detection events seemingly probabilistic (because we can only factor in the known contribution). And if you follow this even further, you realize we have models where we choose to view things exactly like this; this is how we view transparent materials - as absorption not happening because the energy levels are too low for the atoms in the material. And in that case we view the energies as remaining in wave form throughout the materials (as an explanation to refraction).

So it is quite remarkable that Bell Experiment in this context would also yield lower energy levels as per usual cos^2(angle) correlation because you would view it as the actual classical waves getting dampened by their offset to the filter. That would yield a re-oriented "smaller wave" (with a fractional direction component removed), and that would have an impact on the probability of detection at the detection plate - exactly cosine correlation.

Whereas any interpretation where the information/energy passed through the filters as particles with discrete properties, you have to employ either non-realism or non-localism to explain it. Which of course you can. Of course what we call "particles" may well be manifestations of something that has got connections beyond our ability to observe them. Who knows.

I'm happy to discuss more details of possibilities of modeling this type of view, but that's beyond the scope of this thread. I'd like to keep this on a more philosophical level - as is the purpose of this forum.

Cheers
-Anssi

 

[AnssiH]

Well, I don't care if we call detections events "particles". But I care that they happen in pairs.

Yes of course, because they originated from the same emission event. Sorry, I'm not following how is that any different whether or not the emission itself might be particles or waves?

 

[PeterDonis]

the difference between these flavors seems to be philosophical to me, i.e. a matter of interpretation.

Do you think the same about quantum fields? (Note my comment at the end of post #120.) In other words, if I said that what causes the measurement results is neither particles nor waves, but quantum fields, is that also "a matter of interpretation" and "philosophical" to you?

 

[AnssiH]

This is still wrong. As I said, the QM correlation is not a probability of anything. It is an exact prediction of what the correlation will be when you run a large number of experiments on identically prepared entangled pairs.

Your first sentence denies it's about probability, and your next sentence basically describes statistical probability.

Sorry but the underlying mechanism is very much about probabilities so let's not steer away attention from that fact. If you prepare entanglement with identical polarities, then identically aligned filters have 100% probability of detecting the pair. If the filters are exactly orthogonal, they have 0% probability of detecting the pair. Anywhere in between, when one side of the pair is detected, there's only a specific probability that the other side will get detected. That probability follows a cosine shape.

Your first correction was completely valid here, I understand there was a possibility for someone to interpret it in critically wrong way with the way I put it. Now the rest of your disagreement is just semantics, and not very helpful semantics IMO.

Regards,
-Anssi

 

[AnssiH]

Do you think the same about quantum fields? (Note my comment at the end of post #120.) In other words, if I said that what causes the measurement results is neither particles nor waves, but quantum fields, is that also "a matter of interpretation" and "philosophical" to you?

Well in some ways quantum field theory appears to me very much like an interpretation, but with massive caveat that it appears to have more explanatory power than any of the alternatives have alone, which would lift it into the status of a theory / model. So in that sense I don't think "a theory" is a misnomer at all.

And I mean I'm well aware it is commonly viewed that way - my only reason to think it might end up in grey area is that it's impossible to say whether or not the alternatives would yield the same expectations when developed further... I mean that has of course happened in the history of physics, that theories have become unified when people realized they really were just flipsides of the same coin. So ultimately the answer to that question is buried too deep into the complexity of the matter that I can't reasonably investigate it. I just have to take other people's opinion/word for it.

So what is your opinion of that matter?

Cheers,
-Anssi

 

[PeterDonis]

Your first sentence denies it's about probability, and your next sentence basically describes statistical probability.

Correlations between already known results have nothing to do with probability. They can be computed exactly; there is nothing unknown.

You seem to be talking about the correlation as "the probability of detecting a pair", but I don't think that's a correct description of what the experiment is actually doing. See below.

If you want to interpret the predicted correlation as "the probability of the two measurement results for a pair being the same", on a straight frequentist interpretation of probability, I suppose that would be OK.

If you prepare entanglement with identical polarities, then identically aligned filters have 100% probability of detecting the pair. If the filters are exactly orthogonal, they have 0% probability of detecting the pair.

First, as I said, in an ideal experiment of this type, there are no filters. Every pair gets detected. The only question for each run is whether the detection results will be the same or opposite. A simple way to implement this is to have a polarizing beam splitter for each entangled photon of a pair, with two photon detectors behind it, one in each arm of the splitter. For each photon of the pair, the measurement result is then either "detector in the transmitted arm of the splitter registers" or "detector in the refracted arm of the splitter registers". So we don't "detect pairs"; we have two results for each pair, not one, and we can then check if they are the same.

Second, in such an experiment, we don't hold the alignment of the polarization measurements the same and vary the prepared state. We hold the prepared state the same and vary the alignment of the polarization measurements.

the underlying mechanism is very much about probabilities

I thought underlying mechanisms were just "philosophical" and "a matter of interpretation" to you.

In any case, any "underlying mechanism" you postulate is interpretation-dependent. And as the guidelines for this forum will tell you, it is out of bounds to claim that any particular interpretation of QM is "right" or "wrong" here. The same would apply to claims about underlying mechanisms.

 

[zonde]

Sorry, I'm not following how is that any different whether or not the emission itself might be particles or waves?

That's exactly my point. It does not matter how you call emission or detection events as long as they come in pairs. You are the one who is claiming there is difference:

The important part of Bell's Theorem to me is that it implies strongly that at least one of the following concepts must be relaxed by any self-consistent theory / model / interpretation - 1. realism (relating to consciousness effect), 2. localism, or 3. the idea that information propagates literally as particles.

It seems like you do not really know what assumptions are needed to build a a proof about Bell inequalities.
I would suggest you to look at this "proof" of Bell inequalities https://www.physicsforums.com/posts/2817138/
It's very simple so it is easy to identify all the necessary assumptions, either hidden or not so hidden.

 

[AnssiH]

First, as I said, in an ideal experiment of this type, there are no filters. Every pair gets detected. The only question for each run is whether the detection results will be the same or opposite. A simple way to implement this is to have a polarizing beam splitter for each entangled photon of a pair, with two photon detectors behind it, one in each arm of the splitter. For each photon of the pair, the measurement result is then either "detector in the transmitted arm of the splitter registers" or "detector in the refracted arm of the splitter registers". So we don't "detect pairs"; we have two results for each pair, not one, and we can then check if they are the same.

Second, in such an experiment, we don't hold the alignment of the polarization measurements the same and vary the prepared state. We hold the prepared state the same and vary the alignment of the polarization measurements.

That's interesting, but I'm not quite following the setup you are describing How does it measure the polarization exactly? (Pretty important question of course if we are analyzing the possible impact of the measurement method - it seems to me that every polarization measurement implies macroscopic elements that must either pass wave-like information through a filter, or via quantized absorption/emission events)

So may I ask for more details of the intented setup, or perhaps just point to a paper describing a similar experiment?

I thought underlying mechanisms were just "philosophical" and "a matter of interpretation" to you.

Yeah I was being a bit unclear there - by underlying mechanisms I was referring to the underlying logic of quantum mechanics in general. I think the difference in our thoughts there is really just semantics - I simply prefer to think of Bell correlations as a direct result of probabilistic measurements. The mathematics are basically exactly the same whether we are talking about two polarized filters in a chain measuring the probability of something passing through both filters, or two separated polarized filters in opposite directions and passing through entangled information (this was pointed out in that TI paper as well, which I lifted).

Thanks!
-Anssi

 

[AnssiH]

That's exactly my point. It does not matter how you call emission or detection events as long as they come in pairs. You are the one who is claiming there is difference:

It seems like you do not really know what assumptions are needed to build a a proof about Bell inequalities.
I would suggest you to look at this "proof" of Bell inequalities https://www.physicsforums.com/posts/2817138/
It's very simple so it is easy to identify all the necessary assumptions, either hidden or not so hidden.

Actually I've been saying there that there is no difference

And what I was pointing out in what you quoted was that non-locality or non-realism comes to play if you assume real existence of (properties of) a photon (or any particle) prior to observation - that is simply coming from the fact that if the properties of the photon must exist "during the flight", then the eventual measurement event cannot impact the correlation of the pair without some kind of non-local or non-realist mechanism (since you can always change the configuration of the measurement device just before it occurs).

But that limitation is only valid in so far that we assume the real existence of these particles-prior-to-measurement. If instead the quantized properties only appear due to the the measurement event as a result of that interaction itself being a quantized absorption interaction (which according to our models - it is), now that's entirely different ballgame. Now we have a potential opening for local realistic interpretation. The correlations we expect are still the same as in any other (valid) interpretation, as they occur due to transforming a continuous wave description into a quantized description (extremely basic cosine correlation) where obviously the quantized event either occurs or it doesn't (there's no such thing as "partially occurs"). So ultimately we are really only talking about "when and where and in what sense" do we interpret the collapse of a wave function to occur.

One way you can convince yourself that this is logically perfectly valid is to trace your way here from some non-realist interpretation. Logically speaking a non-realist interpretation works the same way whether or not it is the consciousness collapsing wave function, or some other event prior to the information reaching "the mind". If you push that "collapse" down to the moment of the atom absorbing a wave, now you have a better defined location for the collapse, that does not require "consciousness", and yet the wave-nature of the system is still perfectly observable.

Cheers,
-Anssi

 

[PeterDonis]

How does it measure the polarization exactly?

With a polarizing beam splitter: photons of one polarization get transmitted, photons of the orthogonal polarization get reflected by 90 degrees. Put a photon detector in each output beam; for each input photon, one and only one detector will register. Changing the relative orientation of two such beam splitters, one for each of a pair of entangled photons, changes the angle that appears in the quantum correlation formula.

 

[zonde]

So may I ask for more details of the intented setup, or perhaps just point to a paper describing a similar experiment?

Here is one well known experiment: https://arxiv.org/abs/quant-ph/9810080

 

[zonde]

If instead the quantized properties only appear due to the the measurement event as a result of that interaction itself being a quantized absorption interaction (which according to our models - it is), now that's entirely different ballgame. Now we have a potential opening for local realistic interpretation. The correlations we expect are still the same as in any other (valid) interpretation, as they occur due to transforming a continuous wave description into a quantized description (extremely basic cosine correlation) where obviously the quantized event either occurs or it doesn't (there's no such thing as "partially occurs").

So you say there is continuous wave. Fine. But please explain, does this continuous wave have a property "polarization", or no? When it passes polarizer, is the amplitude of the wave changing as we rotate the polarizer around the clock?

 

[zonde]

In which branch particle will end up is determined by pilotwave and initial position of particle.

Exactly; that's what I'm saying. Which means there is no collapse in this interpretation because, given the initial position of the particle, one single measurement result is determined to occur. There is no random choice between alternatives; the "alternatives" in the wave function (pilot wave) are there in the math but not in reality according to this interpretation.

No. Kochen-Specker shows that you can’t assume that all variables have values prior to measurement. But in the Bohm interpretation, only the position variable has definite values. A measurement of other variables such as momentum or spin doesn’t reveal a pre-existing value, but is an artifact of the measurement process.

PeterDonis and stevendaryl, I see sort of contradiction between your answers, and this is related to where I see the problem. In short - is there randomness involved in spin measurement?
In QM we can write the wavefunction in different bases (according to superposition principle), so it would seem that the branches are just a matter of perspective. But then say spin measurement result is predetermined when we write wavefunction in one basis. But is measurement result predetermined when we write wavefunction in different basis? Is there some randomness involved? It seems to me that taking into account Kochen-Specker theorem there should be some randomness involved. And then taking into account Bell theorem (if we take nonlocality out) this randomness should be nonlocally coordinated.
So what I'm missing in Bohmian Interpretation is that nonlocally coordinated "collapse" not of wavefunction but of hidden variables (therefore "collapse" is in quotes).

 

[PeterDonis]

is there randomness involved in spin measurement?

There is in basic QM (the 7 Basic Rules), but some QM interpretations say that that randomness is only apparent, not real. The Bohmian interpretation is one of them; in this interpretation, the apparent randomness is only because we don't know the hidden particle positions. If the particle positions are known, this interpretation is deterministic. (Note that this applies to any measurement, not just spin measurement.)

In QM we can write the wavefunction in different bases (according to superposition principle), so it would seem that the branches are just a matter of perspective.

The branches are due to entanglement, not just superposition. Entanglement is not basis dependent.

 

[Sunil]

The Bohmian interpretation is one of them; in this interpretation, the apparent randomness is only because we don't know the hidden particle positions. If the particle positions are known, this interpretation is deterministic. (Note that this applies to any measurement, not just spin measurement.)

Correction: Except for the position measurement, it is not only the particle position, but also the configuration of the measurement device which has to be known to identify the outcome. (This is what makes BM contextual.)

 

[Demystifier]

Correction: Except for the position measurement, it is not only the particle position, but also the configuration of the measurement device which has to be known to identify the outcome. (This is what makes BM contextual.)

@PeterDonis said positions, not position. The configuration of the device is given by particle positions.

 

[Lynch101]

Well, "at once" is more abstract, but
it could be said then, "All, side by side"

Could it be stated like this: all events on the wordline/worldtube of an observer share equal ontological status i.e. 'past', 'present', and 'future' states co-exist within the overall structure of the universe?

 

[AnssiH]

Coming back with some late replies, hopefully you guys still remember the context (weather's been far too good lately )

With a polarizing beam splitter: photons of one polarization get transmitted, photons of the orthogonal polarization get reflected by 90 degrees. Put a photon detector in each output beam; for each input photon, one and only one detector will register. Changing the relative orientation of two such beam splitters, one for each of a pair of entangled photons, changes the angle that appears in the quantum correlation formula.

Ah yeah, so in that setup the relative orientation of the beam splitters represents the polarization detection mechanism, so the point is we can (and IMO should) still view this system in terms of probabilities. Schrödinger Equation describes a wave function that gets split into one or the other polarization possibility, as a function of the polarization of the input beam; we are literally plotting probabilities of detection according to QM, against relative measurement angles.

My original statement;

"If you prepare entanglement with identical polarities, then identically aligned filters have 100% probability of detecting the pair. If the filters are exactly orthogonal, they have 0% probability of detecting the pair."

just becomes;

"If you prepare entanglement with identical polarities, then identically aligned beam splitters have 100% probability of detecting the pair in their particular correlated detectors. If the beam splitters are exactly orthogonal, they have 0% probability of detecting the pair in the correlated detectors (and hence 100% probability of detection in anti-correlated detectors"

Actually of course you never really get pure 100 or 0% because of noise you can't really avoid, but the gist of both version (and any possible Bell experiment) is the same; wave mechanics describe the experiment completely up to the point of a detection, and if the energy actually travels as a wave, while the detection event itself is quantized (as per Planck's Law it must be), the probability of correlated pair detection actually occurring (as oppose to completely becoming missed) is described by a cosine correlation curve - not linear correlation curve.-Anssi

 

[AnssiH]

Here is one well known experiment: https://arxiv.org/abs/quant-ph/9810080

Thanks Zonde,

Note that the role of the electro-optic modulator prior to the beam splitter is to adjust the relative orientation of the beams, so to have a mechanism to plot the curves in FIG.3. The curves are, as they say "sinusoidal". Quantum theory predicts a sinusoidal dependence for the coincidence rate, because it plots the expectations via a wave mechanism.

Of course if you assume the system had wave-like energies passing through it, leading into a quantized detection at the detection photodiodes, you would end up with exactly same sinusoidal dependence expectation (after making a detection, the implied polarization at the input is probabilistic and plots a sinusoidal wave - as per basic wave mechanics)

So if - and only if - you presume the system had actual photons in free flight, with actual polarization to them at the moment of departure, you would have to use non-realist or non-local mechanisms to explain why these correlations appear as they do (the fundamental problem being that a single photon can't interfere with itself).

Note btw that they are not detecting "every photon". Their detection rate is about 5%. But that's not relevant - what is relevant is that you know at some fair rate which detections are supposed to be the entangled pairs.

Note also that their very method of adjusting the polarization with the electro-optic modulator is best described as a wave system - in fact they do so themselves in footnote 13. The photon perspective of the mechanism they describe is also that of "self-interference of a single photon".

One more note I forgot to mention before;

It seems like you do not really know what assumptions are needed to build a a proof about Bell inequalities.
I would suggest you to look at this "proof" of Bell inequalities https://www.physicsforums.com/posts/2817138/
It's very simple so it is easy to identify all the necessary assumptions, either hidden or not so hidden.

In the description in that post there is that exact same error I've pointed out few times now;

"Starting with two completely identical binary messages, if A's 30 degree turn introduces a 25% mismatch and B's 30 degree turn introduces a 25% mismatch, then the total mismatch (when both are turned) can be at most 50%. In fact the mismatch should be less than 50% because if the two errors happen to occur on the same photon, a mismatch is converted to a match."

They blindly assume that in classical view, if a 30 degree error introduces a 25% mismatch, then a 60 degree error must introduce at most a 50% mismatch. What exactly would be the explanation behind that expectation? Only a straight blind addition logic with no rhyme or reason to it would give that expectation, but a completely classical wave mechanical view most certainly does not imply a linear correlation to the relative detector angles

Cheers,
-Anssi

 

[AnssiH]

So you say there is continuous wave. Fine. But please explain, does this continuous wave have a property "polarization", or no? When it passes polarizer, is the amplitude of the wave changing as we rotate the polarizer around the clock?

Yes of course; polarization is usually associated with wave behavior - it refers to the direction of the oscillation. A wave can be a pulse that is oscillating horizontally, vertically, in any diagonal angle, circularly and so on.

So yes linear polarizers would eat away a direction component from that polarization - some of the amplitude of the wave is eaten away as per cos^2(relative angle). This appears to be what polarization filters are doing (as per experiments).

Note that if a beam splitter outputs two beams at orthogonal polarization, it would yield 50% of the randomly polarized input energy into each path (minus some energy loss from imperfect materials).

But this is an excellent question because it's important to keep in mind what exactly do we suppose happens upon an electron - a wave system in itself - absorbing some energy.

The absorption thresholds are related to the frequency of the wave - makes sense if we are looking at harmonic wave systems (as per Max Planck's theory). It's not possible to achieve the next possible harmonic mode by simply increasing amplitude, you actually have to incite a higher frequency to a harmonic oscillator. But a continuous amplitude can still become reduced to the point where there is no oscillation occurring anymore! At some point before it becomes exactly zero, the implied velocity of the oscillation of the signal starts to approach 0 smoothly.

Usual QM wave function perspective of this is mathematically identical, the only difference is that we would say "the probability of detection starts to approach 0". If you assume Schrödinger Equation represents also an actual wave, the final expectations are the same because even when the actual wave energy starts to approach 0, you will still have noise from the rest of the universe making it possible for a n absorption to occur. So in all practicality, your wave model only gives you the probability of a detection - unless you somehow manage to take the entire universe into account.

The noise being all the excess energies left over from absorption events all across the universe. Which btw is an interesting question I don't here too many people asking themselves - in a photon picture, what happens to the excess energy of a photon that an electron is not able to absorb?

Cheers,
-Anssi

 

[Demystifier]

Today appeared a paper that may be relevant for this thread.
https://arxiv.org/abs/2107.02089

 

[physika]

Could it be stated like this: all events on the wordline/worldtube of an observer share equal ontological status i.e. 'past', 'present', and 'future' states co-exist within the overall structure of the universe?

.
but to be equitable, space should be treated on an equal footing with time, but then, there is no "extension" neither "duration"

it is not a block, it is a point !

.

 

[EPR]

This is wrong. The quoted post was wrong too.

The issue leading to the block world has to do with the relativity of 'now', not with extension or duration.
In a sense, all viewpoints on how old the Universe is are all true. As if they existed at the same time, side by side. For example, from some FOR's your life has already passed as they are moving faster than us leading to time dilation in their FOR.
The resultant journey is not a point but a worldline through spacetime.

 

[Lynch101]

.
but to be equitable, space should be treated on an equal footing with time, but then, there is no "extension" neither "duration"

it is not a block, it is a point !.

I'm not sure I follow your reasoning. It would be the treatment of time as a dimension, in the manner that space is treated as a dimension, which would imply objects must be temporally extended i.e. past and/or present and/or future states must co-exist within the universal structure. If objects aren't extended temporally, then this would mean that time is not a dimension, but a point.

This would leave us with a spatially extended universe, which is not temporally extended i.e. there is only a single global time co-ordinate, thereby necessitating absolute simultaneity.