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/sci/ - Science & Math

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5783768 No.5783768 [Reply] [Original]

Hey guys... I am doing some calculations on relativity... and I just wondered... What is Negative Length?

>> No.5783803

its like positive length, but with a minus sign

>> No.5783804

>>5783803
>its like positive length, but with a minus sign

And what does that MEAN?

>> No.5783808

It means you did a calculation wrong or are misinterpreting your calcluation as a "length", when really it's just a coordinate ir the difference between coordinates. Maybe. Where'd you get the negative length?

>> No.5783812

>>5783768
>Where'd you get the negative length?

hehehe... Superluminal Length Contraction.

>> No.5783819

>>5783812

Shouldn't you get imaginary length for superluminal length contraction?

>> No.5783821

>>5783819
>Shouldn't you get imaginary length for superluminal length contraction?

What do you mean?

>> No.5783823

>>5783821
You get square roots of negative numbers for lambda, or better, a real number over an imaginary number... which when "rationalized" would be a negative imaginary number.

>> No.5783826

>>5783812
You fucked up. That should give you an imaginary number. It's still not a meaningful calculation, though
.

>> No.5783829

>>5783826
>It's still not a meaningful calculation, though

Explain?

>> No.5783840

I'm guessing you're calculating the interval? First off, it's important to note that there are two commonly used conventions for the interval: the (-+++) and the (+---) conventions. In the first (using units where c=1 for simplicity), the interval is defined as:

<div class="math">ds^2=-dt^2+dx^2+dy^2+dz^2</div>
In the second:

<div class="math">ds^2=dt^2-dx^2-dy^2-dz^2</div>
Depending on your convention, a negative interval could mean two completely different things. In the first, it means that the worldline is timelike (i.e. events along the worldline can be causally connected). In the second, it means that the worldline is spacelike (events cannot and are not causally connected).

An example of a timelike worldline would be a particle's path through spacetime. A spacelike interval may correspond to an object's length, for example.

In the first convention, the interval actually corresponds to proper length. In the second it corresponds to proper time.

>> No.5783847

>>5783804
>And what does that MEAN?
That they're behind you?

>> No.5783844

>>5783840
I'm trying to find out the length contraction on a superluminal object.

Does it have an imaginary length?

>> No.5783853

>>5783829

Relativity assumes that light travels at c in every frame. Imagine if an object was traveling faster than c. If you have a flash of light at the superluminal object at t=0, the superluminal object observes (presumably, if the axioms still 'hold') light traveling at c away from it. The observer sees the object in front of the light. You'd have do some crazy stuff to correct that. Might be a fun project to play around with though.

>> No.5783859

>>5783844
>Does it have an imaginary length?

As far as naively calculating things goes, yes. Physically this is meaningless, because tachyons don't exist.

>> No.5783862

>>5783859
>As far as naively calculating things goes, yes. Physically this is meaningless, because tachyons don't exist.

You mean to say that we have never observed tachyons....

And why is this a naive calculation? Isn't the hypothesis of superluminal time travel based on the same equation/principle?

>> No.5783875

>>5783862
>superluminal time travel

I'm not familiar with this, so perhaps you could elaborate on exactly what you mean. I'm familiar with tachyonic antitelephones, where you can send signals to the past. But a superluminal object experiences imaginary time, which doesn't really make any physical sense.

>> No.5783876

>>5783829
The Lorentz transformation is valid for velocities less than c. Plug in a v > c and you're not transforming to a valid reference frame. You end up putting physical objects at imaginary coordinates and putting physical events at imaginary times.

>> No.5783880

>>5783875
>But a superluminal object experiences imaginary time, which doesn't really make any physical sense.

Yes, and Imaginary Length, apparently.... So... this is what I was curious about...

>> No.5783881

>>5783859
And if tachyons did exist, the calculation still wouldn't be valid because we can't transform to an inertial frame in which they are at rest. Attempting to do so by naively plugging in a velocity greater than c is invalid and gives you nonsense.

>> No.5783883

>>5783876
Or they'd be acting more than infinite mass, or apparently, negative imaginary mass.

>> No.5783888

>>5783881
>because we can't transform to an inertial frame in which they are at rest.

Why not?

>> No.5783904

>>5783888
Tachyons follow a spacelike path. You can't Lorentz transform that into a timelike path.

>> No.5783910

>>5783904
>Tachyons follow a spacelike path. You can't Lorentz transform that into a timelike path.

But I'm just talking about speeds > c Not necessarily speeds of infinity.

>> No.5783916

>>5783910

A spacelike path is one where d(ct)^2 is greater than dx^2+dy^2+dz^2.

>> No.5783922

>>5783916
Just because your transforms are constrained by c does not necessarily mean that faster than light particles are automatically infinite speed, though.....

>> No.5784225

>>5783840
>using units where c=1 for simplicity
>not using <span class="math">ct = x^1[/spoiler]
absolutely disgusting

>> No.5784285

>>5784225
>x1
what the fuyck is wrong with you? its x0.

>> No.5784290

>>5783862
They're extremely unlikely to exist. I'm pretty sure the only theoretical reason to consider them is because it's a particle in the string spectrum of bosonic string theory. It's incredibly unstable and the theoretical implications don't even fit with the real world. They were really just a "problem" in early string theory, heteroic and superstring theory don't include tachyons.