JonG

I think you are referring to what the word "dark" means. If there is light around and some of it is entering your eyes, then it isn't dark. So in day time, it isn't dark - it's light. Slightly off the point, even at night time, there is lots of electromagnetic radiation about, but we can't see it because it is at a wavelength which our eyes aren't sensitive to.

I agree that we see by light (electromagnetic radiation in the wavelength range you specified) entering our eyes. We wouldn't see without that happening.

Yes, provided that there are objects in "the dark" which reflect this radiation back to our eyes.

Yes, that sort of argument seems reasonable. Another simple one is n!/n = (n - 1)! and then put n = 1. However it still seems odd that a factorial, which is normally defined as a product of terms, can be identified with 0!. But I suppose that it isn't any more peculiar than x0 = 1. Anyway, my point isn't relevant to the original post - apologies for the diversion, and thank you for your comments.

Some examples in that Wikipedia article don't appear to be problematic - not, to me anyway. For example, I see no problem with x0 = 1. However, the "empty product" 0! = 1 caught my eye. (The article was about empty products) n! is usually defined as n! = n x (n-2) x (n-3) x .... 2 x 1. By "meaningful" I was referring to the fact that it isn't obvious (not to me anyway) how 0! = 1 can be reconciled with that. The article did refer to equating such products to 1 as a convention.

There is another angle on the question of the number zero which I have found to be a bit arbitrary. It is stated in this Wikipedia article: https://en.wikipedia.org/wiki/Empty_product Quote: The notion of an empty product is useful for the same reason that the number zero and the empty set are useful: while they seem to represent quite uninteresting notions, their existence allows for a much shorter mathematical presentation of many subjects. This suggests that the idea of the number zero or the empty set can be convenient, or useful, but not necessarily meaningful. An example of an empty product is given as the factorial, 0! = 1. Having noted that, the same article makes the statement: Quote: As another example, the fundamental theorem of arithmetic says that every positive integer can be written uniquely as a product of primes. I'll leave it to others to find a flaw in that!

No, it doesn't imply a preferred reference frame. Whatever reference frame is chosen, provided that it is characterised by orthogonal axes, different points in the spatial dimensions can all have the same time coordinate. That is a consequence of the axes being orthogonal. The different points could have different coordinate values in different frames of reference, but the general statement will be the case for a particular reference frame.

What I wrote: By the same time I simply mean sharing the same time coordinate as denoted by the time axis. I am not sure that elfmotat did point that out, but I do disagree that it implies simultaneity. Several different spatial points sharing the same time coordinate simply means that they do, indeed, have the same value for t as their time coordinate. It only implies simultaneity if it is also asserted that these points are observable at the same time. If we consider the x-axis in a spacetime diagram, it is clearly possible for different events to have different x coordinates but have the same time coordinate. What we can't do is observe them all at the same time, so it contains no implication of simultaneity.

By the same time I simply mean sharing the same time coordinate as denoted by the time axis. With regard to objects being extended in time, if we agree on that, then - we agree! (I'm finding it difficult to recall what stance contributers have taken earlier on in the thread!)

I'm sorry. I wrote it badly. What I meant was that different points on an object can exist at different points in space at the same time. That is what we mean when we say that an object is extended in space. However, points on an object can't have different temporal coordinates at the same time, but they can have different temporal coordinates, so the object can extend in time. They simply can't have different temporal coordinates "now".

Befuddled as I might be, it seems to me that the apparent conflict arises because it is being assumed that to extend through time means something similar to the phrase to extend through space. But it doesn't. Points on an object can extend through space at the same time but they cannot extend through different points in time at the same time. If an object is said to extend from x,y,z,t1 to x,y,z,t2 all that means is that all points in spacetime between x,y,z,t1 and x,y,z,t2 are* occupied. I can't see what other meaning it could have. Nor can I see that it gives rise to any conflict. *There is a problem in writing this down in a consistent way because these points are not all occupied now, but that's simply because the language we use has evolved to cater for our twisted view that the only time which actually exists is the present. But there isn't an objective present.

It takes me back to my student days and all that stuff about beta decay. Your post reminded me of it.

I admit to being a bit lost here. I can't see why different atoms in an object can't occupy a set of spatial points at time t1 and also occupy the same set of spatial points at a later time t2. None of the atoms at the later time would occupy the same points (in 4D spacetime) as those at the earlier time because they would have different time coordinates. But perhaps that isn't what you are implying.

Wouldn't this be the case if all matter were, by some magical process, to suddenly become antimatter - there would be no fundamental change?

By michel123456; You can't occupy T1 and T2 at the same time. That much I accept. There is a quote from Einstein relevant to this. A lifetime friend of Einstein named Michele Besso died shortly before Einstein died. Einstein is alleged to have said to Besso's widow, "There is a sense, understood by physicists, in which people never die". In relation to your question, I think that implies that existence can extend over T1 and T2. I am inclined to go along with that, but I can't think of any way of proving it other than to note that if people, or things, are assumed to cease to exist as they slip into the past (our idea of past is subjective) then there is no known mechanism which would eliminate their existence. (If Einstein had ever expressed his views on a forum such as this he would probably have been reprimanded for being too philosophical - he was very interested in Philosophy: "Einstein had a lifelong interest in Philosophy. As a schoolboy, he has read Kant" - from "Subtle is the Lord - The Science and the life of Albert Einstein," by Abraham Pais, page 318.)

I'm not a Lord, but here goes anyway. I wasn't sure what point you were making in post 59 and what I write might be irrelevant, but it did bring to mind the idea of the "specious present", according to which the present isn't an instant in time but an interval of time of finite duration (It seems like an instant to me but some claim it can last several seconds!). See here for more: https://en.wikipedia.org/wiki/Specious_present

The centrifugal (or, more accurately, centripetal) force was used in the Bohr model of the hydrogen atom. The starting point was to equate the centripetal force to the Coulomb force of attraction between the electron and the nucleus (a proton). The Bohr model would now be seen as somewhat primitive, but it is remarkable that such Newtonian concepts could play any part in describing something on the atomic scale. This model wasn't entirely classical of course - some quantum mechanical relationships which were known about at the time (early twentieth century) were also inserted.

This is just a note regarding "motion through time*" and motion through space. It is impossible to move through space without also "moving through time". This is simply a consequence of there being a maximum speed at which things can move. However, it is possible to "move through time", i.e. to occupy successive points along the time axis, without moving through space - all you have to do is stand still. These conclusions are another consequence of the time axis being within the light cone and the spatial axes being outside it as I noted in an earlier post. (*The idea of motion through time is hard to define, which is why I prefer to refer to it as "to occupy successive points along the time axis".)

What I believe is summarised in the idea of a "world line". If someone, or an object, is at a point (x1, y1, z1) at time t1 and at a point (x2, y2, z2) at a later time, t2, then the existence of these two events is a matter of fact, and the point (x1, y1, z1, t1) has not been "emptied" at the later time t2. Note that you cannot verify that "ancient" coordinates have or have not been emptied because you can't go back in time to check. But there is no evidence, as far as I know, to support these beliefs. The reason for believing them is simply that the alternative - what you describe as "emptying" , or having events wiped out in some way as they slip into the past - would require a mechanism to explain how they are wiped out, and there isn't one that I am aware of.

The earth has a magnetic field and this must be produced by an electric current in its core. However, the source and mechanism behind this current is unclear.

There is a difference between the time axis and spatial axes (provided we accept the Minkowski metric and regard time and spatial coordinates as real numbers). The time axis is always within the light cone of an observer, whereas the spatial axes are outside. Assuming the observer to be at the origin, points along the time axis can be causally connected, but points along a spatial axis (x,y or z) can't be causally connected. This amounts to ds2 having one sign in one case and the opposite sign in the other case.

By elfmotat: [latex] ds^2= -dt^2+dx^2= dT^2+dx^2 [/latex] We're now completely free to define the variable T as "time." In other words, the numbers we read on clocks are no longer called "time." Instead, we read a number off a clock and we multiply that number by i to get time. If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions. Plus, we get the added bonus that a lot of physics becomes much simpler. The majority of people would consider time to be a real number. Defining it in such a way that it becomes imaginary doesn't help. It wouldn't just make time imaginary, but also velocities and many other things which depend on time. As for, If we define things in this way then the metric is positive definite, and time is no different from any of the other dimensions., it must surely be obvious that if you define time in that way it is clearly very different to spatial dimensions - time would be imaginary and spatial dimensions would be real!

Philosophy!!! What are you referring to? If you make a substitution t = it' (i.e. t' = -it) and after substituting t = it' you do a back substitution t' = -it, you will end up with exactly the equation you started with. ds2 = -c2dt2 + dx2 + dy2 + dz2

I think that most people who have thought about this will have concluded that time is not "flowing", but that we are moving through time. There isn't a defnitive version of the idea because it is will inevitably be related to the working of human consciousness, and there isn't yet a clear understanding of how consciousness works. Just to prevent the discussion going off at a tangent I will reiterate the point I was originally making. If dt represents an increment in time and dx, dy, and dz represent spatial increments, the flat spacetime metric (or Minkowski metric) is: ds2 = -c2dt2 + dx2 + dy2 + dz2 which shows that the temporal term differs from the spatial terms in that it has a negative sign in front of it. Is that true or isn't it? Replacing t by it would give; ds2 = c2dt2 + dx2 + dy2 + dz2 Is it being suggested that this version of the metric is true? (True now, not what is conjectured to have been the case shortly after the Big Bang).

I am not clear what is being stated here. The point is that spatial intervals and time intervals do not appear in the metric in the same way - the relevant terms differ in sign. Replacing [math]t[/math] by [math]it[/math] doesn't change this because the [math] t [/math] which appears in [math]it[/math] isn't what we consider to be time - it is an imaginary number. To avoid confusion, [math]t[/math] should be replaced by something like [math]it'[/math] to make it explicit that [math]t[/math] and [math]t'[/math] are not the same. (Imaginary time has been conjectured as a possibility for the early universe, but I don't think anyone considers that time as we know it now ,rather than at the Big Bang, is imaginary.)