Einstein and General Relativity which made space itself a product of scientific equations and thus something which changed and evolved.
rajnz00 » April 12th, 2017, 12:07 pm wrote:Einstein and General Relativity which made space itself a product of scientific equations and thus something which changed and evolved.
One thing we know about this "body" - the Universe - that people are trying to figure out, our most spectacularly successful theories, General Relativity and Quantum Mechanics, are both wrong. They disagree with each other and are incompatible. GR breaks down at the "singularity", quantum mechanics fails with gravity. In a court of law, they would produce a not guilty verdict, or the null hypotheses fail to be disproved.
rajnz00 » April 12th, 2017, 12:07 pm wrote:The Ptolemaic model, was also spectacularly successful and Newtons equations are used till this day, but they are both wrong.
rajnz00 » April 12th, 2017, 12:07 pm wrote:I just briefly touched on Dirac's hypothesis. It was in response to a problem. At the time he proposed that electrons which completely fill the Universe, when knocked out, formed holes or bubbles these were Protons, because Positrons were not known known then and they annihilate when they come together. He realised the problem with the differences of mass, protons being 1836 times more massive. But since then positrons have been discovered and they do annihilate with electrons.
rajnz00 » 13 Apr 2017, 07:42 wrote:“However, if … the time between event A and event B is greater than the distance between them divided by the speed of light, the order is preserved … "event A precedes event B" in all frames of reference.””
What??!! Don’t we have a formula for absolute simultaneity here? What if the Time between event A and event B is exactly equal to the distance between them divided by the speed of light? Wouldn’t they be simultaneous?
But what “Time between event A and event B” is he talking about? How do we measure it? Unless we have a Universal time?
BurtJordaan » April 13th, 2017, 2:14 am wrote:When "the Time between event A and event B is exactly equal to the distance between them divided by the speed of light", they are said to be separated by a light-like interval in all inertial frames. They are not simultaneous in any inertial frame, because you cannot have an inertial frame where the event lies on the plane of any spatial axis (x,y,z). Why not? Because then light would have to be static/stationary in that inertial frame, which is demonstrably impossible.
Time and distance are always stated relative to some inertial frame. If the time interval dT between two events is larger that than the space interval dX, it is a time-like interval in every inertial frame that exists. Likewise for the reverse, i.e. space-like intervals. Hence, temporal ordering of cause and effect events are maintained absolutely.
When "the Time between event A and event B is exactly equal to the distance between them divided by the speed of light", they are said to be separated by a light-like interval in all inertial frames. They are not simultaneous in any inertial frame, because you cannot have an inertial frame where the event lies on the plane of any spatial axis (x,y,z). Why not? Because then light would have to be static/stationary in that inertial frame, which is demonstrably impossible.
with which you agreed.With a null interval or what BurtJordan is calling "light-like," you can get as arbitrarily close to being simultaneous by choosing the right inertial frame.
rajnz00 » 13 Apr 2017, 12:40 wrote:My question then is, if for these "Null events" or "light-like events", whatever you decide to call them, why is it that we can get as "arbitrarily close" to making them simultaneous, by choosing an appropriate inertial frame but not actually reach simultaneity?
And my previous question was - How to do we measure exactly the times of the events at A and B, to be able to perform those calculations?
rajnz00 » 13 Apr 2017, 20:24 wrote:Let d = 3 x 10^{6} Km
Therefore d/c = 10 sec
If Ta – Tb = 11 sec, Then A occurs before B
If Ta – Tb = 9 sec then does B occur before A?
And if Ta – Tb = 10 sec then events A and B are not simultaneous in any inertial frame?
BurtJordaan » April 13th, 2017, 3:22 pm wrote:rajnz00 » 13 Apr 2017, 20:24 wrote:Let d = 3 x 10^{6} Km
Therefore d/c = 10 sec
If Ta – Tb = 11 sec, Then A occurs before B
If Ta – Tb = 9 sec then does B occur before A?
And if Ta – Tb = 10 sec then events A and B are not simultaneous in any inertial frame?
Nope. In all your cases, B happens before A, so that Tb is smaller than Ta.
In a (x,cT) spacetime diagram, let A be at (xa=0, cTa=11) and B at (xb=10, cTa=1), so that there is a lightlike interval (Ta-Tb=0) between them. The two events are obviously not simultaneous. It is a 45 degree downwards slope line, where simultaneous would be a horizontal line.
Now think what would happen if you just change cTa to 12. Not much, except that the interval is now timelike, with a steeper slope. For cTa changed to 9, the interval is now spacelike, with a shallower slope, but in all cases B happens clearly before A.
rajnz00 » April 14th, 2017, 12:34 am wrote:Ok I felt I needed to figure this out for myself, so I have. This is interesting stuff but I need to move on. Some the interesting things I learned:
(In simple language, without any mumbo-jumbo)
The interval between two events are light-like, if they are (can be) connected by a signal of light.
Pairs of events which are not connected (and cannot be connected) by any signal at all, are called "space-like" events.
The proper time is the time measured by a freely moving observer, carrying a watch with him.
Proper time is an invarient - every observer in every inertial frame will measure the same proper time between the two events.
It is defined by:
Δτ^{2} = c^{2}Δt^{2} − Δx^{2} − Δy^{2} − Δz^{2}
rajnz00 » April 14th, 2017, 12:34 am wrote:Δτ^{2} is positive if you can travel between the two events without travelling faster than light
rajnz00 » April 14th, 2017, 12:34 am wrote:I like to make complicated things simple, that's probably why people listen, even when I post on other's posts like Dave's. Some people flaunt their credentials and feel it gives them authority to spout a whole lot of nonsense about everything under the sun, such as Ptolemy's model and Newtons Gravity being correct.
Yes I figured that out on my own. (So I was not wrong in asking that question). The maths is not complicated, only the jargon is unfamiliar to me, (“spacelike” and “timelike”, and what precisely you meant by dx and dcT)Burt: “Take note that Mitchell is right about the apparent order of spacelike events that can reverse between inertial frames.”
Even “timelike” separated events need not be causally connected, but it does make one think about causality. The question that springs to my mind is, if events that are “spacelike” (my definition of “spacelike” events would be - events closer together in time, than the time taken for light to travel the distance between them, or, mathematically, where dcT < dx, using your jargon) cannot be causally connected, then why did Einstein believe in causality? Or why is it said that GR is causal, like Newton’s mechanics?Burt: “The real issue is that since spacelike separated events (like dx=10, dcT=9 in your example) are not causally connected, in the sense that neither one can be the cause of the other one”
I would make the language clearer for people who can understand maths and English, but are unfamiliar with the terms of relativity. Light can certainly travel between the location of the events, in my example, which are a mere 3 million kilometres apart, just the events are closer together in time, than the time it would take for light to travel between them.Burt: “because not even light can travel between them.”
Rightmitchellmckain: Δτ^{2} = Δt^{2} − (Δx^{2}− Δy^{2} − Δz^{2})/c^{2}
What is "the interval s" or Δs?mitchellmckain: in other words the proper time closely related to the interval s ...
Δτ^{2} = - Δs^{2} / c^{2}
rajnz00 » 14 Apr 2017, 19:15 wrote:The maths is not complicated, only the jargon is unfamiliar to me, (“spacelike” and “timelike”, and what precisely you meant by dx and dcT)
... then why did Einstein believe in causality? Or why is it said that GR is causal, like Newton’s mechanics?
BurtJordaan wrote: It is somewhat expected that if you ask advanced questions (like your the topic title suggests), you know most of the relativistic terms.
mitchellmckain » April 14th, 2017, 2:06 am wrote:Close... for proper time you want the units of time so...
Δτ^{2} = Δt^{2} − (Δx^{2} − Δy^{2} − Δz^{2})/c^{2}
rajnz00 » April 15th, 2017, 9:02 am wrote:Mitchellmckain, I should have caught that obvious, elementary school mistake, made by you, but then it would have been a shame to deprive you the pleasure of correcting your own mistake and making that remark. Getting concepts right are more important than making mistakes. I’m sure it would have given you far greater pleasure catching any mistake I made in the concepts I enunciated in that post.
rajnz00 » April 15th, 2017, 9:02 am wrote:Correcting your elementary algebra mistake is appreciated, but could you shed light on why Einstein believed in causality and GR is said to be causal, when so much of the Universe events cannot possibly be causal according to SR and GR?
What is "the interval s" or Δs?
rajnz00 » 16 Apr 2017, 02:17 wrote:Having a look at Four-dimensional Minkowski space-time, with its static cone of "physical reality", containing static "worldlines", one can only conclude that the future is already there and the past exists.
In Minkowski's 2-D space-time diagram, a beam of light emitted at the origin along the x axis towards positive values of x bisects the quadrant formed by ct-axis and x-axis, does this assume that space and time are moving at the same rate?
Doing a search on my second question I came up with this: "Scientists suggest spacetime has no time dimension..without using time as the fourth dimension of spacetime, the physical world can be described more accurately."
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