Can the height in another dimension look different from different dimensions that we know?
For example, can the width looks different than we see it?
The special theory of relativity may provide a way for measurements to be different from the perspective of four dimentsions rather than from three dimensions. Here is Wikipedia's description of relativity:
Special relativity is based on two postulates which are contradictory in classical mechanics:
- The laws of physics are the same for all observers in uniform motion relative to one another (principle of relativity).
- The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the light source.
Here are two consequences of those two postulates that may be relevant to this question:
- Time dilation: Moving clocks are measured to tick more slowly than an observer's "stationary" clock.
- Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to the observer.
The OP asks, Can the height in another dimension look different?
The measurement of a length from a four-dimensional perspective based on the two postulates mentioned above leads one to assume that lengths in another frame of reference will be "shortened in the direction that they are moving with respect to the observer". From a three-dimensional perspective these lengths would be expected to be the same.
Wikipedia contributors. (2019, April 30). Theory of relativity. In Wikipedia, The Free Encyclopedia. Retrieved 16:07, June 3, 2019, from https://en.wikipedia.org/w/index.php?title=Theory_of_relativity&oldid=894900036