Is Velocity Warping Space? A Look into Einstein's Special Relativity Theory

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In summary, the conversation discusses a formula by Einstein in his special relativity theory that explains how velocities add together at different speeds. At lower velocities, they simply add together, but at higher velocities, they add less and less together. This implies that high velocities can warp space, but it is not clear how. The formula also shows that velocities cannot exceed the speed of light and that hypothetical particles called tachyons may exist. There is also a discussion about how light and electromagnetic waves function differently from physical objects when it comes to speed. Finally, there is an exercise involving the Lorentz transformation and a request for a simplified explanation of the mathematical concept.
  • #1
mayflow
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I saw on this forum a formula by Einstein in his special relativity theory something like

Velocity sum = (velocity one plus velocity two)/ (1+velocity1*velocity2/the speed of light squared)

With small velocities, they simply seem to add together, but at higher velocities, they add less and less together. So, does this imply that high velocities warp space? I guess that is what it says, hmmm? But how? Does increased velocity expand space?

I put the formula into an excel spreadsheet and played a bit and I also notice that if velocities can exceed the speed of light, if you add them, they get slower, at least up until they are each 1 quintillion meters per second, in which case they equal to zero, and no matter how much larger the velocity from there, they still add to zero.

What does this imply?
 
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  • #2
v1 and v2 both have to be less than c.
 
  • #3
bcrowell said:
v1 and v2 both have to be less than c.

I= more than c, now what? Quantum entanglement?
 
  • #4
mayflow said:
Nobody? C'mon some of you are supposed to be experts here., aren't you?

You gave people 4 hours in a saturday morning. What do you expect?

mayflow said:
I= more than c, now what? Quantum entanglement?

What do you mean " I = more than c"? You can't have velocities greater than the speed of light. If you do, then you have the nasty issue of what does it mean to have an imaginary velocity (and a whole chain reaction of non-sense begins if you want to assume that makes sense).
 
  • #5
Seeing as to get to a velocity near c in the first place, you will have to start with some lower velocity (which will be less than c), then when you add another velocity to it (which will also necessarily be lower than c) using the formula, you will never be able to reach a number that's higher than c.

So: no slower than light v can ever reach or exceed c.


HOWEVER... :biggrin:


You have a point that it doesn't really forbid higher than c numbers, but they must start > c - and using the velocity formula you should see that they will never go below c.

You have stumbled upon the case for the hypothetical particles known as tachyons.
 
  • #6
Pengwuino said:
You gave people 4 hours in a saturday morning. What do you expect?



What do you mean " I = more than c"? You can't have velocities greater than the speed of light. If you do, then you have the nasty issue of what does it mean to have an imaginary velocity (and a whole chain reaction of non-sense begins if you want to assume that makes sense).

Well, it is arguable that any velocity is imaginary, and I just don't see any reason why the speed of light needs to be enforced upon innocent drivers if they want to go faster. ((Just saying that I don't believe light (which is just an electromagnetic wave in the frequency spectrum visible to our eyes) is non supersedable in speed.) There just seems to be something missing here.

It is still anti-intuitive to me that two light beams approaching each other are not adding speeds. If you drive down the road one way and I approach from the other way and we are each going 60MPH, we approach each other at 120 MPH. In the special relativity velocity formula, if we changed the speed limit to 60 MPH, we would be approaching each other at 60 rather than 120 MPH. Safer, yes. Realistic, no.
 
  • #7
DaveC426913 said:
Seeing as to get to a velocity near c in the first place, you will have to start with some lower velocity (which will be less than c), then when you add another velocity to it (which will also necessarily be lower than c) using the formula, you will never be able to reach a number that's higher than c.

So: no slower than light v can ever reach or exceed c.


HOWEVER... :biggrin:


You have a point that it doesn't really forbid higher than c numbers, but they must start > c - and using the velocity formula you should see that they will never go below c.

You have stumbled upon the case for the hypothetical particles known as tachyons.

Light or any electromagnetic wave doesn't function like me starting to run or a vehicle
getting up to speed. You turn a light on or you broadcast an RF wave and it instantly is at top speed. This is likely why Einstein used it as a constant. In that regard, I can see why he did so. WOW, isn't that interesting? In a sense light is binary - either on or off.

I am glad I found this forum. You guys really get me think:approve:ing.
 
  • #8
As an exercise, write down the Lorentz transformation that corresponds to a velocity v in the x direction, and apply it to the description of a particle moving at velocity w in the same direction. Find the relationship between the resulting x' and t' coordinates. What do you get?
 
  • #9
Gigasoft said:
As an exercise, write down the Lorentz transformation that corresponds to a velocity v in the x direction, and apply it to the description of a particle moving at velocity w in the same direction. Find the relationship between the resulting x' and t' coordinates. What do you get?

I haven't any education in higher maths, but I can understand simple algebra - would you mind explaining to me the math in that link? Please take it slow and simple (elegant) for me. :smile:
 
  • #10
mayflow said:
If you drive down the road one way and I approach from the other way and we are each going 60MPH, we approach each other at 120 MPH.

No we don't. I "see" you approaching with a speed that is a whisker less than 120 MPH, and you "see" me approaching with the same speed. You can work out the exact number with the velocity-addition formula.
 
  • #11
jtbell said:
No we don't. I "see" you approaching with a speed that is a whisker less than 120 MPH, and you "see" me approaching with the same speed. You can work out the exact number with the velocity-addition formula.

I can but what proves this formula to be correct? Remember my first post? If you implement a speed of 1 quintillion meters per second and another of equal or greater velocity, there would be zero speed. Does the equation actually have any real truth to it?
 
  • #12
mayflow said:
I can but what proves this formula to be correct? Remember my first post? If you implement a speed of 1 quintillion meters per second and another of equal or greater velocity, there would be zero speed. Does the equation actually have any real truth to it?

Yes, see the sticky in this forum that links to this page:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html"
 
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  • #13
DaleSwanson said:
Yes, see the sticky in this forum that links to this page:
http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html"
I don't care about that. I am talking about a certain formula, and whether it is correct at speeds beyond the speed of electromagnetic waves or not. If it does hold true beyond the speed of electromagnetic waves, it means that more increasing velocity eventually stops time dead cold in its tracks.
 
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  • #14
Just so I'm on the right track, the problem you're outlining is that the equations don't work with imaginary (impossible) speeds?
 
  • #15
mayflow said:
I don't care about that. I am talking about a certain formula, and whether it is correct at speeds beyond the speed of electromagnetic waves or not. If it does hold true beyond the speed of electromagnetic waves, it means that more increasing velocity eventually stops time dead cold in its tracks.

The velocity addition formula is derived by taking the derivative of the transformation equations. The Lorentz factor, Gamma, does appear in some of the initial setup equations but eventually drops out in the case of adding (or subtracting) velocities in the same direction. As you know Gamma is undefined for velocities >= c so an equation that contains Gamma cannot apply for any velocity >= c. Additionally all equations that are derived from that equation have the same limitation even if Gamma is no longer present. The physics textbooks seem to assume everybody knows that. Bad assumption.

I know of another example in Newtonian Physics where the same kind of misunderstanding can take place. (I was a victim of that misunderstanding.)

P.S. Most of the big guns on this forum appear to be taking a break. They deserve it.
 
  • #16
mayflow said:
Well, it is arguable that any velocity is imaginary, and I just don't see any reason why the speed of light needs to be enforced upon innocent drivers if they want to go faster. ((Just saying that I don't believe light (which is just an electromagnetic wave in the frequency spectrum visible to our eyes) is non supersedable in speed.) There just seems to be something missing here.

It is still anti-intuitive to me that two light beams approaching each other are not adding speeds. If you drive down the road one way and I approach from the other way and we are each going 60MPH, we approach each other at 120 MPH. In the special relativity velocity formula, if we changed the speed limit to 60 MPH, we would be approaching each other at 60 rather than 120 MPH. Safer, yes. Realistic, no.

It doesn't really matter how you "feel" or what you "believe" in this circumstance. I've said it before, some really thorough thinkers here have said it before, and I'll say it again, If you think that velocities should just add, then nature disagrees, and that's the bottom line. Special relativity has been tested not only numerous times, but in a multitude of different ways, and all tests indicate that in the energy limits appropriate, special relativity is accurate.

Its good to have some intuition, but don't let it keep you from getting to know nature better, nature has spoken.
 
  • #17
mayflow said:
I can but what proves this formula to be correct? Remember my first post? If you implement a speed of 1 quintillion meters per second and another of equal or greater velocity, there would be zero speed. Does the equation actually have any real truth to it?

No. Unless you can tell me what it means to have [tex]3i[/tex] apples in my hand, then it does not make sense for me to talk about having an imaginary velocity.

Intuition falls apart as you approach light speed. Your idea that velocities add in the Newtonian sense is accurate to within the precision that you can typically measure it. If you actually went out and drove two cars at each other at 60 MPH, you'd see them close at something like 120.0000000001mph due to the relativistic effects. Now, can you detect something that is ~0.0000000001% of a difference between Newtonian and relativistic velocity additions? No.

Now when you start colliding particles at large fractions of the speed of light, the differences become extremely obvious.
 
  • #18
Pengwuino said:
No. Unless you can tell me what it means to have [tex]3i[/tex] apples in my hand, then it does not make sense for me to talk about having an imaginary velocity.

Intuition falls apart as you approach light speed. Your idea that velocities add in the Newtonian sense is accurate to within the precision that you can typically measure it. If you actually went out and drove two cars at each other at 60 MPH, you'd see them close at something like 120.0000000001mph due to the relativistic effects. Now, can you detect something that is ~0.0000000001% of a difference between Newtonian and relativistic velocity additions? No.

Now when you start colliding particles at large fractions of the speed of light, the differences become extremely obvious.

Intuition does not fall apart as it approaches lightspeed. Penguin boy, let me tell you what. Probably you or anybody on this forum will not understand a single word or idea I will utter. The faster the speed, the more keen becomes the intuition and if you break lightspeed, things actually slow down for you. In the future I'll likely invent the term of the Universal instant (and then instantly regret it). For a Penquin, you are fun to talk with. :biggrin:
 
  • #19
mayflow said:
Intuition does not fall apart as it approaches lightspeed. Penguin boy, let me tell you what. Probably you or anybody on this forum will not understand a single word or idea I will utter. The faster the speed, the more keen becomes the intuition and if you break lightspeed, things actually slow down for you. In the future I'll likely invent the term of the Universal instant. For a Penquin, you are fun to talk with. :biggrin:

The only problem would be, you can't "break lightspeed".

Everything stemming from there can't have current theories applied to it.
 
  • #20
mayflow said:
Probably you or anybody on this forum will not understand a single word or idea I will utter.

Classic crackpot line right there. "I'm so smart, none of you will ever get what I'm talking about!"
 
  • #21
JaredJames said:
The only problem would be, you can't "break lightspeed".

Everything stemming from there can't have current theories applied to it.

If quantum entanglement can break the lightspeed barrier and rip it to shreds, why do you impose on me that I cannot?
 
  • #22
Char. Limit said:
Classic crackpot line right there. "I'm so smart, none of you will ever get what I'm talking about!"

Well, now you bring up the crackpot checklist...
 
  • #23
Mayflow, this attitude is uncalled for and it won't be tolerated here.

If you want to learn about currently-understood science, you will have to be more open.

If you want to espouse your own ideas without having an understanding of the science involved, PF is not the place do it.

You need to pick one.
 
  • #24
mayflow said:
If quantum entanglement can break the lightspeed barrier and rip it to shreds
AFAIK, quantum entanglement is not FTL. That seems to be a common misunderstanding.We always measure lightspeed to be the same. For this to be true we must experience time dilation, length contraction, altered velocity addition etc as we increase speed. This is a direct consequence of an absolute lightspeed.If you want FTL without disregarding Relativity, use an Alcubierre drive or a wormhole.
 
  • #25
mayflow said:
If quantum entanglement can break the lightspeed barrier and rip it to shreds

Does it really?
why do you impose on me that I cannot?
Well for a start, it is very well tested and proven you cannot. Non-issue.

I see this is now a "I'm asking for some help, but going to ignore you and insist I'm right" thread.
 
  • #26
mayflow said:
Well, it is arguable that any velocity is imaginary, and I just don't see any reason why the speed of light needs to be enforced upon innocent drivers if they want to go faster. ((Just saying that I don't believe light (which is just an electromagnetic wave in the frequency spectrum visible to our eyes) is non supersedable in speed.) There just seems to be something missing here.

It is still anti-intuitive to me that two light beams approaching each other are not adding speeds. If you drive down the road one way and I approach from the other way and we are each going 60MPH, we approach each other at 120 MPH. In the special relativity velocity formula, if we changed the speed limit to 60 MPH, we would be approaching each other at 60 rather than 120 MPH. Safer, yes. Realistic, no.

Indeed you approach each other at 120 MPH as measured with a reference system of the road; as long as you consistently stick to a single reference system you can add speeds in the normal way - that's even a mathematical necessity! Please don't think that anyone asks you to wash the basic rules of mathematics down the toilet. :smile:

According to SR's equations, your perception (measurement) of such things as speed depends on your state of motion. The equations (you only cited the 1D variant) are meant for what you would measure if you would set up an independent reference system in which you are in rest. It cannot be stressed enough that these "composition of velocity" equations are system transformation equations.

Note that the full formula can be found in section 5 of:
http://www.fourmilab.ch/etexts/einstein/specrel/www/

PS: your innocent drivers, as measured from the road, will each need an infinite amount of energy to reach the velocity of light in vacuum. Thus it will be not easy for them to go faster than that. :biggrin:

Does that help for your intuition?

Regards,
Harald
 
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  • #27
mayflow said:
Intuition does not fall apart as it approaches lightspeed. Penguin boy, let me tell you what. Probably you or anybody on this forum will not understand a single word or idea I will utter. The faster the speed, the more keen becomes the intuition and if you break lightspeed, things actually slow down for you. In the future I'll likely invent the term of the Universal instant (and then instantly regret it). For a Penquin, you are fun to talk with. :biggrin:

Dude, you're channeling Charlie Sheen ... that just gets uglier and uglier.:smile:
 

1. How does Einstein's theory of special relativity explain velocity warping space?

Einstein's theory of special relativity states that space and time are not separate entities, but rather are intertwined and affected by the presence of mass and energy. According to this theory, as an object moves through space at high velocities, its mass increases and time slows down. This is known as time dilation and mass-energy equivalence, and it explains how velocity warps space.

2. Can you provide an example of how velocity warps space?

One example of velocity warping space is the phenomenon of gravitational lensing. This occurs when a massive object, such as a galaxy, bends the fabric of space around it. Light traveling through this warped space is also bent, causing the image of a distant object to appear distorted or magnified.

3. How does the concept of space-time play a role in velocity warping space?

The concept of space-time, which combines the three dimensions of space with the dimension of time, is essential in understanding velocity warping space. According to Einstein's theory, the presence of mass and energy warps the fabric of space-time, affecting the movement of objects within it.

4. Is it possible for velocity to warp space without the presence of mass?

No, according to Einstein's theory, velocity alone cannot warp space. The presence of mass and energy is necessary to cause the warping of space-time. In fact, the speed of light, which is the fastest possible velocity in the universe, plays a crucial role in this warping process.

5. What implications does velocity warping space have on our understanding of the universe?

The concept of velocity warping space has significant implications on our understanding of the universe. It explains many phenomena, such as the bending of light, gravitational waves, and the behavior of objects at high velocities. It also provides a more comprehensive understanding of space and time, challenging traditional notions of these concepts.

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