Space-Time equivalence

[TheAndrewSAMA]

Hi,

I was thinking about time being the 4th spatial dimension, thanks to a book I'm reading these days.

Nothing special, till I tried to imagine this in the smallest possible scale.

 

So, I drawn the classic space/time graph and marked two points on each axes:

y and y+Planck lengh on the space axis

x and x+Planck time on the time axis

 

Now, looking at how the smallest 4 dimensional particle could be rapresentend in this graph, I figured out that it should have these attributes:

lenght, width and height equal to the Planck lenght

lenght in the 4th dimension ( or "duration" ) equal to the Planck time

 

But, being time just another spatial dimension, i thought this: what if somehow the Planck time is equal to the Planck lenght?

In other words, if the smallest 3D particle is like a cube, the smallest 4D particle should be an hypercube. And if the cube has equal lenght, width and height, an hypercube should have equal lenght, width, height and duration. Or not?

 

Furthermore, I wrote an equaltion about this.

 

Here it is.

 

Be clement, I'm really not good at math, and if this equation is completely wrong just ignore it.

If it cointains some errors that if corrected could lead to something new for all of us, then feel free to do so.

 

Beside all this, I feel somehow that a turtle runs as fast as a rabbit after all. The only thing that changes is that the rabbit is running more through space than through time. I feel also that for this reason, in someway, the speed of light is not only the max speed possible, but also the minimum. But I'm a bit confused about this. I hope you can help me to clarify.

 

So, what you guys think about all this reasoning? Is it valid? Is it meaningless?

 

I hope I have not waster your time ( space )

 

As you'll probably notice, my english is not so good. Sorry for that.

Edited May 16, 2016 by TheAndrewSAMA

[Strange]

I think you are basically correct: the speed of light can be treated as a conversion factor between time and space. And in Planck units, the speed of light is 1.

[timo]

It is indeed common to consider the speed of light as the conversion factor between length and time. Then, Planck Length and Planck Time are in fact the same thing - by construction. And it is also common to say that in a sense almost everything moves at the speed of light, except with different amounts in time-direction and in space direction (fun fact: the only exceptions are things that move with the speed of light in the classical sense ). "Four-velocity" could be a term to look up if you want to do some Googling on this.

[TheAndrewSAMA]

Thank you for the replyes! I tried to find something on google about what i thought, but I failed. "Four-velocity" seems to be what i was looking for!

I'll sleep better tonight.

 

And what about an object that doesn't travel in time but only in space? It's "Three-velocity" would be higher than c? Would it be infinite?

Or simply the concept of velocity without the spatial dimension of time has no sense?

Edited May 16, 2016 by TheAndrewSAMA

[Mordred]

Describing an object as travelling in time is a poor choice of wording.

 

As time passes regardless of whether or not the object is moving.

[TheAndrewSAMA]

Describing an object as travelling in time is a poor choice of wording.

 

As time passes regardless of whether or not the object is moving.

I'm not sure about that. If time is a spatial dimension, one could go in 2 directions or stay still. We are going forward, but it doesn't mean it's impossible to do something else. For instance, if we are going forward because of some strange conservation of momentum law that acts in 4 dimensions, we could impact on something able to send us backward.

 

An object that is not moving would exist only in a combination of coordinates in space/time and from our point of view it would appear and disappear instantly. What we see as a still object is not really still. Indeed, it is moving in time but not in space.

Edited May 16, 2016 by TheAndrewSAMA

[Mordred]

So time doesn't pass for an object at rest? At rest meaning no momentum.

 

How do you accurately describe an object at rest as travelling through time?

 

It is the time coordinate that changes, yet the object doesn't move.

Edited May 16, 2016 by Mordred

[TheAndrewSAMA]

So time doesn't pass for an object at rest? At rest meaning no momentum.

 

How do you accurately describe an object at rest as travelling through time?

If you mean an object in complete rest, it can be decribed as a point in a 4 dimensional space.

 

An object that is resting only from our point of view of time travelers instead, could be described as a line in a 4 dimesional space.

Edited May 16, 2016 by TheAndrewSAMA

[Mordred]

Yes but that's not the same as stating an object travels (which implies momentum).

[TheAndrewSAMA]

Yes but that's not the same as stating an object travels (which implies momentum).

An object that changes only one ( time ) of the four coordinates that describe its position in a 4D space is not moving?

[Mordred]

Is the object moving or are the coordinates changing ?. What laws are involved when considering inertia? Implying that objects move through time implies falsely that time acts as a force.

 

A good example of the types of misconceptions is say for example spacetime expansion. Which doesn't impart momentum to galaxies. No object gains momentum due to expansion. No object gains momentum due to different time rates.

Remember the laws of physics including momentum must be the same for all observers.

 

For example the four vector length is invariant.

 

http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/vec4.html

When you apply a Lorentz boost your applying a coordinate transformation.

That coordinate transformation does not change the laws of physics in regards to momentum.

This is why the terms proper time and coordinate time is also important.

https://en.m.wikipedia.org/wiki/Coordinate_time

 

For example I am an observer in the same reference frame as a reference clock. There is no time dilation. However another observer with momentum measures that same clock and sees a time dilation.

Mathematically we treat time as a coordinate with the speed of light being invariant to account for these two measured rates of time.

Edited May 17, 2016 by Mordred

[TheAndrewSAMA]

Is the object moving or are the coordinates changing ?

Good question. If I found an object in two different time coordinates, I could say it's moving, but it's not necessarily true. We can experience time instant by instant, so we cannot say if what's in front of us is resting or moving ( in time ).

For example: how could I tell if the frame I see in a movie is another frame whit the same content or the exact same frame I seen the moment before?

 

 

Implying that objects move through time implies falsely that time acts as a force.

Why saying that objects move through time implies that time acts as a force, while saying that objects move throught space doesn't imply that space acts like a force? ( If it doesn't )

 

Speaking about the frames in a movie, in case the frame is the exact same frame, its clock hands should be fixed.

Instead, if it's another frame, its clock hands should sign another time. Because, I suppose, an object cannot be in two different space-time places ( in the same way two electrons whit the same spin cannot be in the same orbital, I would say ), and for this reason there must be a "configuration difference" or "state difference" between the two clocks and frames.

Edited May 17, 2016 by TheAndrewSAMA

[Mordred]

Well now your starting to think.

 

What does the term movement imply?

 

What physical laws are involved to determine movement?

 

So thinking of the above in regards to time dilation. What causes an object to move slower in time compared to another time frame?

 

Ie f=ma.

 

You beginning to see the hazard of stating objects move through time particularly since time isn't invariant?

 

In the expansion example. Take a homogeneous and isotropic fluid and surround every galaxy. At no point is there a higher pressure or force acting on any galaxy in any direction. Yet galaxies still move away from each other.

 

No galaxy gains inertia that requires a pressure difference on a facing. Yet they all appear to be accelerating apart.

 

We describe this simply as geometry change.

 

Same principles apply when describing an object moving in time.

 

You have different measurements of the passing of time on the same object. How do you describe that as movement?

 

It's easy to describe as geometry change.