A Quantum Mechanical Interpretation of the Consequences of Special Relativity

[Bufofrog]

1 hour ago, DanMP said:

Why "a test particle" would do something so elaborate?  And how it knows how to do it, or to "tend" to do it?

If the term 'test particle' bothers you then just substitute the term 'a rock'.  The out come will be the same.

If you toss a rock it won't do anything elaborate, but when it leaves your hand it will trace out a parabola and it doesn't know it is following a parabola.

Markus was trying to help you understand why the rock would move the way it does.

[swansont]

On 1/6/2021 at 11:05 AM, DanMP said:

(Emphasis mine)

Why "a test particle" would do something so elaborate? And how it knows how to do it, or to "tend" to do it?

It's not elaborate. There are principle like this that are simple ways of summarizing how particles behave under a set of conditions. Light and the principle of least time (Fermat's principle), which is a truth about the path light will take, without discussing the particulars of indices of refraction. Related to the principle of least action for mechanics.

Don't anthropomorphize the particles. They hate that.

 

[jamesfairclear]

On 1/5/2021 at 3:46 PM, studiot said:

But you have specified that one clock is moving relative to the other.

The sequence of events in the experiment is:

 

[Bufofrog]

3 hours ago, swansont said:

Don't anthropomorphize the particles. They hate that.

Nice...😄

[Markus Hanke]

16 hours ago, DanMP said:

Why "a test particle" would do something so elaborate? And how it knows how to do it, or to "tend" to do it?

Because there is a general principle in nature that says that all systems will always tend towards that state which represents the lowest energy level, and/or the most stable configuration (in technical terms, the “least action”). This is called the principle of least action, and it is a formal mathematical statement that underlies both the macroscopic world (GR) and the microscopic realm (quantum field theory). The principle of extremal ageing is just a special case of this. 

In the case of test particles under the influence of gravity, the resulting world lines are the simplest possible ones (so it isn’t “elaborate”) - they are geodesics of spacetime, i.e. world lines where proper acceleration vanishes at every point (hence “free fall”), or equivalently the “straightest possible” world lines.

16 hours ago, DanMP said:

Why not?

Because it is mathematically inconsistent. The object that describes the curvature of spacetime, and hence gravity, the Riemann curvature tensor, can be thought of as “made up of” two parts - its trace-free part, the Weyl curvature tensor (which roughly speaking encodes tidal effects, i.e. distortions in shape of a test volume in free fall); and its trace, the Ricci tensor (which encodes the volume itself). If you have only 3 spatial dimensions, the Weyl tensor identically vanishes (a basic result in differential geometry, which can be straightforwardly proven), so there’s no tidal gravity. In fact, since in vacuum the Ricci tensor vanishes as well due to the Einstein field equations, you would have no gravity at all in the exterior of massive bodies - which is clearly not consistent with what we observe. So the universe cannot have only three spatial dimensions, since this is logically at odds with what we see in the world around us.

I can easily formalise this argument mathematically, but I think you understand what I am trying to point out, so there shouldn’t be any need.

15 hours ago, swansont said:

Don't anthropomorphize the particles. They hate that.

Nice one 😄

Edited January 7, 2021 by Markus Hanke

[joigus]

4 hours ago, Markus Hanke said:

Because it is mathematically inconsistent. The object that describes the curvature of spacetime, and hence gravity, the Riemann curvature tensor, can be thought of as “made up of” two parts - its trace-free part, the Weyl curvature tensor (which roughly speaking encodes tidal effects, i.e. distortions in shape of a test volume in free fall); and its trace, the Ricci tensor (which encodes the volume itself). If you have only 3 spatial dimensions, the Weyl tensor identically vanishes (a basic result in differential geometry, which can be straightforwardly proven), so there’s no tidal gravity. In fact, since in vacuum the Ricci tensor vanishes as well due to the Einstein field equations, you would have no gravity at all in the exterior of massive bodies - which is clearly not consistent with what we observe. So the universe cannot have only three spatial dimensions, since this is logically at odds with what we see in the world around us.

Great explanation. The best possible. It's very difficult to explain this in simpler terms than these. For a space with dimension n the number of components of the Weyl are the number of components of the Riemann minus the number of components of the Ricci:

\[ \#(Riemann) = \frac{1}{12} n^2\left(n^2-1\right) \]

\[ \#(Ricci) = \frac{1}{2}n\left( n+1\right) \]

For n=3 that gives precisely 6-6=0 components for the Weyl. So no tidal forces in dim=4 if Markus is right and the Weyl codifies tidal forces. And I'm guessing he is.

Edited January 7, 2021 by joigus
introduced escape symbols in LateX

[DanMP]

19 hours ago, Bufofrog said:

If the term 'test particle' bothers you then ...

It doesn't but thanks anyway.

19 hours ago, swansont said:

It's not elaborate. There are principle like this that are simple ways of summarizing how particles behave under a set of conditions.

It sounded elaborate   Ok, I knew that, but I think that behind any principle should be a reason, an explanation of what and why is actually happening.

4 hours ago, Markus Hanke said:

Because there is a general principle in nature that says that all systems will always tend towards that state which represents the lowest energy level, and/or the most stable configuration (in technical terms, the “least action”). This is called the principle of least action, and it is a formal mathematical statement that underlies both the macroscopic world (GR) and the microscopic realm (quantum field theory). The principle of extremal ageing is just a special case of this. 

In the case of test particles under the influence of gravity, the resulting world lines are the simplest possible ones (so it isn’t “elaborate”) - they are geodesics of spacetime, i.e. world lines where proper acceleration vanishes at every point (hence “free fall”), or equivalently the “straightest possible” world lines.

Wow!  This is the best explanation. Thank you!  +1

4 hours ago, Markus Hanke said:

Because it is mathematically inconsistent. The object that describes the curvature of spacetime, and hence gravity, the Riemann curvature tensor, can be thought of [...]  So the universe cannot have only three spatial dimensions, since this is logically at odds with what we see in the world around us.

Another nice, comprehensive and useful explanation. Thanks!

The underlining is mine and I did it because, in my opinion, the model, not the universe, cannot have only three spatial dimensions. And, as far as I know, this isn't the only possible model, there are graviton-based models in progress, modified Newton models and string theory attempts.

Now I want/need to explain what I meant in my first post: in our world there are things we can feel, like apples and rocks, very real, things we define and measure, like temperature, pressure and time intervals, real enough, things like math, science models and words, real to us, humans, and very useful/powerful, but created not discovered, and things we created/imagined for fun, like unicorns. All these things exist for/to us, but they are not on the same footing.

We kind of feel space by moving through it in all directions, so space is very real. In time we cannot move backwards, stop or "accelerate" forwards, so it is different. Needed, but different. In my opinion time is about change and the rate of change. We can observe change, so change is very real, but time is something made/created/defined by us in order to characterize the change, so it's less real. This is what I meant.

In my understanding, to go back in time is to reverse all the changes in the whole universe. Do you see it different? How?

And the last thing, if spacetime is not just a "tool" in our models, does it mean that the future is already "written", present in this spacetime?

[studiot]

Can I request that DanMP's discussion be split off as totally off topic and not to do with quantum mechanics.

This is not a complaint as his issue is possibly also interesting and certainly deserves a thread of its own and there now seems to be two separate discussions going on at once and becoming intertwined.

 

Edited January 7, 2021 by studiot

[DanMP]

47 minutes ago, studiot said:

DanMP's discussion be split off as totally off topic and not to do with quantum mechanics.

Not totally off-topic:

On 1/3/2021 at 9:50 PM, jamesfairclear said:

Does Time exist?

Physics defines Time as “that which is measured by clocks”; that is all. There is no evidence to substantiate that time exists as part of the fabric of the universe. It is probable that human beings dreamt up the notion of time as a convenient way of 2 or more people being in the same location to share a task.

 

Edited January 7, 2021 by DanMP

[jamesfairclear]

1 hour ago, DanMP said:

It doesn't but thanks anyway.

It sounded elaborate   Ok, I knew that, but I think that behind any principle should be a reason, an explanation of what and why is actually happening.

Wow!  This is the best explanation. Thank you!  +1

Another nice, comprehensive and useful explanation. Thanks!

The underlining is mine and I did it because, in my opinion, the model, not the universe, cannot have only three spatial dimensions. And, as far as I know, this isn't the only possible model, there are graviton-based models in progress, modified Newton models and string theory attempts.

Now I want/need to explain what I meant in my first post: in our world there are things we can feel, like apples and rocks, very real, things we define and measure, like temperature, pressure and time intervals, real enough, things like math, science models and words, real to us, humans, and very useful/powerful, but created not discovered, and things we created/imagined for fun, like unicorns. All these things exist for/to us, but they are not on the same footing.

We kind of feel space by moving through it in all directions, so space is very real. In time we cannot move backwards, stop or "accelerate" forwards, so it is different. Needed, but different. In my opinion time is about change and the rate of change. We can observe change, so change is very real, but time is something made/created/defined by us in order to characterize the change, so it's less real. This is what I meant.

In my understanding, to go back in time is to reverse all the changes in the whole universe. Do you see it different? How?

And the last thing, if spacetime is not just a "tool" in our models, does it mean that the future is already "written", present in this spacetime?

The notion of Time is a measurement of a quantity of events and an event cannot be undone. Thus the notional arrow of time can only be in one direction.

[swansont]

Will you be showing us either of the following

1. a derivation of the time dilation equation from QM

2. a way to test your conjecture in a way that is independent of relativity, or present evidence that already exists that fits this criterion

 

I ask because if you don’t, the thread has to be closed as it does not conform to the speculations rules, which requires a model and/or evidence. 

 

[jamesfairclear]

10 minutes ago, swansont said:

Will you be showing us either of the following

1. a derivation of the time dilation equation from QM

2. a way to test your conjecture in a way that is independent of relativity, or present evidence that already exists that fits this criterion

 

I ask because if you don’t, the thread has to be closed as it does not conform to the speculations rules, which requires a model and/or evidence. 

 

This alternative interpretation is evidenced by the same evidence that substantiates Time Dilation in SR.

[Ghideon]

1 hour ago, jamesfairclear said:

This alternative interpretation is evidenced by the same evidence that substantiates Time Dilation in SR.

We have seen that list of steps a few times by now. I would still preferred o get an answer to the questions raised. I'll try to phrase my question differently: The events each one of the clocks count does not happen all simultaneously. There is something that separates the counted events, referred to as "time" as far as I know. What is it that separates the events in your case if not time? How do you define it without making it identical to time? Given that definition what experiment can be used that shows your idea is correct?   

Edited January 7, 2021 by Ghideon

[jamesfairclear]

1 hour ago, Ghideon said:

We have seen that list of steps a few times by now. I would still preferred o get an answer to the questions raised. I'll try to phrase my question differently: The events each one of the clocks count does not happen all simultaneously. There is something that separates the counted events, referred to as "time" as far as I know. What is it that separates the events in your case if not time? How do you define it without making it identical to time? Given that definition what experiment can be used that shows your idea is correct?   

There is a sequence of events counted by each clock. The clock itself cannot detect anything between each event because there is nothing to detect. Equally a human observer cannot detect anything between each event but can elect to assume notionally that there is an imaginary interval between events and characterise it as a flow of time even though there is nothing that can actually be observed. The alternate interpretation does not preclude making reference to Time for the sake of convenience. Thus we can refer to a measurement of 10 seconds or N events for a given observation.

The alternate interpretation differs in that it proposes a different model substituting Time with a quantity of events.

As previously stated the alternate interpretation is evidenced by any of the copious experiments that have substantiated Time Dilation. For example taking  an atomic clock up in an aircraft , flying around the globe, returning to its starting point comparing its reading to that of a stationary clock located at the starting point. The difference in the readings substantiates that motion reduces the quantity of events. 

[iNow]

The phrase, "missing the point" comes to mind. What is a sequence if there is no time?

[swansont]

4 hours ago, jamesfairclear said:

This alternative interpretation is evidenced by the same evidence that substantiates Time Dilation in SR.

!

Moderator Note

So it’s not evidence that supports your conjecture, to the exclusion of other hypotheses. IOW, it’s not support - it doesn’t show SR to be wrong.

So you have no model, and no evidence. You can’t satisfy the requirements of speculations. We’re done. Don’t bring this up again.