September 2023 – Physics Notes

In QM, how can all people see something and all report the same thing? Wouldn’t 1 person’s observation cause their reality to branch off?

Quantum physics, without any additional “interpretation”, is just a tool for predicting the probabilities of various possible future observations from knowledge of other observations we have made in the past. To do so, it summarizes the observer’s previous observations (up to the point of the observer’s last interaction with the system) in what is called the “state” of the system relative to that observer. Any new observation ends the period of isolation of the system from the observer and so requires that a new relative state be defined taking into account the result of the most recent observation.

(Actually the “observer” of the system here doesn’t have to be a person or any other conscious entity. Any other physical system that it could interact with will do – with observations just corresponding to changes of the state of the observing system relative to any other “external” observer.)

It turns out that all observers who are isolated from the system during an experiment, and who start with the same information about the system, can use the same mathematical object to represent its relative state and for making predictions about the outcome; and this has led to the idea that the state is somehow completely independent of the observer – with various convoluted “interpretations” being added to “explain” what is “really” going on. But none of these adds anything in the way of useful predictions, and they all lead to various kinds of seeming paradox which get seriously multiplied if you mix different “interpretations” (as pointed out in Johann Holzel’s answer ).

Actually, if some friend, or other observers, (or just other physical systems) observe (or just interact with) the system before you do, then the states of the system relative to them “collapse” in the sense that after the observation (or other interaction) the probabilities of future observations are changed (with some becoming no longer possible and others more likely). But the state of the system relative to you does not collapse until you interact with it – either directly (eg by observing it yourself), or indirectly (eg by observing or communicating with your friend).

Usually it is quite hard to keep things isolated, and so just by being in the same room and sharing contact with the same air and ambient radiation you are effectively always interacting with your friend; so even without consciously learning what the friend has observed you have access to that information and so the collapse occurs for you too at the same time as for the friend. But if we were to keep the friend completely isolated in a pure quantum state (which is not possible for a real person, or even a cat, but might be possible for another microscopic system as the “observer”), then the combination of experimental system and “friend” could be in a pure state relative to you which remains uncollapsed until you actually learn the outcome (either by observing the system directly or by checking with your friend).

But as soon as we have been in contact with one another, the you that I see will agree with me about the experiment, and the me that you see will agree with you.

Source: (250) Alan Cooper’s answer to Quantum physics question If reality or superposition is fixed at observation or measurement, how can all people see something and all report the same thing? Would 1 person obseving something different cause their reality to branch off? – Quora

Experimental Confirmation of SR

Fitzgerald and Lorentz showed how if we assume that the structure and dynamics of all matter arises from electromagnetic forces which obey Maxwell’s equations in some particular (“aether”) frame of reference (not necessarily that of the lab itself), then the result would be that moving bodies experience length contraction, slowed vibration, and increased inertial mass – all in such a way that a moving observer would be unable to detect any of these effects on itself and would instead think that objects stationary with respect to the aether were exhibiting them instead.

All experimental results so far (and also, I am sure, the modified Hafele-Keating that I suggested) are consistent with the Fitzgerald-Lorentz prediction of undetectability of the aether and symmetric apparent effects of length contraction, time dilation, and increased inertial mass.

I thought your question was about the symmetry of the situation rather than the existence of a special “aether” frame.

But if you are asking whether any experiment can prove the absence of an aether frame the answer is no. The reason we reject the assumption of an aether frame is just because we don’t need it (and so by Ockham’s Razor we don’t make it).

Source: (169) Alan Cooper’s answer to Are there any (Non-thought) experiments that show that Special relativity is still valid when the Observer is moving in the local gravitational field? (The Dozens I’ve seen all assume the Observer is ‘at rest’ on earth) – Quora

Days of Future Past?

Has the future already happened according to special relativity? – NO.

In fact, in special relativity, the question of whether or not an event has “already happened” depends on the observer and has no meaning if the observer is not specified.

I find it so hard to believe!! – THEN DON’T.

Believe this instead (but only after making sure that you understand it):

What is true according to special relativity is that for any distant observer relative to whom you are moving sufficiently rapidly, some events in your future may be seen as in their past relative to the time on their clock at which you think they are now (or rather at which you will think they were now when you eventually see that “now” event in their lives).

[And for every event in your future there are some possible observers in your “now” (though you will not have actually seen them yet) who, when they finally see that event, will judge it to have happened in their past relative to the time on their clock at which you (will) think they are now.]

So in the world of special relativity, there is no time-ordering of events that all observers will agree on.

Source: (151) Alan Cooper’s answer to Has the future already happened according to special relativity? I find it so hard to believe!! – Quora

What is the reason that carbon dioxide is a good absorber of infrared radiation but not as good an emitter of infrared radiation?

There can be no reason (that CO2 is not as good an emitter as it is an absorber of IR radiation) because the claim is false. CO2 in the atmosphere emits almost exactly the same amount and kinds of radiation as it absorbs.

But, by being both a good absorber and emitter of IR, it scatters the thermal radiation emitted by the Earth in all directions – including sending some of it back where it came from to re-warm the Earth’s surface, which slows down the radiative cooling at any given temperature (or equivalently raises the temperature required for a given cooling rate).

Of course it also does the same to IR radiation coming in from the sun, but not to the higher frequencies which are included in sunlight because the sun is so much hotter; so it’s relative effect on the Earth’s daytime warming is less than on the cooling and this slightly raises the equilibrium temperature (at which the total amount of radiation escaping from the top of the atmosphere over 24 hours exactly matches the daily total amount coming in).

Source: (1000) Alan Cooper’s answer to What is the reason that carbon dioxide is a good absorber of infrared radiation but not as good an emitter of infrared radiation? – Quora

Another Twins Answer

Why should the twin on the spaceship be younger than the other on earth if each of them is supposed to observe the time dilation of the other in his own frame?

The question of which is younger when they are apart and in relative motion has no answer unless we specify the observer who is making the comparison (which could be either of them – or perhaps some other arbiter such as one who is stationary with respect to the Cosmic Microwave Background radiation).

Once they reunite they, and everyone else, will agree that the one who ends up younger is the one who experienced more acceleration towards the other when they were far apart (or more precisely for whom the integral of distance times the negative of its second derivative is greatest). But even though they will agree on the end result, they won’t agree on a moment-by-moment accounting of how their ageing rates compared.

Source: (1000) Alan Cooper’s answer to Why should the twin on the spaceship be younger than the other on earth if each of them is supposed to observe the time dilation of the other in his own frame? – Quora

What’s wrong with saying “General relativity says that the orbiting clocks should tick about 45 millionths of a second faster than they would on Earth”?

There are three main errors in that sentence.

One is more a matter of poor wording but still an error, the second is perhaps just a misprint, and the third is I think at the heart of many misunderstandings of Relativity.

First the minor stuff:

What General Relativity predicts for an orbiting satellite can be written as a sum of two parts, one gravitational (which is the same as what GR predicts for a stationary clock at the same height as the satellite) and the other sometimes called kinematic, but that breakdown is only approximate as there are other higher order terms involved as well (which include products of gravitational and velocity factors). What the quoted sentence has called the prediction of GR is just the gravitational part (which does indeed contribute about 45 microseconds to the daily time advance of the satellite clock). But GR also predicts the kinematic part (of about 17 microseconds per day of retardation), as well as those smaller additional terms, and so it is wrong to identify just the gravitational term as what GR predicts rather than as what GR would predict if the satellite were stationary (and NOT “orbiting”). The writer also left off the “per day” in describing the pure gravitational term, but I am sure that was just a misprint.

But, as I said, all that, though definitely wrong, is relatively minor stuff.

The more serious error is in the description of having a daily advance (or in the purely kinematical part a daily retardation) as ticking “faster” (or slower). It would be perfectly ok if you said ticking faster (or slower) on average, and leaving off the “on average” might seem like a small thing; but it is a serious error because it leads to the wrong idea that it means ticking faster (or slower) all the time. And the reason that is wrong is because different observers (while agreeing on the accumulated time differences recorded on two clocks between times when they are together) may disagree on whether one was always running slower or sometimes slower and sometimes faster (by amounts that give the same net total as in the always slower case). And we have no way of deciding which of them is “right”.

Source: (1000) In the twin paradox it is often stated that the clocks can only be compared at the same location. Why can’t the clocks be compared at space stations synchronized with the earth clock on the travelling twin’s journey? – Philosophy of Relativity – Quora

Is it wrong to assert that a GPS satellite clock runs slower due to kinematical time dilation?

Yes, if you want to be precise about it, and for at least two reasons.

The GPS satellite clock will actually appear to run faster (on average) for all observers (and faster at every time for both itself an observer standing on the Earth, but possibly sometimes slower for an observer in free fall down a deep well). I know you referred to “kinematical” time dilation but that isn’t really a separate thing as the separation of effects into “kinematical” and “gravitational” is only an approximation to the full GR effect.

But it’s still wrong if we just define the “kinematical” part of the approximate split as the effect that would be seen if the satellite was not in orbit but just moving at constant speed in a straight line. In this case it is true that what was the satellite clock now appears from Earth to be slow; but it also appears to the (ex)satellite observer that it is running faster than the Earth clock. And unless we specify a way to decide who’s impression is right then it is wrong to say that either clock actually is running slower.

In the twin paradox it is often stated that the clocks can only be compared at the same location. Why can’t the clocks be compared at space stations synchronized with the earth clock on the travelling twin’s journey?

The traveller’s clock can indeed be unambiguously compared with each space station clock at the event where they pass by one another, but that is still only comparing clocks when they are at the same location. And the problem with saying that comparing one’s time with that on a space station is equivalent to comparing it with the one on Earth is that it depends on agreeing that the space station clocks are properly synchronized. But if the space station clocks appear synchronized with the Earth clock in its own frame, then they will not appear synchronized to the traveller who is passing by them. So the time on the space station clock does not match the traveller’s idea of what is the current time back on Earth.
One can indeed go through the process of keeping track of the space-station clock times compared to the traveller’s clock, and will find that those recorded times are all greater on the space-station clocks by the same Lorentz gamma factor. But so long as the velocity remains constant, the traveller could be part of a lined up fleet of ships all moving at the same velocity past the Earth (and so stationary with respect to one another with the Earth and space stations moving past them), and if they all synchronize their clocks with the traveller then the Earth and space station clocks will record the intervals between successive ships of the fleet as greater than the time differences between the clocks on those ships. In other words the Earth (and space station) observers see the ship times as more closely spaced than their own and the traveller (and fleet ship) observers see the times on space station clocks as more closely spaced than the times (on their own ship-based clocks) at which they pass by them. At first sight perhaps this looks like a paradox, but we need to note that each observer of either kind is comparing times on different clocks of the other kind with successive times on the same clock of their own and each can attribute the effect to an assumption that the other set of clocks is not properly synchronized. So this isn’t really a paradox, but there is still no way of deciding which team is actually synchronized and which is not – and without being sure of that the traveller can’t rely on the space stations as true representatives of the time back on Earth.
Making the traveller turn around and return to Earth is just one way of getting some particular pair of clocks back together for an unambiguous comparison of time intervals. (Another would be to have the Earth chase after the traveller and compare notes when she catches up, and yet another would be to do things symmetrically.) But they all involve having someone change their inertial frame (ie accelerate) and the result depends on the acceleration pattern but is always basically that the one who experienced the most acceleration towards the other when they were far apart is the one who will end up younger.

[In the symmetrical twins story both end up the same age, and are not surprised because each has seen the other age first more slowly and then more rapidly but ending up with exactly the same total amount of ageing as they themselves have experienced. If they use the light travel time to infer when each tick of the other’s clock actually occurred (as opposed to when they see it), then each will infer that the other’s clock was running more slowly during both constant speed parts of the trip, but more rapidly during the period when they felt the force of acceleration during the turn-around process – with the same final result.]

Source: (1000) Alan Cooper’s answer to In the twin paradox it is often stated that the clocks can only be compared at the same location. Why can’t the clocks be compared at space stations synchronized with the earth clock on the travelling twin’s journey? – Quora

Whose idea of Simultaneity is Wrong?

Two inertial observers in motion relative to one another may disagree as to which of two events happened before the other.

They are both drawing reasonably sensible and natural conclusions from their respective observations – assigning what they actually see to a time that is earlier by the light travel time (which they compute from the observed distance and the measured speed of light). But since they disagree one or both must be wrong if they both think their own idea of simultaneity is the only “right” one.

It could be that one of them (or perhaps some other inertial frame) is “right” in some sense and all the rest are “wrong”. But we don’t have any way of exactly identifying the “right” frame, and using that fact as a starting point provides a way of making accurate predictions without needing to make the untestable assumption that some arbitrarily chosen particular frame is in fact the special one.

Source: (1000) Alan Cooper’s answer to In twin paradox, the traveller’s clock ends up with a lesser total elapsed time, so we can tell who made the trip. Does this not contradict the postulate of SR that all physical laws are the same in all frames and all inertial frames are equivalent? – Quora

Where in the universe can we find such an inertial frame? Certainly not on the surface of earth!

SR only applies exactly in the absence of gravity. So in the real world it is just an approximation that works well enough for predicting things where the effect of gravity is small (such as interactions between small high velocity particles in accelerators near the Earth’s surface, or between spacecraft and small bodies like asteroids far from planets, but not for things like apples falling out of trees on Earth).
In regions where it does provide a good approximation, it works just as well for accelerated as unaccelerated frames, but for accelerated frames the formulas needed to express physical laws in terms of the observer’s coordinates are more complicated.