JonG

I am aware of the "neatness" of replacing t by it, however, doing so also makes the speed of light, together with other things, imaginary numbers. I don't think we are as free to make such changes as you suggest. The t which appears in "it" is not the t which would represent time as we know it.

By swansont. I agree that the differences in how we perceive time and spatial distances probably relate to the fact that we accept the scientific description of spatial matters without problems but are inclined to be puzzled by time. However, there is a difference in the way time and spatial increments appear in the flat spacetime metric, but I am unsure how it relates to the matter being discussed. In the flat spacetime metric, the c2dt2 term is opposite in sign to the spatial terms. ds2 = -c2dt2 + dx2 + dy2 + dz2. But it's hard to imagine what things would be like if there wasn't this difference in sign, and I am not sure that it has any bearing on how we perceive time.

By Dr Funkenstein: By swansont: That could be because we perceive length in a way which is similar to the way in which it is represented in Physics. However, our perception of time is quite different. We don't perceive time as a point, or series of points, on an axis, as it is represented in space-time, but as some mysterious flowing entity which is carrying us along with it. The latter view of time, although it now sounds far-fetched from a scientific perspective, is similar to Newton's "absolute time". "Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external,"

It's difficult to see how time can be considered to be an illusion, as it is necessary to describe what we see about us. However, there is a case for regarding such concepts as "the present" or "flow of time" as illusory simply because there is no objective evidence for their existence. Even then, "illusory" might be seen as harsh. Perhaps they should just be labelled as subjective - notions within our heads.

I just want to make a brief note on something that has cropped up a various points within this thread : - is this Physics or Philosophy? There is a well known book on the subject of Time entitled "About Time" by Paul Davies, who is a physicist. He has clearly been fascinated by the topic throughout his life and there are aspects of it that could well be described as Philosophy rather than physics. But the impact that Physics has had on this subject, largely due to the theories of relativity, is very significant so it is no surprise that there is overlap between ideas which might be described as Physics and others which might be described as Philosophy. The crux of the problem appears to be in reconciling two very different notions about time. One is the personal, everyday, usage of the concept; viz that time is characterised by a present, past and a future together with the idea that time is something which flows. The other is time as it appears in Physics;- a coordinate, similar to, but not the same as, a spatial dimension. In this view, sometimes referred to as "block time", there is no place for notions such as past, present and future, nor can any meaning be attached to the idea that time flows. These two views of time are very different and, not surprisingly, of interest to some physicists and some philosophers. Personally, I don't find it at all odd that someone should want to discuss these differences on a Physics forum (or on a Philosophy forum as well).

In addition to what has already been mentioned, there are multiphoton processes, which might not be seen as the "photons interacting with each other", but which involve several photons interacting with an atom simultaneously. A 2-photon process, for example, would involve two photons, each carrying energy E, being absorbed by an atom and giving rise to a transition requiring energy 2E. Processes of this sort are are only observed with light of very high intensity as might be generated by pulsed lasers. Classically, they are described as a kind of non-linear effect. The non-linearity in the interaction between photons and an atom is what causes two or more photons to be absorbed at once. For normal light intensities, 2-photon transition would actually contravene selection rules, but they can become the dominant process at high light intensities.

That could sort the problem out - but that in itself doesn't suggest that a viable quantum theory of gravity could be assembled - I just don't know. My moderate interest in this stems from the sort of comment I referred to earlier in which it is often claimed that an expanding universe entails the expansion of spacetime itself. This is not quite the same as saying that an expanding universe has to be described by an expanding curved coordinate system.It implies that spacetime is something which exists in itself and that could be described as expanding - in fact, the expansion of the surface of a balloon which is being blown up is often cited as an analogy - the two dimensional surface of the balloon being analogous to spacetime. Take this as an example: "If we examine a piece of `empty' space we see it is not truly empty, it is filled with spacetime, " from here: http://abyss.uoregon.edu/~js/ast123/lectures/lec17.html and the following from Stanford : " however, the equations of general relativity are perfectly consistent with spacetimes that contain no matter at all. Flat (Minkowski) spacetime is a trivial example, but empty spacetime can also be curved, as demonstrated by Willem de Sitter in 1916." from here: http://einstein.stanford.edu/SPACETIME/spacetime2.html However, this quote is also given: "General relativity as developed by Albert Einstein, says, and this is a direct quote from Einstein, that 'Space-time does not claim existence in its own right, but only as a structural quality of the [gravitational] field' ". also from Stanford: http://einstein.stanford.edu/content/relativity/q909.html

An interesting example. In everyday speech, many would refer to an electric field as if it were real. But that isn't actually how it is regarded in Physics. It would be seen as graphical way of describing the interaction between charged objects (which would be considered to be real) through the agency of virtual photons (how many people would see those as real is open to question). However, if we didn't have a more fundamental description of electromagnetic fields, we would indeed be left with the same puzzle as we have with gravity. We just don't have such an underlying theory of gravity.

Just a few notes regarding various comments made: 1) To question whether spacetime is a real entity is not the same as questioning the validity or accuracy of General Relativity. It has nothing to do with that whatsoever. We know that a solution of Schrodinger's equation gives us a wavefunction, but no one seriously believes that wavefunctions are real entities in themselves. One can't directly observe a wavefunction, it doesn't have a property such as mass. But the fact that a wavefunction is considered to be an abstract concept rather than a real entity in no way invalidates quantum theory. Pointing out that General relativity is consistent with observation is irrelevant, just as pointing out that quantum theory is successful does not prove that wavefunctions are real entities.. 2) So why should anyone be concerned about whether curved spacetime is a real entity? Because, unlike the quantum mechanical example I mentioned, nothing lies behind curved spacetime. In quantum theory, we know that the wavefunction describes properties of particles such as electrons which are considered to be real, but there is nothing analogous to these particles in the relativistic theory of gravitation - unless one wishes to include things like "gravitons" in some way. To assert that some massive object can interact with an abstract concept which cannot be directly observed is, to me, on a par with a belief in ghosts. Curved spacetime enables a very good description of gravitation. But, surely it can't be the whole story. Please note; THIS IS NOT QUESTIONING THAT THE RELATIVISTIC DESCRIPTION OF GRAVITY LEADS TO THE VIEW THAT SPACETIME IS CURVED. It is to do with whether curved spacetime is something which actually exists - other than in people's heads.

You haven't specified an example so I will take one at random - Feynman diagrams. I doubt that anyone believes that Feynman diagrams have any real existence. But conclusions arrived at with the aid of such diagrams are considered to be valid. Spacetime however, is seen to be very different. For example, it is often pointed out that the expanding universe is not due to galaxies receding from each other - spacetime itself is expanding. This appears to endow spacetime with objective existence. I have often wondered about this. As I mentioned earlier, the notion of action at a distance was once seen as a major obstacle in the understanding of gravitational, electric and magnetic fields. How can two bodies which are separated by empty space exert a force on each other? These concerns gradually faded with time and, when I was a kid at school, the idea of action at a distance wasn't seen as problematic at all (not because we knew all about second quantization - we hadn't heard of it then). I don't think it was because anyone had acquired a deeper or more mature understanding, but simply because we had, as you put it, "adjusted our perspective" - although not necessarily for rational or defensible reasons.

I don't think it could be claimed that general relativity "tells us" that spacetime is curved. Rather, it is "assumed" that spacetime can be curved and the effects of gravitry are then explained on the basis of this assumption. I don't see this as relevant. Newton's theory of gravitation was in accord with the evidence available to Netwon, but he was the first to acknowledge that he could offer no explanation of why his theory worked. The notion of a force acting at a distance was particularly problematic at the time. To question assumptions made in a theory does not imply that the predictions of the theory are incorrect. My point is that to assert that some non-material entity (spacetime) can become curved by the action of massive objects is by no means obvious and I would have expected it to raise a few questions. One could probably explain any field of force by bending and modifying spacetime appropriately. In fact, the Kaluza-Klein theory did something like this in order to unify gravitational and electromagnetic fields.

I believe that Einstein himself had serious reservations about the notion of Minkowski spacetime, dismissing it as "superfluous learnedness", before adopting it as a significant foundation stone in his General Theory of Relativity. The idea that a massive body causes spacetime to become curved has always seemed odd, but that doesn't stop many people accepting it without question. In fact to question it might be seen as a form of blasphemy to some. But how can a massive object cause something which is itself massless to become curved. In fact, one could see spacetime as simply a mathematical device without real existence at all. Does anyone else find something peculiar about this?

The word "efficiency" usually relates to conversion of energy from one form to another - "machine" is a little more vague. If we consider engines, such as an internal combustion engine, these are heat engines which convert heat (from burning fuel) into mechanical energy by a cyclical process. The Carnot cycle is an idealised version of a heat engine. It has higher efficiency than a real heat engine, but its efficiency can never be as high as 100%. Machines such as electric motors do not fall into the cyclical, heat engine variety so the Carnot cycle says little about them. An electric motor will clearly not be 100% efficient because of loss of energy by ohmic heating and frictional losses at bearings. However, my guess is that the original question concerns a general argument which can be used to rule out 100% efficiency in such cases.

The momentum of the train would be (mI + mc).v I'm not sure what "momentum of impact" means. The force exerted on the buffers arising from the change in momentum of the locomotive during the short period of time encompassing the collision could be found from the change in momentum of the locomotive. The change in momentum of the locomotive would be mI.v, if the locomotive were brought to rest. But what has this got to do with defining momentum in terms of point-like particles?

This could be yet another example of the current day tendency to attach ridiculous figures to the cost of projects which have never been done. No one has made a whole gram of antimatter in one go. The cost of doing so seems to be just guesswork. There is little to support it and little to contradict it.

I am a bit puzzled by this. If a body of finite size and of mass m is moving with a velocity v, I would expect its momentum to be mv. I can't see why it is necessary to regard the body as a point. If a non-uniform field of force is acting on the body, the effect of the force might vary from one point within the body to another. But I don't see what this has to do with the definition of momentum. Personally, I have always considered "inertia" to be a vague term referring to a resistance to a change in velocity.

It's difficult to express this notion because the past clearly doesn't exist "now" .Einstein himself appears to have seen the past and future in that way. When his friend Besso died, he wrote to Besso's family ,"Now Besso has departed from this strange world a little ahead of me. That means nothing. People like us, who believe in physics, know that the distinction between past, present and future is only a stubbornly persistent illusion". (source here: https://en.wikipedia.org/wiki/Michele_Besso) He was almost certainly thinking of the idea of time you have mentioned - events don't cease to exist as they slip into the past - it's just that we can no longer access them.

Refractive index is usually explained by considering the interaction between an electromagnetic wave and atoms in the refracting medium. The atoms are regarded as oscillating dipoles rather than atoms with discrete energy levels as described by quantum theory. In short, the treatment is classical rather than quantum mechanical. However, I have seen a treatment in which energy and momentum conservation is considered when photons incident on a refracting surface are split up into reflected and refracted categories and this does indicate that the behaviour of the photons is in accord with Fermat's principle. However, this approach does not, as far as I am aware, extend to explaining variation of refractive index with frequency - dispersion. There are many instances in which light is regarded as an electromagnetic wave rather than a stream of photons, and the reason for this is usually that the classical approach is simpler mathematically.

Minkowski's four-dimensional spacetime, which is what underpins the idea of a block universe, is something which Einstein initially regarded with some contempt, dismissing it as "superfluous learnedness". I don't think it could be described as a "logical consequence" of relativity. It isn't necessary in Special Relativity, but it was an invaluable tool in the formulation of General Relativity. I suspect that whilst all physicists would know what is meant by "spacetime", a few would scratch their heads when "block universe" is mentioned, despite the fact that they refer to the same thing.