Quora Answers – Page 4 – Physics Notes

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

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

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.

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

So the excuse used NOT to apply relativity theory in the twin paradox is a brief period of zero seconds at the turnaround point?

No one who knows what they are talking about has suggested “NOT to apply relativity theory”. On the contrary, the correct application of relativity theory leads to the conclusion that when the twins re-unite they agree on the fact that they have both seen the traveller age less. They just disagree on when during the trip the Earth-based twin aged faster. The one on Earth thinks it happened at a steady rate throughout the trip and the traveller (after actually seeing it during the return trip) thinks (after making the light travel time correction) that it happened quickly during the turn-around.

Prior to the turn around, each sees the other ageing more slowly (due to the Doppler effect) and, even after making the light travel time correction, thinks that part of that slowdown remains unexplained (and so in some sense is “really” happening).

But any claim that during the outbound journey “we know for a fact that the travelling twin is younger than the earth twin” (or vice versa) is completely false. There is nothing that is absolutely true about the relative ages of the twins until they are at rest with respect to one another.