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We say that the wavefunction of the universe always evolves unitarily as everything gets entangled. But there is a huge problem with this reasoning. A clock has to exist outside the universe for us to define unitary evolution of the universe. But there's no clock outside the universe.

It is problematic that the formulations of quantum mechanics rely on the existence of "periodic phenonemena" like clocks, even when such phenomena do not really exist at the fundamental level. If light had been a periodic wave, then we could always refer to it to define our clocks. But light itself is quantum. Since everything is quantum, we can't have clocks at the fundamental level. Clocks only exist as approximate macroscopic phenomena.

So once again we're running into the problem of us defining the microscopic world using macroscopic phenomena, which themselves are an approximation of the microscopic world. This is just like how the definition of collapse also relies on macroscopic phenomena.

So, how can we define quantum mechanics without relying on macroscopic notions like clocks?

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    $\begingroup$ Can you elaborate on what it would mean for a clock to exist "outside the universe", and why that's necessary to define unitary time evolution? Are you referring to the fact that the $t$ which appears in the Schrodinger equation is a local coordinate (as per special/general relativity) rather than a global concept (as it is in Newtonian physics)? $\endgroup$
    – J. Murray
    Aug 20, 2022 at 3:24
  • $\begingroup$ @J.Murray The $t$ in the Schrodingee equation must be defined wrt some clock. And clocks can't be the fundamental objects of our theory, as they're macroscopic phenomena. $\endgroup$
    – Ryder Rude
    Aug 20, 2022 at 3:44
  • $\begingroup$ Comments are not for extended discussion; this conversation has been moved to chat. $\endgroup$
    – ACuriousMind
    Aug 20, 2022 at 23:17

4 Answers 4

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You are assuming that time does not exist without clocks. That is analogous to assuming that space does not exist without rulers, and both assumptions are unjustified.

As far as we know, we live in a four dimensional spacetime which exists whether or not there are any clocks or rulers to quantify its dimensions.

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  • $\begingroup$ By clocks, do you mean counting of periodical processes, or in general any method for measuring time? If former, then I agree - nonexistence of periodical processes does not prohibit time from existing. If latter, then I disagree - we need to have some way of measuring/inferring information about time intervals, otherwise time would be, for all intents and purposes, nonexistent. We would be in the same situation as absolute time of Maxwell-Lorentz theory. $\endgroup$
    – Umaxo
    Aug 22, 2022 at 12:39
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    $\begingroup$ @Umaxo Why do you say that? Why would time stop existing if you cannot measure it? That is like saying that mass stops existing of we have no means of measuring it. Ditto electric charge, ditto length etc. $\endgroup$ Aug 22, 2022 at 14:20
  • $\begingroup$ I said nonexistent for all intents and purposes. Who knows what truly exists and what does not? Physics only concerns itself with measurable/inferable quantities/information (if we ignore quantities created for ease of computations like coordinates and such) and the rest considers off-topic. Again, look at the absolute time of Maxwell-Lorentz theory and how special theory of relativity got rid of it exactly because it was not measurable and became only ghost variable in the theory. $\endgroup$
    – Umaxo
    Aug 23, 2022 at 3:32
  • $\begingroup$ @umaxo I think we are talking at cross purposes. I am a realist in that I believe space, time, matter, charge etc exist whether or not humans are there to philosophise about them. You might believe otherwise. As a realist, I can't see any value in arguing about other possibilities, although you are welcome to consider them. $\endgroup$ Aug 23, 2022 at 5:38
  • $\begingroup$ Believe as you want, but I am talking about physics here, not beliefs. Is our curved spacetime embedded in higher dimensional flat manifold that has no influence on any quantity measured within the spacetime itself? Who knows. But general relativity works without any such space and as far as general relativity is concerned, such higher dimensional space does not exists, even though it might exist in reality. The same would be the case for time in hypothetical universe in which time does not influence any measurable quantities. $\endgroup$
    – Umaxo
    Aug 23, 2022 at 11:11
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I'm not sure an answer exists to your question because it is not stated sufficiently precisely. However I think it is worth pointing out that we need to distinguish between the time coordinate and the flow of time. The former is a very simple concept in physics while the latter does not exist at a fundamental level.

You use the example of a light wave, and we can write such a wave as:

$$ E(t,\mathbf x) = E_0 \sin(\omega t + \mathbf k\cdot \mathbf x) $$

Here the function describing the light wave is a function of two variables, $t$ and $x$, and it is periodic in both so why would we say time flows but space doesn't? Both are just coordinates we use to locate points in a four dimensional manifold with three spatial axes and one time axis. There is no concept of flow implicit in our equation.

When you talk about a clock this is just a correlation between two systems. For example we could have some complex system, $F(t,\mathbf x)$ that we are trying to time. We could use our light wave as a clock, but this just means we are comparing how the variation of $F$ with $t$ compares to the evolution of $E$ with $t$. We could equally compare the evolutions of $F$ and $E$ with $\mathbf x$. This is mathematically just as valid but implies no flow of the space.

Obviously we all experience time as flowing, at one second per second, and this makes it fundamentally different from space, but it is not clear that this is anything more than some quirk of how human consciousness works. This concept of flow does not exist at a fundamental level.

So I think your question is not well founded as we do not need external clocks in the universe. There is just a time axis and for any system we can integrate along this axis to calculate how a system depends on the $t$ coordinate just as we can integrate along the spatial axes.

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  • $\begingroup$ You are right. In special relativity, time exists as a co-ordinate as well as a "correlation between periodic phenomena and other phenomena". So we can define the co-ordinate as the time, as opposed to defining it as something that clocks measure. But in General relativity, the co-ordinates are physically meaningless. So time must be defined using periodic phenomena like EM waves, and hence time is no longer a fundamental entity in GR. Instead, fields become more fundamental than time and space. Is this correct? $\endgroup$
    – Ryder Rude
    Aug 20, 2022 at 7:57
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    $\begingroup$ @RyderRude No. In GR we still have a four dimensional manifold with three spatial and one time axis, and we can still measure time along the time axis by choosing a coordinate system. In fact this is true of SR as well, where different coordinate choices produce different measurements of time and hence the phenomenon of time dilation. $\endgroup$ Aug 20, 2022 at 8:00
  • $\begingroup$ In both SR and GR the natural measurement of a time interval is the proper time, which is a scalar invariant and therefore the same for all observers. $\endgroup$ Aug 20, 2022 at 8:01
  • $\begingroup$ But proper time can't directly be observed (unless we treat clocks as fundamental entities). All that we can directly observe, at the fundamental level, is interacting fields. Time dilation manifests itself only in the form of dilation in the field's frequency. So our only choice is to define fields, with four physically meaningless labels, as the fundamental entities of the theory. Space and time measurements get defined using the fields. In SR, the co-ordinates aren't physically meaningless, which is why we could define time as a fundamental entity independent of fields in SR $\endgroup$
    – Ryder Rude
    Aug 20, 2022 at 8:13
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    $\begingroup$ I think you are again falling into an anthropocentric trap i.e. using observe to mean what a conscious observer perceives, and this brings us back the flow of time. The proper time is just the integral of $ds$ along a trajectory between the two points and this is mathematically well defined. Humans don't need to consciously observe it. $\endgroup$ Aug 20, 2022 at 8:18
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We say that the wavefunction of the universe always evolves unitarily as everything gets entangled. But there is a huge problem with this reasoning. A clock has to exist outside the universe for us to define unitary evolution of the universe. But there's no clock outside the universe.

There is no clock outside the universe by which to judge whether evolution is unitary. The solution to this problem is that the universe as a whole is in a stationary state of a suitable Hamiltonian. In that state there is a clock observable and the relative state of the rest of the universe evolves unitarily with respect to the values of that clock observable. For more details, see

Evolution without evolution: Dynamics described by stationary observables

Evolution without evolution, and without ambiguities

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  • $\begingroup$ I am trying to understand the nature of the problem asked by OP. When you say that the solution to this problem is that the universe is in a stationary state of some $H$, which problem do you mean? How does the non-existence of a clock outside of the universe cause a problem for the formulation of QM? $\endgroup$ Aug 20, 2022 at 18:22
  • $\begingroup$ @doublefelix Quantum theory is typically formulated in terms of a parameter t that is said to be the time. The parameter time t isn't described by a quantum observable, which is how all other real physical quantities are described in quantum theory, so it acts like a clock not represented by any real physical quantity, hence the problem. A stationary state is independent of the time parameter and so using it eliminates the time parameter from quantum theory. $\endgroup$
    – alanf
    Aug 20, 2022 at 20:00
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It's a rather odd assumption why the universal evolution should care about a clock outside of it in the first place. Time can be defined as the unidirectional progress of irreversible processes. This evolution, be it an ever increasing of number of superimposed states evolving, an interaction-induced collapsing wavefunctions (the mechanism of which is unknown), increasing entropy, or an expansion of the universe happens regardless of imaginary ideal clocks or real approximate clocks measuring it. You can put them besides the processes constituting time or you can do that in thought, but the process itself won't care about that.

Maybe the only true periodic process is found in the vacuum itself. The omnipresent virtual particle field can be described mathematically as a superposition of all independent energy and momentum states going back and forth in time simultaneously. So in a sense they constitute ideal periodicity. From this (virtual) state real unidirectional irreversible particle processes can emerge.

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    $\begingroup$ "The omnipresent virtual particle field can be described mathematically as a superposition of all independent energy and momentum states going back and forth in time simultaneously." This doesn't actually mean anything - there is no "virtual particle field" and the rest of this sentence is similarly meaningless. $\endgroup$
    – ACuriousMind
    Aug 21, 2022 at 22:16
  • $\begingroup$ @ACuriousMind But there ís a mathematical description of quantum bubbles filling the vacuum. It's an integral over all momenta, and time. Which is the propagator for the virtual field to which real particles can couple. $\endgroup$
    – Gerald
    Aug 22, 2022 at 9:34

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