Physics Notes

A Quora question asks Does relativity theory give any explanation why time passes more slowly for an observer in a strong gravitational field than it does for an observer in a weaker field?

Well, the obvious one word answer is “Yes”.

But although the above single word is a complete answer to the question as posed, it is probably not what was really wanted, and would in any case be suppressed by Quora because they want to promote more extended answers.

The actual explanation follows from the fact that relativity theory (both Special and General versions) is based on the assumption (which is consistent with all experimental observations that have ever been made) that the laws of physics appear to provide no means of identifying one of two relatively moving inertial frames as more fundamental than the other. A consequence of this assumption is that a clock in an accelerated frame appears to be running more slowly than one in an inertial frame towards which it is accelerating. And for a clock in a gravitational field to remain at the same potential it must either be experiencing what feels like an outwards acceleration or be moving very fast (to remain in orbit at a fixed altitude from the local center of gravitational force). Both of these lead to the clock appearing to run slower than one which is fixed at a greater distance from the center of gravitational force.

Source: (1002) Alan Cooper’s answer to Does relativity theory give any explanation why time passes more slowly for an observer in a strong gravitational field than it does for an observer in a weaker field? – Quora

A recent article in Scientific American promotes the views of someone who “has spent his entire career championing and extending de Broglie’s views” and “recently spoke to Scientific American about his lonely(!) path and why de Broglie might have been on to something” without any specific acknowledgement that the vast majority of physicists are well aware of this “pilot wave” theory and do not believe that there is any significant chance that it “might explain what’s wrong with quantum mechanics“.

Source: Irresponsible Journalism in Scientific American | alQpr

The surface of water in a lake is NOT always perfectly level in the sense of being geometrically flat. It is just “level” in the sense of not having any transverse gravitational field, and follows the curvature of a gravitational equipotential which at the Earth’s surface bends downwards about eight inches per mile.

This is obvious if you ever look across a large lake towards a distant city with tall buildings, but is also possible to notice when swimming in a much smaller lake with your eyes just an inch or two above the surface.

Source: (1002) Alan Cooper’s answer to If the Earth isn’t flat, how come the surface of water in a lake is always perfectly level? Since when does water have the ability to curve and stay curved? – Quora

The “mass” of any complex “body” or system of interacting component “bodies”, defined as its resistance to acceleration from rest, includes not just the masses of its components but also terms corresponding to the kinetic energy of their motions relative to one another and to the force fields acting between them.

The numerical factor relating the amount of energy corresponding to a unit of mass depends on the units of time and distance but it is exactly one if we use years for time and light-years for space or approximately one if we use feet for distance and nanoseconds for time. In terms of more normal units like metres and seconds the conversion factor is very large and one unit of mass corresponds to almost 17 powers of ten (ie 100,000,000,000,000,000 ) in units of energy.

Source: (1002) Alan Cooper’s answer to Can you give an intuitive description of what Einstein’s mass-energy equivalence equation means in one or two short sentences without describing the equation or the math? – Quora

It is a common misunderstanding that what someone once jokingly called the “Big Bang” theory describes the universe as expanding from a single point.

What General Relativity actually suggests is just that in the distant past the universe was very dense (but still of infinite extent) and very hot, with everything flying apart so that since then it has been becoming less dense but not actually “expanding” in the sense of having a boundary that is moving outwards.

With regard to the second question about whether an object can “remain stationary”, in the absence of gravity (ie in Special Relativity) there is no way for an observer to identify whether or not it is moving in any absolute sense. But it is possible to identify whether an object is moving relative to any particular other object, or to the centre of mass of all the other material in its visible universe (so long as that visible universe contains just a finite total mass). And in General Relativity this can be done by checking for isotropy (sameness in all directions) of the microwave background radiation coming from the “Big Bang”.

Source: (1002) Alan Cooper’s answer to What is the rate of expansion of the universe from a single point? Can an object remain stationary in the universe? – Quora

The electron cloud is just a way of predicting what the observer will see on future observations of the electron. When an observation is made, the range of what might be possibly seen in future observations is reduced. So starting right from the moment an observation is made, the observer’s knowledge about the electron is described by a new wave which applies until the observer makes another observation. But the apparent wave behaviour does not cease. It just changes to that new wave, and the electron is never seen to behave like a classical particle. In fact, it is not actually ever either a classical particle with a definite position or a wave of some definite form, and the question of what it “is” may not have any real meaning. All we can talk about are the probabilities of various observations – which we know from experiments do not correspond to any classical picture of what is going on.

Source: (1001) Alan Cooper’s answer to What is it about the act of observing that changes an electron cloud into a single electron that behaves like a particle? – Quora

When swimming you can notice the effect over the width of a small lake:

But if you want to see a noticeable effect over just two meters then it depends on what you mean by “noticeable” (eg it would be a trivial high school exercise to calculate the largest radius at which a two meter tangent line ends at least one mm from the corresponding arc).

Source: (1001) Alan Cooper’s answer to How close to the Earth’s core would you need to be to see an ‘uneven’ water level?Not regarding temperature etc making it impossible, how deep would you have to dig to see a noticeable curvature in, lets say a 2m length of water? – Quora